Methods Note/
PRO-GRADE: GIS Toolkits for Ground Water
Recharge and Discharge Estimation
by Yu-Feng Lin1, Jihua Wang2, and Albert J. Valocchi3
Abstract
PRO-GRADE is an ESRI ArcGIS 9.2 plug-in package that consists of two separate toolkits: (1) the pattern
recognition organizer for geographic information system (PRO-GIS) and (2) the ground water recharge and discharge estimator for GIS (GRADE-GIS). PRO-GIS is a collection of several existing image-processing algorithms into one user interface to offer the flexibility to extract spatial patterns according to the user’s needs.
GRADE-GIS is a ground water recharge and discharge estimation interface using a mass balance method that
requires only hydraulic conductivity, water table, and bedrock elevation data for simulating two-dimensional
steady-state unconfined aquifers. PRO-GRADE was developed to assist ongoing assessments of the water resources in Illinois and Wisconsin, and is being used to assist several ground water resource studies in several
locations in the United States. The advantage of using PRO-GRADE is to enable fast production of initial
recharge and discharge maps that can be further enhanced by using a follow-up ground water flow model with
parameter estimation codes. PRO-GRADE leverages ArcGIS to provide a computer-assisted framework to
support expert judgment in order to efficiently select alternative recharge and discharge maps that can be used
as (1) guidelines for field study planning and decision making; (2) initial conditions for numerical simulation;
and (3) screening for alternative model selection and prediction/parameter uncertainty evaluation. In addition,
PRO-GRADE allows for more easy and rapid correlation of those maps with other hydrologically relevant
geospatial data.
Introduction
Ground water recharge and discharge rates and patterns reflect the relationships between ground water fluxes,
precipitation inputs, and surface water exchanges, and thus
1Corresponding author: Illinois State Water Survey, University of Illinois at Urbana-Champaign, 2204 Griffith Drive, Champaign, IL 61820-7495; (217) 333-0235; fax: (217) 244-0777;
[email protected]
2Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, 205 N Mathews, Urbana, IL
61801; (217) 333-0107; fax: (217) 333-9464; jwang41@illinois.
edu
3Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, 205 N Mathews, Urbana, IL
61801; (217) 333-3176; fax: (217) 333-0687; valocchi@illinois.
edu
Received February 2008, accepted August 2008.
Copyright ª 2008 The Author(s)
Journal compilation ª 2008 National Ground Water Association.
doi: 10.1111/j.1745-6584.2008.00503.x
122
can have a major impact upon management options for
water supply. Recharge and discharge rates and patterns
are difficult to characterize, and currently no single estimation method is effective for all practical applications
(Cherkauer 2004). Despite a long history of investigation,
the complex interaction of factors influencing rates and locations of recharge and discharge remains unclear (Scanlon
et al. 2002). Traditional recharge and discharge studies
usually require time-consuming and labor-intensive field
characterization. Therefore, a fast initial recharge and discharge estimation and mapping methodology will help scientists and decision makers design more accurate and costeffective research plans and management strategies prior to
initiating labor-intensive field measurements. Also, crossanalyzing results from multiple working hypotheses with
related field information will likely be superior to using
only a single estimation.
Several researchers (Dripps and Bradbury 2007; Lin
and Anderson 2003; Cherkauer 2004) have developed
Vol. 47, No. 1—GROUND WATER—January–February 2009 (pages 122–128)
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numerical methods employing readily available information to decrease the processing time for recharge and
discharge estimation in semihumid to humid regions
like Illinois and Wisconsin. We have adapted the approaches described by Lin and Anderson (2003) to
develop a new geographic information system (GIS)–
based plug-in package, PRO-GRADE, to help hydrogeologists estimate recharge and discharge more efficiently
than is possible with traditional methods. The ground water
recharge and discharge estimator (GRADE-GIS) in the
PRO-GRADE package features a user-friendly interface
for estimating ground water recharge and discharge based
on the mass balance concept of Stoertz and Bradbury
(1989). Lin and Anderson (2003) demonstrated a methodology coupling the mass balance method and an imageprocessing approach for more advanced ground water
recharge and discharge estimation. GRADE-GIS requires
relatively short preparation time (hours) using data for
water table, bedrock elevations (aquifer bottom), and
hydraulic conductivities.
