two-level optimization model for lower indus

8/8/2019 Two-Level Optimization Model for Lower Indus

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.Agricultural Water Management 36 1998 1 21

Two-level optimization model for Lower IndusBasin

N.K. Garg ), Abbas Ali

Dept. of Ci

il Engineering, I.I.T., New Delhi-16, India

Accepted 27 November 1997

Abstract

The present study aims at the development of a model to schedule the sowing dates of the

crops in such a manner that the peak water requirements of different crops are more uniformly

distributed over different months and hence, more area can be irrigated for a given canal and tube

well capacities. For this purpose, a two-level optimization model for optimal use of surface andgroundwater has been developed. In the first level, the model gives optimal cropping patterns and

monthly water withdrawals from canal and tube well for a given set of sowing dates to maximize

the net economic returns. At second level, the sowing dates are varied within the allowable limits

and the optimized sowing dates are obtained using an integer programming model. The sowing

dates at the first level are then taken as the sowing dates obtained from the second level. The

process is repeated until it converges. The sensitivity analysis for some of the parameters is also

done. The model is applied to Dadu canal command of Lower Indus Basin. The results show an

overall increase of 40% in the crop intensities and 38% in the benefits over the existing ones by

using the two-level optimization model. q 1998 Elsevier Science B.V.

Keywords: Conjunctive use; Optimal cropping pattern; Irrigation management

1. Introduction

The Indus Basin irrigation system is one of the largest of its kind in the world. The

water demand of the system far exceeds its related water resources. It is, therefore, very

important to optimally manage and use the scarce water resources. Considerable workhas been done on the Indus Basin System Harza Engineering International, 1963;

Revelle, 1964; Irrigation and Agricultural Consultants Association, 1966; Tipton and

)

Corresponding author.

0378-3774r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. .PII S 0 3 7 8 - 3 7 7 4 9 7 0 0 0 5 7 - 7


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( )N.K. Garg, A. Alir Agricultural Water Management 36 1998 1 212

Kalmbach, 1967; Lieftinck et al., 1968; Chaudhry et al., 1974; OMara and Duloy,.1984 . All these studies have recommended the conjunctive use of surface and ground-

water in the Indus Basin to enhance cropping intensities.

Several studies have dealt with the development of models for conjunctive use of .surface and groundwater. Nieswand and Granstron 1971 have developed a set of

chance constrained linear programming models for the conjunctive use of surface and .groundwater. Smith 1973 has developed a linear programming model for irrigation

planning in countries with little experience of major water control efforts. Wanyoung .and Haimes 1974 have developed a systems analysis approach for optimal conjunctive

use of surface and groundwater. They have chosen a two-dimensional asymmetrical grid .network model to represent the aquifer system. Haimes and Dreizin 1977 have

developed a methodology for solving the problem of large scale groundwater systems by .decomposing the large system into interacting submodels. Rydzewski and Rashid 1981

have developed an approach for optimal allocation of surface and groundwater resources

.to three agricultural areas in the Jordan Valley. Khepar and Chaturvedi 1982 havedeveloped the decision models for optimal groundwater management alternatives in

conjunction with optimal cropping pattern using fixed yield and alternative levels of

water use approaches based on water production functions. Bredefoeft and Young .1983 have studied the extent of groundwater development to ensure water availability

against periods of low stream flows. They have used a simulation model which couples

hydrology of the conjunctive stream aquifer system to an economic model. Paudyal and .Gupta 1990 have used the multilevel optimization techniques to solve the problem of

irrigation management in the large heterogeneous basin. They have decomposed the

large system into interconnected subsystems to reduce the dimension of the problem andsolved it through a multilevel iterative process.

All these studies have addressed the various problems associated with the conjunctive

use but none have studied the effects of adjustments in peak water requirements which

can have significant impact on the cropping pattern.

In this study, a two-level optimization model has been developed to obtain the

optimal cropping pattern considering the impact of variation in sowing dates on the peak

water requirements. At the first level, a linear programming model is developed which

optimizes the net return from the crops and depicts the optimal cropping pattern and

monthly water withdrawals from canal and tube well for a given set of sowing dates. Atthe second level, an integer programming model has been developed for optimizing the

sowing dates using a linearized relationship between crop coefficient and percentage

growing season. Both the objective functions are optimized independently at first and

second levels, respectively.

