WATER BUDGET AND SIMULATION OF ONEDIMENSIONAL UNSATURATED FLOW FOR A 

FLOOD- AND A SPRINKLER-IRRIGATED FIELD 

NEAR MILFORD, UTAH

By David D. Susong

U.S. GEOLOGICAL SURVEY

Water-Resources Investigations Report 95-4072

Prepared in cooperation with the 

Utah Department of Natural Resources, 

Division of Water Rights

Salt Lake City, Utah 

1995
U.S. DEPARTMENT OF THE INTERIOR 

BRUCE BABBITT, Secretary

U.S. GEOLOGICAL SURVEY 

Gordon P. Eaton, Director

The use of trade, product, industry, or firm names is for descriptive purposes only and does not imply 

endorsement by the U.S. Government.

For additional information write to: Copies of this report can be purchased from:

District Chief U.S. Geological Survey 

U.S. Geological Survey Earth Science Information Center 

1745 West 1700 South Open-File Reports Section 

Room 1016 Administration Building Box 25286, MS 517 

Salt Lake City, Utah 84104 Denver Federal Center

Denver, Colorado 80225
CONTENTS

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

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

Purpose and scope.................................................................................................................................. 3

Site description...................................................................................................................................... 3

Climate........................................................................................................................................ 3

Hydrology.................................................................................................................................... 3

Physical and hydraulic properties of the soil.............................................................................. 6

Methods of investigation ....................................................................................................................... 6

Water budget..................................................................................................................................................... 9

Precipitation........................................................................................................................................... 10

Irrigation water...................................................................................................................................... 10

Evapotranspiration................................................................................................................................. 11

Runoff.................................................................................................................................................... 13

Soil-moisture storage............................................................................................................................. 13

Recharge................................................................................................................................................ 14

Simulation of one-dimensional unsaturated flow............................................................................................. 19

Discretization......................................................................................................................................... 20

Boundary conditions.............................................................................................................................. 20

Parameters.............................................................................................................................................. 20

Calibration............................................................................................................................................. 22

Simulated water budget for the flood- and the sprinkler-irrigated field for average climate conditions 26

Effects of distribution of flood-irrigation water on recharge................................................................. 27

Sensitivity analysis................................................................................................................................ 27

Limitations of the model........................................................................................................................ 30

Summary ......................................................................................................................................................... 30

References cited............................................................................................................................................... 32

FIGURES

1. Schematic diagram and map showing location of study site, Milford area, Utah ............................. 2

2-15. Graphs showing:

2. Average hourly air temperature and wind velocity and daily precipitation and

evapotranspiration at the study site, Milford area, Utah, 1992 ................................................... 4

3. Average hourly air temperature and wind velocity and daily precipitation and

evapotranspiration at the study site, Milford area, Utah, 1993 ................................................... 5

4. Particle-size distribution of clod and core samples from the flood- and the sprinkler-irrigated

field, Milford area, Utah.............................................................................................................. 8

5. Relation of volumetric soil-moisture content with neutron-count ratio and capacitance probe

Dcounts, flood-irrigated field, Milford area, Utah....................................................................... 10

6. Application of irrigation water to the flood- and the sprinkler-irrigated field, Milford area,

Utah, 1992 and 1993.................................................................................................................... 12

7. Relation between evapotranspiration data of the U.S. Geological Survey and Utah Climate

Center, Milford area, Utah........................................................................................................... 14

8. Volumetric soil-moisture profiles for the flood- and the sprinkler-irrigated field for the 1992

irrigation season and daily soil-moisture profiles for May 1993, Milford area, Utah................. 15

9. Daily water content and change in daily water content in a soil column in the flood- and the

sprinkler-irrigated field, Milford area, Utah, May and June, 1993.............................................. 16

10. Volumetric soil-moisture content at a depth of 1.52 meters in the flood-irrigated field,

Milford area, Utah, 1993 ............................................................................................................ 17

iii
FIGURES Continued

2-15. Graphs showing: Continued

11. Water budget for the flood- and the sprinkler-irrigated field for 1992 and 1993 irrigation

seasons, Milford area, Utah......................................................................................................... 18

12. Composite average particle-size distribution in soil clods from two pits and soil cores from 

four neutron-probe access holes in the flood- and the sprinkler-irrigated field, and 

unsaturated-flow-model textural classes and layers, Milford area, Utah .................................... 21

13. Simulated daily soil-moisture profiles in the flood- and the sprinkler-irrigated field for

1992 and 1993 irrigation seasons, Milford area, Utah ................................................................ 23

14. Simulated cumulative water budget for the flood- and the sprinkler-irrigated field for 1992

and 1993 irrigation seasons, Milford area, Utah ........................................................................ 25

15. Simulated cumulative water budget for the flood- and the sprinkler-irrigated field for average

climate conditions (1961-90) with 1992 and 1993 irrigation applications, Milford area, Utah . 28 

16. Diagram showing simulated (a) uniform and (b) linear distribution of flood-irrigation water

across a field....................................................................................................................................... 29

TABLES

1. Laboratory determined particle-size distribution, organic carbon content, and bulk density of

soil in the flood- and the sprinkler-irrigated field, Milford area, Utah............................................... 7

2. Summary of estimated and simulated water budget for the flood- and the sprinkler-irrigated

field for the 1992 and 1993 irrigation seasons, Milford area, Utah................................................... 26

3. Simulated water budget for the flood- and the sprinkler-irrigated field for average climate

conditions, Milford area, Utah........................................................................................................... 27

4. Water budget for three simulations that demonstrate the sensitivity of the model of the floodand the sprinkler-irrigated field to changes in saturated hydraulic conductivity, Milford 

area, Utah........................................................................................................................................... 30
CONVERSION FACTORS AND VERTICAL DATUM

Multiply_______________By______________To obtain

centimeter (cm) 0.3937 inch (in.)

centimeter per day (cm/day) 0.03281 foot per day (ft/day)

o «3

cubic meter per minute (m /min) 0.1794 cubic feet per minute (ft /min)

hectare (ha) 2.471 acre

kilometer (km) 0.6214 mile (mi)

meter (m) 3.281 foot (ft)

meter per second (m/s) 2.2369 mile per hour (mi/h)

millimeter (mm) 0.03937 inch (in.)

millimeter per day (mm/day) 0.003281 foot per day (ft/day)

Degrees Celsius (°C) may be converted to degrees Fahrenheit (°F) by using the following equation:

°F = 9/5(°C)+32.

Sea level: In this report, "sea level" refers to the National Geodetic Vertical Datum of 1929 a geodetic 

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

called Sea Level Datum of 1929.

Dual units (metric and customary U.S.) are used throughout the text in this report to preserve the integrity of 

the original data, which were in metric form in the model, and at the same time present the data in a comprehensible 

form to the reader.
WATER BUDGET AND SIMULATION OF ONE 

DIMENSIONAL UNSATURATED FLOW IN A 

FLOOD- AND A SPRINKLER-IRRIGATED 

FIELD NEAR MILFORD, UTAH

By David D. Susong 

U.S. Geological Survey

ABSTRACT

Ground-water recharge to basin-fill aquifers 

from unconsumed irrigation water in the western 

United States is being reduced as irrigators convert 

to more efficient irrigation systems. In some areas, 

these changes in irrigation methods may be contributing to ground-water-level declines and reducing the quantity of water available to downgradient 

users. The components of the water budget were 

measured or calculated for each field for the 1992 

and 1993 irrigation seasons. Precipitation was 

about 6.5 cm (2.6 inches) both years. The floodirrigated field received 182 and 156 centimeters 

(71.6 and 61.4 inches) of irrigation water in 1992 

and 1993, and the sprinkler-irrigated field received 

52.8 and 87.2 centimeters (20.8 and 34.3 inches) of 

water, respectively. Evapotranspiration for alfalfa 

was calculated using the Penman-Monteith combination equation and was 95.4 and 84.3 centimeters 

(37.2 and 33.2 inches) for 1992 and 1993, respectively. No runoff and no significant change in soil 

moisture in storage was observed from either field. 

Recharge to the aquifer from the flood-irrigated 

field was 93.3 and 78.1 centimeters (36.7 and 30.7 

inches) in 1992 and 1993 and from the sprinklerirrigated field was -35.9 and 9.3 centimeters (-14.1 

and 3.7 inches), respectively. The daily water budget and soil-moisture profiles in the upper 6.4 

meters (21 feet) of the unsaturated zone were simulated with an unsaturated flow model for average 

climate conditions. Simulated recharge was 57.4 

and 50.5 percent of the quantity of irrigation water 

applied to the flood-irrigated field during 1992 and 

1993, respectively, and was 8.7 and 13.8 percent of 

the quantity of irrigation water applied to the sprinkler-irrigated field.

INTRODUCTION

To reduce water use, irrigators in many areas of 

the western United States are changing irrigation methods to more water-efficient systems. In some areas, 

these changes in irrigation methods may be reducing 

the quantity of recharge to the ground-water system, 

thereby contributing to declines in ground-water levels 

and reducing the quantity of water available to downgradient users. Irrigation water is a major source of 

recharge to some basin-fill aquifers in the Basin and 

Range Physiographic Province (Fenneman, 1931), and 

the quantity of irrigation water that recharges the aquifers is a function of the method used to apply the water 

and the hydrogeologic characteristics and climate of 

each basin.

Irrigators in the western United States are converting from less efficient irrigation methods, such as 

flood irrigation, to more efficient sprinkler systems. 

Flood-irrigation methods include precision-leveled 

flood irrigation, furrow irrigation, and pulse irrigation. 

More efficient irrigation systems such as sprinkler systems reduce water use. In theory, ground-water withdrawals for irrigation likely would decrease as 

irrigation efficiency improves; however, irrigators also 

are increasing irrigated acreage as they improve irrigation efficiency by using water saved from improvements in efficiency to irrigate additional acreage. The 

improvements in efficiency combined with the increase 

in irrigated acreage might affect ground-water levels in 

basin-fill aquifers and the quantity of water available to 

downgradient users. To address this problem, the U.S. 

Geological Survey, in cooperation with the Utah 

Department of Natural Resources, Division of Water 

Rights, did a study in the Milford area of southwestern 

Utah (fig. 1) to quantify and compare the quantity of
Sprinkler-irrigated field

County road (gravel)

Flood-irrigated field

114° 113° 112°

 UTAH

20 40 

I

20 40 60 KILOMETERS

60 MILES 

J

Figure 1. Schematic diagram and location of study site, Milford area, Utah.
ground-water recharge occurring in a flood-irrigated 

field to that occurring in a sprinkler-irrigated field. 

