PASCO COUNTY

HERNANDO COUNTY

PASCO COUNTY

HILLSBOROUGH COUNTY

HILLSBOROUGH COUNTY

POLK COUNTY

PINELLAS COUNTY

28°30′

15′

28°00′

82°45′ 30′ 15′ 82°00′

0 5 10 MILES

0 5 10 KILOMETERS

FLORIDA

STUDY AREA

North Pasco BOUNDARY

Well field

Brooksville

Starkey

Well field

Cross Bar

Ranch

Well field

Cypress

Creek

Well field

Eldridge

Wilde

Well field

Cypress

Bridge

Well field

South Pasco

Well field

Cosme

Odessa

Well field

Section 21

Well field

Morris

Bridge

Well field

Northwest

Hillsborough

Well field

Land O

Lakes

New

Port

Richey

Temple

Terrace

Tarpon

Springs

Clearwater

Tampa

Brandon

Plant City

Zephyrhills

Lakeland

Dade

City

OLD

TAMPA

BAY

GULF

OF

MEXICO

LOCATION OF

STUDY AREA

US 41

SR 52 I-75

Testing the Sensitivity of Pumpage to

Increases in Surficial Aquifer System Heads

in the Cypress Creek Well-Field Area,

West-Central Florida—An Optimization Technique

U.S. Geological Survey

 

TAMPA BAY WATER 

SOUTHWEST FLORIDA WATER MANAGEMENT DISTRICT

WaterResources 

Investigations 

Report 02-4086

Prepared in cooperation with 

and the 
U.S. GEOLOGICAL SURVEY

Water Resources Investigations Report 02-4086 

Tallahassee, Florida

2002

Testing the Sensitivity of Pumpage to 

Increases in Surficial Aquifer System Heads 

in the Cypress Creek Well-Field Area, WestCentral Florida—An Optimization Technique

By Dann K. Yobbi

Prepared in cooperation with 

TAMPA BAY WATER and the

SOUTHWEST FLORIDA WATER MANAGEMENT DISTRICT
Copies of this report can be 

purchased from:

U.S. Geological Survey

Branch of Information Services

Box 25286

Denver, CO 80225-0286

888-ASK-USGS

The use of firm, trade, and brand names in this report is for identification purposes only 

and does not constitute endorsement by the U.S. Geological Survey.

For additional information

write to:

District Chief

U.S. Geological Survey

Suite 3015

227 N. Bronough Street

Tallahassee, FL 32301

Additional information about water resources in Florida is available on the Internet at 

http://fl.water.usgs.gov

U.S. DEPARTMENT OF THE INTERIOR

GALE A. NORTON, Secretary

U.S. GEOLOGICAL SURVEY

CHARLES G. GROAT, Director
Contents III

CONTENTS

Abstract.................................................................................................................................................................................. 1

Introduction ........................................................................................................................................................................... 2

Purpose and Scope....................................................................................................................................................... 3

Description of the Cypress Creek Well Field .............................................................................................................. 3

Ground-Water Flow System ........................................................................................................................................ 3

Description of Models ........................................................................................................................................................... 4

Ground-Water Flow Model.......................................................................................................................................... 5

Optimization Model..................................................................................................................................................... 8

Application of the Optimization Model................................................................................................................................. 10

Steady-State Formulation ............................................................................................................................................ 10

Transient Formulation.................................................................................................................................................. 15

Limitations................................................................................................................................................................... 18

Summary................................................................................................................................................................................ 19

Selected References............................................................................................................................................................... 20

FIGURES

1-2. Maps showing:

1. Location of study area and well fields ............................................................................................................ 2

2. Location of production and selected monitor wells in the Cypress Creek well field ..................................... 4

3. Chart showing generalized stratigraphic and hydrogeologic section, west-central Florida .................................... 5

4-5. Maps showing:

4. Location of rivers and springs......................................................................................................................... 6

5. Model grid used in the simulation of ground-water flow system ................................................................... 7

6. Flow chart of MODOPTIM main program.............................................................................................................. 9

7. Map showing head control cells used in the optimization model............................................................................ 11

8. Graph showing comparison between total optimal pumpage and average head recovery in the 

surficial aquifer system for selected management cases, simulating 1987 steady-state conditions ........................ 12

9. Spatial distribution of head recovery in the surficial aquifer system for Case D (462 head control cells) 

and a 5-foot target recovery, simulating 1987 steady-state conditions.................................................................... 14

10-15. Graphs showing:

10. Distribution of optimal pumpage among the 13 production wells for selected management 

cases and a 2-foot target head recovery, simulating 1987 steady-state conditions ......................................... 15

11. Comparison between total optimal pumpage and head in the surficial aquifer system at TMR-1, 

TMR-2, TMR-4, and TB-22 monitor well cells (Case A), simulating 1987 steady-state conditions............. 16

12. Comparison between total optimal pumpage and head in the surficial aquifer system at the 

13 production well cells (Case B), simulating 1987 steady-state conditions.................................................. 16

13. Comparison between average optimal pumpage and average head recovery in the surficial aquifer 

system for selected management cases, simulating transient-state conditions (180 days with 

no recharge)..................................................................................................................................................... 17

14. Temporal distribution of optimal pumpage considering a 3-foot linear rate of head recovery in 

the surficial aquifer system for selected management cases, simulating transient-state conditions 

(180 days with no recharge)............................................................................................................................ 17

15. Temporal distribution of target recovery head, head at optimal pumpage, and head at unmanaged 

pumpage considering a 3-foot head recovery at TMR-1 and TMR-2 surficial aquifer system well

cells, simulating transient-state conditions (180 days with no recharge)........................................................ 17
IV Contents

TABLES

1. Optimal pumpage and average simulated head recovery in the surficial aquifer system considering 

a 1 to 5 foot target head recovery for 1987 steady-state conditions ....................................................................... 12

2. Temporal change in optimal pumpage considering a 1 to 5 foot linear rate of target head recovery in 

the surficial aquifer system for selected management cases, transient-state conditions (180 days with 

no recharge) ............................................................................................................................................................ 17

CONVERSION FACTORS AND ABBREVIATIONS

*Transmissivity: The standard unit for transmissivity is cubic foot per day per square foot times foot 

of aquifer thickness [(ft3

/d)/ft2]ft. In this report, the mathematically reduced form, foot squared per day 

(ft2

/d), is used for convenience.

Sea level: In this report, “sea level” refers to the National Geodetic Vertical Datum of 1929 (NGVD of 1929)---a geodetic 

datum derived from a general adjustment of the first-order level nets of the United States and Canada, formerly called “Sea 

Level Datum of 1929.” Horizontal coordinate information is referenced to the North American Datum of 1927 (NAD of 

1927).

ACRONYMS USED IN THIS REPORT

Multiply inch-pound unit By To obtain

Length 

foot (ft) 0.3048 meter

mile (mi) 1.6090 kilometer

Area 

acre 0.4047 hectare

square foot (ft2

) 0.0920 square meter

square mile (mi2

) 2.5900 kilometer square

Flow 

inch per year (in/yr) 25.4 millimeter per year

million gallons per day (Mgal/d) 0.04381 cubic meter per second

Hydraulic Conductivity

foot per day (ft/d) 0.3048 meter per day 

Transmissivity*

foot squared per day (ft2

/d) 0.0920 meter squared per day

Leakance

foot per day per foot (ft/d)/ft 1.0 meter per day per meter

CNTB Central Northern Tampa Bay

ET evapotranspiration

MODFLOW U.S. Geological Survey Modular Three-Dimensional Ground-Water Flow Model

MODOPTIM computer program linking MODFLOW with an optimization routine

OROP Optimized Regional Operations Plan

SDI SDI Environmental Services, Inc.

