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Modeling irrigation deliveries for tertiary units in large irrigation systems
Agricultural Water Management, 21 (1992) 197-214
197
© 1992 Elsevier Science Publishers B.V. All rights reserved. 0378-3774/92/$05.00
Modeling irrigation deliveries for tertiary units in large irrigation systems R.A.D. Kemachandra and V.V.N. Murty Irrigation Engineering and Management Program, Asian Institute of Technology, G.P.0. Box 2 754 Bangkok, Thailand
ABSTRACT Kemachandra, R.A.D. and Murty, V.V.N., 1992. Modeling irrigation deliveries for tertiary units in large irrigation systems. Agric. WaterManage., 21: 197-214. A simulation model for the purpose of estimating water deliveries at the tertiary and secondary canal levels of large irrigation systems has been developed. The model is based on a water balance approach for estimating irrigation water requirements for lowland paddy and a soil moisture simulation approach for determining the irrigation requirements of upland crops. Expected rainfall at different probability levels during the irrigation season was estimated using past rainfall data and Leaky law. The model was applied to an irrigation system in Thailand for determining the required irrigation deliveries and for comparing the same with the existing practices. Results of the application indicate that considerable improvements in the water delivery schedules are possible.
INTRODUCTION
In the past two to three decades, several large irrigation systems have come into operation in the developing countries of Asia. These systems usually consist of one or more storage reservoirs and a canal system with related structures. Water is distributed over a large area with varying soils, topography and cropping patterns. In many of these large systems, water deliveries are controlled from a central or a fixed office. In each of the projects a water delivery pattern viz., continuous, intermittent or rotation is predecided. However, daily operation of the system is based upon the information obtained from the command area. This information could consist of the climatic parameters and the crop conditions. Based on the climatic parameters, the soil moisture depletion levels and, consequently, the crop water requirements are assessed and irrigation Correspondence to: Dr. V.V.N. Murty, Irrigation Engineering and Management Program, Asian Institute of Technology, G.P.O. Box 2754, Bangkok, 10510, Thailand.
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R.A.D. KEMACHANDRA AND V.V.N. MURTY
deliveries to different command units are decided. The accuracy of the decisions depend upon the computing facilities available and the methodology followed. In many of the systems where such facilities are not available, irrigation deliveries are decided upon experience and available general information. Such decisions could lead to inequitable deliveries of irrigation water. Computer simulation of irrigation systems has been attempted by several workers for the purpose of efficient operation of the systems. Anderson and Maass ( 1971 ) developed computer simulation procedures to study the effect of water supplies and operation rules on the production and income of irrigated farms. The irrigation model proposed bv Jensen et al. ( 1971 ) uses the climatic, crop and soil data for the purpose of scheduling irrigation using computer based approach. Rajput and Michael (1989) adopted a soil water balance approach for development of an integrated canal scheduling model. The U.S. Department of Interior, Bureau of Reclamation (USBR), has developed programs to assist in irrigation project management (Brower and Buchheim, 1982). Boman and Hills (1989) proposed a model for on-demand canal systems based on linear programming approach. Many of the models cited in the literature are developed for specific conditions and cannot be used directly in all irrigation systems. In the Mae-Klong irrigation project in Thailand, a computer-based water allocation model WASAM (Water Allocation Scheduling And Monitoring) is in use. This model essentially considers the depth of water in lowland paddy fields as the criterion for allocating the water to different tertiary units. Expected rainfall is estimated using the Weibull plotting position. In the present study a computer-based water allocation model that could be used in large irrigation systems is presented. The application of the model to an existing irrigation system is also discussed. MODEL DEVELOPMENT
The purpose of the model developed is to estimate the weekly requirement at the tertiary and secondary levels of the irrigation system. The model estimates the actual crop water requirements for lowland paddy and upland irrigated crops. It takes into consideration the expected rainfall based upon an analysis of the available rainfall data. The theoretical considerations are as follows:
Estimating irrigation requirementsfor lowlandpaddy A generalized water balance equation for a given period in the paddy field as follows: WJ= WJ-' + Rt~- ET~ -SJ+I-~-O{ where,
(1)
MODELING IRRIGATION DELIVERIES FOR TERTIARY UNITS IN LARGE IRRIGATION SYSTEMS
] 99
W j is the water depth in the field at the end of the given period; W:- l the water depth in the field at the beginning of the given period; Rt~ the effective rainfall during the period; ET~ the actual crop evapotranspiration; S j the mean seepage or percolation for the period; Pr the depth of the irrigation; and D~ the surface drainage (if any). All the terms are in depth ( m m ) units. If we define Wmax as the m a x i m u m depth of water possible in the paddy field, Woo, the o p t i m u m depth, and Wmin, the m i n i m u m depth at which irrigation is to be given, the water balance equation can be used for determining the irrigation schedules and the depth of water to be applied in each irrigation. The values of ET: and S ~ are estimated for each day. Rainfall occurring on the day will add to the water balance equation to the extent that the field is capable of retaining the rainfall based on the initial depth of water on the day. Excess rainfall will go as drainage. In the present study ET~ was determined using the pan evaporation method (Doorenbos and Pruitt, 1977) and seepage and percolation were adopted from available data. Storage refers to the amount of water on the paddy basin which is depleted before irrigation is applied. During most of the crop growth period, m i n i m u m depth of water in the paddy basin is maintained constantly to submerge the soil for weed and insect control. In the paddy fields, extra levee height is allowed to catch and store the rainfall. In the present study, lJ~ax has been taken as 14 cm and Wmin has been varied from 3 to 5 cm according to the growth period. Wop~for the first 30 days time was taken as 7 cm and for the rest of 70 days it was 10 cm. At the beginning of the computation, W j-~ is set equal to Wopt. The amount of irrigation was computed as follows: - if WJ> Wmax, there is drainage/)Jr and W ./is set equal to Wmax. -- if Wmi n < WJ< mmax, it becomes the actual depth for the day. - if W:< Wmin,the irrigation to the difference between W o p t and W -/is applied to bring the water level back Woot.
Irrigation requirements of upland crops A soil moisture simulation approach is used to study the irrigation schedules in the irrigated crops other than paddy. The governing differential equation considered is as follows: 0
O0
O0- ffz{D( O)'-~}-o~'K( O)-S(
(2)
where, 0 is the moisture content ( L 3 / L 3 ) ; t the time (T); z the depth (L); D (0) the soil moisture diffusivity (L2/T); K(0) the hydraulic conductivity ( L / T ) ; and S(O) the sink t e r m ( L 3 / L 3 T ) .
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R.A.D. KEMACHANDRA AND V.V,N. MURTY
Equation (2) is non-linear as the parameters K(0), D(O) and S(O) depend on the actual solution of O(Z,t). To solve the equation numerically, the following boundary conditions are set,
O(O,t)= 01(t), t > 0 , Z = 0 O(L,t)=O2( t), t>O, Z=L where, L is the depth of soil profile. In this study the initial moisture content is taken as field capacity, i.e.,
O(Z,O)=Oo(Z)
t=O,O<~Z<~L
Soil moisture pressure of the soil surface is estimated from the mean air temperature and relative humidity of surrounding air and it is assumed that pressure at the soil surface is at equilibrium with the atmosphere, then, ~u(0,t) can be derived from the following relationship (Feddes et al., 1976).
