Calibration and Reliability in Groundwater Modelling (Proceedings of the ModelCARE 96 Conference
held at Golden, Colorado, September 1996). IAHS Publ. no. 237, 1996.
41
Death Valley regional groundwater flow model
calibration using optimal parameter estimation
methods and geoscientific information systems
FRANK A. D'AGNESE, CLAUDIA C. FAUNT,
MARY C. HILL & A. KEITH TURNER
US Geological Survey, Water Resources Division, MS 421, Box 25046,
Lakewood, Colorado 80225, USA
Abstract A three-layer Death Valley regional groundwater flow model
was constructed to evaluate potential regional groundwater flow paths in
the vicinity of Yucca Mountain, Nevada. Geoscientific information
systems were used to characterize the complex surface and subsurface
hydrogeological conditions of the area, and this characterization was used
to construct likely conceptual models of the flow system. The high
contrasts and abrupt contacts of the different hydrogeological units in the
subsurface make zonation the logical choice for representing the
hydraulic conductivity distribution. Hydraulic head and spring flow data
were used to test different conceptual models by using nonlinear
regression to determine parameter values that currently provide the best
match between the measured and simulated heads and flows.
INTRODUCTION
Yucca Mountain on the Nevada Test Site in southwestern Nevada is being studied as a
potential site for a high-level nuclear waste geological repository. In cooperation with
the Department of Energy, the US Geological Survey (USGS) is evaluating the
hydrogeological characteristics of the site as part of the Yucca Mountain Project (YMP).
One of the many USGS studies is the characterization of the regional groundwater flow
system.
This paper describes the calibration of a three-dimensional (3D) numerical
groundwater flow model of the Death Valley regional groundwater flow system
(DVRFS) using geoscientific information system and nonlinear-regression parameter
estimation methods. Groundwater modelling applications of this kind require
representation of subsurface and surface hydrological conditions and characterization of
geological controls to groundwater flow. Representation and characterization can be
substantially aided by using geologically oriented "Geoscientific Information Systems",
or GSIS (Turner, 1991). The term GSIS is used to differentiate these systems from the
more common two-dimensional (2D) GIS products (Raper, 1989).
The study area includes about 100 000 km2 and lies within the area bounded by
latitude 35° and 38°N and longitude 115° and 118°W (Fig. 1). The semiarid to arid
region is located within the southern Great Basin, a subprovince of the Basin and Range
Physiographic Province. The geological conditions are typical of the Basin and Range
province: a variety of intrusive and extrusive igneous, sedimentary and metamorphic
42
Frank A. D'Agnese et al.
115°
35°-l
Fig. 1 Map showing location of the Death Valley regional groundwater flow system,
Nevada and California, USA.
rocks have been subjected to several episodes of compressional and extensional
deformation throughout geological time. Elevations range from 90 m below sea level to
3600 m above sea level; thus, the region includes a great variety of climatic regimes and
associated recharge/discharge conditions.
Previous groundwater modelling efforts in the region have relied on 2D distributed
parameter models which have prevented accurate simulation of the 3D aspects of the
system, including the occurrence of vertical flow components, large hydraulic gradients,
and physical sub-basin boundaries (Waddell, 1982; Czarnecki & Waddell, 1984; Rice,
1984; Sinton, 1987).
Death Valley regional groundwater flow model calibration
43
In contrast, the distributed parameter 3D model used in this work allows
examination of the internal, spatial, and process complexities of the hydrological system.
These models require an accurate understanding of the processes affecting parameter
values and their spatial distribution (Domenico, 1972). The use of these models
introduces several concerns resulting from: (a) the large quantity of data required to
describe the system, (b) the complexity of the spatial and process relations involved, and
(c) the large execution times required to estimate numerous parameters during model
calibration. These problems are effectively managed in the present work by the use of
integrated GSIS techniques and a parameter estimation code. Model calibration is
accomplished in the following stages:
(a) integration of 2D and 3D data sets into a GSIS;
(b) development of a hydrogeological framework model to characterize the 3D
distribution of hydraulic properties and the boundaries of the regional system;
(c) evaluation of the hydrological conditions including regional groundwater recharge,
discharge and potential groundwater movement;
(d) development of a series of numerical model input arrays using an interface between
the GSIS database and the parameter estimation code;
(e) calibration of the numerical model using optimal parameter estimation methods ; and
(f) evaluation of estimated parameter values and their sensitivities.
