J. agric. Engng Res. (1998) 71, 307—313Article No. ag980358

Tillage and Heterogeneity Effects on the Performance of Soil WaterCharacteristic Models

J. Y. Diiwu1; R. P. Rudra1; W. T. Dickinson1; G. J. Wall2

1School of Engineering, University of Guelph, Guelph, ON, Canada N1G 2W1; 2Land Resource Research Centre, Agriculture and Agri-FoodCanada, Guelph, ON, Canada N1H 6N1

(Received 25 April 1998; accepted in revised form 27 July 1998)

The effect of tillage and soil horizon on the perfor-mance of three soil water characteristic models (Hutsonand Cass, van Genuchten, and Verma and Brusaertmodels) was investigated. The impact of field-scale hetero-geneity on the estimated parameters of the models wasalso analysed. Variabilities in model parameters werefound to be significant at 5% significance level. Themodel predictions were more reliable for conventionaltillage treatment than for no tillage treatment. For bothtillage treatments all the models performed equallywell for the A horizon, while the van Genuchten modelwas the best choice for the B horizon. All the modelsaccounted for over 97% of variability of soil water char-acteristics, yet no one model gave a best theoreticalrepresentation of soil water characteristics in both theA and B horizons over the entire field. Precision analyseson the van Genuchten parameters indicated that a givesmore precise estimates of soil water characteristic than gin both the A and B horizons for no tillage and con-ventional tillage treatments.

( 1998 Silsoe Research Institute

1. Introduction

The hydraulic properties of soil determine its capacityto retain and transmit water and contaminants. Per-meability is a hydraulic property which controls the rateat which water moves through soil. Irrespective of thepermeability of the soil, its ability to transmit water willremain low if there is insufficient water available. Theavailability of water is not only affected by supply fromprecipitation and/or irrigation, but also on such losses asthe consumption by plants as well as the water storageability of the soil. The water storage ability is measured interms of soil water characteristic. In the solution of theRichards equation there is a functional relation between

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matric potential t and soil water content, h as well as thefirst derivative of that relation.1 It is this relation which iscalled soil water characteristic.2, 3 Several closed-formanalytical expressions for soil water characteristics havebeen derived and used over the last three decades.4 Thesemodels are briefly discussed in the following subsectionsfollowed by the analytical fit to the observed data fromthe test field.

In this paper, the performances of three of the soilwater characteristic models, the Hutson and Cass,2 vanGenuchten4 and Verma and Brutsaert5 models, are ana-lysed and compared. The performances are evaluatedand compared with respect to soil horizon and tillagetreatment. The relative impact of spatial variability ofsoil properties on the parameters of the models is alsoinvestigated.

2. Theory

Over the years, various forms of models for soil watercharacteristics have been reported.4 Brooks and Corey6

proposed an exponential equation in which the para-meters were physically described and graphically deter-mined. Campbell7 then showed that the parameters in theBrooks and Corey equation were in fact regression coeffi-cients. The Campbell equation as given by Felton andNieber3 and Campbell7 can be written as:

h"hsA

atB

b(1)

where h denotes soil water content in m3/m3, hsdenotes

soil water content at saturation in m3/m3, t denotesmatric potential in m of water and a and b are empiricalparameters.

( 1998 Silsoe Research Institute

308 J. Y. DIIWU E¹ A¸ .

The Campbell model has a singularity at saturationand therefore is not suitable for numerical modelling.Moreover, at low matric potential values, it predictssaturation greater than 100%, which is impossible underfield conditions.2, 3 Hutson and Cass2 therefore proposeda two-equation model to improve prediction in the vici-nity of saturation. In this approach, soil water charac-teristic is obtained in two stages. In the first stage, anempirical value h

iis determined at a matric potential of

ti, and the Campbell model is applied for matric poten-

tial values greater than ti. The parameters h

iand t

i,

which represent the coordinates of the point of inflectionwhere the Campbell model coincides with the Hutsonand Cass model, are computed from optimum values ofa and b. The optimum values can be obtained by non-linear least-squares fit to the Campbell model:2

hi"

2bhs

1#2b(2)

ti"aA

2b1#2bB

~b(3)

For matric potential values less than or equal to tithe

following parabolic expression has been proposed todetermine soil water characteristic:

h"hs!

