d. m. gray and d. i. norumthe effect of soil moisture on infiltration as related to runoff and...

THE EFFECT OF SOIL MOISTURE ON INFILTRATION AS RELATED TO RUNOFF AND RECHARGE

by

D. M. Gray and D. I. Norum

Published in Proceedings of Hydrology Symposium No. 6 Soil Moisture November 1967

National Research Council of Canada Associate Committee on Geodesy and Geophysics

Subcommittee on Hydrology

THE EFFECT OF SOIL MOISTURE ON INFILTRATION AS RELATED TO RUNOFF AND RECHARGE

Don M . Gray and D. I. ~orurnl

SYNOPSIS

The paper provides a general out l ine o f the mechanics of the i n f i l t r a t i o n process. I n the discussions, s p e c i f i c a t t e n t i o n i s given t o the quant i ta t ive influence of the i n i t i a l s o i l moisture content as it a f f e c t s both the i n f i l t r a t i o n ra te and the amount of i n f i l t r a t i o n of frozen and unfrozen s o i l s .

INTRODUCTION

The process of infiltration is by definition the entry of water into the soil, through the soil-atmosphere interface. In most cases, the amount of infiltration which occurs during any given rainfall or snowmelt event represents the major component loss of precipitation to surface runoff or, the potential amount of water which may go to groundwater recharge. As indicated diagrammatically in Figures 1 and 2, depending on the intensity of rainfall or snowmelt rate, relative to the infiltration rate, water may be entirely absorbed by the soil or may accumulate and flow from the area as surface runoff. In Figure 1, the supply intensity, i, is less than the maximum rate at which the soil in its given condition can absorb water, (i = f) and hence the total supply goes to replenishing the soil moisture reservoir and to recharging the groundwater supply (neglecting evaporation and interception losses). In Figure 2 in which i>f some water accu- mulates on the surface and appears as surface runoff.

Because of the importance of the infiltration process in the hydrologic cycle, the phenomenon deserves special attention and study. In these regards, it would be expected that a complete understanding of the process and factors affecting it would assist the hydrologist in quantitatively evaluating infiltration amounts and hence increase his confidence and competence in water balance, hydrologic design and other studies.

1. Don M. Gray and D.I. Norm are respectively, Associate Professor and Assistant Professor, Department of Agricultural Engineering, University of Saskatchewan, Saskatoon.

134 EFFECT OF SOIL MOISTURE ON INFILTRATION

I n t h e i n f i l t r a t i o n process water e n t e r s t he s o i l su r f ace due t o t h e combined inf luence of g r a v i t y and c a p i l l a r y f o r c e s . Both fo rces a c t i n t h e v e r t i c a l d i r e c t i o n t o cause pe rco la t ion downward. Cap i l l a ry f o r c e s a l s o a c t t o d i v e r t water l a t e r a l l y from l a r g e r pores ( feeder canals ) t o c a p i l l a r y pore spaces which a r e much smal ler i n dimension, but may be very numerous. A s t h e process cont inues , t h e c a p i l l a r y pore spaces become f i l l e d and with pe rco la t ion t o g r e a t e r depths t h e g r a v i t a t i o n a l water normally encounters increased r e s i s t a n c e t o flow due t o reduced ex ten t o r dimension of flow channels, increased length of channels, o r an impermeable b a r r i e r such a s rock o r c lay . A t t he same t ime t h e r e may be increased r e s i s t a n c e t o inflow of water a t t h e s o i l su r f ace due t o t h e su r f ace s e a l i n g e f f e c t as a r e s u l t o f t h e mechanical a c t i o n o f ra indrops i n breaking down t h e s o i l aggregates and subsequent inwash o f t h e f i n e r s o i l p a r t i c l e s . The r e s u l t i s a r ap id r educ t ion o f i n f i l t r a t i o n r a t e i n t he f i r s t few hours of a storm, a f t e r which t h e r a t e remains nea r ly cons tant f o r t h e r e - mainder o f t h e per iod o f storm r a i n f a l l excess .

From t h i s q u a l i t a t i v e desc r ip t ion of t h e i n f i l t r a t i o n process it can be recognized t h a t t h e process involves both t ransmiss ion and s t o r a g e of water by t h e s o i l and t h a t t h e r a t e of i n f i l t r a t i o n may be governed by sepa ra t e processes o f :

(a) Entry of water through t h e su r f ace l aye r , and

(b) Downward movement o r pe rco la t ion of water through t h e s o i l p r o f i l e .

THEORY OF INFILTRATION

I n f i l t r a t i o n of water i n t o t h e s o i l , l i k e many o t h e r flow processes i n porous media, is governed by t h e Richards s o i l moisture d i f f u s i o n equation,

i n which €I = t h e volumetric moisture content ,

k = t h e c a p i l l a r y conduct iv i ty , and

@ = t he t o t a l p o t e n t i a l .

Equation 1, is t h e con t inu i ty equation f o r flow which has t h e f l u x , V , a t any po in t def ined by t h e Darcy equat ion ,

I t i s evident from Equation 2 t h a t t h e f l u x a t any po in t i n a s o i l

EFFECT OF SOIL MOISTURE ON INFILTRATION 135

system, inc luding t h e s o i l su r f ace , i s p ropor t iona l t o t h e hydraul ic o r c a p i l l a r y conduct iv i ty , k, and t h e t o t a l p o t e n t i a l g rad ien t , VQ. Therefore, t h e i n f i l t r a t i o n process w i l l be a f f e c t e d by any f a c t o r which a f f e c t s e i t h e r o f t hese two q u a n t i t i e s . A l is t of t h e most pe r t i nen t f a c t o r s is shown i n Table 1.

A s shown i n the t a b l e , t h e moisture content of a s o i l a f f e c t s t h e magnitude of both k and V@. Hydrologists have long recognized t h a t i n f i l t r a t i o n t o a given s o i l decreases with an inc rease i n t h e s o i l moisture content . Even though e a r l i e r s t u d i e s such a s t hose conducted by S c h i f f and Dre ibe lb is (1949) and T i s d a l l (1951) were undertaken i n s p e c i f i c at tempt t o e s t a b l i s h t h i s r e l a t i o n s h i p , it has only been i n r e c e n t years , through t h e o r e t i c a l cons idera t ion of t h e mechanics of t h e i n f i l t r a t i o n process t h a t genera l so lu t ions of t h e equations o f flow have been proposed which may be used t o q u a n t i t a t i v e l y eva lua t e t h e e f f e c t of s o i l mois ture on i n f i l t r a t i o n .