RT In (F) gt(0,t) =~g.g
(3)
where R is the universal gas constant (8.314 J. tool- 1. K - 1); T the absolute temperature (K); g the acceleration of gravity ( 9.81 m- s- 2); M the molecular weight of the water (0.018 kg.mo1-1 ); F the relative humidity in fractions; and ~, the moisture pressure (m). To find the surface soil moisture content the following relation given by Brooks and Corey (1966) was used. 0--0r
where, 0 is the soil moisture content at the surface (cm 3/cm3); Orthe residual moisture content (cm3/cm 3); 0s the saturation moisture content (cm3/cm 3); qJ the moisture pressure (cm); ~b the bubbling pressure of the soil (cm); 2 the pore size distribution index of the soil. Or is the residual moisture content or the residual saturation as defined by Brooks and Corey (1964), a moisture content at which the permeability is assumed to approach zero. In this study values of Or, ~', ~b and 2 and taken from Brooks and Corey (1964). A semi infinite depth with unit gradient in the last depth increment is assumed for the lower boundary condition to the model. It is assumed that the difference between the last two nodal points never exceeds a small factor equal to 0.005. Equation (2) is approximated by the following finite difference solution
MODELINGIRRIGATIONDELIVERIESFORTERTIARYUNITSIN LARGEIRRIGATIONSYSTEMS
201
(implicit form) where the space coordinate is denoted by i and time by j. The implicit formulation is given as follows:
~+1 -0{ At j
/11 { --
/, ~ x j + l / 2 D(O){$ 1/2" d U \ -K(O){ +1/2 AZ 1/2
~OZ)i+l/2 - -
j+l/2 1/2-TS(0 )i+l/2
(5) --D(0)J+ll~2~)
°l-t( i--1/2
l i - l / 2 --
S l ~v, t ~ ]lji+_ ll // 22
The details of the numerical solution for the above are given in Kemachandra ( 1991 ). The time step adopted for the numerical procedure is one day. The numerical procedure gives the soil moisture contents in the root zone at the selected node points and using these values, the soil moisture deficit and hence the irrigation requirements are calculated.
Crop and soil parameters At the start of the season, it is assumed that soil moisture is such that the soil profile is at field capacity. It is assumed that whenever rainfall occurs, it is distributed from the top layers up to an extent that each layer attains field capacity. Water still left over goes as deep percolation. As the areas considered were relatively flat, all the rainfall was considered as adding to the soil moisture. Potential evaporation (PE) is calculated as a fraction of the potential evapotranspiration of a crop.
PE=clexp (-c2La) PETe
(6)
where PETc is the potential crop evapotranspiration; La the leaf area index; and c, and c2 the regression coefficients with Cl = 1.0 and c2= 0.6. The formula gives an acceptable estimation for potential evaporation. In the present study, leaf area index is the leaf area index of sugarcane and it has been linearly interpolated between the available tabulated values. Potential transpiration was obtained by subtracting potential evaporation from crop evapotranspiration. The sink function proposed by Feddes et al. (1976) was used to calculate the moisture extracted by the plant roots from each layer. This approach states that, Pt
S(O) = 0~(0) - -
(7) DRZ where, S(O) is the water uptake by plants (cm3/cm3/day); Pt the potential transpiration ( c m / d a y ) ; DRz the rooting depth (cm); ol (0) the variable depending on soil moisture content (cm3/cm3). oe(0) is assumed to vary linearly between wilting point (oe (0) = 0 ) and field capacity (oe(0) = 1 ). 0~(0) at any moisture content 0 is given by,
R.A.D.KEMACHANDRAAND V.V.N.MURTY
202
(0-0wp) (Ovc-Owp)
(8)
Rainfallanalysis In the monsoon season, rainfall occurs on several days but intermittently. Rainfall contributes to the crop water requirements and it is desirable to consider the expected rainfall in determining the water deliveries from the irrigation system. In this study, past weekly rainfall records were analyzed to determine the expected rainfall at different probability levels. For this purpose Leaky law (Buishand, 1977 ) was used. During the season, the weekly rainfall series could have several zero values. For such a situation, Azhar et al. ( 1992 ) concluded that the Leaky law as outlined subsequently gives satisfactory values of the expected rainfall.
Leakylaw This is a mixed distribution consisting of a probability mass at zero, and a continuous distribution for positive values. I f X is a mixed variable that follows Leaky law with parameters p and O, then its probability distribution can be expressed as (Buishand, 1977), P(x=0) =exp(O)
(9) X
p(xO 1 (-k"~-~f ~ ~7-
(lO)
Equation ( 11 ) can be expressed in terms o f / , , the modified Bessel function of order 1 as:
P(X
x>0
(11)
0
After differentiation, this yields the probability density function as:
f(x)=exp(-O-px)~Oxli(2x/pOx),
x>0
(12)
The statistical parameters of mean, standard deviation and skewness coefficient can be estimated by:
MODELING IRRIGATION DELIVERIES FOR TERTIARY UNITS IN LARGE IRRIGATION SYSTEMS
203
#= E ( X ) = O/p
2=,/5b/p C~ = 3 / x / ~ The parameters p and O can be estimated by the method of moments as follows: p= 2 X / S 2 O= 2 X 2 / S 2
Estimation of these parameters of the Leaky law by the method of maximum likelihood is presented by Buishand ( 1977 ). In the present study this is used to fit weekly rainfall sequences and estimate the expected rainfall. Water allocation and distribution program (WADPRO) The procedures outlined are coded in a simulation program titled as the Water Allocation and Distribution Program (WADPRO), corresponding to a single season. Subprograms named by crops (PADDY and SUGAR) determine irrigation interval, irrigation date and amount of irrigation for the particular crop. Subroutines of PANP and PANS are used to estimate evapotranspiration of paddy and sugarcane, respectively. Subroutine FEDDES computes the values of Feddes sink function which is used in SUGAR subprogram. Subroutine TRID is used for solving the tridiagonal matrix in subprogram SUGAR. Subroutine FWR helps to update the paddy water requirement after incorporating actual water status in the field, while OPTIME computes total opening and closing time of tertiary canals. Subprogram EXRAIN computes the expected rainfall using the Leaky law method while Subprogram SRA calculates necessary statistical parameters for Leaky law. The structure of the program is shown in Fig. 1. Finally, the program WADPRO computes (i) water demand of farm allotment, tertiary canal and secondary canal and (ii) operational time of irrigation for farm allotments and tertiary canal. Water distribution method Principally, two distribution methods can be distinguished. The 'demand' method, where the end user decides about his 'demand' from the system and the 'supply' method, where the irrigation organization decides on the 'supply' to the end users. The former method is mostly combined with the distribution network based on down stream control, while the latter method is mostly combined with the distribution network based on upstream control. The computerized water allocation and distribution program is developed for the 'supply' method. This method is practised in nearly all irrigation systems in Thailand and many other developing countries.
204
R.A.D.KEMACHANDRAANDV.V.N.MURTY WADPRO
I
I
SRA ' Statistical Rainfall Analysis
INPUTS i
1
INPUTS " 35 years Rainfall Data
Data - Crop Data -Ponding Depth ( M a x / Min/Optimum ) - Seepage 8~ Percolation -Climatic
SUGAR
INPUTS i
I
1
-Climatic Data - Crop Data
- R o o t Zone Depth -Leaf
OUTPUTS ' 1 Statistical Rainfall Parameters
Area Index
Content at FC 8~ PWP
-Moisture
- B o u n d a r y Conditions for Governing Eq.
OUTPUT Weekly Water Req.
Expected Rainfall - W a t e r Req. per Irrigation I Interval I -Dote of Irrigation
_I
Computation of Combined Weekly Water Req.
DATA " - Land Area Field Wetness Report No. of AIIotments/T.Canal FAE 8 CCE Flow Rate of Form inlets
F
- Land Pre. Water Reg. - No. of Farm inlets/ Allotment - No. of Tertiary Canals - Max.Canal Capacities
" OUTPUTS - Time of Irrigation/Allotment Basis - Operational Time of Tertiary Canal
I
Water Demand at Head of Tertiary and Secondary Canal
-Weekly
Fig. 1. Structure of the Program WADPRO.
I
MODELING IRRIGATION DELIVERIES FOR TERTIARY UNITS IN LARGE IRRIGATION SYSTEMS
205
Computation of combined water requirement The total water requirement for a given area (e.g., a tertiary unit) consists of the water requirements of both paddy and sugarcane. For paddy, land preparation requires 200 m m of water (Kung, 1971 ) and this is to be included. The existing schedule followed for land preparation in the study area is for six weeks and 200 m m depth of water is distributed throughout this period. Area water requirement for both paddy and sugarcane is calculated by the following equation, Ar WRJ~ WR{_--
(13)
fae
where, WR~ is the area water requirement during the period; Ar the area of crop in the allotment; WR~ the crop water requirement during the period; and Fae the field application efficiency,. In the present study an application efficiency of 70% is assumed based on available information.
