modelling of soil-moisture movement in a field drainage-irrigation system
TRANSCRIPT
Modelling of Soil-Moisture Movement in a Field Drainage-Irrigation SystemAuthor(s): T. BrandykSource: Irish Journal of Agricultural Research, Vol. 24, No. 1 (1985), pp. 79-93Published by: TEAGASC-Agriculture and Food Development AuthorityStable URL: http://www.jstor.org/stable/25556104 .
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Ir. J. agric. Res. 24: 79-93, 1985
Modelling of Soil-Moisture Movement in a Field
Drainage-Irrigation System
T Brandyk1 Land Reclamation Faculty, Warsaw Agricultural University, Warsaw, Poland
Abstract
The mechanisms and basic concepts of irrigation and drainage systems are reviewed, and field data are presented for an experimental system. The following topics are
discussed: the characteristics of an existing drainage-irrigation system; the application of a system approach for the description of soil-moisture water management; the
application of steady- and unsteady-state soil-moisture flow theory for soil-moisture
water management.
Steady-state soil-moisture flow theory is applied for the determination of the
required ground water-table depth and the levels in open ditches for supplying the plant root zone with water by capillary rise. Unsteady-state theory is applied for daily soil
moisture content calculations and the verification of numerical calculations using measured values is given.
Introduction The principal aim of agricultural man
agement of cropland is to obtain long term, large and stable crop yields, which are dependent on several factors. One of them is the rational management of soil
water in the plant root zone. Plant water
requirements fluctuate in the range between the minimum and maximum allowable moisture content. The maxi
mum allowable soil-moisture content
depends on the minimum air content
required and this value varies with both
soil and crop type. The minimum allow
^resent address: Civil Engineering Department,
University College, Earlsfort Terrace, Dublin 2
able soil-moisture content depends on the soil type and in particular on the
moisture-release characteristics of the soil
together with the crop type. To ensure
satisfactory growth the minimum mois ture content prevailing should exceed that at the permanent wilting point by a safe
margin. Brandyk and Wesseling (1983a) have proposed a pF value of 2.7 as the
minimum allowable moisture content for control purposes.
On flat cropland areas with a shallow
depth to the ground water table, open ditch systems are very applicable for soil water management. Soil-moisture content
in such systems can be easily controlled by maintaining the correct water level in
79
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80 IRISH JOURNAL OF AGRICULTURAL RESEARCH, VOL. 24, NO. 1, 1985
ditches. The purpose of this paper is to
apply mathematical modelling of soil moisture processes to the water manage ment problems in agricultural areas. The
significance of the simulation modelling in solving practical problems of water
management for shallow water-table soils was shown in literature by Skaggs (1974; 1976; 1981; 1982) and Skaggs, Fausey and
Nolte (1981). The paper describes the applications of
steady- and unsteady-state soil moisture
flow theory. Steady-state theory is applied for the determination of the required depth to ground water-table and the levels in open ditches for supplying the plant root zone with water by capillary rise.
Unsteady-state theory is applied for daily soil-moisture-content computations and
its verification using field measurements is given.
Characteristics of an Existing Drainage-Irrigation Ditch System
On the flat areas within river valleys and polders allocated to cropland, open ditch systems are very applicable. Fig. 1 illustrates such a system which is in
operation at Solec near Warsaw, Poland.
The soil moisture management of this area (about 320 ha) is based on the main tenance of the water level in the open ditches. During the early spring season and after the periods of high precipita tion, the system operates as a drainage one. However, during the relatively dry summer season the small sluices shown in
Fig. 1 are closed and the system operates as a subirrigation system.
The river R is used both as a main
drainage channel and a water source for
subirrigation. The distribution of water on this area is controlled by sluice number
/rtsj^v|^-maln
ditch LEG?ND
^VmYV ! R " River Ma,a
^f^TV^s^vN I Ft border and number of V~Tsc\K^v water management unit area
x\_f^J\V5 -J? sluice with its number
River i _Jt" -^-^\ ? *?? 4?? 6?? im J
Maia --^r^^Vnrj ! '?'?'?'
