U.S. Army Corps of Engineers
Philadelphia District
Final Groundwater Model Calibration Report Aquifer Storage and Recovery Regional Modeling Study Prepared for U.S. Army Corps of Engineers Jacksonville District Prepared by U.S. Army Corps of Engineers Philadelphia District
February 2011 Table of Contents Executive Summary ....................................................................................................................................... 1 1.0 Introduction ............................................................................................................................................ 3 1.1 Acknowledgements ............................................................................................................................. 3 2.0 Regional Modeling Approach .................................................................................................................. 4 2.1 Concept of Equivalent Freshwater Head ............................................................................................ 4 2.2 Modeling Codes .................................................................................................................................. 6 2.2.1 SEAWAT ........................................................................................................................................ 6 2.2.2 WASH123D ................................................................................................................................... 7 2.3 Model Extent and Spatial Discretization ............................................................................................. 8 2.4 Model Time Discretization ................................................................................................................ 10 2.5 Model Datum .................................................................................................................................... 11 3.0 Conceptual Model ................................................................................................................................. 11 3.1 Topography ....................................................................................................................................... 11 3.2 Geology ............................................................................................................................................. 12 3.2.1 Regional Geology ....................................................................................................................... 12 3.2.2 Hydrogeologic Properties .......................................................................................................... 15 3.2.3 Regional Anisotropy ................................................................................................................... 15 3.3 Boundary Conditions ......................................................................................................................... 16 3.3.1 Surficial Head Boundary Conditions .......................................................................................... 16 3.3.2 Simulation of Ocean Boundary .................................................................................................. 17 3.3.3 Aquifer Head Boundary Conditions ........................................................................................... 17 3.3.4 Confining Unit Head Boundary Conditions ................................................................................ 18 3.3.5 TDS and Temperature at the Boundaries .................................................................................. 18 3.4 Initial Conditions ............................................................................................................................... 18 3.4.1 Salinity (TDS) Distribution .......................................................................................................... 19 3.4.2 Temperature Distribution .......................................................................................................... 20 3.5 Sources and Sinks .............................................................................................................................. 21 4.0 Calibration/Validation ........................................................................................................................... 22 4.1 Steady State Calibration .................................................................................................................... 23 4.1.1 Calibration Process Description ................................................................................................. 26 4.1.2 Calibrated Hydraulic Conductivity Fields ................................................................................... 28 4.1.3 Description of the Steady State Calibration Quality .................................................................. 30 4.1.4 Comparison of Model Results to some Published Information ................................................. 33 4.2 Transient Calibration/Validation ....................................................................................................... 35 4.2.1 Calibration Statistics .................................................................................................................. 35 4.2.2 Transient Calibration Analysis ‐ Heads ....................................................................................... 38 4.2.3 Transient Calibration Analysis – Vertical Gradients ................................................................... 42 4.2.4 Transient Calibration Analysis – Conclusion .............................................................................. 42 4.3 Model Analysis .................................................................................................................................. 43 5.0 Sensitivity Simulations .......................................................................................................................... 44 5.1 Advection Solution ............................................................................................................................ 45 5.2 Porosity ............................................................................................................................................. 46 5.3 Dispersion/Diffusion ......................................................................................................................... 46 5.4 Boulder Zone Thickness .................................................................................................................... 48 5.5 Specified Head Boundaries ............................................................................................................... 49 5.5.1 North Boundary ......................................................................................................................... 49 5.5.2 Southwest Boundary .................................................................................................................. 50 5.5.3 Confining Units Boundary .......................................................................................................... 51 5.6 Ratio of Horizontal to Vertical Hydraulic Conductivity ..................................................................... 52 6.0 Sources of Uncertainty .......................................................................................................................... 53 6.1 Pumping Rate Data Limitations ......................................................................................................... 54 6.2 Temporal Distribution of Pumping Data ........................................................................................... 54 6.3 Salinity Distribution ........................................................................................................................... 55 6.4 Temperature Distribution ................................................................................................................. 55 6.5 Surficial Aquifer Boundary Assumption ............................................................................................ 55 6.6 Spatial Discretization......................................................................................................................... 56 6.7 Variability in Transport Parameters .................................................................................................. 56 7.0 Conclusions/Recommendations ........................................................................................................... 56 8.0 References ............................................................................................................................................ 58 Appendix A: Phase II Groundwater Model Data Collection Appendix B: Grid Resolution Study Appendix C: Selection of Boundary Conditions Appendix D: Pumping Data Report Appendix E: Total Dissolved Solids (TDS) and Temperature Data Evaluation Appendix F: WASH123D and SEAWAT Comparison Appendix G: IMC Comments to Draft Report with Responses Appendix H: IMC Comments to Final Report with Responses
Acronyms APPZ Avon Park Permeable Zone APT Aquifer Pump Test ASR Aquifer Storage and Recovery BTN Basic Transport Package (MT3D) BZ Boulder Zone CERP Comprehensive Everglades Restoration Plan CHD Time‐Variant Specified‐Head Package (SEAWAT) CRM Coastal Relief Model DB Dirichlet Boundary DEM Digital Elevation Model DOH Department of Health DSP Dispersion Package (MT3D) ERDC Engineer Research and Development Center FAS Floridan Aquifer System FDEP Florida Department of Environmental Protection FDM Finite Difference Method HOB Head Observation Package (MODFLOW) IA Intermediate Aquifer IAS Intermediate Aquifer System ICU Intermediate Confining Unit IMC Interagency Modeling Center KASR Kissimmee Aquifer Storage and Recovery Pilot Test LC Lower Confining Unit LE Lagrangian‐Eulerian LF1 First Permeable Unit of the Lower Floridan Aquifer LPF Layer‐Property Flow Package (MODFLOW) MC1 Upper Middle Confining Unit MC2 Lower Middle Confining Unit MAE Mean Absolute Error ME Mean Error NAD North American Datum NAP (North Atlantic Division) Philadelphia District NED National Elevation Data set NGVD29 North Geodetic Vertical Datum of 1929 NOAA National Oceanographic and Atmospheric Administration PDT Project Delivery Team PEST Parameter ESTimation RMS Root Mean Square Error SAJ (South Atlantic Division) Jacksonville District SAS Surficial Aquifer System SFNRC South Florida Natural Resources Center SFWMD South Florida Water Management District SIR (USGS) Scientific Investigation Report SOFIA South Florida Information Access SSM Source & Sink Mixing Package (SEAWAT) SJRWMD Saint Johns River Water Management District SWFWMD Southwest Florida Water Management District TDR Technical Data Report TDS Total Dissolved Solids TEC Topographic Engineering Center TVD Total‐Variation‐Diminishing UF Upper Floridan Aquifer USACE United States Army Corps of Engineers USGS United States Geologic Survey VDF Variable Density Flow Package (SEAWAT) WRDA Water Resources Development Act Executive Summary The primary objective of the Comprehensive Everglades Restoration Plan (CERP) is the “restoration, preservation, and protection of the South Florida Ecosystem while providing for other water‐related needs of the region, including water supply and flood protection (WRDA, 2000).” Aquifer Storage and Recovery (ASR) is one of the alternatives proposed by the CERP to provide long‐term storage of excess water, resulting in a more stable water supply in South Florida. The CERP recommends the construction of 333 ASR wells completed in the Floridan Aquifer System (FAS) and distributed over a large region surrounding Lake Okeechobee. This report is the third in a series of four documents describing the multi‐phased groundwater modeling approach undertaken to evaluate the proposed CERP ASR system. The four documents are: 
ASR Regional Study – Benchscale Modeling (Brown, et al, 2006). This report evaluated several model code options and concluded with the selection of WASH123D and SEAWAT as the best‐
suited to the ASR regional evaluation. 
Draft ASR Regional Study Phase I – Groundwater Modeling (NAP, 2006). This report described the first phase of the model development, including identification of boundaries and regional flow and salt migration pathways; evaluation of model run times and sensitivity to timestep sizes; testing of boundary parameters and the sensitivity of hydraulic and transport parameters; and a comparison of results from WASH123D and SEAWAT. 
Final Groundwater Model Calibration Report, Aquifer Storage and Recovery Regional Modeling Study (this report). This document presents the model setup, boundary condition development and calibration for the regional model, which will be the basis of the model evaluation of the CERP ASR plan. It further analyzes the sensitivity of the regional model to a number of parameters and discusses possible sources of error to the regional model. 
A final report will describe the evaluation of the CERP ASR plan against performance objectives such as rock fracture potential, impacts to nearby wells, recovery efficiency and the effects of ASR on salt water intrusion. This evaluation will be performed by running the calibrated, regional model with the addition of the ASR wells as described in the D13R scenario of the SFWMM model (SFWMD and USACE, 1999) and by the use of inset models, with higher grid resolution, centered on the locations of the Kissimmee ASR Pilot Site and the Hillsboro ASR Pilot Site. This calibration report begins with a review of the modeling codes selected for the model in the Benchscale Report (Brown, et al, 2006), the development of the computational grids as presented in the Phase I Study (NAP, 2006) and the conceptual model, much of which was presented in Reese and Richardson, 2004 and Reese and Richardson, 2008. Other sections of the report describe data analyses and model setup. The boundary conditions and initial conditions for the model were based, wherever possible, on available site data. In areas of sparse data, both were necessarily estimated using available research and local knowledge as described in this report. 1
The most important groundwater flow parameters (principally hydraulic conductivity and specific storage) were set during the calibration process. Calibration proceeded by varying these input parameters and noting their effects on the model output. Parameters were changed until the model results most closely matched field measurements. A combination of hand calibration and automated calibration (PEST) was employed to minimize the time required while still allowing the introduction of engineering judgment in the manipulation of input parameter values. The model was calibrated to two separate periods: October 2003 through December 2004 for calibration, and October 1993 through July 1994 for validation. The final calibration is sufficient for the purpose of the regional model, which is to determine on a coarse, regional scale, the impact of the CERP ASR program on the groundwater system in South Florida. Chapter 4 of the report presents details of the calibration and describes the quality of calibration both qualitatively and quantitatively. Uncertainty in the regional pumping is considered to be the most important source of error in the model. It is recommended that future efforts be directed at collecting better quality data on the rates of extraction at private wells. The report finishes with a description of a number of sensitivity runs, which were made to test the importance of some of the most uncertain model parameters. The sensitivity analyses determined that most of the transport parameters (porosity, diffusion and dispersion) are relatively insensitive. Also insensitive on a regional scale are the advection solution method, timestep size and specified head boundary conditions. The Interagency Modeling Center (IMC) has reviewed this study and their comments on the draft report are listed in Appendix G with responses from the modeling team. While the modeling team addressed most of their comments with additional analyses or text, there are some differences of opinion between the two groups. The IMC comments on the final report and the modeler responses are provided in Appendix H and illustrate the two sides of each issue. The recommendations for the future of the regional modeling study are that the calibrated SEAWAT model be used for evaluation of the regional impacts of the CERP ASR program. SEAWAT should also be used in the development of a pair of local‐scale models, which will be highly resolved and capable of evaluating more local effects of small groups of ASR wells, such as recovery efficiency and well‐to‐well interaction. It is also recommended that the production simulations be performed in a probabilistic manner (e.g. Monte Carlo method) to provide for a quantification of uncertainties inherent in the model and the data. 2
1.0 Introduction The U.S. Army Corps of Engineers (USACE), Philadelphia District (NAP), has prepared this report for the USACE, Jacksonville District (SAJ), and the South Florida Water Management District (SFWMD) in support of the Comprehensive Everglades Restoration Plan (CERP). This report documents Phase II of the regional groundwater modeling calibration effort and is the third in a series of four documents describing the multi‐phased modeling approach undertaken to evaluate the proposed CERP Aquifer Storage and Recovery (ASR) system. The previous two modeling documents include the “ASR Regional Study – Benchscale Modeling Report” (Brown et al, 2006) and the “Draft ASR Regional Study Phase I ‐ Groundwater Modeling” (NAP, 2006). The final document in the series will summarize the local scale model development and evaluation of various CERP ASR alternatives using the regional model. In addition to these modeling reports, an evaluation of the effects of various hydrogeologic theories on groundwater flow in South Florida was presented in the conference paper “Using Density‐Dependent Numerical Models to Evaluate Regional Groundwater Flow Patterns in South Florida” (Bittner et al, 2008). This study was also preceded and is supported by “Groundwater Numerical Model Development Support and Data Collection Report” (CH2MHill, 2005). This report reviews the hydrogeologic framework and a number of previous modeling projects within the current model domain. ASR is one of the alternatives proposed by the CERP to provide fresh water storage in South Florida. The CERP recommends the installation of 333 ASR wells open in the Floridan Aquifer System (FAS) and distributed over a large region with well field clusters near Lake Okeechobee, along the Caloosahatchee River, and at several locations along existing canals in the Lower East Coast Region (Palm Beach and Broward Counties). Figure 1.1 shows the study area and Figure 1.2 shows the approximate location of the proposed ASR well clusters envisioned in the CERP. The proposed plan, with total injection and recovery pumping rates of approximately 1.65 billion gallons per day, is larger than any currently operating ASR project. To evaluate the numerous design considerations and the variation in aquifer response on regional, sub‐regional, and local scales, density‐dependent numerical modeling of the FAS is required as discussed in the ASR Regional Study Project Management Plan developed in 2003. The focus of this report is the Phase II Regional Model calibration. This Phase II effort builds on the findings of the Benchscale and Phase I modeling efforts and includes refinements to the regional conceptualization of the FAS. In addition, the modeling was supported by an extensive data collection effort performed by SAJ to compile and evaluate all pumping, water level, and salinity data available for the model domain. SAJ provided a description of the data collection effort and their report is included as Appendix A to this document. The following sections of this report describe how the available data was incorporated into the regional models and the model calibration process. 1.1 Acknowledgements This report is part of a study prepared for and in cooperation with the SAJ and SFWMD. Thanks are given to the USACE Engineering Research and Development Center (ERDC) and the United States Geological Survey (USGS) for their cooperation, modeling code development assistance, and technical guidance during this study. Thanks are also given to South West Florida Water Management District 3
(SWFWMD), St. Johns River Water Management District (SJRWMD), the Florida Department of Environmental Protection (FDEP) and the Florida Department of Health (DOH) for their assistance in the data collection effort. Special thanks are given to the IMC for their cooperation in the review of the various phases of this study. 2.0 Regional Modeling Approach The first and most important step in the modeling process is to define clear, achievable goals and objectives for each stage of the process based on the desired end results. Both the modeling team and the end user must keep the end goal in mind and have a clear understanding of the capabilities and limitations of the model. The primary objective of the Phase II ASR modeling effort is to evaluate the impacts of the proposed CERP ASR wells on the hydrogeologic conditions in the FAS. This evaluation will be performed by using both regional and local scale models. Each scale of model will be used to address different project objectives. The current report pertains to development and calibration of the regional scale models, which will provide planning level information to address large‐scale issues, such as the regional effect of the ASR well clusters on salt water intrusion, water levels, groundwater flow patterns, groundwater quality, and the potential for rock fracturing. This scale of modeling is not appropriate for evaluating local issues, such as well‐to‐well interaction within an ASR well cluster or ASR well recovery efficiency. These issues will be addressed as part of the next report with local scale models that have significantly finer mesh/grid resolution. Data gaps and constraints on time, resources and budgets necessitate the use of simplifying assumptions in the construction of models. Efforts were made to ensure that assumptions had little or no impact on the primary objectives and goals of the modeling project. Those assumptions which might have impacted the objectives were tested using sensitivity analyses. Table 2.1 is a detailed list of the assumptions made in the development of the regional model. Each assumption is listed with a section of the report where the basis for the assumption, sensitivity analysis or explanation is provided. 2.1 Concept of Equivalent Freshwater Head Because of the close hydraulic relationship between the aquifers in South Florida and the Atlantic Ocean and Gulf of Mexico, there are significant variations in the salinity of the groundwater. Except for small areas in the north part of the model domain, deep aquifers are highly saline due to their close interaction with the ocean. Some areas have been measured with salinity values higher than ocean water due to mineral build up. Surface aquifers are fed more by rainfall, resulting in generally low salinity. Total Dissolved Solids (TDS) was used as a proxy for salinity in the ASR regional model and the two terms are used interchangeably in this report. TDS data was normalized by dividing each measured value by 35,000 mg/L, a commonly accepted TDS value for seawater. This results in a unitless value of approximately 1.0 for seawater and 0.0 for freshwater. 4
Comments from reviewers early in the modeling process indicated that temperature variations might also play a significant role in flow conditions in the model. Deeper aquifers are generally warmer near the west coast, likely due to geothermal effects, and cooler on the east coast, similar to ocean waters at depth. Variations in both temperature and salinity of the groundwater cause variations in density. In addition, due to the significant depths in the model, pressure variations can also impact density. The density in the model is calculated to vary from about 62.2 lb/ft3 to about 64.2 lb/ft3. Temperature does not have as great an effect on water density as salinity, but it is included in the model and treated as another constituent concentration. Pressure has the least impact of the three variables controlling density. Both SEAWAT and WASH123D require the user to enter head boundary conditions and initial conditions as observed head based on local density, or the water level measured in a well. The models then use the temperature and salinity to calculate the equivalent freshwater head, which takes into account TDS, temperature, and pressure to determine the potential energy at a given location. The flow equations are solved based on equivalent freshwater heads and then the solutions are converted back to observed heads for viewing and analysis. The governing equations used by SEAWAT and WASH123D are described in more detail in Section 2.2. Because model results are reported as observed heads, the solutions sometimes appear to show unusual flow patterns. When there are significant differences in salinity, groundwater flow may appear to be moving “uphill.” Since the equivalent freshwater head is actually the potential energy of the water at a given point, fluid flow would be expected to occur from locations of high equivalent freshwater head to locations of lower equivalent freshwater head. If the salinity is markedly different between two points, high observed heads may not correspond to high equivalent freshwater heads. Equivalent freshwater head is calculated from observed head by first calculating the observed density from the TDS, temperature, and pressure, using Equation 2.1:    f  mtds TDS  TDS ref   mtmp TMP  TMPref   mp ( P  Pref )
where:   f mtds = = = TDS = TDSref mtmp TMP TMPref mp P Pref = = = = = = = Equation 2.1
Observed density
Density of water at the reference TDS and temperature Slope of the assumed linear relationship between density and TDS Total dissolved solids in the water (proxy for salinity) normalized by dividing by 35,000 mg/L Reference TDS, normalized by dividing by 35,000
Slope of the assumed linear relationship between density and temperature Temperature in the water (C) Reference temperature
Slope of the assumed linear relationship between density and pressure Pressure of the water calculated in terms of head
Reference pressure calculated in terms of head 5
Once the observed density has been calculated, the equivalent freshwater head can be directly calculated by using Equation 2.2 (Guo and Langevin, 2002): 
hf  

 f
where: = hf h = Z =  f

h  
 

f



Z 

Equation 2.2
Equivalent freshwater head Observed head Elevation of point (using NGVD29 as a datum)
Table 2.2 lists the physical constants used in the flow equations. 2.2 Modeling Codes The Benchscale and Phase I modeling efforts concluded that both the SEAWAT (finite‐difference solution) and the WASH123D (finite‐element solution) modeling codes would be used for the Phase II regional model. Since each code has inherent advantages and disadvantages, the use of both codes ensures a higher degree of reliability in the overall calibration, conclusions, and future recommendations. 2.2.1 SEAWAT The SEAWAT (version 4) model (Langevin, et al, 2008, Langevin, et al, 2003, Guo and Langevin, 2002, Guo and Bennett, 1998) was chosen as one of the codes for the Phase II modeling effort. SEAWAT is a finite difference code that simulates variable‐density flow in three dimensions by combining the flow equations in MODFLOW–2000 (Harbaugh et al, 2000) with the solute transport equations in MT3DMS (Zheng and Wang, 1999) into a single program coupling the flow and solute transport solutions. SEAWAT uses a finite difference approximation for Equation 2.3, the governing equation for variable‐
density flow in terms of freshwater head and Equation 2.4, the governing equation for fate and transport of a contaminant in a three‐dimensional, transient groundwater flow system (Guo and Langevin, 2002). (The reaction term has been removed from Equation 2.4 since the chemical reaction package was not used in this model.) 


 h f    f Z  
 

 K f 
 






f



 h f    f Z 


 K f 







f


 h f    f Z 
h f
 C
 
  S f
  s qs



 K f 

 f  
C t
 
t
 
Equation 2.3
Where: α,β,γ = Orthogonal coordinate axes, aligned with the principal directions of permeability = Equivalent freshwater hydraulic conductivity Kf = Equivalent freshwater specific storage Sf 6
t θ C ρs qs = = = = = Time Effective porosity Solute concentration Fluid density source or sink water Volumetric flow rate of sources and sinks per unit volume of aquifer q
C
   D   C     vC   s C s t