THREE-DIMENSIONAL DATA INTEGRATION
Extensive integration of regional-scale data is required to characterize the hydrological
system, including point hydraulic-head data and other spatial data such as geological
maps and sections, vegetation maps, surface-water maps, spring locations, meteorological data and remote sensing imagery. Data are converted into a consistent digital format
using various traditional 2D GIS products (Faunt et al., 1993). To integrate these 2D
data with 3D hydrogeological data, several commercially available and public domain
software packages were utilized (Fig. 2). This integration allows the modeller ease of
data manipulation and aids in development of the conceptual and numerical models.
DEVELOPMENT OF DIGITAL 3D HYDROGEOLOGICAL CONCEPTUAL
MODELS
The 3D hydrogeological framework describes the geometry, composition and appropriate hydraulic properties of the materials that control groundwater flow. Development
of the framework model began with the assembly of primary data: digital elevation
models (DEM), geological maps and sections, and lithological well logs. Each of these
data types can be manipulated by standard GIS; however the merging of these diverse
data types to form a single coherent 3D digital model requires more specialized GSIS
software products. Construction of a 3D framework model involved four main stages:
(a) DEM data were combined with geological maps to provide a series of points
locating the outcropping surfaces of individual geological formations;
(b) geological sections and well-logs were properly located in 3D coordinate space to
define locations of the same geological units in the subsurface;
Frank A. D'Agnese et al.
44
(Manusciipt)
MAPS
TABLES
(Manuscript and Digital}
(Digital)
1
TEKTRONIX
w
'
ARC/INFO
(Scanning}
,. "
(Data Conversion}
"
INTERGRAPH
GIS
,
"
CPS-3
p
(Data Management, Analysis,
and Modeling}
(Griddins}
1
1
STRATAMODEL
SGM
(Hydrogeologic Framework
Model Construction}
VISUALIZATION
(INTERGRAPH, CPS-3, ARC/INFO,
STRATAMODEL)
OUTPUT
(Plotters, Printers. Files, Slides)
Fig. 2 Flow chart showing logical movement of modelling data through various GS1S
packages.
(c) surface and subsurface data were interpolated to define the tops of hydrogeological
units, incorporating the effects of major faults; and
(d) a hydrogeological framework model was developed by combining hydrogeological
unit surfaces utilizing appropriate stratigraphie principles to accurately represent
natural stratigraphie and structural relationships.
GSIS procedures were utilized to develop framework model attributes describing
hydraulic properties. For each hydrogeological unit, the value of hydraulic conductivity
was based on log-probability distributions developed for the study area by Bedinger et
al. (1989).
The regional groundwater flow system reflects interactions among all the natural and
anthropogenic mechanisms controlling how water enters, flows through, and exits the
system. In the DVRFS, quantification of these system components requires characterization of groundwater recharge through infiltration and groundwater discharge through
évapotranspiration (ET), spring flow and pumpage.
Maps describing the recharge and discharge components of the groundwater flow
system were developed using remote sensing and GIS techniques (D'Agnese el al.,
1996). Multispectral satellite data were evaluated to produce a vegetation map. The
vegetation map and ancillary data sets were combined in a GIS to delineate areas of ET,
including wetland, shrubby phreatophy te, and wet play a areas. Water-use rates for these
areas were then applied to approximate likely discharge.
Death Valley regional groundwater flow model calibration
45
Groundwater recharge estimates were developed by incorporating data related to
varying soil moisture conditions (including elevation, slope aspect, parent material, and
vegetation) into a previously used empirical method (D'Agnese et al, 1996). GIS
methods were used to combine these data to produce a map describing recharge potential
on a relative scale. This map of recharge potential was used to describe groundwater
infiltration as a percentage of average annual precipitation.
Quantification of spring discharge was achieved by developing a point-based GIS
map containing spring location, elevation, and discharge rate. Likewise, water-use
records for the region, which are maintained by surface-water basin and type of water
use, were used to develop a spatially distributed water-extraction map.
The system was simulated as steady-state and was intended to represent long-term
average conditions. This assumes that a long-term average for seasonal and pumpage
variations exists. Although this can not be proven rigorously, nothing about the available
data contradicts this assumption.
Evaluation of 3D hydrogeological data
Once completed, the 3D data sets describing the hydrogeological system were integrated
and compared to develop representations of the DVRFS suitable for simulation. The various configurations of the resulting digital 3D hydrogeological conceptual model help investigators during the modelling process to (a) determine the most feasible interpretation
of the system given the available database, (b) determine the location and type of additional data that will be needed to reduce uncertainty, (c) select the potential physical boundaries to theflowsystem, and (d) evaluate hypotheses about hydrogeological framework.
