Prepared in cooperation with the

NEVADA DEPARTMENT OF CONSERVATION AND NATURAL 

RESOURCES–DIVISION OF WATER RESOURCES

and LAS VEGAS VALLEY WATER DISTRICT

Estimates of Hydraulic Properties from a 

One-Dimensional Numerical Model of 

Vertical Aquifer-System Deformation, 

Lorenzi Site, Las Vegas, Nevada

U.S. Department of the Interior

U.S. Geological Survey

Water-Resources Investigations Report 03–4083
(Back of Cover)
Estimates of Hydraulic Properties from a 

One-Dimensional Numerical Model of 

Vertical Aquifer-System Deformation, 

Lorenzi Site, Las Vegas, Nevada

By Michael T. Pavelko

U.S. GEOLOGICAL SURVEY

Carson City, Nevada

2004

Water-Resources Investigations Report 03-4083

Prepared in cooperation with the

NEVADA DEPARTMENT OF CONSERVATION AND NATURAL 

RESOURCES–DIVISION OF WATER RESOURCES and

LAS VEGAS VALLEY WATER DISTRICT
U.S. DEPARTMENT OF THE INTERIOR

GALE A. NORTON, Secretary

U.S. GEOLOGICAL SURVEY

CHARLES G. GROAT, Director

Any use of trade, product, or firm names in this publication is for descriptive

purposes only and does not imply endorsement by the U.S. Government

For additional information Copies of this report can be

contact: purchased from:

District Chief U.S. Geological Survey 

U.S. Geological Survey Information Services

333 West Nye Lane, Room 203 Building 810

Carson City, NV 89706–0866 Box 25286, Federal Center

Denver, CO 80225–0286

email: GS-W-NVpublic-info@usgs.gov

URL: http://nevada.usgs.gov
CONTENTS III

CONTENTS

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

Introduction............................................................................................................................................................................ 1

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

Study Area.................................................................................................................................................................. 5

History of Land Subsidence in Las Vegas Valley ...................................................................................................... 5

Previous Investigations .............................................................................................................................................. 6

Acknowledgments...................................................................................................................................................... 6

Hydrogeology ........................................................................................................................................................................ 6

Lorenzi Site ................................................................................................................................................................ 8

Mechanics of Vertical Aquifer-System Deformation ............................................................................................................ 8

Principle of Effective Stress ....................................................................................................................................... 9

Theory of Hydrodynamic Consolidation ................................................................................................................... 10

Numerical Model................................................................................................................................................................... 10

Conceptual Model ...................................................................................................................................................... 10

Discretization ............................................................................................................................................................. 12

Boundary Conditions ................................................................................................................................................. 13

Initial Head and Compaction Conditions................................................................................................................... 14

Transient Progression................................................................................................................................................. 14

Hydraulic Properties................................................................................................................................................... 16

Model Calibration.................................................................................................................................................................. 17

Observation Data........................................................................................................................................................ 19

Observation Weights....................................................................................................................................... 20

Sensitivity................................................................................................................................................................... 23

Model Fit.................................................................................................................................................................... 25

Estimated Parameter Values .................................................................................................................................................. 28

Simulated Conditions................................................................................................................................................. 28

Model and Regression Limitations........................................................................................................................................ 30

Summary and Conclusions .................................................................................................................................................... 32

References Cited.................................................................................................................................................................... 33

FIGURES

1. Maps showing the location of Las Vegas Valley and the Lorenzi site, Nevada ..................................................... 2

2. Map showing land-subsidence contours for 1963–2000, benchmarks used to help 

estimate historic compaction trends, wells used to help estimate historic water-level 

trends, selected faults, and the Lorenzi site, Las Vegas Valley, Nevada ................................................................ 4

3–5. Schematic diagram showing:

3. A simplified hydrogeologic cross section of the Las Vegas Valley aquifer 

system, Nevada................................................................................................................................................. 7

4. The generalized hydrogeology, piezometers, and extensometer at the Lorenzi site, 

Las Vegas, Nevada ........................................................................................................................................... 8

5. The generalized hydrogeology of the conceptual model and model grid, including 

a close-up of the model grid showing variable cell spacing, for the Lorenzi model, 

Las Vegas, Nevada ........................................................................................................................................... 11

6. Graph showing the initial, starting preconsolidation, and 1992 conceptual heads 

for the Lorenzi model, Las Vegas, Nevada ............................................................................................................ 13
IV Estimates of Hydraulic Properties for a 1-D Numerical Model of Vertical Aquifer-System Deformation, Lorenzi Site, Las Vegas, NV

7. Hydrographs showing (A) heads for P.J. Goumond and SNMRE wells, used to estimate 

historic specified heads, and historic specified heads used in the Lorenzi model and 

(B) daily average heads for USGS-PZS, USGS-PZM, and USGS-PZD, used as recent

specified heads in the Lorenzi model, Las Vegas, Nevada..................................................................................... 15

8–18. Graphs showing: 

8. (A) Daily average water levels from USGS-PZD, (B) daily deformation 

from USGS-EXT1, and (C) stress-deformation data from USGS-PZD and 

USGS-EXT1, Lorenzi site, Las Vegas, Nevada ............................................................................................ 17

9. USGS-PZD water levels and USGS-EXT1 deformation for July 17–26, 1999, 

a period of diurnal pumping with an extensometer record contaminated by

thermal effects, Lorenzi site, Las Vegas, Nevada.......................................................................................... 18

10. Estimated, interpolated, and extrapolated compaction data used as historic 

observations in the Lorenzi model (1901–95), compaction measured at 

selected benchmarks, relative to 1963, and an InSAR-derived compaction 

estimate (1963–98), Las Vegas, Nevada........................................................................................................ 20

11. (A) daily deformation measured at USGS-EXT1 and (B) time spans for 

recent-period observations, by observation type, for the Lorenzi model, 

Las Vegas, Nevada......................................................................................................................................... 21

12. Composite scaled sensitivities for the estimated parameters of the Lorenzi

model, Las Vegas, Nevada............................................................................................................................. 24

13. (A) historic simulated and estimated and (B) recent simulated and measured 

deformation data for the Lorenzi model, Las Vegas, Nevada........................................................................ 25

14. Simulated deformation versus observed deformation for (A) the historic period 

and (B) the recent period of the Lorenzi model, Las Vegas, Nevada ............................................................ 26

15. Weighted residuals versus time for the (A) entire model and (B) recent period 

of the Lorenzi model, Las Vegas, Nevada ..................................................................................................... 27

16. Simulated heads for selected years of the Lorenzi model, Las Vegas, Nevada............................................. 29

17. Simulated deformation, by aquifer system and aquifer-system unit, for 

(A) the entire model and (B) the recent period, and (C) USGS-PZD specified heads,

for the recent period of the Lorenzi model, Las Vegas, Nevada.................................................................... 30

18. Initial heads and simulated head profiles for the calibrated model and an 

intermediate model, for 2000, the Lorenzi model, Las Vegas, Nevada......................................................... 32

TABLES

1. Well-construction data for piezometers and the extensometer at the Lorenzi site,

Las Vegas, Nevada ................................................................................................................................................. 5

2. Historic observations and weight-related statistics used with the Lorenzi model, 

Las Vegas, Nevada ................................................................................................................................................. 22

3. Reasonable ranges and optimal estimates for the hydraulic parameters estimated with the 

Lorenzi model, Las Vegas, Nevada........................................................................................................................ 28
CONTENTS V

CONVERSION FACTORS AND VERTICAL DATUM

Temperature: Degrees Celsius (oC) can be converted to degrees Fahrenheit (oF) by using the formula oF = [1.8(oC)]+32. 

Degrees Fahrenheit can be converted to degrees Celsius by using the formula oC = 0.556(oF-32).

Sea level: In this report, “sea level” refers to the National Geodetic Vertical Datum of 1929 (NGVD of 1929, formerly called 

“Sea-Level Datum of 1929”), which is derived from a general adjustment of the first-order leveling networks of the United States 

and Canada.

Multiply By To obtain

foot (ft) 0.3048 meter

foot (ft) 304.8 millimeter

feet per day (ft/d) 0.3048 meters per day

inch (in.) 2.54 centimeter

square mile (mi2) 2.59 square kilometer

ABSTRACT 1

ABSTRACT

Land subsidence related to aquifer-system 

compaction and ground-water withdrawals has 

been occurring in Las Vegas Valley, Nevada, since 

the 1930’s, and by the late 1980’s some areas in the 

valley had subsided more than 5 feet. Since the late 

1980’s, seasonal artificial-recharge programs have 

lessened the effects of summertime pumping on 

aquifer-system compaction, but the long-term 

trend of compaction continues in places.

Since 1994, the U.S. Geological Survey has 

continuously monitored water-level changes in 

three piezometers and vertical aquifer-system 

deformation with a borehole extensometer at the 

Lorenzi site in Las Vegas, Nevada. A one-dimensional, numerical, ground-water flow model of 

the aquifer system below the Lorenzi site was 

developed for the period 1901–2000, to estimate 

aquitard vertical hydraulic conductivity, aquitard 

inelastic skeletal specific storage, and aquitard and 

aquifer elastic skeletal specific storage. Aquifer 

water-level data were used in the model as the 

aquifer-system stresses that controlled simulated 

vertical aquifer-system deformation. Nonlinearregression methods were used to calibrate the 

model, utilizing estimated and measured aquifersystem deformation data to minimize a weighted 

least-squares objective function, and estimate optimal property values.

Model results indicate that at the Lorenzi 

site, aquitard vertical hydraulic conductivity is 

3 x 10-6 feet per day, aquitard inelastic skeletal 

specific storage is 4 x 10-5 per foot, aquitard elastic 

skeletal specific storage is 5 x 10-6 per foot, and 

aquifer elastic skeletal specific storage is 3 x 10-7

per foot. Regression statistics indicate that the 

model and data provided sufficient information to 

estimate the target properties, the model adequately simulated observed data, and the estimated 

property values are accurate and unique.

INTRODUCTION

Las Vegas, Nevada (fig. 1), is one of the fastest 

growing metropolitan areas in the United States and 

one of the hottest and most arid regions of the southwest. The rapid population growth has increased 

demand for water supplies. Las Vegas Valley relied 

almost entirely on ground water until the 1970’s, when 

large volumes of Colorado River water began to be 

imported into the valley; by 2000, ground water 

accounted for less than 20 percent of water used in the 

valley (Coache, 2000). Ground-water withdrawals 

from the local alluvial aquifer system exceeded estimated natural recharge by the 1950’s (Malmberg, 

1965), and by 1980, resulted in water-level declines 

of more than 300 ft from predevelopment conditions 

in some areas of Las Vegas Valley (Burbey, 1995). 

Ground-water depletion has caused aquifer-system 

compaction, land subsidence, and earth fissuring 

(Maxey and Jameson, 1948; Malmberg, 1965; Bell, 

1981). The land surface in some areas of Las Vegas 

Estimates of Hydraulic Properties from a One-Dimensional 

Numerical Model of Vertical Aquifer-System Deformation, 

Lorenzi Site, Las Vegas, Nevada

By Michael T. Pavelko
2 Hydraulic Properties from a 1-Dimensional Numerical Model of Vertical Aquifer-System Deformation, Lorenzi SIte, Las Vegas, NV

115°45' 115°30' 115°15' 115°00' 114°45'

36°00'

36°15'

36°30'

0 10 20 MILES

0 10 20 30 KILOMETERS

NEVADA

CALIFORNIA CALIFORNIA

NEVADA

CALIFORNIA

NEVADA

ARIZONA

Lake

Mead

SpringSpring

MountainsMountains

Vegas

ValleyValley

Las

Vegas

Wash

Vegas

Las

Vegas

Las VegasLas

Vegas

Las

Las

Vegas

Wash

Col o rado

Ri ver

Col o rado

Ri ver

Lorenzi Lorenzi

site

Lorenzi

site

California

Area of

map above

Area of Area of

Great Basin Regional Great Basin Regional

Aquifer System Aquifer System

Area of

Great Basin Regional

Aquifer System

Nevada

Arizona

Utah

Idaho Oregon

Base from U.S. Geological Survey digital data 1:100,000-scale

1978-89: Universal Transverse Mercator Projection, Zone 11

Shaded relief from 1:24,000-scale National Elevation Data [NED]

 

Figure 1. Location of Las Vegas Valley and the Lorenzi site, Nevada.
INTRODUCTION 3

Valley has subsided more than 5 ft (Bell and Price, 

1993, pl. 4) and damage to homes, roads, water lines, 

and wells have been attributed to associated earth 

fissures (Bell, 1981; Bell, 1997; Bell and Price, 1993). 

Since about 1988, water levels in some areas have 

stabilized or risen by as much as 100 ft (Wood, 2000), 

likely because of artificial-recharge programs initiated 

by the Las Vegas Valley Water District and the City 

of North Las Vegas that inject treated Colorado River 

water into the aquifer system. In areas where water 

levels have stabilized or risen, the rate of land subsidence has slowed, slight uplift during periods of artificial recharge has occurred, or both, but subsidence 

continues to occur and is the dominant long-term trend 

(Amelung and others, 1999; Pavelko, 2000; Hoffmann 

and others, 2001).

