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 o u t l i n e o f the mechanics of t h e
i n f i l t r a t i o n process. I n t h e discussions, s p e c i f i c a t t e n t i o n i s
given t o t h e q u a n t i t a t i v e influence of the i n i t i a l s o i l moisture
content a s it a f f e c t s both t h e i n f i l t r a t i o n r a t e and t h e 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 accumulates 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. N o r m 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 p r o c e s s water e n t e r s t h e s o i l s u r f a c e
due t o t h e combined i n f l u e n c e 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 f o r c e s 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 p e r c o l a t i o n
downward. C a p i l l a r y 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 ( f e e d e r c a n a l s ) t o c a p i l l a r y pore spaces which
a r e much s m a l l e r i n dimension, but may be v e r y numerous. A s t h e
process c o n t i n u e s , t h e c a p i l l a r y pore spaces become f i l l e d and
with p e r c o l a t i o n 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 i n c r e a s e d r e s i s t a n c e t o flow due t o reduced e x t e n t o r
dimension of flow channels, i n c r e a s e d length of channels, o r an
impermeable b a r r i e r such a s rock o r c l a y . A t t h e same time t h e r e
may be i n c r e a s e d r e s i s t a n c e t o inflow of water a t t h e s o i l s u r f a c e
due t o t h e s u r f a c e 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 r a i n d r o p s 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 a p i d r e d u c t i o n o f i n f i l t r a t i o n r a t e i n t h e f i r s t few hours of a
storm, a f t e r which t h e r a t e remains n e a r l y c o n s t a n t f o r t h e r e mainder o f t h e p e r i o d o f storm r a i n f a l l e x c e s s .
From t h i s q u a l i t a t i v e d e s c r i p t i o n of t h e i n f i l t r a t i o n p r o c e s s
it can be recognized t h a t t h e p r o c e s s involves both t r a n s m i s s i o n
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 s e p a r a t e processes o f :
(a)
Entry of water through t h e s u r f a c e l a y e r , and
(b)
Downward movement o r p e r c o l a t i o n of water through t h e
s o i l profile.
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
p r o c e s s e s 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 c o n t e n t ,
k = t h e c a p i l l a r y c o n d u c t i v i t y , and
@ =
the t o t a l potential.
Equation 1, i s t h e c o n t i n u i t y equation f o r flow which h a s t h e f l u x ,
V , a t any p o i n t d e f i n e d by t h e Darcy e q u a t i o n ,
I t i s evident from Equation 2 t h a t t h e f l u x a t any p o i n t i n a s o i l
EFFECT OF SOIL MOISTURE ON INFILTRATION
135
system, i n c l u d i n g t h e s o i l s u r f a c e , i s p r o p o r t i o n a l t o t h e
h y d r a u l i c o r c a p i l l a r y c o n d u c t i v i t y , k, and t h e t o t a l p o t e n t i a l
g r a d i e n t , VQ. Therefore, t h e i n f i l t r a t i o n process w i l l b e 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 h e s e two q u a n t i t i e s . A l i s t
of t h e most p e r t i n e n t f a c t o r s is shown i n Table 1.
A s shown i n t h e 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 i n c r e a s e i n
t h e s o i l moisture c o n t e n t . Even though e a r l i e r s t u d i e s such a s
t h o s e conducted by S c h i f f and D r e i b e l b i s (1949) and T i s d a l l (1951)
were undertaken i n s p e c i f i c attempt 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 h a s only been i n r e c e n t y e a r s , through t h e o r e t i c a l c o n s i d e r a t i o n
of t h e mechanics of t h e i n f i l t r a t i o n p r o c e s s t h a t g e n e r a l s o l u t i o n s
of t h e equations o f flow have been proposed which may b e used t o
q u a n t i t a t i v e l y e v a l u a t e t h e e f f e c t of s o i l m o i s t u r e on i n f i l t r a t i o n .
Time V a r i a t i o n 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 c o n s t a n t moisture content. Some o f t h e most
common of t h e s e expressions a r e t h e following:
Kostiakov (1932) and Lewis (1937)
Mf = a t n
Gardner and Wid,tsoe (1921) and Horton (1940)
Mf = f c t + de - K t
Kirkham and Feng (1949)
... h o r i z o n t a l
1
Mf = c t ?
+
g
(4)
infiltration
(5)
P h i l i p (1954)
Mf =
st:
+ At
A s i n d i c a t e d , most of t h e equations t a k e t h e form o f an exponential
o r power f u n c t i o n o f time i n which t h e c o n s t a n t s (e.g. a and n of
Equation 3) c h a r a c t e r i z e t h e a b i l i t y of s o i l i n i t s given c o n d i t i o n
t o absorb water.