Conceptual model configurations typically included (a) descriptions of the 3D hydrogeological framework, (b) descriptions of system boundary conditions, (c) estimates of
the hydraulic properties of the hydrogeological units, (d) estimates of groundwater
sources and sinks, (e) hypotheses about regional and subregional flow paths, and (f) a
water budget. These GSIS techniques also aid modellers in developing multiple conceptual models for the flow system by displaying data control on interpreted products.
These methods are also used to discretize the 3D hydrogeological data sets for simulation of groundwater flow in MODFLOWP - the selected parameter estimation code.
OPTIMAL PARAMETER ESTIMATION
The MODFLOWP computer code is documented in Hill (1992), and uses nonlinear
regression to estimate parameters of groundwater flow systems simulated with the USGS
3D, finite-difference modular model, MODFLOW (McDonald & Harbaugh, 1988 ; Hill,
1990). Although the physics represented in the model is flow through porous media, on
the regional scale it is expected to reasonably represent groundwater flow through the
fractured rock characteristic of much of the DVRFS.
Nonlinear regression methods
Nonlinear regression estimates parameter values by finding the values that minimize the
Frank A. D'Agnese et al.
46
weighted sum of squared residuals, S(b), which is calculated as:
S(b) = &- ï?m
- I')
(1)
where, b is an np x 1 vector containing parameter values; np is the number of
parameters estimated by regression; y_ and v_' are n X 1 vectors with elements equal to
measured and simulated (using b) values of, for the DVRFS model, hydraulic heads and
spring flows; n is the number of measured or simulated hydraulic heads and flows; W
is an n x n weight matrix; and T superscripted indicates the transpose of the vector.
The weight matrix is diagonal, with the diagonal entries equal to the inverse of
subjectively determined estimates of the variances of the observation measurement
errors; if the values and the model are accurate the weighting will result in parameter
estimates with the smallest possible variance (Bard, 1974 ; Hill, 1992). In MODFLOWP,
initial parameter values are assigned and then are changed using a modified GaussNewton method that minimizes equation (1); the resulting values are called optimal
parameter values.
Parameter definition
Parameters may be defined to represent most physical quantities of interest, such as
hydraulic conductivity and recharge. MODFLOWP allows these spatially distributed
physical quantities to be represented using zones over which the parameter is constant,
or to be defined using more sophisticated interpolation methods. In either case,
multipliers or multiplication arrays can be used.
Parameter sensitivities
As part of the regression, sensitivities are calculated as: ôy^'/ôbj, the partial derivative
of the ith simulated hydraulic head or flow, }>/, with respect to the y'fh estimated
parameter, £>•, using the sensitivity-equation method (Hill, 1992). Because the
groundwater flow equations are nonlinear with respect to many parameters, sensitivities
calculated for different sets of parameter values will be different.
Besides being used in the regression calculations, sensitivities are useful to the
modeller because they reflect how important each measurement is to the estimation of
each parameter. The composite scaled sensitivity (CSS) is a statistic which summarizes
all the sensitivities for one parameter, and, therefore, indicates the cumulative amount
of information that the measurements contain toward the estimation of that parameter.
Combined scaled sensitivity for parameter j , Cj, is calculated as:
cJ = {[Li=linwl{oyi'!5bJ)2bjlyn}0-5
(2)
and is dimensionless. Parameters with large CSS values relative to those for other
parameters are likely to be easily estimated by the regression; parameters with smaller
CSS values may be more difficult to estimate. For some parameters the available
measurements may not provide enough information for estimation, and the parameter
value will need to be set by the modeller or more measurements will need to be added
to the regression. Parameters with values set by the modeller are called unestimated
Death Valley regional groundwater flow model calibration
47
parameters. Composite scaled sensitivities calculated for different sets of parameter
values will be different, but they are rarely different enough to indicate that a previously
unestimated parameter can subsequently be estimated.
Confidence intervals on the estimated parameter values can be calculated using
linear (first-order) theory with sensitivities calculated for the optimal parameter values.
Parameters with a large CSS tend to have small confidence intervals. Confidence
intervals are useful when trying to decide how many parameters are needed to estimate,
for example, hydraulic conductivity. If, for example, it is thought that four zones are
important, but the regression yields estimates that are within each other's confidence
intervals, it is likely that fewer zones are adequate. If, as would be expected, the
regression using fewer zones yields a similar model fit to the measurements, this result
would indicate that the available measurements are insufficient to distinguish between
a model with four zones or one with fewer zones.
NUMERICAL SIMULATION OF REGIONAL GROUNDWATER FLOW
Prior to numerical simulation, the 3D hydrogeological data sets, which are discretized
at various grid cell resolutions ranging from 100 to 500 m, were discretized for input
to MODFLOWP, for which a 1500 m grid was developed. This process inevitably
results in the further simplification of the flow-system conceptual model. The DVRFS
model is composed of 163 rows and 153 columns. The 74 817 cell model is vertically
discretized into three layers (500, 750 and 1500 m thick), using the methods described
in the following section. Model boundaries are dominantly no-flow with constant-head
boundaries specified for regions where interbasinal flux is believed to occur.