Time Var i a t ion i n I n f i l t r a t i o n

Many equations have been developed o r suggested t o d e f i n e t h e mass o r depth o f water i n f i l t r a t e d , Mf , a f t e r given time, t, i n t o a uniform s o i l a t cons tant moisture content . Some o f t h e most common of t h e s e expressions a r e t h e fol lowing:

Kostiakov (1932) and Lewis (1937)

Mf = a t n

Gardner and Wid,tsoe (1921) and Horton (1940)

Mf = f c t + de - K t (4)

Kirkham and Feng (1949) ... hor i zon ta l i n f i l t r a t i o n 1

Mf = c t ? + g (5)

P h i l i p (1954)

Mf = st: + A t

A s i nd ica t ed , most of t h e equations t ake t h e form o f an exponential o r power funct ion o f t ime i n which t h e cons tants (e.g. a and n of Equation 3) cha rac t e r i ze t h e a b i l i t y of s o i l i n i t s given condi t ion t o absorb water.

One of t h e most s i g n i f i c a n t con t r ibu t ions t o understanding t h e i n f i l t r a t i o n process was given by P h i l i p (1957a) i n which he presented t h e s o l u t i o n t o t h e d i f f u s i o n equation (Equation 1) f o r one-dimensional v e r t i c a l i n f i l t r a t i o n i n t o a uniform, s e m i - i n f i n i t e medium, i n i t i a l l y a t a cons tant moisture content . The r e s u l t i n g equation g ives t h e d i s t a n c e from t h e s o i l su r f ace t o a po in t i n t h e p r o f i l e , a t which t h e moisture content is 0 as ,

Table 1

Factors Affec t ing t n e I n f i l t r a t i o n Rate i n t o unfrozen So i l

Density Proper t ies Viscos i ty

Hydraulic Conductivity

Rate

Gradient of Po ten t i a l

Moisture Content P a r t i c l e S i ze Di s t r ibu t ion

Organic Matter Shrinkage Cracks Root & Animal Ac t iv i ty L

Pore Size , Shape, 1 Porous Medium Dis t r ibu t ion and

Continuity

[&rface Conditions -. T i l l a g e Packing

Layering (Homogeneity) - Colloid Content Col lo id Swelling S a l t Content

] 1nwash-of P a r t i c l e s

Hydros ta t ic Head S o i l Surface -[ Barometric Pressure

1 E o i s t u r e Content JP res su re a t

p e s s u r e Gradient I Wet Front Surface Tension Contact Angle

--I I k r e s s u r e of Confined A i r Grav i t a t iona l Depth t o

Gradient L


Equation 7 is particularly pertinent to the discussion inasmuch as it provides an insight of the importance of the soil moisture content to the infiltration process because the quantities X(e), X(e) and $(e) are functions of e which can be evaluated from capillary conductivity and capillary diffusivity curves, and therefore reflect the quantitative influence of soil moisture on infiltration rates and amounts. It should be noted however that as time approaches infinity. Equation 7 diverges and is no longer valid.

The mass infiltration occurring in time, t, can be expressed

in which Bi = initial moisture content,

en = moisture content maintained at the soil surface (usually saturation), and

ki = capillary conductivity at ei.

Thus, according to Equation 8, the mass infiltration is equal to the sum of the water stored in the profile (represented by the integral) plus the depth of water which has flowed through the profile due to the unit gradient under dry conditions. This latter quantity, kit, can usually be neglected when the initial soil conditions are quite dry since in these cases, ki, will be small.

Note that substitution of Equation 7 into Equation 8 leads to the expression

m

where

a2 = jBn x(e)de + ki, and

8 i

This equation, truncated after two terms, is the same as Equation 6. Similarly, for horizontal flow, only the first term of Equation 9


is necessary t o desc r ibe t h e process and thus i s analogous t o Equation 5.

A t t h i s po in t it i s worthy t o mention t h a t i n 1962 Hanks and Bowers presented a genera l ized numerical s o l u t i o n of t h e s o i l mois ture d i f f u s i o n equat ion which can be used t o compute i n f i l t r a - t i o n i n t o layered s o i l s and s o i l s i n which t h e moisture content i s not uniform. Green (1963) i nd i ca t ed e x c e l l e n t agreement between i n f i l t r a t i o n r a t e s p red i c t ed by t h i s s o l u t i o n and measured f i e l d r a t e s .

E f f e c t of S o i l Moisture on Moisture P r o f i l e s

A s suggested, t h e s i g n i f i c a n c e of P h i l i p ' s equat ions i s t h a t by t h e r e l a t i o n s h i p s he p re sen ted , the q u a n t i t a t i v e e f f e c t of t h e i n i t i a l moisture content of t h e s o i l can be eva lua ted . To exemplify t h i s f a c t , t h e method was used t o c a l c u l a t e t h e moisture d i s t r i b u t i o n p a t t e r n s f o r a sandy loam s o i l i n i t i a l l y a t two d i f f e r e n t moisture l eve l s ; 0.03 cm3/cm3 and 0.23 cm3/cm3. The r e s u l t s of t h e c a l c u l a t i o n s a t two t imes , 60 minutes and 240 minutes, a r e shown p l o t t e d i n Figure 3 i n which t h e mass i n f i l t r a - t i o n ind i ca t ed on t h e f i g u r e were c a l c u l a t e d by t h e fol lowing equat ions ,

The c o e f f i c i e n t s of t h e s e equat ions r e f l e c t t h e r e l a t i v e e f f e c t s t h a t t h e c a p i l l a r y and t h e g r a v i t a t i o n a l fo rces have on t h e i n f i l - t r a t i o n process. That is, t h e f i r s t term ( t1 /2 ) i s used t o d e s c r i b e h o r i z o n t a l flow and thus t h e c o e f f i c i e n t a t t ached t o t h i s term eva lua t e s t h e e f f e c t of c a p i l l a r y f o r c e s . S i m i l a r l y , t h e c o e f f i c i e n t s assigned t o t h e o t h e r terms of t h e equat ion show t h e e f f e c t of g r a v i t y . Thus, it can be observed i n Equations 10 and 11 t h a t t h e n e t e f f e c t on t h e i n f i l t r a t i o n process of i nc reas ing t h e i n i t i a l s o i l mois ture content is t o decrease t h e e f f e c t o f c a p i l l a r y fo rces and inc rease t h e e f f e c t o f g r av i ty . Th i s comes about because of t h e decrease i n c a p i l l a r y g r a d i e n t and t h e in- c r ea se i n c a p i l l a r y conduc t iv i t y o f t h e s o i l with an i nc rease i n mois ture content .