The U.S. Geological Survey (USGS) did this 

study in cooperation with the Nevada Department of 

Conservation and Natural Resources–Division of 

Water Resources and the Las Vegas Valley Water District (LVVWD) to develop a better understanding of the 

relations among land subsidence and uplift, vertical 

aquifer-system deformation, and ground-water-level 

fluctuations. As part of this effort, the Lorenzi site, in 

northwest Las Vegas (figs. 1 and 2), was established in 

1994 to continuously measure vertical aquifer-system 

deformation and water levels (Pavelko, 2000). For this 

report, vertical deformation describes a change in the 

thickness of a horizontal aquifer-system unit. To better 

understand the aquifer-system mechanics, hydraulic 

properties were estimated using a one-dimensional 

(1-D) numerical model that simulated Lorenzi site 

ground-water levels and vertical aquifer-system deformation.

Subsidence and uplift refer to the sinking and 

rising of the land surface, respectively. In Las Vegas 

Valley, subsidence and uplift generally are associated 

with vertical compaction and expansion of the aquifer 

system. The aquifer system primarily consists of sand 

and gravel aquifers (water-transmitting units) and silt 

and clay aquitards (water-impeding units). The aquifer 

system vertically deforms in response to water-level 

fluctuations caused by pumping water out of or 

injecting water into the aquifer system. Generally, 

compaction is associated with declining water levels 

(heads) and expansion with rising heads.

Land subsidence and uplift, aquifer-system compaction and expansion, and head fluctuations have a 

complex relation. In Las Vegas Valley, this complexity 

is increased because the aquifer system is alternately 

pumped during high demand months and artificially 

recharged during other months; thus, the aquifer-system skeleton undergoes seasonal cycles of compression 

and expansion as heads fluctuate. Reasonable estimates 

of aquifer-system hydraulic properties are needed to 

help understand the complex relation among land subsidence and uplift, vertical aquifer-system deformation, 

and head fluctuations. Hydraulic-property investigations in Las Vegas Valley have focused primarily on 

estimating properties in productive aquifer units. Few 

previous studies have focused on hydraulic properties 

of aquitard units (see Previous Investigations section). 

The development of a numerical model constrained by 

vertical aquifer-system deformation and head observations allowed aquitard properties, which are difficult to 

measure directly, to be estimated.

Purpose and Scope

The purpose of this report is to document the 

methods used to estimate hydraulic-property values 

that affect vertical aquifer-system deformation at the 

Lorenzi site and present the estimated values. Values 

were estimated for (1) aquitard vertical hydraulic 

conductivity, (2) aquitard inelastic skeletal specific 

storage, (3) aquitard elastic skeletal specific storage, 

and (4) aquifer elastic skeletal specific storage. A 1-D, 

finite difference, transient ground-water flow model 

for the period 1901–2000 was developed to simulate 

vertical aquifer-system deformation and nonlinearregression methods were used to calibrate the model 

and refine previously estimated property values.

The 1-D model is a simplified representation 

of the portion of the aquifer system that is monitored 

by the Lorenzi site extensometer (USGS-EXT1). Estimated historic compaction and deformation measured 

by USGS-EXT1 do not adequately support a model 

that has a different set of hydraulic-property values for 

each aquifer-system unit. Instead, only two sets of 

property values are estimated, one for aquifers and one 

for aquitards, and the values are considered averages 

for the system units and not necessarily representative 

of any given point in the physical system. Particular 

attention was given to the assignment of specified 

heads and temporal and spatial discretization. Estimated and measured vertical aquifer-system deformation data were used for the nonlinear regression. Model 

results and regression statistics were analyzed to evaluate the model and estimated hydraulic-property values.
4 Hydraulic Properties from a 1-Dimensional Numerical Model of Vertical Aquifer-System Deformation, Lorenzi SIte, Las Vegas, NV

1

0

0

0.5

0.5

0.5

1

2

3

4

5

2

1

2

2

2.5

2.5

5.5

?

?

SNMRE

P.J. Goumond P.J. Goumond

SNMRE

P.J. Goumond

#

P169

V170

Q365 K169 365

P169

V170

Q365 K169

#

EXPLANATION

Lorenzi site

Benchmark and name

Well and name

Subsidence contours—Contours are in feet, interval is variable.

 (Modified from Bell and others, 2000)

1

Fault

P169

SNMRE

0 2 4 6 8 10 MILES

0 2 4 6 8 10 KILOMETERS

Base from U.S. Geological Survey digital data 1:100,000-scale

1978-89: Universal Transverse Mercator Projection, Zone 11

Shaded relief from 1:24,000-scale National Elevation Data [NED]

Las

Vegas

115 ̊22'30" 115 ̊07'30" 115 ̊00' 115 ̊15'

36 ̊15'

36 ̊22'30"

36 ̊07'30"

Figure 2. Land-subsidence contours for 1963–2000, benchmarks used to help estimate historic compaction trends, wells used to 

help estimate historic water-level trends, selected faults, and the Lorenzi site, Las Vegas Valley, Nevada.
INTRODUCTION 5

Aquifer-system mechanics, numerical modeling, 

and parameter estimation are discussed briefly. 

Assumptions, data limitations, model limitations, and 

regression results also are discussed. This report does 

not focus on data and presents only the most pertinent 

data to the model and regression. Other data specific to 

this study can be found in Pavelko (2000) or requested 

from the Henderson, NV, office of the USGS.

Study Area

Las Vegas is in southern Nevada and the Las 

Vegas Valley aquifer system is in the southern part of 

the Great Basin Regional Aquifer System1

 (fig. 1). Las 

Vegas Valley is about 1,600 mi2, with altitudes ranging 

from about 1,600 ft above sea level on the valley floor 

to about 12,000 ft above sea level in the nearby Spring 

Mountains. The northwest-trending valley is bounded 

on all sides by various mountains. The Las Vegas Wash 

and tributaries drain the valley runoff eastward into 

Lake Mead. Average annual precipitation ranges from 

about 4 in. on the valley floor to more than 20 in. on the 

surrounding mountains. Temperatures on the valley 

floor range from below freezing to over 115°F.

The Lorenzi site, established in 1994, is in northwestern Las Vegas (figs. 1 and 2) and consists of three 

nested piezometers (USGS-PZD, USGS-PZM, and 

USGS-PZS) and a vertical borehole extensometer 

(USGS-EXT1; table 1; Pavelko, 2000). The location, 

which is on the southern edge of a large subsidence 

bowl (Bell and others, 2000), was selected by LVVWD 

personnel based on site availability. The site is within 2 

mi of 18 municipal wells, generally to the south and 

west, which pump ground water from about May 

through September and provide artificial recharge from 

about October through May. Of the 18 wells, 12 are 

used to pump ground water, 2 are used to artificially 

recharge the aquifer system, and 4 are dual-use wells 

used to pump and artificially recharge the aquifer system. Additional municipal wells are beyond the 2-mi 

radius.

History of Land Subsidence in Las Vegas 

Valley

Land subsidence in Las Vegas Valley is attributed 

mainly to compaction of the aquifer system caused by 

ground-water withdrawals. Maxey and Jameson (1948) 

first recognized land subsidence from comparisons of 

leveling surveys made by the U.S. Coast and Geodetic 

Survey and the USGS in 1915, 1935, and 1941. Since 

then, repeat surveys of regional networks, newly established benchmarks, local transects, and Global Positioning Satellite (GPS) sites have shown continued land 

1

 Formal hydrographic areas in Nevada were delineated 

systematically by the U.S. Geological Survey and Nevada Division 

of Water Resources in the late 1960’s (Cardinalli and others, 1968; 

Rush, 1968) for scientific and administrative purposes. The 

official hydrographic-area names, numbers, and geographic 

boundaries continue to be used in USGS scientific reports.

Table 1. Well-construction data for piezometers and the extensometer at the Lorenzi site, Las Vegas, Nevada 

[The U.S. Geological Survey (USGS) identifies sites with a unique 15-digit number based on a latitude-longitude grid. The first six 

digits denote degrees, minutes, and seconds of latitude, the next seven digits denote degrees, minutes, and seconds of longitude, and the 

last two digits denote a unique sequence number within a 1-second grid of latitude and longitude. --, not applicable]

Well Name

USGS site 

identification 

number

Date drilled

(1994)

Depth Casing depth

Top of 

screened 

interval

Bottom of

screened

interval

feet below land-surface

USGS-PZD 361410115142601 May 18 703 697 677 687

USGS-PZM 361410115142602 May 18 703 467 447 457

USGS-PZS 361410115142603 May 18 703 320 300 310

USGS-EXT1 361410115142604 April 3 800 780 -- --
6 Hydraulic Properties from a 1-Dimensional Numerical Model of Vertical Aquifer-System Deformation, Lorenzi SIte, Las Vegas, NV

subsidence throughout large portions of the valley. The 

surveys, which were limited in temporal and spatial 

details, indicated that subsidence continued slowly into 

the mid-1960’s after which rates began increasing 

through 1987 (Bell, 1981; Bell and Price, 1993). By the 

1970’s, damages to engineered structures had been 

attributed to subsidence and subsidence-related earth 

fissures (Mindling, 1971; Bell, 1981; Bell and Price, 

1993; Bell, 1997). 

Benchmark and GPS surveys and interferometric 

synthetic aperture radar (InSAR) data (Galloway and 

others, 2000) acquired for 1992–97 (Amelung and others, 1999; Bell and others, 2000 and 2002; Hoffmann 

and others, 2001) have delineated four localized subsidence bowls within a larger, valley-wide subsidence 

bowl (fig. 2). The deepest localized subsidence bowl, 

in the northwestern part of the valley, subsided more 

than 5.5 ft between 1963 and 1998 (Bell and others, 

2000), in addition to nearly 1 ft of subsidence that 

occurred between 1935 and 1950 (Bell, 1981). The 

other localized bowls subsided from about 2.3 to 3.3 ft 

between 1963 and 1998 (Bell and others, 2000). Comparisons of land subsidence and water-level change 

maps show that areas of maximum subsidence do not 

necessarily coincide with areas of maximum head 

declines. One likely explanation is that areas with high 

subsidence rates are underlain by a larger aggregate 

thickness of fine-grained, compressible sediments than 

those areas with lower rates (Bell and Price, 1993).

Since 1988, wintertime artificial-recharge programs have mitigated land subsidence by stabilizing or 

raising heads on a valley-wide scale. Seasonal uplift is 

associated with the periods of artificial recharge, but 

residual compaction continues to dominate the longterm trend.

Previous Investigations

Water-resources investigations primarily on land 

subsidence and related issues in Las Vegas Valley are 

discussed by Malmberg (1964), Mindling (1965, 

1971), Bell (1981), Waichler and Cochran (1991), Bell 

and Price (1993), Jeng (1998), Pavelko and others 

(1999), Pavelko (2000), Sneed and others (2000), and 

Pavelko (2003). Amelung and others (1999), Bell and 

others (2000, 2002), Hoffmann and others (2001), and 

Hoffmann (2003) examine land subsidence in Las 

Vegas Valley using InSAR data. General waterresources investigations that include information about 

land subsidence in Las Vegas Valley include Maxey 

and Jameson (1948), Domenico and others (1964), 

Malmberg (1965), Plume (1989), and Morgan and 

Dettinger (1996). In Las Vegas Valley, Domenico and 

others (1966) studied geologic controls of land subsidence and Harrill (1976) studied ground-water storage 

depletion. General hydrologic investigations of Las 

Vegas Valley include Carpenter (1915).

Ground-water flow, including land subsidence, 

in Las Vegas Valley was simulated by Morgan and 

Dettinger (1996) using a modified “quasi-threedimensional” flow model (Trescott, 1975; Trescott and 

Larson, 1976). Past and future land subsidence were 

simulated for two sites in Las Vegas Valley (Waichler 

and Cochran, 1991) using the COMPAC model (Helm, 

1974, 1975). Jeng (1998) converted the Morgan and 

Dettinger (1996) model to MODFLOW and simulated 

ground-water flow and land subsidence. Okuyan 

(2000) simulated past and future land subsidence 

and rebound for selected sites in Las Vegas Valley. 

Preliminary model results of the Lorenzi model were 

discussed in Sneed and others (2000) and Pavelko 

(2003).

Acknowledgments

The development of the numerical groundwater flow model and application of the compaction 

package were guided by Michelle Sneed, USGS, 

Sacramento, California. Assistance with UCODE and 

nonlinear-regression techniques was provided by 

Claire Tiedeman, USGS, Menlo Park, California. Technical and field assistance with the extensometer, information critical to this project, were provided by Frank 

Riley, USGS, Menlo Park, California. The Nevada 

Power Company allowed the Lorenzi site to be constructed and maintained at their Lorenzi substation.