Where D v qs C S = = = = Equation 2.4
Hydrodynamic dispersion coefficient Fluid velocity Source/sink volumetric flow rate per unit volume of aquifer Solute concentration of water entering from sources or sinks The program contains several methods for solving the solute transport equation including an implicit finite difference method with either upwinded or central‐in‐space weighting, the method of characteristics, and a third order total‐variation‐diminishing (TVD) scheme. All simulations performed for Phase II model calibration and validation used the finite‐difference upwinded solver; however, a final validation simulation was performed using the more robust TVD solver to confirm that any numerical dispersion in this solver was within acceptable tolerances. (See Section 5.1) 2.2.2 WASH123D The October 2009 compile of WASH123D (Yeh et al., 2003) was also used to evaluate the regional effects of the proposed ASR wells. WASH123D is a finite element code that simulates variable‐density flow and reactive chemical and sediment transport in 1‐D channel networks, 2‐D overland regimes and 3‐D subsurface media on an unstructured mesh. For the Phase II model, only the 3‐D subsurface variable‐density flow options were enabled. With WASH123D, the variably saturated, density‐
dependent groundwater flow is described by the modified Richards’ equation (Equation 2.5 and 2.6) and solved with the Galerkin finite element method.  
 
 ph

F
   K   ph 
Z   s q s f
o
t
  f
 
Where: ph = K = F = F  a'
e
ne
Referenced pressure head Hydraulic conductivity tensor Water capacity (see Equation 2.6)   ' e  ne
dS
dh
Equation 2.5
Equation 2.6
7
Where: a’ e ne Β’ S = Modified compressibility of the medium = = = = Effective moisture content Effective porosity Modified compressibility of water Degree of saturation The Lagrangian‐Eulerian (LE) method is employed to solve the subsurface transport equation (Equation 2.4), where particle tracking is used in the Lagragian step to handle the advection term, and the other terms (such as sources, sinks, diffusion, and dispersion) are calculated in the Eulerian step to determine the spatial concentration distribution at the end of each timestep. The use of this methodology provides numerical stability without a Courant number restriction. In addition, the mesh’s Peclet number is limited only by computational accuracy, not numerical stability. A sensitivity analysis of timestep sizing was performed to ensure the numerical accuracy was adequate for the scale and stated goals of the Phase II modeling effort (see Appendix F). More detailed discussion on various types of numerical dispersion and how the LE method deals with these types of numerical dispersion are found elsewhere. (Cheng et al., 1996; Cheng et al., 1998; Yeh et al., 2006). 2.3 Model Extent and Spatial Discretization Both WASH123D and SEAWAT report numerical solutions to partial differential equations governing flow and transport at a set of discrete points. SEAWAT arranges these points as the centers of cube‐shaped cells arranged in rows, columns and layers of a structured grid. WASH123D solves its equations at nodes on an unstructured 3‐D mesh made up of prism‐shaped elements. In each case, the grid or mesh was built to cover the area of interest (the proposed locations of the 333 CERP ASR wells) both horizontally and vertically. The sides of the grid or mesh were placed to coincide with convenient locations for assigning boundary conditions. Both the grid cells and mesh nodes were arranged in layers corresponding to the geologic layering of south Florida. The Phase II model boundaries were established based on conclusions from the Benchscale and Phase I modeling efforts. The side boundaries of the model were generally established along geologic outcrops to the ocean or aligned near observation wells with available data during the calibration and validation periods. Figure 2.1 shows the horizontal extent of the model domain, which covers just over 23,000 square miles of the Floridan peninsula. The eastern boundary of the top model layer is located along the coast of the Atlantic Ocean. Subterranean geologic units extend eastward to their outcrop on the ocean floor, resulting in an additional 7,000 square miles of the model located offshore beneath the Atlantic Ocean. The northern model boundary for all geologic units cuts across the Florida peninsula, through Orlando and slightly to the south of Lake Apopka. The western model boundary closely follows the gulf coast of Florida, beginning at the model’s northwest corner, just west of Tampa. South of Sanibel Island, the model boundary moves inland, crossing the Everglades to intersect the eastern boundary at the south end of Biscayne Bay. (All place names from this section are labeled on Figure 1.1.) 8
The computational grid/mesh resolution was selected to balance the purpose of the model with the constraints of time and computer resources. Higher resolution on the grid or mesh can provide greater accuracy and detail, but can also tax project budgets and computer resources due to the additional time required to compute the solution. The model purpose, as described in the introduction to Section 2.0, is to reasonably replicate the regional groundwater flow fields and effects of the proposed ASR well clusters. Figure 2.1 shows the horizontal resolution of the WASH123D computational mesh and the SEAWAT computational grid. The smallest resolution (1,000 ft. in the WASH123D mesh and 2,000 ft. for the SEAWAT grid) is found at the proposed ASR well cluster locations where accuracy and detail are necessary. In the WASH123D, even finer resolution (100 ft.) is incorporated at the Kissimmee and Hillsboro ASR pilot sites to facilitate future local scale model construction. The size of both the grid cells and the mesh elements increases to 10,000 ft along the model boundary. Vertically, the models extend from near the ground surface to the bottom of the confined Boulder Zone (BZ) member of the Lower Floridan (LF1) aquifer. Although the top layer of the SEAWAT grid is set to coincide with the Surficial Aquifer System (SAS), no calculations were made in this layer. To achieve the same effect in the WASH123D model, the top of the mesh is set at the bottom of the Surficial Aquifer system. This is explained in more detail in Appendix C. Although the depth of the model varies, the topographic high is near elevation 250 ft NGVD29 and the deepest point in the model is about ‐3,600 ft. NGVD29. As shown in Figure 2.2, the models include five confined aquifers and four confining units. The SEAWAT grid also includes the Surficial Aquifer System (SAS), although no calculations are made here. The colors in Figures 2.3 and 2.4 are used to illustrate the arrangement of broadly‐defined hydrogeologic material layers used in the model. Heterogeneity within the model layers was incorporated using zonal modifications to hydrogeologic properties of each geologic unit, or pilot point interpolation of hydrogeologic properties to individual cells of the model. The 3‐D grid contains 22 vertical cell layers and the 3‐D mesh is made up of 23 vertical element layers. Figure 2.3 shows the geologic units associated with each layer in the SEAWAT model, while Figure 2.4 shows the geologic units associated with each layer in the WASH123D model. The 3‐D mesh for this model is comprised of 391,228 nodes and 740,637 elements. The 3‐D grid for this model is comprised of 1,092,256 cells, 823,038 of which are active. (The organized arrangement of the grid cells requires a rectangular shape to the grid. The desired shape of the model is incorporated by inactivating unnecessary cells.) Additional details concerning the model set up are discussed in Section 3. Due to the dipping nature of the geologic layers some concerns were raised about the model resolution and aspect ratio and their possible contribution to model instability and inaccuracy. To respond to these concerns, a sensitivity analysis was performed to evaluate how the model discretization would affect the computed results of the regional models. The results of this analysis indicated that the errors resulting from model discretization were within the model’s error tolerance for the majority of the model domain, including the area of interest for the proposed CERP ASR wells. Grid resolution was shown to 9
have a more significant effect in a small area in the northwest portion of the model near Tampa (where the geologic units thin significantly). However, since this area is north of the Polk County recharge area and does not appear to be influenced by the proposed ASR wells, the inaccuracies introduced by model resolution issues were considered acceptable for the scale and purpose of this modeling effort. Appendix B provides additional details on this sensitivity analysis. 2.4 Model Time Discretization The calibration period selected for the transient calibration of the regional model was October 31, 2003 through December 31, 2004. The SEAWAT model was set up with 15 stress periods – one for each month of the period. Most boundary conditions and source/sink options in SEAWAT require constant values during each stress period. Thus, for head data, the average measured head during each month was applied to the entire month. For pumping data, the total pumped volume was divided by the number of days in the month and applied as a constant flux during the entire month. This simplification can result in some differences between observed and calculated data, but was necessary due to the paucity of reliable pumping data available at many locations in the model domain. Although the WASH123D model does not use stress periods, the same monthly averages were used to allow for direct comparisons between the two models and to minimize additional data collection. The validation period of August 1993 through July 1994 was originally selected to be consistent with the calibration period of the USGS model by Sepulveda (2002). Analysis of the head data indicated that October 1993 was a better starting point for the model since the heads were generally relatively constant during the period leading up to October 1993. The validation period was, therefore, shortened to October 1993 through July 1994. The same process of assigning month‐long stress periods to the model period was followed as explained above. In each case, the first stress period was one day long and was solved as a steady state model to provide a starting condition for the rest of the modeled time periods. Timesteps (times at which the model computed and reported a solution) for both the flow and transport models were spaced evenly through the remaining stress periods. Each month was given 6 equally‐sized timesteps, except for February 2004 and 1994, which only had 5 timesteps. Depending on the length of the month, this provided timesteps that were approximately 5 days long. Head results at the observation points are available at each timestep (approximately every 5 days). Head results on the grid as a whole were output about every 10 days to save on file sizes. For the SEAWAT model, acceptable Courant numbers require a timestep about 8 hours long on average because of some of the thin cells located in the northwest section of the model. The approximately 5‐
day timesteps used for the calibration simulations were selected to provide a faster run time during calibration. At the end of calibration, additional model runs were made using a model‐selected timestep to ensure accuracy of the final result (see Section 5.1). These final simulations used the TVD solution scheme, which used timestep sizes that were less than 1 day. Additional details on the testing used to select the regional model time discretization are given in Appendix B. 10
2.5 Model Datum Numerous data sources were compiled to generate the model input parameters, boundary conditions, and calibration/validation data sets. All data sets were converted to a common horizontal and vertical datum. The horizontal datum used for this model is feet North American Datum 1983 (NAD83), State Plane Florida East. The vertical datum used is feet North Geodetic Vertical Datum 1929 (NGVD29). Any data in a different coordinate system was converted using the coordinate conversion software, Corpscon, version 6.0 (December 2004 release), developed by the Topographic Engineering Center (TEC) of the U.S. Army Corps of Engineers. All elevation data presented in this report are in NGVD29. Water levels (head) are presented as total head elevation, also in NGVD29. 3.0 Conceptual Model Prior to construction of any numerical groundwater model, it is important to properly conceptualize the flow system in question. A conceptual model is a detailed description of the groundwater flow system to be modeled and should identify the hydrologic and hydrogeologic conditions and all important features and drivers of the groundwater system, including sources, sinks, boundary conditions, geophysical features that convey water or interrupt flow, recharge, site stratigraphy, material properties, etc. The conceptual model is generally developed through extensive literature research and data analysis. Most of the conceptualization for the Phase II ASR Regional Model had already been completed during the earlier phases of the project and is presented in previous reports (Brown et al, 2006 and NAP, 2006). However, additional conceptualizations were required for parameters that affect the density of the groundwater: temperature and salinity (represented by Total Dissolved Solids [TDS]). These analyses are presented in Appendix E. The conceptual model should start with the basic components that are expected to have the greatest effect on groundwater flow. The preliminary conceptual model can be used to construct the model grid or mesh and develop the required simulations. Complexity can then be added to the conceptual and computational models as model outputs are compared to known conditions at the site and as the understanding of the flow system is refined. This often is an iterative process where interim numerical model results are used to help direct the research process and improve the conceptual model. When evaluating the results of the WASH123D and SEAWAT models, it is important that the reader have an adequate understanding of the conceptual model so that potential model limitations are fully understood. The following subsections provide a brief description of the features included in the Phase II conceptual model and detail how these features were incorporated into the WASH123D and SEAWAT numerical models. 3.1 Topography The topographic data was provided by SAJ and included bathymetric data for the offshore portion of the models. This data was a compilation of the SFTOPO‐RC5 Topography/Bathymetry, National Elevation Data set (NED), and the National Oceanographic and Atmospheric Administration (NOAA) Coastal Relief 11
Model (CRM) bathymetry. The data was smoothed by SAJ to produce a topographic data set with uniform 1,000‐foot grid spacing. Additional Digital Elevation Model (DEM) data was merged with this data set to ensure coverage across the entire model domain. The vertical datum of the final topographic data is NGVD29. Traditionally, topographic information is often used to define the surface of the 3‐D computational mesh or grid of a groundwater model with recharge and evapotranspiration applied to the surface as a flux boundary condition. However, since the purpose of the Phase II regional models is to evaluate flow in the FAS, the model was simplified by assigning specified heads in the Surficial Aquifer System (SAS) as explained in Section 3.3.1. Because there are no calculations made in the SAS, the top elevation becomes unimportant to the model calculations. The topographic data was useful for visualization of the SEAWAT results, development of regression correlations used to apply surface boundary heads, and for determining the layer outcrop locations in the Atlantic Ocean for both models. This topographic data was also used to determine open intervals for monitoring wells and pumping wells. Usually, surface elevations at wells were not provided and the pumping and/or sampling intervals were reported as depths below ground surface. To estimate the elevations of pumping and sampling intervals at wells, the topographic data set was linearly interpolated to the well points and the depths were subtracted from the interpolated surface elevations. Well interval elevations were then compared to geologic layer elevations to determine the hydrogeologic unit tapped by the well’s open interval. Any error introduced by using these interpolated well surface elevations is small compared to the accuracy of the geologic layer elevations. 3.2 Geology A wealth of geologic and hydrogeologic data is available for the regional model domain. Geologic interpretations were based primarily on the USGS Scientific Investigations Report (SIR) 2007‐5207 (Reese and Richardson, 2008) and a Draft report developed by Reese and Richardson (2004) entitled “The Draft‐Final Report – Task 3.0 Define Preliminary Hydrogeologic Framework” (referred to herein as the Preliminary Hydrogeologic Framework). The following subsections describe the hydrostratographic layering and hydrogeologic data for the regional model. 3.2.1 Regional Geology SFWMD used SIR2007‐5207 and the Preliminary Hydrogeologic Framework to define the surfaces of the hydrostratigraphic units in the Phase II models and provided grids of the elevations (NGVD29) of the tops of the major geologic units. These gridded surfaces were used to develop the computational grid and mesh. Figures 2.2 to 2.4 show a gross conceptualization of all the geologic units used in the Phase II modeling and defined by SFWMD. For the Phase II models, the FAS is divided into 4 producing units: the Upper Floridan (UF), Avon Park Permeable Zone (APPZ), Lower Floridan (LF1), and Boulder Zone (BZ); and three confining units: Upper Middle Confining Unit (MC1), Lower Middle Confining Unit (MC2), and the Lower Confining Unit (LC). The Framework documents divide the LF into LF1, LF2 and LF3, which are not all found at every location. 12
However, the LF, as simulated in this model, represents the first permeable zone of the Lower Floridan Aquifer (LF1). The LC is a composite of any remaining units (permeable or confining) between the first permeable zone and the BZ. The cited studies did not report the precise location of the base of the BZ, but estimated its thickness to be between 200 and 700 feet. The model was built with a uniform thickness of 500 feet for the BZ layer and a sensitivity analysis of the thickness was performed (see Section 5.4). The thickness of each hydrogeologic unit (UF through LC) as defined in the model is presented in Figures 3.1 through 3.6. Although these figures were created from the SEAWAT computational grid, the same thicknesses were applied to the layering of the WASH123D computational mesh. It is also important to note that the term ‘confining unit’ is somewhat relative. The MC1, MC2 and LC are confining units only by comparison to the producing units of the Floridan system. Anderson and Woesner (1992) define a confining bed as a ‘unit of porous material that retards the movement of water.’ The hydraulic conductivities of the MC1, MC2 and LC do not seem very low when compared to those found in other systems. (Materials such as glacial till, clay, unfractured shale or unfractured basalt can have hydraulic conductivities less than 10‐6 ft/d, which is several orders of magnitude lower than most of the conductivity values used in the model for the confining units.) Because the conductivities in the MC1, MC2 and LC are a few orders of magnitude lower than those in the UF, APPZ, LF1 and BZ, they impede groundwater movement and are designated as confining units. As indicated in Figure 2.3, the hydrogeologic layering was subdivided for the layers of the SEAWAT computational grid. The confining units (MC1, MC2, and LC) were each equally divided into two model layers. The aquifers were also equally subdivided into a number of layers based on the expected importance of each aquifer to the planned ASR production runs. Initial plans indicate that all of the CERP ASR wells will be open in the UF, so this layer was equally subdivided into 6 layers. The APPZ was equally subdivided into 3 layers because of the slight possibility that the ASR wells in the UF might impact the heads in the APPZ. Some members of the PDT have expressed an interest in testing ASR wells in the APPZ layer, so the additional layer may become important in the future. The LF1 and BZ layers are not expected to be impacted by the CERP ASR pumping, so they were given 2 layers and 1 layer, respectively, in the SEAWAT model. The FAS is overlain by a complex system of alternating aquifers and confining units often referred to as the Surficial Aquifer System (SAS) and the Intermediate Aquifer System (IAS). Since they are not the focus of this modeling effort, these systems are greatly simplified for the model conceptualization. In the model, the SAS is simplified to a vertically homogeneous unit between the topographic surface to the top of the IAS, as defined in SIR2007‐5207. The IAS consists of everything between the SAS and UF and is conceptualized in two components: the Intermediate Aquifer (IA) and the Intermediate Confining Unit (ICU). The IA exists only in west‐central and southwest Florida (Miller, 1997), but non‐continuous layers (pinch‐outs) are difficult to simulate in either the computational grid or mesh. The IA was modeled by assigning IA aquifer parameters to the west‐central and southwest third of layer 3 of the SEAWAT model. The ICU was modeled in layer 2, 4 and the non‐IAS section of layer 3. Thus, layer 3 has two distinct sections with starkly different aquifer parameters (see Figure 2.3). These simplifications are 13
acceptable since the primary function of the SAS and the IAS in the model is to conduct water from the surface to the FAS. Similarly, the Hydrogeologic Framework (Reese and Richardson, 2008) indicates that the APPZ does not exist in the southwest section of the model (most of Collier and Monroe Counties). This pinchout was approximated by making these layers extremely thin in this area. Each of the three layers thins to a minimum of 2 feet, resulting in a 6‐foot thickness for the entire layer (see Figure 3.3). Since this is also the limestone section of the APPZ, the hydraulic conductivity is very low and the APPZ does not conduct much flow in this area. As previously mentioned, the BZ thickness is assumed to be universally 500 feet across the model domain. However, Reese and Richardson (2008) report that the BZ does not occur in west‐central Florida. To model the non‐existence of the BZ, the hydraulic conductivity for layer 22 in west‐central Florida is set to values similar to that of the LF1. Since the LF1 conductivity is much smaller than the generally present BZ conductivities, this approach results in greatly diminished BZ flow. (Because of the assumed constant thickness of the BZ, a figure similar to Figures 3.1 through 3.6 is not provided for the BZ.) The layering of the WASH123D model was similar to the SEAWAT model as can be seen by a comparison of Figures 2.3 and 2.4. Most of the hydrogeologic unit layers were defined by the same number of model layers. The MC1, MC2 and LC confining units were all divided equally into two model layers. The UF, APPZ and LF1 aquifers were divided into 6, 3 and 2 layers, respectively, just as in the SEAWAT model. However, because of computational differences between the two models, the BZ was divided into two layers and the IAS was divided into four. The additional layer is added to the IA to account for differences between finite difference (SEAWAT) and finite element (WASH123D) computational points and the application of hydraulic conductivity to those points. In SEAWAT, the hydraulic conductivity is assigned to a cell and the center of the cell is the computational point. In WASH123D, the conductivity is assigned to an element and the computational points are at the nodes on the element faces. Figure 3.7 is a diagram that shows the comparison between the SEAWAT and WASH123D computational points in the area where the IA is present. The WASH123D computational point 3 in Figure 3.7 uses the aquifer conductivity from Layers 2 and 3 to compute the heads in the aquifer in a similar way to computational point 2 for SEAWAT Layer 3. The WASH123D computational points 2 and 4 use an average conductivity from the confining unit and the aquifer. Splitting the IA into two layers in the WASH123D model provides a layer of nodes that are assigned the aquifer conductivity and ensures an accurate representation of the recharge entering and moving through the IA. Similarly, the BZ is divided into two layers to provide the model with at least one layer of nodes assigned a BZ hydraulic conductivity value. Pinchouts in the APPZ and BZ in the WASH123D model are handled in the same way as the SEAWAT model. Since the mesh is layered, it is difficult to remove the elements from the mesh. Instead, the elements were made thin and the hydraulic conductivity was used to approximate the condition. As mentioned above, the model simulated APPZ in Collier and Monroe Counties is very thin with a low 14
