Soil-Based Irrigation and Salinity Management Model:II. Water and Solute Movement Calculations

G. E. Cardon* and J. Letey

ABSTRACTThe utility of a new model for irrigation and soil salinity manage-

ment is based largely on the agreement between measured and pre-dicted water and solute movement in the soil profile. Data suitablefor comparison to model calculations is lacking in the literature. Weconducted a greenhouse study designed to obtain detailed temporalsalt and water distribution data under fluctuating shallow saline watertable conditions, and compared simulated and observed data. Ourmodel's calculations for water content and salinity agreed well withthe observed distributions. Willmott's d index (a statistical index ofagreement between measured and observed data) results ranged from0.83 to 0.97 (perfect agreement = 1.0). Agreement was improvedwhen potential evapotranspiration (PET) estimates were adjusted fordata from individual treatment columns in the greenhouse experi-ment. The ({-index values, following adjustment of PET, increased to0.94 or higher, indicating the importance of accurate localized PETestimates for optimum model performance.

A SOIL-BASED NUMERICAL MODEL for transient-state water and solute movement and plant water

uptake is presented in Cardon and Letey (1992). Themodel, called the V-H model, was formulated to ac-count for empirical crop salt- and water-stress toler-ances. In addition, the model was designed to (i) treattemporal variations in plant root growth, PET, andsalt- and moisture-stress tolerance, and (ii) performmultiseasonal simulations including noncropped pe-riods (Cardon and Letey, 1992). A useful feature ofthe V-H model is that it can handle combined satu-rated and unsaturated soil conditions, as would occurif a shallow water table were present. Moreover, themodel will simulate a fluctuating water table levelbased on the relative balance between water uptakeby the plant, water flux to the bottom boundary of thesoil profile, and the bottom boundary flux conditionset by the user.

The V-H model was previously tested by a com-parison between calculated and experimentally mea-sured yields of corn (Zea mays L., cv. Jubilee). Themodel predictions compared well with the experimen-

G.E. Cardon, Agronomy Dep., Colorado State Univ., Ft. Collins,CO 80523; and J. Letey, Soil and Environmental Sciences Dep.Univ. of California, Riverside, CA 92521. Contribution of theUniv. of California, Riverside. Sponsored by the Univ. of Cali-fornia's Salinity/Drainage Task Force. Received 2 Apr. 1991.* Corresponding author.

Published in Soil Sci. Soc. Am. J. 56:1887-1892 (1992).

tal results (Cardon and Letey, 1992). The previoustests were all for unsaturated flow conditions. More-over, comparison between experimentally measuredand predicted water and solute distributions in the soilprofile were not possible.

Experimental data of water and solute distributionin the soil, which are suitable for comparison to V-Hmodel predictions under fluctuating saline water tableand plant water uptake conditions, are lacking. Fieldstudies have been conducted to determine crop wateruse under shallow saline water table conditions (e.g.,Ayars and Schoneman, 1986; Wallender et al., 1979),but these reports generally do not provide detailedprofile distributions of water or solutes. Namken etal. (1969) conducted a lysimeter study that providedgreater detail of soil profile conditions; however, thewater table was maintained at a fixed depth, which isuncharacteristic of field conditions.

To further test the model and compare calculationsagainst experimental data, research was conducted intwo phases. The first phase was a greenhouse studydesigned to obtain detailed water and solute distribu-tions with time and depth under fluctuating saline watertable and plant water uptake conditions for compari-son to model predictions. The second phase was acomparison of V-H model calculations of water andsolute distributions, and crop yield, with the experi-mental data obtained in the greenhouse.

METHODS AND MATERIALSGreenhouse Study

Two-meter-long PVC columns of 0.2-m diameter wereused to contain the soil. Each column was instrumentedwith tensiometers and ceramic solution sampling cups at0.25-m intervals to a depth of 1.5 m. The columns werefilled with soil material from the Ap horizon of a Hanfordsandy loam (coarse-loamy, mixed, nonacid, thermic TypicXerorthent), which had been treated with Krilium (an ag-gregate-stabilizing polymer, Monsanto Chemical Corp., St.Louis, MO) at a rate of 0.3 g/kg soil. The columns wereincrementally filled to the level where a tensiometer-solu-tion sampler set was to be inserted. The sensors were theninserted and the soil packed to ensure good contact betweenthe ceramic cups and soil. This procedure was repeated untilthe column was completely filled and all sensors installed.

