SOIL SCIENCE SOCIETY OF AMERICA

P R O C E E D I N G SVOL. 28 JANUARY-FEBRUARY 1964 No. 1

DIVISION S-l-SOIL PHYSICSSoil Water Relations During Rain Infiltration: IL Moisture Content Profiles During

Rains of Low Intensities1

J. RUBIN, R. STEINHARDT, AND P.

ABSTRACTDuring transient-state infiltration of steady, low inten-

sity rain into laboratory soil columns, moisture contentsat increasing soil depths tended with time to approacha constant level. This level, as well as the observed ratesof wetting-front advance, were higher in cases of moreintense rain. For the conditions studied, soil moisturecontents and wetting-front advance rates associated withponded-water infiltration were generally considerablyhigher than those of rain infiltration profiles.

The differences between the observed and the theo-retically predicted rain infiltration profile data were in-significant for rains of low intensity but significant forthose of higher intensity. The wetting front advanceobservations confirmed certain aspects of the theory pre-sented in part I of this paper.

T HE AVAILABLE EXPERIMENTAL information about thephysics of the transient-state rain infiltration (i.e.,

nonponding or preponding infiltration) into soils is rela-tively scant, in spite of the common occurrence and thewell known significance of this mode of water entry intothe pedosphere.

The only controlled-conditions data on the course ofmoisture content changes in a porous material during raininfiltration seem to have been obtained by Youngs (12),who worked with 0.04 to 0.125 mm. slate dust and withbut two rain intensities. Youngs has subjected his experi-mental findings to a qualitative theoretical analysis.

The available information about the relations betweensoil moisture status and the water entry conditions pre-vailing during infiltration is rather inconclusive. Datainvolving relatively large wetting depths (50 cm. or more)have shown, generally, nonsignificant rain intensity in-fluences upon transmission-zone moisture status in thecases of certain sand, loam, and clay soils (5). However,considerable influences of this kind were inferred fromexperiments with slate dust (12). On the other hand,data associated with shallow wetting depths (20 cm. orless) have shown negligible rain intensity effect in the

case of slate dust (12) and consistently significant in-fluence in the case of certain sandy soils (3).

Quantitative comparisons of transient rain infiltrationprofile data with theory have not as yet been made. Forsufficiently large wetting depths and sufficiently low rainintensities, theory (10) based on a moisture flow equationof diffusion type is in qualitative accord with the slatedust results mentioned above, since for such conditionsit predicts that the more intense the rain the higher mustbe the wetted profile's moisture contents. Theory alsoimplies (7, 10) that there should exist considerable dif-ferences between the rain and the ponded-water infiltra-tion profiles. However, this result is contradicted by con-clusions from the existing experimental data (5).

It was the purpose of this study to augment the currentinformation, outlined above, on infiltration moisture contentprofiles. The investigation was to involve relatively typicalsoil materials of coarse and fine textures, low intensityrains, and medium to large wetting depths. The physicalsignificance of the experimental findings was to be assessedby comparing some of them with calculations based onpreviously presented theory (10).

MATERIALS AND METHODSRehovot sand (finer than 2 mm.) and 0.5 to 1.5 mm. aggre-

gates of a serozemic, highly calcareous Beisan clay were usedin the experiments under consideration. In these experiments,porosity of Rehovot soil was 0.40 and its air dry moisture con-tent was 0.005 cm3, per cm3. The sand, silt, and clay contentsof this soil were 96.8, 1.8, and 1.4%, respectively. The cor-responding texture data of Beisan clay aggregates were 19.2,38.8, and 42.0%. The latter material's porosity was 0.63, whileits Vs bar, 15 bar, and air-dry moisture contents were 0.324,0.196, and 0.053 cm3, per cm3., respectively. Additional informa-tion on water properties of Rehovot sand is presented in figure1, which shows experimental data as well as their calculatedapproximations based on the following fitted empirical equa-tions:

S =; matric suction (millibars) =11.3 +(3.19/w) -0.05e15w + e-575" + a"

K = hydraulic conductivity (cm. per second) =84007 [S5 + ( 14.45 )5]

'Contribution from the Department of Soils and Water, Na-tional and University Institute of Agriculture, Rehovot, Israel.Received Dec. 19, 1962. Approved Aug. 16, 1963.