Incorporation of expected rainfall In paddy fields, to maintain the water depth at optimum level in the first 30 days, the upper optimum level of water depth is considered as 7 cm and during the rest of growing period as 10 cm. Maximum ponding depth, otherwise levee height is considered as 14 cm which was the general practice among the farmers in the area (Azhar et al., 1992 ) and it has been further proved by measuring levee heights of selected paddy fields in the study area. The expected rainfall in the current week is subtracted from the water supply for the same week. The differences of expected and actual rainfall can be adjusted in the water supply of the following week. The equation for incorporation of expected rainfall is as follows: EWR{ =WR{ - E R F +
(ERF-~ -RF-1
)
(14)
where, EWWa is the expected area water requirement during the period; WW the area water requirement during the period; E R F the expected rainfall during the period; E R F - 1 the expected rainfall during the preceding period; and R F - ~the rainfall during the preceding period. For the forecasting of the irrigation requirement of the week, an estimate has to be made of the rainfall during that week. In the Mae-Klong basin, historical daily rainfall data are available for the past 35 years. These daily data have been summarized as weekly values and frequency analysis using Leaky's law has been made, resulting in rainfall values at different probability levels.
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R,A.D. KEMACHANDRA AND V,V.N. MURTY
RESULTS AND DISCUSSION
The model and the approach outlined were applied to an irrigation system in Thailand. The irrigation system considered is the Mae Klong Project. The canal command area of the Tha Maka sub-project right bank of the Mae Klong river, has been chosen for intensive study. The major water distribution facilities in Tha Maka project consist of one main canal with secondary and tertiary canals (Fig. 2). Tertiary canals are connected directly to secondary canals. Check gates are provided along secondary as well as tertiary canals to increase the water level in the canals if needed. As the water supply in the secondary canals is diverted continuously throughout the season, irrigation water is available all the time in the tertiary canals. The system was primarily designed for rice irrigation with a dry season cropping intensity of 100% but at present the cropping patterns consist of both rice and sugarcane. The design peak water requirement at tertiary canal level adopted was 1.4 1/s/ha, covering 20 to 30 farm allotments. The length of the tertiary canal was 2.3 km on average with a maximum length of 3 km. All farm allotments were connected with the tertiary canal by means of farm inlets in the form of a preVAJRALONGKORN DAM
o,
z , ~ SCALE
8
tO km TO G U L F OF THAILAND
Fig. 2. Mae Klong Right Bank Irrigation Project (Tha Maka Sub Project).
MODELING IRRIGATION DELIVERIES FOR TERTIARY UNITS IN LARGE IRRIGATION SYSTEMS
207
fabricated concrete pipe 0.20 m in diameter. The number of farm inlets depends on size of the farm allotment. For the application of the model, the tertiary units situated in the secondary canal (2R-2R) were considered. Schematic layout of this canal is shown in Fig. 3. As stated earlier, the project at present uses a computer based model (WASAM) for determining the water deliveries in the system. The results obtained using the present model with those of WASAM are also compared.
Irrigation scheduling Paddy water requirements calculated by WADPRO on a weekly basis for the dry season of 1991 (February to June) are shown in Table 1. M a x i m u m water requirement occurs in the 6th week and it was found to be 95.5 mm. Since the upper level of the ponding depth is kept at 100 mm, the above is within the tolerable limit of paddy crop. It was found that the total water requirement in the dry season was 879 m m at the field level (1208 m m at head of tertiary canal) with the daily water requirement being typically in the range of 7 m m to 11 mm. Using the procedure outlined earlier, irrigation water requirement, irrigation interval and dates of irrigation of sugarcane in the dry season of year 1991 were determined. Sugarcane irrigation requirements with respect to different management allowed deficiency (MAD) were tested in order to obtain the volume of irrigation water which can be diverted in the tertiary canal throughout the week without exceeding the full capacity. Management allowed deficiency is the degree of soil moisture depletion (SMD) before the next irrigation is applied. Table 2 gives the irrigation schedules for sugarcane predicted by the model at different soil moisture depletion levels. It is generally recognised that 50% soil moisture depletion levels are acceptable for sugarcane. At this depletion, three irrigations were required during the period under consideration and the depths of irrigation calculated could be used for estimating the required canal capacities. Soil moisture profiles in sugarcane were predicted layer by layer on a daily basis throughout the season. As stated earlier, the governing equation for one dimensional vertical flow was solved by finite difference approximation and Feddes sink function was used. Simulation of soil-water content profiles was performed using estimated parameters and measured data. The study area consists of two predominant soil series named as Salaburi soil series (clayey) and Kamphaengsaen soil series (sandy loams). Available soil moisture was found to be 17% and 11% (by volume ) for the two soil series, respectively. In order to validate the soil moisture simulation model, soil moisture samples were collected at 20 cm depths of 120 cm soil profile in the sugarcane crop
208
R.A.D. KEMACHANDRA AND V.V.N. MURTY
DISTANCE (Kin) 0
2R
Main
canal
r'o
I
2(2R-2R)
'i° 4(2R-2R)
1.25
Cl
I(2R-2R)
1.5
2.0
6(2R-2R)
8(2R-2RII
2.2
IO(2R-2R)
2.7
3(2R-2R)
5(2R-2R) 3.1
r I
7(2R-2R)
3.5
9(2R-2R) 5.9
I. 2. 3. 4.
Maximum canal Flow Rate ( I / s ) Length of the canal {Kin) Number of Allotments Cultivation Area (ha)
Fig. 3. Schematic Layout of 2R-2R Secondary Canal.
209
MODELING IRRIGATION DELIVERIES FOR TERTIARY UNITS IN LARGE IRRIGATION SYSTEMS
TABLE 1 WADPRO weekly water requirement for paddy and sugarcane with respect to their irrigation interval Sugarcane
Paddy
Irrigation number /week
Water requirement (mm)
Irrigation number /week
Irrigation interval (days)
Water requirement (mm)
1 2 3 4 5 6 7 8 9 10 11 12 13 14
14.9 36.2 54.3 41.8 65.9 95.5 72.4 36.6 32.4 53.5 74.2 54.9 62.7 30.2
1 2 3
29 31 25
69.8 70.6 70.1
TABLE 2 Irrigation schedules predicated by the sugarcane model at different soil moisture depletion levels Irrig. number
l 2 3 4 5 6
SMD 0.4
SMD 0.5
SMD 0.6
SMD 0.7
lrrig. interval (days)
Depth of irrig, (cm)
Irrig. interval (days)
Depth of irrig, (cm)
Irrig. interval (days)
Depth of irrig, (cm)
Irrig. interval (days)
15 16 17 18 14 14
5.64 5.69 5.71 5.65 5.64 5.67
29 33 25
6.98 7.06 7.01
48 46
8.38 8.42
83
grown in both soil types. Soil samples were collected on 31, 58 and 78 days after the irrigation season had begun. The measured and simulated water contents showed a reasonable agreement as shown in Fig. 4. The details are presented in Kemachandra (1991). The results indicate that the proposed SUGAR model provides satisfactory simulations o f soil moisture profile for sugarcane. Since the sugarcane farmers adopt five irrigations for the season, it can be inferred that they operate at a depletion level between 0.4 and 0.5 of the available moisture.
210
R.A.D. KEMACHANDRAAND V.V.N. MURTY
0
Water Content CC3/CC3 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 .
.
.
0
0
Water Content CC3/CC3 0.05 0.1 0.15 0.2 0.25 03 0.35 0.4
-20
.
-40
-40 = -60i Q.
~
~
- 120
-80
=o -I00 -120
-I00 i
-140
-140
(a) 31 st day
( b I 31st
(Saloburi Soil)
Water Content CC3/CC3 0~ 0.05 0.1 0.15 0.2 0.25 03 0.35 0.4
-20 '
i
i- f _ ~ ~ . . . .
-60 o.
-8o
2
0
~
"~ - 4 0
I I It
I
-,oo -,20
Water Content CC3/CC3 00 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
-
~ -40
day (Kamphoengsean Soil)
" .
.
.
.
.
N .
.
.