2. Study area

The Indus Basin in Pakistan contains one of the largest irrigated area in the world.The available area in the basin is about 20 million ha. The basin can be subdivided into

upper and lower Indus Basin. The lower Indus Basin as shown in Fig. 1 consists of

about 6 million ha area irrigated by three barrages viz. Gudu, Sukker and Kotri.


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( )N.K. Garg, A. Alir Agricultural Water Management 36 1998 1 21 3

Fig. 1. The Study area with Lower Indus Canal System.

The study area, commanded by the Dadu Canal off taking from right bank of Sukker .barrage, consists of 210,000 ha Cultureable Command Area CCA and lies between

.latitude 298N and longitude 678E Fig. 1 . The area is situated in a hot arid zone. The

climate is characterized by large seasonal fluctuations in temperature, sparse rain fall,

with an average annual rainfall of 91 mm, falling mainly in July and August and highpotential evapotranspiration.

The major sources of water include canal water, groundwater and hill torrents.

However, generally very little flow reaches the study area from hill torrents and


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possibilities of its exploring is limited considering the anticipated cost of development.

Most of the area is underlain by a large alluvial sand aquifer and the depth of ground

water ranges between 30 m and 60 m. The canal water is supplied through Dadu canal3 having capacity of 89.00 m rs. Rice is the dominant crop in Kharif from May to

. October , while the other main crops are cotton, sorghum and oilseed. In Rabi from

.November to April , wheat is the principal crop along with mainly gram, mustard andfodder. Sugarcane is growing all year round. The existing cropping intensities are 28%

for Kharif and 50% for rabi. The surface drainage facilities are provided under North

Dadu Surface Drainage Project.

The irrigated area is level flood plain and consists of mainly two soil groups viz.

Indus Alluvial and Piedmont Alluvial. The Indus Alluvial consists of mainly fine sandy

loam and occasional silt clay while Piedmont Alluvial comprises of deep dense clays

and stratified medium to fine textured materials. The Indus Alluvial covers approxi-

mately 75% of the area and the rest is covered by the Piedmont Alluvial.

3. Formulation of optimization model

The two-level optimization model as shown in Fig. 2 has been developed to obtain

the optimal cropping pattern and the sowing dates. The cropping areas are obtained at

first level using a linear programming model for a given set of sowing dates and are fed

at second level into an integer programming model to obtain the optimized sowing dates.

The non-linear relationship between crop coefficient and percentage growing season has

been approximated as the sum of linearized segments. The relationship between the crop

coefficient and the sowing date for a particular crop and month is obtained using

regression analysis. The initial sowing dates at first level is then replaced by new dates

Fig. 2. A schematic representation of the proposed model.


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obtained at second level and new cropping pattern is obtained. The process is repeated

until it converges. From the irrigation project reports prepared for the Lower Indus Basin .Harza Engineering International et al., 1991 , it is found that the actual operation and

.maintenance cost not the subsidized cost of canal water is Rs105 for every ha m .US$1.00sRs.40 while for the tube well water for an average lift this cost is

.Rs950rha m. As the canal water is always cheaper including conveyance losses thanthe tube well water therefore the optimization model will use the groundwater only if the

surface water is exhausted. Hence, the coupling of groundwater hydraulics with surface

water is not considered in the optimization model. However, the interaction between

surface water and groundwater is considered in the model by imposing a groundwater

balance constraint on the groundwater withdrawals on annual basis. The optimum policy

for pumping the optimized volume of groundwater obtained from the proposed model

has been studied separately.

Further, the non-linear relationship between the pumping cost and the pumping head

is also not considered in this study because of the fact that groundwater will be utilizedonly if surface water is exhausted. Therefore, variation in the pumping cost with the

change in pumping head will not effect the optimal pattern and may result in minor

variations in the net benefits only. However the non-linearity has been taken intoaccount while formulating the groundwater withdrawal model work will be reported

.elsewhere .