hst2(1!h

i/h

s)

a2 (hi/h

s)~2b

(4)

The two-equation model has no discontinuities. It pre-dicts finite values at saturation, and is well-defined overthe entire range of matric potentials. It is therefore suit-able for numerical modelling. Some attempts have alsobeen made to relate the parameters a and b to soilproperties.2

Verma and Brutsaert5 presented the following analyti-cal expression for soil water characteristic:

h"hsa

a#tb(5)

where a and b are empirical parameters. The main weak-ness of the Verma and Brutsaert5 model as reported inthe literature is that it predicts 100% saturation at zeromatric potential, which does not agree with the practicalfield situation.3, 4 Nonetheless, it is simple and economi-cal for numerical modelling.

An inverse power relation has been presented by vanGenuchten.4 It is of the form

h"hr#

hs!h

r[1#(at)g](1~1@g)

(6)

where hsdenotes soil water content at saturation, h

rde-

notes soil water content at a matric potential of 150 m ofwater, and a and g are empirical parameters. In the

general setting, the van Genuchten model requires fourparameters, h

s, h

r, a and g. It has been found to represent

the shape and curvature of the soil water characteristiccurve realistically.4

The physical properties of soil in each of the A andB horizons incorporate the effects of physico-chemicalprocesses, development from parent material, and landmanagement. In particular particle size and structure ofsoil depend on such effects. The variability in soil hydrau-lic properties, which depends in part on particular par-ticle size and structure of soil, can therefore be accountedfor by regression coefficients obtained between physicalproperties and soil water content.8–10 Moreover, alongwith analytical expressions for soil water characteristicsas discussed in the preceding paragraphs, it is possible toadequately describe soil water flow in the field withlimited information. Such a description can be useful inplanning and decision-making in connection with thetransport of contaminants through soil and for manage-ment of water resources.

3. Methodology

Soil core samples were collected from a farm located inthe Kettle Creek watershed in Southwestern Ontario,Canada. In 1989, the field was divided into two parts, oneof which had been under no tillage treatment and theother under conventional tillage treatment for manage-ment purposes. The part under conventional tillage treat-ment had been subjected to disk harrow in the spring andmouldboard plough in the fall, while the one under notillage treatment had been left untilled. Cropping on thefield included rotating wheat (¹riticum aestivum L),soybeans (Glycine max L) and corn (Zea mays L). Thethickness of the A horizon varies between 0)25 and 0)3 mand the portion of the B horizon considered for this studyvaries between 0)25 and 0)3 m in thickness. The texturalclassification of soil in the field is essentially silt loam.8, 10

The soil core samples were collected at several loca-tions in the A and B horizons of no tillage and conven-tional tillage treatment sites of the field. In the A horizon,soil samples were collected at the soil surface and in theB horizon they were collected at a depth of 0)4 m fromthe soil surface. For the A horizon, the samples wereobtained by carefully driving a steel cylinder, 0)048 m indiameter and 0)056 m in depth, into the soil at each of thefour sides of 12 rainfall simulation plots. For each tillagetreatment, there were two rows with three rainfall simula-tion plots in each row and any two adjacent plots wereabout 50 m apart. Each rainfall simulation plot measures1 m]1 m at the soil surface. Core samples were alsoobtained from the B horizon by a similar procedure tothat used in the A horizon.10

Table 1Spatial distribution of measured soil water characteristics

Soil water content, m3/m3

Matric No tillage Conventional tillagepotential,

m of water A horizon B horizon A horizon B horizon

0 0)449 0)410 0)414 0)4170)1 0)355 0)363 0)366 0)3511 0)329 0)292 0)344 0)2833)33 0)281 0)277 0)274 0)257

10 0)259 0)255 0)244 0)21315 0)245 0)232 0)225 0)18635 0)231 0)211 0)209 0)15880 0)209 0)186 0)182 0)123