From Figure 3 it is a l s o apparent t h a t ,

(a) Increas ing t h e i n i t i a l s o i l mois ture content increases t h e v e l o c i t y a t which t h e wet t ing f r o n t moves bu t decreases t h e i n f i l t r a t i o n r a t e , and


(b) The i n i t i a l mois ture content of t h e s o i l a f f e c t s t h e shape of t h e mois ture d i s t r i b u t i o n p r o f i l e , e s p e c i a l l y a t s h o r t t imes a f t e r wet t ing .

This l a t t e r c h a r a c t e r i s t i c can a l s o be explained by changes i n t h e d i f f u s i v i t y and p o t e n t i a l g r ad i en t a s soc i a t ed with t h e d i f f e r e n t i n i t i a l s o i l moisture con ten t s . That i s , s i n c e a t t h e h ighe r mois ture content t h e d i f f u s i v i t y i s more n e a r l y cons t an t and t h e mois ture g rad i en t ac ros s t h e wet f r o n t i s sma l l e r ; t h e wet f r o n t i s l e s s a b m p t .

The mois ture p r o f i l e s developed by P h i l i p ' s method ( a s shown i n F igure 3) a r e s i m i l a r i n shape t o t h e experimental p r o f i l e s measured on l abo ra to ry samples by Bodman and Colaan (1943) ( s ee F igure 4 ) . I n comparing these curves , it i s ev ident t h a t t hey d i f f e r p r i m a r i l y i n t h a t t h e experimental curve shows t h e ex i s t ence of a s a t u r a t i o n and t r a n s i t i o n zone near t h e s o i l s u r f a c e whereas i n t h e t h e o r e t i c a l curves t h e t ransmiss ion zone extends t o t h e sur face . The s a t u r a t i o n and t r a n s i t i o n zone i s u s u a l l y p r e s e n t i n s o i l s because near t h e s u r f a c e , a i r may escape from a s o i l and thus i s not t rapped by t h e downward-moving wet f r o n t . This d i f f e r e n c e between t h e a c t u a l and t h e o r e t i c a l mois ture p r o f i l e s should no t , however, in t roduce se r ious e r r o r t o t h e computation of mass i n f i l t r a t i o n by t h e o r e t i c a l methods p a r t i - c u l a r l y on l a r g e samples because (a) t h e depth of t h e s a t u r a t i o n and t r a n s i t i o n zone is smal l and (b) t h e moisture content i n t h e t ransmiss ion zone i s i n t h e o rde r of magnitude of 60-70 p e r cent pore s a t u r a t i o n i n sands and 70-80 p e r cen t pore s a t u r a t i o n i n c l a y s [Moore (1949), Bodman and Colman (1943), Kirkham and Feng (1949) and Norum and Gray (1964) ] . E f f e c t o f S o i l Moisture on t h e I n f i l t r a t i o n Rate

I n t h e example c a l c u l a t i o n , t h e q u a n t i t a t i v e e f f e c t s of changes i n i n i t i a l s o i l mois ture on mass i n f i l t r a t i o n have been demonstrated. However, t h e s e c a l c u l a t i o n s can only be completed when t h e func t ions : X(0), X(0), e t c . o f Equation 7 a r e e x p l i c i t l y known. Evaluat ion of t h e s e func t ions i s u s u a l l y an arduous and d i f f i c u l t t a sk , hence, a s a n , a l t e r n a t i v e method f o r determining t h e e f f e c t of t h e i n i t i a l s o i l mois ture content on t h e i n f i l t r a - t i o n r a t e , P h i l i p (195%) suggested t h a t f o r s h o r t t imes a f t e r i n f i l t r a t i o n has s t a r t e d , t h e i n f i l t r a t i o n r a t e of s o i l , f , v a r i e s approximately a s t h e square r o o t o f t h e d i f f e r e n c e between t h e su r f ace mois ture content , 0, and t h e i n i t i a l s o i l mois ture con ten t , 0 i ( c a p i l l a r y f o r c e s ) . That i s ,

A f t e r long t imes, t h e i n f i l t r a t i o n r a t e becomes independent of t h e i n i t i a l mois ture content because t h e g rad i en t i n t h e upper reg ion approaches u n i t y and t h e i n f i l t r a t i o n r a t e approaches t h e


c a p i l l a r y conduct iv i ty f o r t he zone. Holtan (1961) repor ted a s i m i l a r approach t o de f ine t h e i n f i l t r a t i o n r a t e of a s o i l a s a func t ion of t h e exhaust ion of s o i l moisture s to rage . The expression used i s

i n which S = p o t e n t i a l s o i l moisture s to rage volume o r t h e volumetric d i f f e rence between pore s a t u r a t i o n and t h e 15-bar o r permanent w i l t i n g percentage f o r t h e s o i l zone above t h e con t ro l layer .

f c = f i n a l cons tant r a t e of i n f i l t r a t i o n through t h e con t ro l horizon, and

a ,n = cons tants f o r a p a r t i c u l a r s o i l i n given condi t ion (according t o P h i l i p n = 1/2)

In Equation 13, t h e e f f e c t of i nc reas ing t h e mass i n f i l t r a t i o n , M f , is analogous t o i nc reas ing t h e ( i n i t i a l ) s o i l moisture content which w i l l cause a decrease i n t h e i n f i l t r a t i o n r a t e . A s pointed ou t by Holtan, one important aspec t of Equation 13 a s appl ied t o hydrologic ana lyses i s t h a t by subdividing t h e s to rage p o t e n t i a l i n t o t h e f r e e o r g r a v i t a t i o n a l water volume and t h e c a p i l l a r y water volume t h e i n f i l t r a t i o n recovery between r a i n periods can be computed. In t h i s c a l c u l a t i o n it i s usua l ly assumed t h a t t h e f r e e water i s removed a t t h e r a t e o f g r a v i t y flow (perhaps fc) and t h a t t h e a v a i l a b l e water capac i ty i s deple ted a t a slower r a t e o f evapot ranspi ra t ion . Another f e a t u r e shown i n t h e equation is t h a t when the mass i n f i l t r a t i o n Mf, equals t h e moisture s to rage , S, t h e i n f i l t r a t i o n r a t e is equal t o t h e t ransmission r a t e through t h e c o n t r o l l a y e r . Hanks and Bowers (1962) s u b s t a n t i a t e d t h i s r e s u l t . They concluded t h a t i n f i l t r a t i o n was governed by t h e t r a n s - mission through t h e l e a s t permeable l aye r , once t h e wet t ing f r o n t extended i n t o t h a t l aye r . Estimates of t hese r a t e s f o r s o i l s having d i f f e r e n t s o i l p r o f i l e c h a r a c t e r i s t i c s and ground cover condi t ions can be obtained from t abu la t ed va lues such a s those given by Ayers (1959).