hydraulic conductivity. The absence of the BZ in the northwest part of the model is simulated by setting the hydraulic conductivity to values similar to the LF1. The SAS was not defined as a WASH123D model layer because no flow calculations were made in the SAS. The SAS heads (interpolated from available data) were assigned to the top nodes of Layer 1 of the IAS, as described in Section 3.3.1 and Appendix C. 3.2.2 Hydrogeologic Properties Hydrogeologic properties such as hydraulic conductivity and specific storage were estimated for each model layer based on the available data. Then, during the calibration process (see Section 4), the property values were adjusted until an adequate calibration to available data was achieved. During calibration, the parameter values were required to remain within reasonable ranges as defined in the Preliminary Hydrogeologic Framework, SIR2007‐5207 and APT (Aquifer Pump Test) data provided by SFWMD. Additional information for the Phase II conceptual model was collected from other sources and from online databases including SFWMD’s DBHYDRO, USGS’s South Florida Information Access (SOFIA), the National Park Service’s South Florida Natural Resources Center (SFNRC), CH2MHill’s Groundwater Numerical Model Development Support and Data Collection Report, and a number of published reports and papers (see Section 8). The available field data used to guide the calibration process is presented in Figures 3.8 through 3.15. This field data includes horizontal hydraulic conductivity data for the aquifers (Figures 3.8 through 3.10), vertical hydraulic conductivity data for the confining units (Figures 3.11 through 3.13) and specific storage for the UF and APPZ (Figures 3.14 and 3.15). (Specific storage was converted from storage coefficient by dividing by the aquifer thickness.) The final calibrated hydraulic conductivity and specific storage distribution for each model layer will be presented later in Section 4 (See Sections 4.1.2 and 4.2.4 along with Figures 4.31 through 4. 40 and 4.111 through 4.118). Differences between WASH123D and SEAWAT resulted in slight differences in the material parameters used in the calibration model. Additional properties such as porosity, dispersivity and molecular diffusion coefficient, were found to have little effect on the calibration of the model. Sensitivity analyses of these parameters are presented in Section 5.2 and 5.3. 3.2.3 Regional Anisotropy During the Phase I modeling, the SEAWAT grid angle was set at 18 degrees west of north to align with the axis of the Floridan peninsula. Bittner, et al. (2008) analyzed a number of options for improving the agreement between the initial model results and the estimates of pre‐development heads in the UF from Meyer (1989). This paper concluded that both the inclusion of anisotropy in the aquifers and the inclusion of temperature effects on density could improve the calibration of the model. A lineament study (Fies, 2004) and preliminary results from some image log fracture analysis work at SFWMD indicated that the dominant fracture orientation was NW to SE at an angle of about 38 degrees west of north. For this reason, the regional grid for Phase II modeling was designed with a 38 degree angle, in place of the 18 degree angle used in earlier reports. However, additional analysis by SFWMD 15
indicated that the NW to SE orientation was based on a lumped view of all the UF fractures from all the wells. When the data was split out to look at the dominant orientations from individual wells, it became clear that the dominant orientations varied geographically. The lumped view gave additional weight to a large volume of fractures in the UF at the Kissimmee River pilot location. This led to the conclusion that there is currently no conclusive evidence of regionally dominant orientation for fractures in the UF. The anisotropy option was, therefore, not used in this regional model (although the grid angle of 38 degrees remained). Greater detail will be available on this study when the final report on the lineament study is completed in time for inclusion in the final Technical Data Report (TDR) for the regional study. 3.3 Boundary Conditions Specified head boundary conditions were applied to the sides and top of both Phase II regional models. In SEAWAT, the time‐variant specified‐head boundary (CHD) package was used to specify the heads in the cells on the top and sides of the model. Similarly, in WASH123D, a DB card (Dirichlet boundary condition) was listed in the input file for each node on the sides and top of the mesh. No boundary condition was applied to nodes on the bottom of either model. By default, unassigned nodes on the boundary of the mesh and unassigned boundary cells of the grid are considered to be no‐flow nodes. The use of the no‐flow boundary on the bottom of the model is appropriate because of the much lower conductivity of the Sub‐Floridan confining unit, which underlies the Boulder Zone. Preferential flow in the Boulder Zone is expected to be horizontal with only insignificant flows in or out of the bottom of the model. The following subsections provide a brief summary of the methodology used to set the specified head boundary conditions on the Phase II regional models. Additional details are provided in Appendix C. 3.3.1 Surficial Head Boundary Conditions The heads assigned to the top boundary of the models simulate recharge (precipitation less evaporation, transpiration and runoff) and provide one of the primary sources of water to the models. Generally, groundwater models use a flux‐type boundary condition at the surface to simulate recharge. The flux is often calculated using a flow budget, subtracting such sinks as evapotranspiration and runoff from precipitation to determine the volume of water seeping through surface soils into the model. Runoff and evapotranspiration are usually approximated using empirical equations with estimated parameters based on sparse data. Because of the inherent uncertainty in these calculations, recharge is often used as a calibration parameter and is varied along with hydrogeologic material properties until the model result matches measured aquifer conditions. For these regional ASR models, a specified head was assigned to the top surface of the models, based on an interpolation of available head data from monitoring wells open in the SAS. This approach avoids the difficulties and inaccuracies inherent in calculation of recharge values and seepage rates and makes possible the direct usage of the abundance of SAS head data. The purpose of the Phase II regional models is to evaluate regional flow characteristics in the FAS and estimate the aquifer effects from the proposed CERP ASR wells. Since the ASR pumping is not expected to affect the heads in the SAS, the use of specified heads is considered valid. 16
In the SEAWAT model, the SAS was modeled as the top layer of cells with the top of each cell corresponding to ground surface and the bottom of each cell set at the elevation of the bottom of the SAS. Each cell was assigned a specified head as described above and SEAWAT made no horizontal flow calculations in the top layer. The specified head was calculated based on an interpolation of the average head data at all available wells for each month of the calibration and validation period as described in Appendix C. The same interpolation process was used to assign specified heads to the top layer of nodes in the WASH123D model. The elevations of these nodes correspond to the elevation of the bottom of the SAS layer. Thus, the SAS was not included in the computational mesh. This makes the two models comparable since neither one made horizontal flow calculations in the SAS. See Appendix C for additional details 3.3.2 Simulation of Ocean Boundary Along the eastern boundary, each modeled hydrogeologic layer extends to its projected outcrop in the Atlantic Ocean. The outcrop location was defined by cutting each layer when the geologic unit surface grids provided by SFWMD (see Section 3.2.1) intersected the bathymetry data (see Section 3.1) for the floor of the Atlantic Ocean. The assigned boundary head simulated the level of the ocean and was based on the monthly mean sea level measured at two NOAA tide gauges – one at Virginia Key, near Miami, and the other at Naples, on the west coast of the Florida peninsula. The tide gauge locations are marked on Figure 1.1 and the monthly average water levels for each gauge, plus the average value used in the model are plotted in Figure 3.16. There is some monthly variation in the ocean level, with slightly higher levels in the fall and lower levels in the spring and summer. The annual variation of monthly mean sea levels is less than 1 foot, which is much smaller than the variation in monthly average heads at most observation wells in the model domain. Note that with the coarse time discretization, this model does not attempt to reproduce daily tidal cycles. 3.3.3 Aquifer Head Boundary Conditions Ideally, the west and south boundaries would also extend out to the locations of the outcrops for each layer in the Gulf of Mexico. However, these outcrops occur nearly 150 miles from the Florida coastline. Extension of the model boundary to these outcrops would add significantly to the model size, computational requirements, and the time required to reach a converged solution. This would also add a large area to the model which has not been extensively studied and for which there is no significant data regarding heads, water quality or aquifer characteristics. Instead, the north, west and south boundaries coincide with available water level data points. For each aquifer (IAS, UF, APPZ, LF1, and BZ), heads assigned are based on monthly averaged measured values from wells located near the boundary. Figure 3.17 shows the areas where specified head boundary conditions were applied to the models as well as the location of the available data points. The process used to assign specified heads to the sides of the aquifer layers of the model accounted for all available data and incorporated the conceptual model for the site. It is described in detail in Appendix C. 17
Some concerns have been raised that the use of specified head boundary conditions at these coastal and inland locations might cause inaccuracies since there are numerous pumping wells located very close to the boundary. However, these errors are mitigated by basing the boundary heads on measured heads, which already include the drawdown effects of regional pumping. Near‐field effects of pumping would likely not be captured, but they are beyond the scope of this model and not important to the goals of the regional model (See Section 2.0). 3.3.4 Confining Unit Head Boundary Conditions No‐flow boundaries were used at nodes (WASH123D) and cells (SEAWAT) along the side boundaries of the confining units, except where they outcropped to the ocean. The horizontal flow through the model boundary in these confining units is not believed to be a significant source or sink when compared to flow through the aquifers. A sensitivity analysis confirmed this assumption and is presented in Section 5.5.3. 3.3.5 TDS and Temperature at the Boundaries SEAWAT and WASH123D both allow the user to define the water quality of the flows entering the model at any boundary condition. In SEAWAT, the SSM package (Source & Sink Mixing) was used to assign the TDS and temperature to each cell with a CHD boundary condition and all injection wells. WASH123D has a similar requirement in the form of an RS2 and RS6 card (variable boundary TDS concentration and temperature, respectively) corresponding to each of the specified head nodes and a PS2 and PS6 card (point source TDS concentration and temperature, respectively) for each of the injection wells. For the boundary cells and nodes, the water quality of the incoming water was set based on the initial conditions at that location (see Section 3.4). For injection wells, the TDS values were assigned using available data (see Appendix E). At injection wells where no data was available, it was assumed that TDS values would be similar to nearby injection wells of the same type. The two types of injection wells were deep injection wells (typically have high TDS values) and existing ASR wells (typically have low TDS values). Injected temperature values were assumed to be consistent with the temperature initial conditions for the SAS (see Section 3.4.2). 3.4 Initial Conditions The initial conditions applied to the model included initial head, salinity and temperature. The initial head condition was based on early test runs of the model. It is important to note that while the initial head condition affects the speed at which the steady state solution is reached, it has no effect on the model results. For the transient model, the first stress period was solved in steady state mode to give the starting head condition for the subsequent transient simulation. The initial salinity and temperature conditions were used by the models in the initial calculation of groundwater density. Studies have shown that regional groundwater flow patterns in the FAS can be significantly affected by variations in the groundwater fluid density [Hughes, Vacher, and Sanford (2007), Meyer (1989), Sanford et al (1998), Kohout (1965), Kohout et al (1977)]. The ability of SEAWAT and WASH123D to model density‐
dependent flow was the main criteria in selection of these models. The following subsections describe the data and methodology used to create these initial condition distributions. 18
3.4.1 Salinity (TDS) Distribution For this study, reported measurements of total dissolved solids (TDS) are used as proxy for salinity. The terms ‘TDS’ and ‘salinity’ are used interchangeably in this report. The model requires that initial salinity concentrations be specified at every computational point in the model domain. In order to meet this requirement, an extensive data collection effort was undertaken to identify representative water quality data from the SAS to the BZ. Where possible, water quality data from the beginning of the calibration period (October 2003) was used; however, in areas where data was sparse, reported measurements from other time periods were used to fill data gaps. Since the regional water quality does not normally change drastically over a period of a few years, this method of filling data gaps was considered to be adequate. It is important to note that data at or near injection wells was not used if the samples appeared to reflect the quality of the injected water instead of the native water quality. A variety of data sources were used to collect the available TDS data, including USGS, DOH, SFWMD, SJRWMD, and SWFWMD. Additional details on the data collection effort are summarized in Appendix A. Once the TDS data was collected, it was carefully evaluated by the modeling team to ensure that it reflected the known regional water quality. Several recording errors (e.g. data transposed between zones, significant fluctuation in water quality readings, etc.) were identified and corrected. The TDS at the ocean outcrops was set to 35,000 mg/l to reflect the salinity of seawater. Since the quantity and quality of the TDS data in the confining units was limited, the interpolation results in these layers were compared to the overlying and underlying aquifer water quality to ensure consistency. The validated data for each aquifer was then interpolated to the corresponding model layer. Figures 3.18 to 3.24 show the final TDS initial condition distribution by layer. The quantity of data used in the interpolation and assumptions specific to each layer are explained on each figure. Figure 3.25 shows the same data as a 3‐dimensional fence diagram. For the SEAWAT model, the TDS initial condition values for the FAS (Layers 5 through 22) were specified based on the corresponding aquifer and confining unit values shown in Figures 3.18 through 3.24. The SAS (Layer 1) was given a uniform TDS concentration of 100 mg/l in the land areas and 35,000 mg/l at the ocean. The TDS values for the ICU (Layers 2 and 4 and a portion of Layer 3) were determined by taking the average of the SAS and UF layers. Available data in the IA was interpolated to determine the initial conditions for the aquifer portion of Layer 3. In the WASH123D model, the assignment of the initial conditions were somewhat different than for the SEAWAT model as a result of the differences between finite difference (SEAWAT) and finite element (WASH123D) computational points. For the SEAWAT grid, the computational points are located at the centers of the grid cells, so the initial conditions are required at each grid cell center. The WASH123D computational points and initial condition assignments are located at the nodes on the element interfaces. Figure 3.26 is an illustration that shows the comparison of the SEAWAT and WASH123D computational point locations and the differences in the assignment of TDS initial condition for the two models. In this example of a vertical column of grid cells and mesh elements, there are two confining units and two aquifers, each with a different TDS concentration. For SEAWAT, the assignment of initial conditions for each aquifer and confining unit was straightforward and based on the interpolation of 19
available data as explained previously. However, for the WASH123D assignment, the aquifer TDS values (from the interpolation of the available data) were assigned to any computational point within or at the top or bottom of the aquifer. For confining units, the TDS values from interpolation were only assigned to nodes that were completely surrounded by a single hydrogeologic unit. So, points 2, 3 and 4 were given the interpolated aquifer TDS value of 2000 mg/L, but only point 5 had the interpolated TDS value of 5000 mg/L which was associated with that confining unit. Although the SAS was not explicitly modeled in the WASH123D model, the SAS initial TDS values used in the SEAWAT model were assigned to the top layer of nodes in the WASH123D model, top of Layer 1. The initial TDS values in the remaining layers of nodes representing the IAS, nodes on the interfaces of Layers 2 and 3, were the average of the values for the SAS and UF layers. In general, fresher zones in the deeper geologic units are seen in the northern portion of the model beneath the Polk County recharge area and south of Orlando. The TDS concentration increases to the south and near the geologic outcrops at the ocean. Additional details concerning the procedure used to develop the TDS data sets and initial conditions are presented in Appendix E. Because of the short calibration period (14 months) and validation period (10 months), no appreciable change in the TDS distribution was noted in the model results. Final TDS distributions are quite similar to initial TDS distributions, except in the immediate vicinity of injection wells. Because of the coarseness of the model grid, the model‐calculated TDS close to an injection well cannot be expected to be accurate, and is not important to the regional goals of this study. For this reason, model results of water quality data are not presented in this report. Water quality will be of greater import during the production runs on the local‐scale models, which will look at ASR efficiencies and near‐well effects. 3.4.2 Temperature Distribution The models also required the definition of the initial groundwater temperature at every computational point in the model domain. Temperature data was collected to construct a data set of values from the IAS to the BZ throughout the horizontal extent of the model domain. For the SAS, an average temperature value of 24°C can be assumed for the entire unit because shallow density variations have little impact on model results. Where possible, temperature data from the calibration period was used; however, in areas where data was sparse, reported measurements from other time periods were used to fill data gaps. This approach is based on the assumption that regional water temperature does not vary significantly over a period of a few years. As noted for the TDS data analysis, data at or near injection wells was not used if the samples appeared to reflect the temperature of the injected water and not the native water temperature. In some of these cases, well drilling reports containing native water temperature measurements were available and were used in place of more recent temperature measurements. Several data sources were used to collect the available temperature data, including USGS, SFWMD, SJRWMD, and SWFWMD. On the ocean boundary, temperature variation was estimated using a general temperature‐depth of ocean water profile compiled by the University Corporation for Atmospheric Research (Figure 3.27). 20
The collected data was analyzed to determine the values that best represented the regional temperature in each aquifer and confining unit. The details of this analysis are included in Appendix E. Figures 3.28 to 3.35 show the initial condition temperature distribution for each hydrogeologic layer. The number of data points used in the interpolation and assumptions specific to each layer are described on each figure. The same data is displayed in a 3‐dimensional fence diagram in Figure 3.36. The temperature initial condition values were assigned to the SEAWAT and WASH123D models in a similar manner to the assignment of the TDS initial condition values. See Section 3.4.1 for a description of the differences in model assignments resulting from the differences in the location of their computational points. In general, the temperature increases with depth on the western side of the peninsula and decreases with depth on the ocean boundary. This trend creates a very large temperature variation, from 5⁰C to 44⁰C, in the BZ where temperature effects on density have the largest impacts on model results. The warmer west coast temperatures also extend through the mid‐section of the state toward Lake Okeechobee in most of the geologic units. Because of the short calibration period (14 months) and validation period (10 months), no appreciable change in the temperature distribution was noted in the model results. Final temperature distributions are quite similar to initial temperature distributions, except in the immediate vicinity of injection wells. Because of the coarseness of the model grid, the model‐calculated temperature close to an injection well cannot be expected to be accurate, and is not important to the regional goals of this study. For this reason, model results of water quality data are not presented in this report. 3.5 Sources and Sinks In addition to the model boundaries, pumping wells constitute a significant source/sink for groundwater in South Florida. This pumping includes withdrawal wells (irrigation, water supply, etc.), existing ASR wells, and Class I injection wells. An extensive data collection effort was performed by SAJ to compile and evaluate detailed data sets of the pumping distribution within the model domain. Over 30,000 wells were identified as active during the calibration/validation periods within the model domain. However, many of the wells were missing specific location information such as horizontal coordinates or open interval depths. Also, monthly transient pumping rate records for many wells were often either unavailable or incomplete. As part of the data collection effort, estimates were made to fill these data gaps. Additional details on the data collection effort for the pumping wells and the methodology used to fill the data gaps are summarized in Appendix A. Additional effort was required to appropriately assign the pumping to the grid and mesh. The depths of the top and bottom of the open interval for each pump were converted to elevations based on the approximate ground surface elevation at the point. These elevations were compared to the model‐
