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hydraulic conductivity K were yielded by the Philip formin well over half of the data sets, but all were superseded with positiveK values by use of the new equation which, of the three, also gavethe best fit to the data, in keeping with the additional fitted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 characterization
of 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 Kostiakovequation, 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 <K (Philip, 1957b, p. 261-262; 1969, p. 275).
A rationale that eliminates the time constraint is pro-vided by a new infiltration equation derived as an exactintegration of an infiltration quasi solution (Swartzen-druber, 1987), namely
/ = (S/A)[l - exp(-Atm -Bt- Q3'2 -Et2 -...)] +Kt [3]
where parameters S, A, B, C, E, ... each depend on theinitial and sated volumetric soil water contents, 9n and0o, respectively. We emphasize that Eq. [3] is valid inprinciple for all t > 0; hence, no constraint is presentin the positive time domain. Furthermore, the quasisolution, from which Eq. [3] is derived, does give ahighly accurate description of all tune-evolving watercontent profiles for two extreme cases: Philip's (1957a)light clay soil on the one hand, and the Green and Ampt(1911) step function on the other.
The simplest form of Eq. [3] that still preserves itsexponential character comes from taking B = C = E= ... = 0, thus yielding the three-parameter equationof Swartzendruber (1987):
/ = (SIA)[1 - exp(-^1/2)] + Kt [4]If further simplification is sought by letting A -*• 0, theconsequent indeterminacy in Eq. [4] is easily resolvedwith 1'Hospital's rule, to yield
/ = Stm + Kt [5]which is Eq. [2] with M replaced explicitly and unambigu-ously by K. We emphasize that in progressing from Eq.[3] to Eq. [4] to Eq. [5], nothing has been done to alterthe applicability of all three equations for all t > 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 forEq. [4] were unchanged from previous values (bound K > 0absent). For Eq. [5], each of the nine previous positive Kvalues was also unchanged, as was each corresponding 5 andRMS. Each of the 15 previous negative K values, however,was then superseded by zero, with a decrease in each 5 andan increase in each RMS, so that the fitting of Eq. [5] wasnot improved.
Fitting the data with other modifications of Eq. [3] was alsoattempted, by successively expressing the exponential argumentas (-Atm - Bf), (-At112 - Bt - O3'2), and (-At112 - Bt -G3'2 — Ef). In no case, however, was it possible to fit anyone of these three modified equations to all of the 24 sets ofdata, even when employing special procedures similar to thatjust described for Plot 112 and Eq. [4].
Statistical Analysis of Fitted ParametersThe 24-item set of each of the five fitted parameters (5 and
K of Eq. [4], S of Eq. [5], and G and H of Eq. [1]) wasanalyzed statistically to assess its utility for measuring infiltra-tion differences between cropping-management systems. First,however, it was deemed advisable to determine whether theexperimental errors of each parameter were normally distrib-uted with mean of zero and homogeneous variance, as requiredfor ANOVA. The NORMAL option of the UNTVARIATEpackage of the Statistical Analysis System (SAS Institute, 1990)was used to calculate the W statistic (Shapiro and Wilk, 1965)in a test of normality, whereas homogeneity of error variancewas assessed by Bartlett's (1937) test. Both tests were per-formed on the natural logarithms of the five parameters, aswell as on the parameters themselves. For parameter K, thetests showed conclusively that both normality and homogeneityconsiderations dictated the use of lognormal AT in strong prefer-ence to K itself, thus conforming with the lognormal distributionof hydraulic conductivity reported by Nielsen et al. (1973).For the other four parameters, the use of logarithms was eitherpreferable or acceptable. Therefore, for overall uniformity andconsistency, the natural logarithms of all five parameters wereused in the subsequent ANOVA (completely randomized de-sign) and orthogonal contrasts, as calculated with the GLMpackage and the CONTRAST option (SAS Institute, 1990).
