Salt increase in a heavy clay soil due to capillary rise was simulated by an
analytical model and a numerical model. Predicted values were compared with
experimental data. The analytical model was inadequate in predicting
salinisation in a dynamic crop/soil system. When root growth was accounted
for, the numerical model satisfactorily predicted salt increase in the soil profile

Jayawardene, N.S.

Meyer, W.S.

Prathapar, S.A.

Robbins, C.W.

Northwest Irrigation & Soils Research Laboratory Publications

Predicting salinization in a heavy clay soil subjected to a saline shallow water table

USDA - ARS - NWISRL

1	 76Predicting salinisation in a heavy clay soil subjected to a salineshallow water table.S.A. Prathaparl, C.W. Robbins', W.S. Meyer s and N.S. Jayawardenel1CSIRO Division of Water Resources, Griffith Laboratory, NSW 2680.'USDA-ARS, Soil & Water Management Research Unit, Kimberly, Idaho 83341.AbstractSalt increase in a heavy clay soil due to capillary rise was simulated by ananalytical model and a numerical model. Predicted values were compared withexperimental data. The analytical model was inadequate in predictingsalinisation in a dynamic crop/soil system. When root growth was accountedfor, the numerical model satisfactorily predicted salt increase in the soil profile.IntroductionSalinisation of soil refers to an increase in readily soluble salts in the root zone.The rate of salinisation is influenced by climate, soil type, crops, irrigationpractices, and the depth to and the quality of the shallow water table. Theability to predict such complex phenomenon is of vital importance for managingirrigated heavy clay soils in the Murray basin, where soil salinisation isprimarily caused by capillary rise from shallow saline water tables.Since the rate of salinisation is governed by the movement of water and salt,the mathematical models to predict the rate of salinisation are derived from thegoverning equations of water and salt movement within the root zone. Bothanalytical and numerical models have been formulated. The analytical modelsare efficient and easy to use when data are sparse and uncertain. However,the use of analytical methods is limited to idealised situations such ashomogeneous and isotropic conditions. Numerical models on the other hand,can accommodate spatial and temporal variation of soil properties. But, theapplication of numerical models to complex conditions is generally restricted bythe availability of temporal and spatial data.The objective of this study was to compare an analytical model and a numericalmodel to predict salinisation of a soil profile subjected to a saline water table.Capillary rise and increase in salt within the soil profile predicted by themodels were compared with experimental data.TheoryTransport of water in the unsaturated zone of a non hysteretic, non swellingsoil is given by Richards' equation (eq. 1).Prathapar, S.A., C.W. Robbins,W.S. Meyer, and N.S. Jayawardene.1990. Predicting salinisation ina heavy clay soil subjected to asaline shallow water table.Proc. Symposium "Soils and Land-use in the 1990's". Sponsored byTetra Branch of the Aus. SoilSci. Soc. Bendigo, Victoria.July 2-4., 8 pp.2a (K alp) aK	 ae (1)az	 az) az	 atwherezKIV0t: vertical cartesian coordinate (L): unsaturated hydraulic conductivity (ur): matric potential (L): volumetric water content: time (T)Philip (1988) provides a review of analytical solutions for Richards' equationunder various conditions. Under steady state conditions the capillary rise qfrom a water table in a one dimensional profile without the roots is given by= -K(*) (A + 1dz(2)Transport of salt by diffusion and convection in a one dimensional soil profile isgiven byac= D a2cat	 az2v ac-	 az (3)whereC	 : concentration of salt (M/I2)D	: hydro dynamic dispersion coefficient (12/T): velocity of water (LIT)Van Genuchten and Alves (1982) and Bond (1986) provide reviews of analyticalsolutions for eq. 3 for a variety of initial and boundary conditions.Numerical models to predict salinisation solve equations 1 and 3simultaneously. Addiscott and Wagenet (1985) and Nour el-Din et al. (1988)provide reviews of numerical models to predict salinisation and leaching of asoil profile.Materials & MethodsThe ExperimentData for in this study was obtained from an experiment conducted by Percy etal. 1988. An undisturbed soil core, 0.75 m diameter and 1.4 m deep, of3Mundiwa clay loam was obtained and installed at the CSIRO-DWR, Griffithlysimeter facility. The Mundiwa clay loam is a duplex soil with approximately0.2 m clay loam over lying a heavy clay sub soil. A saline effluent of electricalconductivity (EC) 15.0 dS/m was introduced at the bottom. The saline watertable was maintained at a depth of 1.2 m by a marriot tank.Wheat (var. Bindawarra) was sown on the core. Neutron probe readings wereobtained regularly during the growing season to determine soil water deficit.Irrigation water of approximately 0.1 dS/m electrical conductivity was appliedperiodically to meet the soil water deficit. Water volumes supplied by themarriot tank to maintain the water table at 1.2 m (capillary rise) wasmonitored weekly.Soil samples were obtained