.
t
htl
t \ttr-1
,'-
-140 (e) 76th
day (Salaburi Soil) Simulated
( f ) 76 fh
day (Kamphaengsean Soil)
--+--Measured
Fig. 4. Soil water content versus soil depth at different days of the irrigationseason. Total water requirement for sugarcane in the dry season was 210 mm (289 mm at the head of the tertiary canal) with the daily water requirement being typically in the range of 4 mm to 9 mm. The program developed can be used both for estimating the irrigation water deliveries and evaluating the irrigation schedules at the end of the irrigation season. In the latter case, the program can be used for calculating the required irrigations and these can be compared with the actual irrigations.
Incorporation of expected rainfall A comparison of actual rainfall with the Leaky law method in the EXRAIN program and Weibull plotting position method which is used by WASAM has been made to understand the reliability of expected rainfall. Operational probability of 80% has been used in the Leaky law method. In a separate study (Azhar et al., 1992 ) it has been observed that the expected values of rainfall as predicted by the Leaky law method were more satisfactory than those predicted by the Weibull plotting position method. It may be pointed out that in lowland paddy, consideration of the expected rainfall is more significant during the monsoon season.
MODELING IRRIGATION DELIVERIES FOR TERTIARY UNITS 1N LARGE IRRIGATION SYSTEMS
211
Operational Time (dayl)
011111| Flow Rate (118)
100 r'-N~SAM 90
--4-- WU)PRO ACTUAL
80
70
~]
OPTIME-VIASAM
E~
OPTIME-ACTUAL
OPTIME-~DPRO
60 60 40 30 20 10
0
H 1
2
3
4
6
6
7
8
9
10
11
12
13
14
16
Week No (26102191 to 04/0Q/91)
Fig. 5. Comparisonof operational times and flowrates: canalNo. 7. Operational Time (daya)
Canal Flow Rate (l/s) 100
Y4~SAM
90
I
l ~ l
I
I ~ + ~ - ~ - - - ~ - ~ - - ~
. i
I
WkDPflO ACTUAL
80
OPTIME - 11~,SAM
70
OPTIME -Ni.OPRO
60
E~
40
~
'
OPTIME-ACTUAL
\ 6 4
H' I
2
3
4
6 6 7 8 9 I0 tl Wlek No ('J'1~/02/ill Iio 04106/91)
12
13
14
16
0
Fig. 6. C o m p a r i s o n o f o p e r a t i o n a l t i m e s a n d flow rates: c a n a l N o . 8.
Flow rates and operational time The WADPRO program was also used to calculate the flow rates required in the tertiary canals and consequently the operation time. Table 3 shows for the ten tertiary canals, mentioned in figure 3, the flow rates computed with the WASAM and WADPRO models, the observed flow rate and the maxim u m flow rate. A major cause of the low canal flow rate in the field may be due to the opening of all tertiary canals of the secondary canal throughout the week. There are seven tertiary canals of 0.09 m3/s flow rate while the remain-
212
R.A.D. KEMACHANDRAAND V,V.N,MURTY
Canal Flme Rite (1/I)
Operdk)n,,J ~qme (d~/o)
70 ~M -4-- V ~ R O
80
ACTUAL OPTIME -WLSAM
8O
OPTIME -WLDPRO E~
40
1
2
8
4
6 6 7 8 9 10 11 Week No (28/02/11t la 04/06/9t)
12
18
OPTIME-ACTUAL
14
Fig. 7. C o m p a r i s o n o f operational times and flow rates: canal No. 9.
TABLE3 Averagete~ia~canalflowrates Canal number
l
2 3 4 5 6 7 8 9 10
WASAM flow rate
WADPRO flow rate
Observed flow rate
Maximum flow rate
(l/s)
(l/s)
(l/s)
(l/s)
54 46 34 44 44 35 41 54 25 30
86 85 89 85 87 55 84 88 60 60
41
90 90 90 90 90 60 90 90 60 6O
68 69 41 71 27 38 39 25 25
ing three have 0.06 m3/s. The m a x i m u m capacity of the secondary canal is 0.75 m3/s. Therefore it can be stated that all tertiary canals cannot be operated at the same time at m a x i m u m capacity. Variation of different times of irrigation advised by WASAM, WADPRO and actual conditions with respect to their flow rate are shown for selected tertiary canals in Figs. 5, 6 and 7. WADPRO calculates the total water requirement in a tertiary unit. The flow time or the operation time required is calculated knowing the m a x i m u m canal capacity at the head of the tertiary canal and the total water requirements.
MODELINGIRRIGATIONDELIVERIESFORTERTIARYUNITSIN LARGEIRRIGATIONSYSTEMS
213
It can be seen from Table 3 and Figures 5, 6, and 7 that in the present operation policy low canal flow rates are being used requiring higher operating times. This necessitates almost continuous canal flows in the system resulting sometimes in inefficient utilization. WADPRO model uses the higher canal capacities which results in lower operational time. Since the tertiary units are to be run only for a limited time, it would be possible to close them for some time, resulting in adoption of a rotational system instead of the existing continuous flow system. This aspect requires further study. CONCLUSIONS
The following conclusions can be drawn from this study: 1. In a large irrigation system, for estimating the canal diversions at the tertiary level, models based upon a water balance approach for low land paddy and simulation of soil moisture profiles for sugarcanes proved to be satisfactory. 2. In estimating irrigation requirements for scheduling of irrigation, expected rainfall values were incorporated based upon analysis of previous rainfall records. Leaky law was used to estimate the expected rainfall at different probability levels and was seen to give satisfactory values. 3. The computer program WADPRO (Water Allocation and Distribution Program) which combines the irrigation water requirements and the expected rainfall was found to give satisfactory values for canal diversions at the tertiary and secondary levels. Application of the model to an actual irrigation system indicates the possibility that the system could be operated on a rotational basis instead of the continuous basis as at present. ACKNOWLEDGEMENTS
The first author acknowledges the assistance provided by the Canadian International Development Agency (CIDA) for his studies at the Asian Institute of Technology. The authors wish to thank the anonymous reviewer whose comments vastly improved the presentation.
REFERENCES Anderson, R.L. and Maass, A., 1971. A simulation of irrigation systems. Technical Bulletin No. 1431, U.S. Department of Agriculture. Azhar, A.H., Murty, V.V.N. and Phien, H.N., 1992. Modeling irrigation schedules for low land rice with stochastic rainfall, J. Irrig. Drain. Engrg. ASCE, 118: 36-55. Brooks, R.H. and Corey, A.T., 1964. Hydraulic properties of porus media, Hydrology Paper No. 3, Civil Engineering Dept., Colorado State Univ., Fort Collins, Colorado. Brower, L.A. and Buchheim, J.F., 1982. An irrigation district computerized water management
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system, Ninth Technical Conference of U.S. Committee on Irrigation, Drainage and Flood Control, Jackson, Miss. Boman, B.J. and Hills, R.W., 1989. LP Operation model for on-demand canal system, J. Irrig. Drain. Engrg., ASCE, 115: 687-700. Buishand, T.A., 1977. Stochastic modelling of daily rainfall sequences, H. Veenman and Zonen B.V., Wageningen. Doorenbos, J. and Pruitt, W.O., 1977. Guideline for predicting the crop water requirement. FAO Irrig. and Drain. Paper No. 24, Rome, Italy. Feedes, R.A., Kowalik, P.J. and Zaradny, H., 1978. Simulation of field water use and crop yield. Center for Agricultural Publishing and Documentation, Wageningen. Jensen, M.E., Robb, D.C.N. and Franzoy, G.E., 1970. Scheduling irrigation using climate-cropsoil data, J. Irrig. Drain. Div. Proc. of ASCE. 96(IR1 ): 25-38. Kemachandra, R.A.D. 1991. Interfacing irrigation deliveries in large irrigation system with farm water requirements. M. Engg. Thesis, AIT, Bangkok, Thailand. Kung, P. 1971. Irrigation agronomy in monsoon Asia, FAO, Rome, Italy. Rajput, T.B.S. and Michael, A.M., 1989. Scheduling of canal deliveries. 1. Development of and irrigation canal scheduling model, J. Irrig. Power (Central Board of Irrigation, India), 46: 23-39.