"Soil Physicist and Assistant Soil Physicists, respectively. Thesenior author is now Research Soils Physicist, U. S. GeologicalSurvey, Menlo Park, Calif.

[1]

[2]where w is soil water content (cm3, per cm3.). The generalform of [2] was suggested previously ( 4 ) .

All the measurements for figure 1 were carried out underwetting conditions. The highly structure-sensitive, low ( < 50mbar. ) suction-range data were obtained, employing soilcolumns packed like those of the actual experiments.

The capillary rise method was used to determine matric suc-tion-water content relations for the 10 to 50 mbar. range. Thismethod involved moisture distribution determinations in 60 cm.

SOIL SCIENCE SOCIETY PROCEEDINGS 1964

high laboratory soil columns, essentially in equilibrium withwater table.

Modified pressure plate and pressure membrane instruments(8) were used for the ranges of 100 to 1000 mbar. and 2 to 15bars, respectively. The suction of the air dry soil was estimatedon the basis of air humidity. The zero-suction moisture con-tent was assumed to be equal to soil porosity, calculated fromthe soil's bulk and grain densities.

Steady state soil columns were used in hydraulic con-ductivity measurements when soil suctions were lower than45 mbar. These columns were wetted from above either bya low intensity rain (2) or by an enduring water cover. Inthe latter case the soil was wetted through a ceramic plate,resting upon the soil surface, between the soil and the freewater cover. The plate's saturated hydraulic conductivity wasalways lower than that of the soil tested. Several rain in-tensities and plate saturated permeabilities were used in thevarious measurements. The rain-wetted columns were 70 cm.high and drained into a constant level water table. Thecolumns wetted through a ceramic plate were 15 cm. highand drained into a "Porvic" (11) membrane, maintained at aconstant tension. With both kinds of columns the hydraulicconductivities were calculated from the measured, steady mois-ture flux and tension gradients. The latter were determined attwo or more column heights with the aid of tensiometers. Afterthe conductivities were thus determined, the soil column usedwas sectioned and the average soil water contents within theappropriate height ranges were determined gravimetrically.

The hydraulic conductivity information for suctions > 45mbar. was obtained using pressure-plate apparatus inflow dataand employing the computation methods which take into ac-count the nonnegligible plate impedence (6, 9).

In preparation for the principal experiments of this study,the experimental soil material, sieved and air dried, waspacked uniformly into 5.0 cm. internal diameter lucite cylinderscomposed of three 1.5 cm. high upper sections and of nineteento thirty 3.0 cm. high lower sections. The sections were kepttogether by means of a transparent tape. Small gaps were leftbetween them in order to facilitate the escape of soil air duringinfiltration. Tap water from a container fastened above thevertically held soil cylinder was applied to soil surface throughespecially prepared capillary tubes. The tips of these tubeswere located about 1 cm. above the soil surface. The rate ofwater application could be adjusted by varying the number ofthe capillaries, their diameter, and the head of water abovethem. This rate was kept constant during any given experiment.During infiltration, the soil cylinder was rotated about its verti-cal axis at a rate of 4 rpm. in order to distribute the appliedwater more uniformly throughout the soil surface. The .surfaceof the fine-textured Beisan soil material was protected from thepossible aggregate-breaking action of water drops by a 3 mm.layer of gravel. Such a protection was thought to be unnecessaryin the case of Rehovot sand.

All the rain intensities used with any given soil material wererelatively low. Except for the highest one, they were smallerthan the saturated material's hydraulic conductivity. With

these intensities, and with the trial times employed, pondingdid not occur in any of the reported rain infiltration experiments.

Throughout the course of the infiltration process, the depthof the wetting front was periodically determined, visually. Assoon as the wetting front reached a certain predetermined level(which was always at least 8 cm. above the soil column'sbottom) the water supply was cut off. The column was placedin a horizontal position and separated into its 1.5 cm. or 3.0 cm.high sections. The bulk density and the moisture content ofeach section were determined by drying at 105 °C. However,no attempt was made to measure the moisture content level anddistribution within the section in which the wetting front oc-curred.

While the whole series of operations following the water sup-ply stoppage was carried out as rapidly as possible, it, neverthe-less, took several minutes. Hence, some moisture movementprobably occurred between the time the rainfall was halted andthe time the sectioning was completed.