The pattern recognition organizer (PRO-GIS) in the
PRO-GRADE package uses several image-processing algorithms, organized in a single graphical user interface
(GUI), to estimate and visualize shallow recharge and
discharge patterns and rates with GIS. Additional imageprocessing algorithms can be added to the GUI as (1) existing ArcObjects (Burke 2003); (2) existing codes for traditional algorithms; and (3) code written within PRO-GIS for
new algorithms. In this way, the capabilities of PRO-GIS
may be expanded and tailored to the needs of individual
projects. PRO-GIS is a pattern recognition tool for wide
application, including, but not limited, to ground water
recharge and discharge pattern recognition. PRO-GIS and
GRADE-GIS are individual programs and can be used
independently for different applications, although the output from GRADE-GIS is format ready for PRO-GIS.
The data-processing capabilities of GIS allow the use
of geospatial and hydrologic data sets made widely available by advances in remote sensing and other monitoring
technologies (e.g., the French ERO program, de Dreuzy
et al. 2006; CUAHSI Hydrologic Information System,
http://www.cuahsi.org/his.html). With the GIS platform,
recharge and discharge maps from PRO-GRADE can be
cross-analyzed with ancillary field information (e.g., land
coverage, soil type maps, surface water distribution, and
topographic slope), which has a direct but not easily
quantified relation with recharge and discharge. PROGRADE can provide a fast initial estimate for use in planning labor-intensive and time-consuming field recharge
and discharge measurements.
Interfaces
PRO-GRADE adheres to the default raster file
format developed by the Environmental Systems Research Institute Inc. (ESRI) and uses ESRI ArcObjects
library for spatial data access and mapping. The package
was coded using Microsoft Visual Basic in Microsoft
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Visual Studio 2005. The installation process follows the
standard procedures for Windows programs and customized ArcMap command tools.
Methodology
GRADE-GIS provides ground water recharge and
discharge estimates for two-dimensional aquifers under
steady-state conditions based on the mass balance
approach of Stoertz and Bradbury (1989). Although
unconfined aquifer recharge and discharge can change
dynamically over time, we focus on the simpler case of
long-term steady-state conditions. There are four assumptions in the GRADE-GIS computation:
1. Recharge and discharge are the lump sums for all source
and sink terms.
2. Three GRADE-GIS input rasters, water table, bedrock elevations (aquifer bottom), and hydraulic conductivities,
are available based on prior studies or expert judgment.
3. The water table is always higher than the bedrock elevation. If the water table is less than or equal to the sum of
the bedrock elevation and the minimum saturated thickness, the cell is considered an inactive cell (NoData value
in ArcGIS) and will be excluded from computation.
4. GRADE-GIS output rasters will include NoData values,
rather than recharge or discharge estimates, for cells having NoData values in any of the input raster files.
If all the cells have the same size (which is required
for the raster file), then for every cell(i, j) the mass balance can be expressed as
Qin ¼ Ri;j xi;j yi;j
Qin ¼ Qin west 1 Qin east 1 Qin north 1 Qin south
Qin west ¼ ðhi1;j hi;j Þ=xi1=2;j Ki1=2;j bi1=2;j yi;j
¼ ðhi1;j hi;j Þ=xi1=2;j Ti1=2;j yi;j
Qin east ¼ ðhi11;j hi;j Þ=xi11=2;j Ki11=2;j bi11=2;j yi;j
¼ ðhi11;j hi;j Þ=xi11=2;j Ti11=2;j yi;j
Qin north ¼ ðhi;j11 hi;j Þ=yi;j11=2 Ki;j11=2 bi;j11=2 xi;j
¼ ðhi;j11 hi;j Þ=yi;j11=2 Ti;j11=2 xi;j
Qin south ¼ ðhi;j1 hi;j Þ=yi;j1=2 Ki;j1=2 bi;j1=2 xi;j
¼ ðhi;j1 hi;j Þ=yi;j1=2 Ti;j1=2 xi;j
where xi,j and yi,j are horizontal cell dimensions [L];
xi,j and yi,j with 61/2 in i and j subscripts represent
the lengths between centers of cell (i,j) and its four adjacent cells [L]; Ri,j is the recharge and discharge rate of
cell(i, j) [L t–1 ]; hi,j is the hydraulic head (water table
elevation) of cell(i,j) [L]; Ti,j is the transmissivity of
cell(i, j), Ti,j ¼ Ki,j bi,j for unconfined aquifer [L2 t–1];
and Ti11/2,j is the harmonic mean of transmissivity
between cell(i 1 1, j) and cell(i,j) [L2 t–1]. Ki,j is the
hydraulic conductivity of cell(i,j) [L t–1]; bi,j is the saturated thickness and is equal to hydraulic head minus
bedrock elevation [L].
