VOL. 6, NO. 4 WATER RESOURCES RESEARCH AUGUST 1970

.

Post-Irrigation Movement o[ Soil Water Simultaneous Redistribution and Evaporation

W. R. GARDNER, D. HILLEL, AND Y. BENYAMINI

University o] Wisconsin, Madison, Wisconsin 55706

Abstract. Water content measurements by ,-ray attenuation were made on soil columns during simultaneous redistribution and evaporation following irrigation. Redistribution is shown to reduce evaporation, in some cases appreciably. For a deep irrigation the redistri- bution proceeds at a rate that is relatively independent of the evaporation process, as has been predicted from numerical solutions of the flow equation. Expressions are derived for obtaining an estimate of amount of reduction in evaporation due to redistribution when the redistribution rate is known.

INTRODUCTION

Detailed studies have been conducted in recent years on the various processes compris- ing the field water cycle, including infiltration, redistribution, drainage, evaporation, and evapo- transpiration. Most of these studies, however, have dealt with a single process under idealized conditions that justified disregarding possible interactions with other processes occurring se- quentially or simultaneously.

In the field, however, these processes hardly ever occur independently. In particular, the beginning of evaporation generally follows a wetting or irrigation, at the end of which the typical moisture profile (in the absence of a high water table condition) consists of a wet layer overlying relatively dry soil beneath. Under such conditions, two processes may occur simultaneously in different parts of the profile: (1) evaporation at the surface, which induces upward flow, and (2) redistribution, or internal drainage, by which water moves downward in response to gravitational and suction gradients. With water moving upward at the top. and downward at the bottom of the wetted zone, the profile exhibits a plane of zero flux, or 'water- shed divide', which gradually moves downward into the profile.

There have been a number of previous studies of these processes, for example Richards et al.

* On leave from the Hebrew University of Je- rusalem, Israel.

[1956], and Black et al. [1969]. However, the sand studied by Black and others represents a very special case that could be treated in a simple theoretical fashion and the conclusions may not be generally applicable. Data on a number of soils of different textures are neces- sary to formulate a general description of the processes. It is the purpose of this study to obtain measurements of the soil water content distribution as a function of time during redis- tribution and evaporation following irrigation in order to evaluate the mutual interaction be- tween the two processes. Reference is made to two previous papers by the authors in which the processes of evaporation and redistribution were studied separately [Gardner and Hillel, 1962; Gardner et al., 1970].

EXPERIMENTAL PROCEDURE

A series of evaporation and redistribution trials was conducted with vertical columns of Gilat loess. Air-dry soil was passed through a 2 mm screen and packed mechanically, to a bulk density of 1.47 _ 0.02 grams/cm , in 5 cm ID lucite tubes, 160 cm long. All operations were carried out in a temperature controlled room at 22' 1C. The columns were then ir- rigated repeatedly with 50 mm of water and some. with 100 mm of water at various intervals of time. Parallel sets of columns were allowed to evaporate during the inter-irrigation periods (at a potential evaporativity of about 4 to 5 mm per day) while others were covered with

1148

IO

2o

3o

Movement o[ Soil Water Volumetric water content (%)

I I I I I ', I

A. Redistribution without evaporation

1149

o. I0 I I

I I I

20 ! I I I

.:., i$ , 5

B. Simultaneous evaporation and redistribution

I0

C. Evaporation only

Fig. 1. ,Successive moisture profiles of soil columns following an irrigation of 50 min. Profiles are designated according to number of days after irrigation.

sheets of polyethylene to prevent evaporation. The columns subjected to evaporation alone were only 16 cm or 32 cm long and were wetted to the bottom. The evaporation rate was de- termined by twice daily weighings of the col- umns. The water content profiles were moni- tored repeatedly by means of gamma ray scanner. A separate set of evaporating columns was used for the measurement of the diffusivity- water content relation. These relations are re- ported in a previous paper [Gardner et al., 1970].

RESULTS

Typical sets of successive moisture profile measured during redistribution, evaporation, and simultaneous redistribution and evapora- tion, are shown in Figures 1 and 2. It is seen that the curves of the simultaneous processes resemble the corresponding ones for redistribu- tion alone, except for the evident effect of eva- poration in the surface zone. The lower portions of these curves indicate that evaporation had litfie effect on the shape and rate of advance of the wetting front in the redistributing columns.

1150

Fig. 2.

GARDNER HILLEL, AND BENYAMINI

Volumetric water content (%) 5 I0 15 20 25 0 35 ' ' ' ' I ' 00'

...... :.. ,.. ................. 5 ........

IO

- // E

I

i 4( .

Redistribution only

1 [ Evoporetion + 45 - ' ........... redistribution 50'

Successive moisture profiles of soil columns following an irrigation of 100 mm. Pro- files are designated according to number of days after irrigation.