Abbreviations: PET, potential evapotranspiration; PVC, poly-vinyl chloride; ET, evapotranspiration; WTM, water table main-tenance; EC, electrical conductivity; RMSE, root mean squarederror.

1888 SOIL SCI. SOC. AM. J., VOL. 56, NOVEMBER-DECEMBER 1992

At the conclusion of the experiment, bulk density sampleswere taken at the 25- and 200-cm levels from the first andlast columns filled in each of three experimental blocks.The average bulk density at 25 and 200 cm was 1.422 ±0.022 and 1.413 ± 0.007 Mg/m3; respectively. The overallaverage bulk density was 1.417 ± 0.010 Mg/m3.

Six treatments were used in the study. Two irrigationregimes of 100 and 75% of crop PET were the main treat-ments, with three water table salinities of 3.0, 6.0, and10.0 dS/m as subtreatments. Each treatment was replicatedthree times. The experiment was set up in a randomizedblock design.

Piezometer tubes, inserted at the base of each column tomonitor the water table depth, facilitated saturation of thecolumns from the bottom with saline water to a depth of1.0 m, which was the initial depth of the water table. Thesaline "groundwater" was prepared by dissolving appro-priate amounts of a 1:1 (moljmol^ NaCl/CaCl2 salt mix-ture. Nonsaline water (0.6 dS/m) was applied to the surfacein a preplan! irrigation to wet the surface 1 m to a matricpressure of approximately — 0.01 MPa. A 33 kg/ha N fer-tilization in the form of KNO3 was applied in solution withthe final 1L of preplan! irrigation water to provide adequateN for seedling establishment. No further fertilization wasdone since existing nutrient levels were determined to besufficient.

Alfalfa (Medicago sativa L., cv. Moapa) was planted on4 Oct. 1989. After germination and seedling establishment,the plants were thinned to seven per column. This wasequivalent to a seedling density of approximately 220 plants/m2, which is within the recommended range for plantingdensity (Barnes and Sheaffer, 1985). The alfalfa was pe-riodically clipped during the experiment to control plantgrowth, simulate field cuttings, and provide periods of zeroirrigation during which soil solution samples could be taken.Harvesting was done when approximately one-half of thetreatments in each block were at first-bloom stage. Cuttingswere taken on 19 December, 22 January, and 16 February.

A separate column was set up that had no shallow watertable. This column was placed on a balance (0.2-kg reso-lution) and used as a weighing lysimeter. The lysimetercolumn had two tensiometers. One was installed at 0.25 mand the other at 1.0 m. Alfalfa was also planted in thiscolumn to provide ET values for comparison with the othertreatments in guiding irrigation quantities. Irrigation waterwas applied to the lysimeter when the tension at 0.25 mwas between - 0.01 and — 0.02 MPa. Enough water wasadded to resupply that which was lost. Extra water wasoccasionally added if the tensiometer measurement at 1.0m dropped below — 0.01 MPa.

Irrigations were applied to all treatment columns whentensiometer readings at 0.25 m in any of the treatment col-umns were between — 0.02 and — 0.03 MPa. As originallydesigned, the amount of water applied to the columns wascalculated from water balance data measured with theweighing lysimeter. Toward the end of the first harvestperiod, water table levels for the 100% PET treatments inBlocks B and C began to drop below 1.0 m, indicating thatET was greater than that measured by the lysimeter. Thewater table levels on corresponding treatments in Block Aremained close to 1.0 m or rose somewhat above that level.Irrigating at 100% of PET should, in theory, have kept thewater table levels on these treatments near 1.0 m. Becauseof this consideration, we decided it was not appropriate touse the weighing lysimeter data for further determinationsof irrigation amounts. For the second and third harvest pe-riods, a new irrigation procedure was adopted. Irrigationamounts were determined by the amount of water neededto maintain the water table level of the 100% PET treat-ments at 1.0 m (referred to hereafter as the water tablemaintenance, or WTM, procedure). The 75% PET treat-

ments received 75% of the average amount of water addedto the 100% PET treatments in their respective blocks.