along the profile at 0.15 m depth interval before theintroduction of saline water table and 21 weeks after introducing the salinewater table. EC of 1:2 soil:water suspension were determined from thesesamples.The Analytical modelIn the analytical model, the unsaturated soil profile of 1.2 m was divided into aroot zone of 0.7 m (DRZ) and a sub soil of 0.5 m (DSUB). Roots were assumedto be uniformly distributed within the root zone.A crop coefficient Kc of 0.3 was assigned for the first 20 days after sowing(DAS). Subsequently it was increased linearly to 0.8 until 60 DAS, keptconstant at 0.8 until 150 DAS and decreased linearly to 0.3 until 180 DAS.Evapotranspiration on a particular day was determined by multiplyingobserved pan evaporation by the corresponding ICThe initial total water content of the root zone (WRZ) and the sub soil (WSUB)were determined from volumetric water content 0, and depth of each zone. TheWRZ on a particular day was calculated from the previous day's WRZ bysubtracting evapotranspiration and adding irrigation on the day. Resultant 0of the root zone Or, was determined by dividing the WRZ by DRZ. The changein WSUB was determined using eq. 4 and added to WSUB. Consequently Elbubwas determined by dividing WSUB by DSUB.WSUB = 0.5 *( 02 - 0;7 ) * DSUB	(4)where	e2rz 	 : volumetric water content of root zone on a dayAl	rz	 : volumetric water content of root zone on the previous dayThe jrrz and the 'Cub were determined using Campbell (1974) functions and soilparameters presented in Table 1. Subsequently capillary rise was determinedby eq. 2, using K 11131 T as the potential at the bottom of the root zone and-	 iii4DSUB as the distance over which the capillary rise took place. Total increasein salt within the profile was estimated by multiplying the cumulative capillaryrise by the salt concentration of the water table.Table 1. Soil properties used in the Analytical modelProperty ValueInitial vol. water content of the root zone 0.34Initial vol. water content of the sub soil 0.32Air entry value of the root zone (AEVT) 57 mmAir entry value of the sub soil (AEV.0,) 96 mmBeta of the root zone OW for Campbell equation 17.1Beta of the sub soil (f38w for Campbell equation 20.5Sat. hyd. conductivity of the root zone K.., 630 mm/dSat. hyd. conductivity of the sub soil K.., 8 mm/dSaturated vol. water content of the profile 0, 0.4The Numerical ModelThe numerical model (Wagenet & Hutson, 1989) utilised a one dimensionalfinite difference solution for the transient unsaturated flow equation (eq. 1)together with transient diffusive and convective solute transport equation (eq.3). The numerical model moves the salt as individual ions within the soilprofile and then calculates the electrical conductivity using the method ofRobbins et al. (1980). Furthermore, the model estimates soil evaporation andevapotranspiration from pan evaporation data and crop data. It can also takeinto account of the effects of a user specified root growth rate and rootdistribution pattern.Two simulations were made using the numerical model. The first used auniform root profile to a depth of 0.7 m. This is similar to the root profile usedin the analytical model. The second simulation used a growing root profile forwheat to a maximum depth of 0.7 m (Wagenet & Hutson, 1989).The soil profile was divided into 13 layers, each of 0.1 m in thickness. The13th layer represented the water table. Initial conditions and properties of soillayers used in the simulations are presented in Table 2.5Table 2. Initial conditions used in the Numerical modelLayer AEV (mm) 9, i3 K. EC dS/m1 37 .36 10.7 1900. 1.302 37 .35 13.0 1500. 1.303 55 .34 17.8 950. 1.514 60 .34 18.5 50. 1.515 70 .34 19.2 3. 1.516 70 .33 20.1 3. 2.477 75 .32 20.2 7. 2.978 85 .31 20.3 9. 3.279 90 .31 20.4 9. 3.8510 96 .32 20.5 9. 4.2311 96 .33 20.6 7. 5.2912 96 .36 20.6 6 11.0113 96 .41 20.6 6. 15.50Results & DiscussionsMeasured and predicted cumulative capillary rise for a period of 21 weeks afterinstallation of the core are presented in Fig. 1.Cumulative capillary rise increased rapidly until the end of 4 weeks afterintroduction of saline water table. At installation the8a„b was approximately0.32, which resulted in favourable 	 and IL for a rapid wetting of the subsoil. Rate of capillary rise was markedly reduced when 20 mm of irrigationwater was applied at the end of 4 weeks. This was due to the reduction in wwithin the profile. While irrigation water reduced the w of the top soil, the w,3,,b,was reduced due to capillary rise from the saline water table.Between the fifth week and the eleventh week the cumulative capillary risecontinued to increase at a low rate of approximately 1.4 mm/week. During thisperiod the pan evaporation increased from 12.8 ram/week to 22 ram/week.Further the rooting depth was shallow and the soil water deficit was met bytwo irrigations, each of 35 mm.Inspite frequent application of irrigation water, the rate of capillary riseincreased to 3 6 mm/week between the 11th and 21st week. This was6associated with an increase in root activity in deeper layers of the soil profileand increased pan evaporation from 22 mm/week to 49 mm/week. During