SS sum-of-squares residuals

SWFWMD Southwest Florida Water Management District

TBW Tampa Bay Water

USGS U.S. Geological Survey
Abstract 1

Testing the Sensitivity of Pumpage to Increases in 

Surficial Aquifer System Heads in the Cypress Creek 

Well-Field Area, West-Central Florida–An Optimization 

Technique

By Dann K. Yobbi

Tampa Bay depends on ground water for most of the water supply. Numerous wetlands and lakes in Pasco County have been impacted by the high demand for ground 

water. Central Pasco County, particularly the area within the Cypress Creek well field, 

has been greatly affected. Probable causes for the decline in surface-water levels are 

well-field pumpage and a decade-long drought. Efforts are underway to increase surface-water levels by developing alternative sources of water supply, thus reducing the 

quantity of well-field pumpage.

Numerical ground-water flow simulations coupled with an optimization routine 

were used in a series of simulations to test the sensitivity of optimal pumpage to 

desired increases in surficial aquifer system heads in the Cypress Creek well field. 

The ground-water system was simulated using the central northern Tampa Bay 

ground-water flow model. Pumping solutions for 1987 equilibrium conditions and for 

a transient 6-month timeframe were determined for five test cases, each reflecting a 

range of desired target recovery heads at different head control sites in the surficial 

aquifer system. Results are presented in the form of curves relating average head 

recovery to total optimal pumpage. Pumping solutions are sensitive to the location of 

head control sites formulated in the optimization problem and as expected, total optimal pumpage decreased when desired target head increased. The distribution of optimal pumpage for individual production wells also was significantly affected by the 

location of head control sites.

A pumping advantage was gained for test-case formulations where hydraulic heads 

were maximized in cells near the production wells, in cells within the steady-state 

pumping center cone of depression, and in cells within the area of the well field where 

confining-unit leakance is the highest. More water was pumped and the ratio of head 

recovery per unit decrease in optimal pumpage was more than double for test cases 

where hydraulic heads are maximized in cells located at or near the production wells. 

Additionally, the ratio of head recovery per unit decrease in pumpage was about three 

times more for the area where confining-unit leakance is the highest than for other leakance zone areas of the well field. For many head control sites, optimal heads corresponding to optimal pumpage deviated from the desired target recovery heads. 

Overall, pumping solutions were constrained by the limiting recovery values, initial 

head conditions, and by upper boundary conditions of the ground-water flow model.

Abstract
2 Testing the Sensitivity of Pumpage to Increases in Surficial Aquifer System Heads in the Cypress Creek Well-Field Area, 

West-Central Florida—An Optimization Technique

The Tampa Bay area relies 

heavily on ground water for public 

supply. Much of the public water 

supply in Hillsborough, Pinellas, 

and Pasco Counties is from a 

regional system of 11 interconnected well fields operated by 

Tampa Bay Water (TBW) (fig. 1). 

These well fields currently supply 

about 60 percent of the drinking 

water for the tri-county area. Current year (2001) withdrawals from 

PASCO COUNTY

HERNANDO COUNTY

PASCO COUNTY

HILLSBOROUGH COUNTY

HILLSBOROUGH COUNTY

POLK COUNTY

PINELLAS COUNTY

28°30′

15′

28°00′

82°45′ 30′ 15′ 82°00′

0 5 10 MILES

0 5 10 KILOMETERS

FLORIDA

STUDY AREA

North Pasco BOUNDARY

Well field

Brooksville

Starkey

Well field

Cross Bar

Ranch

Well field

Cypress

Creek

Well field

Eldridge

Wilde

Well field

Cypress

Bridge

Well field

South Pasco

Well field

Cosme

Odessa

Well field

Section 21

Well field

Morris

Bridge

Well field

Northwest

Hillsborough

Well field

Land O

Lakes

New

Port

Richey

Temple

Terrace

Tarpon

Springs

Clearwater

Tampa

Brandon

Plant City

Zephyrhills

Lakeland

Dade

City

OLD

TAMPA

BAY

GULF OF MEXICO

LOCATION OF

STUDY AREA

US 41

SR 52

I-75

Figure 1. Location of study area and well fields.

the 11 well fields are permitted for 

158 million gallons per day 

(Mgal/d). Numerous wetlands and 

lakes have disappeared in Pasco 

County since about 1989. One of 

the areas that has shown considerable decline in ground-water levels 

is in the Cypress Creek well field, 

located in central Pasco County 

(fig. 1). Probable causes for the 

decline in the surface-water levels 

are well-field pumpage and a 

decade-long drought. Efforts are 

underway to increase surface-water 

levels in the affected area by developing alternative sources of water 

supply so that well-field pumpage 

can be cut to 121 Mgal/d by the year 

2002 and 90 Mgal/d by the 

year 2007.

A variety of techniques have 

been used to analyze the watersupply problems in west-central 

Florida, including the use of 

numerical ground-water flow 

models. A common use of the 

numerical models is to predict the 

response of an aquifer to planned 

INTRODUCTION
Introduction 3

stress. Use of these models involves 

simulating one strategy at a time, 

and from a group of related simulations, selecting the best strategy. 

However, simulating one strategy 

at a time does not guarantee an 

optimal or a completely effective 

strategy.

In 1998, TBW developed an 

Optimized Regional Operations 

Plan (OROP) for management of the 

11 regional well fields (Tampa Bay 

Water, 1998). The OROP utilizes an 

integrated hydrologic optimization 

model to manage 172 production 

wells at the 11 well fields. The management objective of the optimization model is to maximize groundwater levels at a select set of surficial aquifer system monitoring sites, 

called control points, while meeting 

projected demands. The optimization model optimizes biweekly production schedules for each of the 

11 well fields (172 wells) and seeks 

to maximize ground-water levels at 

a selected set of monitoring sites 

(currently 32 surficial aquifer 

system monitoring wells). The 

formulation accounts for variations 

in future water levels for a specified 

forecast period, and applies preferential weighting of prevailing 

ground-water levels to established 

target levels at monitor sites (Tampa 

Bay Water, 1998). The monitor 

wells were selected under the 

assumption that they would provide 

reasonable locations to monitor 

hydrologic stress due to well-field 

pumpage.

To facilitate the routine use of 

optimization techniques, the U.S. 

Geological Survey (USGS) in cooperation with Tampa Bay Water and 

the Southwest Florida Water Management District (SWFWMD), 

began a study in 1997 to apply these 

techniques to the existing central 

northern Tampa Bay (CNTB) area 

hydrologic flow model. The study 

included two phases:

(1) application of optimization 

techniques to the existing 

ground-water flow model of the 

central northern Tampa Bay area 

to determine parameter sensitivities and correlations and to estimate parameter values of the 

existing model; and,

(2) development of an optimization model to test the sensitivity 

of optimal pumpage to increases 

in surficial aquifer system heads 

at selected sites in and around the 

Cypress Creek well field.

Phase one was described by 

Yobbi (2000) and addresses the 

parameter estimation issue. Phase 

two is described in this report and 

addresses the management issue.

Calibration and management 

problems must be addressed 

because the relative worth of a 

ground-water management solution 

is dependent on how well the underlying ground-water flow model is 

calibrated. The use of one optimization tool, such as the one used in 

this study, eases the transition from 

model calibration to ground-water 

management and reduces the learning curve for users.

Purpose and Scope

The purpose of this report is to 

describe the use of an optimization 

technique to test the sensitivity of 

optimal pumpage to desired 

increases in surficial aquifer system 

heads at selected locations in the 

Cypress Creek well-field area of 

central Pasco County. The hydraulic 

response of the aquifer system was 

solved using an optimization algorithm (Halford, 1992) combined 

with MODFLOW (McDonald and 

Harbaugh, 1988). The report 

includes brief descriptions of the 

Cypress Creek well field, the 

ground-water flow system, and 

ground-water flow and optimization models. The remainder of the 

report is a discussion of optimization modeling results. Descriptive 

information about the hydrogeology 

and the ground-water flow model is 

contained in reports by SDI Environmental Services, Inc. (SDI, 

1997) and Yobbi (2000).