Recharge is defined for the purposes of this study as 

water that infiltrates to a depth of at least 6.4 m. This 

water also has been referred to as deep percolation in 

other studies and has the potential to infiltrate to the 

water table and recharge the basin-fill aquifer.

Location of irrigated fields in a basin also can 

affect the amount of recharge to the basin-fill aquifer 

and affect ground-water resources. If irrigated fields are 

located in recharge areas for basin-fill aquifers, then 

changes in irrigation methods that reduce recharge are 

likely to have a much greater effect on ground-water 

resources than if the fields are located in discharge 

areas.

Purpose and scope

This report describes the methods of investigation, water budget, and a one-dimensional unsaturatedflow model used to simulate ground-water recharge 

from irrigation water at a flood- and a sprinkler-irrigated field near Milford, Utah. The instrumentation and 

types of data collected are described in the following 

section of this introduction. Precipitation, irrigation 

water, evapotranspiration, runoff, soil-moisture storage, and recharge are discussed in the "Water budget" 

section of the report. The one-dimensional unsaturatedflow model and estimates of ground-water recharge 

from the application of the model to the two irrigated 

fields are presented in the "Simulation of one-dimensional unsaturated flow" section.

Site description

The Milford area is located in a basin of the Basin 

and Range Physiographic Province (Fenneman, 1931) 

in southwestern Utah (fig. 1). The altitude of the basin 

is about 1,525 m (5,004 ft), and the altitude of the highest point in the surrounding mountains is about 2,750 m 

(9,023 ft). Irrigated agriculture is widespread in the 

central part of the basin. The study site is located 

between Minersville and Milford. The study site consists of two adjacent irrigated alfalfa fields: a 5.26-ha 

(13-acre) flood-irrigated field and a 32.4-ha (80-acre) 

center-pivot sprinkler-irrigated field (fig. 1).

The geology of the Milford area includes consolidated rocks of Precambrian to Tertiary age. The mountain ranges to the east and west of the area are

composed mostly of igneous intrusive and volcanic 

rocks of Tertiary age; Coalescing alluvial fans extend 

from the mountains into the basin. The basin-fill deposits are reported in drillers' logs to be up to 261 m (856 

ft) thick and consist of interbedded clay, silt, sand, and 

gravel (Mower and Cordova, 1974, p. 93). These 

deposits are alluvial, fluvial, and lacustrine sediments 

that are associated with Basin and Range faulting and 

mountain uplifts of Tertiary age and Lake Bonneville 

deposits of Pleistocene age.

Climate

The climate of the Milford area is characterized 

by moderate summer temperatures, cool winter temperatures, small amounts of precipitation, and moderate to 

strong winds. Average annual precipitation in the Milford area was 24.81 cm (9.8 in.) during 1960-90 (Robert Hill, Utah State University, written commun., 1994). 

An automated micrometeorology station was installed 

at the study site. Average hourly air temperature and 

wind velocity and daily precipitation and evapotranspiration at the study site for April through September of 

1992 and 1993 are shown in figures 2 and 3. Maximum 

average hourly air temperature for these periods was 

35.0 °C (95 °F) and minimum was -7.5 °C (18.5 °F). 

Maximum hourly wind velocity was 12.0 m/s (27 

mi/h). Total precipitation for April 1 to September 15, 

1992, was 6.70 cm (2.64 in.) and for April 1 to September 30,1993, was 6.40 cm (2.52 in.). Maximum daily 

evapotranspiration in April is a function of high wind 

velocities and warm temperatures. The maximum may 

be an overestimation of actual evapotranspiration 

because during high sustained wind velocities, plants 

compensate by closing stomata and increasing stomatal 

resistance. An alternative explanation of this high 

evapotranspiration value is that during high wind 

speeds, actual evapotranspiration exceeds potential 

evapotranspiration because of sensible heat advected 

from surrounding nonirrigated areas of the basin.

Hydrology

The Beaver River is the only major stream in the 

Milford area. The Beaver River enters the area near 

Minersville and flows north past Milford. Streamflow 

in the river is controlled by releases from Minersville 

Reservoir and by irrigation diversions. The river is 

often dewatered by irrigation diversions near Minersville. Ground water generally flows toward the center
Average hourly air temperature

No record because of instrument failure

Average hourly wind velocity

No record because of instrument failure

20

15 -

t Ul 10 -

cc-i 5 o-d

I 

Daily precipitation

-

, ..I I.

i i i i

1,1 1 ll , . ll

-

-

-> 15

§

< 0

HOC 

<UJ SE°- 10

CLOT 

</>CC 

ZUI

= 5

Nuiz

Daily evapotranspiration

Estimated from Utah Climate Center 

weather-station data

April May June July August

Figure 2. Average hourly air temperature and wind velocity and daily precipitation and evapotranspiration at the study site, 

Milford area, Utah, 1992.
Average hourly air temperature

15

DC- 10

Q.W

55

UJZ

Daily evapotranspiration

April May June July August September

Figure 3. Average hourly air temperature and wind velocity and daily precipitation and evapotranspiration at the study 

site, Milford area, Utah, 1993.
of the basin and exits the area to the north. The groundwater level near the study site in the basin-fill deposits 

is 15.3 to 36 m (50.2 to 118 ft) below land surface and 

has been declining as a result of pumpage and drought. 

Ground-water movement at the study site is from east 

to west (Mower and Cordova, 1974, pi. 4).

Physical and Hydraulic Properties of the Soil

Soils at the study site are in the Taylors Flat series 

(Gordon Crandall, Soil Conservation Service, written 

commun., 1993). Based on particle-size distribution, 

the soil is generally classified as loam to clay loam. Soil 

samples were collected at two sites, one in each field. 

Clods were collected from soil pits (fig. 1) dug to a 

depth of 2.0 m (6.6 ft), and cores were collected from 

selected intervals from 2.0 m to 6.4 m (6.6 to 21.0 ft) 

deep in the neutron-probe access holes. Sample intervals for cores were selected to be representative of the 

major textural layers in the unsaturated zone. The clods 

and cores were analyzed for particle-size distribution, 

bulk density, saturated hydraulic conductivity, organic 

carbon, inorganic constituents, and moisture characteristics by the National Soil Laboratory of the Soil Conservation Service in Lincoln, Nebraska. Particle-size 

distribution, organic carbon content, and bulk density 

of samples from the two soil pits and the two adjacent 

neutron-probe access holes (1 and 3) and two additional 

neutron-probe access holes (2 and 4) are listed in table 

1. The intervals sampled with the clods and cores overlapped in the 124 to 152 cm (48.8 to 59.8 in.) interval 

(hole 1).

The particle-size distribution of clod samples 

collected from the soil pits and core samples collected 

from selected intervals in the adjacent neutron-probe 

access holes in the flood- and the sprinkler-irrigated 

field are shown in figure 4.The particle-size distribution 

indicates that the texture of the unsaturated zone is heterogeneous and layered and that the clay content varies 

from 6.2 to 58.7 percent, silt from 11.2 to 55.8 percent, 

and sand from 1.3 to 81.3 percent (table 1). The distinct 

layering of the unsaturated zone, such as the sandy 

layer beginning about 100 cm (39.4 in) below land surface and the clay and silt layer beginning about 200 cm 

(78.7 in.) below land surface (fig. 4), can influence the 

temporal and spatial movement of water through the 

unsaturated zone.

Saturated hydraulic-conductivity values for 

seven samples were determined by the National Soil 

Laboratory of the Soil Conservation Service and range

from 0.21 cm/day (0.0069 ft/day) to 21.6 cm/day (0.71 

ft/day). The samples are from all four neutron-probe 

access holes and were selected to be representative of 

the major textures in the unsaturated zone. The depth 

interval of the samples and the saturated hydraulic-conductivity values are:

Depth below 

land surface, 

in centimeters

91 to 147

91 to 155

94 to 134

359 to 368

391 to 41 6

396 to 490

61 4 to 640

Saturated hydraulic 

conductivity, 

in centimeters per day

0.21

7.5

8.6

7.8

21.6

6.9

7.7

The saturated hydraulic-conductivity values 

were less than expected when compared with values of 

soils of similar texture (Lappala and others, 1983; 

Rawls and others, 1982). The core samples were collected with a driven core sampler and may have been 

compacted or sheared during collection. The extraction 

of samples from the core-sample tubes also could have 

compacted or disturbed the samples.

Soil-moisture characteristic curves were developed for 10 samples from soil-moisture content measured at negative hydraulic heads of-61 cm (-24 in.), 

-102 cm (-40 in.), -336 cm (-132 in.), -1,020 cm (-402 

in.), and -15,300 cm (-6,024 in.). The curves were fit 

with van Genuchten's (1980) equation for relating negative hydraulic head and moisture content. The van 

Genuchten equation (Lappala and others, 1983) is used 

in the unsaturated-flow model and the coefficients 

determined in the curve fitting are required input for the 

unsaturated-flow model.