197
© 1992 Elsevier Science Publishers B.V. All rights reserved. 0378-3774/92/$05.00
Modeling irrigation deliveries for tertiary units in large irrigation systems R.A.D. Kemachandra and V.V.N. Murty Irrigation Engineering and Management Program, Asian Institute of Technology, G.P.0. Box 2 754 Bangkok, Thailand
ABSTRACT Kemachandra, R.A.D. and Murty, V.V.N., 1992. Modeling irrigation deliveries for tertiary units in large irrigation systems. Agric. WaterManage., 21: 197-214. A simulation model for the purpose of estimating water deliveries at the tertiary and secondary canal levels of large irrigation systems has been developed. The model is based on a water balance approach for estimating irrigation water requirements for lowland paddy and a soil moisture simulation approach for determining the irrigation requirements of upland crops. Expected rainfall at different probability levels during the irrigation season was estimated using past rainfall data and Leaky law. The model was applied to an irrigation system in Thailand for determining the required irrigation deliveries and for comparing the same with the existing practices. Results of the application indicate that considerable improvements in the water delivery schedules are possible.
INTRODUCTION
In the past two to three decades, several large irrigation systems have come into operation in the developing countries of Asia. These systems usually consist of one or more storage reservoirs and a canal system with related structures. Water is distributed over a large area with varying soils, topography and cropping patterns. In many of these large systems, water deliveries are controlled from a central or a fixed office. In each of the projects a water delivery pattern viz., continuous, intermittent or rotation is predecided. However, daily operation of the system is based upon the information obtained from the command area. This information could consist of the climatic parameters and the crop conditions. Based on the climatic parameters, the soil moisture depletion levels and, consequently, the crop water requirements are assessed and irrigation Correspondence to: Dr. V.V.N. Murty, Irrigation Engineering and Management Program, Asian Institute of Technology, G.P.O. Box 2754, Bangkok, 10510, Thailand.
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R.A.D. KEMACHANDRA AND V.V.N. MURTY
deliveries to different command units are decided. The accuracy of the decisions depend upon the computing facilities available and the methodology followed. In many of the systems where such facilities are not available, irrigation deliveries are decided upon experience and available general information. Such decisions could lead to inequitable deliveries of irrigation water. Computer simulation of irrigation systems has been attempted by several workers for the purpose of efficient operation of the systems. Anderson and Maass ( 1971 ) developed computer simulation procedures to study the effect of water supplies and operation rules on the production and income of irrigated farms. The irrigation model proposed bv Jensen et al. ( 1971 ) uses the climatic, crop and soil data for the purpose of scheduling irrigation using computer based approach. Rajput and Michael (1989) adopted a soil water balance approach for development of an integrated canal scheduling model. The U.S. Department of Interior, Bureau of Reclamation (USBR), has developed programs to assist in irrigation project management (Brower and Buchheim, 1982). Boman and Hills (1989) proposed a model for on-demand canal systems based on linear programming approach. Many of the models cited in the literature are developed for specific conditions and cannot be used directly in all irrigation systems. In the Mae-Klong irrigation project in Thailand, a computer-based water allocation model WASAM (Water Allocation Scheduling And Monitoring) is in use. This model essentially considers the depth of water in lowland paddy fields as the criterion for allocating the water to different tertiary units. Expected rainfall is estimated using the Weibull plotting position. In the present study a computer-based water allocation model that could be used in large irrigation systems is presented. The application of the model to an existing irrigation system is also discussed. MODEL DEVELOPMENT
The purpose of the model developed is to estimate the weekly requirement at the tertiary and secondary levels of the irrigation system. The model estimates the actual crop water requirements for lowland paddy and upland irrigated crops. It takes into consideration the expected rainfall based upon an analysis of the available rainfall data. The theoretical considerations are as follows:
Estimating irrigation requirementsfor lowlandpaddy A generalized water balance equation for a given period in the paddy field as follows: WJ= WJ-' + Rt~- ET~ -SJ+I-~-O{ where,
(1)
MODELING IRRIGATION DELIVERIES FOR TERTIARY UNITS IN LARGE IRRIGATION SYSTEMS
] 99
W j is the water depth in the field at the end of the given period; W:- l the water depth in the field at the beginning of the given period; Rt~ the effective rainfall during the period; ET~ the actual crop evapotranspiration; S j the mean seepage or percolation for the period; Pr the depth of the irrigation; and D~ the surface drainage (if any). All the terms are in depth ( m m ) units. If we define Wmax as the m a x i m u m depth of water possible in the paddy field, Woo, the o p t i m u m depth, and Wmin, the m i n i m u m depth at which irrigation is to be given, the water balance equation can be used for determining the irrigation schedules and the depth of water to be applied in each irrigation. The values of ET: and S ~ are estimated for each day. Rainfall occurring on the day will add to the water balance equation to the extent that the field is capable of retaining the rainfall based on the initial depth of water on the day. Excess rainfall will go as drainage. In the present study ET~ was determined using the pan evaporation method (Doorenbos and Pruitt, 1977) and seepage and percolation were adopted from available data. Storage refers to the amount of water on the paddy basin which is depleted before irrigation is applied. During most of the crop growth period, m i n i m u m depth of water in the paddy basin is maintained constantly to submerge the soil for weed and insect control. In the paddy fields, extra levee height is allowed to catch and store the rainfall. In the present study, lJ~ax has been taken as 14 cm and Wmin has been varied from 3 to 5 cm according to the growth period. Wop~for the first 30 days time was taken as 7 cm and for the rest of 70 days it was 10 cm. At the beginning of the computation, W j-~ is set equal to Wopt. The amount of irrigation was computed as follows: - if WJ> Wmax, there is drainage/)Jr and W ./is set equal to Wmax. -- if Wmi n < WJ< mmax, it becomes the actual depth for the day. - if W:< Wmin,the irrigation to the difference between W o p t and W -/is applied to bring the water level back Woot.
Irrigation requirements of upland crops A soil moisture simulation approach is used to study the irrigation schedules in the irrigated crops other than paddy. The governing differential equation considered is as follows: 0
O0
O0- ffz{D( O)'-~}-o~'K( O)-S(
(2)
where, 0 is the moisture content ( L 3 / L 3 ) ; t the time (T); z the depth (L); D (0) the soil moisture diffusivity (L2/T); K(0) the hydraulic conductivity ( L / T ) ; and S(O) the sink t e r m ( L 3 / L 3 T ) .
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R.A.D. KEMACHANDRA AND V.V,N. MURTY
Equation (2) is non-linear as the parameters K(0), D(O) and S(O) depend on the actual solution of O(Z,t). To solve the equation numerically, the following boundary conditions are set,
O(O,t)= 01(t), t > 0 , Z = 0 O(L,t)=O2( t), t>O, Z=L where, L is the depth of soil profile. In this study the initial moisture content is taken as field capacity, i.e.,
O(Z,O)=Oo(Z)
t=O,O<~Z<~L
Soil moisture pressure of the soil surface is estimated from the mean air temperature and relative humidity of surrounding air and it is assumed that pressure at the soil surface is at equilibrium with the atmosphere, then, ~u(0,t) can be derived from the following relationship (Feddes et al., 1976).
