Optimal Allocation of Short-Term Irrigation Supply

Irrigation and Drainage Systems 15: 247–267, 2001.© 2001 Kluwer Academic Publishers. Printed in the Netherlands.

Optimal allocation of short-term irrigation supply

E.C. KIPKORIR1, D. RAES1 & J. LABADIE2

1Institute for Land and Water Management, K.U. Leuven University, Belgium; 2 Departmentof Civil Engineering, Colorado State University, USA (email:[email protected])

Accepted 20 July 2001

Abstract. An optimization model has been developed to aid decision making in real time fordeficit irrigation when conflict between water supply and demand arises in a multiple cropirrigation scheme. The result is the optimal allocation of short-term supply of irrigation water.The optimization model is based on Dynamic Programming. In the optimization model, theshort-term supply is optimized in function of a specified strategy determined by the user. Thestrategies that the user can select from are: maximum benefit, equitable benefit, equitableyield and maintaining equity in the system. The potential of the model has been assessedthrough application of the model to Perkerra irrigation scheme in Kenya. In the 680 ha scheme,maize, onion and chili are cultivated in the irrigation season. Analysis of the results for the1999/2000 season, where the water supply was 35 percent smaller than the demand, indicatesthat improvements in crop production can be achieved through application of the optimizationmodel. Sensitivity of production system to various levels of water restriction is demonstratedby sensitivity analysis.

Key words: irrigation strategy, optimization, real-time management

Introduction

The operation and management of irrigation systems are of growing concernworldwide. This is especially true for developing countries where the need toenhance the agricultural productivity is coupled with decreased availabilityof water for agriculture owing to rapid industrialization and ever-increasingmunicipal needs (Biswas 1994; Lenton 1994). The irrigation systems, in thedeveloping countries are predominantly surface irrigation, having a series ofopen canals network supplying irrigation water. The lack of knowledge aboutirrigation and water management among farmers makes the management ofthe whole scheme the primary responsibility of the irrigation departments(agencies). Since most of these departments presently do not possess anyscientifically based decision support system, the water allocations are fre-quently subject to negotiations with the farmers and politicians (Wade 1983).This results in the ignorance of crop water demands with respect to time and

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quantity of water and leads to the poor performance of irrigation projects(ASCE Task Committee 1993).

In recent years, due to increased stress on improved irrigation manage-ment and planning, a number of optimization and simulation models havebeen developed by various researchers (Wardlaw et al. 1999; Rao et al. 1992;Burton 1994; Sriramany & Murty 1996). However, most of these modelsare site-specific and address local problems. Moreover, these models focusnarrowly either on maintaining equity or attaining maximum benefit of theirrigation system and therefore, may not meet the objectives of the irrigationdepartments dealing with the whole scheme.

Water allocation in time of shortage is a complex process upon whichmay rest the success or failure of irrigation projects (Boubker 1997). Thispaper presents the Multicrop Irrigation Optimization System (MIOS), for op-timal allocation of irrigation water when conflict between supply and demandarises. MIOS attempts to provide a decision support tool which irrigationagencies can use to determine optimal short-term decisions in function of aspecified irrigation strategy. MIOS combines a Dynamic Programming op-timal allocation model and a soil water balance simulation model, in derivingthe short-term decisions for irrigated command areas. MIOS is applied bothto an irrigation project in Kenya to illustrate its advantages in improvedirrigation system management and to a sensitivity analysis to demonstratesensitivity of production system to various levels of water restriction.

Model development

The objective of MIOS is to determine the optimal allocation of short-termirrigation supply. The problem may be considered to be one of maximizingthe utilization of the available water supply when conflicts between supplyand demand arises at a particular moment in the season. The optimization isdone according to one or another irrigation strategy.

System

Let the number of field groups in the system be NF. A field group consistsof an area of land with a particular crop, in a particular crop developmentstage, on a particular soil type and receiving irrigation water from a particularturnout. A field group could consist of only part of a field (often less than 1ha), or of one or more fields (often larger than 10ha). Let the cropping seasonbe divided into NE short-term decision intervals. The length of NE shouldbe longer than the irrigation interval but short enough to avoid fluctuation of

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both water supply and crop water demand. It should also be short enough toassume rainfall is zero. The objective functions are derived for maximizingthe net return/minimizing crop losses from the NF field groups irrigated bywater supplies available at the field level during the jth decision interval whenconflicts between supply and demand arises.