Methods of Investigation

The study site was instrumented to measure soil 

moisture and climate parameters. Much of the data was 

collected at 1- or 5-minute intervals and then averaged 

to hourly values. The measured parameters and their 

frequency of collection are listed at the beginning of 

page 9.
Table 1. Laboratory determined particle-size distribution, organic carbon content, and bulk density of soil in the flood- and 

the sprinkler-irrigated field, Milford area, Utah

[<, less than; mm, millimeter; g/cm3, grams per cubic centimeter; , no data]

Depth below 

land surface 

(centimeters)

Clay 

(<0.002mm) 

(percent)

Silt 

(0.002 to <0.05mm) 

(percent)

Sand 

(0.05 to 2mm) 

(percent)

Organic 

carbon 

(percent)

Bulk density 

(oven dry) 

(g/cm3)

FLOOD-IRRIGATED FIELD 

Soil pit

Oto5

5 to 23

23 to 36

36 to 69

69 to 97

97 to 117

117 to 152

124 to 172

211 to 254

284 to 345

614 to 640

94 to 134

185 to 223

305 to 315

359 to 368

20.3

20.2

23.0

27.6

27.4

26.2

18.2

11.3

42.1

23.6

12.2

6.2

58.2

27.9

24.8

52.4 27.3

53.5 26.3

51.0 26.0

34.3 38.1

37.8 34.8

35.1 38.7

17.9 63.9

Neutron-probe access hole 1

17.7 71.0

55.8 2.1

24.8 51.6

20.8 67.0

Neutron-probe access hole 2

12.5 81.3

40.5 1.3

25.3 46.8

25.0 50.2

SPRINKLER-IRRIGATED FIELD

0.96

.84

.71

.19

.4

.17

.09

.05

.06

.08

.03

.06

.1

.07

.20

1.54

1.45

1.44

1.61

1.55

1.58

1.61

1.73

1.87

1.33

Soil pit

Oto5

5 to 25

25 to 46

46 to 61

61 to 87

87 to 152

21 3 to 274

391 to 416

548 to 564

97 to 147

241 to 274

396 to 490

561 to 594

28.9

29.9

30.4

27.4

33.5

12.0

58.7

39.9

39.3

17.5

19.9

21.0

22.7

45.4 25.7

47.4 22.7

54.5 15.1

49.9 22.7

39.6 26.9

11.2 76.8

Neutron-probe access hole 3

37.8 3.5

24.6 35.5

36.6 24.1

Neutron-probe access hole 4

23.8 58.7

25.6 54.5

32.6 46.4

23.1 54.2

1.7

.63

.31

.34

.54

.08

.12

.11

.13

.20

.05

.16

.12

1.58

1.60

1.47

1.47

1.31

1.51

1.85

1.45
(ADC in

in 

o

III 

O

50

100

150

200

250

300

DC 350 

(0

a

400

450

500

550

600

650

700

I i

Flood-irrigated field, 

soil pit and hole N1

II

Sprinkler-irrigated field, 

soil pit and hole N3

20 40 60 80 20 40 60 80

QUANTITY OF CLAY, SILT, AND SAND, 

IN PERCENT

QUANTITY OF CLAY, SILT, AND SAND, 

IN PERCENT

EXPLANATION

 Clay

 - Silt

.... . .,...., Sand

Figure 4. Particle-size distribution of clod and core samples from the flood- and the sprinkler-irrigated field, Milford 

area, Utah.
Parameter Interval of 

data collection

Soil moisture 

Neutron probe

Capacitance probe 

Air temperature 

Soil temperature 

Relative humidity 

Heat flux of soil 

Net radiation 

Wind velocity 

Wind direction 

Hydraulic head of soil

Amount of applied 

irrigation water 

Amount of runoff

Approximately biweekly 

during 1992, and daily 

during May and part of 

June, 1993

5 minute, averaged hourly 

1 minute, averaged hourly 

1 minute, averaged hourly 

1 minute, averaged hourly 

1 minute, averaged hourly 

1 minute, averaged hourly 

1 minute, averaged hourly 

1 minute, averaged hourly 

hourly, intermittent record, 

1992

periodically

No runoff observed during

site visits

Soil moisture was measured with a soil-moisture 

neutron probe at four locations at the study site, including two locations in the flood-irrigated field and two 

locations in the sprinkler-irrigated field (fig. 1). Aluminum access tubes for the neutron probe were installed 

to a depth of 5.75 m (18.9 ft) or 6.4 m (21.0 ft), except 

for the access tube in the lower end of the flood-irrigated field, which was installed to a depth of 3.65 m 

(12.0 ft). Cemented soil at a depth of 3.65 m (12.0 ft) 

could not be penetrated with the auger. Soil-moisture 

measurements were made with a soil-moisture neutron 

probe at about 2-week intervals in 1992 and daily for 

May and part of June in 1993. The soil-moisture measurements in 1993 were designed to track daily changes 

in soil moisture and would have continued the entire 

season had there not been problems with the neutron 

probe. The soil-moisture measurements were collected 

as neutron-count ratios. The neutron probe was calibrated using soil samples collected during installation 

of the access tubes and soil samples collected from 

holes augured near the access tubes periodically during 

the irrigation season. Soil cores were collected and 

moisture content was determined by the standard gravimetric method (Kramer, Cullen, and Everett, 1992). 

Neutron-probe measurements were made immediately 

following collection of the cores at the depths at which 

the samples were collected and 15 cm (5.9 in.) above 

and below the sample depth. These three neutron-probe

measurements were averaged and used to develop a linear regression curve with the gravimetric soil-moisture 

data. The regression curve and equation (fig. 5) have 

coefficient of determination (R-squared) of 0.86 and a 

p value less than 1 x 10"4 .

Soil moisture also was measured with capacitance probes connected to a data logger in the upper end 

of the flood-irrigated field. These probes were installed 

at depths of 1.52 m (5.0 ft), 2.10 m (6.9 ft), and 3.65 m 

(12.0 ft), recorded soil moisture at 5-minute intervals, 

and averaged the data hourly. These probes were used 

to monitor the movement and timing of water through 

the unsaturated zone. The capacitance probes were calibrated with the same method used for the neutronprobe calibration. The regression curve and equation 

(fig. 5) have an R-squared value of 0.80 and a p value 

less than 1 x 10 . Numerous instrument problems in 

1992 precluded the collection of any useable data. Data 

were collected with the capacitance probes for April to 

September in 1993. The 2.10 m (6.9 ft) and 3.65 m 

(12.0 ft) probes are missing some record as a result of 

moisture penetrating the cable connections. The 1.52 m 

(5.0 ft) probe has a complete set of data.

Climate parameters were measured with an automated weather station located between the flood- and 

the sprinkler-irrigated field (fig. 1). The weather station 

is surrounded by fields of irrigated alfalfa. The field to 

the south of the weather station was planted with alfalfa 

and oats in 1992. All the data were collected once each 

minute and were averaged hourly for April 1 to September 30, 1992, and April 1 to September 30, 1993. 

The weather station was vandalized in 1992 and was 

not operating from June 16 to August 12, 1992. 

Regressed data from the Utah Climate Center Milford 

weather station was used to estimate the missing data. 

The set of 1993 climate data is complete with the 

exception of the data from the net radiometer, which 

was damaged for a short period. The missing data was 

obtained by interpolation.

WATER BUDGET

The components of the water budget for each 

field were either measured at intervals, or were calculated or estimated at the study site. Precipitation during 

the growing season was measured continuously with a 

tipping-bucket rain gage. Evapotranspiration was calculated hourly from climate parameters. The quantity 

of soil-moisture in storage was determined from soil-
W 

DC

fe

-I UJ

O"

o

50

45

40

35

30

25

20

15

10

5

0 

0.4

' I'' " I" " I " " I " " I " " I" " I" " I" " I " "-

y = 0.4090426(ratio) - 0.2133286

R2 =0.86

p < 0.0001 '

0.6 0.8 1.0 1.2 1.4 

NEUTRON-COUNT RATIO

1.6

- y = 0.0007275(Dcounts) - 3.0906

R2 =0.80 

r ~ p < 0.0001

o o o

if) o m <O I"*- Is* §

0000 

m o m o

00 00 O) O) O

CAPACITANCE PROBE, IN DCOUNTS

Figure 5. Relation of volumetric soil-moisture content with neutron-count ratio and capacitance probe Dcounts, floodirrigated field, Milford area, Utah.

moisture measurements made at intervals in 1992 and 

daily in May and June of 1993 with the neutron probe, 

and continuously in 1993 with the capacitance probe. 

The quantity of irrigation water was measured periodically at the pump discharge pipe, under the sprinklers, 

and at the siphons into the field.

The water-budget equation used to estimate daily 

recharge to the basin-fill aquifer is

R = I-ET-RO (1)

where:

R is recharge,

P is precipitation,

I is irrigation water,

ET is evapotranspiration,

RO is runoff, and

AS is change in quantity of soil moisture in 

storage.

The individual components of this equation are discussed in the following sections.

Precipitation

Total precipitation during April 1 to September 

15,1992, was 6.70 cm (2.64 in.), and during April 1 to 

September 30,1993, was 6.40 cm (2.52 in.). Daily precipitation is shown in figures 2 and 3. Precipitation typically falls as rain during storms of short duration. The 

rain gage was unshielded; thus, gaged precipitation 

may be less than actual precipitation. Rain in April, 

May, and June was often associated with frontal passages, and most rain in July and August was associated 

with thunderstorms. Compared with other components 

of the water budget for irrigated fields in the Milford 

area, precipitation during the irrigation season is a relatively minor component.

Irrigation Water

The quantity of irrigation water applied to the 

flood-irrigated field was measured at the discharge pipe 

from the well and at the individual siphon tubes in the 

field. The farmers recorded or estimated dates when 

irrigation water was applied to the field. Water was 

applied to part of the field at about 0.98 to 1.14 m3/min

10
(0.18 to 0.20 ft3/min) through 12 to 16 siphon tubes 

covering about 7.1 m (23.3 ft) of the width of the field. 

Each irrigation application lasted about 12 hours. The 

farmers generally moved their siphon tubes in the 

morning and evening and water was applied to a set of 

furrows from about 7:00 a.m. to 7:00 p.m.; however, the 

movement of the siphon tubes also was subject to other 

activities and may have occurred as early as 6:00 a.m. 

and as late as 9:00 p.m. In this 12-hour period, about 

26 cm (10.2 in.) of water was applied to the field, and 

application of water to the field is assumed to be uniform in distribution. The flood-irrigated field received a 

total of about 182 cm (71.6 in.) of water in 1992 and 

156 cm (61.4 in.) in 1993. The upper end of a flood-irrigated field actually receives considerably more water 

than the lower end; however, a uniform application of 

water to the field was used to calculate the water budget 

because of the lack of data on the distribution of water 

throughout the field. The effects of this assumed distribution of irrigation water on the quantity of recharge 

are examined with the unsaturated-flow model and are 

discussed in the modeling section of this report.

The sprinkler-irrigated field was irrigated using a 

center-pivot sprinkler system that revolved every 3 to 4 

days. The farmers recorded or estimated the dates the 

sprinkler system passed over the neutron-probe access 

tubes in the sprinkler-irrigated field. This record was 

less complete and accurate than that of the flood-irrigated field. Output of the sprinkler system was measured periodically with calibrated buckets and a rain 

gauge in the field. The sprinkler applied 2.6 to 3.8 cm 

(1.0 in. to 1.5 in.) of water per revolution, which typically took 3 to 4 days. The sprinkler-irrigated field 

received about 52.8 cm (20.8 in.) of water in 1992 and 

87.2 cm (34.3 in.) in 1993. Individual applications of 

irrigation water to the flood- and the sprinkler-irrigated 

field during the 1992 and 1993 irrigation seasons are 

shown in figure 6.