Y.-F. Lin et al. GROUND WATER 47, no. 1: 122–128
123
Figure 1. Modified screen capture of the GRADE-GIS GUI and the estimated recharge and discharge map of Buena Vista
Ground Water Basin, Wisconsin. Positive values, represented by blue and green, denote recharge. Negative values, represented
by red and yellow, denote discharge. Surface water features (ancillary field information), as depicted in the National Hydrography Database, are shown as color lines and polygons (modified from Lin et al. 2008a, 2008b). Note: The superimposed
location map of Buena Vista Ground Water Basin is modified from Stoertz and Bradbury (1989).
If cell(i, j) is on the boundary, the flow rate from
the neighbor inactive cell is equal to zero. For example, if the cell is located on the west boundary with
i – 1 ¼ 0, Qin_west ¼ 0. In GRADE-GIS as shown in
Figure 1, the user can specify the minimum saturated
thickness as equal to or greater than 0.0, as noted above
in assumption 2.
PRO-GIS organizes several image-processing algorithms into one GUI as shown in Figure 2. This organization provides an efficient and systematic approach for
scientists to analyze and compare PRO-GRADE results
with ancillary geospatial information (e.g., the National
Hydrography Database [NHD], soil type and land slope).
Three image-processing methods are available in the
present version of PRO-GIS: (1) 2D Moving Average; (2)
Normalization; and (3) TVL1 Low-Pass Filter. Table 1
shows the image-processing implements and approaches
for the three image-processing methods.
Figure 3 shows recharge and discharge maps estimated using the FORTRAN code of Stoertz (1989) and
the same estimates postprocessed using PRO-GIS. The
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Y.-F. Lin et al. GROUND WATER 47, no. 1: 122–128
test data set is from the Buena Vista Ground Water Basin
in Wisconsin (Stoertz and Bradbury 1989). Patterns of
recharge and discharge from previous estimations are
Figure 2. The PRO-GIS GUI in ArcMap 9.2.
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Table 1
Image-Processing Implements and Approaches in PRO-GIS
Methods
2D Moving Average
Implement types Existing ArcObjects
Implement
Directly inherited from Generalization
approaches
ArcObjects in the ArcGIS Spatial
Analyst Extension
Operation
There are two options in 2D Moving
summary
Average: focal statistics (ArcObject:
FocalStatistics) and block statistics
(ArcObject: BlockStatistics). For each
option, several statistical calculations
are available, including majority,
maximum, median, minimum,
minority, range, standard deviation,
and Variety
Normalization
Existing codes from FORTRAN library
Based on the FORTRAN code nscore.f,
in GSLIB
References
Deutsch and Journel (1998)
Burke (2003)
Normal score transformation is
provided in PRO-GIS as an option
for transforming the original input
data to a normal distribution for the
data with significantly asymmetric
distribution due to some extreme
values. The normal score transformation is helpful in reducing the skewness and offers a clearer result
difficult to discern in data that have not been postprocessed (Figure 3a), which are noisy due to scale and
sensitivity problems (Lin and Anderson 2003). PRO-GIS
allows the analyst to distinguish the image patterns and
reduces the image noise by employing several image-processing algorithms.
The flowchart of PRO-GRADE (Figure 4) shows
that the result of GRADE-GIS can be improved by
coupling with (1) pattern recognition functions in PROGIS and (2) parameter estimation procedures to update
hydraulic conductivity and recharge/discharge (as shown
in the postprocessing stages). The recharge and discharge
rates generated by PRO-GRADE are rough estimates that
can be efficiently improved by a calibration process
(e.g., parameter estimation) as Lin and Anderson (2003)
suggested.