RT In (F) gt(0,t) =~g.g
(3)
where R is the universal gas constant (8.314 J. tool- 1. K - 1); T the absolute temperature (K); g the acceleration of gravity ( 9.81 m- s- 2); M the molecular weight of the water (0.018 kg.mo1-1 ); F the relative humidity in fractions; and ~, the moisture pressure (m). To find the surface soil moisture content the following relation given by Brooks and Corey (1966) was used. 0--0r
where, 0 is the soil moisture content at the surface (cm 3/cm3); Orthe residual moisture content (cm3/cm 3); 0s the saturation moisture content (cm3/cm 3); qJ the moisture pressure (cm); ~b the bubbling pressure of the soil (cm); 2 the pore size distribution index of the soil. Or is the residual moisture content or the residual saturation as defined by Brooks and Corey (1964), a moisture content at which the permeability is assumed to approach zero. In this study values of Or, ~', ~b and 2 and taken from Brooks and Corey (1964). A semi infinite depth with unit gradient in the last depth increment is assumed for the lower boundary condition to the model. It is assumed that the difference between the last two nodal points never exceeds a small factor equal to 0.005. Equation (2) is approximated by the following finite difference solution
MODELINGIRRIGATIONDELIVERIESFORTERTIARYUNITSIN LARGEIRRIGATIONSYSTEMS
201
(implicit form) where the space coordinate is denoted by i and time by j. The implicit formulation is given as follows:
~+1 -0{ At j
/11 { --
/, ~ x j + l / 2 D(O){$ 1/2" d U \ -K(O){ +1/2 AZ 1/2
~OZ)i+l/2 - -
j+l/2 1/2-TS(0 )i+l/2
(5) --D(0)J+ll~2~)
°l-t( i--1/2
l i - l / 2 --
S l ~v, t ~ ]lji+_ ll // 22
The details of the numerical solution for the above are given in Kemachandra ( 1991 ). The time step adopted for the numerical procedure is one day. The numerical procedure gives the soil moisture contents in the root zone at the selected node points and using these values, the soil moisture deficit and hence the irrigation requirements are calculated.
Crop and soil parameters At the start of the season, it is assumed that soil moisture is such that the soil profile is at field capacity. It is assumed that whenever rainfall occurs, it is distributed from the top layers up to an extent that each layer attains field capacity. Water still left over goes as deep percolation. As the areas considered were relatively flat, all the rainfall was considered as adding to the soil moisture. Potential evaporation (PE) is calculated as a fraction of the potential evapotranspiration of a crop.
PE=clexp (-c2La) PETe
(6)
where PETc is the potential crop evapotranspiration; La the leaf area index; and c, and c2 the regression coefficients with Cl = 1.0 and c2= 0.6. The formula gives an acceptable estimation for potential evaporation. In the present study, leaf area index is the leaf area index of sugarcane and it has been linearly interpolated between the available tabulated values. Potential transpiration was obtained by subtracting potential evaporation from crop evapotranspiration. The sink function proposed by Feddes et al. (1976) was used to calculate the moisture extracted by the plant roots from each layer. This approach states that, Pt
S(O) = 0~(0) - -
(7) DRZ where, S(O) is the water uptake by plants (cm3/cm3/day); Pt the potential transpiration ( c m / d a y ) ; DRz the rooting depth (cm); ol (0) the variable depending on soil moisture content (cm3/cm3). oe(0) is assumed to vary linearly between wilting point (oe (0) = 0 ) and field capacity (oe(0) = 1 ). 0~(0) at any moisture content 0 is given by,
R.A.D.KEMACHANDRAAND V.V.N.MURTY
202
(0-0wp) (Ovc-Owp)
(8)
Rainfallanalysis In the monsoon season, rainfall occurs on several days but intermittently. Rainfall contributes to the crop water requirements and it is desirable to consider the expected rainfall in determining the water deliveries from the irrigation system. In this study, past weekly rainfall records were analyzed to determine the expected rainfall at different probability levels. For this purpose Leaky law (Buishand, 1977 ) was used. During the season, the weekly rainfall series could have several zero values. For such a situation, Azhar et al. ( 1992 ) concluded that the Leaky law as outlined subsequently gives satisfactory values of the expected rainfall.
Leakylaw This is a mixed distribution consisting of a probability mass at zero, and a continuous distribution for positive values. I f X is a mixed variable that follows Leaky law with parameters p and O, then its probability distribution can be expressed as (Buishand, 1977), P(x=0) =exp(O)
(9) X
p(x
(lO)
Equation ( 11 ) can be expressed in terms o f / , , the modified Bessel function of order 1 as:
P(X
x>0
(11)
0
After differentiation, this yields the probability density function as:
f(x)=exp(-O-px)~Oxli(2x/pOx),
x>0
(12)
The statistical parameters of mean, standard deviation and skewness coefficient can be estimated by:
MODELING IRRIGATION DELIVERIES FOR TERTIARY UNITS IN LARGE IRRIGATION SYSTEMS
203
#= E ( X ) = O/p
2=,/5b/p C~ = 3 / x / ~ The parameters p and O can be estimated by the method of moments as follows: p= 2 X / S 2 O= 2 X 2 / S 2
Estimation of these parameters of the Leaky law by the method of maximum likelihood is presented by Buishand ( 1977 ). In the present study this is used to fit weekly rainfall sequences and estimate the expected rainfall. Water allocation and distribution program (WADPRO) The procedures outlined are coded in a simulation program titled as the Water Allocation and Distribution Program (WADPRO), corresponding to a single season. Subprograms named by crops (PADDY and SUGAR) determine irrigation interval, irrigation date and amount of irrigation for the particular crop. Subroutines of PANP and PANS are used to estimate evapotranspiration of paddy and sugarcane, respectively. Subroutine FEDDES computes the values of Feddes sink function which is used in SUGAR subprogram. Subroutine TRID is used for solving the tridiagonal matrix in subprogram SUGAR. Subroutine FWR helps to update the paddy water requirement after incorporating actual water status in the field, while OPTIME computes total opening and closing time of tertiary canals. Subprogram EXRAIN computes the expected rainfall using the Leaky law method while Subprogram SRA calculates necessary statistical parameters for Leaky law. The structure of the program is shown in Fig. 1. Finally, the program WADPRO computes (i) water demand of farm allotment, tertiary canal and secondary canal and (ii) operational time of irrigation for farm allotments and tertiary canal. Water distribution method Principally, two distribution methods can be distinguished. The 'demand' method, where the end user decides about his 'demand' from the system and the 'supply' method, where the irrigation organization decides on the 'supply' to the end users. The former method is mostly combined with the distribution network based on down stream control, while the latter method is mostly combined with the distribution network based on upstream control. The computerized water allocation and distribution program is developed for the 'supply' method. This method is practised in nearly all irrigation systems in Thailand and many other developing countries.
204
R.A.D.KEMACHANDRAANDV.V.N.MURTY WADPRO
I
I
SRA ' Statistical Rainfall Analysis
INPUTS i
1
INPUTS " 35 years Rainfall Data
Data - Crop Data -Ponding Depth ( M a x / Min/Optimum ) - Seepage 8~ Percolation -Climatic
SUGAR
INPUTS i
I
1
-Climatic Data - Crop Data
- R o o t Zone Depth -Leaf
OUTPUTS ' 1 Statistical Rainfall Parameters
Area Index
Content at FC 8~ PWP
-Moisture
- B o u n d a r y Conditions for Governing Eq.
OUTPUT Weekly Water Req.
Expected Rainfall - W a t e r Req. per Irrigation I Interval I -Dote of Irrigation
_I
Computation of Combined Weekly Water Req.
DATA " - Land Area Field Wetness Report No. of AIIotments/T.Canal FAE 8 CCE Flow Rate of Form inlets
F
- Land Pre. Water Reg. - No. of Farm inlets/ Allotment - No. of Tertiary Canals - Max.Canal Capacities
" OUTPUTS - Time of Irrigation/Allotment Basis - Operational Time of Tertiary Canal
I
Water Demand at Head of Tertiary and Secondary Canal
-Weekly
Fig. 1. Structure of the Program WADPRO.
I
MODELING IRRIGATION DELIVERIES FOR TERTIARY UNITS IN LARGE IRRIGATION SYSTEMS
205
Computation of combined water requirement The total water requirement for a given area (e.g., a tertiary unit) consists of the water requirements of both paddy and sugarcane. For paddy, land preparation requires 200 m m of water (Kung, 1971 ) and this is to be included. The existing schedule followed for land preparation in the study area is for six weeks and 200 m m depth of water is distributed throughout this period. Area water requirement for both paddy and sugarcane is calculated by the following equation, Ar WRJ~ WR{_--
(13)
fae
where, WR~ is the area water requirement during the period; Ar the area of crop in the allotment; WR~ the crop water requirement during the period; and Fae the field application efficiency,. In the present study an application efficiency of 70% is assumed based on available information.