Description of the Cypress

Creek Well Field 

The Cypress Creek well field is 

about 7 mi2

 in areal extent and is 

located in central Pasco County 

between U.S. Highway 41 to the 

west and Interstate 75 to the east 

(fig. 1). The Cypress Creek well 

field is bisected by Cypress Creek, 

which flows southward through the 

center of the well field (fig. 2). The 

creek is poorly defined as it meanders through a large, swampy area 

within the well field. Most of the 

well field lies within a natural, relatively undisturbed area, which is 

surrounded by agricultural and residential areas. About 70 percent of 

the well field is classified as a wetland or lake (Perry, 1987), because 

the water table is at or above the 

land surface for part of the year; the 

remaining area is dry uplands that 

gently slope to Cypress Creek. Several wetlands in the Cypress Creek 

well field are augmented with 

ground water to protect the native 

flora and fauna.

Ground-Water Flow System

The ground-water flow system 

in the area is a multilayered system 

consisting of a thick sequence of 

carbonate rocks overlain by clastic 
4 Testing the Sensitivity of Pumpage to Increases in Surficial Aquifer System Heads in the Cypress Creek Well-Field Area, 

West-Central Florida—An Optimization Technique

deposits (fig. 3), and is described in 

detail by Ryder (1978). The deposits and carbonate rocks are subdivided into a hydrogeologic 

framework that forms a sequence of 

two aquifers and one confining unit. 

This framework includes the unconfined surficial aquifer system and 

the confined Floridan aquifer system. A leaky intermediate confining 

unit separates the aquifers. The 

Floridan aquifer system consists of 

the Upper and Lower Floridan aquifers that are separated by a middle 

confining unit. The middle confining unit contains saltwater in the 

study area, and freshwater flow is 

limited to the Upper Floridan aquifer. Recharge to the Upper Floridan 

aquifer is derived from the overlying surficial aquifer system by 

downward leakage through the 

intermediate confining unit. Part of 

PRODUCTION WELL

AND NUMBER

MONITOR WELL

AND NUMBER

EXPLANATION

TMR-1

9

I-75

N

WELL-FIELD

BOUNDARY

TMR-2

TMR-4

TB-22

TMR-1

CYPRESS

CREEK

SR 52

1 2

3

4

5

7

8

9

10

11

12 13 6

0

0

2 MILES

2 KILOMETERS

Figure 2. Location of production and selected monitor wells in the 

Cypress Creek well field.

this recharge is returned to the surficial deposits within the area as 

upward leakage, and most of the 

remainder leaves the area as it flows 

downgradient within the Upper 

Floridan aquifer.

About 30 million gallons of 

ground water is pumped daily from 

13 production wells in the Cypress 

Creek well field (fig. 2). All the 

wells are completed in the Upper 

Floridan aquifer with depths ranging 

from about 500 to 700 ft. The major 

production zone is from two cavernous zones of a dolomitic section of 

the Avon Park Formation, approximately 400 to 500 ft below sea level 

(Ryder, 1978). Many surficial aquifer system and Upper Floridan aquifer monitor wells have been 

constructed to monitor ground-water 

levels in and around the well field.

Ground-water flow was simulated using the USGS modeling 

software code MODFLOW 

(McDonald and Harbaugh, 1988). 

Optimization modeling is performed by linking the flow model 

code with an optimization routine 

(Halford, 1992). The combined 

ground-water flow code and 

optimization code is called 

MODOPTIM. The optimization 

routine determines the pumping 

rates that are passed in each call to 

MODFLOW and progresses toward 

a pumping solution by comparing 

heads determined by MODFLOW 

from one call to the next. MODFLOW is called repeatedly by the 

optimization routine until an optimal pumpage scheme is determined 

that maximizes the objective function.

DESCRIPTION OF MODELS
Description of Models 5

Ground-Water Flow Model

No optimization model can be 

developed without first having a 

calibrated ground-water flow 

model. The CNTB area hydrologic 

model developed by SDI (1997) 

and modified by Yobbi (2000) was 

used in this study. The SDI model 

was calibrated to transient 

conditions using hydrologic data 

from 1971 to 1993 (approximately 

1,200 weeks). The calibration 

period was the 12-year period 

from 1976 through 1987. Simulation of the 5-year period from 

1971 through 1975 prior to calibration was used to stabilize water 

levels and flows in the model. The Hawthorn Group

Limestone

Stratigraphic unit

Major

lithologic

unit

Hydrogeologic unit

Surficial sand,

terrace sand, phosphorite Sand Surficial aquifer

system

Intermediate confining unit

Undifferentiated

deposits

Peace River

Formation

Suwannee

Limestone

Ocala

Limestone

Oldsmar and

Cedar Key Formation

Avon Park

Formation

Arcadia

Formation

Tampa

Member

Upper

confining

unit

“Water-bearing

units”

Upper

Floridan

aquifer

Lower

Floridan

aquifer

Lower

confining unit

Middle

confining unit

Dolomite

and

limestone

Dolomite

and

limestone

Sand,

clay, and

limestone

Florida aquifer system

Figure 3. Generalized stratigraphic and hydrogeologic section, west-central 

Florida. (From Yobbi, 2000.)

6-year period from 1988 through 

1993, following the calibration 

period was chosen as the model 

verification period.

The model has an area of 

approximately 2,000 mi2 that 

includes all of Pasco County, most 

of Hernando, Pinellas and Hillsborough Counties, and part of Polk 

County. Six rivers (Alafia, Anclote, 

Hillsborough, Pithlachascotee, 

Weeki Wachee, and Withlacoochee) and their tributaries, 

several small streams along the 

coast, and some internally drained 

systems that flow only during 

extreme rainfall events, define the 

surface-water system of the model 

area (fig. 4). The two largest systems are the Hillsborough and 

Withlacoochee Rivers. Hundreds of 

lakes, swampy plains, and intermittent ponds are dispersed throughout 

the study area, ranging in size from 

less than 1/4 acre to more than 

2,500 acres. A total of 17 springs 

are located in the model area and are 

either found inland flowing to adjacent rivers or along the coast discharging directly to the Gulf of 

Mexico. 

Areally, the model is divided 

into a grid of 131 rows by 121 columns (fig. 5). The smallest cells, 

located in the center of the model, 

cover 0.25 mi2; largest cells cover 
6 Testing the Sensitivity of Pumpage to Increases in Surficial Aquifer System Heads in the Cypress Creek Well-Field Area, 

West-Central Florida—An Optimization Technique

1 mi2. The ground-water flow 

model consists of two layers. The 

upper layer (layer 1) represents the 

surficial aquifer system as an 

unconfined layer. The lower layer 

(layer 2) represents the Upper Floridan aquifer as a confined/unconfined layer. Vertical leakage through 

the intermediate confining unit is 

simulated implicitly using a leakance array. A high leakance value 

(0.35 (ft/d)/ft) simulates the absence 

of the confining unit. 

HERNANDO COUNTY

PASCO COUNTY

HILLSBOROUGH COUNTY

POLK

COUNTY

PINELLAS

COUNTY

28°30′

15′

28°00′

82°45′ 30′ 15′ 82°00′

0 5 10 MILES

0 5 10 KILOMETERS

CYPRESS CREEK

WELL FIELD

GENERAL LOCATION OF SPRING

EXPLANATION

WELL FIELD

Weeki Wachee River River

Pithlachascotee

River

Anclote

River

Brooker

Creek

Flint

Creek

Creek

Creek

Rocky

Brushy

Sweetwater

Creek

Hillsborough

River

Hillsborough

Creek

Cypress

Creek

Trout

Blackwater

Creek

Withlacoochee

Alafia

River

STUDY AREA

BOUNDARY

Brooksville

Land O

Lakes

Temple

Terrace

Tarpon

Springs

Clearwater

Tampa

Brandon

Plant

City

Zephyrhills

Lakeland

Dade

City

OLD

TAMPA

BAY

GULF OF MEXICO

Figure 4. Location of rivers and springs.