One of t h e most s i g n i f i c a n t c o n t r i b u t i o n s 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 h e
p r e s e n t e d 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 c o n s t a n t moisture c o n t e n t . The r e s u l t i n g
equation g i v e s t h e d i s t a n c e from t h e s o i l s u r f a c e t o a p o i n t i n
t h e p r o f i l e , a t which t h e moisture c o n t e n t i s 0 a s ,
Table 1
F a c t o r s A f f e c t i n g t n e I n f i l t r a t i o n Rate i n t o unfrozen S o i l
Density
Viscosity
Properties
Moisture Content
Hydraulic
Conductivity
Pore S i z e , Shape,
D i s t r i b u t i o n and
Continuity
Porous Medium
1
Particle Size Distribution
Layering (Homogeneity)
C o l l o i d Content
C o l l o i d Swelling
S a l t Content
Organic Matter
Shrinkage Cracks
Root & Animal A c t i v i t y
L
[ & r f a c e Conditions
Rate
-.
]
S o i l Surface
1
Gradient o f
Potential
I
JPressure
at
p e s s u r e Gradient
Wet Front
--I
L
Gravitational
Gradient
I
Depth t o
Tillage
Packing
1nwash-of P a r t i c l e s
H y d r o s t a t i c Head
Barometric P r e s s u r e
-[
E o i s t u r e Content
S u r f a c e Tension
Contact Angle
k r e s s u r e o f Confined A i r
EFFECT OF SOIL MOISTURE ON INFILTRATION
137
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
8i
This equation, truncated after two terms, is the same as Equation 6.
Similarly, for horizontal flow, only the first term of Equation 9
138
EFFECT OF SOIL MOISTURE ON INFILTRATION
i s n e c e s s a r y t o d e s c r i b e t h e p r o c e s s and t h u s i s analogous t o
Equation 5.
A t t h i s p o i n t it i s worthy t o mention t h a t i n 1962 Hanks and
Bowers p r e s e n t e d a g e n e r a l i z e d numerical s o l u t i o n o f t h e s o i l
m o i s t u r e d i f f u s i o n e q u a t i o n which can be used t o compute i n f i l t r a t i o n i n t o l a y e r e d s o i l s and s o i l s i n which t h e moisture c o n t e n t
i s n o t uniform. Green (1963) i n d i c a t e d 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 r e d i c t e d by t h i s s o l u t i o n and measured
field rates.
E f f e c t o f 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 e q u a t i o n s i s t h a t
by t h e r e l a t i o n s h i p s h e p r e s e n t e d , t h e 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 c o n t e n t o f t h e s o i l can be e v a l u a t e d . 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 e v e l s ; 0.03 cm3/cm3 and 0.23 cm3/cm3. The
r e s u l t s o f t h e c a l c u l a t i o n s a t two t i m e s , 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 i n d i c a t e d 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 following
equations,
The c o e f f i c i e n t s of t h e s e e q u a t i o n s 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 f o r c e s have on t h e i n f i l t r a t i o n process. That i s , t h e f i r s t term ( t 1 / 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 t h u s t h e c o e f f i c i e n t a t t a c h e d t o t h i s
term e v a l u a 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 equation show t h e
e f f e c t o f 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 p r o c e s s of i n c r e a s i n g
t h e i n i t i a l s o i l moisture content is t o decrease 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 and i n c r e a s e t h e e f f e c t o f g r a v i t y . T h i s comes
about because o f t h e d e c r e a s e i n c a p i l l a r y g r a d i e n t and t h e i n c r e a s e i n c a p i l l a r y c o n d u c t i v i t y o f t h e s o i l with an i n c r e a s e i n
moisture content.
From F i g u r e 3 it is a l s o a p p a r e n t t h a t ,
(a)
I n c r e a s i n g t h e i n i t i a l s o i l m o i s t u r e c o n t e n t increases
t h e v e l o c i t y a t which t h e w e t t i n g f r o n t moves b u t
decreases t h e i n f i l t r a t i o n r a t e , and
EFFECT OF SOIL MOISTURE ON INFILTRATION
(b)
139
The i n i t i a l m o i s t u r e c o n t e n t of t h e s o i l a f f e c t s t h e
shape of t h e m o i s t u r e 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 times a f t e r w e t t i n g .