E f fec t of S o i l Moisture Gradient

In t h e preceding d i scuss ions , cons idera t ion has been given t o t h e e f f e c t of s o i l moisture, which is uniform throughout t h e p r o f i l e , on t h e i n f i l t r a t i o n process . In na tu re , of course, t h i s condi t ion r a r e l y p r e v a i l s but most o f t en , p a r t i c u l a r l y i n t h e upper reg ion of t h e p r o f i l e , t h e s o i l moisture content i nc reases with depth. The e f f e c t of t h i s " i n i t i a l " moisture g rad ien t cannot be ca l cu la t ed by t h e P h i l i p ' s method but may be accounted f o r by t h e method proposed by Hanks and Bowers (1962). In manner of summary, it would be expected t h a t f o r a given s o i l t h e e f f e c t of


a moisture g rad i en t would cause t h e i n f i l t r a t i o n r a t e t o de- c r ea se more r a p i d l y than i n a uniformly dry p r o f i l e (see F igure 5 ) .

I n t e r r e l a t i o n s h i p o f S o i l Moisture and Other Fac tors Inf luencing I n f i l t r a t i o n

A s po in ted out i n e a r l i e r d i s cus s ions t h e i n f i l t r a t i o n r a t e of a given s o i l is dependent on many f a c t o r s . There is, however, wide d i f f e r e n c e s i n opin ions among i n v e s t i g a t o r s a s t o t h e r e l a t i v e importance o f t h e d i f f e r e n t f a c t o r s a f f e c t i n g t h e i n f i l t r a t i o n process. For example, Duley and Kelly (1941) i n s p r i n k l e r i r r i g a - t i o n t e s t s conducted on s i l t loam and sandy loam s o i l s found t h a t t h e cond i t i ons of t h e s o i l s u r f a c e had a marked e f f e c t on i n f i l - t r a t i o n and they f e l t i ts in f luence on the i n f i l t r a t i o n r a t e was much g r e a t e r t h m t h e i n f luence of t h e i n i t i a l s o i l moisture. On t h e o t h e r hand, Green (1963) r epo r t ed t h a t t h e antecedent moisture cond i t i ons o f a given s o i l may in f luence i n f i l t r a t i o n r a t e s a s much a s t i l l a g e , s u r f a c e s e a l i n g o r p r o f i l e d i f f e r e n c e s .

Many o f t h e f a c t o r s a f f e c t i n g t h e i n f i l t r a t i o n process a r e in te rdependent . Green found t h a t an " i n i t i a l l y - d r y " s i l t loam was most s t a b l e and r e s i s t e d e ros ion whereas a s i l t y c l a y was most s t a b l e i n an i n i t i a l l y - w e t condi t ion . S imi l a r ly , t h e amount o f shr inkage and swel l ing of a s o i l is dependent, i n p a r t , on i t s s o i l mois ture content . The volumetr ic and s t r u c t u r a l changes which accompany sh r ink ing and swe l l i ng may produce a marked e f f e c t on t h e i n f i l t r a t i o n r a t e e s p e c i a l l y i f t h e s e changes a r e l a r g e such a s t hose which may occur i n a heavy c l a y s o i l on dry ing . When a c l a y is i n a severely-cracked condi t ion , t h e l a r g e c racks s e r v e a s f eede r cana l s which permit d i r e c t e n t r y of water a t t h e s u r f a c e and i ts d i s t r i b u t i o n downward and l a t e r a l l y under p o s i t i v e pressure . Under such condi t ions , t h e i n f i l t r a t i o n r a t e w i l l be much h ighe r than i f t h e s o i l were not cracked. Likewise, t h e dens i ty and s t a n d o f vege t a t i on , which a l s o a f f e c t i n f i l t r a t i o n , a r e a l s o dependent on s o i l moisture.

To t h e w r i t e r ' s knowledge, t h e interdependence o f a l l f a c t o r s a f f e c t i n g i n f i l t r a t i o n and t h e i r r e l a t i v e importance t o t h e process has no t been e s t ab l i shed . In t h e s e r ega rds , it should b e recognized t h a t none of t h e present ly-developed t h e o r i e s expla in ing t h e mechanics o f i n f i l t r a t i o n account f o r changes i n s o i l s t r u c t u r e .

INFILTRATION POTENTIAL OF A WATERSHED

Severa l techniques have been presented which may be used t o e v a l u a t e t h e e f f e c t of t h e i n i t i a l s o i l moisture content on t h e i n f i l t r a t i o n r a t e . In o rde r t o apply t h e s e methods c e r t a i n micro- hydrologic and phys i ca l c h a r a c t e r i s t i c s o f a s o i l must b e known such a s , (a) t h e c a p i l l a r y conduct iv i ty-mois ture content curve,


(b) t h e mois ture- tens ion r e l a t i o n s h i p o r (c) an experimental r e l a t i o n between t h e s o i l mois ture conten t and t h e i n f i l t r a t i o n r a t e (as Equation 13) . I t fo l lows t h a t i f t h e s e p r o p e r t i e s f o r a l l s o i l s i n a watershed have been measured then t h e i n f i l t r a t i o n p o t e n t i a l o f t h e watershed a t any t ime could be eva lua ted from s o i l mois ture measurements. Needless-to-say, t h e work involved i n t h i s computation may be reduced app rec i ab ly i f s o i l s could be grouped a s t o t h e i r i n f i l t r a t i o n p o t e n t i a l based on t h e i r s o i l - mois ture r e t e n t i o n and t ransmiss ion c h a r a c t e r i s t i c s . However, a l though it has been found t h a t s o i l s a r e amenable t o grouping i n accordance wi th t h e i r water i n t ake c a p a c i t i e s i n t h e wet cond i t i on it has no t y e t been e s t a b l i s h e d whether a system can be der ived t o group s o i l s a s t o t h e i r i n f i l t r a t i o n r a t e s t o i nc lude t h e e n t i r e range o f mois ture c a p a c i t i e s .

