CALIBRATION AND SENSITIVITY ANALYSIS OF A ...14. Diagram showing root-mean-square errors of...

CALIBRATION AND SENSITIVITY ANALYSIS OF A GROUND-WATER FLOW MODEL OF THE

COASTAL LOWLANDS AQUIFER SYSTEM IN PARTS OF LOUISIANA, MISSISSIPPI,

ALABAMA, AND FLORIDA

By Angel Martin, Jr., and C.D. Whiteman, Jr.

U.S. GEOLOGICAL SURVEY

Water-Resources Investigations Report 89-4189

Baton Rouge, Louisiana

1990

DEPARTMENT OF THE INTERIOR

MANUEL LUJAN, JR., Sejsretary

U.S. GEOLOGICAL SURVEYI

Dallas L. Peck, Director

For additional information write to:

District ChiefU.S. Geological SurveyP.O. Box 66492Baton Rouge, v LA 70896

Copies of this report can be purchased from:

U.S. Geological SurveyBooks and Open-File Reports SectionFederal Center, Bldg. 810Box 25425Denver, CO 80225

CONTENTSPage

Abstract................................................................. 1Introduction............................................................. 2Hydrogeology............................................................. 2Design of the ground-water flow model.................................... 4Model calibration........................................................ 9

Steady-state model.................................................. 11Transient model..................................................... 11Statistical optimization program.................................... 13Results of calibration.............................................. 14

Sensitivity analysis ..................................................... 24Method of study..................................................... 24Transmissivity and vertical leakance................................ 25Storage coefficient................................................. 34

Summary.................................................................. 53References............................................................... 54

ILLUSTRATIONS

Figure 1. Map showing location of the study area and major streams .... 32. Generalized hydrogeologic section showing zonation of the

aquifer system and direction of regional ground-water flow...................................................... 5

3. Map showing finite-difference grid with the active areaof the model.............................................. 7

4. North-south and east-west schematic sections through the coastal lowlands aquifer system showing representation of the permeable zones as model layers and the simulated boundary conditions....................................... 8

5. Maps showing the differences between model-simulatedand measured water-level altitudes for 1980............... 12

6. Graph showing results from the optimization program showing changes in parameter values and resulting changes in root-mean-square error of water-level residuals................................................. 15

7. Histogram showing the distribution of the residualsbetween model-simulated and measured water levels......... 18

8. Hydrographs showing comparison of model-simulated and measured water levels for selected wells in model layers 2 and 3............................................ 19

9. Hydrographs showing comparison of model-simulated and measured water levels for selected wells in model layers 4, 5, and 6........................................ 20

10-12. Maps showing areal distribution of:10. Transmissivity in the calibrated model for each

permeable zone....................................... 2111. Vertical leakance between the permeable zones in

the calibrated model................................. 2212. Storage coefficient in the calibrated model for

each permeable zone.................................. 23

III

ILLUSTRATIONS~Con1±nuedPage

Figure 13. Diagram showing root-mean-square errors of water-level residuals resulting from changes in transmissivity and vertical leakance of all mDdel layers................. 28

14. Diagram showing root-mean-square errors of water-levelresiduals resulting from changes in the transmissivityof model layer 2 and the vertical leakance betweenmodel layers 1 and 2...................................... 29

15. North-south water-level profiles showing the effect inmodel layers 2, 3, and 4 of changing the transmissivityof all model layers by factors; of 0.2 and 5............... 30

16. North-south water-level profiles; showing the effect in model layers 5 and 6 and in the average of all layers of changing the transmissivityf of all model layers by factors of 0.2 and 5...................................... 31

17. East-west water-level profiles showing the effect in model layers 2, 3, and 4 of changing the transmissivity of all model layers by factors of 0.2 and 5...................... 32

18. East-west water-level profiles showing the effect in model layers 5 and 6 and in the average of all layers of changing the transmissivity of all model layers by factors of 0.2 and 5...................................... 33

19. North-south water-level profiles: showing the effect inmodel layers 2, 3, and 4 of chianging the transmissivityof model layer 2 by factors of: 0.2 and 5.................. 35

20. North-south water-level profiles* showing the effect inmodel layers 5 and 6 and in the average of all layers ofchanging the transmissivity of model layer 2 by factorsof 0.2 and 5.............................................. 36

21. East-west water-level profiles showing the effect in model layers 2, 3, and 4 of changing the transmissivity of model layer 2 by factors of 0+2 and 5..................... 37

22. East-west water-level profiles showing the effect in model layers 5 and 6 and in the average of all layers of changing the transmissivity of model layer 2 by factors of 0.2 and 5................. f ............................ 38

23. North-south water-level profiles showing the effect inmodel layers 2, 3, and 4 of changing vertical leakance between all model layers by factors of 0.2 and 5.......... 39

24. North-south water-level profiles showing the effect in model layers 5 and 6 and in tfae average of all layers of changing vertical leakance between all model layers by factors of 0.2 and 5................................... 40

25. East-west water-level profiles ishowing the effect in model layers 2, 3, and 4 of changing vertical leakance between all model layers by factors of 0.2 and 5.................. 41

26. East-west water-level profiles showing the effect in model layers 5 and 6 and in the average of all layers of changing vertical leakance between all model layers by factors of 0.2 and 5...................................... 42

IV

ILLUSTRATIONS OcxitinuedPage

27. North-south water-level profiles showing the effect inmodel layers 2, 3, and 4 of changing vertical leakance between model layers 1 and 2 by factors of 0.2 and 5...... 43

28. North-south water-level profiles showing the effect inmodel layers 5 and 6 and in the average of all layers ofchanging vertical leakance between model layers 1 and 2by factors of 0.2 and 5................................... 44

29. East-west water-level profiles showing the effect in model layers 2, 3, and 4 of changing vertical leakance between model layers 1 and 2 by factors of 0.2 and 5.............. 45

30. East-west water-level profiles showing the effect in model layers 5 and 6 and in the average of all layers of changing vertical leakance between model layers 1 and 2 by factors of 0.2 and 5................................. 46

31. Diagram showing root-mean-square errors of water-levelresiduals resulting from changes in the storage coeffic ient of all model layers.................................. 47

32. North-south water-level profiles showing the effect in model layers 2, 3, and 4 of changing the storage coefficient of all model layers by factors of 0.2 and 5.................. 48

33. North-south water-level profiles showing the effect in model layers 5 and 6 and in the average of all layers of changing the storage coefficient of all model layers by factors of 0.2 and 5...................................... 49

34. East-west water-level profiles showing the effect in model layers 2, 3, and 4 of changing the storage coefficient of all model layers by factors of 0.2 and 5.................. 50