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 a d i e n t a s s o c i a t e d 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 c o n t e n t s . That i s , s i n c e a t t h e
h i g h e r m o i s t u r e c o n t e n t t h e d i f f u s i v i t y i s more n e a r l y c o n s t a n t
and t h e m o i s t u r e g r a d i e n t a c r o s s t h e wet f r o n t i s s m a 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 m o i s t u r e p r o f i l e s developed by P h i l i p ' s method ( a s shown
i n F i g u r e 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 a b o r a t o r y samples by Bodman and Colaan (1943)
( s e e F i g u r e 4 ) . I n comparing t h e s e c u r v e s , it i s e v i d e n t t h a t
t h e y 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
e x i s t e n c e o f a s a t u r a t i o n and t r a n s i t i o n zone n e a r 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 r a n s m i s s i o n zone
extends t o t h e s u r f a c e . 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 n e a r t h e s u r f a c e , a i r may escape
from a s o i l and t h u s i s n o t t r a p p e d 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
m o i s t u r e p r o f i l e s should n o t , however, i n t r o d u c e s e r i o u s 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 i s s m a l l and (b) t h e moisture c o n t e n t i n t h e
t r a n s m i s s i o n zone i s i n t h e o r d e r o f 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 c e n 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 m o i s t u r e 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 f u n c t i o n s : 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. Evaluation o f t h e s e f u n c t i o n s i s u s u a l l y an arduous and
d i f f i c u l t t a s k , 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 o f t h e i n i t i a l s o i l m o i s t u r e c o n t e n t 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 times a f t e r
i n f i l t r a t i o n h a s 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 s u r f a c e m o i s t u r e c o n t e n t , 0, and t h e i n i t i a l s o i l m o i s t u r e
c o n t e n 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 times, 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 m o i s t u r e c o n t e n t because t h e g r a d i e n t i n t h e upper
r e g i o n 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
140
EFFECT OF SOIL MOISTURE ON INFILTRATION
c a p i l l a r y c o n d u c t i v i t y f o r t h e zone. Holtan (1961) r e p o r t e d a
s i m i l a r approach t o d e f i n e 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
f u n c t i o n of t h e exhaustion of s o i l moisture s t o r a g e . The
expression used i s
i n which S = p o t e n t i a l s o i l moisture s t o r a g e volume o r
t h e volumetric d i f f e r e n c e 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 control layer.
fc
=
f i n a l c o n s t a n t r a t e of i n f i l t r a t i o n through
t h e c o n t r o l horizon, and
a , n = c o n s t a n t s f o r a p a r t i c u l a r s o i l i n given
c o n d i t i o n (according t o P h i l i p n = 1/2)
I n Equation 13, t h e e f f e c t of i n c r e a s i n g t h e mass i n f i l t r a t i o n ,
M f , i s analogous t o i n c r e a s i n g t h e ( i n i t i a l ) s o i l moisture c o n t e n t
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
o u t by Holtan, one important a s p e c t of Equation 13 a s a p p l i e d t o
hydrologic a n a l y s e s i s t h a t by subdividing t h e s t o r a g e 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 u s u a l l y 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 f c )
and t h a t t h e a v a i l a b l e water c a p a c i t y i s d e p l e t e d a t a slower
r a t e o f e v a p o t r a n s p i r a t i o n . Another f e a t u r e shown i n t h e equation
i s t h a t when t h e mass i n f i l t r a t i o n Mf, e q u a l s t h e moisture s t o r a g e ,
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 transmission 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 a y e r , once t h e w e t t i n g f r o n t
extended i n t o t h a t l a y e r . Estimates of t h e s e 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
c o n d i t i o n s can be obtained from t a b u l a t e d v a l u e s such a s t h o s e
given by Ayers (1959).
E f f e c t of S o i l Moisture Gradient
I n t h e preceding d i s c u s s i o n s , c o n s i d e r a t i o n has been given
t o t h e e f f e c t of s o i l moisture, which i s 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 p r o c e s s . I n n a t u r e , of course, t h i s
c o n d i t i o n r a r e l y p r e v a i l s b u t most o f t e n , p a r t i c u l a r l y i n t h e
upper r e g i o n of t h e p r o f i l e , t h e s o i l moisture content i n c r e a s e s
with depth. The e f f e c t of t h i s " i n i t i a l " moisture g r a d i e n t cannot
be c a l c u l a t e d by t h e P h i l i p ' s method b u t may be accounted f o r by
t h e method proposed by Hanks and Bowers (1962). I n 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
EFFECT OF SOIL MOISTURE ON INFILTRATION
141
a moisture g r a d i e n t would cause t h e i n f i l t r a t i o n r a t e t o dec r e a s e more r a p i d l y than i n a uniformly d r y p r o f i l e (see F i g u r e 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 F a c t o r s
Influencing I n f i l t r a t i o n
A s p o i n t e d out i n e a r l i e r d i s c u s s i o n s 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 o p i n i o n s 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 c o n d i t i o n s o f 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 t h e y f e l t i t s i n f l u e n c e on t h e 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 l u e n c e o f 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 e p o r t e d t h a t t h e antecedent
moisture c o n d i t i o n s o f a given s o i l may i n f l u e n c e 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
i n t e r d e p e n d e n t . 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 r o s i o n 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 c o n d i t i o n . S i m i l a r l y , t h e amount
o f s h r i n k a g e and s w e l l i n g o f a s o i l i s dependent, i n p a r t , on i t s
s o i l m o i s t u r e c o n t e n t . The volumetric and s t r u c t u r a l changes
which accompany s h r i n k i n g and s w e l l i n g 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 h o s e which may occur i n a heavy c l a y s o i l on d r y i n g .