4. First level linear programming model

The linear programming model for the first level is conceptually similar to that . .developed by Smith 1970 , and used by Lakshminarayana and Rajagopalan 1977 . Ten

cropsrice, cotton, sorghum, oil seed and fodder in Kharif and wheat, gram, mustard

and fodder in Rabi along with the perennial sugarcane have been considered. These

crops are the major crops growing in Rabi and Kharif seasons and are similar to the

existing pattern. The objective function comprises of four components: return from

crops, cost of operation and maintenance of canal, tube well and surface drainage

respectively. No change in the existing farm practices, i.e., use of fertilizers, seeds, etc.has been assumed in the model. Therefore, the non-water related costs are considered in

the crop production cost while calculating the return from crops. The model is applied

on monthly basis and therefore, the variables in the model are: monthly withdrawals

from the canal and tube well for irrigation, monthly pumpage from tube well to drainage

and areas under different crops on different categories of soil. The objective function can

be mathematically expressed as under.

NC TS

Maximize Zs A )YPH )VPQ i j i j iis1 js1

12

sw gw dwy C swqC gwqpd qC dw 1 . . t t t t ts1


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where Zsobjective function; is index for the crops; js index for the type of soil; .ts index for the time period month ; NCs total number of crops; TSs total types of

.soil; A sIrrigated area of ith crop under jth type of soil ha ; YPH syield per hai j i j .quintalsrha, 1 quintalss100 kg of ith crop under jth type of soil; VPQ svalue peri

. sw gw dwquintal Rsrquintal of ith crop; C , C , C soperation and maintenance cost of

.canal, tube well and drainage respectively Rsrha m ; sw sflow diverted to canal fort .irrigation in tth month ha m ; gwspumping from tube well for irrigation in tth montht

. .ha m ; pd spumpage from tube well to drainage in tth month ha m ; dwswatert t .drained by surface drainage in tth month ha m .dw can be expressed as:t

dwssw RO qa RO qgw RO qpd .t t 1 1 2 t 2 tNC TS

qRF RO yRO ) CF A qRFqRO )CCA . t 2 3 i t i j t 3is1 js1

where RO s fraction of water delivered to canal lost as surface runoff; RO sfraction1 2of water delivered to irrigated area lost as surface runoff; RO sfraction of available3

.water rainfall to non-irrigated area lost as surface runoff; RFs rainfall in the ttht .month mt ; CF scrop factor for ith crop in tth month, equal to 1 if crop i is availablei t

.in tth month otherwise, it is 0; CCAscultureable command area ha ; a s fraction of1canal water delivered to irrigated area. a can be expressed as1

a s1yRO yGR yET1 1 1 1

in which GR sfraction of water delivered to canal, lost as groundwater recharge;1

ET s fraction of water delivered to canal, lost as non-beneficial evapotranspiration.1Limited heterogeneity has been considered in the model by introducing variable soil

types. Further, it is to be noted that the operation cost of canal and drainage system has

been taken as uniform for the entire study area while the tube well operation cost is

calculated by taking the average pumping lift in the well.

The objective function is bounded by several constraints, as follows. .1 Monthly canal diversion must not exceed water available at the river.

swFRW 2 .t t

in which RWswater available at river in tth month.t .2 Monthly water requirement of crops must be met.

NC TS NC TS

A )WR y a a swqgw q CF A )a RF F0.0 3 . . i j t i j 2 1 t t i t i j 2 tis1 js1 is1 js1

where WR swater requirement of ith crop under jth type of soil in tth month;t i ja sfraction of water delivered to the irrigated area, available for consumptive use. a2 2can be expressed as

a s1yRO yGR yET2 2 2 2

where GR s fraction of water delivered to irrigated area lost as groundwater recharge;2ET sfraction of water delivered to irrigated area lost as non-beneficial evapotranspira-2tion.


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gwqpdt tgwn FTWC 7 .t gw gwN )ht

dwtdwn FDC 8 .t dw dwN )ht

where nsw, ngw, ndws ratio of peak to average demand of canal, tube well and drainaget t tsystems in tth month respectively; Nsw, Ngw, Ndwsoperational days of canal, tubet t twell and drainage systems, respectively in tth month; hsw, hgw, hdwsefficiency of

canal, tube well and drainage systems, respectively; CC, TWC, DCsdaily maximum .capacities of canal, tube well and drainage systems ha m , respectively.