Tensiometer data was recorded before and 2 d followingirrigations, and at each harvest period. Solution samplingswere taken at the time of each harvest and analyzed fortheir EC at 25 °C. After the third cutting, a final tensiometerreading was taken and soil samples were removed throughports in the column wall at the level of each tensiometer.Each sample was split and one-half was weighed and driedat 105 °C to determine the soil water content. The matricpressure-water content data obtained in this manner is shownin Fig. 1. The other one-half of the sample was mixed toa saturated paste, and the extract (obtained by suction fil-tration) was analyzed for EC.

Experimental Data SimulationsIn the V-H model, crop water uptake, S (d-1), of van

Genuchten (1987) as a function of depth and time as mod-ified by Cardon and Letey (1992), has the following math-ematical form:

S(z,t) = (a(t)h + Tr\I "50(0 / .

1 +

where Smax(t) is the maximum potential root water uptake(d-1) at the time t (d), z is vertical depth taken positivedownwards (cm), \(z,t) is the depth- and time-dependentfraction of total root mass, h is the matric pressure head(cm), IT is the osmotic pressure head (cm), irSq(t) is thetime-dependent value of the osmotic pressure at which S^^t)is reduced by 50%, and a(t) is a weighing coefficient thataccounts for the differential response of a crop to matricand solute pressure. The coefficient a(t) equals •n-soW^soWwhere h50(f) is the matric pressure at which Smax(f) is re-duced by 50%.

Maas (1986) compiled data on crop salt tolerance fromwhich the values of ir50(f) for alfalfa were obtained. Thedata, however, are expressed as the EC of a saturated pasteextract (ECf). To place the values of irso(0 on a field watercontent basis, the ECe value at which crop yield is reducedby 50% was doubled and then converted to an osmoticpressure (James et al., 1982). This procedure resulted in avalue of — 0.64 MPa for TT50(0> which was then held con-stant with time.

0.50

0.00-0.00 -0.01 -0.02 -0.03 -0.03 -0.04 -0.05

Matric Pressure (MPa)Fig. 1. Greenhouse water characteristic curve as measured by

tensiometers and fitted using the Hutson and Cass (1987)hydraulic property functions.

CARDON & LETEY: IRRIGATION AND SALINITY MANAGEMENT MODEL: II 1889

The calculation of \(z, t) in Eq. [1] requires an input ofthe maximum rooting depth at a given time. An averagegrowth rate of 2.0 cm/d was assumed, which was consistentwith the observance of roots at the bottom of the 75% PETtreatment columns at the conclusion of the experiment. Themaximum rooting depth was restricted to the unsaturatedzone above the water table.

Initial water and salt distributions for each column weretaken from the tensiometer and solution sampling followingthe thinning of seedlings. The lower boundary in the sim-ulations was set at 2 m, with a zero-flux condition.

The V-H model uses the Hutson and Cass (1987) soilhydraulic property functions to calculate the matric pres-sure-water content-hydraulic conductivity relationships.Values for the parameters for these functions were obtainedby a least-squares fit to the water characteristic curve gen-erated from the tensiometer measurements at the conclusionof the greenhouse experiment (Fig. 1). In addition, the sat-urated hydraulic conductivity (^sat) was measured using aconstant-head infiltrometer. Each column was packed withsoil to the average bulk density of the greenhouse columns.Saturation water content (6sat) was calculated from the po-rosity of the experimental soil using the following equationof Williams et al. (1992):

ment (d), expressed as:

= 0.93 1 - [2]

where pt is the soil bulk density. The factor 0.93 was de-rived from data from 118 horizons of 72 profiles sampledin northern Australia and accounts for voids that do notsaturate with water (blocked pores, etc.). A summary ofthe hydraulic parameters is given in Table 1.

Comparison between model simulations and experimen-tal data were made for salt and water distributions in theprofile. Simulations were run for all treatments. Evaluationof predicted vs. measured data was then made throughgraphical inspection and the calculation of two objectivefunctions. The first objective function is the RMSE, whichis calculated in the following manner:

RMSE =N [3]

where Pt and Ot are the ith predicted and observed valuesof interest, respectively. The value of RMSE is in the sameunits as the corresponding data, and is a measure of theaverage deviation of the predicted data from that observed.The second objective function is Willmott's index of agree-

Table 1. Hydraulic parameters used to simulate greenhousesoil properties.