1
Fig. 1: The Solec open ditch drainage ?
subirrigation system
3 which supplies the main ditch D. The water is distributed subsequently between water management unit areas Fl to F6 and F10 to F12 inclusive. Other unit areas, F7 to F9 inclusive and F13, obtain water
directly from the river. The water manage ment unit areas vary from 5 ha to 48 ha. The spacing of the ditches varies from 60 m to 120 m with the average value of 90 m; the average depth of ditches is 1.5 m. The analysis of the hydrological,
hydrogeological, soil and plant conditions of the Solec water-management system was described by Brandyk (1981) and Kaca
(1981). They concluded that water-man
agement unit F5, area 18 ha, is typical and representative of the whole system. The details of unit area F5 are shown in Fig. 2.
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BRANDYK: SOII^MOISTURE MOVEMENT 81
River Mala ?.,
J ana |tf ^ ]
c_3 \ X rt\ 1 main *A ~i ,^^0---^"^^ -v 1 ditch D
V%#x \ SN*^
LEGEND ^\ ^Vjffij level of open water in ditch gauge vX^^o'i
D tensometric meteorological station \Jnmn> O rainfall gauge \?l
?X? water structure
-border of the water management unit area F-5
open ditch with its number
O SO IOO ISO m I_I_I-1
Fig. 2: Unit area F5 of the Solec system
The ground water-table depth reaches its highest value (below the soil surface)
midway between ditches during subirri
gation and its lowest value during drain
age. The depth to the ground water-table at this point is limiting the air-water-soil conditions for plant growth (i.e., the mini
mum air content and the minimum avail
able water in the root zone, during the wet and dry periods, respectively). The conditions prevailing in the root zone, during the growing period, are controlled _
by the operation of the d?+ch drainage and subirrigation system. Water management in the plant root zone requires a know
ledge of the actual soil-moisture content.
Measurement of the soil-moisture content, in spite of several modern
methods (Paetzold, 1983), is still very difficult and time consuming. The deter
mination, maintenance and prediction of
soil-moisture content are essential for
agricultural water management. Mathe
matical models based on the application of steady- and unsteady-state soil-mois
ture flow theory can be helpful in this
regard.
The System Approach for the Soil-Water Management
The components of a soil-moisture
control system are presented in Fig. 3. Each of the components can be represen ted schematically by a reservoir. Water
storage in each reservoir is adjusted by physical phenomena which are presented in Fig. 3 as valves. Arrows represent dir
ections of water flow in the system. The main focus of interest within this system is to quantify soil-moisture changes. The soil-water management system shown in
Fig. 3 can be simplified to three elements: the ditch, the subsoil and the root zone as
( AtmoipNre 1~
"S-? /* I ~f Mm'1""1 A f _ I'front pi ration J
[ Precipitation ^> Q pJ<^ Evaporation | V /
,_I water I ! | at t? I mrfact | j
2 1 L _j_ ?""<* ><i llnmtrotkm >Q 0 <C?p?llorv ri.t j ̂^TStWBSfl
-1 ||
So motit?r? ||-1
| Ptrcototion ^> <j [> <^Copilkiry rfrt~|
f I A ftroundwattr
Fig. 3: The structure of a soil-moisture control water management
system
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82 IRISH JOURNAL OF AGRICULTURAL RESEARCH, VOL. 24, NO. 1, 1985
shown in Fig. 4. This simplified system approach can be very useful where steady
state soil-moisture theory is used to
quantify the transfer of soil moisture between these three elements.