Evapotranspi ration

Evapotranspiration was calculated using the Penman-Monteith combination equation (Alien and others, 

1989; David Stannard, U.S. Geological Survey, written 

commun., 1992) in the form:

where:

KET =

rc + rh 

rh

(2)

is latent heat flux, 

s is slope of saturation vapor-pressure curve, 

jRN is net radiation, 

G is soil heat flux, 

p is density of air, 

cp is specific heat of air, 

es is saturation vapor pressure (Weiss, 1983;

Lowe, 1977),

ea is saturation vapor pressure at dew point, 

y is psychrometric constant, 

re is canopy resistance (Alien and others,

1989), and 

rh is aerodynamic resistance to vapor and heat

diffusion (Campbell, 1977).

The Penman-Monteith equation (Monteith, 

1963) used to estimate actual evapotranspiration is a 

modification of the Penman equation (Penman, 1956) 

for calculating potential evapotranspiration. Both are 

combination methods that combine energy balance and 

aerodynamic terms, and the Monteith variation 

includes the canopy resistance of the vegetation. The 

estimation of evapotranspiration for an arid grassland 

site with the Penman-Monteith equation is succinctly 

described by Tomlinson (1994) and includes an appendix with a step by step calculation of evapotranspiration 

using the Penman-Monteith equation. In this study, es 

and ea were calculated using the equations from Lowe 

(1977) and Weiss (1983). Aerodynamic resistance to 

heat transfer, rh, is approximated by using the equation 

from Campbell (1977). Canopy resistance, re, is typically not measured directly but is determined by computing the latent heat flux by other methods and then 

solving the Penman-Monteith equation for re. The re 

value is highly variable and is a function of available 

moisture, stage of plant 'growth, canopy density, time of 

day, and climatic conditions. Studies in Arizona with 

well- watered alfalfa indicated that re is less than 100 

seconds per meter (330 seconds per foot) for about 20 

days after irrigation and then increases rapidly to about 

2,500 seconds per meter (8,200 seconds per foot) during the next 11 days (Van Bavel, 1967). The re value 

also varies diurnally, approaching 0 at night and 

increasing toward 100 seconds per meter (330 seconds 

per foot) by midday (Van Bavel, 1967).

Because no actual measurements of evapotranspiration were made as part of this study, re was estimated using the method described by Alien and others 

(1989). This method calculates re as a function of leafarea index and average minimum daily value of sto11
cc

UJ

U.UJ

270

265

S 255

250

Flood-irrigated field, 1992

April May June July August

270

of

111

I-W ORE rf DC ^DO

U.UJ

Of. 260

P

<5 255

13

0

250

1 i i .

Flood-irrigated field, 1993 ;

. 

-

~

i

April

40 

CC

K- w oc ^ CC oo

U.1II

21 30

§js

<Z 25

13

0

20

Sprinkler-irrigated field,

-

II

April

40 

CC 

111

^ OK ^ CC ^^ ^ u

11. Ill

OS 30

<S 25

13

0

on

i

Sprinkler-irrigated field,

-

_

i

May

1992

19

I

May

93

i

June

i

I

i

i i

July August

I'

June

i

I,Hill I

July

i

i

1 1

-

I

-

~

September

i

-

-

III!"

August

i

I

_

-

-

_

~

.

-

April May June July August September

Figure 6. Application of irrigation water to the flood- and the sprinkler-irrigated field, Milford area, Utah, 1992 and 1993.

12
matal resistance. Because leaf-area index is a function 

of crop height, the method accounts for the stage of 

plant growth. Evapotranspiration also was calculated 

using a constant re value, which resulted in larger estimates of evapotranspiration. These calculations did not 

account for the stage of plant growth and probably are 

less accurate than the estimates using a variable re 

value.

Evapotranspiration was calculated hourly from 

April 1 to September 15,1992, and from April 1 to September 30, 1993. The hourly values were summed to 

provide daily estimates. Daily evapotranspiration 

ranged from 1.2 to 13.4 mm/day (0.0039 to 0.044 ft/ 

day) in 1992 and from 2.5 to 14.4 mm/day (0.0082 to 

0.047 ft/day) in 1993 (figs. 2 and 3). Cumulative evapotranspiration from April 1 to September 15,1992, was 

95.4 cm (37.6 in.) and for April 1 to September 30, 

1993, was 84.3 cm (33.2 in.). These values are similar 

to the estimated annual crop consumptive use for alfalfa 

of 90.17 cm (35.50 in.) for the Milford area (R.W. Hill, 

Utah State University, written commun., 1994). Evapotranspiration was estimated for the flood- and the sprinkler-irrigated field from a single set of climate data that 

was collected between the two fields. This climate data 

represents an average data set for the area because the 

site was between the study fields, thus, evapotranspiration calculated from it may differ from evapotranspiration actually measured in the fields.

Daily evapotranspiration values missing in 1992 

because of vandalism to the weather station were estimated from climate data obtained from the Utah Climate Center Milford weather station located about 3 km 

(1.9 mi) north of the study site (Utah Climate Center, 

written commun., 1993). The linear regression equation 

and relation between daily evapotranspiration calculated at the study site and at the Climate Center weather 

station are shown in figure 7. The regression equation 

has an R-squared value of 66.88, which is partly 

because the reference evapotranspiration calculated 

from the Climate Center weather-station data does not 

account for the variation in crop height, which is 

included in the evapotranspiration estimates at the 

study site, and because the Climate Center weather station was located in a nonvegetated field for the period 

of record. This data set is not ideal but was the only one 

available.

Runoff

Runoff is irrigation water that is applied to a field 

but does not infiltrate and is not consumed by plants and 

leaves the field through drainage ditches. Because irrigation water rarely reaches the lower end of the floodirrigated field, there is zero to only a small quantity of 

runoff. The alfalfa crop at the lower end of the floodirrigated field was wilted by early July, and soil moisture in the lower end of the field decreased during summer. For this water budget, there was assumed to be no 

runoff from the flood-irrigated field. Because the sprinkler-irrigated field is graded nearly level and the application rate of the water is slow, there is no runoff from 

the sprinkler-irrigated field either.

Soil-Moisture Storage

Soil-moisture measurements are used to determine changes in the quantity of soil moisture in storage. 

Soil moisture was measured with a neutron probe in the 

flood- and the sprinkler-irrigated field at about 2-week 

intervals in 1992 and was measured daily in May and 

part of June of 1993. Soil-moisture profiles for the 

flood- and the sprinkler-irrigated field for 1992 and 

May of 1993 (fig. 8) show the variability of soil moisture measured at about 2-week intervals and measured 

daily. The dates that soil moisture was measured are not 

shown on the graphs because individual lines on the 

graphs are very difficult to distinguish and because the 

variability defined by all the profiles is of interest. Soil 

moisture in the flood-irrigated field varies over a larger 

range than soil moisture in the sprinkler-irrigated field 

(fig. 8). The wettest soil-moisture profiles in the floodirrigated field were measured immediately after an irrigation application. Because the neutron-probe access 

tube partially filled with water during irrigation applications, it was not possible to measure a complete profile. The changes in soil moisture were very transient, 

and soil moisture generally fluctuated in a plus or minus 

5-percent range. Soil moisture increased to saturation 

quickly during an irrigation application. The wetting 

fronts from each application moved through the soil 

column in about 48 hours, after which the soil returned 

approximately to its pre-irrigation moisture content.

Daily water content in the 600-cm (236-in.) soil 

profile in the flood-irrigated field and in the 570-cm 

(224-in.) soil profile in the flood- and the sprinkler-irrigated field and change in daily water content are shown 

in figure 9. The flood-irrigated field was irrigated on

13
O

o

3

O

.- 14

12

10

.DC

zi

0)i

0.

5

LJ

y = 3.884 = 0.923 x 

R2 = 66.88 

p < 0.00001

0 2 4 6 8 10 12 14 16 

DAILY EVAPOTRANSPIRATION, UTAH CLIMATE CENTER, IN MILLIMETERS

Figure 7. Relation between evapotranspiration data of the U.S. Geological Survey and Utah Climate Center, Milford 

area, Utah.

May 23,1993, and it was not possible to measure soil 

moisture because of water in the access tube. The daily 

change in soil-moisture content in the flood- and the 

sprinkler-irrigated field was generally plus or minus 5 

percent. The largest changes in moisture content are 

associated with irrigation applications and with shutting off the sprinkler system on about June 9,1993, for 

the first cutting of the alfalfa.

Soil moisture also was measured continuously 

with capacitance probes at depths of 1.52 m (5.0 ft), 

2.10 m (6.9 ft), and 3.65 m (12.0 ft). The data set for the 

flood-irrigated field during the 1993 irrigation season 

for the probe located at a depth of 1.52 m (5.0 ft) shows 

six irrigation events (fig. 10) during which 26 cm (10.2 

in.) of water was applied to the field. The sudden 1-percent drop in soil-moisture content in the first week of 

August may be the result of recorder problems. In May, 

the soil-moisture content decreased to about 23 percent 

before the first irrigation application, and in September, 

the soil-moisture content decreased to about 25 percent. 

For the entire growing season, at a depth of 1.52 m (5.0 

ft), there is only about a 4-percent change in soil-moisture content. This small change, along with the plus or 

minus 5-percent change in soil moisture observed in the 

soil-moisture profiles, indicates that soil-moisture 

changes are transient and that soil moisture remains 

within a small range during the entire growing season. 

Thus, for the water-budget calculations, the changes in 

soil-moisture storage during the irrigation season are 

assumed to be zero. The lower end of the flood-irrigated field was an exception. The quantity of irrigation 

water was insufficient to meet plant water requirements 

at the lower end of the field, and the entire soil profile 

dried out; however, for the water-budget calculations, it 

is also assumed that irrigation water is applied uniformly over the field.

Recharge

Recharge is water that infiltrates through the 

unsaturated zone and replenishes the basin-fill aquifer. 