While t h e eva lua t ion o f t h e i n f i l t r a t i o n p o t e n t i a l o f a watershed based on t h e i n f i l t r a t i o n c h a r a c t e r i s t i c s o f i nd iv idua l s o i l s o f t h e ba s in may be f e a s i b l e f o r small experimental ca tch- ments on which t h e necessary measurements a r e taken and l abo ra to ry and a n a l y t i c f a c i l i t i e s a r e a v a i l a b l e , t h i s approach would be imprac t i ca l i n a p p l i c a t i o n t o l a rge watersheds p a r t i c u l a r l y f o r t h e p r a c t i c i n g hyd ro log i s t . Thus, r e s o r t i s f r e q u e n t l y made t o t h e use o f an tecedent p r e c i p i t a t i o n o r groundwater i n d i c e s t o r e f l e c t t h e degree-of-wetness o r t h e i n f i l t r a t i o n p o t e n t i a l o f a ba s in . The common assumption made i n us ing t h e s e i n d i c e s i s t h a t t h e degree-of-wetness p r i o r t o t h e storm i s c l o s e l y r e l a t e d t o t h e s o i l mois ture which i s t h e c o n t r o l l i n g f a c t o r of r u n o f f .

Probably, t h e most common form of an tecedent p r e c i p i t a t i o n index (API) i n c u r r e n t use i s

API = 1 btPt t= 1

i n which bt and Pt a r e r e s p e c t i v e l y a cons t an t and t h e amount of p r e c i p i t a t i o n which occur red a t s e l e c t e d t imes preceding t h e s torm event (days) . Usually, t h e cons t an t bt i s assumed t o be some f u n c t i o n of t ime, t , a s b t = l/t o r b t = k t . According t o t h e l a t t e r express ion , t h e e f f e c t o f p r e c i p i t a t i o n o f t h e wetness of t h e b a s i n decreases exponen t i a l l y wi th t ime. Values f o r t h e cons t an t k a r e u s u a l l y assumed t o be i n t h e range 0.80 - 0.98, however, t h e choice of t h e cons t an t i s n o t c r i t i c a l inasmuch a s t h e c a l c u l a t i o n i s used a s an index of mois ture de f i c i ency . The f i n a l computation o f t h e API f o r a given storm i s obta ined by c a l c u l a t i n g t h e cumulative e f f e c t o f a l l p r e c i p i t a t i o n amounts i n t h e s e r i e s . For example,

API = kP1 + k2p2 + k3p3 + . . . . . knPn (15)

where PI, P2, Pg . .. .. Pn a r e t h e amounts of p r e c i p i t a t i o n a t t h e


d i f f e r e n t time in te rva l s (days) preceding the storm event. Any- where up t o 20 - 60 terms may be used i n the s e r i e s .

Frequent use i s made of indices of t h e type mentioned above i n mul t ip le regression o r graphical or co r re la t ion analyses i n which attempts a r e made t o p red ic t basin y ie ld from storm and watershed c h a r a c t e r i s t i c s . For individual s tud ies , these indices may prove extremely valuable, however, t h e i r general a p p l i c a b i l i t y t o watersheds other than those s tudied i s questionable.

Perhaps a b e t t e r index than those which use only p rec ip i t a t ion i s the basin recharge o r "precipi ta t ion minus runoff", s ince storm runoff does not add t o the res idua l moisture i n the bas in . The United S ta tes S o i l Conservation Service (1957) has es tabl ished type curves f o r estimating runoff from r a i n f a l l based on po ten t i a l basin recharge. Other indices may use accumulative evaporation amounts as an index of f i e l d moisture deficiency o r use base flow discharges as an index of the s o i l moisture s torage p o t e n t i a l . In the use of groundwater flows it i s assumed t h a t a high base flow i s associated with a high runoff po ten t i a l . To be e f f e c t i v e , however, the groundwater index should be supplemented by a weighted r a i n f a l l f a c t o r t o include t h e e f f e c t of r a i n s occurring severa l days preceding t h e event s ince these w i l l a f f e c t the current moisture s t a t u s of the basin.

INFILTRATION TO FROZEN SOILS

For Canadian conditions, no discussion of t h e i n f i l t r a t i o n process would be complete without giving some consideration t o the process of i n f i l t r a t i o n t o frozen s o i l s . A t Saskatoon during 1966-67, G i l l i e s (1968) d id considerable study of the phenomenon under P r a i r i e conditions. His f indings indicated t h a t the moisture p r o f i l e under frozen conditions, and with excess moisture ava i l ab le a t the surface, could be divided i n t o two d i s t i n c t zones, (a) a zone of sa tu ra t ion extending t o the s o i l surface i n which the soil-water matrix was completely thawed and i t s temperature was above 3 2 ' ~ and (b) an unsaturated zone extending a shor t d is tance below t h e thawed layer i n which the l iquid- ice-soi l matrix was below 3 2 ' ~ . Further, he found t h a t as melting pro- gressed it appeared t h a t the elongation of the thawed layer was approximately equal t o the increase i n depth of penetra t ion of the unsaturated zone o r wetting f ron t i n t o the frozen s o i l . Un- l i k e the case of water entry i n t o unfrozen s o i l s i t was observed t h a t the advance of the wet f ron t i n the frozen s o i l was inverse ly r e l a t e d t o t h e s o i l moisture content. That i s , t h e lower the moisture content , the f a s t e r the advance. This r e s u l t would be expected inasmuch as an increase i n moisture content would r e s u l t i n (a) an increase i n the number of the s o i l pores blocked with i c e , (b) an increase i n the s p e c i f i c heat of soil-water matrix and


consequently more heat would be needed per u n i t mass t o cause thawing and (c) a decrease i n the c a p i l l a r y gradient .

Many inves t iga to r s have recognized t h a t the s o i l moisture content i s an important f a c t o r governing i n f i l t r a t i o n t o frozen s o i l s . For example, severa l Russian workers (Larkin 1962, Kuznik and Bezmenov, 1964) and others (Post and Dreibelbis, 1942) repor t tha t i f a s o i l is frozen when i t s moisture content is g rea te r than t h e f i e l d capacity, i t s i n f i l t r a t i o n r a t e w i l l be very low and i f sa tura ted , - t h e in take r a t e i s v i r t u a l l y zero. s imi la r ly , Willis e t aZ. (1961) i n t h e i r s tud ies on small p l o t s i n North Dakota repor t t h a t as much a s 90 per cent of t h e snowpack water i s l o s t a s surface runoff when t h e p l o t s were frozen a t high moisture levels . In t h i s study of i n f i l t r a t i o n t o frozen g l a c i a l t i l l s during t h e "major" thaw period, G i l l i e s (1968) found t h a t t h e volumetric r a t i o of t h e amount of water enter ing t h e frozen s o i l and contained i n t h e upper 18-inch depth of t h e p r o f i l e t o t h e depth of ava i l ab le surface water of t h e snowpack could be r e l a t e d t o t h e i n i t i a l s o i l moisture content of t h e 2-inch surface layer. This r e l a t ionsh ip , shown i n Figure 6, ind ica tes t h a t t h e volumetric i n f i l t r a t i o n t o frozen s o i l s decreases exponential ly with t h e moisture content of t h e surface layer . 1n-these experiments a t t h e time of melt, t h e moisture in- the su r face layer was frozen and thus it would be expected t h a t i n f i l - t r a t i o n would decrease with increasing moisture because of the increase i n number of i c e - f i l l e d pores.