HYDROGEOLOGY

Las Vegas Valley is a sediment-filled structural 

trough covering about 1,600 mi2

. The predominantly 

gravel, sand, silt, and clay sediments overlay bedrock 

and form the Las Vegas Valley aquifer system (fig. 3). 

The carbonate-rich assemblage of sediments was 

eroded by wind and water from surrounding bedrock 

highlands. Early on, these sediments were deposited on 

an uneven, faulted bedrock surface and then over some-
HYDROGEOLOGY 7

Approximately 13,000 feet

below land surface

General direction of ground-water flow—Size of arrow indicates

 relative magnitude of ground-water flow

Fault—Arrow indicates direction of relative fault movement. Fault

 locations are hypothetical and intended only to show complexity

 of the aquifer system

Bedrock

Aquifer—Sand and gravel

Aquitard—Silt and clay

EXPLANATION

Not to scale. Modified from Maxey and Jameson (1948, pl. 6B) and Langenheim and others (2001, fig. 12C)

E

Las Vegas Valley

W

what irregular surfaces shaped by previous episodes of 

deposition, erosion, and fault movement. Depending on 

intensity, runoff from rain and snow falling on the 

higher mountain ranges, such as the Spring Mountains 

bounding the valley on the west (fig. 1), transported 

and deposited variously sized sediment onto the valley 

floor. During some of the wetter times of the Quaternary Period, springs, marshes, ponds, and possibly 

lakes (Mifflin and Wheat, 1979; Quade and others, 

1995) that covered the lower parts of the valley floor 

deposited sequences of fine-grained sediments.

From the Miocene through Holocene Epochs 

(Plume, 1989), alluvial and fluvial processes deposited 

a thick accumulation of interbedded and interfingered, 

coarse- and fine-grained sediment. Coarse-grained 

sand and gravel tend to rim the valley forming alluvial 

fans and terraces especially in the northern, western, 

and southern parts of the valley. The sediment assemblages generally thicken and become finer-grained 

toward the central and eastern part of the valley (fig. 3), 

where their total thickness may exceed 13,000 ft 

(Langenheim and others, 1998).

Precipitation runoff enters the alluvial aquifer 

system below the mountainous source areas and flows 

downgradient toward the central and eastern parts of 

the valley, where the depth to bedrock is greatest. At 

higher elevations, ground water flows through sand and 

gravel aquifers, but the flow is increasingly impeded 

and the water confined by low-permeability clay and 

silt aquitards that are interfingered with the aquifers 

downgradient.

In Las Vegas Valley, ground water generally is 

pumped from the upper 2,000 ft of the aquifer system. 

Sediments from about 200 to 2,000 ft deep generally 

are capable of transmitting significant quantities of 

ground water and have been referred to as the principal, 

artesian, or developed-zone aquifer (Maxey and 

Jameson, 1948; Malmberg, 1965; Harrill, 1976; 

Morgan and Dettinger, 1996). The principal aquifer has 

been subdivided into shallow, middle, and deep zones 

that are separated by aquitards. The aquifer units within 

the principal aquifer contain numerous thin, laterally 

discontinuous interbeds of low-permeability silt and 

clay that are interfingered in places. The principal aquifer extends from the sand and gravel deposits along the 

Figure 3. A simplified hydrogeologic cross section of the Las Vegas Valley aquifer system, Nevada.
8 Hydraulic Properties from a 1-Dimensional Numerical Model of Vertical Aquifer-System Deformation, Lorenzi SIte, Las Vegas, NV

margins of the valley and becomes discontinuous and 

less prevalent towards the central and eastern parts of 

the valley, where clay and silt predominate (Plume, 

1989). In places, there may be a decrease in permeability with depth for the deep zone of the principal aquifer 

(Maxey and Jameson, 1948). Overlying the principal 

aquifer, in places, is a 100- to 300-ft thick section of 

clay, sand, and gravel often referred to as the nearsurface reservoir.

Lorenzi Site

Three thick aquifers and three thick aquitards are 

monitored at the Lorenzi site, as indicated by geophysical and lithologic logs from the extensometer borehole (fig. 4; Paillet and Crowder, 1996; Pavelko, 2000). 

Geophysical logs indicate the aquifer depths range 

from 255 to 308, 420 to 500, and 605 to 800 ft below 

land surface (F.L. Paillet, U.S. Geological Survey, 

written commun., 1994). The shallow aquitard (0–255 

ft below land surface) likely corresponds to the nearsurface reservoir and the underlying sediments to the 

principal aquifer (Harrill, 1976). The lithologic log 

indicates that the aquifers consist of sand and gravel 

with interbedded layers of silt and clay, and the aquitards consist mostly of silt and clay (T.J. Burbey, U.S. 

Geological Survey, written commun., 1994). Gravity 

data for Las Vegas Valley (Langenheim and Jachens, 

1996, V. Langenheim, U.S. Geological Survey, written 

commun., 2000, and Langenheim and others, 2001) 

were evaluated to determine the depth of the contact 

between low-density (compactible) sediments and 

underlying higher-density (competent) sediments or 

rock at the Lorenzi site. Data indicate that the gravitypredicted depth occurs between 750–800 ft below land 

surface and is approximately equal to the depth of the 

extensometer (800 ft below land surface). Therefore, 

for purposes of this report, the depth to the base of 

compactible sediments at the Lorenzi site was considered to be equal to the depth of the extensometer.

MECHANICS OF VERTICAL AQUIFERSYSTEM DEFORMATION

The aquitard-drainage model describes physical 

processes associated with aquifer-system head fluctuations and associated vertical deformation. [See 

Holzer (1998) for a history of the aquitard-drainage 

Shallow

aquitard

Shallow

aquifer

Middle

aquitard

Middle

aquifer

Deep

aquitard

Deep

aquifer USGS-PZS

USGS-PZM

USGS-PZD

Screen

USGS-EXT1

800

700

600

500

400

300

200

100

0

DEPTH, IN FEET BELOW LAND SURFACE

Figure 4. The generalized hydrogeology, 

piezometers, and extensometer at the 

Lorenzi site, Las Vegas, Nevada. Horizontal is not to scale.

model.] The focus is on the slow equilibration and vertical compression, or compaction, of aquitards resulting 

from head declines in adjacent aquifers. The most 

important components of the aquitard-drainage model 

are encompassed in the principle of effective stress and 

the theory of hydrodynamic consolidation (Terzaghi, 

1925, 1943). The principle of effective stress describes 

the relation among aquifer-system stresses that contribute to vertical deformation. Vertical deformation is 

dependent, in part, on the storage properties of aquifersystem units, which incorporate the compressibility, 

thickness, and stress history of aquifer-system units. The 
MECHANICS OF VERTICAL AQUIFER-SYSTEM DEFORMATION 9

theory of hydrodynamic consolidation explains the 

slow equilibration and residual compaction of aquitards in response to aquifer-head declines, and is related 

to the stresses, storage properties, thickness, and vertical hydraulic conductivity of aquifer-system units.

Principle of Effective Stress

Vertical aquifer-system deformation in Las Vegas 

Valley primarily is caused by head fluctuations that 

result from pumping water out of, or injecting water 

into, the aquifer system. The storage coefficient of 

aquifer-system sediments is the amount of water 

released from, or taken into, storage per unit area per 

unit decline, or rise, in hydraulic head, respectively. 

Water released from storage comes from the compression of the granular matrix (skeleton) of the aquifer system and expansion of water, and water taken into 

storage causes expansion of the skeleton and compression of water. The principle of effective stress 

(Terzaghi, 1925, 1943) describes the relation of 

fluctuating heads, expressed as equivalent changes in 

pore-water pressure, and vertical stresses related to 

aquifer-system deformation:

, (1)

where is the total stress on the aquifer system (the 

geostatic load, or weight of overlying sediments and 

water), p is the pore-water pressure, and is the 

effective, or intergranular, stress. Thus, pore-water 

pressure and the aquifer-system skeleton support the 

weight of overlying sediments and water. For a confined aquifer system without a water-table aquifer, such 

as at the Lorenzi site, it can be assumed that 

remains constant and a change in p (head fluctuation) 

causes an equal and opposite change in . Changes in 

 of an aquifer system can cause vertical aquifer-system deformation. For example, when water is pumped 

from the system, heads decline and p decreases, which 

results in an increase in ; the increase in causes 

aquifer-system compaction to a degree dependent on 

the compressibility of the sediments and the previous 

stress history.

Aquifer-system sediments have an elastic and 

inelastic compressibility and, generally, the relation of 

the current to the past maximum effective stress, or 

preconsolidation stress, , determine whether 

deformation will be elastic (recoverable) or inelastic 

(permanent). Generally, the inelastic compressibility of 

aquitards is 1 to 3 orders of magnitude larger than the 

elastic compressibility of aquitards, the elastic compressibility of aquitards is about an order of magnitude 

larger than of aquifers, and the inelastic compressibility 

of aquifers is considered negligible. Provided that 

remains below , aquifer-system deformation 

will be elastic. If is exceeded, usually a result 

of heads declining below the past minimum head, 

deformation will be inelastic. 

The compressibilities of aquifer-system sediments are termed skeletal compressibilities and often 

are expressed in terms of skeletal specific storages:

, for , (2)

, for , (3)

, for , and (4)

, for , (5)

where is the skeletal specific storage, is the 

skeletal compressibility, subscripts e and v denote elastic and inelastic properties, respectively, is the water 

density, g is gravitational acceleration, and primes 

denote aquitard properties. Expressed as an equivalent 

head, is called the preconsolidation head; 

when heads are above the preconsolidation head, deformation is elastic and when heads are below the preconsolidation head, deformation is inelastic.

The compressibility of water, , also can be 

expressed as a specific storage:

, (6)

where is the specific storage of water. In the 

inelastic range of stress experienced by most developed 

aquifer systems, is considered negligible, but may 

be a significant component in the elastic range of stress. 

The specific storage of an aquifer-system unit is the 

sum of the skeletal specific storage and the specific 

storage of water. The skeletal storage coefficient of an 

aquifer-system unit is the product of that unit’s skeletal 

specific storage and thickness.

σT p σe = +

σT

σe

σT

σe

σe

σe σe

σe

σe max ( )

σe

σe max ( )

σe max ( )

Ssk Sske αke = = ρg σe σe max ( ) ≤

Ssk Sskv αkv == = ρg 0 σe σe max ( ) >

S'

sk S'ske α'ke = = ρg σe σe max ( ) ≤

S'

sk S'skv α'kv = = ρg σe σe max ( ) >

Ssk αk

ρ

σe max ( )

βw

Ssw βw = ρg

Ssw

Ssw
10 Hydraulic Properties from a 1-Dimensional Numerical Model of Vertical Aquifer-System Deformation, Lorenzi SIte, Las Vegas, NV

Theory of Hydrodynamic Consolidation

The theory of hydrodynamic consolidation 

(Terzaghi, 1925, 1943) describes the delay involved in 

aquitard equilibration when heads are lowered in adjacent aquifers and the associated compaction that continues afterwards. At the onset of pumping, most water 

derived from aquifer systems is withdrawn from aquifers. Because aquitards have a much lower permeability than aquifers, the equilibration and drainage of 

aquitards may proceed slowly, and heads in aquitards 

may lag far behind the changing heads in adjacent 

pumped aquifers. In aquifer systems that have thick 

aquitards and undergo seasonal pumping, such as at the 

Lorenzi site, aquitard heads often do not equilibrate 

with pumped aquifers before the next season of pumping begins, thus aquitards are continuously equilibrating to the effects of past pumping. In thick aquitards, 

the slow drainage and release of water from storage is 

accompanied by the migration of an increased 

towards the inner portions of the aquitard. If the internal stresses exceed , the slow drainage is 

accompanied by inelastic compaction.

Residual compaction is the inelastic aquitard 

compaction that would occur because of an increase in 

effective stress, but has not yet occurred because aquitard heads have not equilibrated to heads in adjacent 

aquifers and are still draining and compacting (Poland 

and others, 1972). The slow drainage and equilibration 

of the aquitards, as described above, can result in 

decades or more of residual compaction for aquifer 

systems with thick aquitards and large head declines 

(Ireland and others, 1984). The time constant of an 

aquitard describes how long a doubly draining aquitard 

will take to achieve about 93 percent of the total possible compaction for a given head decline (Riley, 1969). 

A doubly draining aquitard is an aquitard between two 

aquifers with identical heads that are lower than heads 

in the aquitard and, therefore, the aquitard releases 

water into the overlying and underlying aquifers. The 

time constant (τ) is expressed as:

, (7)

where S'

skv is aquitard inelastic skeletal specific 

storage, b' is the thickness of the aquitard, and K'

v is 

aquitard vertical hydraulic conductivity. For aquitards 

with only one adjacent aquifer, a directly comparable τ

cannot be made but can be estimated by replacing b'/2

with b' (Epstein, 1987).