Rivers are simulated as river cells in 

layer 1 and, in those locations in 

model layer 2 where rivers are probably in direct hydraulic connection 

with the Upper Floridan aquifer. 

Wetlands are modeled as river cells 

in layer 1. Springs are represented 

by a head-dependent drain function, 

and discharge is linearly related to 

head differences between the spring 

pool and the potentiometric surface 

in layer 2. 

Several boundary conditions 

are used to define the lateral extent 

of the simulated ground-water flow 

system. Based on regional groundwater flow, most of the lateral extent 

in layer 1 is a no-flow boundary 

coinciding with flow lines. Conditions coinciding with the coastline 

of the Gulf of Mexico and Tampa 

Bay are represented in the model 

as specified heads. In layer 2, the 

southeastern and most of the northern boundaries are no-flow bound-
Description of Models 7

aries representing flow lines in the 

Upper Floridan aquifer. Part of the 

northern boundary is represented by 

a general head boundary in layer 2 

simulating flow out of the model. 

The extreme eastern edge of the 

model is represented as a specified 

head boundary. The coastline is 

represented as a no-flow boundary. 

130

COLUMNS

120

110

100

90

80

70

60

50

40

30

20

10

1

1 10 20 30 40 50 60 70 80 90 100 110 120

ROWS

PASCO COUNTY

HERNANDO COUNTY

HILLSBOROUGH COUNTY

POLK

COUNTY

PINELLAS

COUNTY

28°30′

15′

28°00′

82°45′ 30′ 15′ 82°00′

0 5 10 MILES

0 5 10 KILOMETERS

EXPLANATION

INACTIVE MODEL CELL

ACTIVE MODEL CELL

STUDY AREA BOUNDARY

Brooksville

Land O

Lakes

New

Port

Richey

Temple

Terrace

Tarpon

Springs

Clearwater

Tampa

Brandon

Plant City

Zephyrhills

Lakeland

Dade

City

OLD

TAMPA

BAY

GULF OF MEXICO

Figure 5. Model grid used in the simulation of ground-water flow system. (Modified from SDI Environmental Services, 

Inc., 1997).

Figures 7 and 8 in Yobbi (2000, 

pp. 9-10) show distribution of the 

boundary cells.

Recharge to the ground-water 

flow system averages 9.6 in/yr. Part 

of the recharge (2.0 in/yr) contributes to additional evapotranspiration 

(ET) and surface runoff. Simulated 

net leakage between the surficial 

aquifer system and the Upper Floridan aquifer was 6.8 in/yr downward, 

which represented 50 percent of the 

total flows in the surficial aquifer 

system. The quantity of total flow 

is in agreement with high leakance 

characteristics of the intermediate 

confining unit. Consequently, 

hydrologic conditions in the 
8 Testing the Sensitivity of Pumpage to Increases in Surficial Aquifer System Heads in the Cypress Creek Well-Field Area, 

West-Central Florida—An Optimization Technique

surficial aquifer system can significantly affect conditions in the 

Upper Floridan aquifer. Likewise, 

hydrologic conditions in the Upper 

Floridan aquifer can substantially 

affect conditions in the surficial 

aquifer system. 

Input data were obtained 

directly from the SDI (1997) and 

the USGS (Yobbi, 2000) models 

and included: starting water-level 

values, hydraulic conductivity of 

the surficial aquifer system, bottom 

altitude of the surficial aquifer system, riverbed conductance values 

and altitudes, intermediate aquifer 

system leakance, transmissivity of 

the Upper Floridan aquifer, horizontal anisotropy values of the 

Upper Floridan aquifer, boundary 

heads and boundary conductance 

values for the Upper Floridan aquifer, pumpage rates, and drain altitudes and conductances for the 

surficial aquifer system and the 

Upper Floridan aquifer. Input data 

arrays also included specified 

recharge and discharge rates to/

from the surficial aquifer system. 

Net recharge rates were calculated 

separately by subtracting ET from 

recharge in each model cell, thus in 

cells where ET exceeds recharge, a 

negative value of recharge was 

obtained. Rejected recharge simulated in the SDI (1997) model was 

simulated in this model by drains, 

where the elevation of the drain was 

set at land surface.

Hydraulic conductivity values 

for the surficial aquifer system 

(layer 1) range from 0.1 to15 ft/d 

and transmissivity values for the 

Upper Floridan aquifer (layer 2) 

range from 10,000 to 500,000 ft2

/d. 

Leakance values for the intermediate confining unit range from 3.5 x 

10-1 to 1.0 x 10-6 (ft/d)/ft with the 

higher value applied in areas where 

the confining unit is absent. A 

detailed description of model input 

parameters and calibration results 

are presented in SDI (1997) and 

Yobbi (2000). 

Optimization Model

The optimization model constructed for this study combines the 

CNTB ground-water flow model 

(Yobbi, 2000) with an optimization 

algorithm (Halford, 1992). The 

method minimizes the sum-ofsquares residuals (SS) between simulated and desired heads and is based 

on a modified Gauss-Newton method 

(Gill and others, 1981). This method 

was selected over other optimization 

methods (such as linear programming) because it does not require a 

feasible solution to maximize the 

objective function. This approach is 

particularly suitable for solution of 

the management problems formulated in this study because the 

optima can lie in the infeasible 

region. The SS is defined as:

(1)

where

hjs is the jth simulated head, in 

feet;

hjm is the jth target recovery 

head, in feet;

wi is the weighting factor; and

n is the number of head comparisons.

The optimization procedure 

uses several gradient-search minimization algorithms, which assume that 

the objective function defines a 

smooth continuous surface. The 

parameter change vector is solved 

using a quasi-Newton algorithm (Gill 

SS

n

Σ

j = 1

 wi hjs hjm [ ] ( ) – 2 = ,

and others, 1981). If the secondorder information fails or there is no 

prior parameter change information, 

then a variant of the Levenberg-Marquardt algorithm (Marquardt, 1963) 

is used. The optimization algorithms 

start with an initial pumping rate and 

converge to a local optimum. The 

magnitude and direction of change is 

based on minimization of the objective function (eq. 1), which is the 

smallest set of differences between 

the simulated and desired heads. The 

first step in the optimization process 

is to perform one execution of the 

model to establish the initial differences (residuals) between simulated 

and desired heads. The residuals are 

squared and summed to produce the 

SS objective function, which is used 

by the optimization program to measure model fit to the desired heads. In 

the next step, the sensitivity coefficients (derivatives of simulated 

water-level change with respect to 

parameter change) are calculated by 

the influence coefficient method 

(Yeh, 1986), using the initial model 

results. After the residuals and the 

sensitivities are calculated, a single 

pumping-estimation iteration is performed. The model is updated to 

reflect the latest pumping estimates 

and a new set of residuals are calculated. The entire process of changing 

pumpage in the model, calculating 

new residuals, and computing a new 

value for pumpage is continued iteratively until the SS is reduced to a 

specified level, or until a specified 

number of iterations is made 

(Halford, 1992). The major steps performed during each optimization 

iteration are summarized in figure 6.

An advantage of this optimization technique is the applicability 

for solving ground-water model 

calibration and ground-water management problems. Implementation 

of the method is straightforward and 
Description of Models 9

the computer code used for this 

application can be employed with 

data and operational requirements 

used for parameter estimation. 

Another advantage of this method is 

that model execution, input preparaOpen and read data files

Compute error statistics of

MODFLOW model

Report model statistics and

parameter estimates

Test convergence criteria

and iteration limit

OPTIN

ERROR

OVRSHOOT

OUTPUT

RANK

HESSUP

STPCHK

CONVER

JACOB

Compute gradients for each

parameter estimated

Rank parameters from most

to least sensitive

Update Hessian matrix

Estimate parameter

changes and constrain if

limits are exceeded

Stop

Yes

No

Yes

No

MODOPTIM

Error increased

and the parameter set has

not changed

Parameter set

changed because of

constraints

Yes

No

Figure 6. Flow chart of MODOPTIM main program.

tion, and output can be integrated 

into a spreadsheet and users can 

quickly set up and graphically compare simulation results. Most importantly, this method provides an 

alternate tool that the knowledgeable hydrologist can employ to 

better evaluate the ground-water 

resources.