Recognition of t h e dependence of t h e i n f i l t r a t i o n process under frozen conditions on t h e s t a t e and amount of moisture i n t h e surface layer is extremely important t o accurate predic t ion of snowrnelt runoff . I t points out the need t o take these measurements a t t h e time of /or immediately preceding melt and t h a t t h e s o i l moisture s t a t u s evaluated a considerable time i n advance of t h e melting period may not necessar i ly r e f l e c t t h e runoff p o t e n t i a l of a watershed. Even though t h e e a r l i e r measurements may ind ica te the runoff p o t e n t i a l of a watershed t o be very low, these condi- t i o n s may be completely changed by ref reezing of small amounts of meltwater which o r i g i n a t e from minor thawing of the snowpack p r io r t o t h e major melt sequence i n t.he surface of t h e s o i l .

In manner of summary, it would appear t h a t t h e shape of t h e i n f i l t r a t i o n - r a t e curves of a frozen s o i l may adopt severa l d i s t i n c t forms dependent on condit ions which p reva i l a t t h e time of f reezing o r thawing.

1. An in take r a t e which i s reasonably constant with time a t a very low value - a condition which would p reva i l i f frozen while a t a high moisture content o r an impervious layer develops a t t h e surface due t o ref reezing of t h e meltwater a t the time of thaw.


2. An i n t a k e r a t e which decreases very r a p i d l y with time from a reasonably-high i n i t i a l va lue t o near zero - a condi t ion which may p r e v a i l when a s o i l is f rozen a t a low mois ture content bu t t h e s o i l temperature i s below f r e e z i n g . Meltwater e n t e r i n g t h e s o i l i s f rozen i n t h e pores and movement i s i n h i b i t e d .

3. An inc rease i n i n f i l t r a t i o n r a t e with time - a cond i t i on which may e x i s t when t h e s o i l is f rozen a t a h igh mois ture content (70-80 pe r cent f i e l d capac i ty ) . For t h i s case , some of t h e meltwater i s a b l e t o p e n e t r a t e t h e s o i l and thus t r a n s f e r h e a t which i s used t o melt t h e i c e - f i l l e d pores . Progress ive ly , a s t h e s o i l warms and more pores mel t , t h e i n f i l t r a t i o n r a t e i nc reases . Zavodchikov (1962) c i t e s examples i n which t h e i n f i l t r a - t i o n r a t e o f a s o i l increased 6 - 8 t imes i t s i n i t i a l r a t e during t h e mel t ing per iod .

REFERENCES

Ayers, H.D. 1959. Inf luence of s o i l mois ture p r o f i l e and vege t a t i on c h a r a c t e r i s t i c s on n e t supply t o runo f f . Proc. of Symposium No. 1 - Spil lway Design Floods. Queen's P r i n t e r and Con t ro l l e r o f S t a t i ona ry . Ottawa. pp. 198-205.

Bodman, G.B., and E . A . Colman. 1943. Moisture and energy condi- t i o n s during downward e n t r y of water i n t o s o i l s . S o i l S c i . Soc. Amer. Proc. 8: 116-122.

Duley, F.L., and L . L . Kel ly. 1941. Surface cond i t i ons o f s o i l and t ime o f a p p l i c a t i o n a s r e l a t e d t o i n t a k e o f water . USDA C i r c u l a r 608.

Gardner, W., and J . A . Widtsoe. 1921. The movement o f s o i l moisture. S o i l S c i . 11: 215-232.

G i l l i e s , J. 1968. I n f i l t r a t i o n t o f rozen p r a i r i e s o i l s . Un- publ i shed M. Sc. Thesis . , Unive r s i t y o f Saskatchewan, Saskatoon.

Green, R.E. 1963. I n f i l t r a t i o n of water i n t o s o i l s a s in f luenced by antecedent mois ture . D i s s e r t a t i o n Abs. 23: 2270-2271.

Hanks, R.J., and S.A. Bowers. 1962. Numerical s o l u t i o n of t h e mois ture flow equat ion f o r i n f i l t r a t i o n i n t o layered s o i l s . S o i l Sc i . Soc. Amer. Proc. 26: 530-534.

Holtan, H.N. 1961. A concept f o r i n f i l t r a t i o n e s t ima te s i n watershed engineer ing . USDA - ARS 41 - 51, Washington, D.C .


Horton, R.E. 1940. An approach toward a phys i ca l i n t e r p r e t a t i o n of i n f i l t r a t i o n capac i t y . S o i l S c i . Soc. Amer. Proc. 5: 399-417.

Kirkham, D. , and C . L . Feng. 1949. Some t e s t s of t h e d i f f u s i o n theory , and laws of c a p i l l a r y flow, i n s o i l s . S o i l S c i . 67: 29-40.

Kostiakov, A.N. 1932. On t h e dynamics of t h e c o e f f i c i e n t o f water p e r c o l a t i o n i n s o i l s and t h e n e c e s s i t y of s tudying it from dynamic p o i n t o f view f o r purposes of amel iora t ion . Trans. 6 t h Comm. I n t . Soc. S o i l S c i . Russian P t . A15-21.

Kuznik, I.A., and A.I. Bezmenov. 1964. I n f i l t r a t i o n of meltwater i n t o f rozen s o i l s . Sovie t S o i l S c i . No. 7, pp. 665-671. (Trans. S c r i p t a Technica, Inc . )

Larkin, P.A. 1962. Permeabi l i ty of f rozen s o i l s a s a f u n c t i o n o f t h e i r mois ture conten t and f a l l t i l l a g e . Sov ie t Hydrology: S e l e c t e d Papers . No. 4, pp. 445-460. (Amer. Geophys. Un. P u b l i s h e r s ) .