TVL1 Low-Pass Filter
New code written within PRO-GIS
Code written within PRO-GIS using
Microsoft Visual Basic in Microsoft
Visual Studio 2005
Total Variation Regularized L1 Function
Approximation (TV1L1) minimizes
the total variation of the image
subject to an L1-norm fidelity term.
The main advantages include
the edge-preserving capacity,
simplicity of parameter selection,
minimal signal distortion,
and the flexibility to extract
variable degrees of spatial details
Chan and Esedoglu (2005); Chen et al.
(2006); Yin et al. (2005)
Applications
Coupling of GRADE-GIS and PRO-GIS enables
users to generate many alternative recharge and discharge
maps in a short time. Comparison with ancillary field
information in GIS permits the user to evaluate the plausibility of the alternative maps (Figure 1). The ranked
recharge and discharge maps can be used as a tool for
field study planning and decision making or as an initial
condition for numerical simulation and parameter estimation. Chamberlin (1890) recommended use of ‘‘multiple
working hypotheses’’ for rapid advancement in understanding of applied and theoretical problems. This fast
production of initial alternative maps and rates can be
leveraged to gain further insight into ground water systems by using follow-up ground water flow models with
Figure 3. Recharge and discharge patterns of the Buena Vista Ground Water Basin, Wisconsin (as shown in Figure 1) generated using (a) the FORTRAN code of Stoertz (1989); (b) Normalization process from (a) in PRO-GIS; (c) the 2D Moving Average process from (a) using function of FocalStatistics and Median with a window size of 10 by 10 cells in PRO-GIS; (d) the
TVL1 Low-Pass Filter process from (a) using maximum 200 iterations with lambda = 0.1 in PRO-GIS.
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Y.-F. Lin et al. GROUND WATER 47, no. 1: 122–128
125
Figure 4. Flowchart of PRO-GRADE: the processes of GRADE-GIS based on the mass balance estimation method by Stoertz and
Bradbury (1989) were improved by coupling it with (1) a pattern recognition approach using several algorithms for image processing (the basis of PRO-GIS) and (2) parameter estimation procedures (as shown in the postprocesses) (Lin and Anderson 2003).
parameter estimation codes such as PEST (Doherty
2007), JUPITER (Banta et al. 2006), and UCODE (Poeter
and Hill 1998). The ranked initial maps can be used as
screening tools for selection of alternative ground water
models (Poeter and Anderson 2005) or for evaluation of
model prediction and parameter uncertainty (e.g., the
Bayesian model averaging approach; Ye et al. 2008).
These new toolkits have been tested using a data set
from the Buena Vista Ground Water Basin (Figure 1),
a well-understood system for which calibrated ground
water flow models are available (Stoertz and Bradbury
1989; Lin and Anderson 2003). It covers approximately
440 km2 in the Central Sand Plains of Wisconsin. This
unconfined aquifer in the Buena Vista Ground Water
Basin is composed of medium to coarse, moderately
sorted outwash sand, bounded below by igneous and
metamorphic bedrock. The field site was simulated as
a two-dimensional, unconfined, and homogeneous sandy
aquifer under steady-state conditions. The postprocess use
of MODFLOW 2000 (Harbaugh et al. 2000) and PEST in
this test is similar to the process suggested by Lin and
Anderson (2003) for comparing with their results
(Table 2). The similar results from this comparison demonstrate the validity of the PRO-GRADE computations.
For example, the flux error in this study is much less than
the three cases from the previous study. Lin and Anderson
(2003) applied some subjective prior information and
additional parameters (such as multiple hydraulic conductivity zones based on soil types) in their calibration in
order to reduce the flux error in those three cases because
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Y.-F. Lin et al. GROUND WATER 47, no. 1: 122–128
their recharge and discharge map was estimated with less
sophisticated methods than PRO-GRADE. Using the
recharge and discharge map generated by PRO-GRADE,
prior information and additional parameters were not necessary for efficient calibration in this case because the
map has more detailed and reliable patterns due to application of more superior image processing and comparison
with ancillary field information. It is anticipated that the
results from the PRO-GRADE approach will improve
upon previous studies due to the enhancement of the computing algorithms (e.g., PRO-GRADE) and hardware that
enables users to generate more complex and accurate patterns with less preparation and computing time than
before. It is expected that this tool will lead ultimately to
improved and more accurate ground water models and to
benefit a wide variety of water resources research, management, and education studies, beyond the specific case
of recharge and discharge maps presented here.