35. East-west water-level profiles showing the effect in model layers 5 and 6 and in the average of all layers of changing the storage coefficient of all model layers by factors of 0.2 and 5...................................... 51

TABLES

Table 1. Results of statistical analysis of water-level residualsof the steady-state calibrated model for 1980 conditions..... 11

2. Results of statistical analysis of water-level residualsof the transient calibrated model for the period 1957-82..... 16

3. Results of statistical analysis of water-level residuals showing the sensitivity of the steady-state calibrated model to changes in the transmissivity of all model layers... 26

4. Results of statistical analysis of water-level residualsshowing the sensitivity of the steady-state calibrated modelto changes in vertical leakance between all model layers..... 27

5. Results of statistical analysis of water-level residualsshowing the sensitivity of the transient calibrated model to changes in the storage coefficient of all model layers....... 52

CONVERSION FACTORS AND ABBREVIATIONS

For the convenience of readers who prefer System) units rather than the inch-pound units be converted by using the following factors:

to use metric (International used in this report, values may

Multiply inch-pound units By To obtain metric units

foot (ft) 0.3048

foot per mile (ft/mi) 0.1894

foot squared per day (ft2/d) 0.09290

inch (in.) 25.4

million cubic feet (Mft3 ) 28,320

million cubic feet per 0.3278

day (Mft3/d)

square mile (mi2 ) 2.590

mile (mi) 1.609

meter (m)

meter per kilometer (m/km)

meter squared per day (m2/d)

millimeter (mm)

cubic meter (m3 )

cubic meter per

second (m3/s)

square kilometer (km2 )

kilometer (km)

Sea level: In this report "sea level" refers to the National Geodetic Verti cal Datum of 1929 (NGVD of 1929) a geodetic datum derived from a general adjustment of the first-order level nets of both the Iftiited States and Canada, formerly called "Sea Level Datum of 1929."

VI

CALIBRATION AND SENSITIVITY ANALYSIS OF A GROUND-WATER FLOW MODEL

OF THE COASTAL LOWLANDS AQUIFER SYSTEM IN PARTS OF LOUISIANA,

MISSISSIPPI, ALABAMA, AND FLORIDA

By Angel Martin, Jr., and C.D. Whiteman, Jr.

ABSTRACT

The coastal lowlands aquifer system, consisting of aquifers in sediments of Miocene age and younger in southern Louisiana, Mississippi, and Alabama and in western Florida, is being studied as part of the U.S. Geological Survey's Gulf Coast Regional Aquifer-System Analysis program. This report describes the calibration and sensitivity analysis of a multilayer, finite-difference ground-water flow model developed to quantify flow in the aquifer system.

Initial calibration of the model by trial-and-error was followed by use of a parameter estimation program. Transmissivities of permeable zones within the aquifer system, vertical leakances between the zones, and the storage coefficient of the aquifer system were varied to obtain the best match between model-simulated and measured water levels for the period 1958-82. The mean error, root-mean-square error (RMSE), and standard deviation of the residuals between model-simulated and measured water levels were used to evaluate the progress of calibration, with greatest weight given to minimizing the RMSE.

Best calibration results were obtained in the model layer that repre sents the uppermost part of the aquifer system. Good results also were obtained in the subsurface part of the rest of the aquifer system where water- level gradients are relatively low and uniform. Calibration of the model is relatively poor in the outcrop areas of the lower part of the aquifer system and near some major pumping centers, where steep and irregular water-level gradients are difficult to simulate at the scale of the model.

Sensitivity analysis of the calibrated steady-state and transient models was performed by varying values of transmissivity, vertical leakance, and storage coefficient; the same parameters were varied during calibration. Changes in RMSE were used as the primary indicator of sensitivity. Near the calibrated values, the model is most sensitive to changes in transmissivity and almost as sensitive to changes in vertical leakance. By layer, the model is most sensitive to changes in the transmissivity of layer 2, which represents the upper part of the aquifer system, and in the vertical leakance between layers 1 and 2, which represents flow between a constant-head upper boundary and the top of the aquifer system. If transmissivity or vertical leakance is changed throughout the model, however, the effects are accentuated in the lower layers because much of the water flowing in these layers passes through and is affected by the overlying layers. The model is relatively insensitive to changes in the coefficient of storage because only a small part of the total flow is derived from storage.

INTRODUCTION

The coastal lowlands aquifer system is Geological Survey's Gulf Coast Regional program (Grubb, 1984). The GC RASA program tions that present a regional overview of the conditions in the principal aquifers of the objective of this study is to describe lowlands aquifer system. A digital flow model was the principal tool used to investigate

Aquif<sr

Gulf ground-water

flow

Calibration and sensitivity analysis wasdevelopment of a ground-water flow model of t^e coastal lowlands aquifer system. Calibration is the process by which model input parameters are adjusted so that model output matches observei conditions to a desired degree of accuracy. Sensitivity analysis involves changing the values of individual model inputs to observe the effects of the changes on model output. If a small change in input results in a large change in output, the model is said to be sensitive to that property. Conversely, if a large change in input produces only a small change in output, the model is insensitive to that

being studied as part of the U.S.-System Analysis (GC RASA)

includes a series of investiga- hydrogeologic and geochemical

Coastal Plain. A majorflow within the coastal

(McDonald and Harbaugh, 1988) in the aquifer system.

an integral part of the

property. Sensitivity analysis is useful in evaluating the confidence to beplaced in the accuracy of the values of aquifer properties adjusted during the calibration process.

This report describes the calibration ar|id sensitivity analysis of the ground-water flow model used to quantify flow in the coastal lowlands aquifer system. A steady-state version of the model for 1980 was used for calibration of transmissivities of permeable zones and vertical leakances between per meable zones within the aquifer system. A transient version of the model was used to calibrate the storage coefficients of! the sands, gravels, silts, and clays that make-up the aquifer system. Steady-state and transient calibra tions were based on miniinizing the mean errorr, RMSE, and standard deviation of the residuals between model-simulated and measured water levels. Initial calibration by trial-and-error was followed by use of an optimization program to check and improve calibration.

Sensitivity of the model was determined by comparing water-level residuals produced by the calibrated model with residuals produced by the model with one aquifer property changed. Propertie&s tested for sensitivity were aquifer transmissivity, vertical leakance, and storage coefficient. Results were evaluated on the basis of mean error, RMSE, and standard deviation.

Calibration and sensitivity results are comparisons of model-simulated and measured areal distribution of input parameter values

presented as statistical v/ater levels, plots showing the

and hydrographs.