Lewis, M.R . 1937. The r a t e of i n f i l t r a t i o n of water i n i r r i g a t i o n p r a c t i c e . Trans. h e r . Geophys. Union. 2: 361-368.

Moore, R.E. 1949. Water conduct ion from shal low water t a b l e . H i lga rd i a 12: 383-401.

Norum, D.I . , and Don M. Gray. 1964. Unlined mole l i n e s f o r i r r i g a t i o n . Unpublished paper presen ted t o Amer. Soc. Agric . Engr. Mtg., Fo r t C o l l i n s , Colo.

P h i l i p , J . R . 1954. An i n f i l t r a t i o n equa t ion wi th phys i ca l s i g n i - f i c ance . S o i l S c i . 77: 153-157.

P h i l i p , J .R . 1957a. Numerical s o l u t i o n o f equa t ions of t h e d i f f u s i o n type wi th d i f f u s i v i t y concentrat ion-dependent . 11. Aus t r a l i an Jou r . Phys. 10: 29-42.

P h i l i p , J . R . 1957b. The theory of i n f i l t r a t i o n : 5. I n f luence o f i n i t i a l mois ture conten t . S o i l S c i . 84: 329-339.

Pos t , F.A., and F.R. Dre ibe lb i s . 1942. Some in f luences of f r o s t p e n e t r a t i o n and microc l imate on t h e water r e l a t i o n s h i p s of woodland, p a s t u r e and c u l t i v a t e d s o i l s . Proc. S o i l S c i . Soc. h e r . 7: 95-104.

Schi f f , L . , and F.R. Dre ibe lb i s . 1949. Pre l iminary s t u d i e s on s o i l pe rmeab i l i t y and i t s a p p l i c a t i o n . Trans. Amer. Geophys. Un. 30: 759-766.


T i s d a l l , A.L. 1951. Antecedent s o i l moisture and i t s r e l a t i o n t o i n f i l t r a t i o n . Aust. Jou r . Agr. Res. 2: 342-348.

Willis, W.O., C.W. Carlson, J . Aless i , and H . J . Haas. 1961. Depth of f r eez ing and sp r ing runoff a s r e l a t e d t o f a l l so i l -mois ture l e v e l . Can. Jou r . S o i l Sc i . 41: 115-124.

United S t a t e s Department of Agr icul ture , S o i l Conservation Service . 1957. Hydrology. Engineering Handbook, Supplement, Sec t ion 4, ( In se rv i ce use ) .

Zavodchikov, A.B. 1962. Snowmelt l o s ses t o i n f i l t r a t i o n and r e t e n t i o n on drainage bas ins during snow melt ing period i n Northern Kazakhstan. Sovie t Hydrology: Se lec ted Papers No. 1 pp. 37-42. (Amer. Geophys. Un. Pub l i she r s ) .


1 1 1 1 1 1 1 1 1 1 Supply

I I Intensity, i

Infiltration Rate, i

Potential Soil Moisture Storage

Percolation to I Groundwater Lw Groundwater Discharge

Fig. I Conceptual Soil Moisture Model ( i ( f )

1 1 l 1 1 1 1 1 1 1 Supply Intensity , i - - = ? - - Surface Runoff

lnf iltration

I Rate, f

Potential Soil --- --- 1-1 I - Moisture S torage

I Percolation to I Groundwater L I , - ;:pger

Fig. 2 Conceptual Soil Moisture Model ( i ) f )


Volumetric Moisture Content (cm3/ cm.3 ) 0.10 0.20 0.30 0.40

t = 60min., Mf= 3.0

Y

C

8 0 1

Fig. 3 Theoretical Moisture Profiles for Infiltration to a Sandy Loam

Volumetric Moisture Content - Saturation and Transition Zone

Fig. 4 Experimental Moisture Profiles of ter Bodman and Colman ( 1943)

t

0, 0

1 Transmission Zone

wetting zone Wet Front

f


Fig.

Fig. 6

Time - 5 Schematic Representation of the Ef fect of

Soil Moisture on Infiltration Rates

80 '0°1

t Q) C

0 K C 0 . - C

Q, C - iz C -

0 +1---- 20 40 60 80 100

Initial Soil Surface Moisture Con tent 0 - 2 inch Depth ( % by wt.)

The Effect of Surface Soil Moisture on Volumet

Initially Dry to Wet

ric Infiltration to Frozen Soi Is under Prairie Conditions

DISCUSSION ON THE EFFECT OF SOIL MOISTURE ON INFILTRATION AS RELATED TO RUNOFF AND RECHARGE

D r . McDONALD r e f e r r e d t o Equations 7, 10 and 11 of t h e paper and s t a t e d t h a t t h e i n f i n i t e s e r i e s represented by Equation 7 is no t convergent f o r t>l . In t h e example, u se i s made o f Equations 10 and 11 which cons ider only t h e f i r s t t h r e e terms of Equation 7 t o c a l c u l a t e i n f i l t r a t i o n t o a t ime o f 4 hours . D r . McDonald asked A) What a r e t h e u n i t s of time, t, i n Equations 10 and l l ? B) I f t>l , what i s t h e accuracy o f t h e s e equat ions f o r t h e t ime used? and C) What i s t h e upper t ime l i m i t f o r which Equations 10 and 11 a r e v a l i d and how is t h i s determined?

D r . NORUM r e p l i e d t h a t t h e u n i t s of t and t h e c o e f f i c i e n t s must be c o n s i s t e n t wi th t h e u n i t s used f o r t h e c a p i l l a r y conduct- i v i t y and d i f f u s i v i t y . In t h i s ca se it i s cent imeters and minutes. I t i s t r u e t h a t t h e s e r i e s w i l l d iverge a f t e r t has approached some va lue . Equating t h e second d e r i v a t i v e of t h e mass i n f i l t r a t i o n equat ion, f o r example Equation 10, t o zero and so lv ing f o r t w i l l g ive t h e t ime when it would appear t h a t t h e i n f i l t r a t i o n r a t e s t a r t e d t o increase . A s t h i s i s not phys i ca l ly t r u e , as f a r a s t h e t heo ry i s concerned, we would know t h a t t h e equat ion could n o t be v a l i d beyond t h i s time. However, it is p o s s i b l e t h a t even be fo re t h i s t ime t h e equat ion d e v i a t e s from t h e t r u e i n f i l t r a t i o n . In t h e p re sen t case t h e t ime a t which t h e i n f i l t r a t i o n r a t e appears t o s t a r t i nc reas ing i s approximately 8 hours .