ETP Prtc.
t i ROOT ZONE
SOIL LAYERS
CAPILLARY INFILTRATION RISE
^7flwi J_I
D,TCH -??*???? "*
5UBSOIt SYSTEM LAYERS
-*- DRAINAGE -
___j [
Fig. 4: Schematic representation of a
simplified soil-water management system
Modelling of Steady-State Soil-Moisture Flow
Theory
Steady-state soil-moisture flow is
governed by Darcy's law:
? -?*.
where
q = soil moisture flux (cm d_1) H = hydraulic head (cm) K = hydraulic conductivity (cm d1) z = vertical coordinate with origin at the soil surface, taken positive upwards (cm).
The hydraulic head can be written as:
H = h + z . 2
where
h = pressure head (negative in unsaturated soil) (cm) z -
gravitational head (cm).
Equation 1 may be written for unsaturated flow in the following form:
q = -K(h)(^+ l)
. 3
where K(h) is the unsaturated hydraulic conductivity which is a function of
pressure head (cm d_1).
Rearranging Equation 3 yields:
dz = -1 . 4
dh 1 + q/K(h)
Integration of Equation 4 yields:
/ dz = / -=J- * 5
zi hi 1 + q/K(h)dh
Starting at the groundwater table where h =
0, one can calculate the pressure head
profiles with depth, i.e., h(z), by means of
Equation 5 for various values of flux, q,
(positive or negative). Equation 5 must be divided into a number of integrals for the calculation of z in layered soil profiles:
h. h
z = / dh _ ; 2 dh _
0 1 + q/Kt(h) hx 1 + q/K2(h)
hn . -
/ dh . 6
Vt 1 + q/Kn(h)
where hl9 h2, hn are the pressure heads
corresponding to the boundaries zx, z2
., zn between adjoining layers. The
values of h^ h2.hn are not known
initially, but must be determined during the integration procedure.
Results of numerical calculations
The numerical solutions of steady-state soil-moisture flow as represented by
Equation 5 or Equation 6 require the
knowledge of only one functional para
meter, the unsaturated hydraulic conduc
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BRANDYK: SOIL-MOISTURE MOVEMENT 83
tivity K(h), for a given soil profile. K(h) can be described in several ways as shown
by Brandyk and Wesseling (1983a,b) and
Wesseling, Bloemen and Kroonen (1983). Determined K(h) functions for the differ ent soil layers in a high-peat bog soil
profile from the Solec system are pre sented in Fig. 5 (Wesseling and Brandyk, 1984). Numerical calculations using Equa tion 6 yield the height of the capillary rise
above specified groundwater-table depths at different soil-moisture fluxes. The
results of the numerical calculations of the height of the capillary rise in the high peat bog, using K(h) functions as shown
in Fig. 5, are presented in Fig. 6 (Brandyk and Wesseling, 1983a).
io3^
101 \ y\ 1 - layer 0-10 cm
>v 2\\ 2 -
layer 10-20 cm
~ 10 *\\V 3 " ,Qyer below 20 cm
j IO'1 L \\
* \w
io-3j- yY
io"sL \W I-1 i_i_i_* >
10? 101 IO2 IO3 104 105 h /cm
Fig. 5: Unsaturated hydraulic conductivity functions K(h) in layered high peat bog soil profile
Estimation of the required depth to the
ground-water table
The results of calculations of the height of the capillary rise can be used to determine the desired ground-water level which is
required to supply water by the action of
capillary rise to the crop root zone at
specified evapotranspiration rates. This
depth can be determined using the follow
ing assumptions: i) the depth of the root zone is known;
ii) the inflow of water through the lower
boundary of the root zone is equal to the outflow at the soil surface;
iii) minimum allowed pressure head in the root zone:
h min = -500 cm, i.e., pF =
2.7;
iv) average evapotranspiration rate is constant during a given time period.