simplified geology to determine the aquifer (or aquifers) impacted by each well. The pumping elevations were adjusted to prevent the model from pumping in confining units. Pump rates for wells covering more than one aquifer were prorated based on the length of open interval and the estimated hydraulic conductivity of each aquifer. SEAWAT requires all pumping to be applied to the center of a 21
cell; WASH123D requires all pumping to be applied to a node. To accommodate these requirements, the wells were moved horizontally to nearest computational point. In SEAWAT, any well located within a grid cell, was automatically moved to the center of the cell and added to the pump rates of any other wells located in the same cell. Vertically, the pumping from each well was divided among the cells or nodes in the aquifer according to the vertical location of the open interval of the well. See Appendix D for more details. For a regional scale model, this methodology is sufficient, but it should be noted that near‐field effects of individual pumping wells are not well‐portrayed in this regional model, since cell and element sizes are as large as 10,000 feet on a side. During of the early stages of calibration, the substantial influence of pumping on the FAS water levels was noted. A substantial portion of the pumping data had been estimated because monthly pumping rates were not available (see Appendix A). For the October 2003 to December 2004 period, there were 5,669 irrigation wells with reported data for all months, 4,206 irrigation wells with reported data in some of the months, and 6,628 wells with no data. A detailed evaluation of the pumping data and its correlation to observed water level and climatologic trends indicated that critical errors were present in this estimated pumping data. The methodology used to estimate missing transient pumping data was reevaluated to better correlate with observed pumping trends and the climatologic patterns that drive irrigation. Additional details on the methodology used to estimate missing transient pumping data are presented in Appendix D. The pumps located in each aquifer are shown in Figures 3.37 to 3.41 and summarized in Table 3.1. 4.0 Calibration/Validation Model calibration is the process of varying model input parameters within a reasonable range until the model output matches observed conditions within some acceptable error criteria. This calibration can be either to steady‐state or transient conditions. Steady‐state model simulations eliminate the time terms in the governing equations (see Equations 2.3 through 2.6) and provide a snap‐shot of the hydraulic conditions in a stable aquifer system. An inherent assumption with this type of simulation is that the system has achieved an equilibrium condition. Steady state results are also commonly used as initial conditions for subsequent transient simulations. For models that are affected by a variety of constantly changing stresses, transient calibration is necessary to ensure that the model is providing a reliable representation of the system. Once a model is considered calibrated, it is then validated against at least one different set of observed conditions using the hydraulic parameters established during calibration. A model is considered validated when the set of model parameters from the calibration process yields a similar satisfactory degree of agreement between field observations and computed model results for the independent validation period(s). If the validation results are not satisfactory, then the model calibration process resumes, continuing until a satisfactory agreement is obtained for the calibration and validation data sets. For the Phase II ASR Regional model, a steady state calibration was first performed to the October 2003 and February 2004 observed water level data sets. Once the steady state model was calibrated, a 22
transient calibration was performed for the 15 month period from October 2003 to December 2004. Finally, a transient validation simulation was performed for a 10‐month transient period from October 1993 to July 1994. Observation wells for calibration were selected from the monitoring well database provided by SAJ. Generally, observation wells were selected when at least 50% of their open section (between the cased and drilled depths) coincided with the model‐simplified geology at that location. Additional wells were removed for a number of reasons: because their data indicated the effects of local pumping; their data was quite sparse; the data indicated a probe error; etc. Some wells located in the Hillsborough River valley north of the Polk County recharge area were removed because there were so many wells in this area that the calibration statistics were being skewed to an area far removed from the proposed CERP ASR sites. Table 4.1 lists all of the wells in the SAJ database and their use in the model (either for boundary conditions or calibration) or the reason for removal from the model. The steady state and transient calibration/validation descriptions below are only for the final calibration of the SEAWAT model. After the draft regional model calibration was completed using both the SEAWAT and WASH123D codes, it was determined that the codes both provided a reasonable calibration of the steady state and transient flow fields. However, it was more difficult to incorporate the widespread heterogeneity of the hydrogeologic model parameters in the WASH123D model due to the zonal method of assigning these parameters in the WASH123D code. Appendix F provides details on the excessive number of WASH123D zones required to provide the necessary heterogeneity in hydrogeologic parameters. In addition, because SEAWAT provides several solver options, it is possible to make many model runs using a less accurate solver (standard finite difference method with upstream weighting) to get close to calibrated results. Once the solution is nearly calibrated, a more accurate but slower running solver (third‐order TVD) can be used to take the last steps to reach the final calibrated solution. The WASH123D code is not equipped with a fast, less accurate solver. The combination of difficulty in assigning widespread heterogeneity and fewer solver options means that the WASH123D model requires more time for calibration. Because programmatic constraints have made it difficult to support the use of more than one code for the future of the project, a decision was made to proceed solely with the SEAWAT model. A comparison of the WASH123D and SEAWAT model results for the draft calibration are included in Appendix F. Although these results are from the draft calibration, the fact that the similarly‐constructed WASH123D and SEAWAT models computed similar results provides reinforcement for the SEAWAT final calibration results. 4.1 Steady State Calibration A steady state calibration was performed for October 2003 and February 2004 by varying the input parameters (principally hydraulic conductivity) until the model output (heads) matched the measured heads at non‐pumping monitoring wells with data for either month. The model for each month was provided with a separate set of specified heads around the edges of the aquifers and at the surface, simulating different hydrologic conditions as reflected in the available data (see Section 3.3). The pumping data was also different for each month and based on the available reported pump rates and estimates as described in Section 3.5. Starting conditions (salinity and temperature), hydraulic conductivity, and all other input parameters were identical for the two steady state calibration models (see Section 3.4). 23
October 2003 was selected for steady state calibration to ensure a good starting condition for the transient calibration. However, analysis of the available head data indicated that water levels declined sharply in many wells during October 2003 as shown in Figure 4.1. This indicates that the aquifers were responding to pumping stresses and that the measured heads in October 2003 do not represent an equilibrium or steady state condition. For this reason, February 2004 was added as an additional steady state calibration period. This month was chosen because many of the monitoring wells have relatively constant heads for a period of a few months ending in February, indicating a more equilibrium condition and less variation in pumping. Calibration to October 2003 continued in order to provide a quality starting condition for the transient calibration, but the measured water levels from the end of October 2003 were used for calibration instead of the average head over the month, since the heads at the end of the month would be expected to be closer to the steady state level caused by the pumping from that month. During February, there was much less pumping and the model calculated heads were compared to the average measured heads for the month. The calibration for both months continued in tandem, with slightly more emphasis placed on the month of February. When head levels at a certain well could not be matched in both months using the same input data set, efforts were made to select parameter values that would calculate the head in one month a little higher than measured and the other a little lower. Table 4.2 lists the wells used for steady state calibration, the observed water levels during the calibration periods, and the modeled water level. The quality of the steady state calibration was evaluated in several different ways, including error statistics, calibration target figures, gradient analysis of well clusters, and comparison to other published information, such as estimates of recharge to the UF and pre‐development heads. The following paragraphs describe each of these evaluations of the steady state calibration. Details pertaining to each model’s calibration will be presented in later sections. A model’s calibration is measured mathematically by the use of error statistics. The three criteria generally used are the mean error (ME), mean absolute error (MAE), and the root mean square (RMS) error, defined by Equation 4.1, 4.2 and 4.3. n
ME 
 (c
i 1
 oi )
i
n
n
MAE 
c
i 1
i
 oi
n
 (c
i 1
Equation 4.2
n
RMS 
Equation 4.1
i
 oi ) 2
Equation 4.3
n
Where: ci = Model calculated head at observation point i oi = Observed head at observation point i n = Number of observation points 24
The mean error (Equation 4.1) is the average of the differences between the observed and calculated heads (or residuals) and can indicate the overall comparison between computed and observed data. Negative and positive residuals can cancel each other out, resulting in a mean error close to zero even when the calibration is not good. The sign of the mean error is an indication of the overall comparison of the model to the data (e.g. a positive mean error indicates the model is generally computing too high). The mean absolute error (Equation 4.2) is the average of the absolute values of the residuals. The absolute value prevents positive and negative residuals from canceling each other, providing a clearer picture of the magnitude of errors across the model, without an indication of the direction (high or low) of the errors. The root mean square (RMS) error (Equation 4.3) is the square root of the average of the squares of the residuals. The RMS adds additional weight to points where the residual is greatest. If the residuals at all points are very similar, the RMS will be close to the mean absolute error. Alternatively, a few points with high errors can add significantly to the RMS for an otherwise well‐calibrated model. For all three of these criteria the optimal value is zero. The spatial variation of the fit between model calculated heads and field measured heads is shown in the calibration target figures which are provided for each of the main aquifers in each model (Figure 4.2 through 4.11, with zooms to specific locations in Figures 4.12 through 4.17). The calibration figures show the head contours (interpolated from the model‐calculated heads at each cell for a specific model layer) and a set of targets placed at the location of each measured head. The targets indicate the calibration quality at that point with its color and the direction of the colored bar. Green bars indicate computed results within 2 feet of the observed head; yellow bars indicate computed results within 4 feet of the observed head. Red bars are for locations where the difference between computed and observed heads is more than 4 feet. The bar in each target is drawn above the center line for points where the computed head is higher than the observed head (positive residual). Conversely, targets below the center line indicate computed heads lower than observed heads (negative residual). The details of the quality of the calibration as shown through these figures will be discussed in Section 4.1.3. The quality of the calibration can be assessed using these figures by noting the color and direction of the target bars. Generally, a well‐calibrated model will show a random field of small errors with no clustering of either positive or negative residuals. Often the reasons for poor calibration at an individual monitoring well can be assessed by noting the location of the point – perhaps it is in an area of steep slopes or close to a large pump. The steady state calibration figures also show a plot of computed vs. observed values with a point plotted for each observation point. In a perfect calibration, all points will lie along the line y=x (shown as a black line). For good calibration, all points should lie close to this line and points should not be clustered in any other part of the plot. The quality of the steady state calibration was also assessed using a gradient analysis of a number of well clusters. This analysis ensures that minor head residuals are not compounded, resulting in 25
unrealistic gradients between aquifers. Figures 4.18 through 4.28 show the model‐calculated head at the center of each cell in a vertical column compared with the heads measured in a number of wells located within this column but screened at different depths. The gradient analysis helps verify that both the direction of flow and the slope of the gradient are accurately reproduced in the model. Finally, the model results were compared to a published estimate of recharge/discharge to the UF (Figure 4.29) and a published estimate of pre‐development heads (Figure 4.30). Although this is not a comparison to actual measured data and therefore, cannot truly be termed calibration, this model’s similarity to other independent, published analyses helps to strengthen its credibility. As stated in Anderson, 1992, “The judgment of when the fit between model and reality is good enough is a subjective one. To date, there is no standard protocol for evaluating the calibration process…” A common rule of thumb is that in a well‐calibrated model, the RMS should be less than 10% of the head difference across the domain. This rule is not especially applicable to the ASR Regional Model, where the head difference across the model domain is over 200 feet. Few would find 20 feet of error acceptable for this model. In reality, the acceptable level of calibration varies across the area and depends on the conditions at each location. In the northern portion of the model, particularly in the Polk County recharge area, the hydraulic gradient is relatively steep. Many of the high residuals at observation wells in this area are due to grid resolution, which is too coarse to accurately portray every nuance of the highly variable hydrogeologic conditions. For example, the pumping wells had to be moved up to 5000 feet to the nearest cell center (see Section 3.5) but the observation points were not moved. Additionally, near well effects are not accurately modeled when the cells are this large. For these reasons, calibration errors up to a few feet might be acceptable in this area. On the other hand, much less head variation is observed in the southern portion of the peninsula. Here, errors caused by grid resolution or the placement of monitoring and pumping wells are less likely to be significant. Thus, acceptable residuals at observation points in this area would be much smaller. Acceptable calibration error also depends on what question the model is answering. This regional model is built specifically to predict the large‐scale effects of the CERP ASR program on the heads and salinities in the groundwater. For this reason, greater residuals are often acceptable for observation wells far from the area of interest or for wells which are directly impacted by local pumping. 4.1.1 Calibration Process Description For reasons described above, the steady state regional ASR model was calibrated to head data collected in both October 2003 and February 2004. The calibration process was a combination of “trial and error” calibration and automated calibration. The “trial and error” calibration involved making small changes to the input files, running SEAWAT and assessing the improvement made. This type of calibration is time consuming, but it also allows the modeler to inject his own knowledge and understanding of the hydrogeologic system into the calibration process. Further, through this tedious process, the modeler 26
develops an important understanding of the hydraulic stresses impacting the model and the sensitivities of both the input parameters and the calibration points. The automated calibration technique employed for this model was an open source code called PEST (Parameter ESTimation), developed by Watermark Numerical Computing. PEST implements a variation of the Gauss‐Marquardt‐Levenberg method of nonlinear parameter estimation and can be strapped around a modeling code so that it calls the code numerous times with slightly different parameter values and analyzes the results (Watermark, 2004). In many cases, PEST can be very efficient, especially when running in parallel. During the course of this project we found it necessary to link up to 30 computers into a “pest nest.” This allowed PEST to run 30 SEAWAT simulations simultaneously, resulting in a significant speed up in the calibration process. A drawback to automated calibration is that PEST only knows as much about the system as the modeler is able to tell it. Not all hydrogeologic knowledge is easily imparted in the PEST input files. Sometimes PEST can move too far from known data in an effort to closely match observed data. During the course of the steady state calibration, it was found that the best calibration method was a combination of “trial and error” calibration with PEST calibration. The calibration results described in this section are the result of thousands of “trial and error” SEAWAT runs and tens of thousands of PEST‐
generated SEAWAT runs. The process also included numerous discussions with scientists from SFWMD to “truth‐check” the calibration parameters against their superior local hydrogeologic knowledge and experience. The main parameters varied for the steady state calibration were horizontal and vertical hydraulic conductivity for layers 2 through 22 (IAS through BZ). Although hydraulic conductivities were assigned to the SAS in the SEAWAT model, no calculations were made in this layer. The assigned hydraulic conductivities had a minor effect on the infiltration of recharge, but the effect was trivial enough that these conductivities were not varied during calibration. The initial conductivity fields for all layers were designed by combining all the available information from the literature along with that provided by SFWMD or available in various online data repositories. The conductivity values were assigned in zones with constant values across each zone. The shapes of the zones were occasionally based on known structural changes, but more often were placed arbitrarily based on the locations of data points. As the calibration proceeded, many of these zones were split into smaller ones and some were combined or reshaped. A reasonable calibration was achieved using this method, although it often resulted in unrealistic sharp corners to head contour lines caused by sudden changes in conductivity between neighboring zones. Eventually, the decision was made to convert the zonal hydraulic conductivity fields to a smooth, interpolated conductivity field. Although the placement of the interpolation points can be as arbitrary as the shape of the conductivity zones, this method allowed for a more credible conductivity field with few sudden changes in flow characteristics. The use of both the “trial and error” and automatic calibration using these interpolated conductivity fields achieved a much better calibration. 27
In PEST, the method for creating the smooth conductivity field is called the “pilot point method.” Each aquifer or confining unit was given a set of “pilot points” placed somewhat randomly, but with a greater density in areas of expected heterogeneity. A hydraulic conductivity value was assigned to each point and a kriging algorithm (distributed with PEST for use with MODFLOW) was applied to assign a unique hydraulic conductivity value to each grid cell. This added an extra step to the calibration process. Each change to the input parameters was made by changing the conductivity of one or more pilot points, and then the kriging was repeated with the new points before SEAWAT was run with the new conductivity surface. When running PEST for automated calibration, an option called “regularization” was employed to reduce the number of degrees of freedom and minimize the heterogeneity of the calibrated conductivity fields. The use of the pilot point method often leads to an under‐constrained problem, where there are more pilot points than there are observation points. This can lead to non‐uniqueness of the calibration solution. In other words, if there are too many pilot points, there will be numerous, possibly quite different, conductivity fields which will yield the same quality of calibration. Some of these sets of conductivity values can be eliminated because of known characteristics of the aquifers, but some cannot be eliminated without additional data. In the regularization method, PEST gives preference to solutions that minimize the variance of conductivity values assigned to neighboring pilot points. Thus, the result of a PEST regularization run is the smoothest set of conductivity fields which will yield a solution that matches the observed data within a user‐defined tolerance. 4.1.2 Calibrated Hydraulic Conductivity Fields Figures 4.31 through 4.40 show the final calibrated maps of hydraulic conductivity for all model layers. Aquifers are shown with horizontal hydraulic conductivities (vertical conductivities were always 1/10 of the horizontal value). Confining units are shown with vertical hydraulic conductivities (horizontal conductivities were always twice the vertical value). The IAS layers are shown in Figures 4.31 through 4.33. In reality, this geologic layer is a complex combination of interbedded confining units and sub‐regional aquifers. Because of the complexity of this system and because the ASR wells are not expected to impact this layer substantially, the IA and ICU were combined into layers 2 through 4 of the SEAWAT grid. The aquifer section was modeled in the northwestern portion of the model domain in layer 3 of the SEAWAT grid. The boundary between the aquifer and aquitard in this model layer is based on a figure in “The Hydrogeology of Florida” (Miller, 1997). All ICU layers have identical vertical hydraulic conductivities in the areas outside of this aquifer zone in both models. (Note that Figure 4.32 shows horizontal hydraulic conductivity, not vertical conductivity, so the colors are slightly different.) Variability was allowed between the ICU conductivities overlying (layer 2) and underlying (layer 4) the aquifer portion of the IAS to provide some variation in the source of pumped water in the IA. It is important to remember that the conductivity distributions for these layers are not expected to replicate reality. The model was not calibrated in the IAS and no attempt has been made to correctly simulate flow in this section. These layers act simply as a conduit for recharge water traveling to the UF and discharge water traveling to the surface. The objective was merely to correctly define these flows. 28
