Keulen, H., van

English

Keulen, van, H.

NARCIS 

The use of simulation models in the study of soil moisture transport processes

Wageningen Yield 

Modeling and Simulation of Water Resources Systems, G.C. VANSTEENKISTE, (Ed.) 
North-Holland Publishing Company (197 5) 
ABSTRACT 
THE USE OF SIMULATION MODELS IN THE STUDY OF SOIL 
MOISTURE TRANSPORT PROCESSES 
H. van Keulen 
Department of Theoretical Production Ecology 
Agricultural University 
Hageningen, The Netherlands 
The development of high speed computers in recent years, along with the 
availability of sophisticated simulation languages facilitate the use of 
computer models in the study of transport processes in soils. 
It is shown that a model of evaporation from the soil surface yields 
satisfactory results and special difficulties encountered during its 
development and operation are discussed. 
Special attention is paid to the hierarchical approach in model building 
as a means of overcoming problems of multilevel models as well as those 
of very costly and time consuming execution of detailed models. 
It is concluded that simulation models are a strong tool in the study of 
transport processes in the soil, not only in solving specific problems but 
also in pinpointing to weak areas in our knowledge and hence to the 
design of new experiments. 
INTRODUCTION 
Transport processes in the rather complicated porous soil system play an 
important role in many disciplines. Agronomists are dealing with them because they 
govern processes of plant growth by supplying the necessary water and minerals to 
the plant root. In more recent years, specially water management engineers, 
responsible for the continuous supply of good quality water for human consumption 
and agricultural purposes are interested in the behaviour of the soil water, and 
those concerned with problems of pollution are forced to predict the fate of 
solutes landed in the soil on purpose or accidentally. 
The transport processes are characterized by a simultaneous change in the 
amount of material with time and place. In mathematics such distributive systems 
are described by partial differential equations. Analytical solutions for these 
equations can in general only be found for problems that are so simple, that they 
are only of academic interest, or under greatly simplifying assumptions making 
the conclusions arrived at of little practical value. Hhere the analytical solutions 
fail to provide an answer, the brute force of the computer may help to solve the 
problem. 
The development of sophisticated simulation languages containing features 
to overcome the main disadvantages of digital calculation machines, which contrary 
to natural systems operate discontinuously and sequentially, has facilitated the 
use of these machines. Moreover these languages easily handle problems of numev£eal 
integration, providing a number of methods each with its own advantages in specific 
situations. 
The application of one of these languages, the Continuous System Modeling 
Program (CSMP), developed by IBM for its 360 and 370 series of machines for the 
291 
292 H. Van Keulen 
development of simulation models for transport processes in the soil has been 
demonstrated by De Wit & Van Keulen (1972). In this paper a model for soil 
evaporation is described and a technique to use such models in plant productivity 
studies is proposed. 
THE EVAPORATION MODEL 
Evaporation from the soil surface is one of the main causes of non-
productive water loss under conditions where the atmospheric demand is high (arid 
and semi-arid regions) and the soil is not or only sparsely covered for prolonged 
periods of time. To estimate the amount of water available for plant growth, it 
is of primary importance to be able to predict the evaporative losses. For this 
purpose a simulation model was developed that calculates the evaporative flux from 
a bare soil surface from meteorological data and from physical properties of the 
soil. A detailed description of this model is presented elsewhere (Van Keulen, 1974). 
Based on the principles of the finite difference method, as pointed out by 
De Wit & van Keulen (1972), the simultaneous flow of heat and water in a soil column 
is calculated. 
Moisture is transported either in liquid form under a potential gradient or 
in the vapor phase under a gradient of vapor pressure, taking into account the 
appropriate transport coefficients. 
Heat is transported by diffusion along a temperature gradient and by mass 
transport along with the flow of water. 
The surface temperature is calculated from the energy balance at the soil 
surface: absorbed short wave radiation, sensible heat loss, outgoing long wave 
radiation, heat flow into or out of the soil and evaporative heat loss. 
The evaporative heat loss is obtained from the difference in vapor pressure 