Fitted parameters:! bB

Measured parameters:Saturated hydraulicconductivitySaturation watercontent (v/v)

1.905.85

-1.64kPa-2.56 kPa

0.35

6.29 cm/h

0.44

d = 1 -" I (Pi ~ O

_«=!

[4]

where P[ = Pt - Om, O[ = 0, - Om, and Om is the meanobserved value (Willmott, 1981). The value old is an indexof how well the predicted and observed deviations aboutOm correspond to each other, both in magnitude and sign.It varies between 1.0 and 0.0, with 1.0 representing perfectagreement and 0.0 representing one of many forms of totaldisagreement. The two objective functions (RMSE and thed index) in conjunction quantify the agreement betweensimulated and observed results.

Of the 54 possible comparisons of water and salt distri-butions (three comparisons on 18 columns) only a limitednumber will be discussed here. Columns in which problemswere observed (primarily leaking) were not considered. Datafrom the 100% PET treatment columns were the most ac-curate PET estimates from the record of water applied underthe WTM irrigation procedure to each individual column.These data also provided an opportunity for comparisonbetween using the weighing lysimeter and the WTM pro-cedure for estimating PET.

The data from three 100% PET treatment columns (onefrpom each block) were chosen as being representative ofcolumns (i) that had an apparent PET less than the lysimeter(Column 1, Block A), (ii) that had an apparent PET greaterthan that of at the lysimeter (Column 5, Block B), and (Hi)that had an apparent PET approximately the same as thelysimeter (Column 3, Block C). Simulation runs were firstmade using PET values calculated from the lysimeter. Thiswas followed by simulations for Columns A-l and B-5 withPET equal to that determined by the WTM irrigation pro-cedure during the second and third harvest periods.

RESULTS AND DISCUSSIONGraphic comparisons between the computed and

measured water and salt distributions, using PET cal-culated from the weighing lysimeter, are shown inFig. 2 to 7. Figures 8 to 11 depict results for ColumnsA-l and B-5 using the PET values calculated by theWTM procedure. For convenience in reporting, saltconcentrations calculated by the model were standard-

0.0

Water Content (v/v)

0.3 0.4 0.5

t Values obtained by a least-squares fit to Hutson and Cass (1987) functions.

-150Fig. 2. Measured (symbols) and model predicted (lines) soil

profile water distributions for all three harvest periods forColumn A-l.

1890 SOIL SCI. SOC. AM. J., VOL. 56, NOVEMBER-DECEMBER 1992

ECSAT (dS m-1)

4.0 6.0 8.0 10.0

-150Fig. 3. Measured (symbols) and model predicted (lines) soil

profile salt distributions for all three harvest periods forColumn A-l.

0.0

Water Content (v/v)

0.1 0.2 0.3

Fig. 6. Measured (symbols) and model predicted (lines) soilprofile water distributions for all three harvest periods forColumn C-3.

Water Content (v/v)

0.1 0.2 0.3 0.4 0.5

-150Fig. 4. Measured (symbols) and model predicted (lines) soil

profile water distributions for all three harvest periods forColumn B-5-

10.0

1st Cut2nd Cut3rd Cut

Fig. 5. Measured (symbols) and model predicted (lines) soilprofile salt distributions for all three harvest periods forColumn B-5.

10.0

-150Fig. 7. Measured (symbols) and model predicted (lines) soil

profile salt distributions for all three harvest periods forColumn C-3.

Water Content (v/v)

0.3 .0.4 0.5

-30 -

o'-60 -

o.<B°-90 :

oW

-120 -

-150Fig. 8. Measured (symbols) and predicted (lines) soil profile

water distributions for Column A-l using potentialevapotranspiration (PET) values determined by the watertable maintenance (WTM) procedure.

ized to saturation water content (linear dilution to 0sat)and converted to EC (ECsat). The values of the objec-tive functions (Eq. [3] and [4]) are summarized inTable 2, and were calculated for the data from all three

cuttings from each column for both the lysimeter andWTM methods for estimating PET.

For Column A-l, simulations using the lysimeterPET values show a consistent underprediction of water

CARDON & LETEY: IRRIGATION AND SALINITY MANAGEMENT MODEL: II 1891

2.0

ECSAT (dS m•')

4.0 6.0 8.0 10.0

-150Fig. 9. Measured (symbols) and predicted (lines) soil profile

salt distributions for Column A-l using potentialevapotranspiration (PET) values determined by the watertable maintenance (WTM) procedure.