The experiments described above were supplemented bydeterminations of flood-water infiltration moisture content pro-files. These determinations differed from the rain infiltrationtrials cnly in two respects. Firstly, the soil columns used werenot rotated. Secondly, water, instead of being supplied in theform of rain drops, entered the soil from a water layer, 2 cm.deep, which covered the soil throughout the infiltration's dura-tion.

All the experiments were carried out in duplicate, in a 28°C.constant-temperature room.

EXPERIMENTAL RESULTS

Water content profile data obtained are presented infigures 2, 3 and 4. The results of duplicate trials were sosimilar that only their means are shown.

In the absence of moisture data for the vicinity of thewetting front, the curves of the figures under considerationwere terminated at the last wetted depth at which meas-urements were made. However, it should be noted that atless than 4.5 cm. below the deepest point of any one ofthese curves the soil was in its initial state. It follows thatbelow such a point each actual curve must be turningrather sharply towards the depth axis. This consideration,and an inspection of the figures discussed, show that thegeneral features of the moisture content profiles studiedare qualitively similar to those observed in connection withinfiltration of flood-water into soils (1) and of rain intoslate dust (12).

The data of figure 2 indicate that as rain infiltrationproceeds, soil moisture contents at increasing depths tendto approach the same constant level. Under the conditions

WATER CONTENT, CM3/CMS

SUCTION CONDUCTIVITYCURVE CURVE

EXPERIMENTAL o o o o o • • • • •

-j W>I-

10' 10' I05 10"

MATRIC SUCTION, MB.

Figure 1—The dependence of Rehovot sand's moisturecontent and hydraulic conductivity upon matric suction.The calculated curves are based on equations [1]and [2].

U

10

20

30

40

50

n — i —— i ———————— iI

INFILTRATION dDURATION, MIN }

5- o 61.0

• 140.0_ x 213.5

-

C %60 J90

120 ;

Figure 2—Influence of rain infiltration duration uponwater content profiles. S and C indicate data of Rehovotsand (47 ± 1 mm./hr. rain) and Beisan clay aggregates(150 ± 1 mm./hr. rain), respectively. The initial watercontents are indicated by Wj.

RUBIN ET AL.: BAIX INFILTRATION: MOISTURE CONTENT PROFILES DURING LOW INTENSITY RAIN

WATER CONTENT, CM3/CM3 WATER CONTENT, CM3/CM3

.000O

.100 .200 .300 .400

12

Z 18

* 24Q.

£ 30_lO 36<f>

42

48

54

Figure 3—Influence of the method and rate of water ap-plication upon soil water content profiles during in-filtration into initially air-dry Rehovot sand. Rainintensities in mm./hr. and the ranges of their variationare indicated below the profile curves to which theycorrespond. The soil's initial water content is representedby w,.

studied, the approximate attainment of this limit at agiven depth occurred at considerably lower moisture con-tent in the case of the sand than it did in the case of theclay.

The influences of the water supply conditions upon in-filtration profiles of similar wetted depths are demonstratedby figures 3 and 4. With the exception of two profiles ofone soil (cf. the lower parts of the Beisan clay curvesfor the highest intensity rain and flood-water infiltrations),the differences between all the profiles of these figureswere highly significant. In particular, it can be seen thatthe profiles moisture contents increased with rain intensityand were the highest in the case of flood infiltration. Fur-thermore, at least for the slower rains, figure 2 demon-strated that at moisture gradient values shown by the in-termediate-depth zones of figures 3 and 4, the rate ofmoisture content change with time is very small. Hencethe two latter figures seem to indicate that at the wettingdepths investigated, the intermediate zones of the profiles

O 20 40 60

TIME, MIN.

100 200 300 40O 500

RAIN INTENSTY, MM/HR.

.000

Figure 5—Influence of time and of rain intensity upon thewetting front advance rates during infiltration into air-dry Rehovot sand. Numbers next to the curves indicaterain intensity in mm./hr.

.400 .600 700

" h12

2 IBoI 24t-Q.U 30O

d 36

W42

48

5470+2 I50±l

(29511

Figure 4—Influence of the method and rate of water ap-plication upon soil water content profiles during in-filtration into initially air-dry Beisan clay aggregates.Rain intensities in mm./hr. and the ranges of theirvariation are indicated below the profile curves to whichthey correspond.

associated with the slower rains nearly approached theirlimiting moisture contents. These figures also show thatthe smaller the limiting moisture contents were, the lowerwere the rain intensities which produced them. The aboveconsiderations imply that the differences between the slowrain profiles under consideration will persist throughoutinfiltration duration. On the other hand, in both soilsstudied, and especially in the clay, the curves correspond-ing to the highest rain intensity exhibited some tendencyto approach the flood-water curves.