The principal disadvantage of 

this optimization technique is that 

constraints are simply “targets” for 

the optimization model to shoot for 

and not “hard limits” as defined by 

other optimization methods, such as 

a linear programming. Thus, constraints can be violated. This is 

likely to happen when the objective 

function is poorly defined or when 

solution of the management problem is infeasible, such as with the 

present management application. 

This shortcoming can be addressed 

by removing those cells with large 

violations from the analysis or by 

increasing the weight given to that 

component of the least-squares 

objective to decrease the magnitude 

of the violation.

The management objective for 

this study is to maximize pumpage 

(Z) from the 13 production wells in 

the Cypress Creek well field such 

that the SS between simulated and 

desired recovery heads at selected 

control sites within and adjacent to 

the well field are minimized. Equal 

weights were applied to each site, 

which eliminates the subjectivity of 

finding the proper value of weight to 

preferentially minimize head deviations at one control site versus head 

deviations at another control site. 

Weights are generally used to adjust 

the relative sensitivity of the optimization routine; however, the optimization problem becomes difficult to 

solve if a proper value of weight is 

not selected.

The decision variable (variables to be determined as part of the 

optimization solution) provides the 

withdrawal quantities and are either 

the lumped or individual pumpage 

rates that represent the total pumpage from wells within the well field. 
10 Testing the Sensitivity of Pumpage to Increases in Surficial Aquifer System Heads in the Cypress Creek Well-Field Area, 

West-Central Florida—An Optimization Technique

The optimization model is subject 

to an inbuilt upper bound on 

hydraulic heads. This bound represents ground surface. The mathematical representation of the 

management objective is:

(2)

where

Qij is the ground-water pumpage 

at site i during time 

period j, 

m is the total number of pumping sites; and 

n is the total number of time 

periods.

The optimization model of the 

Cypress Creek well field and adjacent areas in central Pasco County 

was assigned calibrated parameter 

values (SDI, 1997) and given initial 

and boundary conditions (Yobbi, 

2000). Initial conditions were the 

average annual hydrologic conditions for the 1987 calendar year. 

The 1987 hydrologic conditions 

were considered suitable for several 

reasons.

1. The frequency of data collection 

was sufficient for calculation of 

representative annual averaged 

conditions.

2. Measured annual precipitation 

in 1987 was similar to the longterm average annual value.

3. The small net change in water 

levels measured in wells indicates that the change in storage 

in the aquifer systems was small 

during 1987, reflecting equilibrium conditions of the aquifer.

maximize Z = Qij ,

j

n

∑

i

m

∑

The optimization model was 

used in a series of simulations to 

test the sensitivity of optimal 

pumpage to the number of head 

control locations (4 to 462 sites) 

and desired recovery heads (1 to 

5 ft) in the Cypress Creek well 

field. Five scenarios (or cases) 

were formulated and pumping 

solutions for steady-state and transient conditions were simulated. 

The model was used to simulate 

steady-state ground-water flow for 

constant pumping solutions sustainable for an infinite length of 

time. Transient ground-water flow 

was simulated for short-term pumping solutions for a 6-month management timeframe. The following 

model applications were formulated.

• Case A—Four head control cells 

corresponding to TMR-1, 

TMR-2, TMR-4, and TB-22 surficial aquifer monitor well locations are used in this model 

application (fig. 7). These monitor wells are a subset of control 

points that are currently used by 

the OROP for the Cypress Creek 

well field. The monitor wells are 

located north, south, and west of 

the production wells.

• Case B—Thirteen head control 

cells corresponding to production 

well locations are used in this 

model application (fig. 7). These 

cells serve as a head control and 

pumping site.

• Case C—Eighty-seven head control cells corresponding to the 

area containing the 2-ft steadystate cone of depression pumping 

APPLICATION OF THE 

OPTIMIZATION MODEL

center are used in this model 

application (fig. 7). Case C considers the area most sensitive to 

well-field pumpage.

• Case D—Four hundred and 

sixty-two head control cells corresponding to areas within and 

adjacent to the well field are used 

in this simulation (fig. 7). Case D 

illustrates the sensitivity of the 

pumping solution for the entire 

well field.

• Case E—Six separate simulations are used in this model 

application. Each simulation is 

formulated to include only head 

control cells contained within its 

respective confining unit leakance zone. Therefore, the number of head control cells differs 

for each simulation because the 

number of model cells in each 

leakance zone is different 

(fig. 7). Case E illustrates the 

sensitivity of the pumping solution to changes in the desired target recovery head for separate 

leakance zone areas of the well 

field.

Steady-State Formulation

The management objective for 

these simulations was to maximize 

pumpage from the 13 production 

wells while minimizing deviations 

from the desired target recovery 

heads under equilibrium conditions. Results of the optimization 

simulations are given in table 1 and 

presented in the form of curves 

relating steady-state head recovery 

to optimal pumpage in figure 8. 
Application of the Optimization Model 11

0

0

2 MILES

2 KILOMETERS

EXPLANATION

CASE D--462 Head control cells

(contains all cells within and adjacent to well field)

CASE A-- 4 Head control cells

(contains monitor wells TMR-1, TMR-2, TMR-4, and TB-22)

CASE B--13 Head control cells

(contains all production wells)

CASE C--87 Head control cells

(contains area most sensitive to well-field pumpage)

MONITOR WELL

PRODUCTION WELL

= 1.0 x 10

= 8.0 x 10

= 1.0 x 10

= 2.0 x 10

= 4.0 x 10

= 6.0 x 10

-4

-4

-3

-3

-3

-3

1

2

3

4

5

6

CASE E--Head control cells for individual leakance

zones - Number refers to the following

leakance values (feet per day per foot):

1

50

70

60

55 60 70 75 80 65

65

55

ROWS

COLUMNS

SR 52

I-75

WELL-FIELD BOUNDARY CYPRESS CREEK

3

2

4

1

6

5

2

Figure 7. Head control cells used in the optimization model.
12 Testing the Sensitivity of Pumpage to Increases in Surficial Aquifer System Heads in the Cypress Creek Well-Field Area, 

West-Central Florida—An Optimization Technique

Table 1. Optimal pumpage and average simulated head recovery in the surficial aquifer system 

considering a 1 to 5 foot target head recovery for 1987 steady-state conditions

[Q, optimal pumpage; Mgal/d, million gallons per day]

Target 

head 

recovery, in 

feet

Case A

(4 head

 control cells)

Case B 

(13 head 

control cells)

Case C

(87 head

 control cells)

Case D 

(462 head 

control cells)

Q,

in Mgal/d

Average

simulated

head

recovery, 

in feet

Q,

in Mgal/d

Average 

simulated 

head

recovery,

in feet

Q,

in Mgal/d

Average 

simulated

head

recovery,

in feet

Q,

in Mgal/d

Average 

simulated

head

recovery,

in feet

1 27.1 0.6 28.2 1.0 27.8 0.9 27.4 0.3

2 23.8 1.3 26.6 1.8 25.7 1.8 24.8 0.6

3 20.5 2.0 24.9 2.6 23.2 2.8 21.8 0.9

4 15.9 2.7 22.7 3.6 20.6 3.6 19.0 1.1

5 9.8 3.5 20.7 4.5 18.2 4.3 15.9 1.3 AVERAGE HEAD RECOVERY, IN FEET

1

2

3

4

5

0

TOTAL OPTIMAL PUMPAGE,

IN MILLION GALLONS PER DAY

30 26 22 18 14

EXPLANATION

1.0 x 10-4

8.0 x 10-4

1.0 x 10-3

2.0 x 10-3

4.0 x 10-3

6.0 x 10-3

CASE E--Variable number of head control cells

located in the following leakance zones

(feet per day per foot):

B.