Flow parameter discretization
The cellular data structure of the 3D hydrogeological framework model allows it to be
easily reconfigured for use in MODFLOWP. The GSIS used in this study utilizes a
resampling function that produces horizontal "slices" from the 3D framework model.
In the case of the DVRFS model, these "slices" represent the material properties of
hydrogeological units at 0-500 m, 500-1250 m, and 1250-2750 m below the water table.
The subsurface materials were classified into eight "rock conductivity units" based on
the mean hydraulic conductivity for rocks occurring in each unit determined as described
by D'Agnese (1995). These slices were then reformatted into three 2D GIS maps. To
reduce the number of estimated parameters, these maps were reclassified from the eight
units to four zones representing large (Kl), moderate (K2), small (K3), and very small
(K4) hydraulic conductivity values. The resulting zones were not contiguous; each zone
included cells distributed through the model.
Spatially-distributed source/sink parameters
The GIS-based infiltration and évapotranspiration maps were also easily reconfigured
into arrays for use in MODFLOWP. In the case of évapotranspiration, a series of three
48
Frank A. D'Agnese et al.
maps were used to define inputs. Evapotranspiration is expressed in terms of a linear
function based on land surface elevation, extinction depth, and maximum
évapotranspiration rate. Each of these values were specified from GIS-based data sets
and resampled to a 1500 m grid. The spatial variability of maximum évapotranspiration
is described in a multiplication array that may be adjusted through estimation of a
percentage factor that is defined as an estimated parameter.
Groundwater infiltration is likewise specified using two grid-based GIS maps. To
define groundwater infiltration, the recharge potential map was reclassified into as many
as four zones representing high (RCH3), moderate (RCH2), low (RCH1), and no
(RCHO) recharge potential. A parameter defined for each zone represents the percentage
of average annual precipitation that infiltrates. A multiplication array is used to represent
the more predictable variation of average annual precipitation.
MODEL CALIBRATION
A number of conceptual models were evaluated using the regression methods in
MODFLOWP. For each conceptual model a best fit to head and flow observations is calculated; weighting of these observations was initially assigned by calculating the needed
estimates of variances from head standard deviations of 10 m and flow coefficients of
variation of 10%. The results were investigated for evidence of model error or data
problems, which was used with independent hydrogeological data to modify, and
hopefully improve, the existing conceptual model, observation data sets, or weighting.
Conceptual model evaluations
For the DVRFS model, three major conceptual model variations were evaluated during
calibration. These included changes to (a) the location and type of flow system boundary
conditions, (b) the definition of the extent of areas of recharge, and (c) the configuration
of hydrogeological framework features. The types of flow system boundaries were
adjusted in the north and northeast parts of the model area, where some boundaries were
converted from constant head, simulating flux into the model area, to no-flow, simulating
a closed flow system. The configuration of recharge areas was changed from a fixed,
single percentage of precipitation to a combination of three zones with varying
percentages. Numerous hydrogeological framework variations also needed to be tested
because the GSIS-produced distribution had "smoothed out" some important features.
New areas of small hydraulic conductivity were delineated into new distinct zones
including (a) northwest-southeast trending fault zones, (b) clastic shales, (c)
metamorphosed quartzites, and (d) isolated terrains of shallow Precambrian schists and
gneisses. The location, extent and hydraulic conductivity of these zones were critical in
accurately simulating existing steep hydraulic gradients. Areas of large hydraulic
conductivity were also delineated as new distinct zones. These typically included
northeast-southwest trending zones of highly fractured and faulted terrains. These zones
usually controlled dominant regional flow paths and large-volume flows to spring
discharge areas. All changes to the hydrogeological framework were supported by
hydrogeological information; no changes were made simply to produce a better fit.
Death Valley regional groundwater flow model calibration
49
Data re-evaluation
Model calibration also involved continual re-evaluation of the head and flow observation
data after each parameter estimation run. These inspections often resulted in locating
previously overlooked spurious data, which included: (a) head observations from
potentially perched or local systems located in or adjacent to recharge areas, (b) flow
data for springs that were representative of local conditions, (c) head data that were
clearly recorded incorrectly, and (d) spring elevations that had not been accurately
represented by the averaging algorithm of the GSIS. In addition, the weighting of heads
was modified so that measurements in high gradient areas had smaller weights: for 10
of the 501 heads, the standard deviations were increased from 10 to 30 m. The
coefficients of variation for some flows were decreased from 10% to 5 %. The changes
made resulted in a better model fit and improved parameter estimation runs.