HYDROGBOLOGY

The coastal lowlands aquifer system consists of sediments of Miocene age and younger which occur above the Jackson awl Vicksburg Groups of late Eocene and Oligocene age in parts of Louisiana, Misj-dssippi, Alabama, and Florida and adjoining offshore waters (fig. 1). Sand oaxirring near the top of the under lying Vicksburg Group in some areas was included in the aquifer system.

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The aquifer system is characterized by off-lapping, coastward thickening wedges of fluvial, deltaic, and marine sediments of Miocene age and younger (Martin and Whiteman, 1989, p. 3). Deltaic px>cesses have been dominant during deposition of these sediments. Advanc:.ng deltaic fronts pushed the shoreline and its associated beach, dune, and lagoonal deposits seaward while blankets of fluvial sediments were deposited <xi the coastal plain inland, and extensive marine deposits formed offshore. Hie coastal lowlands aquifer system is underlain by clay, silt, and lime bods of the Jackson and Vicksburg Groups. The Jackson and Vicksburg Groups act as a lower confining unit below the coastal lowlands aquifer system. Flow across the confining unit has a negligible effect on flow in the coastal lowlands aquifer system (Williamson, 1987).

The coastal lowlands aquifer system cons lists primarily of alternating beds of sand and gravel, silt, and clay. The most extensive sand beds cannot be traced with certainty for more than 30 to 50 mi. Dip of individual sand beds is southerly, ranging from about 10 to 50 ft/mi in the outcrop area and shallow subsurface in the northern part of the study area. Dip increases to the south and with increasing depth to over 100 ft/mi at depths of more than 3,000 ft. Individual clay and silt confining beds are not areally extensive. Gravel is common in the northern part of the study area but becomes finer and less common southward. Grain size of the sand also decreases southward, grading to sandy clay or silt and finally to clay. Martin and Whiteman (1989) describe in detail the hydrogeologic setting and regional flow in the coastal lowlands aquifer system.

Regional ground-water flow in the coastal lowlands aquifer system is primarily from north to south. Figure 2 is a generalized schematic diagram showing predevelopment regional flow. Average annual rainfall ranges from about 48 in. on the northern and western parts of the study area to more than 65 in. on coastal areas of Louisiana, Mississippi, and Alabama. Water entering the aquifer system in upland terrace> areas that is not discharged locally to streams or by evapotranspiration moves downward to the regional flow system and then toward discharge areas eit lower altitudes in the coastal plain and along major stream valleys. In places, pumping of ground water hasaltered the natural predevelopment gradients much of the natural discharge area.

and has initiated recharge in

Saltwater occurs downdip in the marine and deltaic parts of the aquifer system. Freshwater moving downdip from recharge areas tends to push the saltwater ahead of it, but the downdip movement of saltwater is blocked where the sand beds in the aquifer system pinch-out or are displaced by faulting. Water can move out of the downdip part of the sand beds only by upward leakage through overlying sediments (Martin and Whitoman, 1989, p. 4).

DESIGN OF THE GROUND-WATER FLOW MODEL

The coastal lowlands aquifer system was divided into five permeablezones, A-E as shown in figure 2, in order tol use a digital ground-water flow model to investigate the lateral and vertical distribution of flow (Weiss and Williamson, 1985). The massive coastward-thLckening wedge of sediments was first divided into zones in intensively-pumpad areas (Baton Rouge, Louisiana,

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Not to scaleEXPLANATION

BASE OF THE FLOW SYSTEM STUDIED

GENERAL DIRECTION OF REGIONAL

GROUND-WATER FLOW

Figure 2. Generalized hydrogeologic section showing zonation of the aquifer system and direction of regional ground-water flow.

to the east and Houston, Texas, to the west) pumpage information. Emphasis was placed on top and progressively thicker downward for flow system where most of the freshwater flow extended along the strike of the beds by zone as the same percentage of the total aqui centers. The zones pinch-out in the updip pattern, where progressively older bands of The lower zones pinch-out in the downdip of individual sand beds and the rise through zone pinches out downdip along the line at contain water with a dissolved-solids (milligrams per liter).

concent; ration

The five permeable zones have been designated, from youngest to oldest,zone A (Holocene-upper Pleistocene deposits),

c*i the basis of water-level and r taking the zones thinnest at the

besrt resolution in the part of theoccurs. The zones were then

maintaining the thickness of eacher system as at the pumping

di]?ection simulating the outcropsediment are exposed (fig. 2).

direcrtion reflecting the pinching out:he section of saltwater. Each

which all sand beds in the zonegreater than 10, OCX) mg/L

zone B (lower Pleistocene-upperPliocene deposits), zone C (lower Pliocene-upjper Miocene deposits), zone D (middle Miocene deposits), and zone E (lower Miocene-upper Oligocene deposits) (Grubb, 1987, table 1). These permeable zones are defined as hydrogeologic units. The series designations are given as a general indication of relative age, and the zones may contain sediments younger or older than the series age designation.

A finite-difference grid consisting of 78 rows by 70 columns of uniform blocks 5 mi on a side (fig. 3) was constructed for use with the digital flow model. The grid covers an area of 390 mi by 350 mi, or 136,500 mi2 . The model grid covers an area considerably larger than the study area, which consists of 58,400 mi2 inland and 10,100 mi2 offshore. Six layers comprise the model (fig. 4). Layers 2-6 represent permeable zones A-E, respectively. Layer 1, the uppermost layer, represents a constant-head upper boundary.

The water level specified for each node of the constant-head upper boundary (layer 1) is the altitude of the wat;er table at the center of that block. Layer 1 acts as a source or sink for all water entering or leaving the simulated flow system through land surface oliher than that removed by pumpage (fig. 4). All of the lateral model boundaritis except the western boundary and a small part of the northern boundary are taiated as no-flow boundaries. Along the eastern and most of the northern sides, the no-flow boundaries for layers 2-6 are at the updip limit of the out<3?op-subcrop area for each layer. A relatively small amount of water flowing into or out of the northern edge of the model in zone A, in the Mississippi River valley, is accounted for by a specified-flux boundary in model layer 2 (fig. 3). Flows across this bound ary, derived from a model of the Mississippi i River alluvial aquifer (D.J. Ackerman, U.S. Geological Survey, written canmun., 1988), were adjusted at the start of each stress period. The southern boundary for each of these layers is at the line along which water in all sands represented by that layer exceeds a dissolved-solids concentration of 10,000 mg/L.

Analysis of water-level data indicated that flow occurs across the western boundary under natural conditions and ini response to pumpage from zone A(model layer 2) in the Lake Charles area in southwestern Louisiana. In modellayers 2-6, the western model boundary was farmed using general-head-boundarynodes (fig. 3). General-head-boundary nodes permit flow across the boundary

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based on the gradient between model-simulated water levels at the boundary and specified water levels outside of the boundary (McDonald and Harbaugh, 1988, p. 11-1 through 11-27). The specified water levels used in this study were derived from a model of the Texas coastal lowlands aquifer system (P.O. Ryder, U.S. Geological Survey, written commun., 1988) and adjusted at each stress period.