TOTAL OPTIMAL PUMPAGE,

IN MILLION GALLONS PER DAY

AVERAGE HEAD RECOVERY, IN FEET

30 26 22 18 14

1

2

3

4

5

A.

0

CASE A-- 4 Head control cells

(contains monitor wells TMR-1, TMR-2, TMR-4, and TB-22)

CASE B-- 13 Head control cells

(contains all production wells)

CASE C-- 87 Head control cells

(contains area most impacted by steady-state pumpage)

CASE D--462 Head control cells

(contains all cells within and adjacent to well field)

EXPLANATION

Figure 8. Comparison between total optimal pumpage and average head recovery in the surficial aquifer system for 

selected management cases, simulating 1987 steady-state conditions.
Application of the Optimization Model 13

Four curves, one for management 

Cases A, B, C, and D, are shown in 

figure 8A and six curves corresponding to individual confiningunit leakance zones (Case E) are 

shown in figure 8B. In these figures, 

the pumpage values represent the 

average optimal pumping solution 

for the 13 production wells, and the 

head recovery represents the average optimal head recovery that was 

simulated at the specified locations. 

Several aspects of the curves are 

apparent.

1. Pumping solutions are sensitive 

to the location of head control 

sites formulated in the optimization problem. More water is 

withdrawn for test cases where 

hydraulic heads were maximized in cells near production 

wells and within the pumping 

center cone of depression 

(Cases B and C).

2. Total pumpage decreases as 

head recovery increases.

3. Changes in head in the surficial aquifer system do not 

respond linearly to changes in 

pumpage.

4. Case B (control sites at production well cells) provides 

the highest rate of pumpage 

and the highest recovery of 

ground-water heads. The rate 

of head recovery per unit 

decrease in optimal pumpage 

for Case B (control sites at 

production well cells) is about 

twice as much as Case A 

(TBW control sites), about 25 

percent more than Case C 

(control sites within pumping 

center cells), and about 5 times 

more for Case D (control sites 

in all cells of well field).

5. The rate of head recovery per 

unit decrease in pumpage is 

greater for areas of the well 

field where permeability of the 

confining unit is higher than 

other areas of the well field 

where permeability of the confining unit is lower.

The highest amount of withdrawn water and the highest head 

recovery are simulated for the two 

cases (Cases B and C) with head 

control sites located in cells near the 

production wells and within the 

pumping center cone of depression. 

This suggests that a pumping advantage could be gained by maximizing 

hydraulic heads in cells near the 

production wells. The head recovery 

per unit decrease in optimal pumpage is more than twice as much for 

Cases B and C than for Cases A and 

D. A ratio of about 2 Mgal/d reduction per foot of average recovery is 

simulated for Cases B and C, while 

a ratio of about 5 Mgal/d and 

10 Mgal/d reduction per foot of 

average head recovery was simulated for Cases A and D, respectively. In other words, for 1 ft of 

average head recovery for Cases B 

and C, a decrease in optimal pumpage of about 2 Mgal/d (from 

30 Mgal/d to about 28 Mgal/d) is 

simulated. In contrast, for 1 ft of 

average head recovery for Case C, a 

decrease in optimal pumpage of 

about 5 Mgal/d (from 30 to about 

25 Mgal/d) is simulated, and a 

decrease of about 10 Mgal/d (from 

30 to about 20 Mgal/d) is simulated 

for Case D.

A pumping advantage also 

could be gained by maximizing 

hydraulic heads in cells where permeability of the confining unit is 

higher. For example, the rate of 

head recovery per unit decrease in 

pumpage is more than triple for the 

highest leakance zone (zone 6, 

fig. 7) than for other leakance zones 

(zones 1-5, fig. 7) of the well field. 

For 1 ft of average head recovery at 

head control sites in leakance zone 

6, optimal steady-state pumpage 

decreased from 30 Mgal/d to about 

25 Mgal/d. For 1 ft of average head 

recovery at head control sites in 

zones 1-6, optimal steady-state 

pumpage decreased from 30 to less 

than 15 Mgal/d.

The areal distribution of head 

recovery for the 5-ft target level 

using the 462 head control cells 

(Case D) is illustrated in figure 9. 

From a management perspective, it 

is unrealistic to control pumping 

using this large number of head 

control sites; however, simulation of 

this optimization problem is helpful 

in identifying areas of the Cypress 

Creek well field where maximizing 

hydraulic heads would most likely 

or least likely affect pumping solutions. Areas not meeting the 5-ft 

recovery target are of particular 

interest in figure 9. The western part 

of the well field and most areas outside of the well field are significantly below the 5-ft target head 

recovery. Several reasons for this 

simulation result are: (1) the 

selected head control sites are near 

the periphery of the steady state 

pumping cone of depression, (2) the 

initial steady-state heads are close to 

ground surface preventing the simulated head from changing substantially for different desired recovery 

heads, and (3) most of this area is 

represented in the ground-water 

flow model as either a river or drain 

boundary cell, which influences the 

upper part of the simulated flow 

system. A pumping advantage probably would not be gained by maximizing hydraulic heads within these 

areas of the well field. In contrast, a 

pumping advantage could be gained 

by maximizing hydraulic heads in 

areas of the well field meeting the 4- 

to 5-ft recovery target (fig. 9). Cells 

with head recoveries of 4 ft or more 

primarily correspond to the northern 
14 Testing the Sensitivity of Pumpage to Increases in Surficial Aquifer System Heads in the Cypress Creek Well-Field Area, 

West-Central Florida—An Optimization Technique

production well area where the 

pumping influence is greatest, confining-unit leakance is highest, and 

surficial aquifer system heads are 

substantially below land surface.

The distribution of optimal 

pumpage for individual production 

wells was significantly affected by 

the location of head control sites 

formulated in the optimization 

problem. The sensitivity of the 

0

0

2 MILES

2 KILOMETERS

BOUNDARY OF LEAKANCE ZONE- Number

is simulated leakance of the intermediate

confining unit, in feet per day per foot

BOUNDARY OF HEAD CONTROL CELLS

(Case D)

MONITOR WELL

PRODUCTION WELL

1x10-4

6x10-5

4x10-3

8x10-4

2x10-3

8x10-4

1x10-3

6x10-3

3x10-4

1x10-2

3x10-3

4x10-5

SR 52

CYPRESS CREEK

I-75

WELL-FIELD BOUNDARY

Less than 1

1 to 2

2 to 3

3 to 4

4 to 5

More than 5

HEAD RECOVERY, IN FEET 1x10-4

EXPLANATION

Figure 9. Spatial distribution of head recovery in the surficial aquifer system for Case D 

(462 head control cells) and a 5-foot target recovery, simulating 1987 steady-state 

conditions.

pumping solution to individual production wells can be determined 

from graphical analysis such as presented in figure 10, which shows the 

distribution of optimal pumping 

among the 13 production wells for 

simulation of the 2-ft target recovery head under steady-state conditions. Similar pumping patterns 

were observed for the 1-, 3-, 4-, and 

5-ft target recovery head simulations. As shown in figure 10, the 

distribution of optimal pumpage for 

Case A is quite different from the 

others. For Case A, most of the 

pumpage is focused in the northern 

portion of the well field close to 

head control sites TMR-1 and 

TMR-2, using production wells 3-5 

and 11-13. In contrast, optimal 

pumpage for Cases B and C is more 

broadly distributed with wells 1, 12, 
Application of the Optimization Model 15

and 13 at the periphery of the well 

field pumping the least amount of 

water.