The estimation procedure of the
required depth to the ground water-table for the Solec system is as follows. The
depth of the root zone for this soil is limited to 20 cm (Brandyk, 1981). Field
measurements showed evapotranspiration
fluxes in the range 3 to 5 mm d1 during the growing period (June-September in
cluded). Using the data of Fig. 6 and the above assumptions the values of the
required depth to the ground water-table in the Solec system at evapotranspiration rates of 3, 4 and 5 (mm d1) are 90, 80 and 70 cm, respectively. The comparison between the calculated and field measured values of pressure head distributions for a
dry period with the average evapotranspir ation rate of 5 mm d1 is shown in Fig. 7. The data show that even for a period up to 2 weeks without precipitation and the rela
tively high evaportranspiration rate, the soil-moisture content is higher than the
minimum allowed value, if the depth to the ground water-table does not exceed
70 cm.
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84 IRISH JOURNAL OF AGRICULTURAL RESEARCH, VOL. 24, NO. 1, 1985
> v
f 120- *
j* 110- / / 100- / / _ _ .
/ / ^_ -q=2mm d '
90- II ^^ 80" / / / -, ^-1 11/
_^^???-q?3mm d 1
z (cm) I I / >< _ -q^mmd'1
J j j/ yS^ ^_.-q=5mm d"1
0 I Til Mill-1-.I_I_ ' ' i i n 11_I_.I-> 10 101 IO2 5x102103 104 10s
h (cm)
Fig. 6: Results of numerical calculations of the height of capillary rise in high peat bog soil profile at ground water-table depth 120 cm
Estimation of the required water level in a ditch The water level in a ditch and the depth to the ground water-table between ditches are
inter-dependent. Fig. 8 shows the ground water-table levels between ditches during subirrigation. Flux to or from a ditch can be calculated as follows:
q =-. 7 T
where
<j>x = level of open water in the ditch (cm)
4>2 =
ground water-level mid-way between
the ditches (cm) T = drainage resistance (d) q = flux from the ditches (cm3 cm2 d_1).
According to Ernst (1962, 1975) the
drainage resistance can be calculated as
|2 T= Lw + ?. 8
8KD
where:
L = spacing between ditches (m) w = radial resistance (d nr1) K = saturated hydraulic conductivity for
horizontal flow in the saturated zone (m d1)
D = average thickness of the aquifer (m). The radial resistance can be found from
the equation presented by Ernst (1962):
w = -lln-a . 9 *K Bw
where:
D0 = thickness of the aquifer below the
water level in the ditch (m)
Bw = wetted ditch perimeter (m).
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BRANDYK: SOII^MOISTURE MOVEMENT 85
h (cm)
10? '?1 IO2 5?I02 "' I I I i I m|-1?r-r i rmj-1?r?r-i
(cm) 3?
/// / HW /// /
SO #//
LEGEND
1 - measured 20 May I960
2 - measured 25 May 1980
3 - measured 3! May 1980
4 - calculated
s - minimum allowed soil moisture content in the root zone
?2_- ground water table depth
Fig. 7: Comparison between calculated and field measured values of soil moisture
pressure head for a dry period 20 to 31
May 1980 at Solec, at an average evapo
transpiration rate 5 mm d1
v- --i
Infiltration-^-^ >--7-Evapotranspiration
! A t it i r if i
I % X 0 q
>s- Soil moisture profile I under consideration
Impermeable layer ?J
Fig. 8: Schematical representation of steady-state ground-water-flow conditions
between two ditches with subirrigation
From Equations 7, 8 and 9, knowing the
required ground water level (</>2)> evapo
transpiration rate (q) and drainage resis
tance (T), the required water level in the
open ditch can be determined. In the Solec
example the value of T is 39.4 (d). The values of the required depth to the ground water-table and the corresponding ditch water levels calculated for the Solec system are shown in Tkble 1.
