# An Infiltration Equation to Assess Cropping Effects on Soil Water Infiltration

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An Infiltration Equation to Assess Cropping Effects on Soil Water InfiltrationA.-S. I. All and D. Swartzendruber*

ABSTRACTThe effect of crop plants on the infiltration of water into soil has

been difficult to characterize. This study was conducted to determinewhether a new three-parameter infiltration equation, obtained froma recent infiltration quasi solution, could be validated and used forimproved characterization of infiltration. For field plots under differentcropping conditions of corn (Zea mays L.), sorghum [Sorghum bicolor(L.) Moench], soybean [Glycine max (L.) Merr.], and fallow, water-infiltration data from ponded double-ring infiltrometers were fittedby nonlinear least squares to the new equation, and, for comparison,to the two-parameter Philip form and to the strictly empirical Lewisequation. Physically problematic negative values of the sated (near-saturated) hydraulic conductivity K were yielded by the Philip formin well over half of the data sets, but all were superseded with positiveK values by use of the new equation which, of the three, also gavethe best fit to the data, in keeping with the additional fitted parameter.Statistically, by using orthogonal-contrast analysis of the several equa-tion parameters, the new equation also produced the largest numberof significant differences between crops and crop sequences (rotations).Grain sorghum created the largest sorptivity 5, whereas corn decreasedit. Soybean produced the smallest K, but corn and grain sorghumcaused moderate and equal increases in K. The new equation andthese findings offer promise for improved characterization and under-standing of plant effects on water infiltration.

IT is well recognized that crop plants exert an influenceon water infiltration into soil. The characterizationof this influence, however, in common with other influ-A.-S.I. All, Soil Research Center, Abu-Ghraib, Baghdad, Iraq; and D.Swartzendruber, Dep. of Agronomy, Univ. of Nebraska, Lincoln, NE68583. Contribution from the Agricultural Research Division, Univ. ofNebraska, Lincoln; Journal Series Paper no. 9085. Received 10 Dec.1992. *Corresponding author.

Published in Soil Sci. Soc. Am. J. 58:1218-1223 (1994).

ences on infiltration, has not been simple, due largelyto the nonlinear nature of the infiltration process. Forinfiltration into field soils in the absence of living plants,Swartzendruber and Huberty (1958) addressed the matterof nonlinearity by utilizing the parameters contained innonlinear infiltration equations. Best success was ob-tained with the strictly empirical Lewis (1937) equation1:

/ = GtH [1]where G and H are the characterizing parameters, and/ is the cumulative infiltration (volume of water per unitcross-sectional bulk area of soil) after time t followingthe initial and instantaneous ponding of water on the soilsurface. Attempted use (Swartzendruber and Huberty,1958) of the theoretically derived equation of Green andAmpt (1911), however, produced some negative valuesof the sated (or satiated [Miller and Bresler, 1977]) K.For soil surfaces not initially ponded with water, Skaggset al. (1969) also fitted the Green and Ampt equationand encountered negative K values in about one-third oftheir data sets. Negative K values were even more fre-quent from fitting of the two-term equation of Philip(1957b):

/ = Stm + Mt [2]

1 This power-of-time form has oftentimes been called the Kostiakov

equation, but it should be attributed to Lewis (1937) as explained bySwartzendruber (1993).

Abbreviations: RMS, residual mean square; Sg, continuous grain sor-ghum; C, continuous corn; B, continuous soybean; C-B, corn after soy-bean; Sg-B, grain sorghum after soybean; F-B, fallow after soybean; C-Sg, corn after grain sorghum; Sg-C, grain sorghum after corn; ANOVA,analysis of variance.

ALI & SWARTZENDRUBER: INFILTRATION EQUATION FOR CROPPING EFFECTS 1219

where S is the water sorptivity of the soil. Parameter M,akin to a hydraulic conductivity, can be linked rigorouslywith Philip's (1957a) theoretical tia series solution onlyby constraining t from being too large, so that 0 < M 0.Therefore, if Eq. [3], [4], or [5] is fitted to experimentaldata, whatever shortcomings are observed do not arisemerely from the use of unconstrained time values.

Equation [4] is also capable of describing nine pre-viously published infiltration equations within a maxi-mum error of 2.5% (Swartzendruber and Clague,1989), with each of the nine equations having its ownvalue of A. So, with but slight error, Eq. [4] includeseach of the nine equations as a special case of itself andthus constitutes the inclusive general equation worthy offirst priority for experimental testing. Included amongthe nine special cases is the implicit three-parameterform of Parlange et al. (1982).