Incorporation of expected rainfall In paddy fields, to maintain the water depth at optimum level in the first 30 days, the upper optimum level of water depth is considered as 7 cm and during the rest of growing period as 10 cm. Maximum ponding depth, otherwise levee height is considered as 14 cm which was the general practice among the farmers in the area (Azhar et al., 1992 ) and it has been further proved by measuring levee heights of selected paddy fields in the study area. The expected rainfall in the current week is subtracted from the water supply for the same week. The differences of expected and actual rainfall can be adjusted in the water supply of the following week. The equation for incorporation of expected rainfall is as follows: EWR{ =WR{ - E R F +
(ERF-~ -RF-1
)
(14)
where, EWWa is the expected area water requirement during the period; WW the area water requirement during the period; E R F the expected rainfall during the period; E R F - 1 the expected rainfall during the preceding period; and R F - ~the rainfall during the preceding period. For the forecasting of the irrigation requirement of the week, an estimate has to be made of the rainfall during that week. In the Mae-Klong basin, historical daily rainfall data are available for the past 35 years. These daily data have been summarized as weekly values and frequency analysis using Leaky's law has been made, resulting in rainfall values at different probability levels.
206
R,A.D. KEMACHANDRA AND V,V.N. MURTY
RESULTS AND DISCUSSION
The model and the approach outlined were applied to an irrigation system in Thailand. The irrigation system considered is the Mae Klong Project. The canal command area of the Tha Maka sub-project right bank of the Mae Klong river, has been chosen for intensive study. The major water distribution facilities in Tha Maka project consist of one main canal with secondary and tertiary canals (Fig. 2). Tertiary canals are connected directly to secondary canals. Check gates are provided along secondary as well as tertiary canals to increase the water level in the canals if needed. As the water supply in the secondary canals is diverted continuously throughout the season, irrigation water is available all the time in the tertiary canals. The system was primarily designed for rice irrigation with a dry season cropping intensity of 100% but at present the cropping patterns consist of both rice and sugarcane. The design peak water requirement at tertiary canal level adopted was 1.4 1/s/ha, covering 20 to 30 farm allotments. The length of the tertiary canal was 2.3 km on average with a maximum length of 3 km. All farm allotments were connected with the tertiary canal by means of farm inlets in the form of a preVAJRALONGKORN DAM
o,
z , ~ SCALE
8
tO km TO G U L F OF THAILAND
Fig. 2. Mae Klong Right Bank Irrigation Project (Tha Maka Sub Project).
MODELING IRRIGATION DELIVERIES FOR TERTIARY UNITS IN LARGE IRRIGATION SYSTEMS
207
fabricated concrete pipe 0.20 m in diameter. The number of farm inlets depends on size of the farm allotment. For the application of the model, the tertiary units situated in the secondary canal (2R-2R) were considered. Schematic layout of this canal is shown in Fig. 3. As stated earlier, the project at present uses a computer based model (WASAM) for determining the water deliveries in the system. The results obtained using the present model with those of WASAM are also compared.
Irrigation scheduling Paddy water requirements calculated by WADPRO on a weekly basis for the dry season of 1991 (February to June) are shown in Table 1. M a x i m u m water requirement occurs in the 6th week and it was found to be 95.5 mm. Since the upper level of the ponding depth is kept at 100 mm, the above is within the tolerable limit of paddy crop. It was found that the total water requirement in the dry season was 879 m m at the field level (1208 m m at head of tertiary canal) with the daily water requirement being typically in the range of 7 m m to 11 mm. Using the procedure outlined earlier, irrigation water requirement, irrigation interval and dates of irrigation of sugarcane in the dry season of year 1991 were determined. Sugarcane irrigation requirements with respect to different management allowed deficiency (MAD) were tested in order to obtain the volume of irrigation water which can be diverted in the tertiary canal throughout the week without exceeding the full capacity. Management allowed deficiency is the degree of soil moisture depletion (SMD) before the next irrigation is applied. Table 2 gives the irrigation schedules for sugarcane predicted by the model at different soil moisture depletion levels. It is generally recognised that 50% soil moisture depletion levels are acceptable for sugarcane. At this depletion, three irrigations were required during the period under consideration and the depths of irrigation calculated could be used for estimating the required canal capacities. Soil moisture profiles in sugarcane were predicted layer by layer on a daily basis throughout the season. As stated earlier, the governing equation for one dimensional vertical flow was solved by finite difference approximation and Feddes sink function was used. Simulation of soil-water content profiles was performed using estimated parameters and measured data. The study area consists of two predominant soil series named as Salaburi soil series (clayey) and Kamphaengsaen soil series (sandy loams). Available soil moisture was found to be 17% and 11% (by volume ) for the two soil series, respectively. In order to validate the soil moisture simulation model, soil moisture samples were collected at 20 cm depths of 120 cm soil profile in the sugarcane crop
208
R.A.D. KEMACHANDRA AND V.V.N. MURTY
DISTANCE (Kin) 0
2R
Main
canal
r'o
I
2(2R-2R)
'i° 4(2R-2R)
1.25
Cl
I(2R-2R)
1.5
2.0
6(2R-2R)
8(2R-2RII
2.2
IO(2R-2R)
2.7
3(2R-2R)
5(2R-2R) 3.1
r I
7(2R-2R)
3.5
9(2R-2R) 5.9
I. 2. 3. 4.
Maximum canal Flow Rate ( I / s ) Length of the canal {Kin) Number of Allotments Cultivation Area (ha)
Fig. 3. Schematic Layout of 2R-2R Secondary Canal.
209
MODELING IRRIGATION DELIVERIES FOR TERTIARY UNITS IN LARGE IRRIGATION SYSTEMS
TABLE 1 WADPRO weekly water requirement for paddy and sugarcane with respect to their irrigation interval Sugarcane
Paddy
Irrigation number /week
Water requirement (mm)
Irrigation number /week
Irrigation interval (days)
Water requirement (mm)
1 2 3 4 5 6 7 8 9 10 11 12 13 14
14.9 36.2 54.3 41.8 65.9 95.5 72.4 36.6 32.4 53.5 74.2 54.9 62.7 30.2
1 2 3
29 31 25
69.8 70.6 70.1
TABLE 2 Irrigation schedules predicated by the sugarcane model at different soil moisture depletion levels Irrig. number
l 2 3 4 5 6
SMD 0.4
SMD 0.5
SMD 0.6
SMD 0.7
lrrig. interval (days)
Depth of irrig, (cm)
Irrig. interval (days)
Depth of irrig, (cm)
Irrig. interval (days)
Depth of irrig, (cm)
Irrig. interval (days)
15 16 17 18 14 14
5.64 5.69 5.71 5.65 5.64 5.67
29 33 25
6.98 7.06 7.01
48 46
8.38 8.42
83
grown in both soil types. Soil samples were collected on 31, 58 and 78 days after the irrigation season had begun. The measured and simulated water contents showed a reasonable agreement as shown in Fig. 4. The details are presented in Kemachandra (1991). The results indicate that the proposed SUGAR model provides satisfactory simulations o f soil moisture profile for sugarcane. Since the sugarcane farmers adopt five irrigations for the season, it can be inferred that they operate at a depletion level between 0.4 and 0.5 of the available moisture.
210
R.A.D. KEMACHANDRAAND V.V.N. MURTY
0
Water Content CC3/CC3 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 .
.
.
0
0
Water Content CC3/CC3 0.05 0.1 0.15 0.2 0.25 03 0.35 0.4
-20
.
-40
-40 = -60i Q.
~
~
- 120
-80
=o -I00 -120
-I00 i
-140
-140
(a) 31 st day
( b I 31st
(Saloburi Soil)
Water Content CC3/CC3 0~ 0.05 0.1 0.15 0.2 0.25 03 0.35 0.4
-20 '
i
i- f _ ~ ~ . . . .
-60 o.
-8o
2
0
~
"~ - 4 0
I I It
I
-,oo -,20
Water Content CC3/CC3 00 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
-
~ -40
day (Kamphoengsean Soil)
" .
.
.
.
.
N .
.
.