between the soil surface and the atmosphere and the aerodynamic resistance for 
vapor transport above the soil surface. The aerodynamic resistance is calculated 
from the wind speed, taking into account the roughness height of the surface 
elements, according to a semi-empirical formula developed by Chamberlain (1968). 
The vapor pressure at the soil surface is obtained from the surface temperature, 
taking into account the vapor pressure depression due to increasing soil moisture 
potential. 
Sensible heat loss is calculated from the temperature difference between 
the soil surface and the atmosphere and the resistance for heat exchange, the latter 
being proportional to the vapor exchange coefficient. Outgoing long wave radiation 
is estimated with an empirical formula given by Brunt (1932). Soil heat flux is 
calculated from the difference in temperature between the soil surface and the 
middle of the first, I em thick, compartment, and the moisture content dependent 
heat conductivity of the soil. 
In figure I the measured and calculated cumulative evaporation of a uniform 
loss column under laboratory conditions is given, while in fig. 2, the measured 
(y-ray attenuation)and calculated soil moisture profiles are compared. The agreement 
in the cumulative evaporation is excellent, the moisture profiles however show 
deviations. This may be attributed to disturbances in the soil column, as the 
drying of the soil caused shrinkage, leading to cracks at the soil surface and 
to the development of air spaces at some points along the perspex walls. These 
disturbances presumably caused changes in the hydraulic properties of the soil, 
while in the simulation program constant K-8 and ~-8 relations are used. Moreover 
these relations were determined in duplicate columns, which may not have been 
completely identical, thus causing different hydraulic properties too. 
Simulation models in soil moisture transport processes 
cumulative evaporation 
100 
5 10 
-><-simulated 
o measured 
15 20 
time 
days 
Fig. 1. Comparison between measured and simulated cumulative evaporation 
from a uniform column of loss . 
. 05 .10 
.10 .15 .20 .25 _30 cml cm-l 
10 \ "·~ \ 
., \\ '- \1 • \ ·'-, -.....-.......... '\. ' 
\ '\ \ \~ \~:. 
\ "'·,, '"-, 
~ \ \ 
20 \ \ \, ~ 
\\\o ""\ ! 30 '\ '-.zo \ \. \ \: \ \ \ \! 
40 \. \\ : \\ ~ '\ \1 50 
60 
70 
60 
em 
90 
\ ·~ 
\\~ I 
I \ i 
\ \ \ i 
\ \ \\ 
\\\\\ 
i 
(a) (b) 
depth depth 
Fig. 2. Measured (a) and simulated (b) soil moisture profiles in a 
uniform loss column under constant evaporative conditions. 
Numbers along the graph indicate days after the start of the 
experiment. 
293 
294 H. Van Keulen 
It may be concluded however that the present model gives satisfactory results in 
predicting the evaporative water loss from a bare soil surface. This is supported 
by the results shown in figure 3, where the same model has been applied to a field 
situation. 
5 
10 
15 
20 
.05 .10 .15 .20 .25 .30 .35 cml em- 3 
•·• •• •S-;,:.. ""-.,. moisture content 
··---....:::.:···,t=4"\ rinrtial A·'·\·~ 
h14. ~ \ t\ 
'\'\ \\\ 
\\·::\ 
-•- simulated 
'\, '•\ \\ "(\\ ···•··· measured \I \\ ', 
25 ~ \! 
em depth • l I 
3o --- -- - _ -- _ - ______ L __ U _ 
60 
50 
40 
30 
20 
10 
cumulative 
evaporation 
-•- soil evaporation 
••• •••• penman evaporation 
time 
~--------~----------~----------~~days 
Fig. 3. Comparison be t~.;reen 
measured and simulated soil 
moisture profiles and 
cumulative evaporation from 
a field experiment in Avdat, 
Israel. 
The determination of the physical parameters of the soil, specially under 
field conditions, is still one of the biggest problems in the modeling approach. 
Although it is possible to test the validity of a model under laboratory conditions 
and to estimate the physical properties from a given field by successive trial and 
error through comparison with actual field data, this procedure remains 
unsatisfactory as one is never sure that not a difference in response of the system 
between field and laboratory occurs. It seems to me therefore of the greatest 
importance, that the methods to determine the physical properties of soils in situ 
are improved. 
THE APPLICATION OF SOIL MOISTURE TRANSPORT MODELS 
Apart from gaining more insight into the relevant processes, which is one 
of the purposes for the development of simulation models, in our case the main 
aim is the application of such models to predict the availability of water for 
plant growth. 
It turns out however, that, while the periods of interest for plant 
production are in the order of a hundred days, the time constant of the soil water 
Simulation models in soil moisture transport processes 295 
system is in the order of minutes or even seconds due to the explicit method of 
integration. To simulate such systems, one has to proceed in time with intervals 
