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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



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.



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




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



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.




> 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).




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).



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



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 ? ?




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




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



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



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




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

Brandyk, T. (1981). Regulowanie uwilgotnienia gleby torfowomurszowej w systemie nawodnien pod siakowych. PhD. thesis, Warsaw Agricultural

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verzadigde zone en hun berekening bij aanwezigheid van horizontale open leidingen. Verslagen van het

Landbouwkunding Onderzoek 67. 15. Centre for

Agricultural Publishing and Documentation

(PUDOC), Wageningen, 189pp.

Ernst, L. F. (1975). Formulae for groundwater flow in areas with sub-irrigation by means of open conduits with a raised water level. Miscellaneous

Reprint 178, Institute for Land and Water Manage ment Research, Wageningen, The Netherlands, 32pp. Feddes, R. A., Kowalik, P. J. and Zaradny, H. (1978). Simulation of field water use and crop yield. Simulation Monographs, Centre for Agricultural Publishing and Documentation (PUDOC), Wagen ingen, The Netherlands, 188pp.

Kaca, E. (1981). Model matematyczny procesu podnoszenia sie zwierciadla wody gruntowej przy nawodnieniu podsiakowym. Ph.D. thesis, Warsaw

Agricultural University. Kunze, R. J., Uehara, G. and Graham, K. (1968). Factors important in the calculation of hydraulic conductivity. Proceedings. Soils Science Society of

America 32: 760-765.

Paetzold, R. F. (1983). Methods of measuring soil moisture ? a bibliography. Technical Report, AGRI

STARS, USDA-ARS Hydrology Laboratory, Beltsville, USA.

Remson, I., Hornberger, G. M. and Molz, F. J.

(1971). "Numerical methods in subsurface

hydrology". Wiley Interscience, New York, 389 pp. Skaggs, R. W. (1974). The effect of surface drainage on water table response to rainfall. Transactions of the American Society of Agricultural Engineers 17: 406-411.

Skaggs, R. W. (1976). Evaluation of drainage-water table control systems using a water management

model. Proceedings of the Third National Drainage Symposium, ASAE Publication 1-77, pp. 61-68.

Skaggs, R. W. (1981). Water movement factors

important to the design and operation of sub

irrigation systems. Transactions of the American

Society of Agricultural Engineers 24: 1553-1561.

Skaggs, R. W. (1982). Field evaluation of a water

management simulation model. Transactions of the American Society of Agricultural Engineers 25: 666-674.

Skaggs, R. W., Fausey, N. R. and Nolte, B. H. (1981). Water management model evaluation for North Central Ohio. Transactions of the American Society of Agricultural Engineers 24: 922-928.

Stakman, W. P., Valk, H. A. and van der Harst, G. G. (1969a). Soil moisture retention curves. 1. Sand box apparatus. Range pF 0.0 to 2.7. 1CW, Internal

Report, Wageningen, The Netherlands.

Stakman, W. P., Valk, H. A. and van der Harst, G. G. (1969b). Soil-moisture retention curves. 2. Pressure membrane apparatus. Range pF 3.0 to 4.2.

ICW, Internal Report, Wageningen, The Netherlands.

Wesseling, J. G., Bloemen, G. W. and Kroonen, W. A. J. M. (1983). Computer program "CAPSEV" to calculate: I. Soil hydraulic conductivity from grain size distribution; II. Steady state water flow in



BRANDYK: SOIL-MOISTURE MOVEMENT 93

layered soil profiles. ICW, Wageningen, The Nether

lands, Nota 1500.

Wesseling, J. G. and Brandyk, T. (1984). Steady-state infiltration and capillary rise in high bog peat soil.

Proceedings of the 7th International Peat Congress, Dublin, pp. 396-409.

Zakowicz, S. and Brandyk, T. (1982). Determining unsaturated porous medium permeability during drainage of vertical soil columns. Annals of Warsaw

Agricultural University SGGW-AR Land Reclamation 21: (in press).

Received July 31, 1984



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