Figures 4.34 and 4.36 show the calibrated horizontal hydraulic conductivity values for the UF and APPZ. Small dots indicating measured conductivity values are overlain on the calibrated conductivity field in both figures for comparison between the model calibration and the field data. There was a significant amount of data available for both these layers; consequently, conductivities were not allowed to vary significantly from what has been measured during the calibration process. The UF (Figure 4.34) shows a zone of somewhat low conductivity along the Kissimmee River, with higher conductivities in the southern portion of the model. It is important to note that the lower conductivities found in the west portion of the model coincide with greater thickness, so the transmissivity does not drop as low as it may seem from this figure. This is also the area where the Hawthorn and Suwannee units are found. This model has combined both of these units into the UF, so the conductivities may vary somewhat from known measurements in either of these units. It is also interesting to note that the Kissimmee River ASR Pilot Project (KASR) is located in a small area of high conductivity. The drop in conductivity towards the east is documented, but the exact location and nature of this anomaly is unknown. The areas of lower conductivity which surround KASR may significantly impact the efficiency of the proposed CERP ASR wells in this area. The conductivities in the APPZ (Figure 4.36) are low along the north‐south ridges west of Kissimmee River and reach higher levels on the east side of the model, including an area of very high conductivity directly beneath the low conductivity area in the UF near KASR. The line between the northern dolomite rock and the southern limestone is one of the few sudden changes in conductivity in this model. The location of the interface between the two rocks is based on USGS Scientific Investigation Report 2007‐5207 (Reese and Richardson, 2008) though its exact location may be unknown. Suggestions were made to try to soften the conversion from dolomite to limestone. Some early sensitivity analyses were run to determine the importance of the placement of that line, but the effects were minor and localized. Since the precise location of this line did not affect the regional calibration, the location of this interface was kept consistent with that depicted in USGS Scientific Investigation Report 2007‐5207 (Reese and Richardson, 2008). Figures 4.38 and 4.40 present the horizontal hydraulic conductivity fields for the LF1 and BZ layers of the model. Very little data was available for either layer. The final calibrated results show generally increasing conductivity to the southeastern portion of the model domain. This distribution is consistent with the current understanding of these deeper aquifers (Reese and Richardson, 2008). As mentioned previously, the northwest section of the BZ has been assigned conductivity values similar to those found in LF1 to account for the absence of the BZ in this area. Finally, Figures 4.35, 4.37, and 4.39 show the vertical hydraulic conductivity values selected for the three confining units in the Floridan system. Although some data was available for these layers, it was used only as a loose constraint on the range of conductivities in each layer. The conductivity values in these layers were valuable tools in the calibration process since the model was highly sensitive to these parameters. 29
4.1.3 Description of the Steady State Calibration Quality Figures 4.2 through 4.11 show the calibration target plots and the error statistics separated by layer and month. The UF steady state head solution and corresponding calibration targets in Figures 4.2 and 4.6 (February 2004 and October 2003, respectively) shows a good calibration. The RMS in both months is less than 2.2 feet with the mean error values very close to zero. The majority of the calibration targets are green, indicating a match within 2 feet of the measured head value. The exceptions are due to steep head gradients, near‐well pumping effects or the inability to calibrate both months simultaneously (likely due to errors in the pumping estimates or lack of a local steady state condition). Some of these exceptions are described below: o
ROMP 33 TMPA/SWNN in Manatee County and ROMP TR 5‐2 SWNN and ROMP 22 SWNN in Sarasota County (See zoom on Figure 4.12): All three points calibrate well in one of the two steady state calibration months, but have a residual error of 2.0 to 2.5 feet in the other month. The inability to better calibrate these points for both October 2003 and February 2004 is likely due to pumping estimates or simplifications in the model in these counties. This error is considered acceptable for an area distant from the proposed ASR wells. o
ROMP 32 SWNN and ROMP 25 SWNN near the boundary between Manatee and Hardee Counties (See zoom on Figure 4.12): The calibrated model calculates 2.5 and 3.2 feet low in October 2003 and about 3.0 and 1.5 feet high in February 2004 for ROMP 32 and ROMP 25, respectively. The inability to calibrate these points for both October 2003 and February 2004 is likely due to pumping estimates or simplifications in the model. In these situations, the aim was to model a state between the two months’ data with a closer emphasis on February data. o
L‐2528 and L‐2435, two wells in the Cape Coral area of Lee County (See zoom on Figure 4.13): These wells are greatly affected by large scale pumping. Because of the resolution of the grid, these near‐field effects are not accurately simulated in the model. Additionally, the actual pumping locations had to be altered to coincide with cell centers, while observation well locations were not moved. Better calibration in this area cannot be expected on a model of this regional scale and is not necessary to evaluate the CERP ASR program. These wells are responsible for much of the RMS error of the UF. When these 2 wells are removed from the calculations, the RMS in February 2004 is 1.13 ft and in October 2003 is 1.26 ft. o
ROMP DV‐1 SWNN, CONE RANCH CM‐10S UPL SUR, and Alston Deep FLDN in the northeast corner of Hillsborough County; and Lake Sawyer Well in the southwest corner of Orange County (see zoom in Figure 4.14): These wells are located in the steep gradient area around the recharge zone. Small changes to the horizontal locations of the substantial number of monitoring wells in these areas would result in improvements in the calibration. Since this area is not near the area of interest for the CERP ASR program, the resolution of the grid is coarse near these calibration points, preventing a better calibration. Further, the flow at these wells is from the recharge area towards the boundary and will not affect the CERP ASR sites, which are the main areas of emphasis for this model. 30
o
PBF‐2 and PBF‐3 in the central coastal area of Palm Beach County (see zoom in Figure 4.15): The calibrated heads for PBF‐2 in October and February are both low by about 3 feet. A much better match is shown at PBF‐3, approximately 3 miles away, where the calibrated heads for both months are only about 1 foot high. The model contours show that the computed heads drop off toward the coast along the length of Palm Beach County. Because the 2 wells are only 2 model cells apart and because the well closer to the coast (PBF‐2) had a higher observed head, it would be very difficult for the model to calibrate both points. The calibration goal was to split the error between PBF‐2 and PBF‐3. Because PBF‐3 is part of a UF, APPZ, LF1 well cluster, this well was favored in the calibration split. The statistics and calibration targets for the APPZ steady state calibration are shown on Figures 4.3 and 4.7 (February 2004 and October 2003, respectively). These plots show slightly less error than the UF with the RMS less than 1.6 in both months. Most of the calibration points in this layer show a close similarity between calculated and measured heads. A few exceptions, described below, skew the statistics, but do not materially affect the usefulness of the model. o
ROMP 86A AVPK located in Pasco County near the northwest boundary of the model (see zoom in Figure 4.16): This well is located at the edge of the recharge zone in an area of very steep gradient. A small change to the horizontal location of this well would result in improvement to the calibration at this point. Since this area is not near the area of interest for the CERP ASR program, the resolution of the grid is coarse near these calibration points, preventing a better calibration. Further, the flow at this well is from the recharge area towards the boundary and will not affect the CERP ASR sites, which are the main areas of emphasis for this model. o
ROMP 30 AVPK and ROMP 25 AVPK in Hardee County and ROMP 28 AVPK in Hillsborough County (see zoom in Figure 4.17): The model calculates the October 2003 head 2.3, 1,4 and 2.2 feet low, respectively and the February 2004 head 1.4, 3.7 and 0.5 feet high, respectively. The inability to calibrate these points for both October 2003 and February 2004 is likely due to pumping estimates or simplifications in the model. In these situations, the aim was to model a state between the two months’ data with a closer emphasis on February 2004 data. o
ROMP 33 AVPK in Manatee County (see zoom in Figure 4.17): This well calibrates high by 2.2 feet in February 2004 and low in October 2003 by about 0.4 feet. Wells in this area are greatly affected by the Manatee County pumping, so the calibration error at this well is probably due to errors in pumping estimates or grid resolution. Figures 4.4 and 4.8 show the head solution and calibration information for the LF1, while Figures 4.5 and 4.9 show the same data for the BZ. The unusual shapes in the head contours are due to the influence of density as caused by salinity and temperature and a great depth. At this depth, there is much less data for comparison, but the figure shows that all data has been matched very closely and the RMS values are impressive at less than 1 foot. Due to the small number of calibration points in the LF1 and BZ, an expanded calibration was performed in these layers. 31
Figures 4.10 and 4.11 show the head solution and a comparison of model results from the LF1 and BZ to data that has been collected for these units during a time period other than the calibration period. Since the water level data used for this expanded calibration was not from the modeled period, these figures use a confidence interval of 5 ft rather than the 2 ft interval used in the other calibration plots (i.e. green bars indicate agreement within 5 feet). The error statistics for this expanded calibration are consistent with that seen in the other layers of the model. Another important aspect of the calibration is the comparison of gradients in the model to those measured in the field. Minor head differences in neighboring wells, if the residuals are of opposite signs, can impact flow rates significantly due to changes in gradient. This series of figures (4.18 through 4.28) presents the vertical gradients computed by the SEAWAT model (February 2004) as compared to gradients measured in the field. Figure 4.18 presents the gradient comparison for the calibration model in February 2004 at the Alligator Alley well cluster in western Broward County. The model and the field data match very closely through the UF wells (G‐2619 and G‐2618) and the APPZ well (G‐2617), showing almost no vertical gradient. Although there is no field data to verify the model‐computed gradient changes in the confining unit, the overall gradient between the APPZ (G‐2617) and the LF1 (G‐2296) is nearly identical in the two plots. Some readers may feel some concern about the shape of the head gradient plot presented at the left of Figure 4.18. Initially, it may seem that the plot indicates upward flow from the UF/APPZ to the surface and downward flow from the APPZ to the BZ. The reason for this seemingly anomalous result is that the heads presented here are observed heads, not equivalent fresh water heads. When the density effect is included by converting the observed head values to equivalent freshwater heads, the resulting gradient plot looks like that shown in the upper right corner of Figure 4.18. The deep layers with high levels of TDS actually exert a greater pressure on the water column resulting in an upward gradient in all layers. The remainder of the gradient plots will be shown with observed head values since this is the data measured in the field. However, the reader should be aware than these heads are not necessarily indicative of water flow direction. (See Section 2.1) The majority of the well clusters shown in Figures 4.18 through 4.28 indicate a close agreement between model‐calculated head gradients and field measured head gradients. All figures show February 2004 calibration results from the SEAWAT model. The following bullets will present a few comments on the plots of well clusters with poorer correlation in vertical gradient. o
ROMP 86A in southwest Pasco County (Figure 4.19): This well is poorly calibrated with a head residual of about 5 feet in both the Suwannee and Avon Park zones. This well is located on the north side of the recharge area and so flow at this location has no effect on the ASR well locations to the south. However, it is encouraging to note that despite the head error (due likely to steep gradients and coarse grid resolution) the model is correctly calculating the gradient between the UF and APPZ layers of the model as shown by a nearly identical slope in the two lines. 32
o
ROMP 13 in the southeast corner of De Soto County (Figure 4.21) and ROMP TR 7‐4 in Manatee County (Figure 4.23): Both the modeled gradient and the measured gradient at these wells are nearly flat between the UF and APPZ zones. The main differences in the plots are in the IAS layers and the SAS. As explained in Section 4.1.2, this model made no attempt to model either the SAS or the IAS section of the subsurface. The SAS was included only to simulate recharge and the IAS layers were intended only as a pass‐through layer to regulate water reaching the UF or exiting at the surface. The small differences in gradient shown at these clusters are not important to the purposes of this ASR Regional Model. o
Intercession City well cluster just west of the Kissimmee River in Osceola County (Figure 4.22): Here the gradient calculated by the model closely matches that measured in the field, with the exception of OSF‐97. In this area, there is a very sudden, stark change in salinity which may not be replicated in the model because of lack of data and coarse vertical grid resolution. Because there is only one layer of cells in the BZ, the location of the salinity change in the model must be linear between the two bottom cells, making it difficult to precisely match the head at OSF‐97. This area is deep and far from the ASR locations, so this minor error is not expected to be of great concern to the purposes of the model. o
Hillsboro ASR well cluster in Palm Beach County (Figure 4.28): The model calculated gradient through the UF and APPZ layers closely matches the field measured data. Although the head variations in the MC2 layer cannot be verified because of a lack of field data, the overall gradient between the APPZ and the LF1 is nearly perfect at this well. 4.1.4 Comparison of Model Results to some Published Information In an effort to further verify the model, the results were compared to the conclusions from two published reports. It is important to note that the conclusions in these reports were based on numerous assumptions, other models and sometimes minimal data. Minute differences between these published conclusions and the ASR regional model are not of concern. The purpose in this comparison was simply to show general agreement with other published work and analysis. First, the model calculated recharge and discharge to the Upper Floridan layers was compared to the generalized recharge map published in USGS Water‐Resources Investigations Report 88‐4057 (Aucott, 1988). The recharge map presented in this USGS publication included data collection, analysis and some modeling. Figure 4.29 shows the comparison between the regional ASR model results and the USGS estimated recharge/discharge areas. Although there are minor differences, it is encouraging to note that the coastal areas and the southern half of the model domain are generally shown to be discharge areas by both analyses. Interestingly, the location of the model‐calculated change from discharge to recharge north of Lake Okeechobee is very close to the estimated interface shown in the USGS figure. The northwest boundary area of the ASR regional model shows small areas of large discharge, interspersed with small areas of large recharge. These areas are likely caused by large changes in topography and coarse grid resolution in the ASR Regional Model. The fact that these areas of discharge are not shown in the USGS map is not cause for concern, especially since this area is separated from the ASR locations by the main recharge area. 33
The second comparison was made by rerunning the calibrated February 2004 SEAWAT model with all pumping removed (See Figure 4.30). The result of this “no‐pumping” simulation was compared to the USGS (Bush and Johnston, 1988) published pre‐development head contours for the UF. Because of the specified head boundary conditions along the south, west and north boundaries of the calibration model, it is impossible to completely remove pumping from the model. Drawdown caused by pumping would necessarily impact the measured heads in wells near the boundary, which were used to set the specified heads. However, despite this drawback, the correlation between the USGS estimated pre‐
development heads and the ASR no pumping heads is reasonable. The maximum head at the top of the recharge zone is nearly perfect, though the location is slightly different. The southern extent of the computed 70‐foot contour is in good agreement with the USGS contour although along the eastern and western sides of the recharge area, the model underpredicts the USGS 70‐foot contour by 5 to 10 feet. This discrepancy is the result of the discharge of the UF to low‐lying river valleys where the surface heads are low. Another feature of the predevelopment heads captured in the model is that the 50‐foot contour curves out along the eastern shore in Saint Lucie and Martin Counties more than the Bush and Johnston contour. Differences in the 40‐ and 50‐foot contours along the west coast are mostly due to the implicit inclusion of pumping effects in the data used to determine the specified heads at the western boundary. The most notable difference between the USGS predevelopment head contours and the computed head contours is the discontinuity of the computed 60‐foot contour between the area of recharge from the surface and the southern 60‐foot high southwest of Lake Okeechobee. Computed heads in this “trough area”, in the vicinity of Lake Okeechobee and west along the Caloosahatchee River, are between 55 feet and 60 feet. While the difference is within the range of other differences observed between the predevelopment heads and computed heads, the trough indicates that Upper Floridan water south of Lake Okeechobee originates from a location other than the recharge area north of Lake Okeechobee. Bush and Johnston (1988) argued against this hypothesis. No data from the predevelopment time period exists to clarify whether the head trough existed. Head data from 2003‐2004 at LaBelle and Kissimmee River Pilot site is less than 53 feet indicating a shallow trough similar to that shown in the model results exists under current “with‐pumping” conditions. Geochemical data from a recently published study (Morrissey, S. K., et al, 2010) provides evidence that water found in the Upper Floridan aquifer in south Florida “is consistent with recharge from meteoric water during the last glacial period” rather than recent recharge from areas north of Lake Okeechobee. Considering this new evidence, it is entirely possible that a head trough such as that shown in the predevelopment model head results through the Caloosahatchee River/Lake Okeechobee area was present prior to development. Although the match between the ASR regional model and these published conclusions cannot be considered to carry the same weight as comparisons to actual measured data, the close agreement helps to validate the model and shows concurrence with the conclusions being drawn by other scientists in South Florida. 34
4.2 Transient Calibration/Validation In order to model the successive recharge, storage and recovery periods for the ASR wells, it was necessary that the ASR regional model be transient (i.e. include the time term in Equations 2.3 through 2.6). The addition of the time term necessitates a substantial increase in the number of parameters which can be varied during calibration. The hydraulic conductivity values had been tentatively set during the steady state calibration, though some iteration between the steady state and transient models occurred. Most of the transport parameters (porosity, dispersivity, and molecular diffusion coefficient) proved to be relatively insensitive on a regional scale due to the minimal TDS and temperature transport occurring on the small time scale of the model calibration and validation periods (15 months or less). Specific storage was found to be the most sensitive parameter during the transient calibration. The convergence of the transient model was good in all timesteps for both flow and transport. Table 4.3 shows the mass balance and percent discrepancy for the flow portion of the model. The maximum percent discrepancy between flows in and out of the model is 0.0539%. Table 4.4 shows the percent discrepancy in the transport of the two modeled constituents: TDS and temperature (heat). All discrepancies are on the order of 10‐8% and 10‐6% for constituent transport. The transient SEAWAT calibration proceeded in a manner similar to the steady state SEAWAT calibration. Initial specific storage values were assigned to polygonal zones and based on the available data. The storage data provided was divided by the aquifer thickness to derive the specific storage term used in the model. Storage data was much sparser than conductivity data. Calibration proceeded as a combination of “trial and error” calibration and automated calibration. PEST was again used as the code for automated calibration. Eventually, when significant progress had been made using the zonal specific storage fields, the pilot point method was again implemented to create smoothed fields of specific storage. Figures 4.41 through 4.94 show the SEAWAT calibration at a number of observation wells which had significant data available. In each case, the observed and calculated heads are plotted during the 15 month calibration period (October 2003 through December 2004). Note that because of differing ranges of heads measured and calculated at each well, each plot has a different head scale on the y‐axis. In order to facilitate the analysis of these plots, every graph has a horizontal grid line at every foot of head. In this way, the reader can tell, at a glance, whether the well has a large swing in heads (many grid lines) or has very little head variation (few grid lines). 4.2.1 Calibration Statistics In addition to the visual inspection of the calibration at each observation point, a number of statistics were calculated at each point to aid in the calibration process. Each statistic compared the mean monthly heads in the observation dataset with the mean monthly heads from the model output. The first statistics were the mean residual error (ME), mean absolute error (MAE) and the RMS error. These equations were provided in Section 4 with the discussion of the steady state calibration (see Equations 4.1, 4.2 and 4.3). Additional statistics included the Coefficient of Determination (r2) and the Nash‐
35
Sutcliffe Model Efficiency Coefficient (E) as shown in Equations 4.4 and 4.5. The statistics for each point are listed in tables on Figures 4.41 through 4.94 and all are shown together on Figures 4.95 through 4.99. 2