150 0)199 0)167 0)169 0)100

Gravitywater,m3/m3 0)168 0)133 0)140 0)160

Capillarywater,m3/m3 0)082 0)110 0)105 0)157

TILLAGE AND HETEROGENEITY EFFECTS ON THE PERFORMANCE OF SOIL WATER 309

The soil samples were used to determine soil watercharacteristics at matric potentials of 0, 0)1, 0)25, 0)5, 1,3)33, 10, 15, 35, 80, 150 m of water by means of thepressure plate method suggested by Hillel.1 The dataobtained were used to evaluate and compare the perfor-mances of three soil water characteristic models sugges-ted by Hutson and Cass,2 van Genuchten4 and Vermaand Brutsaert.5 The effects of tillage treatment and soilhorizon on the performances of the selected models arealso discussed. Whereas the results of the individualapplication of each of these soil water characteristicmodels have been reported in literature, their perfor-mances have not been compared to reflect the effects ofheterogeneity and tillage treatment.3 The relative impactof tillage treatment and heterogeneity on the parametersof these models is therefore discussed in this paper. Theperformance of the Campbell7 model is not evaluated dueto an inherent singularity and its unrealistic overpredic-tion of soil water content at low matric potential values.The parameters for each soil water characteristic modelwere obtained by a non-linear least-squares regressionanalysis of the corresponding analytical expression.SYSTAT statistics program11 was used for the analysis.

4. Results and Discussion

4.1. Soil water characteristics

The data on soil water characteristics for no tillage andconventional tillage treatments are presented in Table 1.These data also show the retention capacity of soil whichhas been described by the amount of gravity water andcapillary water. Gravity water was determined by takingthe difference between water content at saturation and thatat field capacity. Capillary water has been computed bytaking the difference between water content at field capa-city and permanent wilting point which correspond tomatric potentials of 3)33 and 150 m of water, respectively.

In the case of no tillage treatment, the greater amountof gravity water in the A horizon than in the B horizonmay be attributed to the presence of Macropores. Capil-lary water depends inversely on organic matter content.Higher organic matter content of A horizon than B hori-zon.8–10 is therefore the most probable cause of highercapillary water in B horizon than in A horizon for bothno tillage and conventional tillage treatments.

4.2. Determination of optimum parameters for soil watercharacteristic models

The parameters for each model were obtained by per-forming a non-linear least-squares regression for each

analytic expression, using the SYSTAT statistical pro-gram.11 Two parameters h

sand h

rof the van Genuchten

model were assumed. The soil water content at satura-tion determined in the laboratory was used to representhsand soil water content corresponding to matric poten-

tial of 150 m of water was assumed to represent hr. The

soil water contents were determined in the laboratory bythe gravimetric method.1 Optimum values for the para-meters of the three soil water characteristics models,along with the corresponding standard error of estimate(SEE) values and the coefficient of determination (R2)values, are presented in Table 2. Comparison of theobserved soil water characteristics with those predictedusing the three models in the A horizon are presented inFigs 1 and 2. Similar comparisons were made for theB horizon.

All parameters, except the g parameter of the vanGenuchten model, vary drastically between tillage treat-ments. Except the a parameter of the two-equation modelfor conventional tillage treatment and the g parameter ofthe van Genuchten model for both tillage treatments, allparameters vary drastically between the A and B hori-zons. The variabilities were found to be statistically sig-nificant at the 5% significance level, except for a of thetwo-equation model for the conventional tillage treat-ment, a for the van Genuchten model for conventionaltillage treatment and g for the van Genuchten model forboth tillage treatments. These variabilities in the modelparameters may be attributed to variabilities in soil physi-cal properties in the field.8, 9 For no tillage treatment, the

Table 2Parameters for the three soil water characteristic models

No tillage Conventional tillage

A B A BModel Horizon Horizon Horizon Horizon

¹wo-equation a, m 3)730 6)365 38)499 38)300(Huston and Cass) b 10)101 9)362 6)327 4)500

SEE* 0)012 0)013 0)026 0)035R2- 0)995 0)997 0)995 0)973

Verma and Brutsaert a, m 6)872 9)617 23)296 29)226b 0)230 0)271 0)381 0)477

SEE 0)01 0)013 0)022 0)037R2 0)997 0)993 0)995 0)982

van Genuchten a, 1/m 0)627 0)310 0)149 0)185b 1)230 1)215 1)219 1)205

SEE 0)011 0)012 0)028 0)037R2 0)995 0)998 0)994 0)985

*SEE: Standard error of estimate; -R2: Coefficient of determination.