Figure 3 gives the cumulative evaporation versus time curves for the columns subject to evaporation only, in comparison with those for the correspondingly irrigated columns in which evaporation and redistribution occurred to- gether. Figure 4 gives the cumulative drainage. It can be seen that evaporation has little effect on drainage (in each case reducing it by only about 10%). This corroborates statements by Rubin [1967] and by Remson et al. [1967], who carried out numerical analyses of the re- distribution process. On the other hand, redis- tribution detracted greatly from evaporation, reducing it in fact by about three fourths. A comparison of Figures 3 and 4 suggests, in- terestingly, that for a shallow wetting of an

initially dry profile the two processes, when they take place independently, give roughly equal rates of water outflow. The potential evapora- tion rates employed in these experiments were approximately those found, on the average, in the field in the region from which the soil was obtained.

Figures 5 and 6 show the localized moisture co.ntent decrease with time at two depths dur- ing redistribution and evaporation, independ- ently and simultaneously. It is seen that except at the very surface, the moisture content de- crease due to redistribution is more rapid at first than that due to evaporation. However, after several days (depending on the depth) as the redistribution process slows down and as the

Movement o Soil Water 1151

Evaporation following IOOmm irrigation

Evaporation fol lowing 50mm irrigation

Evaporation redistribution following IOOmm irrigation

Evaporation + redistribution (repeated 50mm irrigations)

Io 20 5o Time (days)

Fig. 3. Cumulative evaporation in evaporating and redistributing columns.

effect of evaporation extends into the profile, it is predominately the latter process that re- duces downward redistribution, as it subtracts from the amount of water that would otherwise be available for redistribution. On the other hand, redistribution can be expected to detract from evaporation more strongly than vice versa, as it tends to decrease the water content (and hence both the overall gradient and the diffusivity) in the upper zone subject to evapo- ration. This interaction can be important in practice, as it can enhance the effect of evapora- tion retardants in water conservation. Surface treatments that retard evaporation only dur- ing the initial stage of drying may have little effect on cumulative water loss in the long run in a profile in which evaporation is occurring without internal drainage. However, if such initial retardation of evaporation can allow more of the infiltrated water to move into deeper layers (beyond the reach of subsequent evaporation), surface treatments such as mulch- ing may conserve water in the long run as well as during the initial stage.

An exact quantitative treatment of the prob- lem requires solution of the unsaturated flow equation and, quite possibly, inclusion of tem- perature gradients and their effect upon liq- uid and vapor transport [Rose, 1968]. However, an analytical expression, even though very ap- proximate, could be of considerable value in predicting evaporation and redistribution under various conditions.

The data above, that reported by Black et al. [1969], and the calculqtions by Remson et al. [1967] indicate that the redistribution process

is influenced only slightly by the evaporation process, particularly immediately after irriga- tion when the drying front has not penetrated very deeply into the soil. Thus the simplest as- sumption that can be made is that used im- plicitly by Gardner and Gardner [1969], which might be called the field capacity assumption, which is that the redistribution is virtually complete after only a short time and that one then uses the solution of the flow equation in the absence of redistribution and with the initial soil water diffusivity corresponding to the water content after complete redistribution has occurred.

Cumulative evaporation from a deeply wetted soil can be treated as evaporation from a semi- infinite soil profile for several days immediately after wetting. With infinite evaporativity the cumulative evaporation increases as the square root of time [Gardner, 1959]

E -- 2i(( D t/Tr) 1/2 (1) where (D) is the weighted mean diffusivity over the range of water contents involved and 06 is the average water content of the profile at the start of the evaporation process. The uppermost curve in Figure 3 obeys equation i very well except for the first day or two, in which the evaporation rate is undoubtedly limited partly by external conditions.

What is perhaps more surprising is that the cumulative evaporation for the columns in which redistribution was occurring also fol- lowed the square root of time within the pre- cision of the experiments. Their behavior is as though most of the redistribution occurred very early in the evaporation process and that eva-

Redistribution following IOOmm irrigation

evaporation

With evaporation

X'Without evaporation evaporation

Redistribution following 50 mm evaporat ion

I0 20 50 Time (days)

Fig. 4. Cumulative drainage through the initial wetting front in evaporating and redistributing columns.

1152 GARDNER HILLEL.,

o ,

.,.,

o >, O.

Redistributio

evaporation

__Redistribution

poration

Fig. 5.