 n
  ci  c oi  o 
 r 2  n i 1
n
2
2
 c i c   oi  o 
i 1
where r2 = ci = c = oi = o = Equation 4.4
i 1
Coefficient of Determination Average model calculated head during month i Average calculated monthly head over all months Average observed head during month i Average observed monthly head over all months  o  c 
E  1
 o  o 
2
i
i
2
Equation 4.5
i
where E = Nash‐Sutcliffe Model Efficiency Coefficient (Nash and Sutcliffe, 1970) None of these statistics alone can perfectly describe the calibration quality at every point. Each provides some information, but they all must be used together, coupled with a visual inspection of the model results. The mean error (Equation 4.1) shows the average residual between model calculations and observed data. Its optimum value is zero. The drawback to the use of this statistic is that positive and negative errors can cancel each other out, resulting in an unnaturally low mean error. An example of this effect is shown in the plot for Sarasota Well 9 (Figure 4.58). Here, the positive residual during the summer of 2004 cancels out the negative residual during the fall of 2004, resulting in a mean error of only 0.346. This low mean error overstates the calibration quality at this point. This canceling effect can be best captured with a comparison between the mean error and the mean absolute error (Equation 4.2). In the calculation of the mean absolute error, the absolute value of the residual is taken before it is averaged. Again, the optimum value is zero. When the mean absolute error is very close to the mean error or when it is a similar value with the opposite sign, the cancelation effect is small. See OS0231 (Figure 4.52) where the mean error is ‐1.319 and the absolute error is 1.319 showing that there has been no cancelation of positive and negative residuals – all residuals in this case are negative. For Sarasota Well 9 (Figure 4.58), the mean absolute error is 1.991, much higher than the mean error, indicating significant cancelation of positive residuals with negative residuals. The root mean square error (RMS) gives additional weight to large residuals and minimizes the impact of residuals less than 1.0 (Equation 4.3). Its optimum value is also zero. This result can help indicate the 36
variations in the residuals when it is compared to the mean absolute error. See, for example, PBF‐2 (Figure 4.72). Here, the mean absolute residual is 2.997, while the RMS is only slightly higher at 3.036. The similarity of these two numbers indicates that every residual value was very close to ‐3 feet. Conversely, at ROMP 33 TMPA/SWNN (Figure 4.57), the mean absolute error is 3.691 while the RMS is larger, at 4.647. The difference in these two values is caused by a few months where the residual is large (November 2003, April 2004 and December 2004). The mean error, mean absolute error and RMS do not take into account the ranges of observed heads at each well. All observation wells are held to the same standard whether they have wide swings in head values, or stay at a relatively constant head level. To account for this, the figures report each RMS value as a percentage of the range of observed heads at the well. Compare, for example, the Edgeville Deep Well 3 (Figure 4.60), with an RMS value of about 2.5, to BF‐4S (Figure 4.74), which has an RMS value of about 1.5. A visual inspection of the two plots shows that, despite its higher RMS value, the Edgeville well calibration is much better than that at BF‐4S. The variability at the Edgeville well is much larger – over 25 feet, compared to a range of only about 4 feet at BF‐4S. The closer calibration at Edgeville is quantified by comparing the RMS values as percentages of the observed range – about 10% at Edgeville and 34% at BF‐4S. Some modelers advocate a rule of thumb, requiring that the RMS of a calibrated model be less than 10% of the range of observations. The optimum value is, of course, zero. The coefficient of determination (r2) is a measure of the correlation of the observed vs. computed head values to a straight line (Equation 4.4). Its optimum value is 1.0. The importance of this statistic can be understood if one imagines a plot with the calculated heads on the y‐axis and the observed heads on the x‐axis. The model results and the observed dataset are used to place a point for each month in the calibration period. In a perfectly calibrated model, the computed head would equal the observed head, and all points would fall along the line y=x and the r2 value would be 1.0. However, the r2 value will also be 1.0 if the points fall along any straight line with any offset from the x axis or any slope. See, for example, TFRO‐5 (Figure 4.84). The r2 value at this well is 0.916, which is quite high compared to many of the other points. Although this point is fairly well calibrated, the model calculated head consistently falls about 1.8 feet higher than the observed head. The high r2 value is an indication that the observed vs. computed heads would fall along a line with the equation y = x + 1.8. Some of the other statistics, such as the mean error and mean absolute error, alert us to the fact that the model is calculating slightly high. In this case, the high r2 value when combined with an equivalent mean error and mean absolute error indicate that although the initial condition (based on a steady state run) is not perfectly calibrated, the heads at this well correctly respond to model stresses. The rise in head caused by the fall wet season closely matches that seen in the observed data. ROMP 30 AVPK (Figure 4.80) is another example of a well where the high r2 value (0.925) is deceiving. Here, the model is over‐estimating the heads during the summer dry period and underestimating the heads during the fall of 2004 when the observed heads rise. The line that these points fall along is y=mx + b where m is less than 1.0 and b is greater than zero. Despite these points, this well is not a particularly poorly calibrated point. The RMS is only 12% of the observed range of heads, but the quality of calibration is not as high as that indicated by the coefficient of determination. 37
The final statistic presented is the Nash‐Sutcliffe Model Efficiency Coefficient (Equation 4.5). This equation was developed for quantifying the efficiency of a model for forecasting river flow and is seldom used for groundwater modeling studies. It is included at the request of IMC reviewers. When the Nash‐
Sutcliffe value is greater than zero, the model output is better than the observed data as a predictor of future conditions. When it is less than zero, the model is inefficient, i.e. the variation between calculated and observed values is greater than the variance in the observed data. The optimum value is 1.0. The comparison to the observed data variance takes into account the different head ranges at each well. In other words, points with smaller variations are held to higher standards than those with large variations. When taken together, these statistics can help to quantify the calibration quality at any of the points. For example, OS0230 (Figure 4.52) has possibly the closest agreement between the observed and model calculated data. All of the statistical measures of the calibration at this point are very close to optimum values. Conversely, the worst calibration probably occurs at ROMP 17 SWNN (Figure 4.61) where all the statistical measures are far from optimum. 4.2.2 Transient Calibration Analysis ­ Heads Because of the time discretization (constant boundary conditions and pumping for each month) it is impossible for the model to correctly calculate the head every single day. The goal of the calibration effort was to match gross seasonal variations in head, including the average head during the driest period (usually during the month of June 2004) and the average head during the wettest period (usually late fall 2004). Because the model can only attempt a calculation of the average monthly heads, it is not surprising that the model will seldom match the lowest measured head (usually during the first few days of June 2004). Further, the time discretization often results in the lowest model‐calculated head occurring several weeks after the lowest measured head. During June 2004, the head changes on nearly all observation wells indicate that significant pumping occurred during the first few days of the month and then abruptly stopped, causing a steep rise in water levels. Because of the ASR regional model’s time discretization, this high pumping is averaged over the entire month, resulting in the lowest heads being calculated at the end of the month. See for example, the results at ROMP 9 SWNN in Sarasota County (Figure 4.62). The continued pumping during the month of June causes the model to calculate a lower head for the whole month of June, but the measured data shows a sudden, steep increase in head beginning in the first week of June. It is significant that the pumping across the region exerts a much greater effect on the transient head data than the specific storage values. Section 3.5 and Appendix D detail some of the difficulties in collecting and using the pumping data. A huge percentage of the pumping data had to be estimated based on well type and seasonal averages. These estimates of pumping caused additional problems during calibration. These are made clear by comparing the results at Edgeville Deep Well 3 in Manatee County (Figure 4.60) and BF‐6 in Broward County (Figure 4.73). At Edgeville, the calibration is good until the last month of the model (December 38
2004). During December, the model results indicate a significant reduction in pumping which is not replicated in the measured data at this well. This implies that the pumping in the model in this area is incorrect – likely due to the failure of the assumptions made during the pumping estimated (described in Appendix D). There are a number of observation wells that show similar problems in the calibration during the month of December 2004. Conversely, at BF‐6, there is clearly a reduction in pumping during the months of November 2003 and January 2004, with a return to normal, seasonal pumping rates during December 2003 and after January 2004. In this case, the pumping data used in the model appear to closely match reality, as shown by the close similarity of the heads at this well. Pumping estimation errors can also be the cause of the failure of the model to reproduce the low heads in the summer of 2004 or the high heads in the fall of 2004. As will be explained later in Section 6, the pumping data quality represents the single largest source of error to this model. The estimates made to fill in missing data are only sufficient to provide enough accuracy for gross, regional‐scale estimates of the effects of the CERP ASR program. Because of pumping errors, the regional model cannot be used for near‐scale problems or to answer questions requiring high accuracy. The greatest effort during calibration was exerted to improve the agreement of the model to the observed heads near Lake Okeechobee and the other proposed ASR sites. For this reason, calibration near the north boundary is often poor. Especially near the Hillsborough River Valley, there are numerous wells and some are clearly reacting to stresses not included in the model. Many of the wells are located very close to the boundary, which was given a specified head boundary condition based on an average of the measured heads in nearby wells. Many wells near the model boundary can be recognized from their stair‐step model results. See, for example, the Green Swamp Marsh well and the Eva Well Deep (Figure 4.45). Because these wells are so close to the boundary, they feel the effects of head changes immediately, and the computed head is nearly constant during each stress period. No changes to conductivity or storage would improve the calibration at the Eva Well. Only a change to the boundary condition could change this. However, the Eva well was determined to be too far from the boundary for use in the selection of boundary condition heads (See Appendix C). Some wells (especially in the northwest) are very closely controlled by the specified heads in the SAS. See for example, the Alston Deep Well (Figure 4.46). Perhaps some improvement in the calibration at this point could be brought by reducing the hydraulic conductivity in the ICU layers, to reduce the impact of the SAS on the UF calibration point. However, this point is north of the Polk County recharge area and so the heads here will have little impact on the proposed CERP ASR sites. The calibration in the northeast quadrant of the model (north of Lake Okeechobee and east of the Kissimmee River) is generally quite good. Most of the observation wells show a steep drop in head between February and May 2004, with a matching steep rise in head from June to October 2004. The model easily reproduces this effect. There are a few points with some possible data errors, which impact the statistics. For example, the observed data at SLF‐74 (Figure 4.84) shows a sudden drop of about 1 foot during December 2003. The model more closely matches the data after this apparent 39
probe movement. The model is not able to perfectly reproduce the head rise during the late summer of 2004, but it does correctly time all major slope changes. SLF‐76 (Figure 4.84) is at the same location in the APPZ and similarly does not perfectly match the rising head slope. This could be the result of slight errors in the regional pumping. A similar probe error seems to have occurred at TCRK_GW2 (Figure 4.83) in June 2004. The model closely matches the observed heads before this time and follows the expected trend after this error. The statistics, which cannot account for the probe movement, are slightly worse than they would be if the error had not occurred. The east coast calibration is fairly good between St. Lucie and Biscayne Bay. Generally, the steady state result used as the starting condition is within 1 or 2 feet of the observed value. However, because the variability in observed heads over the 15‐month calibration period is so low, some of the statistics (notably the RMS as a percentage of observed range and the Nash‐Sutcliffe value) are lower than could be hoped. Generally, the model is able to reproduce the effects of simulated stresses, despite the small errors in starting condition. For example, see PBF‐2 and PBF‐3 (Figure 4.72). PBF‐2 is located closer to the coast, but its head is generally measured about 2 feet higher than PBF‐3. This is caused by an unknown anomaly which is not included in the model. Therefore, the model computation sets the starting condition at PBF‐2 about 2.5 feet too low while that at PBF‐3 is about 1 foot too high. Because heads tend to drop close to the coastline towards the ocean outcrops, no acceptable changes to hydraulic conductivity can improve the steady state calibrations of these points. Since the error in starting condition is large compared to the range of measured heads, the statistics are far from optimum values. The Nash‐Sutcliffe values are greatly negative in each case and the RMS values are large compared to the observed range of heads. The r2 values are reasonable, which is an indication that the model is correctly reproducing the effects of seasonal stresses at these wells. The shape of both calibration plots is similar to that shown in the observed dataset, but the heads are shifted up or down. This calibration is as good as can be expected without a more detailed, more highly refined model. Without a better understanding of the local effects resulting in the reversal of heads in this area, no model can hope to reproduce these observations. BF‐4S (Figure 4.74) is an example of a problem with the pumping database. The model easily reproduces the sudden reduction in pumping which occurred in late January 2004, but does not hold the high heads long enough, nor does it reproduce the sudden resumption of pumping in June 2004. The model also shows the effects of a short stoppage in the pumping in October 2004 which is not shown in the observed water level dataset. The problems in collecting the pumping data and implementing it in the model are described in detail in Section 3.5 and Appendix D. This well shows an area where the assumptions used in that process did not hold true. No changes to either hydraulic conductivity or specific storage could improve the calibration at this point. Only better pumping data could improve the calibration in this area. The calibration in the southern portion of the model (south of Lake Okeechobee and inland of the eastern coast) is generally quite good. At most points, the model calculated heads are within 1 or 2 feet of the observed heads and gross trends are correctly reproduced. As observed near the east coast, 40
some of these wells also suffer from poor statistics because of the small head variations seen in the observed datasets. While the mean error, RMS and r2 values are generally quite good, the RMS as a percentage of the observed range and the Nash‐Sutcliffe values are both poor. This is not especially worrisome since the model reproduces the trends seen in the observed datasets and the actual differences between observed and calculated heads are small. The section of the model just south of Tampa Bay (Manatee and Sarasota Counties) is generally well calibrated. The statistics in this area are all near optimum values and the visual comparison between calculated and observed heads shows a close similarity. The largest head swings in the model occur in this area, resulting in an advantage in the statistics. The area which caused the greatest problems during the transient calibration is the area surrounding Port Charlotte (DeSoto, Charlotte and Lee Counties). The statistics in these areas are generally poor and visual inspection of the results indicates that the heads at several wells are not acceptably reproduced by the model. During trial and error calibration, substantial heterogeneity was added to the storage in this area. Wells located near each other were found to have quite different storage requirements. It is believed that the calibration issues in this area are the result of a number of complications. Head variations in the IAS in this area exert a marked effect on the lower layers. There is a great deal of pumping in this area, including the Peace River ASR. The model has also been simplified in this area by combining the Suwannee and Hawthorn aquifers into the UF and by simplifying the IAS and ICU layers. Because this area is away from the proposed CERP ASR sites, the cell sizes are large. The main conclusion after extensive calibration efforts focused on this area was that this model is too coarse and over‐simplified in this region to accurately reproduce the measured heads in all of the observation wells. This is not unexpected in a regional model of this scale and is not worrisome since most of the ASR locations are away from this area. The closest CERP ASR site to this area is located at Riverbend on the Caloosahatchee River, which is about 10 miles east of the problem area. LAB‐MZ1 (located close to the Riverbend site; Figure 4.66) calibrates quite well. The greatest effort in calibration was applied in the areas around Lake Okeechobee where most of the CERP ASR wells are proposed. Calibration at these points is generally good. See Figures 4.68, 4.70, and 4.71 for a visual analysis of the calibration in the UF. Statistics at these wells (L2‐PW2, MF‐37, PBF‐7U, and OKF‐100) are also quite good, with Nash‐Sutcliffe values all above zero, r2 values above 0.5, and RMS values less than 25% of the observed head ranges. The calibration near the Hillsboro Pilot Site (and proposed site for 30 CERP ASR wells) is not as good as that around the Lake Okeechobee sites. See the calibration plot for PBF‐10R in Figure 4.73. Although the steady state calibration resulted in a starting condition about 1 foot higher than the observed October 2003 head, the transient model reproduced relative head changes quite well until September 2004. During the last few months of the model, the head in this area seems to be heavily impacted by the cessation of pumping nearby. But this impact is not felt in the observed dataset. This is probably the result of an error in the pumping dataset or in the assumptions used to estimate missing data. These few months of poor calibration, in conjunction with the small range of heads measured at this well (just over 2 feet of variation), result in the poorer calibration statistics at this point. 41
4.2.3 Transient Calibration Analysis – Vertical Gradients Figures 4.100 through 4.110 show the vertical gradient plots (similar to those in Figure 4.18 through 4.28 for the steady state calibration). In these plots, the model results are compared to measured data at the end of May 2004 and October 2004. May and June 2004 generally represent the lowest heads of the period, while the highest heads of the period are often measured in October 2004. Generally the gradients do not change significantly during the year. The model tends to do a better job of predicting fall 2004 gradients and heads than it does for summer 2004. As explained above, this is generally due to coarse time and grid discretization and the likelihood of errors in the pumping data, especially where it was estimated. 4.2.4 Transient Calibration Analysis – Conclusion In general, the model is a good representation of groundwater conditions on a regional scale. Although some measured data in a few areas could not be reproduced by the model, the areas nearest the proposed ASR sites have good calibrations. This meets the goal of the regional modeling effort, since it was never the intent to reproduce local anomalies or near field effects of pumping wells with this scale of model. The specific storage terms used in the calibrated transient model are presented in Figures 4.111 through 4.118. Conductivity values were the same as those used for the steady state model (See Section 4.1). Table 4.5 presents the other transport parameters used in the transient model. These parameters were selected to be similar to generally accepted values. Their sensitivity will be discussed in Section 5.2 and 5.3. In addition to the 2003/2004 calibration period, the final set of hydraulic conductivity and specific storage values were applied to the validation period from October 1993 to July 1994. These results are presented in Figures 4.119 through 4.150. Like the calibration model, the first timestep of the validation model (October 1993) was run in steady state mode to develop a starting condition for the model. There is less agreement between the field data and the model results in October 1993 than in October 2003 (start of the transient calibration model period). This causes an initial offset in the transient validation result plots. Some of the problem wells had no available data in the 2003/2004 calibration period, so they were not included in the steady state calibration process. Others are probably the result of errors in the assumptions made during the estimation of missing pumping data or in the estimation of missing head data for the boundary conditions. Still, despite these starting condition errors, the model was able to reproduce the general shape of the head plots in the majority of the observation wells. ROMP 58 NRSD in Polk County (Figure 4.140) was measured with a nearly constant head around 120 feet for the last 8 months of the validation period. However, the model produced a widely varying head signature with the highest heads about 110 feet in the winter and fall seasons, and the lowest heads, about 100 feet, in the late spring. It is believed that the data for this well is faulty or a pump that was not operational during the validation period was wrongly incorporated into the model, resulting in modeled heads that are lower and have more variation than the observed data. 42
As with the calibration period, the statistics for the transient validation run are shown spatially on Figures 4.151 through 4.155. The validation exercise indicates that this regional model can be used for answering broad, regional questions whenever the pumping and boundary heads are known to a reasonable degree. Use of this model to reproduce D13R periods or to predict future aquifer changes must be made only with the understanding that the results are only as good as the estimates for pumping and boundary conditions. 4.3 Model Analysis An analysis of the model calculations of velocity, flow directions and boundary flux can be instructive. Figures 4.156 through 4.159 show the model results when converted to equivalent freshwater head using Equations 2.1 and 2.2. Unlike the observed type heads output from the model, equivalent freshwater heads (which include density effects) are a measure of potential energy, and groundwater flows perpendicular to these contours from areas of high to low head. Because of the shallow depths and low salinity levels, the UF equivalent freshwater heads are not significantly different from the model output observed heads (see Figure 4.156), with the exception of the Atlantic Ocean outcrop location (where salinities are high). Generally, recharge occurs in Polk County and water flows towards the ocean to the east, south and west. Significant pumping is clear at several points along the west coast, especially in the Pasco County Area and in Lee County. Both figures show an area of high heads southwest of Lake Okeechobee. Differences between observed head and equivalent freshwater head are also minor in most areas of the APPZ (Figure 4.157). Most differences are at the coastline where salinities are higher. As with the UF, the main source of water is the recharge in Polk County. The bubble of high head in Hendry County is also visible More significant disparity is observed when the model output is compared to equivalent freshwater heads in the LF1 layer (Figure 4.158). Here, the high salinity has caused a significant depression in measured heads in many areas of the model. Flow is still infiltrating from the surface in Polk County and significant flows still move east and west towards boundary sinks in Hillsborough and Brevard Counties. Additional flow seems to be moving northward from the Everglades area. Much of this flow moves upward into more shallow layers (APPZ, UF) in the center of the peninsula (Charlotte, Glades, and Palm Beach County) instead of continuing northward in the LF1 layer. Because of its high salinity, great depth and large temperature variation, the calculation of equivalent freshwater head has the greatest impact on the BZ layer (Figure 4.159). Density effects cause huge changes in head values. The recharge from the surface in Polk County is still visible. But a large contingent of the flow comes in from the east and south coast, moving north and northwest to exit in Hillsborough or Orange Counties. The BZ provides a significant amount of pressure on the upper layers and is an important component of the groundwater system in south Florida. Flow vectors are shown for a number of cross‐sections of the model in Figures 4.160 and 4.161. Vectors in these plots are printed for every eighth cell, so closely spaced vectors occur where cell sizes are small 43
to provide additional resolution and accuracy (see Section 2.3). These figures make several important points clear: 
Flow is mostly horizontal in the aquifers and vertical in the confining units 
Recharge in Polk County causes downward flow all the way to the BZ. 
Inward flow in the BZ along the lower east coast is a significant source of water pressure throughout the model. 
