Download - Dynamic Simulation Model of Vertical
-
8/10/2019 Dynamic Simulation Model of Vertical
1/10
This article was downloaded by: [139.228.38.243]On: 02 October 2014, At: 02:35Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registeredoffice: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK
Hydrological Sciences JournalPublication details, including instructions for authors andsubscription information:http://www.tandfonline.com/loi/thsj20
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
PLEASE SCROLL DOWN FOR ARTICLE
Taylor & Francis makes every effort to ensure the accuracy of all the information (theContent) contained in the publications on our platform. However, Taylor & Francis,our agents, and our licensors make no representations or warranties whatsoever as tothe accuracy, completeness, or suitability for any purpose of the Content. Any opinions
and views expressed in this publication are the opinions and views of the authors,and are not the views of or endorsed by Taylor & Francis. The accuracy of the Contentshould not be relied upon and should be independently verified with primary sourcesof information. Taylor and Francis shall not be liable for any losses, actions, claims,proceedings, demands, costs, expenses, damages, and other liabilities whatsoeveror howsoever caused arising directly or indirectly in connection with, in relation to orarising out of the use of the Content.
This article may be used for research, teaching, and private study purposes. Anysubstantial or systematic reproduction, redistribution, reselling, loan, sub-licensing,systematic supply, or distribution in any form to anyone is expressly forbidden. Terms& Conditions of access and use can be found at http://www.tandfonline.com/page/terms-and-conditions
http://dx.doi.org/10.1080/02626669109492497http://www.tandfonline.com/page/terms-and-conditionshttp://www.tandfonline.com/page/terms-and-conditionshttp://dx.doi.org/10.1080/02626669109492497http://www.tandfonline.com/action/showCitFormats?doi=10.1080/02626669109492497http://www.tandfonline.com/loi/thsj20 -
8/10/2019 Dynamic Simulation Model of Vertical
2/10
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
Downloadedby[139.228.38.243]at02:3502October2014
-
8/10/2019 Dynamic Simulation Model of Vertical
3/10
-
8/10/2019 Dynamic Simulation Model of Vertical
4/10
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.
Downloadedby[139.228.38.243]at02:3502October2014
-
8/10/2019 Dynamic Simulation Model of Vertical
5/10
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:
Downloadedby[139.228.38.243]at02:3502October2014
-
8/10/2019 Dynamic Simulation Model of Vertical
6/10
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.
Downloadedby[139.228.38.243]at02:3502October2014
-
8/10/2019 Dynamic Simulation Model of Vertical
7/10
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,
-
8/10/2019 Dynamic Simulation Model of Vertical
8/10
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
-
8/10/2019 Dynamic Simulation Model of Vertical
9/10
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
-
8/10/2019 Dynamic Simulation Model of Vertical
10/10
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
Downloadedby[139.228.38
.243]at02:3502October201
4