Objective functions

The problem may be considered to be one of maximizing the utilization ofthe available water supply when conflicts between supply and demand arisesat a particular moment in the season. Benefit based or equity based objectivefunctions can be formulated.

Benefit based objective function

If the objective is to maximize the gross return (variable and fixed costs notconsidered) from the NF field groups, the objective function can be expressedas

R = max

NF∑i=1

PiAiY ai (1)

where for the crop in field group i, Pi is crop market price, Ai is the croppedarea and Yaiis actual crop yield.

In the form of Equation (1), however, the function would be difficult tooptimize, and simplification is required. Jensen (1968), found that crop yieldresponse to water can be expressed in the following form:

Yai

Ymi

=Ni∏k=1

(ET aki

ET cki

)λki

(2)

where for crop in field group i, Ym is maximum crop yield under the givenmanagement conditions, k is crop growth stage, N is the total number ofgrowth stages, ETa is actual crop evapotranspiration, ETc is crop evapotran-spiration without water stress and λ is crop sensitivity index to water (functionof crop and stage of growth). For the current decision interval j and assuming(ETa/ETc = 1) for j = j+1 to j=NE, Equation (2) can be rewritten as:

Yai

Ymi

= βj−1,i

(ET aj,i

ET cj,i

)λki

and (3)

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βj−1,i =j−1∏j=1

(ET aj,i

ET cj,i

)λj,i

(4)

where βj−1,i (dimensionless) is the crop production status at the end ofdecision interval j − 1. The relative evapotranspiration in Equation (4) iscalculated using a soil water balance model. The growth stage sensitivityindex is transformed to a decision interval sensitivity index, using a graphicalmethod (Tsakiris 1982).

In this study the assumption is made that the ratio of actual to cropevapotranspiration without water stress will be the same as the ratio of fieldirrigation supply to demand (ETa/ETc = FIS/FIR). This assumption is validfor condition for water stress and can be justified as follows. For deficit irrig-ation the assumption may lead to a different result only for the first irrigation(at the beginning of water shortage period), since the soil water reserve maysupply some water for plant needs. However, in succeeding deficit irrigationevents, the readily available soil water is depleted before the next irrigation isapplied therefore ETa can be considered as the amount of applied water. Us-ing Equation (3) the objective function given in Equation (1) during decisioninterval j may be written as follows:

R = max

NF∑i=1

PiAj,iYmiβj−1,i

(FISj,i

F IRj,i

)λj,i

(5)

where FIS and FIR are respectively the field irrigation water supply and re-quirement. Note that for j = 1 βi = 1.0. Rainfall is assumed to be equal tozero during the short-term decision interval i.e. rainfall does not contribute toFIS. MIOS model has the possibility to run with effective dependable rainfallof a specified level contributing to FIS. In other studies (Darine et al. 1991;Ghahraman et al. 1997; and Wardlaw et al. 1999) similar assumptions havebeen made.

Equity based objective functions

If the objective is to maximize crop yields, or minimize yield losses, withsome measure of equity, then the objective function can be expressed as

R = min

NF∑i=1

1

Ymi

(Ymi − Yai)2 (6)

The above function would, subject to system constraints, result in the samerelative crop yield in all field groups. In the form of Equation (6), however,

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the function would be difficult to optimize, and simplification is required.Doorenbos and Kassam (1986), found that crop yield response to water canbe expressed in the following form:(

1 − Ya

Ym

)= Ky

(1 − ET a

ET c

)(7)

where Ky, the crop yield response factor to water, is a function of crop andstage of growth. If it can be assumed that the ratio of actual to crop evapotran-spiration without water stress will be the same as the ratio of field irrigationsupply to demand (ETa/ETc) = (FIS/FIR) then it can be shown that

1

Ym(Ym− Ya)2 = YmKy2

(1 − FIS

FIR

)2

(8)

Using Equation (8), the objective function given in Equation (6) duringdecision interval j may be written as follows:

R = min

NF∑i=1

YmiKy2ji

F IR2ji

(F IRji − FISji)2 (9)

An alternative form of the function, with different sensitivity would be

R = min

NF∑i=1

YmiKyji

F IRji(F IRji − FISji)

2 (10)

If the crop yield response factor is set to 1.0 and it is thereby assumed thatthe maximum crop yield under the given management conditions is identicalin the different field groups, Equation (10) revert to water allocation function(Equation 11), in which the objective is to meet specified irrigation demandswith equity throughout the system.

