Dynamic Simulation Model of Vertical

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Dynamic simulation model of vertical

infiltration of water in soilVALERIJ YURIEVICH GRIGORJEV a& LSZL IRITZ b

aState Hydrological Institute , 2 Linija 23, SU-199053,

Leningrad, USSRbDepartment of Hydrology , Uppsala Univeristy , Vstra gatan24, S-753 09, Uppsala, SwedenPublished online: 29 Dec 2009.

To cite this article:VALERIJ YURIEVICH GRIGORJEV & LSZL IRITZ (1991) Dynamic simulationmodel of vertical infiltration of water in soil, Hydrological Sciences Journal, 36:2, 171-179, DOI:10.1080/02626669109492497

To link to this article: http://dx.doi.org/10.1080/02626669109492497

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Hydrological Sciences - Journal - des Sciences Hydrologques, 3 6 ,2, 4/1991

Dynamic s imulat ion model o f vert ica l

infiltration of water in soil

VALERIJ YURIEVICH

GRIGORJEV

State Hydrolog ical Institute, 2 Linija 23, SU-199 053 Leningrad, USSR

LSZLmrrz

Uppsala

Univeristy,

Departm ent of Hydrolog y, Vstra gatan 24,

S-753 09 Uppsala, Sweden

Abstract One of the most important problems of hydrological

forecasting is to obtain a reliable estimation of effective rain.

Infiltration is one of the variables which greatly influences the

partitioning of rainfall into surface runoff and subsurface flow.

This paper presents an infiltration model which describes the

unsaturated zone as a multi-layer system. For this purpose a

relationship developed by Denisov (1978) for total hydraulic

potential versus soil moisture conten t has been used. The model

contains a system of ordinary differential equations for describing

soil moisture movement and it can be interpreted as an aggre

gated simulation model with lumped param eters. Som e basic

equations and results of simulation runs are presented.

Modle dynamique de simulation de l'infiltration verticale de l'eau

dans le sol

Un des plus importants problmes dans la prvision hydrologique

est l'estimation fiable des prcipitations efficaces. Dans ce cas

l'infiltration est considre comme tant un point crucial. Ce

papier prsente un modle d'infiltration qui dcrit la zone non

sature comme un systme multicouche. Le modle comport un

systme d'quations diffrentielles dcrivant le mouvement de

l'humidit du sol et peut tre considr comme un modle de

simulation global avec des paramtres globaux. Quelques quations

de base ainsi que les rsultats des simulations sont prsents.

INTRODUCTION

The estimation of infiltration is one of the most difficult problems of

hydrological forecasting. The infiltration capacity of soil largely influences, in

the first phase, the amount and temporal partitioning of rainfall into runoff

and surface storage during a given storm. Infiltration is primarily controlled

by factors governing water movem ent in the soil. Initial wa ter conten t and

variations in soil water characteristics near saturation have a very strong

influence on predicted infiltration. Although the character of the phenomenon

is complex, sophisticated methods are rarely applied because of the

Open for discussion until 1 October 1991

111

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173

Dynamic simulation

m odel of

vertical infiltration

rate and includes five varying parameters estimated off-line.

There are many infiltration equations that have originated

in

the analysis

of field data. Field applications are usually based

on

either simplified concepts

or empirical formulae expressed

in

time and some othe r soil parameters. The

parameters

for

such models

are

obtained from soil water measurements

or

are estimated (Skaggs

&

Khaleel, 1982). Num erous empirical formulae have

been developed attempting

to

approximate

the

infiltration rate

of

water

through the soil surfaceby decreasingit monotonically with time. Oneofthe

simplest was proposed by Kostiakov (1932). Ho rton (1939) gaveanempirical

formula which

is

still widely used today.

Some benefits may be obtained from coupled models which jointhe

simple methods

and the

physics involved

in the

Richards equation.

The

model proposed

by

Pingoud

&

Orava (1980)

is an

approximate lumped

type model which uses the conservation equation to derive an analytical

formula

for the

flow rate from

one

storage

to

another.

The

soil

is

divided into layers having certain physical soil constants . Each layer

is

considered

to be a

storage

for

moisture.

The

flow ra te from

one

layer

to

the next is assumed to be proportional to the gradient in moisture

content between layers.

PROPOSED SIMULATION MODEL

The lumped parameter model

of

the m ulti-layer system described below trie s

to avoid

the

above-mentioned problems because

it

does

not

require

the

complete solution

of

the Richards equation,

but

the physical meanings

of

the

parameters remain.

The soil is approximated as several layers each with certain soil

characteristics

of

their own,

as

presented

in

Fig.

1. The

mass conservation

equationfor each moisture storageof the systemisgiven as:

df

i-IT =*/-*/+ C

1

)

where

P.is the

porosity; tj>

(

.

is the

relative m oisture conten t (degree

of

pore

saturation)

in

layer

i

with thickness A. (which varies

for

different layers); and

q

i

is

the flux

of

water through layer

i

and across the boundary between layers

/ andi + 1.

For simplicity the condition:

- = 0 2)

is assumed

for the

layer

n.

Physically, this means that

the

level

of the

groundwater table

is

constant.