TABLE 1: Ground-water-table depths and water
levels in ditch calculated for Solec
conditions (ditch spacing L = 90 m)
Evapotranspiration (mm day"1)
3 4 5
Ground-water-table depth (cm) 90 80 70
Water level in ditch
(cm) 80 65 55
Modelling of Unsteady-State Soil-Moisture Flow
Theory The process of unsteady, unsaturated soil
moisture flow in the presence of water
uptake by plant roots, can be described by Richards' parabolic differential equation with a sink term which can be written in
the following form (Feddes, Kowalik and
Zaradny, 1978):
3t C(h) 3z L Vg2 /J C(h) where:
h = soil water pressure head (negative in
unsaturated soil) (cm) t = time (d)
C = differential moisture capacity, d#/dh
where 0 is the volumetric soil water
content (cm3 cm3) z = vertical coordinate, with origin at the
soil surface directed positive upwards
(cm) K = unsaturated hydraulic conductivity
(cm d1) S = water uptake by roots (d1).
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86 IRISH JOURNAL OF AGRICULTURAL RESEARCH, VOL. 24, NO. t, 1985
The schematic illustration of the struc
ture of Equation 10 is shown in Fig. 9.
Equation 10 is non-linear because the
functional parameters K(h), C(h) and S(h) are dependent on the actual solution
h(z,t). The finite difference scheme as des
cribed by Feddes et al (1978) was used to
solve Equation 10. The finite difference
net scheme is presented in Fig. 10. This
finite difference method leads to the set of
linear simultaneous equations which can
be solved using the so-called Thomas
(tridiagonal) algorithm as described by
Remson, Hornberger and Molz (1978). Richards* equation can be solved numeri
cally for given initial and boundary conditions, as well as the following func
tions: soil-moisture content, 6, versus
pressure head, h, i.e., h(0), unsaturated hy draulic conductivity, K, versus pressure
head, h, i.e., K(h), water uptake by plant roots S versus pressure head, h, or depth, z, i.e., S(h) or S(z) or on both h and z, i.e.,
S (h, z).
Soil and plant parameters Numerical modelling is now applied to the
high peat bog soil of the Solec Region.
Some properties of the soil are presented in Table 2. The data show that it is a
typical layered soil profile with the highest degree of decomposition in the top layers of peat and a lower degree in the bottom
layers. On the basis of the properties shown, the soil profile can be divided into two essential layers: (i) root zone 0-20 cm
deep and (ii) subsoil below 20 cm. Mea surements of the so-called soil-moisture
retention curves were performed accor
ding to the method described by Stakman, Valk and Harst (1969a; 1969b). Soil moisture retention curves, expressed as the
h(0) function for each characteristic layer in the soil profile under consideration, are shown in Fig. 11.
The hydraulic conductivity values were
measured according to the instantaneous
soil-moisture-profile method as described
by Brandyk and Kowalik (1981) and Zako wicz and Brandyk (1982). For a functional
description of measured K(h) values an
empirical equation as proposed by Kunze, Uehara and Graham (1968) was used. Cal culated values of this K(h) function for each of the two essential layers in the high peat bog soil profile are shown in Fig. 11.
functional parameters
Cthl Klhl S(h) Mz,t)
V_t_V
in^Xn' ( M Clh)||!--^rKlh)|h]_3K(M_S(hl I-|_!?!H?on variables |^_^ at 3zL dzJ 3z h(z,t)
A ̂ A dependent variable
h o(z,r) = 0 h^lzzO.t) h
2(z=Z,t)
0<z$Z(O) t?0 \%0 v V_ ZsZltl7
. . . V y initial condition boundary conditions
Fig. 9: Schematic diagram of the structure of the Richards' partial differential equation with sink term
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BRANDYK: SOIl^MOISTURE MOVEMENT 87
_i Iuppn boundary condition \ 2 3 > 1-t i UI
1^2 M ^
fl 11 M TT 11s T F D E 1 l
pn?i ?M???it N 1 D) I 1 JI j
J"' iLi ?n???M
4-rrf rk ;hhr rk
I tow?r boundary condition
Fig. 10: Finite element difference net,
superimposed on the depth-time region
The shape of S(h) function based on the
influence of air-water conditions on soil
water uptake by plant roots, was taken as
described by Feddes et al (1978). This
function is also shown in Fig. 11.