In this study, water that reaches a depth of 6.4 m (21 ft) 

is referred to as recharge. It is also referred to as deep 

percolation in other studies. Implicit in this definition

14
(0 

DC

UJ 100

UJ

UJ

UJ

200

3 300

(0

O

\

I 400

UJ 

CO

a soo 

o

600

0

(0

U 100 

UJ

Flood-irrigated field, 1992

UJ

200

300

500 -

600

Flood-irrigated field, May 1993

Sprinkler-irrigated field, 1992 Sprinkler-irrigated field, May 1993

0 20 40 60 80 0 20 40 60 80 

VOLUMETRIC MOISTURE CONTENT, IN PERCENT VOLUMETRIC MOISTURE CONTENT, IN PERCENT

Figure 8. Volumetric soil-moisture profiles for the flood- and the sprinkler-irrigated field for the 1992 irrigation season 

and daily soil-moisture profiles for May 1993, Milford area, Utah.

15
280

Z </>

UJ(/)UJ 0_n

l_ s 260 Is!

220

Q O

200

40

Flood-irrigated field

20

uj~-J o 0^0

-20 

190

Flood-irrigated field

UJ(/)UJ

170-

O O

160

10

UJ--J

OtO

§8

-10

Sprinkler-irrigated field

10 15 20 25 30 1 10

May June

Figure 9. Daily water content and change in daily water content in a soil column in the flood- and the sprinkler-irrigated field, 

Milford area, Utah, May and June, 1993.

16
UJ

o

cc

UJ 

O.

44

42

40

38

HI 36

§ 34

UJ 

OC

P 32

30

O

O 

OCt 28

E

3 26

May June July August September

Figure 10. Volumetric soil-moisture content at a depth of 1.52 meters in the flood-irrigated field, Milford area, Utah, 1993. 

Six periods of irrigation during which 26 centimeters of water were applied are visible.

is the assumption that water that infiltrates to a depth of 

6.4 m (21 ft) recharges the basin-fill aquifer. At 6.4 m 

(21 ft), the water is below the root zone of most plants 

and thus has the potential to recharge the basin-fill aquifer. However, it cannot be known for certain that water 

that infiltrates to 6.4 m (21 ft) actually reaches the water 

table. There is evidence that vapor transport removes 

water from great depths in the unsaturated zone. The 

unsaturated basin-fill deposits below 6.4 m (21 ft) were 

not monitored because of the cost of drilling monitoring 

wells to the water table. In the water budget for the 

flood- and the sprinkler-irrigated field (fig. 11), the precipitation and irrigation components of the water budget are summed and runoff and change in soil-moisture 

content are assumed to be zero as discussed previously. 

Cumulative recharge is determined by subtracting 

cumulative evapotranspiration from the cumulative 

sum of precipitation and irrigation. If cumulative 

recharge is positive, then water is available to recharge 

the aquifer. If cumulative recharge is negative, then the 

crop is receiving insufficient water to meet plant water 

requirements. The water budget for the two fields is 

summarized at the top of page 19.

Estimated recharge for the flood-irrigated field in 

1992 was 93.3 cm (36.7 in.) and in 1993 was 78.1 cm 

(30.7 in.). Estimated recharge is 49 and 48 percent, 

respectively, of the sum of precipitation and irrigation 

during April to September in 1992 and 1993, assuming 

that change in the quantity of soil moisture in storage 

and runoff from the field is zero and that 100 percent of 

precipitation is effective. If there is an increase in moisture stored in the soil or if there is runoff from the field, 

then recharge would decrease. The recharge could be 

attributed to the large volume of irrigation water that is 

applied in about 12 hours and to the hydraulic characteristics of the soil.

Estimated recharge in the sprinkler-irrigated field 

in 1992 of-35.9 cm (-14.1 in.) indicates that insufficient 

moisture was available to satisfy plant water requirements and that no recharge occurred in 1992. In 1993, 

there was 9.3 cm (3.7 in.) of recharge. Precipitation plus 

irrigation for 1993 was 34.1 cm (13.4 in.) greater than 

in 1992, and evapotranspiration was less in 1993. These 

factors account for the estimated recharge in 1993. The 

farmers applied more water and adjusted their sprinklers more often in 1993 than in 1992 so that the application rate changed frequently during the irrigation

17
200

150 

(/)

oc

UJ

i

p 100

UJ

o

Ul 50

I

U. 

O

-50

-100

Sprinkler-irrigated field Sprinkler-irrigated field

j______L

APR MAY JUNE JULY AUG SEPT APR MAY JUNE JULY AUG SEPT 

1992 1993 

EXPLANATION

Cumulative precipitation and irrigation

Cumulative precipitation and irrigation minus cumulative evapotranspiration (Cumulative recharge)

Cumulative evapotranspiration

Figure 11. Water budget for the flood- and the sprinkler-irrigated field for 1992 and 1993 irrigation seasons, Milford area, Utah.

18
Field and Irrigation plus Change in soilyear Evapotranspiration precipitation Recharge moisture storage 

(centimeters) (centimeters) (centimeters) (centimeters)

Flood, 1992

Flood, 1993

Sprinkler, 1992 

Sprinkler, 1993

95.4

84.3

95.4 

84.3

188.7

162.4

59.5 

93.6

93.3

78.1

-35.9 

9.3

0

0

0 

0

Runoff 

(centimeters)

0

0

0 

0

Irrigation plus 

precipitation water 

that is recharge 

(percent)

49

48

0 

7.0

season (Troy Hardy, farmer, oral commun., 1993). For 

the water budget, application rates of 3.6 or 3.8 cm (1.4 

or 1.5 in.) per rotation were used. These rates were the 

maximum rates measured in the fields. If the 1992 

application rate of 2.6 cm (1.0 in.) per rotation were 

used for 1993, there would be no recharge in 1993.

Water moving through the unsaturated zone is 

assumed to move only in the vertical direction. This 

assumption is required because data were not collected 

on flow in the unsaturated zone in the horizontal direction. Other detailed studies of flow in the unsaturated 

zone have noted a component of flow in the horizontal 

direction and large heterogeneities in soil hydraulic 

properties in the horizontal direction (Bowman and others, 1991). If horizontal flow occurs in the root zone, 

which includes about the upper 1.52 m (5.0 ft) of soil, 

then water could be distributed in the unsaturated zone 

and removed by evapotranspiration in the fields or 

beyond the boundaries of the fields. The net result 

would be to decrease the amount of recharge. Soilmoisture measurements in the lower end of the floodirrigated field do not indicate that horizontal flow is 

occurring in the upper 3.5 m (11.5 ft) of soil; however, 

horizontal flow could be occurring below this depth.

The drillers' logs from 18 wells located within 2 

km (1.2 mi) of the study site were examined to see if 

there were any continuous, thick clay layers in the basin 

fill that would prevent infiltrating water from reaching 

the basin-fill aquifer. Because the water levels in the 

basin-fill aquifer are generally 15 to 30 m (49 to 98 ft) 

below land surface near the study site, the upper 30 m 

(98 ft) were examined in each drillers' log. Clay layers 

greater than 6 m (20 ft) thick were noted because a clay 

layer of this thickness would provide hydraulic resistance to vertical flow and would probably be recorded 

on a driller's log. Only five of the driller's logs recorded 

clay layers greater than 6 m (20 ft) thick in the upper 30 

m (98 ft) of the well. On the basis of the drillers' logs,

these clay layers could not be correlated among wells. 

There is no continuous clay layer in the basin fill near 

the study area that would impede or prevent irrigation 

water from infiltrating and recharging the basin-fill 

aquifer.

SIMULATION OF ONE-DIMENSIONAL 

UNSATURATED FLOW

The U.S. Geological Survey unsaturated-flow 

model VS2DT (Lappala, and others, 1983; Healy, 

1990) was used to simulate vertical infiltration through 

the upper 6.4 m (21 ft) of the unsaturated zone. Water 

that infiltrated to a depth of 6.4 m (21 ft) was assumed 

to recharge the basin-fill aquifer because it would eventually drain through the entire unsaturated zone to the 

water table. A one-dimensional simulation was used 

because of lack of sufficient data for a two-dimensional 

simulation and because of the heterogeneity of the 

basin-fill deposits.

The model was constructed and calibrated using 

measured and estimated water-budget components and 

soil-moisture profiles from the flood- and the sprinklerirrigated field. The data were collected during the 1992 

and 1993 irrigation seasons (April to September). The 

model was used to simulate ground-water recharge 

from different irrigation methods and was used to 

investigate the effects of irrigation method and waterapplication rates and distributions on ground-water 

recharge.

Because the soil characteristics for the flood- and 

the sprinkler-irrigated field are similar, they were averaged to create the soil column used in the model. The 

average soil column allows for direct comparison of the 

simulated water-budget components of the two fields. 

The model simulates unsaturated flow at the upper end 

of the flood-irrigated field and in the sprinkler-irrigated

19
field. The model simulates daily evapotranspiration, 

infiltration into the soil column, flow out of the soil column, and the change in quantity of soil moisture in storage in the soil column.

Discretization

The model is defined to simulate one-dimensional vertical flow. A 6.4-m (21-ft) column was subdivided into 64 10-cm (3.9-in.) cells. This discretization 

allowed for adequate representation of the layering in 

the unsaturated zone. The model consists of four textural classes and five-layers (fig. 12). A textural class is 

defined by a set of soil properties. The textural classes 

were determined from log probability plots of particlesize distribution of clay, silt, and sand (Klusman, 1980, 

p. 28). The subpopulations determined in the log probability plots define three textural classes, with each textural class having a specified range of clay, silt, and 

sand. The three textural classes, however, failed to adequately reproduce the soil-moisture profiles observed 

in the field. A fourth textural class therefore was created.

The end points of the clay and sand subpopulation and the sand/clay ratio subpopulation for each textural class were overlaid on the particle-size 

distribution of the soil profile used in the model (fig. 

12), and five to eight layers were defined. The layering 

is defined by particle-size distribution and also is a 

function of the core-sampling interval. Sample cores 

were collected at selected representative intervals. The 

soil data from these samples were used in adjacent 

unsampled intervals. Five layers were used in the 

model because this was the simplest model possible and 

the layers were well defined by the data (fig. 12).