The lower boundary of the model in the northern part of the study area, where freshwater is present throughout the coastal lowlands aquifer system, is at the top of the thick clays of the Vicksburg and Jackson Groups. Water leaking vertically between the underlying Eocene sediments and the coastal lowlands aquifer system is accounted for by a specified-flux boundary in layer 6. The specified fluxes used in this study, adjusted at each stress period, were derived from a model of the underlying Mississippi Embayment aquifer system (J.K. Arthur, U.S. Geological Survey, written commun., 1988). The rate of leakage is small in comparison to the volume of flow in the coastal lowlands aquifer system. To the south, where the lower part of the aquifer system contains saltwater, a no-flow boundary is placed at the bottom of the lowest sand bed containing water with no more than 10,000 mg/L dissolved solids.

Regionally extensive confining units do not occur within the coastal lowlands aquifer system as defined for this study, but large water-level differences do occur vertically within the flow system. In order to simulate the vertical restriction to flow by interbedded clays within the aquifer system, clays in vertically adjacent zones were treated as being equivalent to a single clay bed between the zones (Bredehoeft and Finder, 1970, p. 884). Leakance between the zones was computed by dividing an average value of vertical hydraulic conductivity for the clays by the total thickness of clay between midpoints of the zones. Computing leakance in this way provides an area! variability in leakance that corresponds to area! variations in the restriction to vertical flow that occur within the aquifer system.

MODEL CALIBRATION

Model calibration consists of adjusting model input parameters, initial conditions, and boundary conditions so that the model simulates the aquifer system to a desired degree of accuracy. The calibration process involves matching water levels, water-level changes, hydraulic gradients, flow rates, volumetric budgets, or a combination of these. The model simulating the coastal lowlands aquifer system was calibrated to 1980 steady-state conditions by matching model-simulated water levels to measured water levels. Although not at true steady state throughout the area in 1980, the rate at which water levels were changing was not considered to be significant in relation to the scale of the aquifer system (Martin and Whiteman, 1989, p. 14). The model was calibrated for transient conditions by matching water levels for the period 1958-87. The mean error, RMSE, and standard deviation of the residuals between model-simulated and measured water levels were used as quantitative comparisons during calibration. The RMSE shows the variation of the residuals about measured water levels. Standard deviation shows the variation of the residuals about the mean of the residuals. The RMSE and standard deviation are defined by:

root-mean-square error =

N

standard deviation =

N

, and

where hs is the nodel-siinulated water level; h is the measured water level; h is the mean of the residuals; and N is the number of water-level pairs com pared. Due to the relatively coarse lateral and vertical discretization of the aquifer system for modeling, a precise water-level match was not expected.

Flow rates and volumetric water budgets cjould not be measured with enough accuracy for quantitative comparison with model results because inherent errors in measurement of surface-water flow in the study area may be greater than total flow in the ground-water system. Model-computed flow ratjes, however, provided qualitative checks or results. The model cannot be considered to be adequately calibrated even though model-simulated and meas ured water levels may closely match if siimilatied flows are not reasonable.

Parameters adjusted by trial-and-error and optimization methods during calibration were the transmissivities of the regional zones, the vertical leakances between zones, and the storage coefficients of the zones. Boundary conditions and pumpage were assumed to be correct and were not changed after initial refinements described in Martin and Whiteman (1989). Transmissivity of each zone was calculated as the product of total sand thickness within the zone and an average lateral hydraulic conductJ.vity of the sands and is pre sented in this report in units of foot squared per day. Vertical leakance between zones was calculated as the average vtartical hydraulic conductivity of the clays within and between the zones divided by the total thickness of clay between midpoints of the zones and is given in units of inverse day (day1 ). The storage coefficient of each zone was calculated by summing the products of the total thickness of sand times an average specific storage for sand and the total thickness of clay times an average specific storage for clay. Storage coefficient is dimensionless. |

Initial adjustments of transmissivity and vertical leakance were made over the full extent of each zone. After preliminary calibration, changes made to improve one part of the model would worsen calibration in other parts of the model. To further refine the calibration, each model layer was divided into areas based on hydrologic distinctions in the corresponding permeable zone, such as the outcrops and areas of intense pumpage.

10

Steady-State Model

Results of steady-state calibration are shown in terms of mean error, RMSE, and standard deviation of water-level residuals for each model layer and for the entire model in table 1. Values of RMSE and standard deviation are similar because the means of the residuals In all model layers are small. Model layer 2 (zone A), on average, is most accurately simulated in the model. Model layers 3-5 (zones B-D) show increasing values of RMSE, indicating that calibration of the model becomes progressively poorer downward. The RMSE of layer 6 (zone E) is somewhat lower than that of layer 5, but the mean error of layer 6 is higher than that of any other layer.

Table 1. Results of statistical analysis of water-level residuals of the steady-state calibrated model for 1980 conditions

Modellayer

23456

All

Numberof

observations

34973164278132996

Meanerror(feet)

-0.246.595.69.74

17.093.81

Root-mean-square error

(feet)

14.7533.2240.1156.1245.8439.74

Standarddeviation

(feet)

14.7532.5639.7056.1242.5439.56

The largest differences between measured and model-simulated water levels occur in the outcrop areas of the lower zones and near major pumping centers (fig. 5). Ground-water gradients are steep over much of the outcrop areas of the lower zones because of relatively large topographic relief. Gradients are also steep near major pumping centers. The finite-difference blocks used in the model are large in relation to the distances over which large water-level changes occur, making it difficult or impossible to accurately simulate water levels in these areas.

Transient Model

The transient simulations use nine stress periods to simulate the period 1898-1987. The first three stress periods, each 20 years in length, simulate the calibration period 1898-1957. Six periods, each 5 years in length, simulate the calibration period 1958-87. Water-level and pumpage data prior to 1958 were too sparse for quantitative use in calibration. Available water- level and pumpage data were used qualitatively for the first three stress periods to adjust pumpage to cause simulated water levels at the end of each period to match available measured levels as closely as possible. This allowed the fourth, stress period to begin with transient conditions similar to those present in the aquifer system.

11

Values of transmissivity and vertical leakance from the steady-state calibration were used as initial values in transient calibration and were not significantly changed as a result of the trial-and-error transient calibration process. Initial values of storage coefficients for the transient simulation were determined using values of specific storage of 1.0 X 10 " 6 for sand (Lohman, 1972, p. 8) and 4.0 X 10~6 for clay (Ireland and others, 1984, p. 148-149). Storage coefficients were adjusted uniformly throughout the model to achieve the best match between model-simulated and measured water levels.