3O

Time (days) Moisture decrease with time at a depth

of 25 cm.

poration is governed also in this case very nearly by equation 1 but with a reduced dif- fusivity due to the reduction in the water con- tent caused by the redistribution. That this o seems to be the case is shown by calculating the evaporation to be expected under such condi- tions. The initial water content of the soil was about 0.38 for the evaporation experiment with- out redistribution. After about two days, re- o. distribution reduced the water content of the soil to about 0.30, a ratio of water contents of about 1.3. For this soil the diffusivity is pro- portional to 0 '8 [Gardner et al., 1970]. The ratio of the cumulative evaporation E, without redistribution, to E,, that with redistribution, would be according to this simple model'

= 20,(D,t/r) /' > o.I -- =

Examination of the curve in Figure 3 for evaporation alone compared with the curve for evaporation plus redistribution following 100 mm irrigation shows that the ratio is, in fact, very close to 2.6.

Cumulative evaporation from a soil wetted

AND BENYAMINI

to a finite depth does not follow the square root of time indefinitely. The data of Gardner and Gardner [1969] can be fitted by a theoretical expression based upon the same assumption as that made in this paper, for example, that of an instantaneous redistribution. However, this as- sumption cannot be expected to. be valid for deep irrigations and long evaporation times. The data of Richards et al. [1956] indicate an initial evaporation rate that is roughly propor- tional to the square root of time but the time dependence of the evaporation rate decreases so that after about 30 days the cumulative eva- poration increases as about t '. One possible way in which to estimate the evaporation under such conditions is to assume that the water con- tent of the soil decreases at a rate determined by the redistribution process, and to substitute this decreasing water content and an appro- priately decreasing diffusivity into equation 1. From the analysis and data in a previous paper [Gardner et al., 19'70] an expression of the form

0/0, = (t + c)-b (3) where b and c are constants, may be used to describe the decrease in water content with time due to redistribution. The present experi-

...__Redi s tri but ion Redistributi evaporation

vo n

Fig. 6. Time (days)

Moisture decrease with time at a depth of 10 cm.

Movement o Soil Water 1153 ments were not continued for a sufficiently long time to test this approach quantitatively, but it is consistent with the data of Richards et al. [1956].

The above analysis was made without specific reference to an upper boundary condition in which actual evaporation is limited by the ex- ternal evaporativity. Under conditions of low evaporativity there would be an even greater tendency toward redistribution. The assumption of a single weighted mean diffusivity based upon some water content ]ess than the initial water content tends to underestimate the evaporation during early times. However, the occurrence of a finite initial evaporation rate controlled by external conditions is in the direction that tends to compensate partially for this underestima- tion. On the other hand, under conditions of ex- tremely low potential evaporation, equation 1 is invalid since it assumes infinite evaporativity, and the approach described here should over- estimate the evaporation. The interaction of evaporation and redistribution in the presence of a mulch requires further analysis and experi- mental study. The present analysis also dis- regards the role that vapor transport, thermal gradients, and hysteresis might play in the in- teraction between redistribution and evapora- tion.

Acknowledgment. This project was supported by the U.S. Department of Agriculture under Public Law 480, grant FG-Is-163, and was con- ducted in cooperation with the Soil and Water

Conservation Research Division, Agricultural Re- search Service.

REFERENCES

Black, T. A., W. R. Gardner, and G. W. Thurtell, The prediction of evaporation, drainage and soil water storage for a bare soil, Soil Sci. Soc. Amer. Proc., 33, 655-660, 1969.

Gardner, YI. R., and W. R. Gardner, Relation of water application to evaporation and storage of soil water, Soil Sci. Soc.' Amer. Proc., 33, 192- 196, 1969.

Gardner, W. R., Solutions to the flow equation for the drying of soils and other porous media, Soil Sci. Soc. Amer. Proc., 23, 183-187, 1959.

Gardner, W. R., and D. I. Hillel, The relation of external evaporative conditions to the drying of soils, J. Geophys. Res., 67, 4319-4325, 1962.

Gardner, W. R., D. I. Hillel, and Y. Benyamini, Post-irrigation movement of soil water, 1, Re- distribution, Water Resour. Res., 6(4), 000-000, 1970.

Remson, I., A. A. Fungaroli, and G. M. Horn- berger, Numerical analysis of soil moisture sys- tems, J. Irrig. Drain. Div., Amer. Soc. Civil Eng., 3, 153-166, 1967.

Richards, L. A., W. R. Gardner, and Gen Ogat, Physical processes determining water loss from soil, Soil Sci. Soc. Amer. Proc., 30, 310-314, 1956.

Rose, C. W., Evaporation from bare soil under high radiation conditions, Trans. 9th Int. Congr. Soil Sci., 1, 57-66, 1968.

Rubin, J., Numerical method for analyzing hyst- eresis-affected, post-infiltration redistribution of soil moisture, Soil Sci. Soc. Amer. Proc., 31, 13- 20, 1967.

(Manuscript received August 18, 1969; revised December 30, 1969.)