4.3
Simulation
of
field water
use and
crop yield
R.A. Feddes
4.3.1 Introduction
This contribution differs
in two
respects from
the
preceding sections
on the
simulation model ARID CROP.
The
model ARID CROP, written
in
CSMP,
simulates transpiration
and dry
matter production
of
vegetations growing
on
homogeneous soil profiles and in absence
of
a
soil water table.
As a
result
of
the
long integration interval
of one day, the
description
of the
soil physical pro-
cesses had
to
be simplified and treated somewhat differently than
is
usual in soil
physics.
The
approach
to
simulation
of
the soil water balance presented
in
this
section describes
a
field situation
in a
temperate climate with
a
heterogeneous
soil profile
and a
high groundwater table.
The
program
of the
water balance
section
in
this model
is
executed with fairly small time steps,
so
that the descrip-
tion
of
its processes
can
follow more closely
the
classical soil physics approach
to water
in
soils.
Figure 57 depicts
a
typical situation that can
be
simulated with the model
de-
scribed below.
It
shows
how
flow takes place under cropped field conditions
in
a layered soil,
the
boundaries
of
which include
two
ditches
on the
side
and a
pumped aquifer
at the
bottom.
In
addition
to the
effect
of
these boundaries,
fluctuations
of
the
water-table are caused by water uptake by the crop (the roots
precipitation
euapotranspiration
A
i
sub-irrigation
root zone
peat
sand
|
freatic flux
!
freatic surface
I
I
hydraulic head aquifer
•HMHIMpi
3
f99999/9f
9/9999999*9*9
99/9 99 99999J9J/9//}
poorly
permeaDie layeryffiywyWy
*
ti.'» I
«,!.'•«
iM
*
** *,»|iM4 M
l,k*J.t,((t/</i/t*t*
I
•
•
•.•••••
I
.• ..'•••'• ••
•
VbaBp Afifl ^| mm *
• . •
T
Figure
57.
Scheme
of
the water balance
for
the case
of
sub-irrigation from open water
courses, upward flow from the water-table
to
the root zone, and leakage into
a
pumped
aquifer. Because
of
the symmetry, only half
of
the vertical cross-section between
two
ditches
is
given.
194
X
of which grow with time) and evaporation at the soil surface. The total of influ-
ences constitutes the so-called water balance. To be able to handle such
a^
system, a rather detailed knowledge of the factors concerned is needed.
...<"'
Originally, effects of water management, of groundwater recharge, of soil
;
improvement and of other measures were often measured by establishing repre-
/
sentative experimental fields, collecting as much data as possible, making
vari-
Y
ous changes in the prevailing circumstances and analyzing the results. With the \
introduction of the computer it became possible to simulate the
effects
with the \
aid of physical-mathematical models, which ideally should react in the same
manner to any changes made as the actual system. In the following, two models
of Feddes, Kowalik & Zaradny
(1978)
will be presented that can be used either
separately or conjointly. The
first
model, program SWATR, calculates the actual
transpiration of a crop (Subsection 4.3.2). The second model, program CROPR,
calculates the actual growth rate of a crop (Subsection 4.3.3). Finally, a discus-
sion of strong and weak points of these models is presented (Subsection 4.3.4).
A diagram illustrating the approach is given in Figure 58. It shows the flow
patterns and the action of various factors in the soil - plant - atmosphere sys-
tem.
The water balance of the soil
-
root system is shown on the left hand side
of Figure 58. Irrigation or rain water that is not intercepted by the crop will
(SOLAR
RADIATION]
6RQSSPH0TQSYNTHESIS
OF
STANDARD CANOPY WITH
OPTIMAL WATER SUPPLY
POTENTIAL GROWTH RATE
OF ACTUAL
CANOPY
WIIH
OPTIMAL WATER SUPPLY
ACTUAL 6R0WIH RATE
OF ACTUAL CANOPY WITH
ACTUAL WATER SUPPLY
CUMULATIVE
YIELO
Figure 58. Flow chart of the integrated model approach to assess effects of changes of
environmental conditions upon crop water use and crop yield (Feddes et
al.,
1978).
195
reach the
soil.
Part of
it
will become soil moisture, only to be lost by soil evapo-
ration or transpiration. The part of rainfall that does not infiltrate
will be
lost as
surface
runoff.
The excess of soil moisture will percolate downward to the
groundwater table and recharge the groundwater storage.
The transformation of solar radiation into actual crop yield is schematically
shown in the right hand side of Figure
58.
Gross potential photosynthesis of a
'standard
crop
canopy*
can be calculated according to a model of
de
Wit (1965)
taking into account the height of the sun, the condition of the sky, the canopy
architecture and the photosynthesis function of the individual leaves (cf.
Sub-
section 3.2.4). A
'standard
canopy*
is defined as a canopy with a leaf
area
index
5 (5 m
2
of leaves per square metre of soil surface) that is fully supplied with
nutrients and water. Under actual
field
conditions these maximum photosynthe-
sis rates will never be reached and corrections have to be made for actual con-
ditions of
light
energy flux, for air temperature, for fraction of
soil
covered and
for amounts of roots. Moreover, the growth rate is lower than the rate of
photosynthesis as a result of respiration losses and investment of dry matter in
roots.
Accounting for these
effects
yields the potential growth
rate
of an actual
canopy with optimal water supply. Finally, the actual dry matter yield can be
calculated by introducing the actual water uptake of the root system.