The seven orthogonal contrasts, objectively selected in thesense of being based on the nature of the crop and the cropsequence, were posed and labeled as follows: (i) Sg vs. C —for continuous cropping how would one grass (sorghum) com-pare with another grass (corn)? (ii) Sg and C vs. B—forcontinuous cropping how would two grasses (sorghum andcorn) compare with a legume (soybean)? (iii) C-B vs. Sg-B—for rotation cropping how would one grass (corn) comparewith another grass (sorghum) when the previous crop had beena legume (soybean)? (iv) C-Sg vs. Sg-C - for rotation croppinghow would one grass (corn) compare with another grass (sor-ghum) when the previous crop had been the other grass? (v)
F-B vs. C-B and Sg-B-for rotation cropping how wouldfallow compare with two grasses (corn and sorghum) whenthe previous crop had been a legume (soybean)? (vi) B, C,and Sg vs. the others—how would continuous cropping (soy-bean, corn, and sorghum) compare with rotation croppingincluding fallow? and (vii) C-Sg and Sg-C vs. F-B, C-B, andSg-B—how would two grasses in rotation (corn and sorghum)compare with the same grasses and fallow when the previouscrop had been a legume (soybean)?
Initial Water Content and SorptivitySorptivity S as defined by Philip (1957b) depends on both
6n and 90, with the further suggestion (Philip, 1957c) of Sbeing proportional to (00 - 6n)"2, as reiterated by Elrick andRobin (1981) in the form
S = R(Q0 - 0n)1/2 [6]where R is essentially constant for a given soil as used here.For the top 300 mm of soil, measurements were taken thatenabled estimation of 00 and 9n. By specifying a correctedvalue 5 = S, at the mean (00 - 0n) for all replications, Eq.[6] is used to write Sr = R((Q0 - 0n))"2, which in conjunctionwith Eq. [6] itself yields
- en)/(60 - en)i1/2 [7]where, as calculated from the 5 and (60 — On) of each replicate,the corrected sorptivity 5r should be free of any variations in(00 — 0n) among replicates. Equation [7] was used to determinewater-content-corrected sorptivities from the fitted S of bothEq. [4] and [5], and each such set of 5r values was statisticallyanalyzed in the same way as its counterpart set of uncorrected5 values. Detailed comparison showed that the statistical con-clusions were essentially unaffected by the use of Eq. [7], so thatdifferences among S values were not attributable to variations inwater content. Hence, the statistical results are presented interms of the 5 values as such, without adjustment by Eq. [7].
RESULTS AND DISCUSSIONThe results of fitting Eq. [4], [5], and [1] to the
experimental field data are given in Table 1. The fitted-parameter values from Eq. [1] and [5], except for unitsand several slight and inconsequential numerical differ-ences, are the same as those of Fahad et al. (1982),including the same negative values of K (in 15 of the24 data sets) from the fitting of Eq. [5]. In distinctcontrast, the fitting of the new infiltration Eq. [4] inits three-parameter form (Swartzendruber, 1987) hasyielded positive, physically acceptable K values in allcases, with only one instance wherein special modifica-tion of the fitting procedure was required (Plot 112 asdescribed above). Six cases do remain (Plots 111, 204,113, 310, 108, and 201) in which the least-squaresprocess still selected Eq. [5] by fitting A of Eq. [4] asessentially zero.
Goodness of FitFrom Table 1, the RMS in 16 cases are distinctly
smaller from fitting Eq. [4] than from fitting Eq. [5],the RMS in seven cases are essentially the same (mainlyfor fitted zero A in Eq. [4]), and in only one case (the
ALI & SWARTZENDRUBER: INFILTRATION EQUATION FOR CROPPING EFFECTS 1221
Table 1. Fitted parameters of infiltration equations, along with residual mean squares (RMS).
Cropsequence!
B
C
Sg
C-B
Sg-B
F-B
C-Sg
Sg-C
Plotno.