Boundary Conditions

The model is defined with active nodes at the top 

and bottom of the soil column and no-flow boundaries 

on the sides of the column. The top boundary condition 

changed from an evapotranspiration boundary to a 

specified-flux boundary when irrigation water was 

being applied. The specified-flux boundary accounts 

for ponding on the surface and can switch to a specified-potential boundary when ponding occurs (Lappala 

and others, 1983, p. 38). This option was required in the 

flood-irrigated field. The lower boundary condition was 

a seepage face (Lappala and others, 1983, p. 44). 

Because water is assumed to recharge the ground-water

system after it infiltrates the upper 6.4 m (21 ft) of the 

unsaturated zone, a seepage water-table interface was 

used to simulate flux at the bottom of the soil column. 

Internal sinks, such as plant root extraction to a depth of 

130 cm (51 in.), also were used in the simulation.

Parameters

The initial soil-moisture content of the soil column was set to equilibrium with a negative hydraulic 

head of -300 cm (-120 in.) of water. The soil-moisture 

profile resulting from this head was similar to the soilmoisture profiles measured in the field and simulated 

with the model. This initial condition also provided 

enough water in the soil column to satisfy plant water 

requirements before the first application of irrigation 

water.

The soil properties and derived parameters 

required by the model are saturated hydraulic conductivity, specific storage, porosity, and the van Genuchten 

equation parameters a, 6r, and p. The van Genuchten 

equation describes the relation between soil-moisture 

content and negative pressure head, often referred to as 

the moisture characteristic curve (Lappala and others, 

1983). Lappala and others (1983) have reformulated 

the van Genuchten equation and use parameters -a', 6r, 

and P'. Soil properties were determined from laboratory analyses, selected from tables of parameters based 

on textural class, and calculated from laboratory data. If 

multiple laboratory analyses were available for a soil 

interval, the laboratory-determined parameters were 

averaged and the average value for the textural class 

was used. The initial values used in the model are listed 

by textural class at the top of page 22.

Saturated hydraulic conductivity was determined 

by using a falling-head permeameter for selected cores 

collected when the neutron-probe access holes were 

drilled. Laboratory saturated hydraulic-conductivity 

values ranged from 0.21 to 21 cm/day (0.0069 to 0.69 

ft/day). These data were compared with tabulated data 

of Lappala and others (1983) and Rawls and others 

(1982) and were generally less than reported values for 

a textural class. Saturated hydraulic conductivity for a 

given soil texture can vary by several orders of magnitude. Specific storage is generally very small and was 

set to 1 x 10"6/cm (3.9 x 10"7/in.) for each textural class 

(R.W. Healy, U.S. Geological Survey, oral commun., 

1992). Porosity was determined by laboratory analyses 

of the clod and core samples.

20
50

100

150

200

CO 

DC 

UJ

250

P 

UJ

U

300

u

350

400

Q.

UJ 

Q

450

500

550

600 -

650 -

700

Textural class 1

. -I Layer 1 J

Textural class 2

Layer 2

Textural class 3

_____.___i

Layer 3

Textural class 4

I

r

Layer 4 -

Textural class 2

Layer 5

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

PARTICLE-SIZE DISTRIBUTION, IN PERCENT

EXPLANATION

 Clay

 Silt

rommnanmii Sand

Figure 12. Composite average particle-size distribution in soil clods from two pits and soil cores from four neutron-probe 

access holes in the flood- and the sprinkler-irrigated field, and unsaturated-f low-model textural classes and layers, Milford 

area, Utah.

21
Textural

class

1

2

3

4

Saturated

hydraulic

conductivity

(centimeters

per day)

6.9

86.0

2.0

10.0

Specific

storage

(per

centimeter)

1 x 10'6

1 x 10'6

1 x 10-6

1 x 10'6

Porosity

0.45

.38

.47

.42

van Genuchten -a'

(centimeters)

-800

-80

-3,300

-150

van Genuchten

residual

moisture

content, 6r

0.12

.082

.165

.15

van Genuchten

P'

2.5

2.05

1.6

2.0

The van Genuchten equation relating soil moisture and negative hydraulic head has the three coefficients -a', 6P and P' (Lappala and others, 1983) where 

-a' is a scaling factor and P' is a pore-size distribution 

parameter. The parameters -a' and p' were estimated 

for each textural class by fitting the laboratory-determined soil-moisture characteristic curves with the van 

Genuchten equation. The residual moisture content, 6P 

is determined in the laboratory.

Evapotranspiration was simulated using monthly 

cycles. The values used in the model are mean monthly 

values of the average daily evapotranspiration. The 

model accounts for plant-root extraction from the 

unsaturated zone and requires the input of the root-pressure potential, plant-root activity function, and root 

depth (Lappala and others, 1983). Root-pressure potential was set to -10,000 cm (-3,940 in.) of water (Lappala 

and others, 1983). The plant-root activity function in 

the model is a linear function, and the top and bottom 

end points of the function are required and ranged from 

0.35 to 0.90 cm'2 (0.14 to 0.35 in.'2). Root depths were 

set from 100 to 130 cm (39.4 to 51.2 in.) on the basis of 

observations in the soil pits and on the laboratory-determined organic carbon content of soil clods and cores.

The model input is divided into recharge periods 

(Lappala and others, 1983). A recharge period is a time 

period when the recharge or evapotranspiration, boundary conditions, and iteration parameters are specified. 

The recharge periods for the simulations were defined 

by the application of irrigation water to each field. Each 

day the fields were irrigated was a recharge period, and 

the days between applications also were defined as 

recharge periods even though no recharge was occurring. For example, the center-pivot sprinkler rotated 

around the field once every 3 to 4 days; thus, the day the 

sprinkler system passed over the field instruments 

would be a 1-day recharge period when water was 

applied to the field. This recharge period would be followed by a 3-day recharge period when no water was 

applied but evapotranspiration occurred. Simulation in 

the flood-irrigated field consisted of 15 (1992) and 13 

(1993) recharge periods, and simulation in the sprinkler-irrigated field consisted of 41 (1992) and 56 (1993) 

recharge periods.

Calibration

The model was calibrated to the water budget 

(fig. 11) and to the soil-moisture profiles for the upper 6 

m (20 ft) of the unsaturated zone (fig. 8). No runoff 

from the field was assumed. This assumption is important because several of the laboratory-derived model 

input parameters were modified to ensure that there was 

no runoff from the field. Because the soil profile used in 

the model is a composite profile, reproduction of the 

actual soil-moisture profiles was not possible. However, the simulated soil-moisture profiles reflect the 

general shape of the actual soil-moisture profiles (figs. 

8 and 13) and indicate that the simulated profiles are 

representative of actual soil texture. The simulated soilmoisture profiles were calibrated to reproduce the soilmoisture variations observed in the field.

Saturated hydraulic conductivity for a soil texture can vary by several orders of magnitude. Laboratory saturated hydraulic-conductivity values from cores 

collected in this study are less than tabulated values for 

similar textural classes (Lappala and others, 1983; 

Rawls and others, 1982). These lower values may be a 

result of compaction of the samples during collection 

by using a trailer-mounted auger and core barrel. Saturated hydraulic-conductivity values measured in the 

field also are often more than an order of magnitude 

larger than those measured in the laboratory (R.W. 

Healy, U.S. Geological Survey, oral commun., 1993). 

The saturated hydraulic-conductivity values used as 

initial conditions were laboratory values and were mod22
100

200

300

DC 

(0

Q 400

JiJ 500

m

£

UJ

0 600

Flood-irrigated field, 1992 Flood-irrigated field, 1993

700

0 10 20 30 40 50 0 10 20 30 40 50 

VOLUMETRIC MOISTURE CONTENT, IN PERCENT VOLUMETRIC MOISTURE CONTENT, IN PERCENT

Figure 13. Simulated daily soil-moisture profiles in the flood- and the sprinkler-irrigated field for 1992 and 1993 irrigation 

seasons, Milford area, Utah.

23
ified during calibration. The modifications maintained 

the relative differences among the model textural 

classes as much as possible. The other model parameters have smaller ranges, and adjustments to these 

parameters during calibration were minimized.

Saturated hydraulic conductivity in each textural 

class was varied in the following ranges:

Textural 

class

1

2

3

4

Initial conditions 

(centimeters 

per day)

6.9

86

4

10

Range 

(centimeters 

per day)

6.9-700

86-8,600

4-400

10-1,000

Simulations using the initial laboratory values of 

saturated hydraulic conductivity were not possible 

because the model numerically failed to converge. The 

numerical problem was in the first layer with the application of 26 cm (10 in.) of water in the 1-day recharge 

period. The model numerically converged if saturated 

hydraulic conductivity was increased from 6.9 to 14 

cm/day (0.23 to 0.46 ft/day) in textural class 1, but surface runoff was generated, recharge was less than in the 

field water budget, and there were large changes in soil 

moisture. To prevent runoff and large changes in soil 

moisture, it was necessary to increase saturated hydraulic-conductivity values in all the textural classes. The 

field water budget and the simulated water budget were 

similar for simulations in which initial saturated 

hydraulic conductivity was increased by a factor 

greater than 2; however, the soil-moisture profile had 

ponding on layer 3 and experienced soil-moisture variations greater than 20 percent. Saturated hydraulic-conductivity values in the calibrated model were increased 

by a factor of 10 over the initial laboratory values. Field

saturated hydraulic-conductivity values typically are 

greater than laboratory values because the laboratory 

core samples do not sample larger soil structure that can 

affect conductivity values (Rick Healy, U.S. Geological 

Survey, oral commun., 1993). Saturated hydraulic conductivity was increased from 20 to 40 cm/day (0.66 to 

1.3 ft/day) to reduce ponding on layer 3. The simulated 

water budget was similar to the field water budget (fig. 

11) when these hydraulic-conductivity values were 

used, but variations in soil moisture were still greater 

than 20 percent in the soil-moisture profile.

The van Genuchten -a' parameter partly controls 

variation in soil moisture in a textural class. In textural 

classes 1 and 2, -a' was decreased from -800 to -1,000 

(textural class 1) and from -80 to -200 (textural class 2) 

to decrease the variability of the soil-moisture profiles. 

The objective was to limit the range of soil moisture in 

these textural classes to less than 20 percent with most 

of the variation in soil moisture in a layer less than 10 

percent.

The soil hydraulic parameters for the calibrated 

model are listed at the bottom of this page.