Fahad et al. (1982) found that fitting of Eq. [5] yieldednegative K values in 15 of 24 data sets, whereas thefitting of the empirical Lewis (1937) Eq. [1] was notattended by any apparent complications. Using the com-posite infiltration parameter /24o = C?(240)H from Eq.[1], where 724o is the cumulative infiltration at 240 min(14.4 ks), a statistical analysis of the /240 values revealedonly one significant difference between cropping se-quences (0.05 probability level). Therefore, considerableneed still exists to better describe the infiltration process.Our present objectives were to (i) evaluate the capability

of Eq. [4] for fitting the field-plot data of Fahad et al.(1982), which include the influence of living plants; (ii)test the fitted S and K of Eq. [4] for statistical quantifica-tion of infiltration differences between crops and cropsequences; and (iii) compare 5 and K of Eq. [4] with Gand H of the Lewis Eq. [1] and 5 of Eq. [5], as regardsboth fitting capability and the statistical quantification ofinfiltration differences.

MATERIALS AND METHODSField Data

The experimental field plots were located at the Univ. ofNebraska Field Laboratory near Mead, NE, on a Sharpsburgsilty clay loam (fine, montmorillonitic, mesic Typic Arguidoll).Annual sequences of soybean, corn, grain sorghum, and fallowhad been established on the plots, from which eight differentsequences were selected in 1976 for infiltration measurements,namely: B, C, Sg, C-B, Sg-B, F-B, C-Sg, and Sg-C. In thepairs above, the first symbol denotes the crop on the plot whenthe infiltration measurements were taken in August, 1976, andthe second symbol denotes the crop on the plot during theprevious year, 1975. The eight crop sequences were replicatedthree times in a completely randomized design.

On each of the 24 plots, infiltration measurements wereobtained with a double-ring infiltrometer. The two concentricrings (short metal cylinders), of 300-mm inner-ring diameterand 450-mm outer-ring diameter, were inserted into the soilto a depth of 150 mm. At time zero, water was quickly pondedabout 20 mm deep in both rings and maintained with Mariottereservoirs for the duration of the experiment, usually on theorder of 14 ks (4 h). At selected times, the correspondingcumulative volumes of water delivered to the inner ring werenoted and then divided by the cross-sectional area of the innerring, thus providing an experimental value of/, as in Eq. [4],at each selected time t. More details on procedures and theexperiments are given by Fahad et al. (1982) and Fahad (1979).

Fitting of EquationsThe fitting of Eq. [4], [5], and [1] to the data by nonlinear

least squares was performed with the NLIN program of theStatistical Analysis System (SAS Institute, 1990), using theMarquardt searching option, along with appropriate input de-rivatives, and with no bounds on the values of fitted parameters.The parameters were computed at the minimum point of anobjective function involving the residual sum of squares bymeeting a selected convergence criterion of 10~12. For fittingEq. [5], the starting value of K was Afa taken as the averageslope of the last three to six data pairs (I,t), because I(t) atlarge t should approach a straight line of slope K; the startingvalue of S was taken near but not equal to the fitted 5 of Fahadet al. (1982). For Eq. [4], the starting S was the fitted S fromEq. [5], the starting A was 2.0 X 10~3 s~"2, and the startingK was either the fitted K from Eq. [5] if positive or K, if thefitted K from Eq. [5] was negative. For Eq. [1], the startingH was 0.5 and the starting G was near but not equal to thefitted G of Fahad et al. (1982). After meeting the convergencecriterion, a second fitting was carried out with each startingparameter 10% less than its first fitted value, followed by athird fitting with each starting parameter 10% greater than itsfirst fitted value. The fitting process was deemed completeonly after agreement of the final results of these three exercises.

After the three rounds of fitting Eq. [4], 23 of the 24 datasets immediately yielded positive K values, but the C-B Plot112 gave A = 0, with 5 = 2.031 mm s'"2, K = -2.87 urn

1220 SOIL SCI. SOC. AM. J., VOL. 58, JULY-AUGUST 1994

s"1, and a RMS of 12.87 mm2, just as from the fitting of Eq.[5]. The next step was to fix K at K, = 6.95 urn s"1 in Eq.[4], from which the consequent fitting of A and S yielded A =18.6 X 10~3 s'"2, S = 2.301 mm s""2, and RMS = 31.99mm2. This major increase in K (from 2.87 to 6.95 u.m s~')thus caused a large change (148%) in RMS but only a 13.3%change in S. Because of this relative stability in S, its valuein Eq. [4] was fixed at the mean (2.166 mm s~"2) of theserelatively close S values (2.031 and 2.301 mm s"1'2), whereuponA and K were then fitted. Because the consequent RMS of16.82 mm2 was only modestly larger than the original 12.87mm2, this fitting was the one selected for the data of Plot 112.

Equations [4] and [5] were also fitted for the bound K > 0imposed on the NLIN program, but the values so fitted

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