Most flow is upward in the southern half of the model (south of Lake Okeechobee) Figure 4.162 shows the discharge and recharge to the top of the IAS, UF, APPZ and LF1 layers. In this figure, recharge (green, yellow and red colors) indicate downward flow while discharge (blue colors) indicates upward flow. As expected the southern and eastern parts of the model show upward flow in every layer. The Polk County recharge area is clearly depicted with downward flow in every layer. As explained previously, the mottled red and blue sections at the northwest boundary of the model are caused by significant variability in the topography and the specified surface heads, combined with a course grid resolution. Finally, Figure 4.163 tabulates the flow in and out of the boundaries of the model in each aquifer layer. Of note are the large flow into the model through the BZ Atlantic boundary and the larger flow out of the model through the UF Northern Boundary. Initially it appears that the majority (78%) of the BZ Atlantic inflow (589 mgd) is being lost through the western boundary (460 mgd). However, the BZ is also home to a number of large injection wells, which add a significant amount of flow to the model. Major injectors include 17 Miami‐Dade South wells, 4 of the 5 G.T. Lohmeyer wells, 6 Broward County wells and 3 City of Sunrise wells. Together, these wells inject nearly 200 mgd during February 2004. Most of this flow exits through the western boundary in the BZ, accounting for over 40% of the outward flow through the western boundary. When taken together these visualizations of the model results indicate that the major sources of flow to the model are the Boulder Zone along the southern and eastern boundaries of the model and the precipitation recharge in the highlands of Polk County. BZ flow continues north and west, eventually moving upward to meet other layers of the model. The effects of recharge in Polk County reach as deep as the BZ and result in radial flow vectors out to the south, east and west from the recharge area. An area of high freshwater head is also found southwest of Lake Okeechobee from which flow vectors move radially outward (See Section 4.1.4 for additional details). 5.0 Sensitivity Simulations In order to evaluate the effect of various assumptions made in the modeling process, several sensitivity analyses were performed. The following subsections describe these analyses and the uncertainty inherent in the model. 44
5.1 Advection Solution SEAWAT provides several solver options for the advection solution. The majority of the model runs made during calibration used the standard finite difference method with upstream weighting. The timesteps were set to about 5 days. (See Section 2.4) Using these settings, a steady state solution could be computed in less than 3 minutes and a transient solution in less than 1.5 hours, for most available computers. This method is known to be less accurate than the third‐order TVD scheme, but it is also much faster. In order to ensure that the accuracy loss due to time constraints was not excessive, a sensitivity run was made for the transient calibrated model using the TVD scheme. Since the first timestep of the transient model computes a steady state solution, both model types were tested together in this way. When this solution method is used, the model selects the timestep size based on the user defined Courant number. The transient model was run with Courant number set to 1.0 and 0.5. With these settings, the transient models took between 12 and 15 hours to run to solution. The transient TVD model results are compared to the transient FDM results at the timestep with the maximum differences in Figure 5.1. This timestep corresponds to December 10, 2004 which is Day 407 of the total of 428 days modeled. The head difference between the TVD and FDM solutions was over one foot at only a few isolated cells. None of the calibration points show changes significant enough to have affected the calibration. The maximum head change at any observation point during the first (steady state) timestep was less than 0.5 feet, with the average difference less than 0.2 feet. For the transient solutions at each timestep, the maximum head difference was 2.7 feet, but the average was less than 0.1 foot. Most of the differences are found during precipitous changes in head. At these times, the TVD solution has a slightly greater change (perhaps 0.5 feet) immediately after the change begins, but within 2 or 3 timesteps, it again matches the FDM solution. Only nine observation wells were impacted by more than 1.0 foot when the solution method was changed. All nine are located in Hillsborough, Manatee, De Soto or Sarasota County and have head variations of 20 to 45 feet over the calibration period, indicating significant impacts from pumping. Similarly, the head differences shown in Figure 5.1 across the model domain are most significant in this area. Salinity and temperature results when the TVD advection scheme is activated are also nearly identical to the calibration run salinity and temperature results. A few, isolated cells where the initial salinity gradient between neighboring cells is large (especially near the ocean outcrop) were affected with differences up to about 1,050 mg/L TDS for the final timestep. The temperature differences in the Floridan aquifer at the final timestep vary from ‐1.3˚C to 0.6˚C in isolated cells near the model boundaries. That the selection of a solver had little effect on the model results or the calibration supports the early decision to calibrate with the FDM solver, despite concerns about the accuracy of the results. The biggest impact occurred where pumping and head variations were largest. Because the ASR program will involve significant pumping and large head changes, final production runs of the CERP ASR program should be calculated using the TVD solver. However, because the differences are minor, intermediate runs will continue to be made using the FDM solver in order to take advantage of the significant time savings. The opportunity to achieve these time savings using the SEAWAT FDM solver is part of the 45
reason that the WASH123D model will not be used in the future phases of this project. WASH123D does not provide a faster solver alternative. 5.2 Porosity Transport properties such as porosity were largely ignored during calibration. Because the model does not have a traditional “plume,” with a sharp front, whose movement through the model domain is being estimated, porosity was not expected to be a significant factor in the model results. In the calibrated model, aquifers were given a porosity of 0.25, the IAS, a value of 0.4 and all other confining units, a value of 0.3. Three additional sensitivity runs were made to ensure that the results were not sensitive to porosity. The porosity values used are shown in Table 5.1. These porosity changes made no discernible difference to any of the heads at the calibration points. Across the grid, the head differences were minor. When compared to the calibration run, the greatest difference in head occurred in the Boulder Zone in Porosity Sensitivity Run 1 during the last time step of the model. During this time step, there were 39 cells with a difference in head ranging from 1 foot to 14.5 feet. The areas that showed the greatest difference were isolated and coincident with the locations of deep injection wells along the coast in Indian River, Palm Beach, Broward, and Miami‐Dade Counties. Porosity Sensitivity Run 3 resulted in smaller head differences when compared to the calibration run, with 25 cells having a difference between 1 foot and 6 feet in the Boulder Zone during the last time step. The differences were observed in the same locations as the differences in Run 1. Porosity Sensitivity Run 2 showed no differences in head greater than 1 foot when compared to the calibration run. Over the majority of the model domain, the difference was less than 0.1 feet for all the sensitivity runs. Regionally, the differences were small enough to eliminate the need for a figure. Variations in porosity also caused only minor differences in calculated salinity and temperature. The greatest difference occurred in the Boulder Zone during the final time step of Sensitivity Run 1. A few isolated areas of the Boulder Zone in Broward County had differences of up to 5,500 mg/L TDS and 2˚C in this time step, but most differences were less than 10 mg/L TDS and 0.1˚C across the rest of the model. These runs indicate that the sensitivity of the regional model is within the acceptable error of the calibration. The difference caused by changes to input porosity is negligible. It is anticipated that porosity will have a more marked effect on the local scale models which simulate the ASR pumping schedules in more detail. 5.3 Dispersion/Diffusion Like porosity, dispersion and diffusion were expected to have minimal effects on the flow of temperature or salinity in the groundwater because the concentration and temperature gradients are usually not very sharp. During calibration, the longitudinal dispersivity was set at 2.5 feet with the ratios for horizontal to transverse and vertical to transverse dispersivity set to 1 (meaning dispersivity in every direction was 2.5 feet). In order to verify that this parameter is unimportant to the regional model, four additional model runs were made with varying dispersivity as shown in Table 5.2. 46
Figures 5.2 through 5.9 show the difference in head between the calibrated model and each sensitivity run. Runs 2 through 4 (Figures 5.4‐5.9) had only minor effects on the calibration point heads. Run 1 (Figures 5.2 and 5.3), which increased longitudinal dispersivity from 2.5 feet to 25.0 feet, did have a marked effect on some of the calibration points. Most of the differences in head between the calibrated model and the sensitivity runs can be attributed to wells injecting fresh water into a comparatively more saline aquifer. Overall, there is little effect near the proposed ASR project sites. Additional calibration of the dispersivity values will be performed with the local scale models using the ASR pilot study data at the Kissimmee and Hillsboro sites. Further, the results of this sensitivity run indicate that a range of dispersivity values should be used in the running of the production runs on the regional model. Molecular diffusion was ignored for both salinity and temperature during calibration by setting the effective molecular diffusion coefficient to 0.0 ft2/d. To test its sensitivity, an additional run was made using published information to estimate effective molecular diffusion coefficients for salinity and temperature. Fetter (1999) provides a table of diffusion coefficients for common ions and recommends multiplying by ω, a coefficient related to tortuosity. The ions in Fetter’s table have diffusion coefficients ranging from 5.5e‐4 ft2/d to 8.7e‐3 ft2/d. Fetter quotes Freeze and Cherry (1979) as giving a range for ω of 0.01 to 0.5. When this range is applied, the result is a range of effective molecular diffusion coefficients of 5.5e‐6 ft2/d to 4.3e‐3 ft3/d. 5.0e‐4 was selected since it is close to the upper end of this range and is near the value for Na+. The source for the diffusion coefficient for heat was obtained from the 2007 SEAWAT manual (Langevin, et al). This report provides the following equation for molecular diffusion of heat: Dm _ temp 
k Tbulk
c Pfluid
Where kTbulk = θ = ρ = cPfluid = Bulk thermal diffusivity Porosity Fluid density Specific heat capacity of fluid Equation 5.1
Langevin, et al, suggests calculating the bulk thermal diffusivity using either an arithmetic mean or geometric mean (weighted by volume) of the water and solid. The accompanying table lists the bulk thermal diffusivity of freshwater at 0.58 W/mK and for limestone at 1.26 – 2.15 W/mK. However, this calculation (with a range of porosities from 0.25 to 0.4) yields a range of bulk thermal diffusivities of 0.92 to 1.61 W/mK. When applied to Equation 5.1 with the same range of porosities, a density of 2.7e3 kg/m3 for limestone and specific heat capacity for freshwater of 4.186 (both from Table 2 in Langevin, et al), a range of effective diffusion for heat is 0.2 to 0.5 ft2/d. The maximum value (0.5) was used in the sensitivity analysis. Clearly, this can only be an estimate since not all materials in the model are 47
limestone and not all the water is fresh. However, the variation is sufficient to indicate the sensitivity of the parameter. As expected, molecular diffusion proved to be an insensitive parameter. At the calibration points, there was no discernible difference between the calibration run and the sensitivity run. When compared at each cell in the Floridan aquifer, a few cells (primarily in deep layers) had head differences up to about 2.5 feet, but the vast majority of the cells had head differences less than 0.1 feet. The highest head differences occurred at isolated locations in the Lower Confining Unit in Hardee County and on the border of Manatee and Sarasota Counties, well away from the proposed ASR locations. Differences in salinity caused by the diffusion coefficient changes were negligible, with a maximum difference of less than 100 mg/L TDS. Similarly, the diffusion coefficient changes caused no more than about 2 C change in the temperature calculated at the end of the 15 month simulation. As with porosity, the sensitivity of diffusion was not significant enough to warrant a figure. 5.4 Boulder Zone Thickness As explained in Section 3.2.1, there was no specific data on the thickness of the Boulder Zone. Available estimates of the thickness were roughly averaged to 500 feet. This thickness was applied uniformly to the bottom layer of the model. However, because the flow in the Boulder Zone can have a large impact on flow and pressure conditions in all areas of the model, a number of sensitivity runs were made in an attempt to quantify the uncertainty introduced to the model by this assumption. The first two sensitivity runs simply changed the thickness of the layer across the domain. One doubled the thickness to 1000 feet and the other halved the thickness to 250 feet. The next two sensitivity runs were made by changing both the thickness of the bottom layer and the assigned horizontal and vertical conductivity values for this layer. Data on the hydraulic material properties for this layer were nearly as sparse as thickness data. Although the thickness may be wrong, the calibrated conductivity value is based on this thickness and there may be a number of combinations of thicknesses and conductivity values which will lead to the same result. In the absence of local flow impacts such as wells, Darcy’s law indicates that when the thickness of the aquifer is doubled, horizontal flow rates can be preserved by halving horizontal conductivity. Conversely, vertical flow can be retained by doubling vertical conductivity. Thus, two additional sensitivity runs were made to test this theory. The complete list of sensitivity runs testing the effect of the Boulder Zone thickness is shown in Table 5.3. For the transient model, these changes had no effect on the rate of head change or the shape of the head vs. time plot. The Boulder Zone properties only affected the initial steady state stress period and thus, the starting condition of the plot. Each run was a nearly perfect copy of the calibration run with an offset which varied based on the location of the well and the particular sensitivity run. For this reason, the remainder of this section will deal only with the steady state solution comparisons. As expected, Runs 1 and 2 resulted in rather large changes to the steady state head solution. The heads in the south and east portions of the model were significantly higher for Run 1 (with a thicker BZ layer) than for the calibration run and they were lower for Run 2 (which had a thinner BZ layer). This is 48
because the BZ provides a large portion of the water to the southern part of the model. The heads in the northwest section of the model were much less affected by Boulder Zone changes. Runs 3 and 4 were much less different from the Calibration results. The changes to the conductivity did not perfectly remove the effects of the thickness change due to complexities in the flow conditions. The calibration statistics for the February 2004 steady state model are shown in Table 5.4. Notice that Run 2 and 4 often have statistics nearly as low as the calibration run, and in some cases, the statistics are lower than the calibration run. Figure 5.10 shows the Upper Floridan aquifer solution and the calibration targets as an example. Similar effects were seen in the deeper layers. This study indicates that although the thickness of the Boulder Zone is an unknown and can cause marked effects on the results of the model, the effects of the zone thickness can be offset by the effects of the zone conductivity values, which are equally poorly known. The combination of Boulder Zone thickness and Boulder Zone conductivity have resulted in a calibrated model which can be used to estimate the effects of ASR wells on a gross, regional scale. When the production scenarios are built to evaluate the CERP ASR program, a range of BZ thicknesses and conductivity values will be used to ensure that uncertainty due to this data gap is considered in evaluating model predictions. 5.5 Specified Head Boundaries As explained in Section 3.3, the use of specified head boundaries is not recommended where there is the possibility of impacts to boundary heads from interior hydraulic conditions. The reasons for selection of specified heads despite the drawbacks are outlined in Section 3.3 and Appendix C. There are two areas of the boundary where available head data was sparse and specified heads assigned are questionable: along the north boundary between Orlando and Tampa, and along the boundary as it passes through Everglades National Park. In order to ascertain the impacts of the assumption of specified heads at these areas, several additional sensitivity runs were made. 5.5.1 North Boundary Between Orlando and Tampa, the north boundary of the model passes through some areas of increased head and low salinity, caused by high recharge. Some data is available in the upper layers of the model, especially the UF and APPZ. As explained in Appendix C, the gradient in this area was assumed to be downward, but not especially steep. Equivalent freshwater heads in the deeper layers were set just slightly below the values found in the upper layers. Two sensitivity runs were made to verify that possible errors in the assumptions made in setting up the northern specified head boundaries are unimportant to the purposes of the model. A section of cells from Tampa to Orlando were selected. In one run, the specified heads in the LF1 were dropped by 5 feet and the heads in the BZ were dropped by 10 feet. This assumes a small but significant downward gradient. For the second run, the specified heads in the LF1 were decreased by 20 feet and the heads in the BZ were decreased by 40 feet. This assumes a large downward gradient. For simplicity’s sake, the change in boundary conditions was not gradual near Tampa or Orlando, so the local flow conditions at 49
each end of the selected section of cells are expected to look unusual. However, this simple method is sufficient to determine the regional impact of possible errors in the head assigned at the boundary. These changes to the north boundary had only a localized effect on the results of the model. The effect was only to the starting condition (initial steady state solution for October 31.) The transient solutions were parallel to the transient calibrated solution. Only a few observation wells displayed differences in head. The largest differences were at the Intercession City observation well in both the LF1 and the BZ. The first sensitivity run (which reduced the Boulder Zone specified head by 10 feet and the LF1 specified head by 5 feet) resulted in a reduction in head at the Intercession City well of about 1 foot in both aquifers. The second run (reducing the Boulder Zone head by 40 feet and the LF1 by 20 feet) caused a drop at Intercession city of about 4 feet in both aquifers. Smaller differences were also observed at two northern LF1 observations wells, OSF‐82L and OS0025. The differences at these wells were 0.1 feet and 0.5 feet at OS0025 and 0.7 feet and 2.8 feet at OSF‐82L for the first and second sensitivity runs, respectively. Figure 5.11 shows the head changes caused by these alterations to the BZ and LF1 boundary conditions. As expected, the greatest changes are in the immediate vicinity of the northwest boundary. The effect of the boundary condition extends less than 50 miles from the boundary and does not affect the heads at the proposed ASR well locations. No discernible differences were observed in any of the other aquifer layers. Although there may be disagreement about the applied gradient at the northwest boundary of the model, it has no effect on the end purposes of the ASR Regional Model. 5.5.2 Southwest Boundary Some concern has been raised about the specified head assigned through the Everglades because of the impression that there is very little data available in this area. As shown in Figure 3.17, there are actually several wells in this area which were used for assigning the specified heads at this boundary. However, in order to verify these values, two sensitivity runs were made to show that there is very little impact to the interior of the model. In one sensitivity run, all of the specified heads in the UF were removed from the counties of Collier, Monroe and the western half of Miami‐Dade. This is equivalent to defining a no‐
flow boundary at this location. The second run removed all specified heads in same area for all layers. Neither of these sensitivity runs had significant effects on the calibration of the steady state model as shown in Table 5.5 which compares the RMS of the calibration runs to the RMS from these two sensitivity runs. Cutting off flow through the UF boundary on the southwest edge of the model resulted in no change to the calibration statistics in the UF, APPZ, and BZ and a change of only 0.01 in the LF1. The change is greater when the flow in all aquifers is cut off, but it is still very small, with a maximum change in RMS of 0.4, occurring in both the APPZ and the LF1. Figures 5.12 and 5.13 show the difference between the head calculated by the calibration model run and each of these sensitivity runs. When the outbound flow in the UF is blocked along the southwest boundary, the head in the UF rises in the area of the Everglades and decreases in the Naples area. However, the area of difference is small – about 25 miles from the boundary ‐‐ and the head change is less than 1 foot. This boundary change also impacted the APPZ in about the same area, though the 50
heads right at the boundary are fixed, so there is no change in the first line of cells. Some small changes occurred in the IAS, but there was no impact to either the LF1 or the BZ. When the flow was blocked to all aquifers (Figure 5.13), the magnitude of the head changes are greater and the area of impact is greater – extending nearly 100 miles in from the boundary for the UF, APPZ, LF1 and BZ. The extent of the effects in the IAS is smaller – extending only 55 miles from the boundary. However, the highest magnitude changes in head occur in the IAS with a maximum drop of 73 feet. In the calibrated model, significant IAS pumping in Collier County pulls water into the model from the boundary. When this boundary inflow is blocked, pumping drawdown increases. It is also interesting to note that the effects are less pronounced in the BZ. Initially, this appears to contradict the flow regime shown in Figure 4.163, which indicates a significant flow component exiting the model through the BZ in the Everglades region. However, because of the larger conductivities present in the BZ, the excess water is able to more easily move to a secondary exit location (the south end of the model in Miami‐Dade county, just outside the Everglades boundary). Layers above the BZ (LF1 and APPZ) have a smaller flow component crossing this boundary in the calibration model, but the effects of the boundary condition change are greater because lower conductivity values make it harder for water to find other avenues to leave the model and the heads build up. Although the results of the sensitivities show that some minor impacts would extend to areas near proposed ASR wells, the sensitivities represent an extreme condition. By assigning a no‐flow boundary to all the layers along the southwest boundary, the heads respond in a way that is not supported by available data. Figure 3.17 shows there are several available data points along the southwest boundary in the IAS, UF, APPZ, and LF1 that were used to set a specified head. Thus a no‐flow boundary is not reasonable in this region. 5.5.3 Confining Units Boundary As explained in Section 3.3, the SEAWAT model uses time‐variant specified‐head boundary conditions for the aquifers and Atlantic Ocean outcrops of the confining units. No‐flow boundaries were assigned to the confining units on the inland sides of the model (north, west, south) because horizontal flow in these cells is limited and not believed to be a significant source or sink of groundwater. IMC reviewers raised the concern that horizontal flow in these units might be important. To determine the effect of boundary condition choice on the computed model results, a new steady state SEAWAT simulation was created using data from October 2003 and changing the no‐flow boundary conditions to specified heads along the north, west and south boundaries of the confining unit layers. Linear interpolation between the overlying and underlying aquifer heads was used to determine the head for each new specified head cell. A steady state simulation was run using the newly created specified head boundary conditions, and the results were compared to the October 2003 calibration. Only minor differences in head were observed when comparing the two model runs, with none of the observed differences having an effect on the groundwater at the proposed CERP ASR sites. The greatest differences in head are located along the boundaries of the confining units. Figure 5.14 shows the difference in head in the confining unit layers between the October 2003 calibration and the sensitivity 51