D r . DAVAR commented on t h e apparent i s o t r o p i c n a t u r e o f k, i n t h e Richards s o i l mois ture d i f f u s i o n equat ion (Equation 1 ) . He thought t h a t under f i e l d condi t ions 'k ' would probably be non- i s o t r o p i c and thus t a k e on t e n s o r p r o p e r t i e s r a t h e r than s c a l a r , a s t h e equat ion i n d i c a t e s .

Under t h e l a t t e r condi t ions , he asked, A) Would t h e equat ion s t i l l be v a l i d ? and B) What modi f ica t ions would be necessary i n t h e i n t e r p r e t a t i o n of t h i s equat ion?

D r . NORUM i n r e p l y s a i d t h a t when k t a k e s on t enso r p r o p e r t i e s Equation 1 is s t i l l v a l i d a s i t s t ands . I t is s t i l l mathematical ly c o r r e c t , a s a t enso r t imes a v e c t o r is s t i l l a vec to r . However, he d id not know o f any work i n unsa tura ted f low where k has been considered a s anything b u t a s c a l a r .

D r . FREEZE added t h a t Liakopoulos and o t h e r s have published works showing t h a t k i s a symmetric t enso r f o r s a t u r a t e d flow.

D r . BACHMAT s a i d t h a t i n t h e ca se o f an a n i s o t r o p i c s o i l and homogeneous l i q u i d phase and assuming t h a t t h e Darcy law is s t i l l

15 1

152 DISCUSSION ON EFFECT OF SOIL MOISTURE ON INFILTRATION

val id , Equation 1 on page 134 would read:

- ae - - div (k grad a) a t

o r , i n a ca r t e s ian co-ordinate system:

where, k, is a symmetric second order tensor , the p r inc ipa l values and, consequently, t h e p r inc ipa l d i rec t ions of which a r e functions of t h e degree of sa tu ra t ion , e/n, of the l iqu id phase (here n is t h e so-cal led e f f e c t i v e poros i ty of t h e s o i l ) and of t h e density and v i scos i ty of t h a t phase.

D r . DAVAR asked why only, t h e c a p i l l a r y conductivity was used i n Equation 1 when V a contains both a c a p i l l a r y and gravi- t a t i o n a l component.

D r . NORUM r e p l i e d t h a t t h e term c a p i l l a r y conductivity r e f e r s t o t h e hydraulic conductivity when t h e porous medium is unsaturated. I t does not mean t h a t it is only associa ted with the flow due t o c a p i l l a r y forces.

D r . ELRICK pointed out t h e one-dimensional nature of t h e i n f i l t r a t i o n equations prescribed i n the paper i . e . flow i n e i t h e r a hor izonta l o r v e r t i c a l d i rec t ion . A s i n watershed s tud ies , t h e r e i s a g rea t v a r i a b i l i t y i n s o i l s , and hence i n f i l t r a t i o n proper t ies , he wished t o know how these equations could be s a t i s f a c t o r i l y applied t o predic t i n f i l t r a t i o n .

D r . NORUM explained t h a t i f there appears t o be a s i g n i f i c a n t d i f ference i n the i n f i l t r a t i o n c h a r a c t e r i s t i c s of the s o i l over the watershed, then, t h i s watershed w i l l have t o be sub-divided i n t o smaller basins which have more uniform i n f i l t r a t i o n c h a r a c t e r i s t i c s .

D r . GRAY emphasized t h e pe r t inen t nature of D r . E l r i ck ' s statement and added t h a t whereas we may assume t h a t some of t h e i n f i l t r a t i o n equations a r e t h e o r e t i c a l l y cor rec t , t h e problem of t h e i r appl ica t ion t o a watershed u n i t i s very complicated. On a watershed basin not only do we need t o consider the v a r i a b i l i t y of i n f i l t r a t i o n but we must a l s o consider the spac ia l and temporal v a r i a b i l i t y of p rec ip i t a t ion .

In many respects , he bel ieves t h a t t h e c l a s s i f i c a t i o n of a watershed as t o i t s runoff-producing c h a r a c t e r i s t i c s must be consis tent with t h e object ive of our inves t igat ion. That i s , f o r example, i n engineering design i n determining flood peaks on l a rge

DISCUSSION ON EFFECT OF SOIL MOISTURE ON INFILTRATION 153

watersheds, because we a r e deal ing with storms o f long du ra t ion o f reasonably uniform d i s t r i b u t i o n and t h e s to rage elements of t h e watershed a r e s i g n i f i c a n t , it may well be t h a t we can use a s i n g l e i n f i l t r a t i o n curve which r ep resen t s t h e in t eg ra t ed e f f e c t o f a l l s o i l condit ions with reasonable success. Conversely, on small watersheds, on which t h e major po r t ion of t h e runoff may be produced from a small a r ea wi th in t h e bas in , we must employ a source-area concept i n determining t h e peak flow. Obviously, f o r t h i s l a t t e r case we r e q u i r e a much more d e t a i l e d sub-division of a bas in a s t o i t s i n f i l t r a t i o n p r o p e r t i e s i n add i t i on t o a dense p r e c i p i t a t i o n network.

M r . VERMA asked i f Equation 8 could be appl ied t o t h e d e t e r - mination of i n f i l t r a t i o n t o so lone tz i c s o i l s which a r e h ighly cracked a t the su r f ace? If not , then what equation ( i f any) would be app l i cab le f o r t hese s i t u a t i o n s ?

D r . NORUM r e p l i e d i n t h e negat ive s t a t i n g t h a t t h e equations t h a t a r e presented a r e f o r uniform s o i l . I f t h e s o i l is h igh ly cracked a t t h e su r f ace t h e i n i t i a l apparent i n f i l t r a t i o n r a t e w i l l be very h igh and a s soon a s t h e cracks have f i l l e d i t w i l l de- c rease very r ap id ly .

D r . McDONALD a l s o quest ioned Equation 8 and thought t h a t i n s t e a d o f t h e mass i n f i l t r a t i o n being represented by

xde i t should be A e = en - e i . 8 i

D r . NORUM explained t h a t i n Equation 7, x is a funct ion o f t h e moisture content 0 . That i s t o say f o r a given 0 we can c a l c u l a t e t h e depth x a t which t h i s moisture content occurs. We a r e not assuming t h a t t h e s o i l i s s a t u r a t e d above some po in t x. Consequently, we w r i t e t h e i n t e g r a l a s presented i n Equation 8 because we have x as a funct ion of 0 from Equation 7.

d. m. gray and d. i. norumthe effect of soil moisture on infiltration as related to runoff and...

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