The positive moisture gradients shown by portions ofthe high water content profiles in figure 3 probably indicatethat some drainage took place in certain sand columnsafter the infiltration process was interrupted. However, theobserved differences between the various profiles weresuch that they could hardly be explained by the possibledrainage influences.

Data about the wetting front advance rates during ex-periments in which this front reached the depth of about

TIME, MIN. RAIN INTENSITY, MM/HR.

Figure 6—Influence of time and of rain intensity uponthe wetting front advance rates during infiltration intoair-dry Beisan clay aggregates. Numbers next to thecurves indicate rain intensity in mm./hr.

SOIL SCIENCE SOCIETY PROCEEDINGS 1964

50 cm. are shown in figures 5 and 6. Parts A of thesefigures demonstrate for representative cases the effect ofinfiltration time upon mean advance rates computed fornonoverlapping duration increments. Mean rates wereused in order to decrease the interference of short-termrandom fluctuations in the actual rates. It appears that inthe case of rain infiltration the mean rates changed butlittle with infiltration time. This is in sharp contrast withthe situation which prevailed when a similar soil depthwas wetted by flood-water infiltration.

Figures SA and 6A show that the higher the rain in-tensity, the larger were the wetting front advance rates.Such a relation was observed also by others (3, 5, 12).The nature of this relation is further demonstrated infigures 5B and 6B. The rates in these figures were calcu-lated for the whole duration of the appropriate infiltrationtests.

COMPARISON OF EXPERIMENTAL DATA WITHTHEORETICAL PREDICTIONS AND DISCUSSION

The qualitative features of the experimental profiles ob-tained with rain intensities smaller than the saturatedsoil's hydraulic conductivity are in general agreement withYoungs' long-term predictions (12) as well as with thetheory presented in (10). In particular, these profileshapes and their dependence upon infiltration durationand upon rain intensity are similar to those of theoreticalprofiles. However, the data obtained do not exhibit thedrainage phenomena predicted and observed by Youngsfor the shallow-wetting stages of rain infiltration. Perhapssuch a process would have been observed had the in-filtrations studied been of shorter durations. Furthermore,the data under consideration point to a frequent occur-rence of a shallow, maximum-water-content, uppermostzone, the existence of which was not predicted by thetheoretical calculations (10, figure 1). This zone mightowe its presence to the raindrop-created, wetting anddrainage cycles near the soil surface, which were not takeninto account by the theory under consideration.

Quantitative tests of the latter theory's applicabilitywere carried out only for the profiles of Rehovot sand, thestructure of which was considered sufficiently stable tojustify one of the theory's assumptions. Examples of theresults obtained from these tests are given in figure 7.This figure shows three sets of experimental data as wellas corresponding theoretical curves, the latter beingdetermined with the aid of equations [1] and [2], andthe numerical method of (10).

The figure under consideration shows that the experi-mental data resemble to a certain degree the theoreticalcurves, but differ from them in three respects. Firstly, theyexhibit the shallow, high-water-content uppermost region,already discussed above. Secondly, their lowest wettedregion is characterized by a more rapid transition fromthe high to the initial moisture contents. Thirdly, in thecase of the higher rain intensity curves shown, the moisturecontent level which seems to be approached with time inthe experimental profiles' intermediate zones is significantlylower than the one predicted by the results of the calcu-lations.