107215304115208312111204308112205309110203307102210314113206310108201305
Fitting of Eq. [4]S
mms-"2
2.0202.0291.4060.7591.6861.1791.5222.6573.7982.16611.8532.1951.6541.3571.8162.8052.7472.5302.1062.7593.2552.0351.4331.016
A10-' s-"2
31.982.945.711.028.121.000
45.17.2
63.089.720.118.632.440.8
131.955.60
22.6000
37.7
K
urn s'12.720.550.324.304.882.984.284.882.871.932.000.703.127.502.885.980.55
36.8518.554.03
10.0330.7514.602.92
RMSmm2
9.865.010.844.052.052.49
17.3436.864.55
16.822.330.872.224.074.456.283.55
10.6427.1115.53
364.5919.473.732.62
Fitting of Eq. [5]S
mms""2
1.3990.7730.8650.7011.2170.9631.5222.6572.2172.0310.8780.8911.3521.1241.2601.7180.8021.1802.1062.2323.2552.0351.4330.630
Klirn s"'-4.97-4.62-5.00
1.92-1.45-1.62
4.284.88
- 10.35-2.87-3.40-5.57-3.12
2.53-4.08-3.98-5.1829.8218.55
-7.1810.0330.7514.60
-0.62
RMS
mm2
26.4337.8412.053.95
10.484.87
17.3436.8678.4412.8718.5727.976.706.60
17.4842.9244.5940.7927.1131.57
364.5919.47
3.736.83
Fitting of Eq. [1]G
nun s~H
3.6205.0704.2690.4371.8401.4920.8981.8189.2552.5623.4085.9672.4260.7593.1553.7276.2640.1850.6504.8011.7320.4280.3720.969
H
0.34800.19790.22780.57780.44070.43200.58470.55980.27350.45840.29450.18390.40700.56520.35630.38560.16000.83870.69640.37520.59830.76980.72330.4413
RMS
mm2
16.8111.518.315.395.893.42
15.5330.4823.2221.492.756.194.80
10.219.57
17.0410.9294.8714.3029.30
244.1013.117.015.20
t B = soybean; C = corn; Sg = grain sorghum; F = fallow.$ Employed as a constant in Eq. [4], with A and K fitted.
modified fitting for Plot 112) does the RMS from Eq.[4] somewhat exceed that from Eq. [5]. Also, in 19cases, the RMS from Eq. [4] is smaller than that fromthe Lewis (1937) Eq. [1], while in the remaining fivecases (all with fitted zero A), the reverse is true. There-fore, in comparison with Eq. [5] or [1], the form of Eq.[4] with its additional parameter A has improved the fit
—— Eq. [1] fitted.RMS = 244.10 mm2
—— Eq. [4] fitted
PLOT 310RMS = 364.59 mm2
(largest forzero A)
PLOT 204RMS = 36.86 mm2
(2nd largest for zero A)
PLOT 112RMS = 16.82 mm2
(largest for nonzero A)
by reducing the RMS in a strong majority of cases.Further elucidation of the meaning and role of A, how-ever, is deferred to future research, because here wefocus primarily on the more familiar parameters 5 andK, with A manifesting its influence indirectly.
Visual displays of the fit of Eq. [4] to the data pointsare given in Fig. 1 and 2. Although the visual qualityof fit of Eq. [4] for the largest RMS in Fig. 1 (Plot 310,
700 -
600 -
500g£
400
LJ 300
3Z35Z3O
200
100
15TIME t (ks)
—— Eq. [4] fitted
PLOT 108RMS = 19.47 mm*(4th largest
for zero A)
PLOT 113RMS = 27.11(3rd largestfor zero A)
PLOT 206RMS = 15.53 mm2
(2nd largest for nonzero A)
Fig. 1. Nonlinear least-squares fitting, to experimental field data, ofthe new infiltration equation in three-parameter form, Eq. [4] (solidcurves), with one example of the fitting of Eq. [1] (broken-linecurve).
5 10TIME t (ks)
15
Fig. 2. Nonlinear least-squares fitting, to experimental field data, ofthe new infiltration equation in three-parameter form, Eq. [4].
1222 SOIL SCI. SOC. AM. J., VOL. 58, JULY-AUGUST 1994
fitted zero A) does leave something to be desired, onlya slightly perceptible improvement is afforded by fittingEq. [1], as depicted by the broken-line curve. To examinewhether data-point deviations from a fitted curve weresystematic or random, we used a statistical analysis ofruns (Draper and Smith, 1981, p. 157-162). A run isa sequence of consecutive data points all of which areeither above or below the fitted curve, as exemplifiedby the last five points for Plot 310 in Fig. 1. At aprobability level of 0.05, the statistical runs analysisindicated significant systematicness for Plot 310 for bothfitted curves (solid and broken line), which is consistentwith the visual quality of fit (Fig. 1). For all 24 datasets as fitted by Eq. [1], 16 gave significant systematicnesswhile the remaining 8 gave randomness (nonsignificantsystematicness). For the fittings of Eq. [5], 16 data setsagain gave significant systematicness, with randomnessin 8 sets. For the fittings of Eq. [4], significant systematic-ness was reduced to 10 sets, with randomness increasedto 14 sets. Hence, compared with Eq. [1] and [5], Eq.[4] again has provided improvement, even though it hasnot totally eliminated the significant systematicness.