In

general this restriction

is

quite limiting but

itisacceptablefor the estimationof excess precipitation.



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Valerij Yurievich Grigorjev Lszl Iritz

174

n

layer

TABLE LEVEL

Fig. 1 Multi-layered system of soil in the model: z. is thickness of

layer i; and q

i

is flux of water through the bounda ry between

layers i and i+1.

The general formula of the flux can be expressed as:

->

q =

-K(4>)grad

i

_

1

,4>)

W ) - W

M

)

z z

,

4)

where K

{

is the harmonic mean between the hydraulic conductivities of layers

(J?

- 1) and

i.

Its value can be computed as has been given by Rees & Sparks

(1969):

K:

2K(0.)

KW..J

K .)

K(4>

,-.

j)

(5)

Denisov (1978) proposed to express the hydraulic conductivity of a

partially saturated soil as:

* ( * , )= K

s

t

i a - 4>,r

(6)

where K

s

is the hydraulic conductivity in saturated conditions. A frequently

used form for the conductivity of a partially saturated soil, developed by

Irmay (1966), is:



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175

Dynamic simulationmodel ofvertical infiltration

K = K

i - v

1 - * ,

7)

0 J

where

4>

0

is the immobile water conten t of the dry sample. The range of

variation of i/

0

is between 0.0 and 0.1. The hydraulic conductivity computed

by equation (6) for lower saturations approaches half the value given by

equation (7), and the computed values are close to each other when the

saturation degree, , is close to 1.

The total hydraulic potential of soil moisture was expressed by Denisov

(1978) as:

m

t

)=

-Z i

+

A

y

+ ( 1 -

4>i)'

h

+A

2i

In

1 + (1 - 0. )

1 - (1 - * ,)

Vi

8)

where A

u

, A

2i

and m are hydrophysical characteristics of the soil related

to the matric and capillary potentials.

The proposed model includes equations (1), (2), (4), (5), (6) and (8).

This system of ordinary differential equations has been solved by the

Adams-Multon algorithm for given initial conditions (initial moisture profile

of the soil) h = 0,

iQ

i e [1,n] and input r(f). The block scheme of

initial and upper boundary conditions is shown in Fig. 2.

A,;: A

2 i

i m; Z;; P|: K.

h ; f i o ; r ( t ) ; T

i ;

T

2

So l u t i o n o f t h e sys t e m

o f t h e o r d i n a r y d i f f e -

r e n t i a e q u a t i o n s

INPUT

LOGICAL CONDITIONS

h(t), f(t)

OUTPUT

Fig. 2 Block scheme of initial and upper bounda ry co nditions.



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Valerij Yurievich Grigorjev Lszl Iritz 176

The rainfall excess is given by:

h{t) =r(t) - q

x

(9)

where

r(t)

is the rainfall rate and

q

i

is the surface infiltration flux into the

first storage and written as:

1\

r(t) if q^>r(f)

0 ifr{t)= 0

qy> otherwise

(10)

where

q^

is given by the model equations . The infiltration into the first layer,

q

v

is a dynamic param eter which depends on the rainfall rate and on the soil

moisture redistribution between the neighbouring layers. The hydrostatic

pressure of the ponded water height

(h

0) is not taken into account.

According to Schmid (1989), the errors produced by neglecting this influence

on rainfall excess are sufficiently small compared to the uncertainty

introduced by inaccurate soil data.

Using absolute values under the roots in equation (8) for total hydraulic

potential versus soil moisture, one can avoid the problems which occur when

0. is close to 1.0. Physically, that means that the soil has a flexible defor

mation and that the soil total hydraulic potential function,


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177 Dynamic simulationm odel ofvertical infiltration

With a given rainfall rate (Fig. 3: (I)), excess rainfall was simulated on

unlayered and layered homogeneous soil profiles (Table 1: simulation runs

( l ) - (3) ) .

The infiltration was stabilized at different levels for 1.5 h in all three

cases but the number/thickness of layers strongly affected the calculated

volume of excess rainfall (Fig. 3). Excess rainfall appeared first on the profile

divided into a maximum of ten layers and last on homogeneous soil. The

excess rain on average for a soil with five layers is twice as high as on the

unlayered soil, and 2.5 times higher on ten layers of soil than on five.

mm/hour

3.0

hours

0 -

/

/

/

, ' /

/ /

/

1

1

/

1

/

1

/

/

/ /

^-~~~

-~

A n h o

h o

1 0 l a y e r s ( 3 )

5 l a ve r s / 9 1

mog


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Valerij Yurievich Grigorjev Lszl Iritz

178

within the profile is simulated by movement of the intermediate block

boundaries (upward and downward) in response to the potential gradient

between adjacent blocks. This method was further improved by Markar &

Mein (1987).

With the rainfall rate (II), excess rainfall was simulated on a homoge

neous (4) and an inhomogeneous (5) soil profile (Table 1). In the case of the

inhomogeneous profile, the second layer in the unsaturated zone had low

conductivity (assuming e.g. clay). The excess rainfall on the inhomogeneous

profile turned out to be twice as high as on the homogeneous one (Fig. 3).