R = min

NF∑i=1

1

FIRji(F IRji − FISji)

2 (11)

The introduction of an economic factor to objective function Equation (10)can be achieved by multiplying the maximum crop yield under the givenmanagement conditions (Ym) by the market price of the crop (P), the result-ing objective function is expected to provide an equitable relative economicreturn from the field groups in the system.

R = min

NF∑i=1

PiYmiKyji

F IRji(F IRji − FISji)

2 (12)

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A further issue to be considered is that of the cumulative impact of waterstress on the crop in determining water allocations. This can be achieved byintroducing a crop production status factor βj−1,i at the end of decision in-terval j-1 (Eqquation 4). Objective function Equation (10) and Equation (12)can respectively be written as Equation (13) and Equation (14).

R = min

NF∑i=1

YmiKyjiβj−1i

F IRji(F IRji − FISji)

2 (13)

R = min

NF∑i=1

PiYmiKyjiβj−1i

F IRji(F IRji − FISji)

2 (14)

Irrigation strategies

Maintain equity in the system

The objective function given by Equation (11) is used for equity strategy inthis study. It maintains equity in the system for the NF field groups duringdecision interval j subject to the constraint equations.

Equitable yield

If the objective is to maximize crop yields, or minimize crop losses, withsome measure of equity, Wardlaw and Barnes (1999), showed that an object-ive function similar to that given in Equation (13) is an appropriate function touse. The objective function Equation (13) is minimized during the jth decisioninterval, subject to the constraint equations. In their earlier work, Wardlawand Barnes (1999) assumed Ym to be constant in the system and also they didnot consider the cumulative impact of water stress on the crop in determiningwater allocations, in this work this is solved by the introduction of the cropproduction status factor (βj−1,i).

Equitable benefit

If the objective is to maximize crop revenue, or minimize crop revenue losses,with some measure of equity, Wardlaw and Barnes (1999), showed that anobjective function similar to that given in Equation (14) is an appropriatefunction to use. The objective function Equation (14) is minimized during thejth decision interval, subject to the constraint equations.

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Maximum benefit

If the objective is to maximize the crop return from the NF field groups,without considering the variable and fixed costs, the objective function Equa-tion (5) is the appropriate one to use. Equation (5) is maximized during thejth decision interval, subject to the constraints equations.

Constraints equations

The field level irrigation water supply FISj,i during decision interval j for fieldgroup i, is constrained by the water supply Wj available at the headworksduring the decision interval j. This can be expressed as:

Uj,i = FISj,i

Eci(15)

Wj =NF∑i=1

Uj,i (16)

where Eci is the conveyance efficiency from the headwork to the field groupinlet and Uj,i is the decision variable. Doorenbos and Kassam (1986) assumedthat Equation (7) is valid for most crops for water deficits in the range (1-ETa/ETc ≤ 0.5). Therefore, the priority of irrigation during decision intervalj can be introduced by using a factor ωji with a valid range of (0.5 ≤ ωj,i ≤1.0). This can be expressed as:

ωj,iF IRj,i ≤ FISj,i ≤ FIRj,i (17)

By use of factor ωji and objective function Equation (11), three differenttypes of allocation rules commonly found in water-short situations can bestudied:Rule 1: The shortage is equally shared among all the fields. If there is a 20%shortfall, all fields water supply is reduced by 20% (i.e. ωji= 0.8).Rule 2: This rule is based on appropriation water law which simply states thatthose who have settled first in the system have the full right to the water (firstin time, first in line). Therefore, those fields at the head receive all or almostall their demand (ωji ≈ 1.0) and those at the tail receive none (ωji= 0.0).Rule 3: This rule spread the shortage over all the fields but not in an equalmanner. Those at the head will receive a greater proportion of their demandthan those at the tail (the value of ωji decrease from head to tail). This isprobably the most common functional rule.