Although significant systematicness exists in all curvefittings of Fig. 1 and 2, the statistical runs analysis doesnot reflect the magnitudes of the data-point deviationsfrom the fitted curve. In contrast, the RMS, being amean square of these magnitudes, is indeed a sensitiveindicator of how closely the data points conform to thefitted curve, regardless of systematicness or randomness.For Plot 204 in Fig. 1, the RMS is about one-tenth thatof Plot 310, with a corresponding and drastic improve-ment in the visual conformity of points to the fitted curve.The visual fit in Fig. 1 and 2 continues to improve withthe progressive decrease in RMS. For the 18 remainingdata sets, the visual fits were even better than in Fig. 2because the RMS still decreased. Overall, the goodnessof fit of Eq. [4] is considered to be excellent for fielddata, the worst case (l-in-24) Plot 310 notwithstanding.
Statistical Analysis of Fitted ParametersThe seven orthogonal contrasts were carried out on
the natural logarithms of each of the five parameterswhose numerical values are listed in Table 1 (S and Kof Eq. [4], 5 of Eq. [5], and G and H of Eq. [1]).Four of the contrasts showed one or more statisticallysignificant difference (0.05 probability level or smaller)in one or more of the parameters of Eq. [4], [5], or [1]and are given in Table 2. The other three contrasts (iii,v, and vi) failed to exhibit even one significant difference(0.05 probability level) for any of the five parameters.
With the statistical analyses conducted on the naturallogarithms of the observations (parameters), a contrastmean for a group of observations should, strictly, bethe arithmetic mean of the logarithms, but this mean (oflogarithms) is not easy to envisage and interpret. Toobtain a mean value more consonant with the observa-tions, the arithmetic mean logarithm was exponentiated,but this value turns out to be simply the geometric mean
Table 2. Geometric means of parameters analyzed by objectivelyselected orthogonal contrasts (i, ii, iv, and vii) for response tocrop or crop sequence. Analysis conducted on natural logarithmsof parameters.__________________________
Fitting ofOrthogonalcontrast
(i)Sgvs.C
(ii)SgandCvs.B
(iv)C-Sgvs.Sg-C
(vii)C-Sg and Sg-Cvs.F-B, Sg-B,
andC-B
L llllllg VI
Smm s""2
2.486**
1.147
1.689NS
1.793
2.664*
1.436
1.956NS
2.071
1̂ 4. itjK
\ua s"1
3.91NS3.97
3.94*0.78
9.08NS
10.94
9.97*
3.04
1̂ 4. i-jj
S
nuns""2
2.077*0.937
1.395NS
0.978
2.483*
1.225
1.744NS
1.194
1'llllllg Ul
G
mms~H
2.472NS
1.063
1.621NS
4.279
1.755NS
0.536
0.970NS
2.220
L 1̂ 4. HJ
H
0.4473NS
0.4792
0.4630NS
0.2503
0.5387NS
0.6263
0.5809*
0.3615*, ** Contrast geometric means are significantly different at probability lev-
els of 0.05 and 0.01, respectively; NS, not significantly different atprobability level 0.05.
of the observations in the given group. These geometricmeans are employed in Table 2.
Perusal of Table 2 reveals that the parameters S andK of Eq. [4] have yielded four statistically significantcontrasts, three at the 0.05 probability level and one atthe 0.01 probability level. The S of Eq. [5], althoughshowing statistical significance in Table 2 for the sametwo contrasts as the S of Eq. [4], nonetheless does sofor Sg vs. C only at the weaker probability level of 0.05(instead of 0.01). The statistical superiority of 5 and Kof the new Eq. [4] compared with the empirical G andH of the Lewis (1937) Eq. [1] is also very evident, inthat G and //together yield only one significant difference(0.05 probability level). This result for Eq. [1] is consis-tent with a similar finding of only one significant differ-ence by Fahad et al. (1982), albeit for a different compari-son (between C-Sg and 13).