Many authors have emphasized that the hydrological importance of the

topmost layer is extremely large because infiltration depends strongly on its

actual sta te. Numerical analysis in this study pointed out also that the initial

water content of the first layer (0 to some 300 mm from the surface) has a

particularly important role.

CONCLUSION

There are many questions in hydrology (e.g. water erosion, pollutant transport,

aspects of human activities etc.) which require the application of complex

watershed models. In those models, all the main processes such as

evaporation, overland flow, infiltration, etc. should be modelled in a more

complex manner than can be done by simplified methods. The movement of

water through and within the upper zone of soil has a very high practical

importance for surface flow generation. At the same time, the character of

the phenomenon makes the theoretically well-based methods complicated. On

the other hand, empirical formulae abandon a large part of the physical

significance. That is the reason why an approximate method was tested

herein. The model tested does not require the complete solution of the

Richa rds equation. Relationships developed by Denisov (1978) for hydraulic

conductivity in unsaturated soil and for total hydraulic potential versus soil

moisture content have been used in this model.

The authors of this paper are well aware that the model presented is an

approximate on e. It may be accurate enough, however, for practical purposes,

and due to its comparatively simple structure it is well suited for use as a

component within a complex watershed model.

Acknow ledgements The authors wish to thank Professor L. Bengtsson and

Dr H. B. Schmid for their valuable editorial suggestions and Dr R. Saxena

for language editing.

REFERENCES

Abbo t M. B., Bathurst, J. G, C unge J. A., O'Connell, P. E. & Rasm ussen J. (1986a) An intro

duction to the Euro pean H ydrological System - Systme Hydrologique Europen , SHE . 1:

History and philosphy of a physically-based, distributed modelling systyem. /. Hydrol. 87,

45-69.

Abbo t M. B., Bathu rst, J. C , Cunge J. A., O'Connell, P. E. & Rasm ussen J. (1986b) An intro-

Downloadedby[139.228.38

.243]at02:3502October201

4


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179

Dynamic simulation

mo del of

vertical infiltration

duction to the Eu ropean Hydrological System - Systme Hydrologique Euro pen, SHE . 2:

Structure of a physically-based, distributed modelling sysryem. /. Hydrol.87,61-77.

Clapp, R. B. (1982) A wetting front m odel of soil water dynamics. PhD d issertation, D epart

me nt of Environm ental Sciences, University of Virginia, C harlottesville, Virginia, USA.

Denisov, U. M. (1978) The movement of water vapor and salts in soil. /.Met. Hydrol.3,Moscow

(in Russian), 71-79.

Gre en, W. H. & Ampt, G. A. (1911) Studies of soil physics. Flow of air and water through soils.

/ .Agric. Sci.no. 4, 1-24.

Ho rton , R. E . (1939) Analysis of runoff plot experim ents with varying infiltration ca pacity.

Trans. AGUVart IV, 693-694.

Irmay, S. (1966) Solution of the nonlinear diffusion equation with a gravity term in hydrology.

IAHS

Symposium

on

Water

in the

Unsaturated

Zone, Wageningen, The Netherlands.

Kostiakov, A. N. (1932) On the dynamics of the coefficient of water perco lation in soils and

necessity for studying it from a view for purposes of amelioration, Trans. 6th Com. Int.

Soc. Soil

Sci.,

Russian Part A,

17-21.

Kovcs, G. (1981) Hydrological investigateion of the soil-moisture zone . In: Subterranean Hydro

logy,d. G. Kovcs, Water Resources Publications, Colorado, USA, 227-402.

M arkar, M. S. & Mein, R.G . (1982) Modeling of vapotransp iration from hom ogeneous soils.

Wat.

Resour.

Res.23(10), 2001-2007.

Mein, R. G. & Larson, C. L. (1973) Modeling infiltration during a steady rain. Wat. Resour.

Res.

9(2), 384-394.

Morel-Seytoux, H. I. (1981) Application of infiltration theo ry for determ ination of excess

rainfall hyetograph.

Wat. Resour. Bull.

17(6), 1012-1022.

Philip, J. R. (1957) The theory of infiltration: Sopriviry and algebraic infiltration equatio ns.

Soil Sci.84, 257-264.

Pingoud , K. & Orava, P. J. (1980) A dynamic model for vertic al infiltration of wa ter into the

soil.InstituteofSystemSciences,11(12).

Ree s, K. P. & Sparks, W. F. (1969) Algebra and Trigonometry.McGraw-Hill Book Co. Inc., New

York, USA.

Ric hard s, L. A. (1931) Capillary conduction through porou s media.Physics1,313-318.

Schmid, B. H. (1989) On ove rland flow modelling: Can rainfall excess be trea ted as

independent of flow depth. /.

Hydrol.

107,1-8.

Skaggs, R. W. & Khaleel, R. (1982) Infiltration. In: Hydrological Modeling of Small Watersheds

ed. T. C. Haan, H. P. Johnson & D. L. Rakensiek, ASEA Monograph no. 5, Michigan,

USA, 121-166.

Received 30 May

1990;

accepted 15 November 1990

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Dynamic Simulation Model of Vertical