Conclusions
PRO-GRADE provides the utilities to process data
and integrate the modeling results from various methods
for estimating ground water recharge and discharge. This
ArcGIS plug-in package has been thoroughly tested and
benchmarked (Lin et al. 2008a), and will address a common problem underlying the management of natural resources, that of pattern recognition with noisy spatial
data. Consequently, PRO-GIS has the ancillary benefit of
providing pattern recognition functions supporting
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Table 2
Calibrated Results and Comparison between Previous Study and This Study
Flux
Number of Calibrated Max.
Min.
STD Flux Value
Error (%)
R/D Zones K (m/d) DH (m) DH (m) DH (m)
(m3/d)
50
26
13
40
54.77
77.04
118.94
77.80
2.93
1.98
2.68
2.14
–2.50
–2.23
–1.08
–1.20
0.78
0.51
0.58
0.46
3757.22
12852.60
5992.73
17651.00
–79.25
–29.01
–66.90
–2.51
Max.
D (m/d)
Max.
R (m/d)
MODFLOW
Error (%)
–1.1700 3 10–2
–1.1733 3 10–2
–5.5350 3 10–3
–5.7135 3 10–3
6.0400 3 10–3
5.9646 3 10–3
4.7453 3 10–3
6.3681 3 10–3
0.01
0.02
0.01
0.05
Notes: Gray-shaded data are from Lin and Anderson (2003). The data without shaded color are results based on a 40-zone recharge and discharge map generated using
PRO-GRADE and postprocessed using MODFLOW 2000 and PEST. ‘‘R/D zones’’ stands for ‘‘recharge and discharge zones.’’ Max. H is the maximum error over target value in head. Min. H is the maximum error under target value in head. STD H is the standard deviation of error in head. Flux error ¼ (flux value – target
value)/target value, where the flux values are calculated in MODFLOW-2000 with PEST (40-zone case in this study), and MODFLOW-96 with UCODE (three
gray-shaded cases from Lin and Anderson 2003). The flux target value is 18104.66 m3/d measured at Fourmile Creek from Lin and Anderson (2003). Max. D is the
maximum discharge rate (negative value indicates discharge). Max. R is the maximum recharge rate (positive value indicates recharge). MODFLOW error is the percent discrepancy of mass balance in MODFLOW computation.
virtually any spatial decision support system used in land
and water resources management. By coupling with
GRADE-GIS, initial recharge and discharge maps and
rates can be quickly generated using widely available geospatial and hydrologic data. This fast production of initial alternative maps can be used as initial conditions for
numerical models, screening tools for selection of alternative models, and guidelines for field study planning and
decision making in a timely manner.
Availability
The software package is free to download at: http://
www.sws.uiuc.edu/gws/sware/prograde/.
The package includes an installation program, user’s
guide, and example files. The source code is available
free from the corresponding author at [email protected].
Acknowledgments
This project was sponsored by the USGS and National
Institutes for Water Resources, National Competitive
Grants 104G. Data for the example case were provided by
the USGS, Wisconsin Water Science Center, Middleton,
Wisconsin; the Wisconsin Geological and Natural History
Survey and the Central Wisconsin Ground Water Center of
the University of Wisconsin—Extension. We appreciate
the advice on implanting TV1L1 from Dr. Chung-Hsien
Huang and Dr. Terrence Chen in the Department of Electrical and Computer Engineering at University of Illinois at
Urbana-Champaign. We thank Dr. Randall J. Hunt from
the USGS (Wisconsin Water Science Center), Dr. Ming Ye
from Florida State University, and the other beta testers for
helping us to improve this software package. We sincerely
appreciate the helpful comments from Mr. Ray Wuolo, Dr.
Radu Gogu, and an anonymous reviewer.
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