.6 Total water withdrawal from aquifer in a year must not exceed the mining rate.

12

pd qgw yGR )swyGR a swqgw . . t t 1 t 2 1 t tts1

NC TS NC TS

yRF )GR ) CF A yRF )GR CC Ay CF A t 2 i t i j t 3 i t i j /is1 js1 is1 js1

qAETqARFqASTSqASDyASFS

yAARFAMR 9 .

.where AETsannual evapotranspiration from aquifer ha m ; ARFsannual aquifer . .return flow ha m ; ASTSsannual seepage to streams and lakes ha m ; ASDsannual

. .spring discharge ha m ; ASFSsannual seepage from streams and lakes ha m ; .AARsannual recharge from adjoining aquifer ha m ; AMRsallowable mining rate.

In the preceding groundwater balance equation, the determination of many terms is

quite difficult because of non-availability of relevant data in the study area. We have

assumed that total withdrawal from the system through pumping can not exceed the

groundwater recharge available by seepage from the canal, irrigated area and rainfall in

the study area. The groundwater balance equation thus becomes:

12

pd qgw yGR )swyGR a swqgw . . t t 1 t 2 1 t tts1

NC TS

yRF )GR ) CF A t 2 i t i jis1 js1

NC TS

yRF )GR CCAy CF A F0.00 10 . t 3 i t i j /is1 js1

5. Second level optimization model

At the second level the authors propose an integer programming model to obtain the

optimized sowing dates. The peak demand of different crops can coincide in a particular


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month exhausting the available water supply and limiting the total crop production. The

peak period of different crops is a function of the sowing dates of those crops.

Therefore, a model is proposed as Second Level Optimization to minimize the peak

water requirement by adjusting the sowing dates. The variation in the sowing date is

restricted within reasonable bounds by bringing forward or postponing from the normal

sowing date.In order to calculate the crop water requirement, any of the four methods described

.by Doorenbos and Pruitt 1977 can be used to determine reference crop evapotranspira-

tion E. For converting E values into crop water requirement, suitable crop coefficientst tk should be evolved for different crops, soils and climatic conditions and also for

different stages of growth of the same crop. As far as possible, k values should be

verified from the direct methods available to determine the crop water requirements.

Therefore, monthly crop water requirement, in general, can be expressed as

NC TS

Monthly WR s A E k 11 . t i j i j t t i jis1 js1

where Es reference crop evapotranspiration in tth month; k scrop coefficient of thet t i jith crop in tth month under jth type of soil.

.The crop coefficient k is a non-linear function of percentage growing season. The

relationship between the crop coefficient and percentage growing season for a particular

month can be approximated as a linear one. The percentage growing season is a function

of sowing date and therefore, the crop coefficient for a particular month depends upon

the sowing date of a particular crop. The relationship between crop coefficient andsowing date for a particular month, soil and crop is obtained through regression analysis.

This relationship can be expressed as

k sm x qc 12 .t i j j i j

where x ssowing date for the ith crop in the region; m and c are regressioni j jconstants for jth type of soil.

. .Using Eqs. 12 and 11 , the monthly water requirement for a particular month in

terms of sowing date will become:

NC TS

Monthly WR s A E m x qc 13 . . t i j i j t j i jis1 js1

The objective function for the second level will then become the minimization of the

monthly water requirement, subject to the constraint that the sowing date can only be

varied within the allowable limits and can be formulated as the following integer

programming model:

NC TS

Minimize WR s A E m x qC . t i j i j t j i jis1 js1

.Subject to PR Fx FPT is1,2,3, . . . ,NC , where PR smaximum bringing forwardi i i ilimit of the ith crop; PTsmaximum postponing limit of the ith crop.i


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Additional constraints can be imposed in the model considering the available

resources. For example, it may be desirable to keep a minimum difference in the sowing

dates of different crops of a particular cropping season. It is to be noted that the bringing

forward and postponing of the sowing of the crops are restricted within a limit such that

the variations do not effect the crop yield. From the studies conducted on the Indus basin

.Sir M. MacDonald and Partners et al., 1988 , it is revealed that the sowing date of acrop can vary with in 1 month without effecting the yield. Otherwise, the crop yield

must also be changed at first level according to the optimized sowing dates obtained

from the second level in successive iterations. The optimal cropping areas obtained from

first level are taken as the crop areas for the second level objective function.