Hydrographs comparing model-simulated and measured water levels for the period 1958-87 were used throughout transient calibration. In addition to wells with long-term hydrographs, many wells were measured once to a few times during the calibration period. Water-level measurements made near the ends of stress periods 3-9 (1957, 1962, 1967, 1972, 1977, 1982, and 1987) were com pared with model-simulated water levels for the ends of the stress periods. Mean error and RMSE of the water-level residuals calculated after each model run during the trial-and-error calibration process were used to guide changes in input parameters for the next model run. Water-level measurements were not available for 1987 for the entire model area at the time of calibration of the transient model, so statistics for stress period 9 (1983-87) were not used in the calibration process.

The model is relatively insensitive to changes in storage coefficient, as discussed later, so calibration was less useful in refining the values of storage coefficient than it was for transmissivity and vertical leakance. Conversely, a broad range of uncertainty in the values of storage coefficient is acceptable because of the insensitivity. Final values of storage coeffic ients used throughout the aquifer system were one-half of the initial values. Although sensitivity analysis showed that mean error and RMSE could be reduced slightly by lowering the storage-coefficient values to one-tenth of the values actually used, this was not done because the resulting values would be unrea sonably low.

Statistical Optimization Program

Following trial-and-error calibration, a statistical optimization program (Durbin, 1983) was applied to the model in an attempt to improve the calibration. This program uses a modified Gauss optimization technique (Wilde and Beightler, 1967, p. 299) based on minimizing an objective function propor tional to the RMSE. The program executes the model many times, changing the value of a single parameter for each run. Parameter changes may be made for the entire model, by layer or by areas within layers. After each run, a comparison of water-level changes versus an initial base run is made and the tested parameter is then returned to its former value. Testing of the param eters is continued until each parameter to be optimized has been tested once. The program solves simultaneously for new values of all the parameters to be optimized based on the previous tests. The new parameter values should improve the water-level match. The new values for all of the tested param eters are then used to make a model run that forms the base run for another round of parameter changes. This iterative process is continued until change

13

of the RMSE of the entire model from one iteration to the next is less than aspecified level (closure criterion) or until a is exceeded. The closure criterion allows thelittle improvement in model results occurred as a result of the latest itera tion. Specifying a maximum number of iteratiors prevents the program from running indefinitely if the closure criterion cannot be met.

A.total of 27 parameters were initially included transmissivity of each layer and of model layers, with several layers divided and-error calibration. Storage coefficients whole and not by layer or area. Because directly proportional to the number of were eliminated if no significant changes of the first few program iterations.

into WE see

execution parametcsrs

specified number of iterations optimization program to stop if

selected for optimization. These vertical leakance between each pair

subareas as in the trial- optimized for the model as atime of the program is

being optimized, parameters parameters occurred duringtiie

The optimization program made relatively small changes from trial-and- error calibration results. Figure 6 shows the results from an optimization test in which transmissivities and vertical leiakances were optimized by layer and the storage coefficient was optimized for the entire model from trial-and- error calibrated values. Transmissivity values for all layers except 4 and 5 and vertical leakance between all layers excepb 1 and 2 were slightly higher than for the trial-and-error calibration. Thei largest changes were for trans missivity of layer 2 (1.1 times the initial value) and vertical leakance between layers 4 and 5 (slightly less than 1.1 times the initial value). Transmissivity for layers 4 and 5 each decreased slightly and storage coeffi cient increased slightly. Improvement in the RMSE of the entire model was about 0.2 ft, achieved after 15 iterations. The optimization program did not significantly improve the trial-and-error calibration in terms of RMSE, and the tested model input parameters were not significantly changed.

Results of Calibration

The best optimization program results were used in the final version of the model. Values of mean error, FMSE, and standard deviation for each model layer and for the entire model for stress periods 3-8 are shown in table 2. Values of standard deviation generally show the same relation to RMSE as in the steady-state calibration.

As with the steady-state version of the model, layer 2 (zone A) showsthe best match and layer 5 (zone D) shows themeasured water levels. Significant difference MS in mean error and RMSE occur for the same model layer in different stress jjeriods. This may be primarily due to the varying number and locations of mecisured water levels available for comparison.

poorest match of simulated and

layerjs iNegative mean-error values for all layer)s in stress period 3 indicate that model-simulated water levels generally ate lower than measured water levels. One explanation for this might be that simulated pumpage in stress period 3 may have been greater than the actual pumpage. Positive mean-error values for stress periods 4-8 indicate that midel-simulated water levels generally are higher than measured water levels.

14

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Model layer

23456

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the transient

Number of

observations

30155627020508

3449616718074

861

283121252222116994

348151301365150

1,315

34843716429555

calibrated model for the period 1957-82

Mean error (feet)

Stress period 3, 1

-0.82

Root-mean- igquare error

(feet)

957

18.27-17.22 33.17-18.00 32.42

-.23 44.57-6.00 38.05-4.81 27.86

Stress period 4, 1062

3.187.06-3.4916.9229.45

18.3530.5232.7046.5457.30

7.45 34.36


3.876.94.39

12.4521.09

15.2527.8634.5248.0848.26

7.29 35.37

Stress period 6, :

-1.363.566.80

18.0118.168.68

.972

19.5731.3138.0653.8246.8640.00


2.24 17.704.97 25.383.65 39.559.16 37.1527.304.74

54.4727.58

Standard deviation (feet)

18.2528.3626.9644.5737.5727.44

18.0829.6932.5143.3549.1633.54

14.7526.9834.5146.4443.4134.61

19.5231.1037.4550.7143.2039.04

17.5624.8939.3836.0047.1327.17

16

Table 2. Results of statistical analysis of water-level residuals of the transient calibrated model for the period 1957-82 Continued

Number Mean Root-mean- StandardModel of error square error deviationlayer observations (feet) (feet) (feet)


2 349 -0.18 14.75 14.753 73 7.09 33.40 32.644 164 6.74 40.31 39.745 278 2.64 55.84 55.776 132 19.70 46.82 42.48

All 996 4.92 39.83 39.52

Overall model, stress periods 3-8, 1957-82

23456

All

1,973539

1,0171,179

5215,229

1.113.411.78

11.6120.395.77

17.4530.4936.5450.9048.9235.96

17.3029.4535.9349.1043.9934.50

A histogram of the differences between model-simulated and measured water levels for stress periods 3-8 (fig. 7) shows that layer 2 has the best fit of simulated to measured water-level altitudes with 1,615 of 1,973 simu lated water levels within 20 ft of the measured water levels. The poorest fit is for layer 5 with 460 of 1,179 simulated water levels differing by more than 40 ft from the measured water levels.