Boundary conditions The following three types of boundary conditions, after Feddes et al (1978), can
be distinguished:
i) The so-called Dirichlet condition which represents the specification of the function value at the top or at the
bottom of an unsaturated zone. For
the solution of Equation 10, this con
dition can be written for upper and lower boundaries as presented in Fig. 9.
ii) The Neuman condition which, for un
saturated soil-moisture flow, can be
represented as a flux through boun
daries, i.e.:
q(t) = -K(h)(it- l).
11
iii) So-called "mixed condition" which is the combination of i) and ii). This
condition specifies the values of the
function at one boundary and the flux
through the second boundary.
Meteorological observations at Solec were used to compute the upper boundary condition. Ait the soil surface the Newman
condition which represented the difference
between daily evaporation and precipita tion as a flux q(z = 0,t) was applied. As an illustrative example the variation of
maximum possible infiltration or evapora tion with time for the growing period of
TABLE 2: Physical properties of high bog peat-soil profile
Saturated hydraulic
Depth Bulk Particle Total Ash conductivity
(cm) density density porosity content _^ y ^_
(gem-') (gem') <%vol.) (ft DM) ^^ Horizontal K kh
5-W 0.364 1.76 79.4 28.42 0.78 0.30 15-20 0.240 1.65 85.4 20.27 0.12 0.52
25-30 0.176 1.67 89.5 17.70 0.14 0.38 35-40 0.168 1.58 89.4 12.17 ? ?
45-50 0.175 1.63 89.3 13.07 0.20 0.59 55-60 0.184 1.74 89.4 16.02 ? ?
65-70 0.183 1.70 89.2 16,02 0.28 ?
75-80 0.174 1.66 89.5 13.78 ? ?
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88 IRISH JOURNAL OF AGRICULTURAL RESEARCH, VOL. 24, NO. 1, 1985
K
10"' - 7 A
/X
to-' I- JS
KT? r /
lO'11 - / LEGENP
/ 1, upp?r toy?r of soil profile / (0-20 cm)
K>"'3 - / 2, lowtf lay?r of soil croftl* / (b*low20cm)
/ capHtary conductivity function Kt8J 1CT15 -
1-0 075 0-5 0-25 0-1 0-3 0-5 0;7 0-9
?<**-'-i-r-ssB-r-'-' '
'l/^|
^*^****^ - y,s^r soil moisturt
wat?r uptak* by ptcnt toot* >0^ retention function Slh) 6^ ht<8l
10* * V Mcml
Fig. 11: Soil and plant parameters in high
peat bog soil profile
1978 is shown in Fig. 12. The boundary condition at the bottom of the unsatur
ated zone was formulated on the basis of
daily ground-water-table depth obser vations. The time varying soil column
height was given by measurements of the
water-table depth. The value of h = 0 was
assumed at the bottom of the unsaturated zone. As an illustrative example of this condition the variation of the measured
ground-water-table depth with time during the growing period in 1979 at Solec is
shown in Fig. 13.