By choosing the sowing dates corresponding to the maximum of these optimized

monthly minimum values will ensure that the water demand for different crops for the

peak month will be minimum. Therefore, the dates corresponding to the months having

Fig. 3. The flow chart for the proposed two-level optimization model.


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Fig. 4. The relationship between crop coefficient and percentage growing season for sugarcane.

maximum values of second level objective function for Kharif and Rabi crops respec-

tively, are selected for the input in the model at first level. The process is repeated until .it converges. The approach has been schematically presented in flow chart Fig. 3 . The

first level linear programming model is solved using simplex method and second levelinteger programming model is solved using cutting plane technique Billy and Gillett,

.1976 . .To elaborate Eq. 12 , an example calculation, showing the relationship between the

crop coefficient and sowing dates for sugarcane crop, is presented here. .The non-linear relationship between crop coefficient k and percentage growing

.season for sugarcane is shown in Fig. 4. To obtain regression constants m & c , the

sowing dates are varied within the allowable bringing forward and postponing limits and .the crop coefficients for various sowing dates are obtained from the curve Fig. 4 after

calculating the percentage growing season on monthly basis. The values of monthly crop

coefficient corresponding to various sowing dates are given in Table 1.

The sowing dates also include the sowing month. It would require an adjustment for

the month also if the sowing dates are varied within the allowable limits which may

change the sowing month. To adjust for the month, integer variable x is varied betweenimaximum bringing forward and postponing limits, that is 0 30 the data from the area

.Sir M. MacDonald and Partners et al., 1988 , indicates the bringing forward and

.postponing limit to be 15 days and the normal sowing date has been assumed at x iequals to 15. For example, the sowing date of sugarcane is March 1, therefore x s0iwould mean February 14, x s30 means March 16 and x s15 means normal sowingi idate.

Once the crop coefficients corresponding to the different sowing dates are obtained, .the linear regression analysis is performed to obtain the regression constants m and c

for each month. The values of regression constants for sugarcane for each month of its

growth period are given in Table 1.

6. Model application

The two-level optimization model, formulated in previous section, has been applied

to the Dadu canal command of the Lower Indus Basin. The main data for this command


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Table 1

The values of crop coefficients and regression coefficients for sugarcane

.Sowing date x Monthly crop coefficient k

March April May June July August

Feb. 14 0 0.58 0.68 0.77 0.86 0.95 1.00 Feb. 21 7 0.56 0.66 0.74 0.84 0.93 1.00

March 1 15 0.54 0.63 0.72 0.81 0.90 1.00

March 9 23 0.53 0.61 0.70 0.79 0.88 0.97

March 16 30 0.52 0.59 0.68 0.77 0.86 0.95 .Monthly regression coefficient m y0.00223 y0.00302 y0.00288 y0.00302 y0.00302 y0.00171

.Monthly regression constant c 0.5814 0.6794 0.7653 0.8594 0.9494 1.0096


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Fig. 5. The process of convergence.

.has been obtained from Harza Engineering International et al. 1991 and Sir M. .MacDonald and Partners et al. 1988 and some important data are given in Appendix A.

Monthly crop water requirement has been calculated using A Guide for Estimating

Irrigation Water Requirements, 1984, which has extensively used data from Doorenbos .and Pruitt 1977 . The required data for calculating the crop water requirement are taken

.from the work of Harza Engineering International et al. 1991 and Sir M. MacDonald .and Partners et al. 1988 . These calculated crop water requirement values are verified

from the available field values.

The existing pattern shows 30% losses in conveyance system and 32% losses in the

field. The same figures have been taken in this study.