Hydrographs of measured and simulated water levels (figs. 8 and 9) show comparisons between measured and simulated water levels through time at dis crete points within the aquifer system. The simulated water levels used in these figures were interpolated to the locations of the measured water levels by distance-weighted averaging of water levels computed at the centers of the grid blocks encompassing the measured level. The model-simulated water levels, which represent the average water level in several grid blocks, do not closely match the measured water levels, but general water-level trends are reproduced. Model calibration, illustrated by figures 8 and 9 and table 2, is satisfactory given the limitations of the model and of the input and compari son data. Further calibration effort would not significantly improve water- level matches.

The areal distribution of calibrated values of transmissivity, vertical leakance, and storage coefficient are shown in figures 10-12. Calibrated transmissivity values (fig. 10) increase downdip in all zones as zone thickness and total sand thickness increase. Maximum transmissivity values generally occur some distance north of the downdip limit of the zones because the thickness of the zones decreases near their downdip limit. Transmissivity

17

900

800

700

600

oI I

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400

300

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10DEL TOTAL NUMBER OFAVER OBSERVATIONS

Z?l 2 1,973

PHI 3 539

E2B 4 1,017

life 5 1,179

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Figure 7. The distribution of the simulated and measured

18

residuals between model- water levels.

MODEL STRESS PERIOD

3 40

ft50: 100JKS*P 200

%- is« « 300

_

. . j:!

I

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WELL Cu-635

CALCASIEU PARISH. LOUISIANA

MODEL LAYER 2

Location shown on figure 3

MODEL-SIMULATED WATER LEVEL

MEASURED WATER LEVEL

140


WELL Or-42

ORLEANS PARISH. LOUISIANA

MODEL LAYER 2



- YEAR8 -


WELL EB-301

EAST BATON ROUGE PARISH, LOUISIANA

MODEL LAYER 3

Location shown on figure 3MEASURED WATER LEVEL

Figure 8. Comparison of model-simulated and measured water levels for selected wells in model layers 2 and 3.

19

MODEL STRESS PERIOD

I______I______I______I______I


WELL EB 90

EAST BATON ROUGE PARISH. LOUISIANA

MODEL LAYER 4




WELL EB 468

EAST BATON ROUGE PARISH. LOUISIANA

MODEL LAYER 5


MODEL SIMULATED WATER LliVEL

WELL M011

PERRY COUNTY MISSISSIPPI

MODEL LAYER 6

Location shown on ligure 3

MODEL SIMULATED WATER LEVELMEASURED WATER LEVEL

Figure 9. Comparison of model-simulated and measured water levels for selected wells in model layers 4, 5, and 6.

20

distributions generally foOJcw the same pattern as total sand thickness within each zone (Martin and Whiteman, 1989, figs. 14-18). Overall, transmissivities are highest in the upper zones and decrease downward. Transmissivities for large areas in zones A and B are greater than 30,000 ft2/d, whereas most values in zone E are less than 10,000 ft2/d.

Calibrated vertical leakance (fig. 11) varies widely within the model area. Values range from less than 10~6 day-1 to more than 10"4 day'1 . Ver tical leakance is highest in and near the outcrop areas of the permeable zones and generally decreases downdip as zone thickness and total clay thickness within the zones increase generally the thicker the clay, the lower the vertical leakance. Variations of this pattern occur where values of clay vertical hydraulic ccnductivity are significantly higher or lower than the regional average for the zone. Overall, vertical leakance decreases in the lower permeable zones. Most values between the constant-head boundary and zone A are greater than 10~ 5 day'1 , whereas most values between the lower zones are less than 10 ~ 5 day1 .

Calibrated storage coefficients range from 1.0 X 10" 5 to 5.0 X 10"3 (fig. 12). Values increase downdip as sand and clay thicknesses increase in each zone. Because the specific storage of sand is lower than that of clay, the storage coefficient of a zone varies inversely with the sand percentage of the zone.

SENSITIVITY ANALYSIS

The approach to sensitivity analysis and the presentation of results in the following section were patterned, in part, on a report describing sensi tivity analysis of the Southeastern Coastal Plain aquifer system (Pernik, 1987). Results of the sensitivity analyses from other flow-modeling studies covering parts of the study area were used as a guide in changing aquifer properties.

Method of Study

Sensitivity of the model to changes in transmissivity, vertical leak ance, and storage coefficient was evaluated using steady-state and transient versions of the calibrated model. Transmissivity and vertical leakance were varied from 0.01 to 100 times calibrated values in the steady-state model. Storage coefficient was varied from 0.1 to 100 times the calibrated value using the transient model. Analyses of water levels, flow rates, and volu metric water budgets during calibration indicate that transmissivity of layer 2 (zone A) and vertical leakance between layers 1 and 2 (the constant-head upper boundary and zone A) were more sensitive than equivalent properties of other layers.

In sensitivity analysis, transmissivity was varied uniformly for all layers through the range of values and independently in layer 2. Similarly, vertical leakance was varied uniformly throughout the model and independently between layers 1 and 2% Storage coefficient was varied uniformly in all layers through the range of values. The mean error and RMSE of the residuals

24

between model-simulated and measured water levels were used to quantify the sensitivity test results. As during calibration, the standard deviation of the water-level residuals was also calculated to show variation of water-level residuals about the mean.

Transmissivity and Vertical Leakance

Model sensitivity to changes in transmissivity and vertical leakance through the range of values for all model layers is shown in tables 3 and 4 and figure 13. Values of FMSE and standard deviation indicate that, in terms of water-level changes, the model is more sensitive to reductions of transmis sivity and vertical leakance than to increases in these parameters (tables 3 and 4). Figure 13 shows the effects of varying both transmissivity and vertical leakage throughout the model. The FMSE ranges from less than 40 ft for the calibrated model (parameter multipliers equal to 1.0) to 65 ft when both parameters are increased by two orders of magnitude (factor of 100) to 4,750 ft when both parameters are decreased by two orders of magnitude (factor of 0.01). Within an order of magnitude of the calibrated values, the model is more sensitive to changes in transmissivity than to changes in vertical leakance.

The effects of varying the transmissivity of layer 2 and the vertical leakance between layers 1 and 2 are shown in figure 14. The pattern of changes in RMSE closely resembles the pattern formed when the parameters of all layers are varied (fig. 13) except that the range of changes in FMSE is less. The FMSE increases from the calibrated value of slightly less than 40 ft to 47.8 ft when both parameters are multiplied by 100 and to more than 1,050 ft when both parameters are multiplied by 0.01.