4.3.2
The
model for field
water
use,
SWA
TR
To describe one-dimensional water flow in a heterogeneous soil-root system
we start with the continuity equation (see also Section 4.2):
56
8a
=
—
-S
(61)
where
0
is the volumetric water content (cm
3
cm~
3
),
/
the time
(d),
S
the
volume
of water taken up by the roots per unit bulk volume of soil in unit time (cm
3
cm~
3
d~
J
)
and z the vertical coordinate
(cm),
with origin at the soil surface and
directed positive upwards.
The integral of the sink term over the rooting depth
z
r
(cm,
using
positive
values) yields the actual rate of transpiration
T(cm
d
_1
):
T=
J
Sdz
(62)
o
A major difficulty in solving Equation
61
stems from S being unknown. In
the
field
the root system will vary with the type of
soil
and usually changes with
depth and time. Thus root properties, such as root density, root distribution,
root length, etc., will also change with depth and time. Experimental and accu-
rate evaluation of such root functions is both time consuming and costly. For
these reasons Feddes et
al.
(1978)
propose to use a root extraction term, S, that
only depends on the soil-moisture pressure head,
h,
and the maximum extrac-
tion rate,
b
max9
as?
196
S =
a(h)S,
max
(63)
with:
9
—
u
max
m
(64)
Z
r
where
T
m
is the maximum possible, i.e. the potential transpiration rate (cm
d~
l
).
It is assumed (see Figure 59) that under conditions wetter than a certain
'an-
aerobiosis
point'
{h
x
)
water uptake by roots is zero. Under conditions drier than
wilting point
(/?
4
)
water uptake by roots is also zero. Water uptake by the roots
is assumed to be maximal when the pressure head in the soil is between
h
2
and
hy
When h is below
h
3
but larger than
h
4
,
it is assumed that the water uptake
decreases linearly with h to zero. Although it is recognized that
h
3
depends on
the transpiration demand of the atmosphere (reduction in water uptake occurs
at higher (wetter)
/i
3
-values
under conditions of higher demand), the limiting
point is taken to be a constant.
Equations 63 and 64 can be combined to:
S =
a(h)
m
(65)
Z
r
which means that potential transpiration rate,
T
m
,
is distributed equally over the
rooting depth,
z
n
and reduced for prevailing water shortages by the factor
a(h).'
It is emphasized that Equation
65
is also a drastic simplification, made in the in-
terest of practicality. One of the advantages of
this
model is that the root system
-
is characterized by the rooting depth,
z
n
only (as in ARID CROP, Subsection
4.2.3). In practice this parameter is easily measured. Also the proportionality
factor
a
is a simple function of soil-water pressure head h.
An alternative formulation for
S,^
has recently been made by
Hoogland
et
al.
(1981). To account for effects of soil temperature, soil aeration, rooting in-
tensity and
xylem
resistance upon
S
max9
these authors assumed a linear reduc-
tion of
S
max
with soil depth according to:
o^h^,)
h
1
h
2
LQJ,
|(cm water)
Figure 59. General shape of
the
dimensionless sink term variable,
a(h)
f
as
a function of
the absolute soil water pressure head, h (Feddes et al., 1978).
197
Sm« =
a-b|z|
for \z\
<z
r
(66)
where a and b are constants, in principle to be determined from measured root
water uptake data. As a first estimation we assume that 0.01 < a < 0.03 cm
3
cm
-3
d"
*,
with a mean value of about 0.02, as often found in the literature. The
value of b is even more difficult to assess. (If no information about b is avail-
able,
one may as a first approximation set b equal to zero, giving
S
max
a
constant
value.) The formulation for the modified sink term now becomes:
S
=
a(h).
S
max
(z)
(67)
The water uptake summed over all layers cannot exceed the potential transpira-
tion rate, thus:
o
j
Sdz<
T
m
for
|z|
<z
r
(68)
And because water extraction is calculated in the program from the top layer
downwards, this formulation permits the simulation that water is extracted pre-
ferentially from the upper, relatively wet soil layers. The potential transpiration
demand can be met as long as the plant does not extract water from all soil layers
of the root zone.
By combination of Equations
61,
Darcy's
law and
63
and introduction of the
differential moisture capacity C =
dd/dh
9
one arrives at the partial differential
flow equation that describes flow of water in the soil
-
root system as:
bh
1 6
bh
S(h)
[K(h)(
— + 1)] -
-Li-
(69)
8t C(h) bz
bz C(h)
with
S(h)
defined according to Equation
65.
To obtain a solution, Equation 69
must be supplemented by appropriate initial and boundary conditions. As initial
conditions (at
/
= 0) the pressure head is specified as function of
z:
h(
Zt
t =
0)
=
h
p
(z)
(70)
At the lower boundary (-L) the pressure head is specified as:
h(z=
-L,0
=
/*-L«
*(70
The
soil-water
(Darcian) flux,
q,
at the upper boundary is governed by the
meteorological conditions. The soil can lose water to the atmosphere by evapo-
ration or gain water by infiltration. While the maximum possible (potential)
rate of evaporation from a given soil depends only on atmospheric conditions,
the actual flux across the soil surface is limited by the ability of the porous me-
dium to transmit water from below. Similarly if the potential rate of infiltration
(e.g. the rain or irrigation intensity) exceeds the absorption capacity of the soil,
part of the water will be lost by surface
runoff.
Here, again, the potential rate of
infiltration is controlled by atmospheric (or other) external conditions, whereas
the actual infiltration depends on antecedent moisture conditions in the soil.
198