When a c l a y i s i n a severely-cracked c o n d i t i o n , t h e l a r g e c r a c k s
s e r v e a s f e e d e r c a n a 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 t s 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
p r e s s u r e . Under such c o n d i t i o n s , t h e i n f i l t r a t i o n r a t e w i l l b e
much h i g h e r t h a n i f t h e s o i l were n o t cracked. Likewise, t h e
d e n s i t y and s t a n d o f v e g e t a t i o n , 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
p r o c e s s h a s n o t been e s t a b l i s h e d . In t h e s e r e g a r d s , it should b e
recognized t h a t none o f t h e presently-developed t h e o r i e s e x p l a i n i n g
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
structure.
INFILTRATION POTENTIAL OF A WATERSHED
S e v e r a l techniques have been p r e s e n t e d which may b e 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 c o n t e n t on t h e
i n f i l t r a t i o n r a t e . In o r d e r t o apply t h e s e methods c e r t a i n microhydrologic and p h y s i c a 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 c o n d u c t i v i t y - m o i s t u r e c o n t e n t curve,
142
EFFECT OF SOIL MOISTURE ON INFILTRATION
(b) t h e m o i s t u r e - t e n s i o n r e l a t i o n s h i p o r ( c ) an e x p e r i m e n t a l
r e l a t i o n between t h e s o i l m o i s t u r e c o n t e n t and t h e i n f i l t r a t i o n
r a t e ( a s Equation 1 3 ) . I t f o l l o w s 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 t h e n 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 i m e c o u l d b e e v a l u a t e d from
s o i l m o i s t u r e measurements. Needless-to-say, t h e work i n v o l v e d
i n t h i s computation may b e reduced a p p r e c i a b l y 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 m o i s t u r e r e t e n t i o n and t r a n s m i s s i o n c h a r a c t e r i s t i c s . However,
a l t h o u g h it h a s been found t h a t s o i l s a r e amenable t o g r o u p i n g i n
accordance w i t h t h e i r water i n t a k e c a p a c i t i e s i n t h e wet c o n d i t i o n
it h a s n o t y e t been e s t a b l i s h e d whether a system can b e d e r i v e d
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 n c l u d e t h e
e n t i r e range o f moisture c a p a c i t i e s .
While t h e e v a l u a t i o n 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 n d i v i d u a l
s o i l s o f t h e b a s i n may be f e a s i b l e f o r s m a l l e x p e r i m e n t a l c a t c h ments on which t h e n e c e s s a r y measurements a r e t a k e n and l a b o r a t o r y
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 b e
impractical i n a p p l i c a t i o n t o large 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 h y d r o l o g 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 u s e o f a n t e c e d e n t 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
b a s i n . The common assumption made i n u s i n g 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 m o i s t u r e 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 .
P r o b a b l y , t h e most common form of a n t e c e d e n t p r e c i p i t a t i o n
i n d e x (API) i n c u r r e n t u s e 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 c o n s t a n t and t h e amount o f
p r e c i p i t a t i o n which o c c u r r e d a t s e l e c t e d t i m e s p r e c e d i n g t h e
U s u a l l y , t h e c o n s t a n t bt i s assumed t o b e
s t o r m e v e n t (days)
some f u n c t i o n of t i m e , 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 e x p r e s s i o n , 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
o f t h e b a s i n d e c r e a s e s e x p o n e n t i a l l y w i t h t i m e . Values f o r t h e
0.98,
c o n s t a n t k a r e u s u a l l y assumed t o b e i n t h e r a n g e 0.80
however, t h e c h o i c e o f t h e c o n s t a n 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 i n d e x o f m o i s t u r e d e f i c i e n c y . The
f i n a l computation o f t h e API f o r a g i v e n storm i s o b t a i n e d 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 +
where PI, P2, Pg
..... Pn
.. .. . knPn
(15)
a r e t h e amounts o f p r e c i p i t a t i o n a t t h e
EFFECT OF SOIL MOISTURE ON INFILTRATION
d i f f e r e n t time i n t e r v a l s (days) preceding t h e storm event.
where up t o 20 - 60 terms may be used i n t h e s e r i e s .