NUMERICAL MODEL

A numerical model of the Lorenzi site was developed to simulate vertical aquifer-system deformation 

and estimate aquitard vertical hydraulic conductivity 

(K'

v), aquitard inelastic and elastic skeletal specific 

storage, S'

skv and S'ske, respectively, and aquifer 

elastic skeletal specific storage (Sske). The estimated 

hydraulic-property values are considered average 

values for the composite thickness of aquifer-system 

unit types. A conceptual model was developed using 

geophysical, lithologic, head, and vertical-deformation 

data collected at the site. MODFLOW-96 (McDonald 

and Harbaugh, 1988; Harbaugh and McDonald, 1996), 

a modular finite-difference ground-water flow model, 

was used to develop the 1-D, vertical numerical model 

of the Lorenzi site conceptual model. The Flow and 

Head Boundary (FHB1) package was used to specify 

heads at selected times and depths (Leake and Lilly, 

1997). The Interbed-Storage (IBS1) package was 

used to simulate deformation (Leake and Prudic, 

1991). The Block-Centered Flow package was used to 

simulate transient ground-water flow and the Strongly 

Implicit Procedure package was used to solve a set of 

simplified ground-water flow equations (McDonald 

and Harbaugh, 1988; Harbaugh and McDonald, 1996). 

The ground-water flow equations were solved iteratively to compute heads in each cell for each time step. 

For each iteration, calculated heads were compared 

to heads from the previous iteration until the head 

differences between iterations were less than 0.0001 ft.

Conceptual Model

The conceptual model of the Lorenzi aquifer system is a simplified and qualitative physical description 

of the geometry and processes of the aquifer system 

and was developed using geophysical logs (F.L. Paillet, 

U.S. Geological Survey, written commun., 1994), 

lithologic logs (T.J. Burbey, U.S. Geological Survey, 

written commun., 1994), and head and vertical-deformation data collected at the Lorenzi site.

σe

σe max ( )

τ

S'

skv( ) b' ⁄ 2 2

K'

v

= -----------------------------
NUMERICAL MODEL 11

Lithology unknown

below 800 ft

DEPTH, IN FEET BELOW LAND SURFACE

Deep aquifer

605-800 ft

Deep aquitard

500-605 ft

Middle aquifer

420-500 ft

Middle aquitard

308-420 ft

Shallow aquifer

255-308 ft

Shallow aquitard

65-255 ft

Cell node

Model cell

900

800

700

600

500

400

300

200

100

0

Close up shows details of variable

spacing and fine discretization used in

the model grid. Cells ranged in thickness

from 1 to 8 feet, with the thinnest

cells located near aquifer-aquitard

boundaries. The top and bottom cells of

aquifers (black cells in close up) were

specified-head cells and all other cells

were variable-head cells.

The conceptual model consists of three aquifers 

and three aquitards constituting a total thickness of 735 

ft, from 65 to 800 ft below land surface (fig. 5). The 

uppermost 65 ft of sediment were not included in the 

model because that depth interval likely is unsaturated 

and, therefore, not subject to compaction. The aquifers 

and aquitards are assumed to have homogeneous and 

isotropic hydraulic properties, and each unit type is 

assumed to have an identical set of hydraulic-property 

values. Heads and ground-water flow in aquifers are 

considered to be controlled entirely by pumpage and 

artificial recharge, and heads and flow in aquitards 

are controlled entirely by aquifer heads. Aquifer 

hydraulic conductivity is sufficiently high that aquifers 

equilibrate instantaneously throughout their thickness 

to head changes. However, aquitard conductivity is 

sufficiently low that large, nonlinear, vertical-head 

gradients form within each aquitard unit as heads in 

Figure 5. The generalized hydrogeology of the conceptual model and model grid, 

including a close-up of the model grid showing variable cell spacing, for the 

Lorenzi model, Las Vegas, Nevada.
12 Hydraulic Properties from a 1-Dimensional Numerical Model of Vertical Aquifer-System Deformation, Lorenzi SIte, Las Vegas, NV

adjacent aquifers change. For the purposes of the 1-D 

model, head fluctuations and aquifer-system deformation account for all storage changes—no ground water 

is assumed to flow into or out of the system.

All aquifer-system deformation in the conceptual 

model is assumed vertical and a result of head fluctuations. Generally, compaction occurs when heads 

decline and expansion occurs when heads rise. Deformation occurs as elastic compaction and expansion in 

aquifers and aquitards and inelastic compaction in 

aquitards—inelastic compaction does not occur in 

aquifers. The majority of elastic deformation occurs in 

aquifers and inelastic deformation occurs only when 

aquitard heads are below their preconsolidation head. 

Residual compaction occurs only in aquitards and 

when all or portions of the aquitard have heads below 

their preconsolidation head. Because the middle and 

deep aquitards (fig. 5) are doubly draining and the 

shallow aquitard only drains downward, the assumption is made that the shallow aquitard equilibrates and 

therefore compacts much more slowly than the other 

aquitards.

A conceptual history of heads at the Lorenzi 

site was developed to guide the transient progression of 

the numerical model. From about 1901 to 1915, the 

system was in steady-state equilibrium (Carpenter, 

1915; Maxey and Jameson, 1948; Malmberg, 1965) 

with higher heads in lower units and naturally occurring seasonal fluctuations. Beginning around 1915, 

ground-water pumpage caused heads to decline and 

they declined until about 1992, although from about 

1940 to 1992 they declined much more rapidly than 

from 1915 to 1940. Since about 1950, seasonal pumpage has amplified annual cycles of head fluctuations. 

Also around 1950, increased pumpage in deeper units 

caused the distribution of aquifer heads to reverse such 

that the shallow units had higher heads. By 1992, estimated heads had declined by as much as 320 ft in the 

deep and middle aquifers and 250 ft in the shallow 

aquifer. Large, nonlinear, vertical-head gradients 

formed in the aquitards during this time (fig. 6) because 

their low vertical hydraulic conductivity prohibited 

water from equilibrating as quickly as the declining 

aquifer heads, and new preconsolidation heads were 

established in the aquifers. Since 1992, heads around 

the Lorenzi site have been rising because artificial 

recharge has increased. After 1992, as aquifer heads 

generally were rising and aquitard heads continued to 

equilibrate (decline) with aquifers, nonlinear head 

gradients between adjacent aquifers and aquitards 

decreased.

The equilibration of the relatively high aquitard 

heads to the lower aquifer heads caused inelastic residual compaction to occur in the aquitards. From 1988 to 

1996, during seasons of artificial recharge and rising 

aquifer heads, the rates of aquitard residual compaction 

were higher than rates of aquifer expansion, such that 

aquifer expansion was masked entirely. Since 1997, the 

rate of aquifer expansion during periods of artificial 

recharge exceeded the rate of aquitard residual compaction (Pavelko, 2000).

Discretization

Although the conceptual model was developed 

as a 1-D vertical model, the numerical model was 

spatially discretized into a 1-D horizontal model 

to take advantage of the layer-wise formatting of 

MODFLOW-96 data arrays. Thus, a 1-ft wide vertical 

column of the conceptual aquifer system (fig. 5) was 

represented by a 1-ft tall numerical layer and the 735-ft 

thickness of the aquifer system was represented by a 

single row of 250 numerical columns that varied in 

width in the row-wise dimension. To accommodate 

the column-to-layer translation, the assignment of 

hydraulic properties in the model needed to be modified. Hydraulic properties that describe vertical flow 

were assigned to data arrays typically reserved for 

horizontal properties. For example, vertical hydraulicconductivity values were assigned using the transmissivity data array. The translation modification, 

described in the IBS1 documentation (Leake and 

Prudic, 1991), also was used to simulate 1-D, vertical, 

aquifer-system deformation in Antelope Valley, 

California (Sneed and Galloway, 2000). This report, 

and the figures and tables within, refers to model 

columns as layers to maintain the terminology and 

geometry of the conceptual aquifer system.

Spatially, there were 250 model layers (fig 5). 

The three aquifers were represented by 93 layers, 

which ranged in thickness from 1 to 8 ft, for a total of 

328 ft. The three aquitards were represented by 157 

layers, which ranged in thickness from 1 to 3 ft, for a 

total of 407 ft. The model was finely discretized into 

thin layers to minimize a limitation of the IBS1 package in simulating residual compaction (see Model and 

Regression Limitations section). The resultant model 
NUMERICAL MODEL 13

0 100 200 300

HEAD, IN FEET BELOW LAND SURFACE

0

100

200

300

400

500

600

700

800

900

DEPTH, IN FEET BELOW LAND SURFACE

Deep

aquifer

Deep

aquitard

Middle

aquifer

Middle

aquitard

Shallow

aquifer

Shallow

aquitard

Decades of ground-water withdrawals

caused nonlinear head gradients to

form in aquitard units

1992 conceptual heads

Starting preconsolidation heads

Initial heads

grid generally had thicker layers for aquifers than for 

aquitards and the thinnest layers were near aquiferaquitard boundaries (fig. 5).

The model simulated deformation from January 1, 

1901, to November 19, 2000. The historic period, 1901 

through 1994, was simulated using ninety-four 1-year 

(365.25 days) stress periods, each with twelve 1-month 

(30.4375 days) time steps. The recent period, 1995–

2000, was simulated using forty-three 50-day stress 

periods, each with four-hundred 3-hour time steps. The 

historic period of the model established the hydrologic 

conditions for the recent period, including preconsolidation heads and aquitard-head distributions, which 

were important for simulating recent-period deformation. The temporal discretization of the recent period 

was finer than the historic period to facilitate use of the 

high measurement frequency and more accurate data 

from the Lorenzi site. The shorter time steps also provided for a better evaluation of simulated seasonal and 

shorter-term deformation. 

Boundary Conditions

The simplified hydrologic processes of the conceptual model were implemented into a numerical 

model, in part, by designating boundary conditions to 

appropriate model cells. The top and bottom cells of 

each aquifer unit were designated as specified-head 

cells, in which estimated or measured heads were 

assigned at specified model times using the FHB1 

package (Leake and Lilly, 1997). All other model cells 

Figure 6. The initial, starting preconsolidation, and 1992 conceptual heads for the Lorenzi model, Las 

Vegas, Nevada.
14 Hydraulic Properties from a 1-Dimensional Numerical Model of Vertical Aquifer-System Deformation, Lorenzi SIte, Las Vegas, NV

were designated as variable-head cells (fig. 5), which 

allowed heads to fluctuate according to heads in adjacent cells. By default, the lateral, upper, and lower 

boundaries of the vertical column (fig. 5) are no-flow 

boundaries and, therefore, only vertical flow is simulated and no water can enter or exit the system, except 

as specified-head changes.

Initial Head and Compaction Conditions

Initial conditions described the conceptual steady 

state of the predevelopment aquifer system in 1901. 

Initial conditions were assigned to each cell with 

initial-head, preconsolidation-head, and starting-compaction data. Initial aquifer heads (fig. 6) were based 

primarily on Carpenter (1915) and adjusted during 

model calibration. Carpenter suggests that a 274-ft 

deep, unnamed well approximately 1 mi from the 

future Lorenzi site had a head of 2,279 ft above sea 

level. Thus, assuming a relatively flat head gradient, the 

head in USGS-PZS, a 305-ft deep well, would have 

about the same water-level altitude as the unnamed 

well, which would equate to a head of approximately 

30 ft below land surface. During calibration, initial 

heads for USGS-PZS were varied from 0 to 70 ft below 

land surface, and the relation of shallow to middle and 

deep aquifer heads were adjusted to find the best combination to simulate historic data. Initial-head values of 

35, 25, and 20 ft below land surface were chosen for the 

shallow, middle, and deep aquifers, respectively. Initial 

aquitard heads were linearly interpolated between estimated heads in adjacent aquifers under the assumption 

that the system was in equilibrium. Initial preconsolidation heads (fig. 6) for aquifers were estimated by 

comparing historical trends of land subsidence and 

heads to determine what the approximate heads were 

in about 1935, when land-subsidence rates began to 

significantly increase. Similar to initial aquitard-head 

distributions, preconsolidation heads for aquitards 

were linearly interpolated between heads in adjacent 

aquifers under the assumption that the top and bottom 

fringes of the aquitards were in equilibrium with the 

bounding aquifers when subsidence began. Based on 

available historic data, the starting compaction was 

assumed zero.

Transient Progression

The FHB1 package (Leake and Lilly, 1997) was 

used to assign heads to cells designated as specifiedhead cells (fig. 5). From 1901 to 1950, one head per 

year; from 1950 to 1995, three heads per year; and from 

1995 to 2000, one head per day were specified. FHB1 

linearly interpolated heads for specified-head cells for 

model time steps that were not assigned specified 

heads.

Specified heads for the historic period were 

estimated for each aquifer (fig. 7A). Heads from 1901 

to 1942 were based on water-use trends and head contour maps (Maxey and Jameson, 1948; Domenico and 

others, 1964), because limited head data exist for wells 

near the Lorenzi site. From 1943 to 1994, trends for 

Lorenzi heads were estimated from water-use trends 

and heads measured in the P.J. Goumond well (fig. 1). 