It is of interest that 5 and K of Eq. [4] do not respondin the same way in the several contrasts of Table 2, withS displaying significant differences in contrasts (i) and(iv) and K in contrasts (ii) and (vii). Thus, the croppingeffects may indeed be expressed differently by 5 (unsatu-rated soil) than by sated K (very wet soil). Under continu-ous cropping, the contrasts (i) and (ii) for 5 of Eq. [4]in Table 2 exhibit the order Sg > B > C, with S being2.2-fold larger for sorghum than for corn. For K, theorder is Sg = C > B, with K being fivefold smaller forsoybean than for sorghum and corn. Therefore, sorghumis the strongest enhancer of 5 and corn is the strongestdegrader. In contrast, soybean is the strongest degraderof K, while sorghum and corn are indistinguishable.
When examining the rotation-cropping effects on Sand K of Eq. [4], the matter of making comparisonsbecomes more complicated. Because infiltration mea-surements were taken in midseason (August) of 1976,
ALI & SWARTZENDRUBER: INFILTRATION EQUATION FOR CROPPING EFFECTS 1223
Table 3. Rotation cropping sequences, as shown for given plots indifferent years of soybean (B), corn (C), fallow (F), and sorghum(Sg); in the pairs, the first and second symbols designate thecrops in 1976 and 1975, respectively.
C-SgSg-C F-B Sg-B C-B
Year 113 206 310 (3 plots) (3 plots) (3 plots) (3 plots)
19761975197419731972
CSgFBC
CSgSgBC
CSgFBC
SgCBFSg
FBCSgF
SgBFCSg
CBSgFC
that current crop therefore had only an approximate halfseason in which to manifest its influence. Hence, theprevious whole-season (1975) crop may well have ex-erted a predominant effect, while the still-earlier 1974crop might have had some residual effect; crops before1974 probably had still less or even negligible influence.With these considerations in mind, we examine the sig-nificant (0.05 probability level) 5 contrast (iv), C-Sgvs. Sg-C (Table 2) but must also be aware that thiscontrast does not merely represent a simple yearly alter-nating sequence of corn with sorghum. That is, as shownfor C-Sg in Table 3, the key years of sorghum in 1975and of sorghum and fallow in 1974 may well havesustained S of Eq. [4] against the half-season degradationfrom corn in 1976, particularly compared with Sg-C(Table 3) and its strong corn-induced degradation of Sin 1975, its intermediate soybean-induced degradationof 5 in 1974, and only its weaker, half-season sorghum-induced restoration of 5 in 1976. In this sense, then, theS response in the crop-rotation contrast C-Sg vs. Sg-C is in reasonable conformity with the 5 response in thecontinuous-cropping contrasts (Sg vs. C and Sg and Cvs. B) as already discussed.
A similar examination of the significant (0.05 prob-ability level) K contrast (vii) in Table 2 (i.e., C-Sg andSg-C vs. F-B, Sg-B, and C-B), ultimately construesthe 3.3-fold K reduction to be associated with proximityin time to soybean in the rotation. That is, for C-Sgand Sg-C (Table 3), there had been no soybean fordegrading K since 1973 and 1974, respectively, whereasfor F-B, Sg-B, and C-B the strong (whole-year) soybeandegradation of K during 1975 would only have beenrestoratively influenced by fallow, sorghum, or cornduring the first half season of 1976. Hence, the # degrada-tion from soybean in the crop rotation can be placed inreasonable conformity with that found from soybean in thecontext of continuous cropping as already discussed.
Overall, the three-parameter Eq. [4] has been shownto be a very successful infiltration equation for character-izing the field data here considered. Fitting of the equationhas produced physically acceptable positive values ofsated K, and the statistically lognormal aspects of theresulting K values are compatibly akin to the lognormalfindings of Nielsen et al. (1973) for hydraulic conductiv-ity. In contrast, the mixture of positive and negative Kvalues, produced by the fitting of Eq. [5], cannot evenbe analyzed in the lognormal sense because logarithms of
negative numbers would be involved. Also, the generallysuperior data-fitting capability of the equation is evident,in comparison with the two-term Eq. [5] and the Lewis(1937) Eq. [1]. Furthermore, the excellent capabilityof the parameters of Eq. [4] for showing statisticallysignificant differences in crop-plant effects on infiltrationhas important implications. Finally, for both continuousand rotation cropping, the sorptivity enhancement by sor-ghum and the degradation by corn, and the sated-conductivity enhancement by sorghum-corn and the deg-radation by soybean, would appear to offer promisingnew insights for characterizing and understanding theseimportant plant effects on infiltration.