The optimal steady-state heads 

for control sites used in formulations of Case A (TBW control sites) 

and Case B (control sites at production well sites) compared to optimal 

pumpage are presented in figures 11 

and 12, respectively. The graphs 

were generated using simulation 

results for target recovery heads of 

1 to 5 ft above the initial heads. The 

graphs can serve as approximate 

estimates of the required optimal 

pumpage to meet optimal steadystate heads in the cell containing the 

head control sites. Heads increase 

EXPLANATION

CASE A -- 4 Head control cells

(contains monitor wells TMR-1, TMR-2, TMR-4, AND TB-22)

CASE B -- 13 Head control cells

CASE C -- 87 Head control cells

STEADY STATE

(contains all production wells)

(contains area most impacted by steady-state pumpage)

4

3

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12 13

PRODUCTION WELL

OPTIMAL PUMPAGE, IN MILLION GALLONS PER DAY

4

3

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12 13

STEADY STATE

4

3

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12 13

CASE A

CASE B

4

3

2

1

0

1 2 3 4 5 6 7 8 9 10 11 12 13

CASE C

Figure 10. Distribution of 

optimal pumpage among the 

13 production wells for selected 

management cases and a 2-foot 

target head recovery, simulating 

1987 steady-state conditions.

with a decrease in pumpage for all 

locations. The small recovery in 

optimal head simulated for sites 

TMR-4 and TB-22 is of particular 

interest. The reason for the small 

change in head is due primarily to 

initial steady-state heads that are 

near land surface, thus preventing 

the simulated head from changing 

substantially for different desired 

recovery heads. The sites also are 

located in cells that are near the 

periphery of the pumping influence, which also limits the head 

recovery. Flattening of the line for 

production well 7 cell (fig. 12) indicates that heads are constrained by 

land surface.

Transient Formulation

The test period was chosen specifically to investigate the effects on 

the aquifer system that could be 

expected within a short period of 

time (180 days) with no recharge. 

Simulation of this management 

problem is useful in demonstrating 

the temporal performance of the 

optimization model and providing a 

comparison with the steady-state 

solution. Three of the five management formulations of the optimization problem (Cases A, B, and C) 

were evaluated. The objective function maximizes ground-water mining (withdrawal of more water than 

is recharged for a period of time), 

subject to desired target recovery 

heads. The optimization model was 

designed to maximize head recovery within a 6-month management 

timeframe and was divided into six 

time periods, each of 30 days (30, 

60, 90, 120, 150, and 180 days total 

elapsed time). The analysis was 

done in two steps. First, the 1987 

hydraulic head distribution was 

used as the initial conditions and run 

for 180 days with no recharge. The 

simulated hydraulic-head distribution at each of the six time periods 

was used as the basis for assigning 

the desired recovery target heads at 

head control sites. Second, 30-day 

pumping rates were determined by 

specifying recovery heads of 1 to 

5 ft at selected cells with a linear 

rate of recovery at respective time 

periods. These target recovery heads 

were specified based on the 

simulated response of the aquifer 

system using the 180-day transient 

simulation (step one).

Pumping solutions at respective 

time periods considering a linear rate 

of recovery for Case A (TBW control 

sites), Case B (control sites at production well cells), and Case C 

(control sites within pumping center
16 Testing the Sensitivity of Pumpage to Increases in Surficial Aquifer System Heads in the Cypress Creek Well-Field Area, 

West-Central Florida—An Optimization Technique

cells) are given in table 2 and graphically shown in 

figures 13 and 14, which relate average optimal head 

recovery at specified time periods to total optimal 

pumpage. The transient rate of pumpage for the planning period decreases when the target head recovery is 

raised (fig. 13). As with the steady-state results, formulating head control sites at or near production well 

cells (Cases B and C) in the optimization problem provide the highest rate of withdrawn water and the highest average optimal head recovery. Optimal pumpage 

averages about 23.7 Mgal/d for Case B, about 

22.5 Mgal/d for Case C, and about 19.6 Mgal/d for 

Case A. The change in head per unit decrease in 

pumpage is more than triple for Cases B and C than 

for Case A. A ratio of about 3 Mgal/d reduction of 

optimal pumpage per foot of recovery is calculated for 

Cases B and C, while a ratio of 9 Mgal/d reduction of 

optimal pumpage per foot of recovery is simulated for 

Case A. Results also indicate that the decrease in optimal pumpage is rather significant for higher target 

recovery heads than at lower target recovery heads. 

For example, the pumping solution at 180 days for 

Case A for the 1-ft recovery is 25.1 Mgal/d whereas 

the pumping solution at 180 days for the 5-ft target 

recovery head is 4.6 Mgal/d.

The temporal distributions of head at TMR-1 and 

TMR-2 control sites for simulation of the 3-ft target 

recovery head are presented in figure 15. The target 

recovery heads and the “unmanaged” simulated heads 

at the two sites also are included in this figure for 

30 26 22 18 14

75

TOTAL OPTIMAL PUMPAGE, IN MILLION GALLONS PER DAY

HEAD, IN FEET ABOVE SEA LEVEL

TMR-1

TMR-2

TMR-4

TB-22

70

65

60

55

12

Figure 11. Comparison between total optimal pumpage 

and head in the surficial aquifer system at TMR-1, TMR-2, 

TMR-4, and TB-22 monitor well cells (Case A), simulating 

1987 steady-state conditions.

comparison with “optimized” heads. The head deviation between the optimized heads and the desired 

target recovery heads is of particular interest. For well 

TMR-1, the optimized head at the end of 180 days is 

about 0.5 ft higher than the target recovery head and 

about 0.2 ft lower than the target recovery head for the 

cell containing observation well TMR-2. For most 

head control cells, the recovery head corresponding to 

optimal pumpage at the respective time period deviated somewhat from the target recovery head at the 

respective time period. This is a shortcoming of the

optimization technique used in the study because 

head violations are allowed. Overall, pumping solutions were constrained by the limiting recovery 

values, initial head conditions, and by upper 

boundary conditions of the ground-water flow model.

TOTAL OPTIMAL PUMPAGE, IN MILLION GALLONS PER DAY

HEAD, IN FEET ABOVE SEA LEVEL

TOTAL OPTIMAL PUMPAGE, IN MILLION GALLONS PER DAY

HEAD, IN FEET ABOVE SEA LEVEL

9

10

8

7

6

5

4

3

11

2

12

1

13

30 28 26 24 22 20

30 28 26 24 22 20

56

58

60

62

64

66

68

70

56

58

60

62

64

66

68

70

Figure 12. Comparison between total optimal pumpage 

and head in the surficial aquifer system at the 13 

production well cells (Case B), simulating 1987 steadystate conditions.
Application of the Optimization Model 17

Table 2. Temporal change in optimal pumpage considering a 1 to 5 foot linear 

rate of target head recovery in the surficial aquifer system for selected 

management cases, transient-state conditions (180 days with no recharge)

[Mgal/d, million gallons per day; ft, feet]

Time, in 

days Target head recovery

1 ft 2 ft 3 ft 4 ft 5 ft

 Case A (4 head control cells) Pumpage in Mgal/d

 30 27.7 25.6 23.4 20.9 19.0

 60 27.1 24.6 22.0 18.8 15.3

 90 26.7 23.9 20.8 16.9 13.7

120 26.3 23.1 19.6 14.6 11.3

150 25.8 22.3 18.4 12.9 8.6

180 25.1 21.2 16.8 10.0 4.6

Case B (13 head control cells) Pumpage in Mgal/d

 30 28.5 27.0 25.6 24.1 22.6

 60 28.4 26.7 25.0 23.4 21.8

 90 28.1 26.1 24.1 22.2 20.2

120 27.8 25.6 23.4 21.1 18.9

150 27.6 25.1 22.6 20.1 17.7

180 27.4 24.7 22.0 19.4 16.7

Case C (87 head control cells) Pumpage in Mgal/d

 30 28.1 26.2 24.3 22.4 20.5

 60 27.9 25.8 23.8 21.7 19.6

 90 27.6 25.3 22.9 20.5 18.0

120 27.4 24.7 22.0 19.3 16.8

150 27.2 24.2 21.3 18.4 15.5

180 27.0 23.9 20.8 17.7 14.6

30 26 22 18 14 10

0

1

2

3

4

5

AVERAGE HEAD RECOVERY, IN FEET

AVERAGE OPTIMAL PUMPAGE, IN MILLION GALLONS PER DAY

CASE A (4 head control cells)

CASE B (13 head control cells)

CASE C (87 head control cells)

EXPLANATION

Figure 13. Comparison between average optimal 

pumpage and average head recovery in the surficial 

aquifer system for selected management cases, simulating 

transient-state conditions (180 days with no recharge).