Heads measured in the SNMRE well (fig. 1) from 1971 

to 1994 also were used to estimate historic-period 

heads for the Lorenzi site. Additionally, the estimated 

hydrographs incorporated historic valley-wide head 

trends and, finally, consideration was given to head 

trends measured at the Lorenzi site. Before the late 

1940’s, vertical ground-water flow was upward 

because heads in the shallow aquifer were lower than 

heads in the middle aquifer, which had lower heads 

than the deep aquifer. Between the late 1940’s and early 

1960’s, ground-water development in the deeper units 

caused heads at the Lorenzi site and vicinity to lower in 

the middle and deep aquifers and ground water began 

to flow downward (Domenico and others, 1964; 

Harrill, 1976). The reversal, in which the vertical flow 

of water changes from upward to downward, was a 

result of pumping deeper aquifers and increasing secondary recharge to shallow aquifers.

Heads for the recent period (1995–2000; fig. 7B) 

were daily mean heads from the Lorenzi site. During 

periods of daily pumpage, heads fluctuated as much as 

20 ft/d and, conceptually, those fluctuations caused 

daily fluctuations in deformation rates. However, the 

limited accuracy and efficiency of the extensometer 

prohibited those relatively quick, head-fluctuation 

induced, deformation-rate changes from being measured. When measured heads were used in the model, 

deformation-rate fluctuations were simulated and large 

errors resulted. For this reason, daily mean heads in 

wells USGS-PZD, USGS-PZM, and USGS-PZS were 

assigned to the specified-head cells of the deep, middle, 
NUMERICAL MODEL 15

1995 1996 1997 1998 1999 2000

YEAR

USGS-PZS

USGS-PZM

USGS-PZD

1900 1920 1940 1960 1980 2000

HEAD, IN FEET BELOW LAND SURFACE

350

300

250

200

0

50

100

150

200

250

300

350

B

A

USGS-PZS

USGS-PZM

USGS-PZD

SNMRE

P.J. Goumond

and shallow aquifers, respectively. For periods of missing data, hourly heads were estimated based on data 

from other Lorenzi wells or were linearly interpolated 

between existing data, then averaged to obtain daily 

means.

Aquifer-system compaction and uplift were 

simulated using the IBS1 package (Leake and Prudic, 

1991). The IBS1 package (1) assigns, tracks, and 

changes preconsolidation heads according to simulated 

head changes; (2) assigns elastic and inelastic skeletalstorage values to cells, dependent upon the relation 

between current heads and preconsolidation heads; and 

(3) tracks vertical deformation for each cell. MODFLOW-96 accounted for changes in ground-water storage attributable to the compression and expansion of 

water; the IBS1 package accounted for changes in storage attributable to the compaction and expansion of the 

aquifer-system skeleton and computed the deformation.

Simulated ground-water flow in the Lorenzi 

model was driven entirely by the specified heads (fig. 

7) assigned to aquifer cells and deformation was driven 

by the simulated flow between aquifers and aquitards. 

Aquitard heads fluctuated in response to changes in 

Figure 7. Hydrographs showing (A) heads for P.J. Goumond and SNMRE wells, used to estimate historic specified 

heads, and historic specified heads used in the Lorenzi model and (B) daily average heads for USGS-PZS, USGSPZM, and USGS-PZD, used as recent specified heads in the Lorenzi model, Las Vegas, Nevada.
16 Hydraulic Properties from a 1-Dimensional Numerical Model of Vertical Aquifer-System Deformation, Lorenzi SIte, Las Vegas, NV

heads that were specified in the aquifers. When the 

head in a cell was higher than the preconsolidation 

head, the elastic skeletal storage coefficient was used to 

calculate deformation. When the head in a cell declined 

below the preconsolidation head, the inelastic skeletal 

storage coefficient was used to compute compaction 

and the preconsolidation head was reset to the new, 

lower head.

Hydraulic Properties

Aquifer vertical hydraulic conductivity and 

inelastic skeletal specific storage were not estimated by 

regression because the conceptual model dictated that 

they be constrained. Model cells representing aquifers 

were assigned the relatively large constant value of 

0.1 ft/d for aquifer vertical hydraulic conductivity to 

ensure that head gradients could not form between 

model time steps, in accordance with the conceptual 

model. Model cells representing aquifers were 

assigned a constant value of 0 ft-1 for aquifer inelastic 

skeletal specific storage to ensure that no inelastic compaction in aquifers occurred, in accordance with the 

conceptual model. Aquitard vertical hydraulic conductivity (K'

v), aquitard inelastic skeletal specific storage 

(S'

skv), aquitard elastic skeletal specific storage (S'ske), 

and aquifer elastic skeletal specific storage (Sske) were 

estimated during model calibration by regression. Reasonable ranges for the estimated hydraulic properties 

were based on past studies of Las Vegas Valley and 

other alluvial basins in the southwestern United States 

because of their similar hydrogeologic settings (see 

Previous Investigations section). Data collected at the 

Lorenzi site also were used to estimate specific-storage 

values. Reasonable ranges of estimated properties were 

not used as model input, but rather were compared to 

regression-derived estimates to assist in determining if 

the regression-derived values were realistic.

The reasonable range for K'

v was 2 x 10-6 to 

7 x 10-3 ft/d. Waichler and Cochran (1991) obtained 

estimates that ranged from 2 x 10-6 to 4 x 10-5 ft/d, by 

using the numerical model COMPAC (Helm, 1974, 

1975) to simulate vertical aquifer-system deformation 

for two sites in Las Vegas. An estimated K'

v value of 8 x 

10-6 ft/d was based on stress-deformation analyses of 

aquifer systems in central California (Riley, 1969). 

Sneed and Galloway (2000) estimated values for K'

v

that ranged from 1 x 10-5 to 2 x 10-5 ft/d by using the 

numerical model MODFLOW-96 (Harbaugh and 

McDonald, 1996) to simulate vertical aquifer-system 

deformation for an extensometer borehole in Antelope 

Valley, California. Harrill (1976) estimated values for 

K'

v that ranged from 7 x 10-4 to 7 x 10-3 ft/d for Las 

Vegas Valley and less than 1 x 10-3 ft/d for the area 

around the Lorenzi site, based on vertical hydraulic 

gradients, thickness of aquitards, and the distribution of 

evapotranspiration.

The reasonable range for S'

skv was 7 x 10-6 to 

1 x 10-3 ft-1. Hanson (1989) estimated values for S'

skv

that ranged from 7 x 10-6 to 3 x 10-4 ft-1 by using the 

numerical model COMPAC (Helm, 1974, 1975) to 

simulate vertical deformation for extensometers in 

Tucson Basin and Avra Valley, Arizona. Morgan and 

Dettinger (1996) estimated values for S'

skv that ranged 

from 6 x 10-5 to 1 x 10-4 ft-1 by using the numerical 

model MODFLOW-88 (McDonald and Harbaugh, 

1988) to simulate ground-water flow in Las Vegas 

Valley, Nevada. Sneed and Galloway (2000) used the 

numerical model MODFLOW-96 (Harbaugh and 

McDonald, 1996) to simulate vertical aquifer-system 

deformation for an extensometer borehole in Antelope 

Valley, California, and estimated values for S'

skv that 

ranged from 4 x 10-5 to 4 x 10-4 ft-1. Harrill (1976) 

estimated values for S'

skv that ranged from 1 x 10-4

to 1 x 10-3 ft-1 for Las Vegas Valley, based on land 

subsidence measurements, head declines, and the 

approximate thickness of aquitards.

The reasonable ranges for S'

ske and Sske were 

based on Hanson (1989). Hanson estimated values of 

S'

ske that ranged from 1 x 10-6 to 2 x 10-5 ft-1 and 

values of Sske that ranged from 3 x 10-8 to 2 x 10-6 ft-1, 

by using the numerical model COMPAC (Helm, 1974, 

1975) to simulate vertical aquifer-system deformation 

for extensometers in Tucson Basin and Avra Valley, 

Arizona.

Stress-deformation analyses (Riley, 1969) of 

USGS-PZD and USGS-EXT1 data were applied to 

refine literature-derived storage estimates. The estimated values, however, did not fall within the reasonable ranges of estimates of past studies. The stressdeformation derived estimates ranged from 2 x 10-7

to 2 x 10-6 ft-1 for the elastic skeletal specific storage of 

the aquifer system (a property that comprises both 

aquifer and aquitard storage) and from 6 x 10-7 to 

1 x 10-6 ft-1 for S'

skv .
MODEL CALIBRATION 17

0 0.02 0.04 0.06 0.08 0.10

VERTICAL DEFORMATION, IN FEET

225

250

275

300

325

350

HEAD, IN FEET BELOW LAND SURFACE

1995 1996 1997 1998 1999 2000

YEAR

VERTICAL DEFORMATION,

IN FEET

USGS-EXT1

HEAD, IN FEET

BELOW LAND SURFACE

USGS-PZD

B

A C

0

0.02

0.04

0.06

0.08

0.10

225

250

275

300

325

350

The discrepancies were possibly because of 

seasonal data trends and daily anomalies. Results from 

stress-deformation analyses are best when seasonalhead cycles have declining annual peaks with corresponding cycles of compaction and expansion and 

when residual compaction is minimal. At the Lorenzi 

site, however, for 1995–97 USGS-PZD had declining 

annual peaks without cycles of compaction and expansion, and for 1998–2000, USGS-PZD had rising annual 

peaks (fig. 8; Pavelko, 2000). Additionally, during 

summer months the extensometer record was contaminated by thermal effects on the extensometer (Pavelko, 

2000) caused by daily air-temperature fluctuations of 

as much as 55°F in the extensometer shed. The daily 

thermal effects on the extensometer were recorded as 

vertical deformation fluctuations contrary to the conceptual model: daily head declines were associated 

with aquifer-system expansion and daily head recovery 

with aquifer-system compaction (fig. 9). Barometric 

pressure and borehole-air temperature did not affect 

extensometer data (Pavelko, 2000) or the stress-deformation analyses.

MODEL CALIBRATION

The numerical model was calibrated with a combination of trial-and-error and nonlinear-regression 

methods. Before and concurrent with the regression, 

the numerical model, including hydraulic-property values, was manually changed by trial-and-error methods 

until the model fit and regression statistics indicated 

that the physical system was sufficiently represented 

and simulated data were reasonable. Nonlinear regression was performed by UCODE, a computer code for 

universal inverse modeling (Poeter and Hill, 1998). 

During regression, selected parameter values, in this 

case hydraulic properties, were adjusted to minimize 

differences between simulated and observed data to 

obtain optimal parameter estimates. The observed 

data were historical compaction estimates and recent 

extensometer measurements. The calibrated model 

and estimated parameter values were evaluated by 

examining the water budget of the numerical model, 

analyzing the sensitivity of observed data to the 

Figure 8. Graphs showing (A) Daily average water levels from USGS-PZD, (B) daily deformation from USGS-EXT1, and 

(C) stress-deformation data from USGS-PZD and USGS-EXT1, Lorenzi site, Las Vegas, Nevada.
18 Hydraulic Properties from a 1-Dimensional Numerical Model of Vertical Aquifer-System Deformation, Lorenzi SIte, Las Vegas, NV

276

279

282

285

288

291

294

HEAD, IN FEET BELOW LAND SURFACE

0.07525

0.07550

0.07575

0.07600

0.07625

0.07650

0.07675

0.07700

0.07725

AQUIFER-SYSTEM VERTICAL DEFORMATION SINCE NOVEMBER 1994 , IN FEET

17 18 19 20 21 22 23 24 25 26

JULY 1999

Shaded area highlights

a period of head decline

not associated with

aquifer-system compaction

Daily deformation fluctuations

correspond to air-temperature

fluctuations and do not track

head fluctuations

Daily head fluctuations

correspond to daily changes

in pumping rates

Deformation in USGS-EXT1

Head in USGS-PZD

estimated parameters, comparing simulated vertical 

deformation to observed data, examining simulated 

aquitard heads, and examining regression statistics.

UCODE iteratively ran the numerical model and 

systematically adjusted parameter values for each 

model run. The results of each model run were evaluated by UCODE to identify the run with the smallest 

objective function, which, statistically, is the run with 

the set of optimal parameter-value estimates. The 

weighted least-squares objective function (S) used in 

UCODE is defined as:

, (8)

where n is the total number of observations; wi is the 

weight of the ith observation; yi

 is the ith observation; 

 is the ith simulated value; and is the residual 

for the ith observation and a measure of the model fit 

to yi. Observation weights were assigned to reflect the 

estimated accuracy of the observations. Observation 

weights were derived by trial-and-error methods during 

the regression process. A modified Gauss-Newton 

method (Cooley and Naff, 1990; Hill, 1992, 1998) was 

used by UCODE to minimize the objective function.