NkDrth-south and east-west water-level profiles of individual model layers and the water-level average of all layers showing the effects of varying calibrated values of transmissivity of all layers by a factor of 5 are shown in figures 15 to 18. Higher transmissivity values generally produce lower water-level gradients, with lower water levels in the recharge areas and higher water levels in the discharge areas. Conversely, lower transmissivity values produce higher water-level gradients, with higher water levels in the recharge areas and lower water levels in the discharge areas. This effect is shown most clearly in the north-south profiles (figs. 15 and 16). Varying transmissivity in all layers accentuates water-level changes in the deeper layers because much of the water flowing into or out of the deeper layers passes through and is affected by overlying layers.

In contrast to the sensitivity of the model to decreases in transmis sivity shown by water-level changes, total flow circulating within the aquifer system is more affected by increases in transmissivity than by decreases. Increasing calibrated transmissivities of all layers by a factor of 5 increases the total flow circulating within the aquifer system under 1980 conditions by about 63 percent, from 380 to 621 Mft3/d. Lowering transmis sivities to one-fifth the calibrated values reduces total flow in the aquifer system by about 22 percent, from 380 to 297 Mft3/d.

25

Table 3. Results of statistical analysis of wajber-level residuals shewingthe sensitivity of the steady-state calibratJBd model to changes in thetransmissivity of all model layers

[Multiplier is the factor by which the calibratedvalues of transmissivity were varied]

Multiplier

0.01

.10

1

10

100

Modellayer

23456

All

23456

All

23456

All

23456

All

23456

All

Numberof

observations

34973164278132996

34973164278132996

34973164278132996

34973164278132996

34973164278132996

1Mean Root-mean-error square error(feet) (feet)

-186.69 926.75-201.77 470.60-113.34 332.32-93.17 397.60

-.31 159.60-124.92 619.70

-28.31 128.58-39.78 100.10-33.74 116.32-35.98 155.459.93 76.24

-27.07 127.54

-.24 14.756.59 33.425.69 40.11.74 56.12

17.09 45.843.81 39.74

24.21 36.0941.04 71.4752.13 84.5240.73 81.5936.91 67.9436.29 66.83

40.23 54.2043.09 100.7459.80 108.8443.59 97.8215.05 73.3841.22 84.20

Standarddeviation(feet)

909.05428.13313.37387.23160.21607.29

125.6192.49111.67151.5075.87124.70

14.7532.5639.7056.1242.5439.56

26.8058.9266.7470.8257.2556.15

36.3891.7091.2387.7272.0973.46

26

Table 4. Results of statistical analysis of water-level residuals showingthe sensitivity of the steady-statevertical leakance

[Multiplier

between all model

is the factor by

calibrated model to changeslayers

which the calibrated valuesvertical leakance were

Multi- Modelplier layer

23

0.01 456

All

234

.10 56

All

23

1 456

All

23

10 456

All

23

100 456

All

Number of

observations

34973164278132996

34973

164278132996

34973

164278132996

34973164278132996

34973164278132996

Mean error(feet)

-367.79-209.21-342.94-512.36-542.59-415.75

-77.37-16.74-58.35

-121.81-104.75-85.88

-.246.595.69.74

17.093.81

22.2426.8132.7740.2857.9434.07

24.7727.9935.7145.0462.6737.48

varied]

Root-mean- square error

(feet)

432.25258.14373.98544.37549.80465.08

101.4057.4185.99150.23127.36116.25

14.7533.4240.1156.1245.8439.74

32.2741.7456.4364.8473.9853.98

36.1344.8163.6570.6579.1159.10

in

of

Standard deviation(feet)

227.42152.29149.64184.2589.13

208.55

65.6355.2963.3688.0872.7278.39

14.7532.5639.7056.1242.5439.56

23.4232.2246.0750.9046.1841.89

26.3435.2052.8357.5048.4645.69

27

100

60 LINE OF MEAN Interval in is variable

0.01 0.1 1

MULTIPLIER FOR TRANSMISS VITIES OF ALL LAYERS

Figure 13. Root-mean-square errors of ting from changes in transmissivity model layers.

100

water-level residuals resul- and vertical leakance of all

28

100

cvj

ROOT-MEAN-SQUARE

.01 0.1 1 10 MULTIPLIER FOR TRANSMISSIVITY OF MODEL LAYER 2

100

Figure 14. Root-mean-square errors of water-level residuals re sulting from changes in the transmissivity of model layer 2 and the vertical leakance between model layers 1 and 2.

29

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Increasing and decreasing only the transmissivity of layer 2 by a factor of 5 produces relatively small changes in the water levels of all layers (figs. 19-22). The effects of these changes ai?e relatively uniform throughout the model and are not accentuated in the deeper layers, as when the transmissivities of all layers are changed.

iNorth-south and east-west water-level profiles showing the results of

increasing and decreasing vertical leakance be'bween all layers by a factor of 5 from calibrated values are shown in figures !23-26. In general, these figures show that higher vertical-leakance values increase water levels throughout the aquifer system and lower values decrease water levels. Much of the effect of changing vertical leakances results from the effect these changes have en flow between the aquifer system and the constant-head upper boundary. As with transmissivity, changes in vertical leakances of all layers produce accentuated water-level changes in the deeper layers.

Total flow circulating in the aquifer system is more affected by increases in vertical leakance than by decreases. Increasing the calibrated values of vertical leakage by a factor of 5 increases total flow in the aquifer system by about 47 percent, from 380 to 558 Mft3/d. Lowering vertical leakances to one-fifth (0.2 times) the calibrated values reduces total flow in the aquifer system by about 22 percent, from 380 to 296 Mft3/d.

Varying vertical leakance between the constant-head upper boundary and layer 2 from 0.2 to 5 times the calibrated value produces relatively small and uniform changes In water levels throughout the aquifer system (figs. 27-30). These changes are not strongly accentuated in the lower layers.

Storage Ooefficisnt

Model sensitivity to changes in storage cx>efficient of all model layers is shown in table 5 and figures 31-35. The relative insensitivity of the model to changes in storage coefficient is besrt shown in figure 31. Large changes in storage-coefficient values result in relatively small changes in RMSE and standard deviation of individual layers and of all layers combined. Table 5 shows that mean error and RMSE could be lowered slightly by reducing the storage-coefficient values to one-tenth of the calibrated values; but, as noted in the section en calibration of the mcxtel, the resulting values would have been unreasonably low. The model is more sensitive to increases in the value of the storage coefficient above the calibrated value than to decreases.

Water-level profiles show the results of increasing and decreasing the calibrated value of storage coefficient by a factor of 5 (figs. 32-35). Water-level residuals resulting from changes in storage coefficient are greater in the lower model layers representing deeper zones. This is probably the result of the cumulative effect of water moving into or out of storage in the upper zones that impact the flow distribution in the lower zones.