Comparison between computed and
measured values
Numerical calculations of soil-moisture
dynamics were performed according to a
computer program SWATR, as described
by Feddes et al (1978). A meteorological tensiometric station was located midway in the space (L = 90 m) between ditches
32r 28
24
2Q. + infiltration
e i2
8 -
-evaporation -8L
;_; !_1_ 23 31 IO 20 30 \0 20 31 IO 20 31 IO 20 30
May June July August September
Fig. 12: Variation of the upper boundary condition q (z - OJ) during summer growing
period in 1978
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BRANDYK: SOII^MOISTURE MOVEMENT 89
May June July August September 20 31 IO 20 30 10 20 31 IO 20 31 tO 20 30
Or-r*-1-1-r*-,-.-r*-1-1-^-?-1-1?> t Id)
Ground water table depth 20
z (cm)
P(mmj
40^ Precipitation
20
oL_L-_J_1_. ill_.ll I. .Ji lii III 11. I. _.-lu->t(dl
Fig. 13: Variation of the lower boundary condition with time during the summer
growing period in 1979
23 and 24 (see Fig. 2) to collect data for the field test. Standard meteorological parameters and ground water-level depths were taken at the station. Field measure
ments and numerical calculations were carried out for the two growing seasons of 1978 and 1979. The comparison between the measured and computed values of soil-moisture pressure heads is shown in
Fig. 14a, b, c for 1978 and in Fig. 15a,
b, c, d, e, for 1979; these calculated and measured values were compared using a statistical method. Linear regression equations between measured and calcula
ted soil-moisture pressure head values were analysed. These linear relationships are presented in Fig. 16a,b,c for 1978, and in Fig. 17a,b,c,d,e for 1979 and also in
Table 3. Generally, good agreement was found between the measured and the cal culated values. Only the calculated data for the upper 10-cm layer slightly under estimated measured values during drying periods. These differences in the upper
10-cm layer are understandable, because,
at the top of the soil profile, soil moisture movement can be affected by other pheno mena such as thermal and vapour water
movement which are not taken into account in the model.
Conclusions
i) Numerical solutions of steady-state soil-moisture theory can be applied for the control of soil moisture in the plant root zone of soils with a shallow water-table.
The control concept assumes adjustment
of open water level in a ditch system and this is very easy to maintain. This water
level also determines the ground water
level midway between the ditches and also the moisture-air conditions in the root
zone. Steady-state theory can be applied
for long-term soil-moisture control if the
following parameters are known (mea
sured or calculated): unsaturated hydrau
lic conductivity function, K(h); average
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90 IRISH JOURNAL OF AGRICULTURAL RESEARCH, VOL, 24, NO. 1, 1985
May Jun* July August S?pt?mb?r 30 SO 10 ao 30 IO 30 30 IO 20 10 IO 30 30
Oj-r|-T-,-.J?r- fit.. .( ,- i -r*>\6)
ot-. .
iooI
[ - calculated
'*?r . measured
f?0
30 30 IO JO 30 IO 20 30 \Q 20 20 IO iO 30 Or-H-1-.-ri-1-.-H-f-*-H-1-<-i-*1 td)
:: a .. M^/Vr^ 60L' '^v/^V^f
. ^v
Ulcml (b)
20 30 IO 20 30 IO 20 SO tO 20 30 >0 SO 30 t (J.
Oj-rf-,-,-rf-,-,-H-1-jr-H-1-1-!-*>? <*'
60L
%Mcm> (c>
Fig. 14: Comparison between measured and calculated soil-moisture pressure heads at (a) 10 cm, (b) 20 cm, (c) 30 cm
below the soil surface of high peat bog soil
profile during summer growing period 1978
evapotranspiration rate, q; and drainage
resistance, T.
ii) Numerical solutions of unsteady state soil-moisture theory can be applied for daily soil-moisture content compu
tations. For these calculations the follow
ing parameters are required: soil-moisture
retention characteristics h(0); unsaturated
hydraulic conductivity, K(h); water uptake by plant roots S(h) or S(z); and initial and
boundary conditions at the top and the bottom of the unsaturated zone.
Hoy June July August September 20 3o >o 20 30 ?o 20 30 to 20 so to 20 30 Hdl
toi ?i '?
?r^? Ti '?:?1~"? ?*?