The simulated cumulative water budget is shown 

in figure 14 and the estimated and simulated water budget is summarized in table 2. The simulated water-budget components are generally within 5 cm (2 in.) of the 

estimated water budget. Recharge simulated for 1992 is 

the result of drainage from the initial soil profile (fig. 

13), and there is no recharge in the sprinkler-irrigated 

field in 1992. The variations in simulated soil moisture 

(fig. 13) are less than 20 percent, with most of the variation in the soil-moisture profile in the 10-percent 

range. The variations in the simulated soil-moisture 

profiles are greater than in the field soil-moisture profiles. To reduce these variations would require large 

changes in the van Genuchten parameters, which are a 

function of soil texture. The difference in evapotranspiTextural

class

1

2

3

4

Saturated

hydraulic

conductivity

(centimeters

per day)

69

860

40

100

Specific

storage

(per

centimeter)

1 xlO'6

1 xlO'6

1 xlO'6

1 xlO'6

Porosity

0.45

.38

.47

.42

van Genuchten -a'

(centimeters)

-1,000

-200

-3,300

-150

van Genuchten

residual

moisture

content, 6r

0.12

.082

.165

.15

van Genuchten

P'

2.5

2.05

1.6

2.0

24
200

Sprinkler-irrigated field, 1992

-100

EXPLANATION

^^ Recharge

 Precipitation plus irrigation

 *m*m, Evapotranspiration

 Soil-moisture storage

Figure 14. Simulated cumulative water budget for the flood- and the sprinkler-irrigated field for 1992 and 1993 irrigation 

seasons, Milford area, Utah.

180

25
Table 2. Summary of estimated and simulated water budget for the flood- and the sprinkler-irrigated field for the 1992 and 

1993 irrigation seasons, Milford area, Utah

Field and 

year

Flood, 1992

Flood, 1993

Sprinkler, 1992

Sprinkler, 1993

Evapotranspiration 

(centimeters)

Estimated

95.4

84.3

95.4

84.3

Simulated

94.5

79.3

94.3

79.6

Irrigation plus 

precipitation 

(centimeters)

Estimated

188.7

162.4

59.5

93.6

Simulated

188.8

162.1

54.7

90.2

Recharge 

(centimeters)

Estimated

93.3

78

-35.9

9.3

Simulated

98.3

83.9

-1.7

16.3

Change in soilmoisture storage 

(centimeters)

Estimated

0

0

0

0

Simulated

-2.6

.04

-41.1

-4.3

ration between the estimated field water budget and the 

simulations is a result of rounding during the simulation 

and monthly averaging.

Simulated Water Budget for the Flood- and the 

Sprinkler-Irrigated Field for Average Climate 

Conditions

The water budget for the flood- and the sprinklerirrigated fields was simulated with the model for average climate conditions to compare the quantity of 

recharge to the aquifer from the different irrigation 

methods. The model calibrated to the 1992 and 1993 

irrigation seasons was used for the simulation. Average 

net irrigation requirements for alfalfa for 1961-90 for 

the Milford area were used for the evapotranspiration 

values in the model. The average net irrigation requirements were calculated by Hill and others (1993) (R.W. 

Hill, Utah State University, written commun., 1994) 

using the calibrated Blaney Griddle equation of the Soil 

Conservation Service. The average net irrigation 

requirement is growing-season evapotranspiration 

minus effective precipitation. The Blaney Griddle 

equation was calibrated using 5 years of data from an 

agricultural micrometeorology station, with evapotranspiration calculated using the Kimberly version of 

the Penman equation (Hill and others, 1993). The 30-

___________April______May

Net irrigation

requirement 2.31 15.92

(in centimeters)

June

15.19

year average monthly net irrigation requirements 

(1961-90) for alfalfa in the Milford area (R.W. Hill, 

Utah State University, written commun., 1994), assuming that 80 percent of precipitation during the growing 

season is effective, are listed at the bottom of the page.

Precipitation was subtracted from model input 

because it is accounted for in the net irrigation requirements. Applications of irrigation water for the 1992 and 

1993 irrigation seasons were used in the simulations to 

produce a range of irrigation applications. The seven 

applications to the flood-irrigated field in 1992 were 

more than the normal six applications for the Milford 

area. There were six applications in 1993. The application to the sprinkler-irrigated field in 1992 was less than 

crop water requirements because of the amount of 

water applied with each rotation and because of 

mechanical problems with the sprinkler system. The 

sprinkler-irrigated field received more frequent and 

larger quantities of water in 1993, with sufficient water 

applied to meet crop water requirements.

The simulated water-budget components for 

average climate conditions (fig. 15) are listed in table 3. 

The simulated water budgets in table 3 for each year do 

not balance exactly because of numerical approximation and rounding. Recharge from the flood-irrigated 

field in 1992 is 57.4 percent of the applied irrigation 

water. In 1992, there were seven irrigation applications,

July

20.62

August

16.18

September

9.86

Annual

80.08

26
Table 3. Simulated water budget for the flood- and the sprinkler-irrigated field for average climate conditions, Milford area, 

Utah

Field and

year Evapotranspi ration Irrigation Recharge 

(centimeters) (centimeters) (centimeters)

Change in soil Irrigation water 

moisture in storage Runoff that is 

(centimeters) (centimeters) recharge

(percent)

Flood, 1992

Flood, 1993

Sprinkler, 1992

Sprinkler, 1993

78.8

78.9

78.8

78.8

182.0

156.0

52.8

87.2

104.2

78.8

4.5

14.2

0.15

.34

-30.2

-4.4

0

0

0

0

57.4

50.5

8.7

13.8

of which two were in a 1-week period, thereby increasing recharge. In 1993 there were six irrigation applications, which is normal for the Milford area, and 50.5 

percent of the applied irrigation water became recharge. 

The irrigation water applied to the sprinkler-irrigated 

field in 1992 was less than crop water requirements, but 

8.7 percent of the applied irrigation water in the simulation became recharge. This recharge is the result of 

drainage from the soil profile because of the initial soilmoisture profile for the soil column. This drainage from 

the initial soil-moisture profile might be similar to 

drainage that might occur from infiltration of snowmelt 

through the soil in the spring. In 1993 the sprinkler-irrigated field received 87.2 cm (34.3 in.) of irrigation 

water, of which 13.8 percent became recharge. Part of 

the 1993 recharge, 8.7 cm (3.4 in.), can be attributed to 

drainage from the initial soil-moisture profile. Actual 

recharge in 1993 was 5.1 cm (2.0 in.).

Effects of Distribution of Flood-Irrigation 

Water on Recharge

The distribution of irrigation water across a 

flood-irrigated field is nonuniform, with the upper end 

of the field receiving more irrigation water than the 

lower end. The estimated water budget and the model 

simulations assume a uniform distribution of water 

across the field. Simulation of unsaturated flow for the 

flood-irrigated field for 1993 was used to investigate the 

effects of water distribution on recharge from the field. 

The model was used to simulate the water budget for a 

uniform distribution and for a linear distribution of 

water on the field. The amount of water applied to the 

field was equal in both simulations, and there was no 

runoff from the fields.

The simulated uniform and linear distributions of 

water across the field and the evapotranspiration and

recharge for each distribution are shown in figure 16. 

Simulations were done along the length of the field and 

extended for a width of 1 meter. The quantity of water 

applied to the fields, evapotranspiration, and recharge 

from the fields are:

Water

distribution

Uniform

Linear

Applied

irrigation

water

(cubic

meters)

600

600

Evapotranspiration

(cubic

meters)

304

262

Recharge

(cubic

meters)

296

338

Applied

water

that is

recharge

(percent)

49

56

For the linear distribution, the lower end of the 

field does not have sufficient water to meet the water 

demands of plants; therefore, simulated evapotranspiration is less than in the uniform distribution. When 

water is uniformly distributed across the field, 49 percent of the irrigation water becomes recharge. For the 

linear distribution, 56 percent of the irrigation water 

becomes recharge. The assumption of a uniform distribution of water across the field underestimates recharge 

from irrigation by 7 percent for the simulation, and the 

underestimation would likely increase as evapotranspiration increases.

Sensitivity Analysis

Saturated hydraulic conductivity is an important 

parameter that controls flow through the unsaturated 

zone. Saturated hydraulic-conductivity changes 

between soil layers can cause ponding on layers, generate surface runoff, and force water to flow horizontally 

rather than vertically. The water budget determined 

from three selected model simulations used in the 

model calibration is shown in table 4. These simula27
200

Sprinkler-irrigated field, 1993

-150

150 180

EXPLANATION

mm^ Recharge

,.... ... _ . Precipitation plus irrigation

««».««., Evapotranspiration

 Soil-moisture storage

Figure 15. Simulated cumulative water budget for the flood- and the sprinkler-irrigated field for average climate conditions 

(1961-90) with 1992 and 1993 irrigation applications, Milford area, Utah.

28
a. Uniform distribution of 1.56 meters of water across field 

Quantity of irrigation water applied, 600 square meters 

Recharge, 296 square meters 

49 percent of applied water becomes recharge

Recharge

0.79 meters -> 

0.77 meters 11.56 meters

Lower end of field Field length. 385 meters Upper end of field

b. Linear distribution of water across field is 3.12 meters at top of field, 0 meters at bottom of field 

Quantity of irrigation water applied, 600 square meters 

Recharge, 338 square meters 

56 percent of applied water becomes recharge ^^f^flll 0.79 meters<

3.12 meters

2.33 meters'

95 meters 

Lower end of field Field length, 385 meters

Upper end of field

290 meters

Upper end of field

Lower end of field

Figure 16. Simulated (a) uniform and (b) linear distribution of flood-irrigation water across a field.

tions show the effect of changes in saturated hydraulic 

conductivity on the water budgets. Simulation 1 used 

laboratory values of saturated hydraulic conductivity, 

except for textural class 1, in which the saturated 

hydraulic-conductivity value was increased from 6.9 

cm/day to 14 cm/day (0.23 to 0.46 ft/day). This increase 

was necessary to reduce the quantity of surface runoff 

from the field. In simulation 2, the hydraulic-conductivity values were increased from the laboratory values by 

a factor of 2 for each textural class. Simulation 3 is the 

calibrated model, which uses saturated hydraulic-conductivity values that are increased from the laboratory 

values by a factor of 10.