thisperiod 11 irrigations totalling 427 mm were made.The analytical model did not predict initial wetting of the sub soil satisfactorily.This was due to the calculated low value of KB„ L. With gradual calculatedwetting of the subsoil, Kew, increased such that a rapid capillary rise wasestimated from the end of the seventh week. However the sudden introductionof a water table to a dry soil will not generally occur in nature. Thus theinability of the steady state model to predict initial wetting satisfactorily shouldnot override our assessment of the potential usefulness of this model in moregeneral applications.Following the second irrigation (week 8) daily capillary rise values weregenerally within an expected range for this soil and water system. Howeverthe daily values estimated immediately prior to an irrigation were extremelyhigh. This was due to the drier root zone resulting in lower yrn and nearlysaturated sub soil resulting in higher K. Over estimated capillary rise priorto irrigation could partially be attributed to a uniform root zone assumed in theanalytical model.The numerical model predicted the initial wetting of the soil profilesatisfactorily during both simulations. However, when a uniform and staticroot distribution was assumed the numerical model predicted higher rates ofcapillary rise than those measured between weeks 4 and 15. This is due to theassumed removal of water at deeper layers which resulted in steeper hydraulicgradients and higher capillary rise. The measured and predicted capillary risewere closer after the 15th week of the same simulation.When a growing root system was assumed, the prediction of capillary rise bythe numerical model was exemplary. Results from the numerical simulationsshow that the capillary rise could be predicted well when initial conditions andthe properties of soil profile and root growth functions were accurately known.Measured cumulative capillary rise and increase in salt within the soil profileare compared with predicted values in Table 3. The increase in salt within theprofile was calculated from the concentration of salts of the water table andcumulative capillary rise. Consequently, the increase in salt predicted by thenumerical model assuming a growing root profile was closer to the measuredincrease in salt than the other two.Fig. 2 compares the measured EC ex values 21 weeks after introducing salinewater table with EC ex values predicted by the numerical model. Simulationassuming the uniform and static root distribution under estimated the ECex inthe upper profile and over estimated it in the lower profile. The simulationwith growing root had the same weakness, but to a lesser degree.7160150 -140 -130 -120 -110-100 -90 -80-70 -60 -50 -40 -30 -20 -10 -•Fig. 1. Capillary risennnnnL1.>:\aaUa)aEUn•-ft+1+44141+414144.4{}{{_..4401RootsRootsRoots25nnnnn111111111i4iii i5	 10	 15	 20MeasuredNumerical uniformNumerical growing+++++ Analytical uniformo0Weeks after installationFig. 2. EC profile after 21 weeks- 0.3 -•IN •• no_ 0 7 - •	 •0•- 0.9 -•	 Measured	  Numerical growing roots	 • •n n n n n Numerical uniform roots• IN- 0.1 --1.30.0 0.5	 1.0	 1 1.5	2.0	2.5EC of 1:2 soil water extract ( dS/m3.08Table 3. Comparison of capillary rise and salinisationCapillary RisemmA in salt kg/m2Observed 93.4 2.58Numerical Model-Growing Roots 93.1 2.57Numerical Model-Constant Roots 156.1 4.31Analytical Model 131.0 3.62ReferencesAddiscott, T.M. and R.J. Wagenet. 1985. Concepts of solute leaching in soils: areview of modelling approaches. Journal of Soil Science. 36:411-424.Bond, W.J. 1986. Velocity dependent hydrodynamic dispersion duringunsteady, unsaturated soil water flow: Experiments. Water Resour. Res.22(13):1881-1889.Campbell, G. 1974. A simple method for determining unsaturated hydraulicconductivity from moisture retention data. Soil Sci. 117:311-314.Nour el-Din, M.M., I.P. King, K.K. Tanji. 1988. Salinity management model: I.Development. ASCE Journal of Irrigation and Drainage Engineering.113(4):440-468.Percy, H., A. van der Lelij and W.S. Meyer. 1988. Salt accumulation in soilssubjected to high water tables. Internal Report. NSW-DWR, Griffith.Philip, 1988. Quasianalytic and analytic approaches to unsaturated flow.International symposium proceedings on 'Flow and transport in the naturalenvironment'. Australian Academy of Sciences, Canberra, ACT.Robbins, C.W., R.J. Wagenet and J.J. Jurinak. 1980. A combined salttransport-chemical equilibrium model for calcareous and gypsiferous soils. SoilSci. Soc. Amer. J. 44:1191-1194.van Genuchten, M. Th. and W.J. Alves. 1982. Analytical solutions of theconvective-dispersive solute transport equation. USDA Tech. Bull. 1601.United States Salinity Laboratory. Riverside, California.Wagenet, R.J. and J.L. Hutson. 1989. LEACHM: A process based model ofwater and solute movement, transformations, plant uptake and chemicalreactions in the unsaturated zone. Center for Environmental Research, CornellUniversity, Ithaca, New York.

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Predicting salinization in a heavy clay soil subjected to a saline shallow water table

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