7. Optimum cropping pattern and monthly water releases

The two types of crop area variation patterns have been considered. In the variation

pattern-1, the sowing date for a particular crop is kept the same throughout the command

area and the normal sowing dates are optimized using the second level optimization

model while in the variation pattern-2, the crop area of a particular crop is divided into

different zones and the sowing dates are optimized for each of such cropping zones

Fig. 6. The optimal cropping pattern.


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Fig. 7. Water releases for crop area variation pattern-1.

Fig. 8. Water releases for crop area variation pattern-2.

allowing the flexibility in sowing dates of the same crop in the same command in

different zones. The crops considered for distributed shifting includes sugarcane, rice,

cotton, oilseed, wheat and fodder which are the major crops of pattern-1 and the crop

areas are divided into four zones. The model required a maximum number of two

iterations to converge. The process of convergence is shown in Fig. 5.

The optimal cropping pattern and water releases obtained from two-level optimization

model for both the crop area variation patterns are presented in Figs. 68.

The results show a considerable improvement over the existing cropping pattern as

shown in Fig. 9. There is an improvement of 24.4% in crop intensities and benefits with

normal sowing dates. There is a further increase of 15.6% in cropping intensities and

13.7% in benefits after optimizing the sowing dates at second level optimization model

Fig. 9. The comparison between existing and proposed cropping patterns.


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Fig. 10. The crop water requirement for crop area variation pattern-1.

with an overall improvement of 40% over the existing cropping intensities and 38% over

the benefits. A further improvement of 5.4% in crop intensities and 4.2% in benefits is

obtained by using variation pattern-2. It may be noted that there is a total increase of

45.3% in cropping intensities with 42.2% increase in benefits as compared to the

existing ones.

8. Variation of water requirement with sowing dates

Fig. 10 shows the crop water requirements for each month obtained for crop area

variation pattern-1 and Fig. 11 shows these results for crop area variation pattern-2. .Comparing the crop water requirements for normal sowing dates Fig. 12 with the

pattern obtained from the model for both the crop area variation patterns, it can be seen

that the total monthly water requirements of all the crops are now more uniformly

Fig. 11. The crop water requirement for crop area variation pattern-2.


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Fig. 12. The crop water requirement for normal sowing dates.

distributed. The optimized distribution of peak water demands of different crops now

makes it possible to cultivate more area within the existing water availabilities, canal

and tube well capacities.

9. Effect of increasing tube well capacities

The existing tube well capacities are exhausted during peak demand period while the

slackness is found in the groundwater balance constraint and it is behaving as inequality

constraint. Therefore the annual recharge is more than the annual withdrawals from the

groundwater and more benefits can be achieved by increasing the tube well capacities.

Fig. 13 shows the effect of increasing the tube well capacities on benefits. The results

show a maximum increase of 56.4% in crop intensities with 60.8% in benefits as

compared to the existing ones and the tube well capacities can be increased up to a

Fig. 13. The effect of increasing tube well capacities on optimal benefits.


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Fig. 14. The optimal tube well capacities corresponding to seepage losses.

maximum limit of 76% more than the existing ones. The increase in tube well capacities

can be achieved within the overall framework of the existing infrastructure.

10. Effects of seepage losses

Fig. 14 shows the optimal tube well capacities corresponding to the seepage losses

from the conveyance systems and the irrigated fields. It can be seen that the existing

tube well capacities are more than the required optimal capacities for the seepage losses

up to 10%. The optimal tube well capacities will increase to 57% more as compared tothe existing ones corresponding to 20% seepage losses and will attain a maximum value

of 76% more than the existing ones for the 47% seepage losses.

Fig. 15 shows the effect of seepage losses on the benefits assuming both the optimal

and existing tube well capacities. It can be seen that the benefits obtained from both the

capacities are almost same for the seepage losses up to 20%. Beyond 20% losses, the

benefits are more with optimal capacities as compared to the existing ones. Further, the

benefits are maximum corresponding to 20% seepage losses and the seepage losses can

be reduced up to this limit. As the difference in benefits obtained from optimal and

existing capacities for 20% losses is insignificant, the existing tube well capacities will

Fig. 15. The optimal benefits corresponding to the existing and optimal tube well capacities.