In simulation 1, runoff is generated from the 

flood-irrigated field even after doubling the saturated 

hydraulic conductivity because the applied irrigation 

water does not all infiltrate and is not accounted for by 

evapotranspiration, soil moisture in storage, and 

recharge. The percentage of precipitation and irrigation 

that infiltrates as recharge in the flood-irrigated field of 

about 50 percent in simulations 2 and 3 indicates that

saturated hydraulic conductivity does not limit recharge 

in these simulations. However, the distribution of soil 

moisture is different between simulations 2 and 3. The 

soil-moisture profiles from the two simulations show 

that water ponds over layers with low hydraulic-conductivity values. This ponding, if near the root zone, 

can make more water available to plants, thereby 

increasing evapotranspiration and reducing recharge. 

This simulation demonstrates the importance of not 

only determining the water budget but also of monitoring the distribution of soil moisture in the soil profile.

There was no recharge in the sprinkler-irrigated 

field in 1992 in any of the simulations. The sprinklerirrigated field received more irrigation water in 1993 

than in 1992 and evapotranspiration was less because of 

climate conditions; therefore, recharge occurred in all 

three 1993 simulations. If evapotranspiration in 1993 

had been equal to that in 1992, there would have been 

recharge only in simulation 3.

29
Table 4. Water budget for three simulations that demonstrate the sensitivity of the model of the flood- and the sprinklerirrigated field to changes in saturated hydraulic conductivity, Milford area, Utah

[ , evapotranspiration is greater than precipitation plus irrigation, thus no recharge occurs and no water is added to soil-moisture storage]

Field Irrigation

and plus

year precipitation

minus runoff

(centimeters)

Flood, 1992 182.4

Flood, 1993 150.1

Sprinkler, 1992 54.7

Sprinkler, 1993 90.2

Flood, 1992 188.9

Flood, 1993 160.1

Sprinkler, 1992 54.7

Sprinkler, 1993 90.2

Flood, 1992 188.8

Flood, 1993 162.1

Sprinkler, 1992 54.7

Sprinkler, 1993 90.2

Evapotranspiration

(centimeters)

94.8

79.5

94.5

79.6

94.5

79.4

94.4

79.6

94.5

79.3

94.3

79.6

Change

in soil

moisture Recharge

Fraction of

irrigation

plus precipitation

in storage (centimeters) minus runoff

(centimeters)

Simulation 1

6.1 74.8

9.1 61.7

-39.8 0

3.3 7.4

Simulation 2

-.77 95.5

1.2 80.1

-4U -1.7

-3.1 14.2

Simulation 3

-2.6 98.3

.04 83.9

-41.1 -1.7

-4.3 16.0

consumed by

evapotranspiration

(percent)

52

53

100

88

50

50

100

88

50

49

100

88

Fraction of

irrigation

plus precipitation

minus runoff

that is

recharge

(percent)

40

41

8

51

50

15

52

51

17

Fraction of

irrigation plus

precipitation

minus runoff

that is change

in storage

(percent)

3.3

6

4

0

1

-3

-1

0

-5

Limitations of the Model

The model simulates vertical one-dimensional 

flow through the upper 6.4 m (21 ft) of the unsaturated 

zone at the field site. Model solutions are nonunique 

because different combinations of parameters can produce the same result. Because evapotranspiration 

accounts for about 50 percent of the water budget, 

errors in the estimation of evapotranspiration could 

cause large errors in the water budget. The model does 

not account for any horizontal flow, nor does it account 

for the fate of water once it infiltrates below 6.4 m (21 

ft). The model was discretized and calibrated to a specific soil profile. The simulations allow comparison of 

probable recharge for soil profiles with similar hydraulic properties and allow comparison of probable 

recharge resulting from the use of different irrigation 

methods. The simulations use estimates of evapotranspiration from field data, and the uncertainty in these 

estimates is carried over to the simulation results.

Summary

Irrigators in the western United States are converting from less efficient irrigation methods, such as 

flood irrigation, to more efficient sprinkler systems. In 

theory, ground-water withdrawals for irrigation 

decrease as irrigation efficiency improves; however, 

many irrigators are increasing irrigated acreage as they 

improve irrigation efficiency. Ground-water withdrawals are thereby maintained and may reduce recharge 

from unconsumed irrigation water and contribute to 

ground-water-level declines. A cooperative study 

between the U.S. Geological Survey and the Utah 

Department of Natural Resources, Division of Water 

Rights, was initiated to quantify and compare the quantity of ground-water recharge from irrigation water 

using flood- and sprinkler-irrigation methods.

The study site is in the Milford area of southwestern Utah and consists of two adjacent irrigated alfalfa 

fields; a flood-irrigated field and a center-pivot sprinkler-irrigated field. The soils at the study site are generally classified as loam to clay loam. Soil samples from

30
pits and cores from selected intervals were collected. 

The particle-size distribution indicates that the texture 

of the unsaturated zone is heterogeneous and layered.

The study site was instrumented to measure soil 

moisture and climate parameters. Soil moisture was 

measured with a soil-moisture neutron probe at two 

locations in the flood-irrigated field and two locations 

in the sprinkler-irrigated field. Soil-moisture measurements were made at about 2-week intervals in 1992 and 

daily for May and part of June in 1993. Climate parameters were measured with an automated weather station 

sited between the flood- and the sprinkler-irrigated 

field. Measurements were not made in the fields.

The components of the water budget for each 

field were measured at intervals, or calculated or estimated at the study site. Precipitation at the study site 

during April to September was about 6.5 cm (2.6 in.) in 

1992 and 1993. The farmers recorded application dates 

of irrigation water to the flood- and the sprinkler-irrigated field. The flood-irrigated field received about 182 

cm (71.6 in.) of water in 1992 and 156 cm (61.4 in.) in 

1993. The sprinkler-irrigated field was irrigated using a 

center-pivot sprinkler system that revolved every 3 to 4 

days. The sprinkler applied 2.6 to 3.8 cm (1.0 to 1.5 in.) 

of water per revolution. The sprinkler-irrigated field 

received about 52.8 cm (20.8 in.) of water in 1992 and 

87.2 cm (34.3 in.) in 1993.

Evapotranspiration was calculated using the Penman-Monteith combination equation. Daily evapotranspiration ranged from 1.2 to 13.4 mm/day (0.0039 

to 0.044 ft/day) in 1992 and from 2.5 to 14.4 mm/day 

(0.0082 to 0.047 ft/day) in 1993. Cumulative evapotranspiration was 95.4 cm (37.6 in.) for April 1 to September 15, 1992, and 84.3 cm (33.2 in.) for April 1 to 

September 30,1993. Evapotranspiration was estimated 

for both the flood- and the sprinkler-irrigated field from 

a single set of climate data that was collected between 

the two fields. This climate data represents an average 

data set for the area because the site was surrounded by 

irrigated alfalfa fields, thus, evapotranspiration calculated from it may differ from evapotranspiration actually measured in the fields. No runoff was observed 

from either the flood- or the sprinkler-irrigated field.

Soil moisture was measured about every 2 weeks 

in 1992 and daily in May and part of June of 1993. The 

soil moisture varied plus or minus 5 percent and did not 

change substantially from the beginning to the end of 

the irrigation season; thus, for the water budget, no 

change in the quantity of soil moisture in storage is 

assumed. The lower end of the flood-irrigated field was

an exception. The quantity of irrigation water was 

insufficient to satisfy plant water requirements at the 

lower end of the field, and the entire soil profile dried 

out.

Estimated recharge for the flood-irrigated field in 

1992 was 93.3 cm (36.7 in.) and in 1993 was 78.1 cm 

(30.7 in.). The estimated recharge is 49 percent and 48 

percent, respectively, of the sum of precipitation and 

irrigation during April to September in 1992 and 1993. 

Estimated recharge in the sprinkler-irrigated field in 

1992 was -35.9 cm (-14.1 in.) and in 1993 was 9.3 cm 

(3.7 in.).

An unsaturated-flow model was used to simulate 

vertical infiltration through the upper 6.4 m (21 ft) of 

the unsaturated zone. Water that infiltrated to a depth of 

6.4 m (21 ft) was assumed to recharge the basin-fill 

aquifer. The model was constructed and calibrated 

using measured and estimated water-budget components and soil-moisture profiles from the flood- and the 

sprinkler-irrigated field. A composite soil column was 

created for the model from data from both fields that 

includes four textural classes and five layers. Initial soil 

properties and derived parameters required by the 

model were laboratory determined or were calculated 

from laboratory-determined values.

Model calibration required adjustment of the saturated hydraulic-conductivity values and the van Genuchten equation parameters to prevent surface runoff, 

ponding on soil layers, and large variations in soil moisture. Saturated hydraulic-conductivity values were 

increased by an order of magnitude, and the van Genuchten -a' was decreased in two of the textural classes. 

Simulations with the calibrated model-computed 

water-budget components are generally within 5 cm of 

the estimated water budget. The variations in simulated 

soil moisture are less than 20 percent, with most of the 

variation in the soil-moisture profiles in the 10-percent 

range.

The water budget for the flood- and the sprinklerirrigated field was simulated with the model for average 

climate conditions to compare recharge to the aquifer 

by means of each irrigation method. Recharge from the 

flood-irrigated field in 1992 is 57.4 percent of the 

applied irrigation water. In 1992, there were seven irrigation applications, of which two were in a 1-week 

period, thereby increasing recharge. In 1993 there were 

six irrigation applications, which is normal for the Milford area, and 50.5 percent of the applied irrigation 

water became recharge. The irrigation water applied to 

the sprinkler-irrigated field in 1992 was less than crop

31
water requirements, but 8.7 percent of the applied irrigation water in the simulation became recharge. This 

recharge is the result of drainage from the soil profile 

because of the initial soil-moisture profile for the soil 

column. This drainage from the initial soil-moisture 

profile might be similar to drainage that might occur 

from infiltration of snowmelt through the soil in the 

spring. In 1993 the sprinkler-irrigated field received 

87.2 cm (34.3 in.) of irrigation water, of which 13.8 percent became recharge.

The one-dimensional model was used to simulate 

the water budget for a uniform distribution and for a linear distribution of water on the field. In these simulations, 49 percent of the irrigation water from the 

uniform distribution became recharge and 56 percent of 

the irrigation water from the linear distribution became 

recharge. If evapotranspiration increases, then the percentage of irrigation water that is recharge would 

increase for the linear distribution relative to the uniform distribution.

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