that are in the same order as the time constant of the system. It is obvious, that 
computer time and budget will soon become the limiting factors for the application 
of such models. It is therefore necessary to introduce a different approach in 
the description of soil moisture flow in models that are mainly aimed at the 
calculation of crop production. 
For the process of infiltration a simplification is introduced in which the 
water entering the soil is divided over the soil compartments from the top one, 
each one successively filling up to field capacity till all the water is dissipated 
or till the remainder has drained below the maximum rooted depth . 
.05 .10 
5 
fO 
I .. ::~* 
15 1/"l 
v 20 
I 
: 
I 
I 
25 I I 
I 
I 
I 
I 
30 depth I I 
I 
I 
I 
em I 
I 
: 
.15 .20 . 25 .30 cm 3 cm- 3 
' I 
/t-2days/ 
1
,'t•1day 
water content 
I ,' 
I •' I / , ., 
~:~' 
,,• 
------ initial moisture content 
-- simplified moisture distribution 
···•·· simulation model 
RAIN•1Bmm 
Fig. 4. Comparison of the moisture distribution after ilfiltration 
calculated with the simulation model and with the "simplified" 
method. 
In figure 4 a comparison is shown of the moisture distribution in an initially dry 
soil profile after a rain of 18 mm, calculated with the simplified model and with 
the simulation model (Van Keulen & VanBeek, 1971; Stroosnijder et al., 1972). It 
shows that after one day about 95% of the water is in the same soil zone in both 
cases, while the differences in actual moisture content at various depths will 
hardly influence the availability to the roots. Under various conditions, the 
results may deviate somewhat, leading to differences of about 25% in storage in 
the same soil zone. It is emphasized however that a different situation exists 
when so much irrigation water is applied that the storage capacity of the soil, 
i.e. the amount that can be stored in the potential root zone, is highly exceeded. 
Under perma-dry conditions which exist in most of the arid and semi-arid zones, this 
schematisation gives satisfactory results. Such simplifications should however 
always be compared with the results of models based on physical laws. 
To describe the process of evaporation from the soil surface in a simple 
way, a "mimicking" procedure has been developed. The term "mimicking" is used here 
to define a procedure in which the response of the system to a given set of external 
conditions is obtained by a special programming or calculation scheme, which in 
296 H. Van Keulen 
itself has no physical or physiological meaning. Such a "black box" may also be 
constructed in situations where the causal relations are not known (Jansen, 1974). 
To obtain the evaporation, first the potential evaporation is calculated 
with the formula of Penman (1956), which gives good agreement with the calculated 
soil evaporation as shown in figure 3. The actual rate of evaporation is then 
determined by the moisture potential at the soil surface. Because redistribution 
of the water between soil compartments as a result of developing potential gradients 
is omitted in the crop growth model, the total evaporative water loss must be 
divided over the various compartments. For each compartment the rate of water 
extraction is written as: 
E = F x AEVAP 
X 
with F (8-8 ) * e (-Pxd) 1 
10 
20 
30 
40 
50 
60 
70 
em 
80 
150 
mm 
100 
5'0 
in which 8 
8 
pl 
d 
~simulation model 
---- .. mimic" procedure 
depth 
actual water content in compartment 
water content at air dryness 
proportionality factor 
depth of centre of compartment below soil surface 
.30 .35 cm3 cm·3 
1 water content 
I 
I 
Fig. 5. Comparison of the moisture 
distribution and the cumulative 
evaporation, calculated with the 
simulation model and with the 
"mimicking" procedure. 
cum~t~~~~otion __ ..----· 
/
·-0 
0 
0 
-simulation model 
o .mimic • procedure 
o/ time 
5 10 15 20 25 days 
Simulation models in soil moisture transport processes 
In figure 5 a comparison is shown between the results of the simulation 
model and the "mimicking" procedure, in which for P the value 15 was used. It is 
obvious that this value depends on the moisture transmission properties of the 
soil under consideration. As the relation between the two depends both on the 
actual value of the conductivity and on the shape of the K-8 relationship no 
attempt is made to give a general formula, but it is proposed to calculate the 
value of P by comparison of the simulation model with the "mimicking" procedure 
for each soil. 
CONCLUSION 
From the foregoing it is concluded that simulation models are a strong 
297 
tool in the prediction of the behaviour of soil moisture under varying conditions. 
A serious disadvantage is however the very small time constant of the soil moisture 
system, which limits their use in general to short term processes, although 
simplifications may be introduced on basis of the results obtained with the 