Model fit
To obtain a clearer understanding of model strengths and inadequacies, the model was
examined for fits to hydraulic heads in areas of flat and steep hydraulic gradients,
reproduction of steep hydraulic gradients, and fits to spring flows. In areas of flatter
hydraulic gradients, simulated hydraulic heads are within 75 m of observed values
everywhere in the model and are generally within 50 m. In areas of steep hydraulic
gradients, the differences between simulated and observed heads are sometimes larger
(as large as 150 m), but all simulated gradients are within 60% of the gradients evident
from the data. The match is good considering the 2 000-m head drop across the system.
Matching spring flows was difficult but provided important information to the
calibration. Currently, the sum of all simulated springflowsis 60 000 m3 day"1; the sum
of observed spring flows is 120 000 m3 day"1. When weighted as described above, S(b)
for heads equals 21 000, for flows it is 4000, and the total is 25 000.
PARAMETER VALUES AND SENSITIVITIES
Figure 3 shows the CSS for a set of parameters currently providing the best model fit.
Based on this information, the seven parameters identified in black are estimated by
regression. The optimized parameter values and the values assigned to the unestimated
parameters are shown in Table 1. All values are reasonable; unreasonable optimized
values would have indicated likely model error (Poeter & Hill, 1996), so their absence
makes it more likely that the model accurately represents the groundwater system.
CONCLUSIONS
The available state-of-the-art GSIS and parameter estimation techniques utilized in this
study materially assisted in modelling the complex DVRFS. Three-dimensional
hydrogeological framework modelling allows characterization of the "data-sparse"
subsurface, while integrated image processing and hydrological process modelling using
50
Frank A. D'Agnese et al.
• ANIV3
• K5
• K1
• K2
Q
LU
• K3
• K4
a
t
DGHBg
z z
• GHBo
UJ
co
m ^
g CO
O
O
DGHBf
• GHBa
DGHBt
• RCH2
DANIV1
m
„r
O
m
T
O
PARAMETERS USED IN REGRESSION
(Black = Estimated; White = Not Estimated)
Fig. 3 Bar chart of combined scaled sensitivities for estimated (black) and unestimated
(grey) parameters used in the DVRFS model.
Table 1 Current parameter values used in the DVRFS model.
Parameter
Definition
Value
Kl
Large hydraulic conductivity
2 x 10° m day"1
K2
Moderate hydraulic conductivity
1 x 10"1 m day 1
K3
Small hydraulic conductivity
7 x 10"3 m day 1
K4
Very small hydraulic conductivity
1 x ÎO"4 m day 1
K5
Very large hydraulic conductivity
5 x 102 m day 1
ANIV1
Vertical anisotropy layers 1 and 2
1.0
ANIV3
Vertical anisotropy layer 3
200.0
RCH1
Percent average annual precipitation in recharge zone 1
0.010(1.0%)
RCH2
Percent average annual precipitation in recharge zone 2
0.075 (7.5%)
RCH3
Percent average annual precipitation in recharge zone 3
0.200(20%)
GHBg
Spring conductance (Grapevine Springs)
11.0
GHB0
Spring conductance (Oasis Valley)
2.00
GHBf
Spring conductance (Furnace Creek)
7.00
GHBa
Spring conductance (Ash Meadows)
20.0
GHB,
Spring conductance (Tecopa)
1.00
Death Valley regional groundwater flow model calibration
51
traditional GIS techniques support surface-based characterization efforts. The different
configurations of the digital 3D hydrogeolpgical conceptual model allows rapid
evaluation of various likely representations of the flow system.
While groundwater inverse problems are generally plagued by problems of
nonuniqueness, this work clearly demonstrates that, even for a complex groundwater
system, substantial constraints can be developed from groundwater model calibration.
The constraints used in this work include (a) a geological framework, which constrains
the alternative conceptual models; (b) testing possible conceptual models by determining
the parameter values needed to produce a best fit to the hydrological data (heads and
spring flows) using inverse modelling; and (c) testing the validity of the model by
considering the fit between the data and the associated simulated values and by
comparing simulated global budgets terms to field data. Because this is a real system,
the problem of nonuniqueness is never completely eliminated. But by effectively
satisfying more constraints, the probability is increased that the resulting model
accurately represents the physical system. The key is development and use of the proper
3D data sets which result in effective constraints on the model. The utilization of both
GSIS techniques and parameter estimation using nonlinear regression contributes
significantly to these objectives.
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