310 J. Y. DIIWU E¹ A¸ .

goodness of fit was better in the B horizon. For conven-tional tillage treatment the goodness of fit was better inthe A horizon. It appears that for each tillage treatmentthe soil water characteristic models performed better inthe soil horizon for which there is the possibility of fewermacropores. For example, for no tillage treatment, theA horizon is likely to have more macropores than the

Fig. 1. Comparison of observed and predicted soil watercharacteristics in A horizon for no tillage treatment: Ob-served; ¹wo-equation; van Genuchten; »erma

& Brutsaert

B horizon due to greater biological activity in the A hori-zon. In the case of conventional tillage treatment, theB horizon is likely to have more continuous macroporessince tillage has the possibility of breaking the continuityof macropores in the A horizon.

The variability of soil water characteristic in the A hori-zon for no tillage treatment could be best accounted for

Fig. 2. Comparison of observed and predicted soil water charac-teristics in A horizon for conventional tillage treatment: Ob-served; ¹wo-equation; van Genuchten; »erma

& Brutsaert

Table 4Analysis of efficiency of the three models

Root mean square error, m3/m3

No tillage Conventional tillage

A B A BModel Horizon Horizon Horizon Horizon

Two- 0)04751 0)04480 0)01844 0)03523equation

Verma and 0)05110 0)01428 0)02410 0)01574Brutsaert

van 0)08912 0)09045 0)04383 0)04789Genuchten

TILLAGE AND HETEROGENEITY EFFECTS ON THE PERFORMANCE OF SOIL WATER 311

by the Verma and Brutsaert model while in the B horizonthis is best done by the van Genuchten model. Forconventional tillage treatment all the three models seemto perform equally well in the A horizon, while the vanGenuchten model accounts mostly for the variability insoil water characteristics in the B horizon. Even thoughall the three models seem to account for over 97% ofvariability of soil water characteristics in the field, noneof the models gives a best theoretical representation ofthe soil water characteristics in both the A and B hori-zons for both tillage treatments. This poor performanceof all the three models is probably because the causes offield scale heterogeneity, such as aggregation and macro-porosity, are not accounted for in either of the modelsbeing discussed.

4.3. Bias and efficiency of models

The modelling bias, determined as the observed soilwater content minus those predicted by means of thethree models, are presented in Table 3. The correspond-ing model efficiency, presented in terms of the root meansquare error, is shown in Table 4. The bias and effi-ciency are intended to provide additional information onthe relative performance of the models. The van Genuch-ten and the Verma and Brutsaert models are of fairlyclose bias and efficiency at matric potentials betweensaturation and field capacity, as well as at matric poten-tials in the vicinity of permanent wilting point. At matricpotentials between field capacity and wilting point, boththe van Genuchten and the Verma and Brutsaert modelsperformed poorly in the A and B horizons for both notillage and conventional tillage treatments.

The two-equation model performed better in theB horizon than in the A horizon for both tillage treat-ments. Of the three methods, the van Genuchten modelperformed best in predicting soil water characteristics

Table 3Analysis of bias of the three models

Bias, m3/m3

No tillage Conventional tillage

A B A BModel Horizon Horizon Horizon Horizon

Two- 0)00409 !0)00543 !0)03116 !0)02361equation

Verma and !0)04711 !0)01053 !0)0061 0.00394Brutsaert

van 0)01174 0)01203 0)07069 0)07563Genuchten

over the entire range of matric potentials. However, forno tillage treatment high underpredictions were noticedat matric potentials between saturation and field capa-city. Also for conventional tillage treatment, poor fit ofsoil water characteristic was obtained at matric poten-tials of about 0)5—2 m of water. These poor fits, asso-ciated with the range of gravity flow, may be attributed tothe effect of macropores and aggregation in the soil.

The bias, computed as the deviations of the predictedsoil water content from the observed values, show thatthe van Genuchten model gave about 7% underpredic-tion in both A and B horizons for no tillage treatment,and about 1% underprediction in both horizons forconventional tillage treatment. The Verma and Brutsaertmodel gave about 5% overprediction in the A horizonand about 1% overprediction in the B horizon for notillage treatment. For conventional tillage treatment,overprediction was about 1% in the A horizon andunderprediction of less than 1% in the B horizon. Thetwo-equation model gave about 3 and 2% overpre-diction in the A and B horizons, respectively, forconventional tillage treatment, and less than 1% under-prediction and over prediction in the A and B horizons,respectively, for no tillage treatment. Hence, for the threemodels, the bias for each tillage treatment is greater in thehorizon which is more likely to have a greater number ofmacropores and aggregates.8, 10 The bias is also greaterfor no tillage treatment where there is more likely a possi-bility of macropores and stable aggregates than conven-tional tillage treatment.