No aquitard-head data were available to use as 

observations, which meant that the objective function 

was minimized based only on deformation-data errors 

but allowed for simulated aquitard heads that did not 

conform to the conceptual model and unreasonable 

estimated-parameter values. Regression-statistics 

analyses were complicated further by statistics from 

model runs with different weighting schemes, because 

subjective weight data influenced the statistics as much 

as quantitative simulated data. For example, a run with 

small weights and a poor fit, and a run with large 

S wi yi y'

i [ ] – 2

i = 1

n

= ∑

y'

i yi y'i –

Figure 9. USGS-PZD water levels and USGS-EXT1 deformation for July 17–26, 1999, a period of diurnal pumping with an 

extensometer record contaminated by thermal effects, Lorenzi site, Las Vegas, Nevada.
MODEL CALIBRATION 19

weights and a good fit could have similar objective 

functions. To account for these complications, acceptable model runs were chosen based on regression 

statistics, qualitative analyses of simulated aquitard 

heads, and whether the estimated parameter values 

were reasonable.

As a result of head changes, the volume of water 

in a cell could have changed from compression or 

expansion of water, or compression or expansion of 

the skeletal matrix, or both. At the end of each stress 

period, a cumulative volumetric budget was calculated 

that detailed the volume of water that flowed into or out 

of each source. The budget calculations were independent of the flow-equation solution process, and therefore provided independent evidence for a valid solution 

(McDonald and Harbaugh, 1988). For the Lorenzi 

model, cumulative volumetric discrepancies at the end 

of each stress period were less than 0.05 percent of the 

total volume of water exchanged, which indicates an 

acceptable solution to the ground-water flow equations 

in the numerical model.

Observation Data

Simulated data were compared to observation 

data to evaluate model fit during calibration. Observation data typically were chosen because they provided 

important information about the parameters being estimated by regression. UCODE determined the set of 

parameter values associated with the minimized objective function. Weights were assigned to observation 

data to reflect their accuracy and importance to the 

regression. Observation data used for the Lorenzi 

model were either estimated or measured deformation 

data. Historic observations were based on land subsidence measurements and estimates. Recent studies 

support using land-subsidence data as compaction estimates for the Lorenzi site. For example, Langenheim 

and Jachens (1996) and Langenheim and others (2001) 

used gravity (V. Langenheim, U.S. Geological Survey, 

written commun., 2000) and borehole-lithologic data to 

estimate the thickness of basin fill. These studies indicate that there are about 800 ft of low-density (compactible) sediments at the Lorenzi site, the base of 

which corresponds to the bottom depth of the USGS 

extensometer. Another study (Hoffmann and others, 

2001) compared annual trends of land subsidence 

measured with InSAR to aquifer-system compaction 

measured by the extensometer and the values are 

similar.

Historic observations consisted of 21 compaction 

estimates derived from benchmark surveys and InSAR 

data (fig. 10). Contour maps and cross sections based 

on data from repeat surveys between 1935 and 1987 

(Malmberg, 1965; Mindling, 1971; Harrill, 1976; Bell, 

1981; Bell and Price, 1993) outlined valley-wide 

subsidence trends based on altitude changes of benchmarks. InSAR data collected between 1992 and 1997 

showed that the distribution of land subsidence in Las 

Vegas Valley is controlled, to a large degree, by faults 

(fig. 2; Amelung and others, 1999) and, thus, indicated 

that the benchmark data from past studies were contoured erroneously. Bell and others (2000) used benchmark data and InSAR-derived subsidence patterns to 

revise a contoured land subsidence map for 1963–98 

(fig. 2). The new map indicated that much less subsidence occurred at the Lorenzi site than previously estimated. Consequently, historic subsidence observations 

were derived from historic trends delineated in past 

studies, current trends measured at the Lorenzi site, 

and recent trends and patterns measured with InSAR. 

Figure 10 shows land-subsidence data for benchmarks 

K169, P169, Q365, and V170, an estimate of subsidence for the Lorenzi site based on InSAR (Bell and 

others, 2000, fig. 4), and historic observations for the 

Lorenzi model; figure 2 shows the locations of the 

benchmarks.

Compaction estimates for 1901–63 were based 

on ranges of land subsidence measured by benchmark 

surveys, trends of head declines, and the trend of subsidence extrapolated from the subsidence contour map 

from Bell and others (2000, fig. 4). Values for 1963–87 

were based largely on the Bell and others (2000, fig. 4) 

contour map for 1963–98, but trends of head declines, 

trends of historical subsidence from benchmark surveys, and recent trends of deformation measured at the 

Lorenzi site were considered. The trend of estimated 

compaction for 1989–94 was based on the trend of 

extensometer data and was estimated by extrapolating 

from the 1987 observation value.

Based on limited water-use data, no subsidence 

before 1901 and 0.01 ft by 1935 was assumed. Surveys 

in 1935 and 1941 indicated that 0.01–0.04 ft of land 

subsidence occurred at the Lorenzi site (Malmberg, 

1965; Mindling, 1971). Surveys indicated that by 1950 

0.1–0.3 ft of subsidence occurred and by 1963 0.2–

0.6 ft occurred (Malmberg, 1965; Mindling, 1971). By 
20 Hydraulic Properties from a 1-Dimensional Numerical Model of Vertical Aquifer-System Deformation, Lorenzi SIte, Las Vegas, NV

-0.5

0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

COMPACTION, IN FEET

1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000

YEAR

Start point (1963)

for benchmark and

InSAR data

Estimated

Interpolated

Extrapolated

K169

P169

Q365

V170

InSAR

1972 an additional 1 ft of subsidence occurred (Harrill, 

1976), from 1963 to 1980 about 1.6 ft was measured 

(Bell, 1981), and from 1963 to 1987 about 2.25 ft was 

measured (Bell and Price, 1993). These estimated 

ranges of subsidence were used to determine historicperiod compaction observations.

Extensometer data were smoothed to obtain 72 

recent-period observations that represented measured 

deformation for periods ranging from 25 days to almost 

5 years (fig. 11). The selection of the timing and duration of observations were guided by trends of measured 

deformation (fig. 11A). Seasonal trends of total compaction, residual compaction, and expansion and periods of transition from compaction to expansion, or 

vice-versa, were delineated by 24 short-term and 22 

seasonal observations that ranged from 25 to 256.25 

days (fig. 11B). Fourteen long-term observations that 

ranged from 281.25 to 743.75 days and 12 cumulative 

observations that ranged from 112.375 to 2,112.375 

days corresponded to longer vertical-deformation 

trends. Figure 11 shows the timing and span of recentperiod observations and their relation, in time, to daily 

vertical deformation. Recent observations ranged from 

0.0056 ft of expansion to 0.0894 ft of compaction and 

averaged 0.0147 ft of compaction.

Observation Weights

Observation weights quantify each observation’s 

relative influence on the regression. Accurate observations and observations that are especially important to 

the regression typically are assigned relatively high 

weights. Weights for Lorenzi observations primarily 

were based on the importance of observations to the 

regression, although observation accuracy, which generally was unknown, was considered.

Figure 10. Estimated, interpolated, and extrapolated compaction data used as historic observations in the Lorenzi 

model (1901–95), compaction measured at selected benchmarks, relative to 1963, and an InSAR-derived compaction 

estimate (1963–98), Las Vegas, Nevada.
MODEL CALIBRATION 21

SHORT

TERM SEASONAL

LONG

TERM CUMULATIVE

RECENT OBSERVATIONS, BY TYPE

1995 1996 1997 1998 1999 2000

0

0.02

0.04

0.06

0.08

0.10

VERTICAL

DEFORMATION,

IN FEET

B

A

In UCODE, the weight is calculated as the inverse 

of the variance of measurement error of an observation. 

For the Lorenzi model, a standard deviation or coefficient of variation for observation errors were input and 

the variance and weight were calculated by UCODE 

from these quantities.

Historic observation errors were caused by survey-measurement errors, contouring errors, and estimation errors. The observation errors were too difficult 

to quantify accurately; instead, errors were assumed to 

be related to the magnitudes of the observations. For 

years with repeat benchmark surveys, the actual 

amount of compaction was assumed to be within ±50 

percent of the estimated observation values and, for 

years without repeat surveys, the actual amount of 

compaction was assumed to be within ±100 percent of 

the estimated observation values. These assumptions 

were used to calculate a coefficient of variation of 0.25 

for observations in years with repeat surveys and 0.50 

for observations in years without repeat surveys, except 

1901. For the 1901 observation, a standard deviation of 

0.005 ft was assigned because no compaction occurred 

by 1901 and a zero value cannot be assigned a coefficient of variation. Table 2 shows historic observations, 

error statistics, and weights.

Recent observation errors included extensometermeasurement errors and inaccuracies resulting from 

smoothing extensometer data. The extensometermeasurement errors resulted from the resolution of the 

measuring device and frictional and thermal effects 

(Pavelko, 2000). Errors associated with the resolution 

of the measuring device likely were insignificant relative to the frictional and thermal effects. Frictional 

“stick-slip” effects were caused by instantaneous 

releases of frictional energy created by the extensometer pipe rubbing against the borehole casing (Riley, 

1986) and resulted in false step-like shifts in the 

recorded deformation data (Pavelko, 2000). Stick-slip 

effects greater than 0.0001 ft were removed from the 

record by shifting data after the event to align with data 

Figure 11. Graphs showing (A) daily deformation measured at USGS-EXT1 and (B) time spans for 

recent-period observations, by observation type, for the Lorenzi model, Las Vegas, Nevada.
22 Hydraulic Properties from a 1-Dimensional Numerical Model of Vertical Aquifer-System Deformation, Lorenzi SIte, Las Vegas, NV

Table 2. Historic observations and weight-related statistics used with the Lorenzi model, Las Vegas, Nevada

[The 1901 weight was based on a standard deviation and for all other historic observations, UCODE calculated weights based on 

coefficients of variation. Observations with a coefficient of variation of 0.25 correspond to years with repeat benchmark surveys. 

Abbreviations: ft, feet; ft2, square feet; --, not applicable]

Year of 

observation

Observation 

value 

(ft)

Coefficient of 

variation

Standard 

deviation 

(ft)

Variance

(ft2)

Weight

(1/ft2)

1901 0.00 -- 5.0 x 10-3 2.5 x 10-5 4.0 x 104

1935 0.01 0.50 5.0 x 10-3 2.5 x 10-5 4.0 x 104

1941 0.03 0.25 7.5 x 10-3 5.6 x 10-5 1.8 x 104

1944 0.08 0.50 4.0 x 10-2 1.6 x 10-3 6.3 x 102

1947 0.13 0.50 6.5 x 10-2 4.2 x 10-3 2.4 x 102

1950 0.18 0.25 4.5 x 10-2 2.0 x 10-3 4.9 x 102

1953 0.22 0.50 1.1 x 10-1 1.2 x 10-2 8.3 x 101

1957 0.28 0.50 1.4 x 10-1 2.0 x 10-2 5.1 x 101

1960 0.32 0.50 1.6 x 10-1 2.6 x 10-2 3.9 x 101

1963 0.36 0.25 9.0 x 10-2 8.1 x 10-3 1.2 x 102

1966 0.49 0.50 2.5 x 10-1 6.0 x 10-2 1.7 x 101

1969 0.63 0.50 3.2 x 10-1 9.9 x 10-2 1.0 x 101

1972 0.76 0.25 1.9 x 10-1 3.6 x 10-2 2.8 x 101

1975 0.89 0.50 4.5 x 10-1 2.0 x 10-1 5.0 x100

1977 0.98 0.50 4.9 x 10-1 2.4 x 10-1 4.2 x 101

1980 1.10 0.25 2.8 x 10-1 7.6 x 10-2 1.3 x 100

1983 1.23 0.50 6.2 x 10-1 3.8 x 10-1 2.6 x 100

1986 1.36 0.25 3.4 x 10-1 1.2 x 10-1 8.7 x 100

1989 1.45 0.50 7.3 x 10-1 5.3 x 10-1 1.9 x 100

1992 1.55 0.50 7.8 x 10-1 6.0 x 10-1 1.7 x 100

1994 1.60 0.50 8.0 x 10-1 6.4 x 10-1 1.6 x 100
MODEL CALIBRATION 23

from before the event. Frictional “dead-band” effects 

(Riley, 1986), which can be difficult to detect in an 

extensometer record, also were likely present in the 

extensometer data, but no effort was made to correct for 

them.

Daily temperature fluctuations of as much as 

55°F in the extensometer shed caused components of 

the extensometer to thermally expand and contract, 

which resulted in recorded daily fluctuations (fig. 9) 

that likely reflected diurnal temperature trends rather 

than deformation trends (Pavelko, 2000). To minimize 

the effects of daily temperature fluctuations on the 

extensometer record, while maintaining longer-term 

trends, the extensometer data were smoothed.