143
Any-
Frequent use i s made of indices of t h e type mentioned above
i n m u l t i p l e regression o r graphical o r c o r r e l a t i o n analyses i n
which attempts a r e made t o p r e d i c t basin y i e l d from storm and
watershed c h a r a c t e r i s t i c s . For i n d i v i d u a l s t u d i e s , 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 o t h e r than those s t u d i e d i s questionable.
Perhaps a b e t t e r index than those which use only p r e c i p i t a t i o n
i s t h e basin recharge o r " p r e c i p i t a t i o n minus runoff", s i n c e storm
runoff does not add t o t h e r e s i d u a l moisture i n the b a s i n . The
United S t a t e s S o i l Conservation Service (1957) has e s t a b l i s h e d
type curves f o r estimating runoff from r a i n f a l l based on p o t e n t i a l
basin recharge. Other indices may use accumulative evaporation
amounts a s an index of f i e l d moisture deficiency o r use base flow
discharges a s an index of t h e s o i l moisture s t o r a g e p o t e n t i a l . In
t h e use of groundwater flows it i s assumed t h a t a high base flow
i s associated with a high runoff p o t e n t i a l . To be e f f e c t i v e , however, t h e 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 s e v e r a l
days preceding t h e event s i n c e t h e s e w i l l a f f e c t t h e current
moisture s t a t u s of t h e 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
t h e 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 i d considerable study of t h e phenomenon
under P r a i r i e conditions. His findings indicated t h a t t h e
moisture p r o f i l e under frozen conditions, and with excess moisture
a v a i l a b l e a t t h e surface, could be divided i n t o two d i s t i n c t zones,
(a) a zone of s a t u r a t i o n extending t o t h e s o i l s u r f a c e i n which
t h e soil-water matrix was completely thawed and i t s temperature
was above 3 2 ' ~ and (b) an unsaturated zone extending a s h o r t
d i s t a n c e below t h e thawed l a y e r i n which t h e l i q u i d - i c e - s o i l
matrix was below 3 2 ' ~ . Further, he found t h a t a s melting progressed it appeared t h a t t h e elongation of t h e thawed l a y e r was
approximately equal t o t h e increase i n depth of p e n e t r a t i o n of
t h e unsaturated zone o r wetting f r o n t i n t o t h e frozen s o i l . Unl i k e t h e case of water entry i n t o unfrozen s o i l s i t was observed
t h a t t h e advance of t h e wet f r o n t i n t h e frozen s o i l was i n v e r s e l y
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 t h e
moisture content, t h e f a s t e r t h e advance. This r e s u l t would be
expected inasmuch a s an increase i n moisture content would r e s u l t
i n (a) an i n c r e a s e i n t h e 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
EFFECT OF SOIL MOISTURE ON INFILTRATION
144
consequently more h e a t would be needed per u n i t mass t o cause
thawing and (c) a decrease i n t h e c a p i l l a r y gradient.
Many i n v e s t i g a t o r s have recognized t h a t t h e 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, s e v e r a l Russian workers (Larkin 1962, Kuznik
and Bezmenov, 1964) and o t h e r s (Post and Dreibelbis, 1942) r e p o r t
t h a t i f a s o i l i s frozen when i t s moisture content i s g r e a t e 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 s a t u r a t e d , - t h e i n t a k e r a t e i s v i r t u a l l y zero. s i m i l a r l y ,
Willis e t aZ. (1961) i n t h e i r s t u d i e s on small p l o t s i n North
Dakota r e p o r t t h a t a s much a s 90 p e r cent of t h e snowpack water
i s l o s t a s s u r f a c e runoff when t h e p l o t s were frozen a t high
moisture l e v e l s . 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 e n t e r i n g 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 a v a i l a b l e s u r f a c e 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
s u r f a c e layer. This r e l a t i o n s h i p , shown i n Figure 6, i n d i c a t e s
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
exponentially with t h e moisture content of t h e s u r f a c e l a y e r .