The root mean square error values as presented inTable 4 are the standard deviations of the predictionerrors using the three models. The values for the vanGenuchten and the two-equation models indicate thatthe prediction of soil water characteristic for conven-tional tillage treatment are more reliable than those forno tillage treatment. For the Verma and Brutsaert modelthe prediction of soil water characteristic is more reliable

Fig. 4. Fitted van Genuchten model in A horizon for conventionaltillage treatment: Fitted; Measured

312 J. Y. DIIWU E¹ A¸ .

in the B horizon than in the A horizon for both tillagetreatments. In particular, in the A horizon, the predictionis better for conventional tillage treatment than for notillage treatment.

The less reliable prediction of soil water characteristicfor no tillage treatment than for conventional tillagetreatment for all the three methods may be attributed tothe effect of macropores and stable aggregates.12 Thisdifference in efficiency of the models for no tillage andconventional tillage treatments tends to be greater in theA horizon than in the B horizon, since there is thepossibility of discontinuity of macropores and breakingof stable aggregates under conventional tillage treatment.

4.4. Precision analysis of van Genuchten parameters

The preceding discussion has indicated that none ofthe three models was the best for fitting soil water charac-teristics in the A and B horizons for no tillage andconventional tillage treatments. However, the vanGenuchten model was selected for further analysis toinvestigate the precision of the parameters of a soil watercharacteristic model. The fitted van Genuchten model forsoil water characteristics in the A horizon are presentedin Figs 3 and 4.

The precision analysis performed on a and g showedthat for no tillage treatment and at matric potentialsclose to permanent wilting point, a 95% precision in

Fig. 3. Fitted van Genuchten model in A horizon for no tillagetreatment: Fitted; Measured

a achieves 99% precise estimates of soil water character-istic. In the case of 95% precision in g, between 90 and95% precise estimates of soil water characteristic wereobtained. In the range of gravity flow, a 95% precision ina gives about 95% precise estimates of soil water charac-teristic in the A horizon compared to 99% precise esti-mates of soil water characteristic in the B horizon. Soilwater characteristic estimates based on g were not veryprecise at all matric potentials in the A horizon, and leastprecise at matric potentials less than field capacity andclose to permanent wilting point in the B horizon. Forconventional tillage treatment the precision of soil watercharacteristic estimates based on a did not change muchwith matric potential in both horizons, but was lowbased on g at matric potentials beyond field capacity andclose to permanent wilting point in both A and Bhorizons.

5. Conclusions

The soil water characteristics were found to be variablewithin each horizon between no tillage and conventionaltillage treatments, and between the A and B horizons foreach tillage treatment. Non-uniform distribution of or-ganic matter in the soil may be one probable cause forthese variations. The spatial distribution of structuralvoids such as macropores as well as aggregates in thefield may be other probable causes of the variability ofsoil water properties.

TILLAGE AND HETEROGENEITY EFFECTS ON THE PERFORMANCE OF SOIL WATER 313

The analysis has indicated that while all the soil watercharacteristic models evaluated perform equally in theA horizon for conventional tillage treatment, the vanGenuchten model seems to be the better choice for theB horizon for no tillage and conventional tillage treat-ments and the Verma and Brutsaert model seems to bethe better choice for the A horizon for no tillage treat-ment. All the three models account for over 97% of thevariability of soil water characteristics, but none of themodels gives best theoretical representation of soil watercharacteristic in both the A and B horizons for no tillageand conventional tillage treatments. This may be at-tributed to field-scale heterogeneity such as macroporos-ity and aggregation which are not accounted for in eitherof the models evaluated.

Acknowledgements

The financial support of each of the following organi-zations to this work is greatly appreciated: NaturalScience and Engineering Research Council (NSERC) ofCanada, the Canadian Commonwealth Fellowship Pro-gramme, and the Water Resources Research Institute ofCSIR of Ghana.

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