90
no -
ISO
ISO -
I70 - calculated
"?" < measured
2(0
(0 1
250 - v Mcml
20 30 IO 20 30 IO 20 SO IO JO 30 >0 20 30 tlcl O,-H-,-1-ri-1-1?-tH- -1-rl-1-1-r? 1 i-i \
BO -
,...1 . "'""* lb} hfcml
May Jui? July August September 2Q 3Q( IO 20 3Q IO 20 3Q 10 20 3Q )Q 3Q 30 f (d )
60 ,, [c j -calculated
h (cm) measured
20 30, IO 20 30, tO 20 30. tO 20 30, 10 20 30 tfdl O] yyt-1-^j^L^-,-rl-1-t--H-1-1-j?*>
40 - \Z-J i (dl
hlcm)
20 30l IO 20 30, IO 20 30 IO 20 30 10 20 30 Md)
Mem) ?eJ
Fig. 15: Comparison between measured and calculated soil-moisture pressure
heads at (a) 10 cm, (b) 20 cm, (c) 30 cm,
fd) 40 cm, (e) 50 cm below the soil surface of high peat bog soil profile during
summer growing period in 1979
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BRANDYK: SOILMOISTURE MOVEMENT 91
A r =0 795. /A * -M0 . / -80 i- -60
/ hm = 1-24hc-l2-2 hm=1-2lhc*3-58 "'60 / r =0-911 ..-../ r*0-906 ../
-100 j / / I -*0- -/ .
-40- /.
-40- /?
"2?- /
"20- /
0-20-40-60-80-100-120* hc 0 -20 '
-40 -60 -80* hc
0 '
-2C '
-40 '
-60 '
-80* hc
'ol lb) (Cl
Fig. 16: Linear regression equations between measured hm and calculated hc soil
moisture pressure heads at (a) 10 cm, (b) 20 cm, (c) 30 cm below the soil surface of high peat bog soil profile during summer growing period in 1978
-240 '
I -220 - I -60- . , * . - ,_ . / hfn-1-0 hc-5?35
-200 /
r * 0-969 .\j/
-,d?: 7 -40- -A - i6o . / a -140- / hm* 2-57 hc-53-3 Jf _I20- /
r 0-590 -20- A'"
-lOO '/;' . \A> -so- / ; oLa?i?i_i_i_i i ? he ,~ / ; O -20 -40 -60
- 4? - 4& {c) -20- ./'
" hm
/ A O -20-40-60-80-I00-(20 C "
hm ?0-780 hc-0'9O3 , . -40 - t ?0-966 .
(a ) y 1 * m .o<4
,uu hro*l-26hc-W*< .Av'
r ? 0-877 ;.. /
'
.A^' 80 . / O=20^40
."/ Id)
J?' f
_40. /f hm-0Whc-1-39
/;;; ' ~40" r .0-974
-20-
:^(\ _20. >^
ol?Z?1?1?1?.?1?1?i?1?1?*bc A@* H O -2D -40 -6O -BO -IOO fc
O '
-20 '
-40 '?
lb) <*?
F/g. 77: Linear regression equations between measured hm and calculated hc soil
moisture pressure heads at (a) 10 cm, (b) 20 cm, (c) 30 cm, (d) 40 cm, (e) 50 cm below the soil surface of high peat bog soil profile during summer growing period 1979
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92 IRISH JOURNAL OF AGRICULTURAL RESEARCH, VOL. 24, NO. 1, 1985
TABLE 3: Results of model verification3 for 1978 and 1979
Depth Number of Correlation
(cm) data pairs coefficient r
10 130 0.795 1978 20 130 0.911
30 130 0.906
10 130 0.590
20 130 0.877 1979 30 130 0.969
40 130 0.966
50 130 0.974
aCritical value of r at a = 0.001: 0.228 in all cases
The comparison of the results of the
computer simulation with field measure
ments of soil-moisture pressure head for
the high peat bog soil profile under con ditions at Solec showed good agreement.
Unsteady-state numerical modelling can
be used for short-term soil-moisture
control.
References
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BRANDYK: SOIL-MOISTURE MOVEMENT 93
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Received July 31, 1984
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