The combined errors associated with the resultant 

observation data set were too difficult to quantify accurately. The errors were assumed the same for all recent 

observations because each consisted of two measurements made by the same device. Thus, a standard deviation was estimated to determine weights rather than a 

coefficient of variation, which would have assigned 

weights based upon the magnitude of observation 

values. To estimate the standard deviation, several sets 

of weighting schemes were tested with UCODE runs. 

When weights were skewed to emphasize the historic 

period, historic observations were simulated well but 

recent observations were matched poorly. Similarly, 

when weights were skewed to emphasize the recent 

period, the recent period was simulated well but the 

historic period was simulated poorly. Trial-and-error 

weight adjustments indicated that a balanced simulation of the two periods would result when recent observation errors were assigned a standard deviation of 

0.005 ft. Implications and limitations to assigning 

qualitatively derived weights are discussed in the 

Sensitivity section. 

Sensitivity

The sensitivity of the model to parameter values, 

observation values, observation weights, and the conceptual model was analyzed with sensitivity statistics 

and by testing alternative conceptual and numerical 

models. Sensitivity statistics reveal information about 

how sensitive a model is to changes in parameter values 

and how important observations are to estimating 

parameters. Parameter sensitivities calculated by 

UCODE for the calibrated model were analyzed to 

determine if the numerical model and observation data 

provided enough information to adequately estimate 

the parameters (Hill, 1998). Sensitivity to model thicknesses, initial preconsolidation heads, and observation 

weights also were tested.

The composite scaled sensitivity (CSS) of an 

estimated parameter represents the sensitivity of a 

model to a change in a parameter value, summarizes 

the importance of all observation data to estimating the 

parameter, and is defined as:

, (9)

where b is the parameter value. Relatively large CSS 

values indicate that the simulated equivalents of the 

observation data are sensitive to those parameters 

and therefore those parameters are more likely to be 

adequately estimated. If estimation by regression is 

attempted for parameters with CSS values less than 

0.01 times the largest CSS value, the regression may 

have difficulties converging and the estimated parameter values may not be accurate or unique. The CSS 

values calculated for the estimated parameters (fig. 12) 

indicated that the model and observation data provided 

sufficient information to estimate the parameters by 

regression because the largest CSS value was less than 

100 times the smallest CSS value (Hill, 1998).

Dimensionless scaled sensitivity (DSS) values 

(Hill, 1992) were calculated for each observation. DSS 

values are used to determine the importance of individual observations to estimating each parameter value 

and the importance of individual parameters to calculating simulated observation values (Hill, 1998). Generally, observations that represented more deformation 

had relatively large absolute values of dimensionless 

scaled sensitivities, which indicated that they were 

more important to the regression than observations 

that represented less deformation. DSS values also 

indicated that all observations generally were most 

sensitive to S'

skv, shorter-term observations were 

relatively more sensitive to Sske, and longer-term 

observations were relatively more sensitive to S'

skv. The 

relatively large CSS and DSS values for S'

skv indicated 

that observation data as a whole are most sensitive to 

that parameter.

Simulated deformation was sensitive to the thickness of the simulated aquifer system. Because UCODE 

does not evaluate aquifer thickness, a sensitivity 

CSS wi

i = 1

n

∑

∂y'

i

∂b --------b ⎝ ⎠ ⎛ ⎞ 2

n ------------------------------------

1

2

--

=
24 Hydraulic Properties from a 1-Dimensional Numerical Model of Vertical Aquifer-System Deformation, Lorenzi SIte, Las Vegas, NV

PARAMETER

S' S skv ' K ske '

v Sske

0

5

10

15

20

25

30

35

COMPOSITE SCALED SENSITIVITY

6

9

6

33

analysis was done to determine the magnitude of 

change, if any, an increased aquifer thickness would 

have on estimated hydraulic-property values, simulated 

deformation, and simulated aquitard heads. Although 

data only support a model no deeper than 800 ft below 

land surface, a thicker, simplified conceptual model 

was constructed by repeating below the original model 

the 735-ft sequence of sediments measured with geophysical methods (fig. 5). The 1,470-ft thick model 

approximates Plume’s (1989) estimate of about 1,600 ft 

of sediments at the Lorenzi site. Regression-derived 

estimates of hydraulic properties from the thicker 

model ranged from about two times higher (S'

skv) to 

three orders-of-magnitude lower (Sske) than calibrated 

model estimates. Additionally, the deformation and 

aquitard-head profiles simulated with the thicker model 

did not adequately match estimated or measured data. 

Therefore, the sensitivity analysis indicates that the 

thickness of the calibrated conceptual model more 

appropriately simulated deformation than the thicker 

model, but does not confirm that there are no compactible sediments below 800 ft.

Simulated deformation was sensitive to initial 

preconsolidation heads, which were not considered 

in sensitivity statistics. To examine the sensitivity to 

initial preconsolidation heads, the 1.65 ft of total simulated deformation from the final model was compared 

to simulated deformation from alternative models. 

When initial preconsolidation heads were increased by 

10 ft, total deformation was 1.72 ft and when initial 

preconsolidation heads were deceased by 10 ft, total 

deformation was 1.58 ft. The significant figures of 

these simulated values are given only to show the variation produced when changing initial preconsolidation 

heads and do not imply a level of accuracy.

Figure 12. Composite scaled sensitivities for the estimated parameters of the Lorenzi model, Las Vegas, Nevada.
MODEL CALIBRATION 25

VERTICAL DEFORMATION, IN FEET

1995 1996 1997 1998 1999 2000

YEAR

Simulated

Measured

1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000

COMPACTION, IN FEET

Simulated

Estimated

Interpolated

Extrapolated

B

A

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.10

-0.25

0

0.25

0.50

0.75

1.00

1.25

1.50

1.75

Model Fit

Model fit was evaluated by comparing simulated 

deformation to observation data, examining regressionerror statistics, and analyzing weighted residuals. A 

good model fit indicates that, at the scale of the model 

and given the simplifying assumptions and limitations, 

the estimated parameter values are representative of the 

hydraulic-property values. The close match between 

simulated deformation and observation data indicates 

a good model fit that can be seen in a plot comparing 

simulated, observed, and measured deformation 

(fig. 13) and a plot of simulated versus observed 

deformation values (fig. 14). These plots are unaffected 

by the weights associated with observations and therefore provide an analysis independent of weights and 

any uncertainties associated with the weights.

The standard error of regression and fitted error 

statistics are quantitative measures of model fit (Hill, 

1998). The standard error of regression (s) is a measure 

of overall model fit to the weighted observation data, 

and is computed as:

, (10)

where S is the sum of weighted squared residuals for 

all observations and p is the number of estimated 

parameters. For a model fit that is consistent with 

s

S

n p – ----------- ⎝ ⎠ ⎛ ⎞

1

2

--

=

Figure 13. Graphs showing (A) historic simulated and estimated and (B) recent simulated and measured deformation 

data for the Lorenzi model, Las Vegas, Nevada
26 Hydraulic Properties from a 1-Dimensional Numerical Model of Vertical Aquifer-System Deformation, Lorenzi SIte, Las Vegas, NV OBSERVED VERTICAL DEFORMATION, IN FEET

-0.01 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

SIMULATED VERTICAL DEFORMATION, IN FEET

-0.01

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.10

Short term

Seasonal

Long term

Cumulative

-0.2 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8

-0.2

0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

B

A

observation-data accuracy, as indicated by the weighting, s is 1.0. The standard error of the Lorenzi regression was 0.36, which indicated that simulated 

deformation fit observed data better than the weighting 

implied, but did not indicate a lack of model error. 

Trial-and-error weighting adjustments for the Lorenzi 

model indicated that the best combination of model fit 

and regression statistics was achieved with the weights 

used in the calibrated model. The standard error of the 

Lorenzi model is only as accurate as the estimated 

weights and therefore the standard error is more representative of model fit to the conceptual model and 

observation data rather than a measure of model fit to 

the real system.

Fitted error statistics represent the overall fit 

achieved for simulated values (Hill, 1998). Fitted error 

statistics are more intuitive measures of error than the 

standard error because they have the same units as the 

observed values. The statistics are calculated by multiplying s by the statistic used to calculate weights. For 

Figure 14. Simulated deformation versus observed deformation for (A) the historic period and (B) the recent period of 

the Lorenzi model, Las Vegas, Nevada.
MODEL CALIBRATION 27

example, the fitted standard deviation of recent observations (0.002 ft) was the standard error (0.36) multiplied by the standard deviation of recent observations 

(0.005 ft). The fitted standard deviation indicated that, 

overall, simulated deformation values for the recent 

period matched the 72 observed values within 0.002 ft. 

The fitted coefficient of variation was 0.18 ft for the 14 

historic-period observations for years without surveys 

and 0.09 ft for the 6 historic-period observations for 

years with surveys. Fitted error statistics generally are 

meaningful only for a large number of observations 

(Hill, 1998) but were presented for the historic period 

as general indicators of the errors associated with that 

period.

A weighted residual is the difference of an 

observed value and simulated value, multiplied by the 

square root of the observation weight. Weighted residuals, which were evaluated individually and as groups, 

are indicators of observation errors, model fit, and the 

validity of a regression.

Weighted residuals with significantly larger absolute values than other weighted residuals indicate possible problems with observation data or model fit, or 

both. Five historic and three recent weighted residuals 

have absolute values greater than 0.5 (fig. 15), indicating that, generally, few problems exist associated with 

observation data or model fit. Historic period outliers 

likely resulted from inaccurate observation values or 

Short term

Seasonal

Long term

Cumulative

WEIGHTED RESIDUAL

1995 1996 1997 1998 1999 2000 2001

YEAR

WEIGHTED RESIDUAL

1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

Recent

Extrapolated historic

Interpolated historic

Estimated historic

Area enlarged

in (B)

B

A

-0.75

-0.50

-0.25

0

0.25

0.50

0.75

-2

-1

0

1

2

Figure 15. Weighted residuals versus time for the (A) entire model and (B) recent period of the Lorenzi model, Las Vegas, 

Nevada.
28 Hydraulic Properties from a 1-Dimensional Numerical Model of Vertical Aquifer-System Deformation, Lorenzi SIte, Las Vegas, NV

weights, whereas recent period outliers, which were 

associated with transitional periods and periods of 

expansion, likely resulted from errors in the optimal 

estimated hydraulic-parameter values, but mechanical 

inefficiencies associated with the extensometer may 

have had an effect. The generally good model fit (figs. 

13 and 14) indicates that the weighted residual outliers 

do not indicate significant model errors.

ESTIMATED PARAMETER VALUES

The estimated parameter values from the calibrated Lorenzi model were obtained after evaluating 

the conceptual model, testing different sets of parameters to be estimated, and evaluating regression statistics 

for different observation and weighting scenarios. 

Optimal hydraulic-parameter estimates for the Lorenzi 

model are 3 x 10-6 ft/d for K'

v, 4 x 10-5 ft-1 for S'skv, 

5 x 10-6 ft-1 for S'

ske, and 3 x 10-7 ft-1 for Sske (table 3).

The true property values of a physical system 

cannot be accurately quantified and therefore the accuracy of the estimated values cannot be quantified. The 

accuracy of the estimated values, then, were assessed 

on how reasonable the values were based on what was 

known about this and other similar systems; correlation 

coefficients; and simulated conditions, including 

model fit to observed data (figs. 13 and 14) and adherence to the conceptual model.

Unreasonable parameter estimates are indicators 

of model error (Hill, 1998) because it is reasonable to 

expect that parameter values associated with the minimized objective function are realistic values, providing 

that the physical system is adequately represented by 

the model and the observation data provide sufficient 

information about the estimated parameters. For the 

calibrated model, the estimated values were within 

their reasonable ranges (table 3; see the Hydraulic 

Properties section).

Parameter correlation coefficients are a measure 

of the interdependence of two parameters and were 

analyzed to determine if parameter values could be 

uniquely estimated with the information provided by 

the model and observation data (Hill, 1998). Correlation coefficients can range from -1.0 to 1.0 and absolute 

values greater than 0.95 are indicative of potential 

problems for unique parameter-value estimation 

(Hill, 1998). For the Lorenzi model, no parameters 

were correlated above 0.60, indicating that the estimated values were unique and relatively unaffected by 

model or observation errors.

Simulated Conditions

A calibrated model should produce a good model 

fit and agree with the conceptual model. Based on 

comparisons of observed and simulated data (figs. 13 

and 14), examination of regression error statistics, and 

analyses of weighted residuals, as discussed in the 

Model Fit section, the model fit to aquifer-system 

deformation data was considered sufficient and therefore indicates that the estimated parameter values were 

reasonable.