.
t
htl
t \ttr-1
,'-
-140 (e) 76th
day (Salaburi Soil) Simulated
( f ) 76 fh
day (Kamphaengsean Soil)
--+--Measured
Fig. 4. Soil water content versus soil depth at different days of the irrigationseason. Total water requirement for sugarcane in the dry season was 210 mm (289 mm at the head of the tertiary canal) with the daily water requirement being typically in the range of 4 mm to 9 mm. The program developed can be used both for estimating the irrigation water deliveries and evaluating the irrigation schedules at the end of the irrigation season. In the latter case, the program can be used for calculating the required irrigations and these can be compared with the actual irrigations.
Incorporation of expected rainfall A comparison of actual rainfall with the Leaky law method in the EXRAIN program and Weibull plotting position method which is used by WASAM has been made to understand the reliability of expected rainfall. Operational probability of 80% has been used in the Leaky law method. In a separate study (Azhar et al., 1992 ) it has been observed that the expected values of rainfall as predicted by the Leaky law method were more satisfactory than those predicted by the Weibull plotting position method. It may be pointed out that in lowland paddy, consideration of the expected rainfall is more significant during the monsoon season.
MODELING IRRIGATION DELIVERIES FOR TERTIARY UNITS 1N LARGE IRRIGATION SYSTEMS
211
Operational Time (dayl)
011111| Flow Rate (118)
100 r'-N~SAM 90
--4-- WU)PRO ACTUAL
80
70
~]
OPTIME-VIASAM
E~
OPTIME-ACTUAL
OPTIME-~DPRO
60 60 40 30 20 10
0
H 1
2
3
4
6
6
7
8
9
10
11
12
13
14
16
Week No (26102191 to 04/0Q/91)
Fig. 5. Comparisonof operational times and flowrates: canalNo. 7. Operational Time (daya)
Canal Flow Rate (l/s) 100
Y4~SAM
90
I
l ~ l
I
I ~ + ~ - ~ - - - ~ - ~ - - ~
. i
I
WkDPflO ACTUAL
80
OPTIME - 11~,SAM
70
OPTIME -Ni.OPRO
60
E~
40
~
'
OPTIME-ACTUAL
\ 6 4
H' I
2
3
4
6 6 7 8 9 I0 tl Wlek No ('J'1~/02/ill Iio 04106/91)
12
13
14
16
0
Fig. 6. C o m p a r i s o n o f o p e r a t i o n a l t i m e s a n d flow rates: c a n a l N o . 8.
Flow rates and operational time The WADPRO program was also used to calculate the flow rates required in the tertiary canals and consequently the operation time. Table 3 shows for the ten tertiary canals, mentioned in figure 3, the flow rates computed with the WASAM and WADPRO models, the observed flow rate and the maxim u m flow rate. A major cause of the low canal flow rate in the field may be due to the opening of all tertiary canals of the secondary canal throughout the week. There are seven tertiary canals of 0.09 m3/s flow rate while the remain-
212
R.A.D. KEMACHANDRAAND V,V.N,MURTY
Canal Flme Rite (1/I)
Operdk)n,,J ~qme (d~/o)
70 ~M -4-- V ~ R O
80
ACTUAL OPTIME -WLSAM
8O
OPTIME -WLDPRO E~
40
1
2
8
4
6 6 7 8 9 10 11 Week No (28/02/11t la 04/06/9t)
12
18
OPTIME-ACTUAL
14
Fig. 7. C o m p a r i s o n o f operational times and flow rates: canal No. 9.
TABLE3 Averagete~ia~canalflowrates Canal number
l
2 3 4 5 6 7 8 9 10
WASAM flow rate
WADPRO flow rate
Observed flow rate
Maximum flow rate
(l/s)
(l/s)
(l/s)
(l/s)
54 46 34 44 44 35 41 54 25 30
86 85 89 85 87 55 84 88 60 60
41
90 90 90 90 90 60 90 90 60 6O
68 69 41 71 27 38 39 25 25
ing three have 0.06 m3/s. The m a x i m u m capacity of the secondary canal is 0.75 m3/s. Therefore it can be stated that all tertiary canals cannot be operated at the same time at m a x i m u m capacity. Variation of different times of irrigation advised by WASAM, WADPRO and actual conditions with respect to their flow rate are shown for selected tertiary canals in Figs. 5, 6 and 7. WADPRO calculates the total water requirement in a tertiary unit. The flow time or the operation time required is calculated knowing the m a x i m u m canal capacity at the head of the tertiary canal and the total water requirements.
MODELINGIRRIGATIONDELIVERIESFORTERTIARYUNITSIN LARGEIRRIGATIONSYSTEMS
213
It can be seen from Table 3 and Figures 5, 6, and 7 that in the present operation policy low canal flow rates are being used requiring higher operating times. This necessitates almost continuous canal flows in the system resulting sometimes in inefficient utilization. WADPRO model uses the higher canal capacities which results in lower operational time. Since the tertiary units are to be run only for a limited time, it would be possible to close them for some time, resulting in adoption of a rotational system instead of the existing continuous flow system. This aspect requires further study. CONCLUSIONS
The following conclusions can be drawn from this study: 1. In a large irrigation system, for estimating the canal diversions at the tertiary level, models based upon a water balance approach for low land paddy and simulation of soil moisture profiles for sugarcanes proved to be satisfactory. 2. In estimating irrigation requirements for scheduling of irrigation, expected rainfall values were incorporated based upon analysis of previous rainfall records. Leaky law was used to estimate the expected rainfall at different probability levels and was seen to give satisfactory values. 3. The computer program WADPRO (Water Allocation and Distribution Program) which combines the irrigation water requirements and the expected rainfall was found to give satisfactory values for canal diversions at the tertiary and secondary levels. Application of the model to an actual irrigation system indicates the possibility that the system could be operated on a rotational basis instead of the continuous basis as at present. ACKNOWLEDGEMENTS
The first author acknowledges the assistance provided by the Canadian International Development Agency (CIDA) for his studies at the Asian Institute of Technology. The authors wish to thank the anonymous reviewer whose comments vastly improved the presentation.
REFERENCES Anderson, R.L. and Maass, A., 1971. A simulation of irrigation systems. Technical Bulletin No. 1431, U.S. Department of Agriculture. Azhar, A.H., Murty, V.V.N. and Phien, H.N., 1992. Modeling irrigation schedules for low land rice with stochastic rainfall, J. Irrig. Drain. Engrg. ASCE, 118: 36-55. Brooks, R.H. and Corey, A.T., 1964. Hydraulic properties of porus media, Hydrology Paper No. 3, Civil Engineering Dept., Colorado State Univ., Fort Collins, Colorado. Brower, L.A. and Buchheim, J.F., 1982. An irrigation district computerized water management
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system, Ninth Technical Conference of U.S. Committee on Irrigation, Drainage and Flood Control, Jackson, Miss. Boman, B.J. and Hills, R.W., 1989. LP Operation model for on-demand canal system, J. Irrig. Drain. Engrg., ASCE, 115: 687-700. Buishand, T.A., 1977. Stochastic modelling of daily rainfall sequences, H. Veenman and Zonen B.V., Wageningen. Doorenbos, J. and Pruitt, W.O., 1977. Guideline for predicting the crop water requirement. FAO Irrig. and Drain. Paper No. 24, Rome, Italy. Feedes, R.A., Kowalik, P.J. and Zaradny, H., 1978. Simulation of field water use and crop yield. Center for Agricultural Publishing and Documentation, Wageningen. Jensen, M.E., Robb, D.C.N. and Franzoy, G.E., 1970. Scheduling irrigation using climate-cropsoil data, J. Irrig. Drain. Div. Proc. of ASCE. 96(IR1 ): 25-38. Kemachandra, R.A.D. 1991. Interfacing irrigation deliveries in large irrigation system with farm water requirements. M. Engg. Thesis, AIT, Bangkok, Thailand. Kung, P. 1971. Irrigation agronomy in monsoon Asia, FAO, Rome, Italy. Rajput, T.B.S. and Michael, A.M., 1989. Scheduling of canal deliveries. 1. Development of and irrigation canal scheduling model, J. Irrig. Power (Central Board of Irrigation, India), 46: 23-39.