1n-these experiments a t t h e time of melt, t h e moisture i n - t h e
s u r f a c e l a y e r 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 t h e
i n c r e a s e 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 s u r f a c e l a y e r i s extremely important t o accurate p r e d i c t i o n
of snowrnelt runoff. I t p o i n t s out t h e need t o t a k e t h e s e measurements a t t h e time o f / o r 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 o f
t h e melting period may not n e c e s s a r i l y 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 i n d i c a t e
t h e runoff p o t e n t i a l of a watershed t o be very low, t h e s e condit i o n s may be completely changed by r e f r e e z i n g of small amounts o f
meltwater which o r i g i n a t e from minor thawing of t h e snowpack p r i o r
t o t h e major melt sequence i n t.he s u r f a c e 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 s e v e r a l
d i s t i n c t forms dependent on conditions which p r e v a i l a t t h e time
of f r e e z i n g o r thawing.
1.
An i n t a k e r a t e which i s reasonably constant with time a t
a very low value
a condition which would p r e v a i l i f
frozen while a t a high moisture content o r an impervious
l a y e r develops a t t h e s u r f a c e due t o r e f r e e z i n g of t h e
meltwater a t t h e time of thaw.
-
EFFECT OF SOIL MOISTURE ON INFILTRATION
145
2.
An i n t a k e r a t e which d e c r e a s e s v e r y r a p i d l y with time
from a reasonably-high i n i t i a l v a l u e t o n e a r z e r o - a
c o n d i t i o n which may p r e v a i l when a s o i l is f r o z e n a t a
low m o i s t u r e c o n t e n t b u 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 r o z e n i n t h e
pores and movement i s i n h i b i t e d .
3.
An i n c r e a s e i n i n f i l t r a t i o n r a t e with time - a c o n d i t i o n
which may e x i s t when t h e s o i l is f r o z e n a t a h i g h
m o i s t u r e c o n t e n t (70-80 p e r c e n t f i e l d c a p a c i t y ) . For
t h i s c a s e , some o f 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 t h u s 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 p o r e s . P r o g r e s s i v e l y , a s t h e s o i l warms
and more p o r e s m e l t , t h e i n f i l t r a t i o n r a t e i n c r e a s e s .
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 i n c r e a s e d 6 - 8 times i t s i n i t i a l
r a t e during t h e m e l t i n g p e r i o d .
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Kuznik, I.A., and A.I. Bezmenov. 1964. I n f i l t r a t i o n o f m e l t w a t e r i n t o f r o z e n s o i l s . S o v i e t S o i l S c i . No. 7, pp. 665-671.
( T r a n s . S c r i p t a Technica, I n c . )
L a r k i n , P.A.
1962. P e r m e a b i l i t y o f f r o z e n s o i l s a s a f u n c t i o n
o f t h e i r m o i s t u r e c o n t e n t and f a l l t i l l a g e . S o v i e t Hydrology:
S e l e c t e d P a p e r s . No. 4, pp. 445-460.
(Amer. Geophys. Un.
Publishers).
1937. The r a t e o f i n f i l t r a t i o n o f w a t e r i n i r r i g a t i o n
Lewis, M.R.
p r a c t i c e . T r a n s . h e r . Geophys. Union. 2: 361-368.
Moore, R.E.
1949. Water c o n d u c t i o n from s h a l l o w water t a b l e .
H i l g a r d 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 p a p e r p r e s e n t e d t o Amer. Soc. A g r i c .
Engr. Mtg., F o r t C o l l i n s , Colo.
Philip, J.R.
1954. An i n f i l t r a t i o n e q u a t i o n w i t h p h y s i c a l s i g n i f i c a n c e . 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 e q u a t i o n s of t h e
d i f f u s i o n type with d i f f u s i v i t y concentration-dependent.
11. A u s t r a l i a n J o u r . Phys. 10: 29-42.
1957b. The t h e o r y o f i n f i l t r a t i o n : 5. I n f l u e n c e
Philip, J.R.
o f i n i t i a l m o i s t u r e c o n t e n t . S o i l S c i . 84: 329-339.
P o s t , F.A., and F.R. D r e i b e l b i s . 1942. Some i n f l u e n c e s o f f r o s t
p e n e t r a t i o n and m i c r o c l i m a t e on t h e w a t e r 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.
S c h i f f , L . , and F.R. D r e i b e l b i s . 1949. P r e l i m i n a r y s t u d i e s on
s o i l p e r m e a b i l i t y and i t s a p p l i c a t i o n . T r a n s . Amer. Geophys.
Un. 30: 759-766.
EFFECT OF SOIL MOISTURE ON INFILTRATION
147
1951. Antecedent s o i l m o i s t u r e and i t s r e l a t i o n t o
T i s d a l l , A.L.
i n f i l t r a t i o n . Aust. J o u r . Agr. Res. 2: 342-348.