Water levels rise throughout the aquifer system with increases in the storage coefficient and fall with decreases. More water enters the modeled aquifer system from storage with an increase [in storage coefficient, resulting in higher overall water levels. When storage; coefficients decrease fromcalibrated values, water levels must decline induce more recharge.

34

throughout the aquifer system to

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3»

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Figure 2

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evel

profiles

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6 and

in t

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Figure 2

1. E

ast-

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wat

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del

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, 3,

and

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Figure 22.

Eas

t-we

st w

ater-level p

rofiles

showing

the

effect i

n model la

yers

5 a

nd 6

and

in t

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verage of

all

laye

rs of

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rans

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Figure 23.

Nor

th-s

outh

water-level p

rofiles

show

ing

the effect i

n model

laye

rs 2

, 3,

an

d 4 of

cha

ngin

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all model layers by

fact

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Figure 2

4. North-south water-level pro

file

s sh

owin

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e ef

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in mo

del

laye

rs 5

and

6

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in t

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Figu

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6. East-west water-level p

rofiles

show

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Figu

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Nor

th-s

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Figure 28.

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s showing

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rs 5

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6

and

in t

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vera

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Figure 2

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Figu

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pro

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and

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verage of all

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ging

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tica

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ayers

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Figu

re 32. North-south water-level profiles

show

ing

the ef

fect

in mo

del

laye

rs 2

, 3, and

4 of cha

ngin

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e st

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3. N

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400

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300

400

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Figure 34. East-west water-level p

rofi

les

showing

the ef

fect

in model

laye

rs 2

, 3,

and

of changing

the

storage

coefficient of

all

mod

el l

ayer

s by

factors of 0.2

and

5.

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200

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sed

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LE

GR

EA

TLY

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GE

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TE

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GA

PS

IN

DIC

ATE

INA

CT

IVE

NO

DE

S

Laye

r 5

Lay

er 6

100

20

0

300

400

100

200

30

0

40

010

0 20

0 3

00

40

0

DIS

TA

NC

E F

RO

M W

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T E

DG

E O

F M

OD

EL

, IN

MIL

ES

Figu

re 35. East-west water-level p

rofi

les

show

ing

the

effect i

n model

layers 5

and

6 a

nd

in t

he a

vera

ge of

all

laye

rs o

f ch

angi

ng t

he s

torage c

oefficient o

f all model

layers b

y fa

ctor

s of

0.2 a

nd 5

.

Table 5. Results of statistical analysis of water-level residuals showingthe sensitivity of the transient calibrated. model to changes in thestorage coefficient of all model layers

[Multiplier is the factor by which the calibrated values of storage coefficient were varied]

Multi plier

0.10

1

10

100

Model layer

23456

All

23456

All

23456

All

23456

All

Number of

observations

1,973539

1,0171,179

5215,229

1,973539

1,0171,179

5215,229

1,973539

1,0171,179

5215,229

1,973539

1,0171,179

5215,229

Mean error (feet)

1.01

Root-mean- square error

(feet)

17.462.85 30.35.86 36.48

10.32 50.8118.61 48.105.02 35.80

1.11 17.453.411.78

11.6120.39

30.4936.5450.9048.92

5.77 35.96

2.66 17.367.918.5119.7626.8610.61

12.33

32.1537.8552.5853.4237.50

21.2614.55 36.2718.04 45.3627.8931.3219.07

57.9356.9042.26

Standard deviation (feet)

17.3129.3835.9849.2843.8434.53

17.3029.4535.9349.1043.9934.50

17.0730.3235.9648.5645.6434.58

18.8132.4940.0250.6846.7236.75

Increasing calibrated storage coefficients of all layers by a factor of 5 increases the amount of water derived from jstorage for the period 1898-1987 from 110,000 to 433,000 Mft3 . Lowering storage coefficients to one-fifth the calibrated values decreases the amount of wator derived from storage for the same time period from 110,000 to 23,000 Mft3 .| Although these results show a large difference in the amount of water derived from storage due to changes in storage-coefficient values, this amount of wafcer is only a small part of the total simulated flow in the aquifer system. With storage-coefficient values 5 times the calibrated values, the volume of water derived from storage is about 5 percent of the total simulated flow. With storage-coefficient values one- fifth of calibrated values, the volume of water derived from storage is less than 1 percent of the total simulated flow.

52

SUMMARY

A six-layer, finite-difference ground-water flow model was developed, calibrated, and tested for sensitivity in order to quantify regional flow in the coastal lowlands aquifer system of Louisiana, Mississippi, Alabama, and Florida. The model was initially calibrated by trial-and-error by varying values of transmissivity of the aquifers, vertical leakances between the aquifers, and the storage coefficients of the aquifer system in order to match model-simulated and measured water levels under steady-state and transient conditions. The mean error, RMSE, and standard deviation of the residuals between model-simulated and measured water levels were used to quantitatively evaluate the progress of calibration.

After trial-and-error calibration, a statistical optimization program was used to see if calibration could be improved. The program improves model calibration by minimizing an objective function which is proportional to the RMSE. The optimization program did not significantly change trial-and-error calibration results.

The model was calibrated best in layer 2, which represents the upper, youngest section of the coastal lowlands aquifer system. Calibration generally worsened in the lower model layers that represent older sections of the aquifer system. Relatively high residual errors in water levels in the lower model layers are largely due to topographic variations in the outcrop areas of the permeable zones represented by these layers. Large topographic variations within a grid block covering 25 mi2 produce steep, irregular water- level gradients which are difficult to reproduce in the model. Steep water- level gradients and relatively high water-level residuals may also occur near major pumping centers.

Sensitivity analyses of the calibrated steady-state and transient models show the effects of varying values of transmissivity, vertical leakance, and storage coefficients. In terms of mean error, RMSE, and standard deviation, results show that within an order of magnitude of calibrated values the model is most sensitive to changes in transmissivity. The model is more sensitive in terms of water-level change to reductions of transmissivity and vertical leakance than to increases in these parameters. The model is relatively insensitive to changes in storage coefficient over a wide range of values because only a small part of the total flow in the aquifer system is derived from storage.

When values of transmissivity or vertical leakance are changed one layer at a time, results obtained during calibration show that transmissivity of layer 2 and vertical leakance between layer 2 and the constant-head upper boundary are most sensitive. When transmissivity or vertical-leakance values are changed in all layers at the same time, the deeper model layers become more sensitive because flow between the constant-head upper boundary and the deeper layers is affected by the changes made in all intervening layers.

53

REFERENCES

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