Water Content (v/v)

0.0

-150Fig. 10. Measured (symbols) and predicted (lines) soil profile

water distributions for Column B-5 using potentialevapotranspiration (PET) values determined by the watertable maintenance (WTM) procedure.

2.0

ECSAT (dS m-1)

4.0 6.0 8.0 10.0

-150

Fig. 11. Measured (symbols) and predicted (lines) soil profilesalt distributions for Column B-5 using potentialevapotranspiration (PET) values determined by the watertable maintenance (WTM) procedure.

content for each cutting and an overprediction of salttransport into the profile for the third harvest period

Table 2. Descriptive statistics and objective function resultsfor observed (obs) water (WAT) and salinity (SALT) data,and for predictions using the lysimeter (LYS) and watertable management (WTM) methods of estimating potentialtranspiration.

A1-WAT4LYSWTMobs

Al-SALT:LYSWTMobs

B5-WAT:LYSWTMobs

B5-SALT:LYSWTMobs

C3-WAT:LYSobs

C3-SALT:LYSobs

Mean

0.250.280.30

2.622.622.32

0.300.250.23

3.373.533.24

0.270.26

3.073.08

SD

0.120.120.11

1.911.981.52

0.120.130.11

3.242.702.85

0.120.11

2.832.57

RMSEf

0.0650.052

—

0.8430.856

—

0.0960.048

—

1.5720.948

—

0.043—

0.938—

dindext

0.920.95

—

0.940.94

—

0.830.96

— '

0.930.95

—

0.96—

0.97—

t Root mean squared error.tWillmott's index of agreement (Willmott, 1981)

(Fig. 2 and 3, Table 2). Reducing the PET value forthis column (according to the WTM irrigation proce-dure) improves the agreement with the observed dis-tributions, especially for water content. Theimprovement in agreement is reflected in the increasein the d index and decrease in the RMSE values listedin Table 2 and illustrated in Fig. 8 and 9.

The computed water content distributions for Col-umn B-5 using the lysimeter PET values are shownin Fig. 4. The model predicted less water uptake thanactually occurred, particularly for the final harvest pe-riod. As a result, salt movement into the profile isunderpredicted (Fig. 5). When PET values determinedby the WTM procedure were used, the predictions ofboth water content and salt distribution were improvedconsiderably, as represented by the increase in the dindex and decrease in RMSE in Table 2 and as illus-trated in Fig. 10 and 11.

Results of the simulation runs for Column C-3 (Fig.6 and 7, Table 2) show good agreement with the mea-sured vertical water and salt distributions for the firsttwo harvest periods. For the final harvest period, thereis an underprediction of water uptake and salt move-ment into the profile. This deviation may have beencaused by a small increase in ET above the lysimeterrate during this period; this increase was not detect-able by the resolution of the measured water tabledepth fluctuations.

The improvement in agreement for Columns A-land B-5, when PET was properly represented, hasimportant implications. Accurate results in model pre-dictions can only be obtained when accurate estimatesof PET are available. Regional averages of PET, ifmuch different from local conditions, may not providethe type of accuracy that is necessary in evaluating anirrigation practice. In the V-H model, PET values arecalculated from regional climatic conditions rep-

1892 SOIL SCI. SOC. AM. J., VOL. 56, NOVEMBER-DECEMBER 1992

resented by a reference ET estimate (ET0) multipliedby a crop coefficient (K). For modeling purposes, caremust be taken to ensure accurate estimates of bothET0 and K. Error in either parameter can cause de-viation between predicted and actual soil profile con-ditions.

CONCLUSIONSThis study demonstrates the utility of the V- H

model for obtaining detailed soil water and solute dis-tribution data important to irrigation and soil manage-ment applications. Reasonable agreement was foundbetween model predictions and experimentally mea-sured data for the conditions tested. The results showthat the estimate of PET used is critical to model per-formance. Estimates for this input variable must beaccurate for local ET conditions in order for the modelto provide the best results. The simulations performedin this study indicate that accurate estimates of PETare especially important for calculating the distribu-tions of water and solutes in the soil profile. Errors inPET estimates can result in significant under- or over-prediction of water and solute movement.