30 60 90 120 150 180

16

18

20

22

24

26

TIME, IN DAYS

OPTIMAL PUMPAGE,

IN MILLION GALLONS PER DAY

CASE A (4 head control cells)

CASE B (13 head control cells)

CASE C (87 head control cells)

EXPLANATION

Figure 14. Temporal distribution of optimal pumpage 

considering a 3-foot linear rate of head recovery in the 

surficial aquifer system for selected management cases, 

simulating transient-state conditions (180 days with no 

recharge).
18 Testing the Sensitivity of Pumpage to Increases in Surficial Aquifer System Heads in the Cypress Creek Well-Field Area, 

West-Central Florida—An Optimization Technique

30 60 90 120 150 180

TIME, IN DAYS

55

60

65

70

HEAD, IN FEET ABOVE SEA LEVEL

EXPLANATION

TMR-1 TARGET RECOVERY HEAD

TMR-1 HEAD AT UNMANAGED PUMPAGE

TMR-1 HEAD AT OPTIMAL PUMPAGE

TMR-2 TARGET RECOVERY HEAD

TMR-2 HEAD AT UNMANAGED PUMPAGE

TMR-2 HEAD AT OPTIMAL PUMPAGE

Figure 15. Temporal distribution of target recovery head, 

head at optimal pumpage, and head at unmanaged 

pumpage considering a 3-foot head recovery at TMR-1 

and TMR-2 surficial aquifer system well cells, simulating 

transient-state conditions (180 days with no recharge).

Limitations

This optimization model is 

designed not as a predictive tool, 

but as an interpretative one. The 

model applications are intended 

to provide insight about maximizing hydraulic heads and 

pumpage in the Cypress Creek 

well field given the proposed 

management formulations. However, the optimization method 

used in this study is not without 

limitations. (1) Practical 

uncertainties in the simulation 

(arising from model parameter 

uncertainties) and optimization 

(arising from the algorithms) 

components of the technique 

make it impossible to guarantee 

that the unique optimum solution 

will be found (if one exists). (2) 

The technique does not insure 

feasibility. As indicated earlier, 

recovery heads used in this model 

application are simply “targets” 

for the optimization model to 

shoot for and not “hard limits” as 

are defined in a linear programming model. As such, target 

recovery heads in this model can 

be violated. (3) Results of this 

optimization model are not 

unique, and different pumping 

solutions could be obtained with 

other optimization methods and 

different formulations of the optimization problem. Regardless of 

these limitations, the results presented here indicate that the technique is a useful alternative 

method for evaluating a variety of 

management alternatives for 

maximizing ground-water levels 

and pumpage in the Cypress 

Creek well field.
Application of the Optimization Model 19

The Tampa Bay area relies heavily on ground water for water supply. Numerous 

wetlands and lakes have been impacted in Pasco County, in particular, within the 

Cypress Creek well field in central Pasco County. An optimization model developed 

by Tampa Bay Water is being used to assist in the management of ground-water 

resources in the area. The optimization model relies on surficial aquifer wells to 

monitor hydrologic stress and to provide managed heads for the optimization model. 

Plans have been made to develop alternate sources for water supply so that pumpage 

from the well fields can be cut to 90 Mgal/d by the year 2007. Identification of optimal pumping solutions will provide better management of ground-water resources.

The ground-water flow system in the Cypress Creek well-field area consists of 

an unconsolidated surficial aquifer system, an intermediate confining unit, and a carbonate rock comprising the Upper Floridan aquifer. The thickness and leakance characteristics of the clay beds in the lower part of the surficial aquifer system are the 

principle controls on the vertical movement of water.

An optimization technique was used to test the sensitivity of optimal pumpage to 

increases in surficial aquifer system heads at selected locations in the Cypress Creek 

well field. The ground-water system was simulated using the USGS model MODFLOW and linked to an optimization routine. The ground-water flow model is based 

on data and information presented by SDI Environmental Services, Inc., and the 

USGS. Five management cases, which involved different head control sites, were 

evaluated using the optimization technique. The management objective was to maximize total pumpage in the Cypress Creek well field such that the sum-of-squares differences between simulated and target recovery heads at selected sites are 

minimized.

Pumping solutions for selected management cases were determined for 1987 

steady-state conditions and for a 6-month management timeframe. Results of the optimization simulations are presented in the form of curves relating average head recovery 

to total optimal pumpage. Pumping solutions are sensitive to the location of head control sites formulated in the optimization problem and as expected, total optimal pumpage decreased as optimal recovery head increased. Results suggest that a pumping 

advantage could be gained when hydraulic heads are maximized in cells near the production wells, in cells within the steady-state pumping center cone of depression, and 

in cells within the area of the well field where confining unit leakance is the highest. 

More water was pumped and the ratio of average head recovery per unit decease in 

withdrawn water was more than twice as much for test cases where hydraulic heads are 

maximized in cells located at or near the production wells. Additionally, the ratio of 

average head recovery per unit decrease in withdrawn water is about three times greater 

for the area where the confining unit leakance is the highest than for other areas of the 

well field. For most cells, recovery heads corresponding to pumping solutions are less 

than the maximum specified. This is a shortcoming of the optimization algorithms used 

in this study because head violations are allowed. Recovery heads are simply “targets” 

for the optimization model to shoot for and not “hard limits” as are defined in constrained linear programming techniques.

SUMMARY
20 Testing the Sensitivity of Pumpage to Increases in Surficial Aquifer System Heads in the Cypress Creek Well-Field Area, 

West-Central Florida—An Optimization Technique

SELECTED REFERENCES

Gill, T.E., Murray, W., and Wright, 

M.H., 1981, Practical 

optimization: Orlando, Fla., 

Academic Press, Inc., 401 p.

Halford, K.J., 1992, Incorporating 

reservoir characteristics for 

automatic history matching: 

Baton Rouge, Louisiana State 

University, Ph.D. dissertation, 

150 p.

Marquardt, D.W., 1963, An algorithm 

for least-squares estimation of 

nonlinear parameters: Journal of 

the Society for Industrial Applied 

Mathematics, v. 11, no. 2, p. 431-

441.

McDonald, M.G., and Harbaugh, A.W., 

1988, A modular threedimensional finite-difference 

ground-water 

flow model: U.S. Geological 

Survey Techniques of WaterResources Investigations, book 6, 

chap. A1, 

576 p.

Perry, R.G., 1987, Staff evaluation of 

CUP 203650 (Cypress Creek Well 

field): Southwest Florida Water 

Management District, Brooksville, 

Florida.

Ryder, P.D., 1978, Model evaluation of 

the hydrogeology of the Cypress 

Creek well field of west-central 

Florida: U.S. Geological Survey 

Water Resources Investigations 

Report 78-79, 68 p.

SDI Environmental Services, Inc., 

1997, Water resources evaluation 

and integrated hydrologic model 

of the northern Tampa Bay region: 

Consultant’s report in the files of 

Tampa Bay Water, Clearwater, 

Florida, 146 p.

Tampa Bay Water, 1998, Revised 

optimized regional operations 

plan: Tampa Bay Water, 

Clearwater, Florida, variously 

paged.

Yeh, W.W-G., 1986, Review of 

parameter identification 

procedures in groundwater 

hydrology: The inverse problem: 

Water Resources Research, v. 22, 

no. 2, p. 95-108.

Yobbi, D.K., 2000, Application of 

nonlinear least-squares regression 

to ground-water flow modeling, 

west-central Florida: U.S. 

Geological Survey Investigations 

Report 00-4094, 58 p.