The latter conclusion is further supported and extendedto other rain intensities by the following considerations.Data on hand seem to indicate that all except possibly thetwo wettest moisture content profiles of figure 3 reachedessentially zero intermediate zone moisture gradients.Hence, by proposition 1 of (10) the soil's hydraulic con-ductivity in these intermediate zones must be and mustremain approximately equal to the rain intensity. Anestimate of the intermediate zone properties can be ob-tained by calculating for every curve of figure 3 the meanof all the moisture contents shown, except for the deepestand the two uppermost ones. Such a procedure yields aver-

age intermediate zone moisture contents of 0.110, 0.169,0.187, 0.211, and 0.265 cm.3 per cm.3 for rain intensitiesof 2 ± 1, 13.4 ± A, 26 ±2, 47 ± O, and 150 ± 1 mm.per hour, respectively. On the basis of steady state andequilibrium data (equations [1] and [2]) the abovemoisture contents are equivalent to hydraulic conductivitiesof 3, 13, 18, 28, and 70 mm. per hour, respectively. Itseems from the above that the differences between thecalculated values of hydraulic conductivities and the onesexpected on the basis of rain data increase with rain in-tensity. Actually, these differences are insignificant for the2 lowest but significant for the 3 remaining intensities.

The above discrepancies between the experiment andthe theory may have been due to the following: the in-adequacy of the current, unsaturated flow theory; theinexactness of the assumptions made in connection withthe boundary conditions; the lack of precision in thesteady state or equilibrium data used; and finally, thewater movement occurring after infiltration interruption.The data on hand do not suffice to choose any one of theabove causes as significant. However, if it is assumed thatthe intermediate zone moisture gradients of the profilesunder consideration were essentially zero, it seems thateither the first or the third of the above stated possiblereasons were of importance.

As pointed out in a previous publication (10, cf. also12), when rain intensity is smaller than the saturatedsoil's hydraulic conductivity, Philips' theory for infinite-time flood-water infiltration (7) is applicable to the in-finite-time rain infiltration. In particular. Philips' equationfor the rate of advance of a given soil moisture contentlevel during an infinite-time ponded-water infiltration (7,equation [35]) is applicable. It follows from this equationand Proposition 1 (10) that during infinite-time rain in-filtration:

u = [R-K(Wi)j / [WL-W,]where u is the advance rate of a given moisture contentlevel (cm. per second) and where R is the rain intensity(cm. per sec.), WL is the limiting transmission-zone moisture

WATER CONTENT, CM3/CM3

.000 .060 .120 .180 .000 .060 .IEC .180 .240 .300

Figure 7—Comparison of theoretical rain infiltration watercontent profiles of Rehovot sand with the correspondingexperimental data. A and B represent infiltrations of13.4 mm./hr. rain and 47 mm./hr. rain, respectively.Crosses represent experimental points obtained withshort and black discs—with long infiltration durations.Continuous lines represent the theoretical curves.

RICHARDS ET AL.: RELATIVE VAPOR PRESSURE OF WATER IN THE SOIL

content and W( is the initial moisture content. Since in theexperiments under consideration K(w() = O, it followsthat

u (WL—wO / R = 1.[3]

Youngs (12) suggested a similar equation, except forthe Wj term which was omitted.

In every pertinent profile studied, the intermediatezone's upper part had nearly zero moisture gradients, andthus almost stable moisture contents, when 50 cm. depth ofwetting was reached. Hence, it might be justified to testthe above infinite time equation using the data of thedrier profiles in figures 3 and 4. Furthermore, if it is as-sumed that the wetting front moisture content is constant,the rate of advance of this front can be described by uof equation [3], In order to check the applicability of[3] and the above considerations to the case of Rehovotsand, the average intermediate zone moisture content (cf.above) was used as WL. In the case of Beisan clay ag-gregates, WL was assumed to be equal to the average ofsoil water contents at the four depths, S1/^, 5%, 8% and11% cm. (i.e., counting from the soil surface, at the thirdto sixth points of figure 4). Furthermore, in both soils theaverage rates during 50 cm. deep infiltrations weredesignated as u. Thus calculated values of U(WL—W[)/Rfor Rehovot sand at rain intensities of 13.4, 26, 47, and150 mm. per hour were 1.01, 0.96, 1.00, and 0.97,respectively. Comparative values for infiltration of rainswith intensities of 35, 70 and 150 mm. per hour into Beisanclay aggregates were 0.99, 0.99, and 1.03, respectively.This internal consistency of the experimental data sug-gests the correctness of the models chosen, provided theadditional assumptions made in connection with thetested equation were correct.

The experimental results presented in this paper demon-strated clearly the possible effects of the manner and therate of water application upon soil moisture contents of

infiltration profiles. Furthermore, the analysis aboveshowed that qualitative and in some cases—quantitativeprediction of these results can be provided by the pre-viously presented theory based on certain idealized soiland rain models.