Willis, W.O., C.W. Carlson, J . A l e s s i , and H . J . Haas. 1961. Depth
of f r e e z i n g and s p r i n g r u n o f f a s r e l a t e d t o f a l l s o i l - m o i s t u r e
l e v e l . Can. J o u r . S o i l S c i . 41: 115-124.
United S t a t e s Department o f A g r i c u l t u r e , S o i l Conservation S e r v i c e .
1957. Hydrology. Engineering Handbook, Supplement, S e c t i o n
4, ( I n s e r v i c e u s e ) .
1962. Snowmelt l o s s e s t o i n f i l t r a t i o n and
Zavodchikov, A.B.
r e t e n t i o n on d r a i n a g e b a s i n s d u r i n g snow m e l t i n g p e r i o d i n
Northern Kazakhstan. S o v i e t Hydrology: S e l e c t e d Papers No. 1
pp. 37-42.
(Amer. Geophys. Un. P u b l i s h e r s ) .
148
EFFECT OF SOIL MOISTURE ON INFILTRATION
I
I
-
Supply
Intensity, i
1111111111
I
Percolation to
Groundwater
Infiltration
Rate, i
Potential Soil
Moisture Storage
Lw
Groundwater
Discharge
Fig. I Conceptual Soil Moisture Model ( i ( f )
1 1 l 1 1 1 1=1 ?1 1---
1-1
lnf iltration
Rate, f
I
---
I
---
I Percolation
I
Supply Intensity ,i
Surface Runoff
to
Groundwater
,
Potential Soil
Moisture S torage
I
L
;:pger
Fig. 2 Conceptual Soil Moisture Model ( i ) f )
EFFECT O F SOIL MOISTURE ON INFILTRATION
149
Volumetric Moisture Content (cm3/ cm.3 )
0.20
0.10
t
0.30
0.40
= 60min., M f =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
t
Transmission Zone
0,
0
1
wetting zone
f
Wet Front
Fig. 4 Experimental Moisture Profiles of ter
Bodman and Colman ( 1943)
EFFECT OF SOIL MOISTURE ON INFILTRATION
150
t
Q)
C
0
Initially Dry to Wet
K
C
.0
-
C
Q,
C
iz
C
Time
-
Fig. 5 Schematic Representation of the E f f e c t of
Soil Moisture on Infiltration Rates
'800° 1
0+
1
20
40
60
80
100
Initial Soil Surface Moisture Con tent
0 - 2 inch Depth ( % by wt.)
Fig. 6 The E f f e c t of Surface Soil Moisture on Volumet 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 o f 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 r e p r e s e n t e d by Equation 7 i s
n o t convergent f o r t > l . I n t h e example, u s e i s made o f Equations
10 and 11 which c o n s i d e r o n l y t h e f i r s t t h r e e terms o f 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 time o f 4 hours. D r . McDonald
asked A) What a r e t h e u n i t s o f 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 equations f o r t h e time
used? and C) What i s t h e upper t i m e 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 o f 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 w i t h t h e u n i t s used f o r t h e c a p i l l a r y conducti v i t y and d i f f u s i v i t y . I n t h i s c a s e it i s c e n t i m e t e r s 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 i v e r g e a f t e r t has approached some
v a l u e . 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
equation, f o r example Equation 10, t o zero and s o l v i n g f o r t w i l l
g i v e t h e time 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 is not physically true, as f a r as
t h e t h e o r y i s concerned, we would know t h a t t h e equation could
n o t be v a l i d beyond t h i s time. However, i t i s p o s s i b l e t h a t even
b e f o r e t h i s time t h e e q u a t i o n 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 r e s e n t case t h e time 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 n c r e a s i n g i s approximately 8 h o u r s .
D r . DAVAR commented on t h e a p p a r e n t 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 m o i s t u r e d i f f u s i o n equation (Equation 1 ) .
He thought t h a t under f i e l d c o n d i t i o n s 'k' would probably be noni s o t r o p i c and t h u s 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 equation i n d i c a t e s .
Under t h e l a t t e r c o n d i t i o n s , h e asked, A) Would t h e equation
s t i l l b e v a l i d ? and B) What m o d i f i c a t i o n s would b e n e c e s s a r y i n
t h e i n t e r p r e t a t i o n o f t h i s equation?