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be sufficient up to this limit. The seepage losses can be reduced either by lining the

conveyance systems or by improving the farm water management techniques.

11. Conclusion

A two-level optimization model is developed in this study and is applied to Dadu

canal command of the lower Indus Basin. The results show an overall increase of 40%

in the crop intensities and 38% in benefits over the existing ones. This increase is

obtained mainly by optimizing the crop sowing dates and without making any change in

the infrastructure. An additional 5.4% increase in area and 4.2% increase in benefits will

be obtained by just dividing the crop area in four zones having different sowing dates

which can also be managed within the existing infrastructure. An increase of 56.4% in

crop intensities from existing ones can be obtained by increasing the tube well capacities

to 76%. The irrigation efficiencies taken in this study are the same as the existing ones.

Further improvement in the cropping intensities can be obtained by improving the

existing efficiencies. The two-level optimization model is quite general and can be

applied to other irrigation management systems.

Acknowledgements

The writers wish to express their sincere thanks to Prof. M.C. Chaturvedi for his

valuable comments and suggestions.

Appendix A

The important data used in the present study are given below:

Canal capacity 89 m3rs

Tube well Capacity 19.84 m3rs

Drainage capacity 25.51 m3rs

Canal efficiency 80%

Ratio of peak to average demand 1.1Runoff losses from conveyance system 10%

Recharge losses from conveyance system 15%

Evaporation losses from conveyance system 5%

Runoff losses from irrigation field 10%

Recharge losses from irrigation field 12%

Evaporation losses from irrigation field 10%

Canal water cost Rs105rha m

Tube well water cost Rs950rha m

Drainage water cost Rs60rha mMaximum preponing limit for sowing dates 15 days

Maximum postponing limit for sowing dates 15 days


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Appendix B. Notation

The following symbols are used in this paper:

A Irrigated area under a crop

AAR Annual aquifer rechargeAET Annual evaporation from water table

AMR Annual mining rate

ARF Annual return flow

ASD Annual spring discharge

ASFS Annual seepage from streams and lakes

ASTS Annual seepage to streams and lakes

c Regression constant

Cdw Operation cost of drainage system

Cgw Operation cost of tube wellCsw Operation cost of canal

CC Maximum capacity of canal

CCA Cultureable Command Area

CF Crop factor

DC Maximum capacity of drainage system

dw Water drained by surface drainage system

E Reference crop evapotranspiration

ET , ET Fraction factors for non-beneficial evapotranspiration from canal1 2

and irrigated area respectivelyGR , GR , GR Fraction factors for groundwater recharge from canal, irrigated1 2 3

area and non-irrigated area respectively

gw Pumping from tube well for irrigation

i Index for crops

j Index for types of soil

k Crop coefficient for a particular month

m Regression coefficient

N Number of days of operation

NC Number of cropspd Pumpage from tube well to drainage

PR Maximum preponing limit in terms of days

PT Maximum postponing limit in terms of days

RF Rainfall

RO , RO , RO Fraction factors for surface runoff loss from canal, irrigated area1 2 3and non-irrigated area respectively

Rs Pakistani rupees

RW Water available at river

sw Flow diverted to canalt Index for month

TCA Total cropped area

TCP Total existing crop production


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TIA Total available area for irrigation

TS Total types of soil

TWC Maximum capacity of tube well

VPQ Value per quintal

WR Monthly water requirement of crop

x Sowing date of a cropYPH Yield per hector

Z Objective function

a Fraction of canal water delivered to irrigated area1a Fraction of water delivered to the irrigated area, available for2

consumptive use

b Fraction of total crop production allotted to ith crop for theiexisting production

g Fraction of total crop production allotted to ith crop for theimaximum production

u Fraction of cultureable command area under jth type of soiljhsw, hgw, hdw Efficiency of canal, tube well and drainage systems, respectively.

nsw, ngw, ndw Ratio of peak to average demand of canal, tube well and drainaget t tsystems in tth month, respectively

References

A Guide for Estimating Irrigation Water Requirements, 1984. Government of India, Ministry of Irrigation,

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