simulation models. 
The determination of the soil physical parameters in situ should get proper 
attention to improve the applicability of the simulation models. 
REFERENCES 
Brunt, D. (1932). Notes on radiation in the atmosphere. Q.J. Roy. Met. Soc. 58: 389. 
Chamberlain, A.C. (1968). Transport of gases to and from surfaces with bluff 
and wave-like roughness elements. Q.J. Roy. Met. Soc. 94: 318. 
Janssen, J.G.M. (1974). Simulation of germination of winter annuals in relation 
to microclimate and microdistribution. Oecologia (Berlin) 14: 197. 
Keulen, H. van and G.C.E.M. van Beek (1971). Water movement in layered soils-
A simulation model. Neth. J. agric. Sci. 19: 138. 
Keulen, H. van (1974). Simulation of soil and plant water relations in arid regions. 
Simulation Monographs, Pudoc, Wageningen (in prep.). 
Penman, H.L. (1956). Evaporation: An introductory survey. Neth. J. agric. Sci. 
4: 9. 
Stroosni]der, L., H. van Keulen and G. Vachaud (1972). Water movement in layered 
soils. 2. Experimental confirmation of a simulation model. Neth. J. agric. 
Sci. 20: 67. 
Wit, C.T. de and H. van Keulen (1972). Simulation of transport processes in soils. 
Simulation Monographs, Pudoc, Wageningen. 
Current research field of author : Investigation and modeling of crop growth in 
arid regions~ with special emphasis on water use.- Modeling of evaporation - Crop 
growth modeling in general. 
298 H. Van Keulen 
DISCUSSION 
It seems to me that you take great pride in being as precise as possible 
in doing the modeling and you then are extremely loose when you start using words 
as better~ best~ good. You never tell us what you mean by these statements. Another 
point is~ you made a statement which I think is extremely dangerous~ you said~ if 
you did not get an agreement you went back and you put in more detail. That's not 
necessarily a good way of getting a better agreement. (YOUNG) 
I did not specify good, better, best due to lack of time. The second one, 
I think you probably misunderstood : the point is not that putting in more detail 
should give you any better result a priori but the point is that, when you have 
described a process with a number of equations which you think are representing the 
processand you don 1 t get agreement between the observed and the calculated results 
you should go back to your set of mathematical equations, study them again and see 
if you did not leave anything out. (VAN KEULEN) 
I might say there is a very close analogy between your material energy ba-
lance use and the one that we did on the rivers where we look at the evaporative 
enthalpy loss of heated water to the atmosphere. Do you have an evarorative enthalpy 
loss term ? (DAVIDSON) 
No. (VAN KEULEN) 
We found that in the river the evaporative enthalpy loss term is roughly 
50 % of the heat loss when you look at the long way~ the short way~ the force con-
duction and then look at the evaporative enthalpy loss term itself~ which is a large 
quantity. I suspect you have to look at it. The second question has to do with the 
time base for input data in your heat exchange formulas. We found that using daily 
average versus data based say on hourly readings~ you can pick up another 30 to 
40 % deviation between the cumutative effects and those which are actually accumu-
lating on your integral or shorter time history. The heat exchange factors change 
enormously over a cycle of 24 hours. (DAVIDSON) 
Yes, when possible we use weather data on the smallest base that is avai-
lable, that means on the base of the calculation. In many cases you don 1 t have 
them. We have developed some procedures which convert daily averages back into 
daily courses. (VAN KEULEN) 
You mentioned that you have very small timesteps like minutes~ I was won-
dering whether this would not be a direct consequence of using CSMP which I under-
stand is quite an explicit procedure. Using evaporation data like we did~ we could 
use timesteps of a day or more. (NEUMAN) 
In the runoff model where we use evaporation, I use timesteps of a day with 
this limiting procedure, I got satisfactory results. (VAN KEULEN) 
What kind of integrator do you use ? (TODINI) 
Either Runge Kutta or Milne with variable timesteps. (VAN KEULEN) 
You can have larger timesteps. (TODINI) 
I agree with that. (VAN KEULEN) 


Evaporation: An introductory survey.

Notes on radiation in the atmosphere.

Simulation of germination of winter annuals in relation to microclimate and microdistribution. Oecologia

Simulation of soil and plant water relations in arid regions.

Water movement in layered soils. 2. Experimental confirmation of a simulation model.

Water movement in layered soilsA simulation model.

The use of simulation models in the study of soil moisture transport processes

Abstract

Similar works

Full text

Available Versions

NARCIS

Wageningen Yield