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 e n s o r p r o p e r t i e s
Equation 1 i s s t i l l v a l i d a s i t s t a n d s . I t i s s t i l l mathematically
c o r r e c t , a s a t e n s o r times a v e c t o r i s s t i l l a v e c t o r . However,
he d i d n o t know o f any work i n u n s a t u r a t e d flow where k h a s 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 e n s o 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 c a s e 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 i s s t i l l
151
152
DISCUSSION ON EFFECT OF SOIL MOISTURE ON INFILTRATION
v a l i d , Equation 1 on page 134 would read:
ae at
d i v (k grad a)
o r , i n a c a r t e s i a n co-ordinate system:
where, k, i s a symmetric second order t e n s o r , t h e p r i n c i p a l values
and, consequently, t h e p r i n c i p a l d i r e c t i o n s of which a r e functions
of t h e degree of s a t u r a t i o n , e/n, of t h e l i q u i d phase (here n i s
t h e s o - c a l l e d e f f e c t i v e p o r o s i t y of t h e s o i l ) and of t h e density
and v i s c o s i t y 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 g r a v i 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 i t is only a s s o c i a t e d with t h e 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 t h e paper i . e . flow i n e i t h e r
a h o r i z o n t a l o r v e r t i c a l d i r e c t i o n . A s i n watershed s t u d i e s ,
t h e r e i s a g r e a 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
p r o p e r t i e s , he wished t o know how t h e s e equations could be
s a t i s f a c t o r i l y applied t o p r e d i c t i n f i l t r a t i o n .
D r . NORUM explained t h a t i f t h e r e appears t o be a s i g n i f i c a n t
d i f f e r e n c e i n 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 of t h e s o i l over
t h e 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
characteristics.
D r . GRAY emphasized t h e p e r t i n e n t n a t u r e of D r . E l r i c k ' 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 c o r r e c t , t h e problem of
t h e i r a p p l i c a t i o n t o a watershed u n i t i s very complicated. On a
watershed basin not only do we need t o consider t h e 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 t h e s p a c i a l and temporal
v a r i a b i l i t y of p r e c i p i t a t i o n .
In many r e s p e c t s , he b e l i e v e s t h a t t h e c l a s s i f i c a t i o n of a
watershed a s t o i t s runoff-producing c h a r a c t e r i s t i c s must be
c o n s i s t e n t with t h e o b j e c t i v e o f our i n v e s t i g a t i o n . That i s , f o r
example, i n engineering design i n determining flood peaks on l a r g e
DISCUSSION ON EFFECT OF SOIL MOISTURE ON INFILTRATION
153
watersheds, because we a r e d e a l i n g with storms o f long d u r a t i o n
o f r e a s o n a b l y uniform d i s t r i b u t i o n and t h e s t o r a g e elements o f
t h e watershed a r e s i g n i f i c a n t , it may w e l l b e t h a t we can u s e a
s i n g l e i n f i l t r a t i o n curve which r e p r e s e n t s t h e i n t e g r a t e d e f f e c t
o f a l l s o i l c o n d i t i o n s with r e a s o n a b l e s u c c e s s . Conversely, on
s m a l l watersheds, on which t h e major p o r t i o n o f t h e r u n o f f may be
produced from a s m a l l a r e a w i t h i n t h e b a s i n , we must employ a
s o u r c e - a r e a concept i n determining t h e peak flow. Obviously, f o r
t h i s l a t t e r c a s e we r e q u i r e a much more d e t a i l e d s u b - d i v i s i o n o f
a b a s i n 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 a d d i t i o n 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 a p p l i e d t o t h e d e t e r mination o f i n f i l t r a t i o n t o s o l o n e t z i c s o i l s which a r e h i g h l y
cracked a t t h e s u r f a c e ? If n o t , then what e q u a t i o n ( i f any) would
be a p p l i c a b l e f o r t h e s e 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 n e g a t i v e s t a t i n g t h a t t h e e q u a t i o n s
t h a t a r e p r e s e n t e d a r e f o r uniform s o i l . I f t h e s o i l is h i g h l y
cracked a t t h e s u r f a c e t h e i n i t i a l a p p a r e n t i n f i l t r a t i o n r a t e w i l l
be v e r y h i g h and a s soon a s t h e c r a c k s have f i l l e d i t w i l l decrease very rapidly.
D r . McDONALD a l s o q u e s t i o n e d 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 b e i n g r e p r e s e n t e d by
xde i t should b e
Ae
=
en
-
ei.
8i
D r . NORUM e x p l a i n e d t h a t i n Equation 7, x is a f u n c t i o n o f
t h e m o i s t u r e c o n t e n t 0 . That i s t o s a y 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 c o n t e n t o c c u r s . 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 p o i n t x.
Consequently, we w r i t e t h e i n t e g r a l a s p r e s e n t e d i n Equation 8
because we have x a s a f u n c t i o n of 0 from Equation 7.