run. The difference in head is mostly observed along the boundary or within one or two cells of the boundary. The exception to this is seen in layers 2, 3, and 4 in Collier County and is due to a minor oversight in assigning the original boundary conditions to the IA (layer 3). When the boundary conditions were initially set, the specified head boundary applied to layer 3 was terminated just north of the southern border of Collier County (see Figure 3.17) at the last point with available observation data. However, the aquifer portion of layer 3 extends slightly farther southeast into Monroe County, leaving a small section of the aquifer with no boundary condition assigned. This section of aquifer boundary without an applied specified head boundary condition resulted in the difference in head seen in Figure 5.14 in layers 2 through 4. Even with this omission, the effects do not extend to any of the proposed CERP ASR sites. In the aquifers, the only notable difference in computed head was observed within one to two cells of the boundary in the vicinity of Cape Coral. These differences were also only seen in the UF and APPZ. The maximum head difference in the UF is less than 0.9 feet, and less than 100 cells were changed by more than 0.1 feet. In the APPZ, the maximum head difference is less than 0.6 feet, with less than 50 cells being changed by more than 0.1 feet. These results indicate that the use of a no‐flow boundary condition on the land boundaries of the confining units is an acceptable simplification to the model. 5.6 Ratio of Horizontal to Vertical Hydraulic Conductivity As explained in Section 4.1.2, the ratio between horizontal and vertical conductivity was set at 10:1 for aquifers and 2:1 for confining units. The exception to this rule was the third layer, whose western section represents the IA, while the remaining part is lumped with layers 2 and 4 to simulate the ICU. In layer 3, the horizontal to vertical conductivity ratio was set to 10:1. The ratios were set using MODFLOW’s array multiplier option, so only a single multiplier could be used in any layer. These ratios were selected with little data based on the expectation that the majority of the flow would be horizontal in the aquifers and vertical in the confining units, so the calibration would be insensitive to the conductivity in the cross‐flow direction. IMC comments indicated that this might not always be true, and recommended a sensitivity run to quantify this effect. Four separate sensitivity runs were developed as follows: 1. Set the ratio of horizontal to vertical conductivity to 1:1 in all layers (2‐22), keeping the horizontal conductivity in the aquifers and the vertical conductivity in the confining units at their calibrated values. 2. Set the ratio of horizontal to vertical conductivity to 1:10 in the aquifers (layers 3, 5‐10, 13‐15, 18‐19,22) and 1:2 in the confining units (layers 2, 4, 11‐12, 16‐17, 20‐21), keeping the horizontal conductivity in the aquifers and the vertical conductivity in the confining units at their calibrated values. 3. Repeat Run 1 in layers 5‐22 only. Layers 2 through 4 keep their calibrated values and ratios. 4. Repeat Run 2 in layers 5‐22 only. Layers 2 through 4 keep their calibrated values and ratios. 52
The reason for runs 3 and 4 is related to the use of MODFLOW’s array multipliers to make these changes quickly and easily. No single multiplier could keep the horizontal conductivity in layer 3 constant in the west (IA), while keeping the vertical conductivity the same in the east (ICU). Although this effect could have been achieved by changing the arrays, the decision was made to check the sensitivity on the existing runs before expending the effort to redevelop the arrays. The results generally support the original hypothesis – that the calibration is not sensitive to either horizontal conductivity in the confining units or vertical conductivity in the aquifers. The few exceptions include the recharge area and a few areas with heavy pumping, where one might expect significant vertical movement of water in the aquifers. The effect of the changes on the calibration was minimal. For the runs with changes to layers 2 through 4, the maximum head change at any calibration point for the February 2004 run is less than 2 feet, with the average at about 0.2 feet. When layers 2 through 4 were left unchanged from the calibration values, the maximum head change at any calibration point was less than 0.5 feet and the average change was about 0.03 feet. As expected, Runs 1 and 2 caused more significant and widespread effects on the February 2004 steady state run in layers 2 through 4. Figure 5.15 shows the differences in head in these layers for the first two sensitivity runs for these upper layers. These differences propagate down into deeper layers, but they diminish with depth and are largely undetectable in the LF, LC and BZ layers. Figure 5.16 shows the comparison between the first two and last two runs in the UF and indicates the areas of greatest impact at the major pumping location in Lee County. Overall, the effects to proposed CERP ASR sites are minimal – even with Runs 1 and 2, which caused such large changes in the IAS. These results indicate that flow is generally horizontal in the aquifers and vertical in the confining units, except in areas of changes to the direction of flow or where there is significant recharge or pumping. Because the CERP ASR plan calls for significant pumping in several areas, it is possible that the ratio of horizontal to vertical conductivity will affect the outcome of the production scenarios as flow directions change to provide water to the ASR wells. To quantify this uncertainty, the ratio will be the subject of some sensitivity and Monte Carlo simulations on the final selected CERP ASR regional model run. 6.0 Sources of Uncertainty Overall, the model does a good job replicating observed field conditions. There is a high degree of confidence that it will provide valuable insights to the CERP ASR program. As with all models, uncertainty exists in the input data and in the simplifying assumptions. It is important to identify these areas of uncertainty and quantify them so that the model results can be used in an informed way. The following subsections describe the major sources of uncertainty, including some of these assumptions, and how they may affect model results and overall goals of the project. 53
6.1 Pumping Rate Data Limitations Limitations in the pumping data constitute the principal source of error in this model. Figure 6.1 shows the drawdown occurring throughout the UF due to seasonal pumping in February 2004, which is a relatively low pumping period. Drawdown exceeds 30 feet in some areas of the northwest part of the model (Manatee, Hillsborough and Polk County) and in the Cape Coral area. A huge portion of the peninsula is impacted by pumping activities to a lesser, but significant degree. Head changes in numerous monitoring wells show swings in head greater than what can be caused by seasonal rainfall changes. The available data indicates head changes on the order of only 1 to 5 feet in the SAS within our model domain. (See Figures 4.41‐4.94 for measured head changes during the calibration period.) Pumping rate errors are the likely reason for poor calibration at almost all the observation points described in Section 4.1.3. Clearly, it is important that the model correctly incorporate pumping. As explained in Section 3.5 and Appendix D, the information on the pumping rates of permitted wells is sparse. SAJ made valiant efforts to gather as much available data as possible, but a large part of the data had to be estimated based on the well type, capacity/allocation information and other available pumping data. Figures 3.37 through 3.41 and Table 3.1 show how much of the pumping in the model is based on estimates. In each month of the calibration period, between 20% and 25% of the volume of pumped water is based on estimates. It is of special importance that the largest estimated pump rates occur at wells in the middle swath of the model – along the Caloosahatchee River, the southern reach of the Kissimmee River and into St. Lucie County. These areas caused the greatest problems in the calibration of the model and contain many of the proposed CERP ASR sites. Figure 6.2 presents the results of a sensitivity analysis on the October 2003 steady state model to demonstrate the effect of the estimated pumping on the model calculation. All of the estimated pumping for this month was reduced by 50%. Reported (known) pump rates remained the same. Figure 6.2 shows the difference between the heads calculated by the calibrated model and this sensitivity run. Differences of one foot or more are found covering nearly half of the model domain. Smaller areas with much larger head differences are scattered across the region. It is clear that errors or poor assumptions in the estimation of missing pumping data can have a marked effect on the model results. Any pumping errors have a significant impact on the calibrated aquifer parameters and will influence predictions made by the model and recommendations based on model predictions. A variety of sensitivity analyses will be performed on the ASR production simulations. During the PDT evaluation of the CERP ASR program, the uncertainty due to pumping must be kept in mind and carefully evaluated. 6.2 Temporal Distribution of Pumping Data Because of the difficulties associated with gathering pumping data for over 30,000 wells in the South Florida region, an early decision was made to average the pumping over each month of the model period. This resulted in a much simpler (though still arduous) data collection effort and likely had only minimal effects on the calibration. For consistency, the same process was applied to heads assigned as boundary conditions on the edges of the aquifers and on the surface of the model. The temporal distribution of the pumping data and boundary conditions meant that the transient calibration could not 54
be expected to match measured head data on a daily basis, but rather that it was calibrated until the general trends and average monthly heads were similar to measured data. When the model is used to evaluate ASR well placement, pump rates and schedules, this coarse temporal distribution of the pumping data may have a minor effect on the results of the model. Although the time constraint may be lifted for ASR wells, boundary conditions and nearby pumping will still be on the monthly schedule and some daily effects might not be entirely accurate. 6.3 Salinity Distribution The initial condition salinity distribution was developed as an interpolation of the available TDS data. Data is more plentiful in the shallower layers and becomes much sparser in the deep layers. Unfortunately, since the impact of density differences becomes greater with depth, the model is much more sensitive to the TDS in the deep layers than in the shallow layers. Early sensitivity runs showed that density changes (caused by TDS) can have a great effect on both the direction of flow and the impact of head changes. The results of these early tests led to the use of measured TDS data whenever possible. Further, a Monte Carlo analysis is planned for the production runs to determine the effect of variation in TDS on the ASR system predictions. 6.4 Temperature Distribution The initial condition temperature distribution was developed as an interpolation of the available temperature data. Like TDS data, temperature data was sparser in deep layers of the model. Temperature exerts a much smaller impact on the density of water – even at deep elevations. Errors in the temperature data probably exert only a minor effect on the calibration or the future production runs of the ASR regional model. 6.5 Surficial Aquifer Boundary Assumption The decision to apply a specified head boundary condition to the surface of the model was made to simplify both data collection and model implementation. As explained in Section 3.3.1, the application of a flux boundary condition at the surface to simulate recharge and discharge would have required additional data such as rainfall, evapotranspiration, seepage rates, etc. This data is available only sparsely and in most models, the inability to appropriately assign recharge/discharge rates at the surface leads to problems with the model. Many models include recharge as a calibration parameter. By applying specified heads to the surface, many of these problems were alleviated and the heads used to interpolate the SAS head boundary had already been collected as part of the data gathering effort. The downside of this type of boundary condition is that ASR scenarios which impact the SAS will not be accurately simulated in the model. This is expected to be a minor problem since impacts to the SAS will most likely occur after other performance measures (rock fracturing potential, impacts to nearby wells) have already eliminated the scenario as a viable option. 55
6.6 Spatial Discretization Due to time and computational constraints, the spatial discretization of the model is quite coarse. In the SEAWAT grid, the largest cells are 10,000 feet on a side (nearly 2 miles). Even at the ASR well locations, cell sizes only drop to 2,000 feet. At this discretization level, only regional effects of the ASR well scenarios can be simulated. Near‐well effects for ASR wells or any other wells cannot be evaluated on this model. In order to minimize the impact of the spatial discretization to the ASR program, the next study will utilize a number of telescopically refined models. These models will be smaller in regional extent and will have smaller grid cells. They will take their boundary conditions from the regional model. With smaller computational cells at the ASR wells, near well effects will be more easily simulated. The small regional extent will allow the models to reach converged solutions on available computers in a reasonable amount of time. 6.7 Variability in Transport Parameters Very little attention was paid to the transport parameters inherent in the SEAWAT equation. These parameters include porosity, dispersivity and molecular diffusion. Because the calibration models were run for no more than 15 months, the salinity and temperature did not change significantly from the initial conditions (except near injection wells). Some sensitivity runs were made to verify their low sensitivity and are presented in Section 5.2 and 5.3. The selection of transport parameters likely has little effect on either the calibration models or any short‐term production runs. However, as the process moves forward and longer ASR runs are made to evaluate the freshwater bubble at the ASR wells or seawater intrusion, these transport parameters may become more important. Production simulations will be conducted for an extended time period time period (10 years or more). Variability in the transport parameters will be evaluated as part of this modeling effort as well as in the local scale modeling during the next study phase. 7.0 Conclusions/Recommendations The goal of this modeling effort was to develop a tool to evaluate the regional impacts of the CERP ASR program on the hydrogeologic conditions in the FAS. An extensive data collection and multi‐phase modeling effort has been undertaken to ensure that the models achieve this goal. This report presents the details of the construction, calibration and sensitivity analysis of the models that will be used to evaluate the regional effects of the CERP ASR program. As with any numerical model, uncertainty in the input data and computational methodology are inherent in the ASR Regional Model. In order to address these issues, numerous sensitivity analyses have been performed to determine how the model reacts to various input stresses. Pumping (both into and out of the FAS) has a substantial impact on the water levels in the FAS. Unfortunately, the pumping data used for this regional modeling effort also has a high degree of uncertainty, primarily resulting from the lack of pumping records. On‐going improvements in the recording of FAS pumping will be critical in protecting the long term water quality of the aquifer. In addition to pumping, various other model 56
inputs (including BZ parameters and density distributions) were determined to be sensitive in the regional model calibration. Given this uncertainty in the input data, the calibrated regional models do an excellent job reproducing the FAS flow system and will serve as a useful baseline against which the CERP ASR program can be evaluated. However, to appropriately assess the impacts of the CERP ASR program it is anticipated that additional sensitivity analyses will be performed on any production simulations that will be performed on this calibrated model. The complex numerical methodology required to address the variable density flow system present in the FAS may also have inherent uncertainty. In order to address this issue, the ASR Regional Model was developed using two numerical codes: WASH123D and SEAWAT. The model inputs for these codes were nearly identical. As presented in Appendix F, both codes replicate the regional steady state and transient flow fields of the FAS. As such, it would be reasonable to perform subsequent model simulations (regional production and local scale modeling effort) using either code. However, due to programmatic constraints it will be more efficient to proceed with the ASR modeling effort using a single numerical code. Although the finite element distribution afforded in the WASH123D mesh provides an efficient framework for placing higher resolution in the areas of interest, the substantial complexity and heterogeneity of the FAS is difficult to incorporate. This is primarily due to zonal methodology used by WASH123D to incorporate hydrogeologic parameters. The hydrogeologic complexity of the local scale models is anticipated to be greater than that of the regional model in order to accurately replicate the formation, mixing and collapse of the ASR freshwater “bubble”. In these local scale models, parameters such as dispersivity and porosity, which were relatively insensitive in the regional model, are expected to be more sensitive, requiring a greater degree of variation. Other hydrogeologic parameters, such as hydraulic conductivity and storage, are also anticipated to be highly heterogeneous in the local scale models. This hydrogeologic complexity can be more easily incorporated into SEAWAT. Therefore, it is anticipated that SEAWAT will be the primary model used in the local scale modeling effort. It is also anticipated that refinements of the regional hydrogeologic properties based on the local scale model calibration will be incorporated into the calibrated regional model. This iterative process will ensure consistency between the models and provide the best numerical platform against which the CERP ASR program can be evaluated. In conclusion, the models developed and calibrated in this Phase II modeling effort do an excellent job of replicating the regional flow system in the Floridan Aquifer System. A variety of previous modeling and scientific studies have been used to develop and evaluate this model. The hydrogeologic framework is consistent with numerous detailed studies of specific areas of the FAS. Improvements have been made to this framework during the course of the modeling study as various hydrogeologic theories have been evaluated using the physics in the models. The final calibrated model not only calibrates to steady state snap shots of the aquifers, but also reasonably replicates the effects of transient stresses in the FAS. As such, this model will be a useful tool in the evaluation of the proposed CERP ASR system. 57
8.0 References Anderson, Mary P. and William W. Woessner, 1992. “Applied Groundwater Modeling: Simulation of Flow and Advective Transport”, Academic Press, London. ASR Contingenct Study Team, 2008. Central and Southern Florida Project Comprehensive Everglades Restoration Program Aquifer Storage and Recovery Contingency Study: A Reconnaissance Level Assessment and Proposed Path Forward Strategy Toward Development of and Aquifer Storage and Recovery Contingency Plan. Aucott, Walter R., 1988. Areal Variation in Recharge to and Discharge from the Floridan Aquifer System in Florida, U.S. Geological Survey Water‐Resources Investigations Report 88‐4057. Bittner, Laura D., Emily Richardson, Christian D. Langevin, Stephen M. England, and Glendon T. Stevens, 2008. Using Density‐Dependent Numerical Models to Evaluate Regional Groundwater Flow Patterns in South Florida. Brown, C.J, England, Steve, Stevens, G.L. Cheng, H‐P, and Richardson, Emily, 2006. ASR Regional Study—
Benchscale Modeling, Final Report. Bush, P.W. and R.H. Johnson, 1988. Ground‐Water Hydraulics, Regional Flow, and Ground‐Water Development of the Floridan Aquifer System in Florida and in Parts of Georgia, South Carolina, and Alabama, U.S. Geological Survey Professional Paper 1403‐C. Cheng, H.‐P., J.‐R. Cheng, and G.‐T. Yeh, 1998. “A Lagrangian‐Eulerian method with adaptively local zooming and peak/valley capturing approach to solve three‐dimensional advection‐diffusion transport equations.” International Journal for Numerical Methods in Engineering, 41(4), 587‐
615. Cheng, J.‐R., H.‐P. Cheng, and G.‐T. Yeh, 1996. “A Lagrangian‐Eulerian method with adaptively local zooming and peak/valley capturing approach to solve two‐dimensional advection‐diffusion transport equations.” International Journal for Numerical Methods in Engineering, 39(6), 987‐
1016. CH2MHill, 2005. Sub‐Task No. 3 – Groundwater Numerical Model Development Support and Data Collection Report. Divins, D.L., and D. Metzger, NGDC Coastal Relief Model, http://www.ngdc.noaa.gov/mgg/coastal/coastal.html Fetter, C.W., 1999. Contaminant Hydrogeology. New Jersey: Prentice‐Hall. Fies, Michael, 2004. Comprehensive Everglades Restoration Plan, Lineament Analysis South Florida Region Aquifer Storage and Recovery Regional Study. U.S. Army Corps of Engineers, Jacksonville, FL. Available from http://www.evergladesplan.org/pm/projects/project_docs/pdp_asr_ combined/013007_asr_lineament_dtmt.pdf 58
Freeze, R. Allen, and John A. Cherry, 1979. Groundwater. New Jersey: Prentice‐Hall. Guo W., and Bennett, G.D., 1998. Simulation of saline/fresh water flows using MODFLOW. In: MODFLOW ’98 Conference, Golden, Colorado. pp; 267‐274. Guo, W., and C.D. Langevin, 2002. User’s Guide to SEAWAT: a Computer Program for Simulation of Three‐Dimensional Variable‐Density Ground‐Water Flow. Open‐File Report 01‐ 434. U.S. Geological Survey, Tallahassee, Fla. Harbaugh, A.W., Banta, E.R, Hill, M.C., and McDonald, M.G., 2000. MODFLOW—2000, the U.S. Geological Survey modular ground‐water model—User guide to the modularization concepts and the ground‐water flow process. U.S. Geological Survey Open File Report 00‐92, 121 p. Huges, Joseph D., Vacher, H.L., Sanford, Ward E, 2007. Three‐dimensional flow in the Florida platform: Theoretical analysis of Kohout convection at its type locality. Geology. Vol 35, Issue 7, pp663‐
666. Kohout, F.A.,H.R. Henry, and J.E. Banks, 1977. Hydrogeology related to geothermal conditions of the Floridan Plateau. In The geothermal nature of the Floridan Plateau, edited by D.L. Smith and G.M. Griffin, 1‐41. Florida Geological Survey Special Publication no. 21. Kohout, F.A., 1965. A hypothesis concerning cyclic flow of salt water related to geothermal heating in the Floridan aquifer: New York Academy of Sciences Transactions, ser. 2, v. 28, no. 2, p. 249‐271. Langevin, C.D., Shoemaker, W.B., and Guo, W., 2003. MODFLOW‐2000, the U.S. Geological Survey Modular Ground‐Water Model—Documentation of the SEAWAT‐2000 Version with the Variable‐
Density Flow Process (VDF) and the Integrated MT3DMS Transport Process (IMT), U.S. Geological Survey Open‐File Report 03‐426, 43 p. Langervin, Christian D., Daniel T. Thorne, Jr., Alyssa M. Dausman, Michael C. Sukop, and Weixing Guo, 2008. SEAWAT Version 4: A Computer Program for Simulation of Multi‐Species Solute and Heat Transport, U.S. Geological Survey Techniques and Methods Book 6, Chapter A22. Meyer, Fredrick W., 1989. Hydrogeology, Ground‐Water Movement, and Subsurface Storage in the Floridan Aquifer System in Southern Florida, U.S. Geological Survey Professional Paper 1403‐G. Miller, James A., 1997. The Hydrogeology of Florida. In The Geology of Florida, edited by Anthony F. Randazzo and Douglas S. Jones. p. 69‐88. Morrissey, Sheila K., Jordan F. Clark, Michael Bennett, Emily Richardson, and Martin Stute, 2010. Groundwater reorganization in the Floridan aquifer following Holocene sea‐level rise. Nature Geoscience, doi:10.1038/NGEO956. Nash, J.E. and Sutcliffe, J.V., 1970. River Flow Forecasting Through Conceptual Models Part I – A Discussion of Principles. Journal of Hydrology 10:282‐290. 59
National Oceanic and Atmospheric Administration (NOAA), http://tidesandcurrents.noaa.gov/geo.shtml?location=8723214 National Oceanic and Atmospheric Administration (NOAA), http://tidesandcurrents.noaa.gov/geo.shtml?location=8725110 National Park Service’s South Florida Natural Resources Center (SFNRC), http://www.nps.gov/ever/naturescience/sfnrc.htm Reese, Ronald S., 2000. Hydrogeology and the Distribution of Salinity in the Floridan Aquifer System, Southwest Florida, U.S. Geological Survey Water‐Resources Investigations Report 98‐4253. Reese, Ronald S., 2004. Hydrogeology, Water Quality, and Distribution and Sources of Salinity in the Floridan Aquifer System, Martin and St. Lucie Counties, Florida, U.S. Geological Survey Water Resources Investigations Report 03‐4242. Reese, Ronald S., 2002. Inventory and Review of Aquifer Storage and Recovery in Southern Florida, U.S. Geological Survey Water‐Resources Investigations Report 02‐4036. Reese, Ron and Emily Richardson, 2008. Synthesis of the Hydrogeologic Framework of the Floridan Aquifer System and Delineation of a Major Avon Park Permeable Zone in Central and Southern Florida, U.S. Geological Survey Scientific Investigations Report 2007‐5207. Reese, Ron and Emily Richardson, 2004. Task 3.0 Define Preliminary Hydrogeologic Framework, ASR Regional Study. Sanford, Ward E., Whitaker, Fiona F., Smart, Peter L., Jones, Gareth, 1998. Numerical analysis of seawater circulation in carbonate platforms: I. Geothermal convection. American Journal of Science. Vol 298, Issue 10, pp801‐821. Sepúlveda, Nicasio, 2002. Simulation of Ground‐Water Flow in the Intermediate and Floridan Aquifer System in Peninsular Florida, U.S. Geological Survey Water‐Resources Investigations Report 02‐
4009. Sibson, R., 1981. A brief description of natural neighbor interpolations, In Interpreting Multivariate Data, Ed. V. Barnett, Chichester, 21‐36, John Wiley. South Florida Water Management District’s environmental database (DBHYDRO), http://my.sfwmd.gov/dbhydroplsql/show_dbkey_info.main_menu SFWMD and USACE, April 1999. The Central and Southern Florida Project Comprehensive Review Study. Spechler, Rick M., and Sharon E. Kroening, 2007. Hydrology of Polk County, Florida, U.S. Geological Survey Scientific Investigations Report 2006‐5320. 60
Torres, A.E., L.A. Sacks, D.K. Yobbi, L.A. Knochenmus, and B.G. Katz, 2001. Hydrogeologic Framework and Geochemistry of the Intermediate Aquifer System in Parts of Charlotte, De Soto, and Sarasota Counties, Florida, U.S. Geological Survey Water‐Resources Investigations Report 01‐4015. U.S. Army Corps of Engineers Philadelphia District (NAP), 2006. Draft ASR Regional Study Phase I ‐ Groundwater Modeling. U.S. Geological Survey’s Digital Elevation Model (DEM), http://seamless.usgs.gov/ U.S. Geological Survey’s National Elevation Dataset (NED), http://ned.usgs.gov/ U.S. Geological Survey’s South Florida Information Access (SOFIA), http://sofia.usgs.gov/ Ward, William C., Kevin J. Cunningham, Robert A. Renken, Michael A. Wacker, and Janine I. Carlson, 2003. Sequence‐Stratigraphic Analysis of the Regional Observation Monitoring Program (ROMP) 29A Test Corehole and its Relation to Carbonate Porosity and Regional Transmissivity in the Floridan Aquifer System, Highlands County, Florida, U.S. Geological Survey Open‐File Report 03‐
201. Watermark Numerical Computing, 2004. PEST Model‐Independent Parameter Estimation User Manual: 5th Edition. WRDA, 2000, 33 CFR 385. Yeh, G.‐T., G. Huang, H.‐P. Cheng, F. Zhang, H.‐C. Lin, E. Edris, and D. Richards, 2006. “A First‐Principle, Physics‐Based Watershed Model: WASH123D, Chapter 9, Watershed Models”, 653 pp., Edited by V. P. Singh and D. K. Frevert, CRC Press, Taylor & Francis Group. Yeh, G.‐T., H.‐P. Cheng, G. Huang, F. Zhang, H.‐C. Lin, J.‐R. Cheng, E. Edris, and D. Richards, 2003. “A Numerical Model Simulating Water Flow and Contaminant and Sediment Transport in WAterSHed Systems of 1‐D Stream‐River Network, 2‐D Overland Regime, and 3‐D Subsurface Media (WASH123D: Version 2.0)”. Zheng, C. and P.P. Wang, 1999. MT3DMS: A Modular Three‐Dimensional Multi‐Species Model for Simulation of Advection, Dispersion and Chemical Reaction of Contaminants in Groundwater Systems: Documentation and User’s guide, SERDP‐99‐1: U.S. Army Engineer Research and Development Center, Vicksburg, MS. 61