Table 3. Reasonable ranges and optimal estimates for the 

hydraulic parameters estimated with the Lorenzi model, Las 

Vegas, Nevada

[Abbreviations: K′

v, aquitard vertical hydraulic conductivity; S′skv, aquitard 

inelastic skeletal specific storage; S′

ske, aquitard elastic skeletal specific storage; 

Sske, aquifer elastic skeletal specific storage; ft/d, feet per day; 1/ft, per feet]

K′v S′

skv S′ske Sske

(ft/d) (1/ft)

Upper reasonable 

value 7 x 10-3 1 x 10-3 2 x 10-5 2 x 10-6

Optimal estimate 3 x 10-6 4 x 10-5 5 x 10-6 3 x 10-7

Lower reasonable 

value 2 x 10-6 7 x 10-6 1 x 10-6 3 x 10-8
ESTIMATED PARAMETER VALUES 29

0 50 100 150 200 250 300 350

SIMULATED HEAD, IN FEET BELOW LAND SURFACE

0

100

200

300

400

500

600

700

800

DEPTH, IN FEET BELOW LAND SURFACE

Deep aquifer

Deep aquitard

Middle aquifer

Middle aquitard

Shallow aquifer

Shallow aquitard 2000

1995

199019701950

1901

Simulated aquitard heads, estimated aquitard 

time constants, and simulated vertical deformation 

were examined to determine if simulated data were in 

agreement with the conceptual model. If the physical 

system was adequately represented and observation 

data were sufficient, simulated delayed aquitard drainage and associated residual compaction would be 

expected. Figure 16 shows that aquitard heads declined 

much more slowly than aquifer heads and that during 

the recent period, when aquifer heads generally were 

rising, aquitard heads continued to decline. Figure 17 

shows that delayed aquitard drainage was associated 

with simulated residual compaction. Figure 17B shows 

that during the recent period, residual compaction 

occurred in aquitards when aquifer heads were recovering. An indicator of the rate of residual compaction is 

the time constant, , which describes how long a doubly draining aquitard will take to achieve about 93 percent of the total possible compaction for a given head 

decline (eq. 1; Riley, 1969). Strictly speaking, the aquitards at the Lorenzi site are not doubly draining; the 

shallow aquitard only drains downward and the simulated heads in the three aquifers are not identical. At the 

end of the simulated period, the approximate simulated 

heads were 217 ft below land surface for the shallow 

aquifer, 251 ft below land surface for the middle aquifer, and 262 ft below land surface for the deep aquifer. 

A modified equation (Epstein, 1987), described in the 

Mechanics of Vertical Aquifer-System Deformation 

section of this report, was used to calculate for the 

shallow aquitard, and, despite the discrepancies in 

aquifer heads, an approximate was calculated to 

determine if residual compaction based on estimated 

properties conformed to the conceptual model. The 

shallow, middle, and deep aquitards had time constants 

that were about 1,310; 110; and 100 years, respectively. 

The values conform to the conceptual model because 

they indicate that the middle and deep aquitards, which 

τ

τ

τ

Figure 16. Simulated heads for selected years of the Lorenzi model, Las Vegas, Nevada.
30 Hydraulic Properties from a 1-Dimensional Numerical Model of Vertical Aquifer-System Deformation, Lorenzi SIte, Las Vegas, NV

1995 1996 1997 1998 1999 2000

YEAR

350

225

300

275

250

225

HEAD, IN FEET

BELOW

LAND SURFACE

USGS-PZD

1995 1996 1997 1998 1999 2000

-0.01

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.10

SHIFTED VERTICAL

DEFORMATION, IN FEET

Shallow aquitard

Middle

aquitard

Deep aquitard

Deep aquifer

Aquifer

system

Shallow aquifer Middle aquifer

1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

-0.25

0

0.25

0.50

0.75

1.00

1.25

1.50

VERTICAL 

1.75

DEFORMATION,

IN FEET

Shallow aquitard

Middle

aquitard

Deep

aquitard

Shallow, middle, and deep

aquifer deformation was

minimal and indistinguishable

at this scale. See graph (B)

Aquifer system

C

B

A

are approximately doubly draining and relatively thin, 

will achieve about 93 percent of their ultimate compaction much faster than the shallow aquitard, which is 

singly draining and about 55 percent thicker than the 

middle and deep aquitards.

MODEL AND REGRESSION LIMITATIONS

The Lorenzi numerical model was limited by 

the accuracy of the conceptual model, simplifications 

and limitations inherent in the mathematical codes that 

represented the physical systems and processes, and the 

availability and accuracy of data. A primary cause of 

Lorenzi model limitations was insufficient or inaccurate data. A lack of data necessitated simplifications, 

and therefore limitations, in the conceptual and numerical models; observation-data errors that could not be 

quantified resulted in subjective observation weights; 

and a lack of aquitard-head data resulted in an objective 

function that allowed for poorly simulated heads. 

These limitations affected the usefulness of regression 

statistics and the estimation and accuracy of the estimated hydraulic-property values. Limitations also 

arose from assumptions and simplifications embedded 

in the computer codes that made up the model.

The lack of sufficient data to account for all of the 

spatial variations in physical and hydraulic properties 

required that the Lorenzi conceptual and numerical 

models were 1-D simplifications of the surrounding 

Figure 17. Simulated deformation, by aquifer system and aquifer-system unit, for (A) the entire model and (B) the recent period, 

and (C) USGS-PZD specified heads, for the recent period of the Lorenzi model, Las Vegas, Nevada.
MODEL AND REGRESSION LIMITATIONS 31

ground-water flow system, ground-water flow processes, and vertical-deformation processes. Furthermore, any data used in the model but not as observation 

data, such as initial heads, initial preconsolidation 

heads, and specified aquifer heads, likely had inaccuracies that affected simulations. The simplifications and 

data errors likely affected the magnitude and timing of 

simulated deformation and resulted in estimated property values that were averages for the unit types.

Compaction data for the Lorenzi site could not 

support a model that estimated separate hydraulicproperty values for each aquifer-system unit or more 

than one value per unit. Instead, each unit type was 

assumed to be homogeneous and have an identical set 

of hydraulic-property values. This assumption resulted 

in hydraulic-property estimates that are averages for 

the composite thickness of each unit type and not 

necessarily representative of a particular depth interval.

The limiting effects of data on the objective function are related to the accuracy of the observation-data 

weights and the types of data included within the objective function. During the iterative calibration process, 

several weighting scenarios were tested, but because 

weights were included in many of the diagnostic statistics, including the objective function, statistical comparisons of model results were misleading if the runs 

did not have the same weights. Therefore, (1) weighting schemes were chosen subjectively, based on visual 

matches to observation data and the reasonability of 

simulated aquitard heads and estimated parameter 

values and (2) diagnostic statistics were helpful during 

calibration to identify runs that were bad, but the statistics could not be used as comparative tools for runs 

with different weighting schemes. 

The objective function, and therefore the estimated parameter values, also was affected by a lack 

of variety of data. Ideally, the objective function, and 

therefore observation data, should include as many 

types of data and as much data as reasonably possible. 

The Lorenzi model simulated vertical deformation and 

aquitard heads, but there were no aquitard-observation 

data. The lack of aquitard observations resulted in 

several intermediate runs that fit the deformationobservation data well, but did not fit the conceptual 

model. For example, figure 18 is a plot of simulated 

heads for the calibrated model and an intermediate run 

that was identical except that the recent period weights 

were larger. The two runs had simulated deformation 

curves that were very similar, but the intermediate run 

had simulated aquitard heads that conceptually were 

not correct because there was almost no delayed drainage within aquitard units. The objective function as a 

diagnostic tool was misleading because although the 

two runs had comparable objective function values 

(good fits to deformation) the intermediate run was a 

much worse run because of the poorly simulated aquitard heads. Inclusion of aquitard-head data as an observation would have improved the value of the objective 

function.

Model and regression limitations also resulted 

from documented limitations associated with the various computer codes used in the model (McDonald and 

Harbaugh, 1988; Harbaugh and McDonald, 1996; 

Leake and Lilly, 1997; Leake and Prudic, 1991; Poeter 

and Hill, 1998). In particular, the IBS1 package does 

not calculate deformation for specified-head cells, 

which likely resulted in a slight underestimation of 

aquifer deformation or a slight overestimation of storage values, or both. All specified-head cells in the 

Lorenzi model were 1-ft thick, which equated to an 

aggregate thickness of 5 ft, or about 0.7 percent of the 

total model thickness. Another limitation arose from 

the assumption embedded within the IBS1 package that 

elastic aquifer-system deformation is proportional to 

effective stress changes and that inelastic compaction is 

proportional to effective stress increases, even though 

inelastic aquitard compaction is more likely proportional to increases in the logarithm of effective stress 

(Jorgensen, 1980; Leake and Prudic, 1991). Leake and 

Prudic indicate that errors resulting from this assumption are minimal.

The deformation formulation used in the IBS1 

package (Leake and Prudic, 1991) is based on the 

assumption that within a model cell a change in head 

will result in an instantaneous change in ground-water 

storage. Thus, deformation in individual model cells 

occurs instantaneously with a change in head rather 

than at a rate controlled by hydraulic properties. This 

shortcoming for simulating delayed drainage and 

residual compaction was minimized by using a finely 

discretized model grid for aquitards.
32 Hydraulic Properties from a 1-Dimensional Numerical Model of Vertical Aquifer-System Deformation, Lorenzi SIte, Las Vegas, NV

Initial heads

Intermediate model

Calibrated model

0 50 100 150 200 250 300

HEAD, IN FEET BELOW LAND SURFACE

0

100

200

300

400

500

600

700

800

DEPTH, IN FEET BELOW LAND SURFACE

Deep aquifer

Deep aquitard

Middle aquifer

Middle aquitard

Shallow aquifer

Shallow aquitard

SUMMARY AND CONCLUSIONS

Las Vegas is in Las Vegas Valley, in southern 

Nevada, and is the Nation’s fastest growing metropolitan area. Decades of ground-water withdrawals have 

resulted in aquifer-system compaction, over 5 ft of land 

subsidence, and earth fissuring. Since 1988, artificial 

ground-water recharge programs have slowed the 

rate of subsidence and caused seasonal aquifer-system 

expansion and land uplift. The aquifer system at the 

Lorenzi site, which is in Las Vegas and monitors 

ground-water levels and vertical aquifer-system 

deformation, was numerically modeled to estimate 

hydraulic properties that affect vertical aquifer-system 

deformation.

The conceptual model used to construct the 

numerical model was based on geophysical and lithologic logs collected at the site and established theories 

of aquifer-system mechanics. The numerical model 

consisted of three thick aquifers and three thick aquitards. Fine spatial discretization of the model allowed for 

the simulation of residual compaction; fine temporal 

discretization allowed for better analyses of short-term 

deformation trends and nonlinear-head distributions. 

Ground-water flow, and therefore aquifer-system 

deformation, was controlled entirely by transient heads 

that were specified for selected aquifer cells.

The model simulated ground-water flow and vertical aquifer-system deformation from January 1, 1901, 

to November 19, 2000. The initial conditions and specified heads for the historic period, 1901–94, were 

estimated from previously published reports. For the 

recent period, 1995–2000, specified heads were daily 

average heads collected at the Lorenzi site.

Nonlinear-regression techniques were applied to 

the model for calibration and estimation of aquitard 

vertical hydraulic conductivity, aquitard inelastic skeletal specific storage, and aquitard and aquifer elastic 

skeletal specific storage. The observation data used for 

the regression consisted of 21 estimates of compaction 

Figure 18. Initial heads and simulated head profiles for the calibrated model and an intermediate model, for 2000, the 

Lorenzi model, Las Vegas, Nevada.
REFERENCES CITED 33

for the historic period and 72 deformation measurements from smoothed extensometer data for the recent 

period.

The optimal estimates for the hydraulic properties 

were: 3 x 10-6 ft/d for aquitard vertical hydraulic conductivity, 4 x 10-5 ft-1 for aquitard inelastic skeletal 

specific storage, 5 x 10-6 ft-1 for aquitard elastic skeletal specific storage, and 3 x 10-7 ft-1 for aquifer elastic 

skeletal specific storage. The regression, and therefore 

estimated parameter values, was negatively affected by 

a lack of aquitard-head data. Acquiring and incorporating aquitard data into the model would have better 

constrained the regression and resulted in a more quantitative set of parameter estimates. Given the limitations of the numerical model to represent the physical 

system and inaccuracies related to observations, model 

fit, regression statistics, and simulated aquitard heads 

indicated that the numerical model and observation 

data provided sufficient information to estimate the 

target parameters, the regression was valid, and the 

estimated hydraulic-property values were reasonable.

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36 Hydraulic Properties from a 1-Dimensional Numerical Model of Vertical Aquifer-System Deformation, Lorenzi SIte, Las Vegas, NV
Since 1879, the U.S. Geological Survey has been providing maps, reports, and information to help others 

who manage, develop, and protect our Nation’s water, energy, mineral, land, and biological resources. We 

help find natural resources, and we supply scientific understanding needed to help minimize or mitigate 

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our efforts touch the daily lives of almost everyone.

Pavelko—ESTIMATES OF HYDRAULIC PROPERTIES FROM A ONE-DIMENSIONAL NUMERICAL MODEL OF VERTICAL AQUIFER-SYSTEM DEFORMATION, LORENZI SITE, 

LAS VEGAS, NEVADA—USGS WRIR 03–4083