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Problem solution

The real time irrigation water management problem is one of providing thebest distribution of scarce water resources, such that a specified objectiveis maximized. It has a special structure that can be exploited in attemptingto solve the problem. This structure arises because decisions are often carriedout in a sequential manner in space, or they can be conceptually viewed in thisway. Dynamic programming (DP) is particularly well suited for these kindsof sequential decision problems. By this method, large operational problems,like the real time irrigation water management problem can be decomposedinto a series of smaller decision problems, which are readily solvable. Thedegree of generalization and availability of generalized computer codes islimited for DP. Labadie (1990) recognized this and developed a comprehens-ive generalized Dynamic programming package called CSUDP, which hasbeen employed in research programs in water resource management world-wide. The most recent version of CSUDP, Labadie (1999) is used in thisstudy.

In this study, a field group constitutes a DP stage. Irrigation intervals varyfrom seven to ten days therefore the decision interval is set to 14 days. Thestate variable Xi is defined as the amount of water left for the remaining fieldgroups after field groups 1 through i-1 have received water. The state equationin the inverted form, during decision interval j is given as Equation (18). Thebackward looking dynamic programming recursive algorithm is used Equa-tion (19). For maximum benefit strategy, Equation (19) is maximized instateof minimizing.

Uj,i = Xj,i − Xj,i+1 (18)

Fj,i (Xj,i) = minXj,i+1

�fj,i , Uj,i, Xj,i+1)+ Fj,i+1(Xj,i+1)� (19)

(for i.=NF, NF–1,. . . ,1).

Fj,NF+1(Xj,NF+1) = 0. (20)

The schematic set up of the DP model and the soil water balance modelthat updates the system is shown in Figure 1. Optimal water allocation to DPstage i during decision interval j, U∗

j,i , is the ouput from the DP model. Thisis used to calculate the relative evapotranspiration (ETa/ETc). The calculated(ETa/ETc) is subsequently translated into an alternative irrigation schedule,where by the irrigation interval is increased to cover the water shortage, byusing a soil water balance iterative calculation procedure shown in Figure 2.

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Figure 1. Set up of the DP model and soil water balance model.

For the purpose of this study MIOS model is applied to Perkerra irrigationscheme in Kenya. The model has the possibility to run in two modes. The firstmode is by setting the crop production status equal to one (βj−1,i = 1.0) at thebeginning of each decision interval. This could represent a common situationin most projects where updating of the system is not immediately possibledue to the long time it some times take, for the implemented decisions andclimate data in the past decision intervals to be processed. The second mode isby updating the system with decisions implemented in the previous decisioninterval, thereby updating the crop production status up to the beginning ofeach decision interval.

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Figure 2. Flow chart for translation of relative evapotranspiration into an irrigation interval.

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Example application

Study site

The Perkerra irrigation scheme (PIS) situated near Marigat Township inBaringo District in Kenya was used as an application example of MIOSmodel. It is located on clay loam soils, with available mean soil moistureof 148 mm(water)/m(soil depth), in a semi-arid region where the averagemonthly crop reference evapotranspiration calculated using the FAO Penman-Monteith method (Allen et al., 1998) ranges between 4.0 and 5.4 mm/day.The annual dependable rainfall in a wet, normal and dry year is 781, 637 and492 mm, respectively. National Irrigation Board (NIB) which was formed byan act of parliament in 1966 provides the management and extension serviceto PIS. The schematic layout of the irrigation system of PIS is illustrated inFigure 3.

The irrigation water in PIS is drawn from Perkerra River by gravity andfed through a system of canals and feeders. The water fee paid by the farmersis fixed per unit area. The current water fee is Ksh 450 per ha (1 US$ = 75Ksh in 2000). Furrow method of irrigation is adopted. Since the inceptionof PIS in the 1940s, Perkerra River has gradually decreased in flow. Criticalwater shortage in PIS started in 1987 with the launching of Greater Nakuruwater project, upstream of Perkerra River and PIS. Other factors attributedto the river flow decrease are destruction of the forests in the catchment areaand cultivation on the riverbanks. As a result of the decrease in flow andunreliability of the rains in the area, the irrigated area has decreased from theoriginal developed irrigation area of 680 ha to the current irrigated area ofabout 400 ha. The available water to the cropped area in a season is sharedequitable. The crops currently cultivated in the irrigation season in PIS aremaize, onion and chili.

Data

Two cropping calendars namely, the 1999/2000 season (Figure 4) where thewater supply was 35% smaller than the demand and an hypothetical croppingcalendar (Figure 5) are used in this study. The latter is used to demonstratethe sensitivity of production system to various levels of water restriction. Thelength of the short-term decision intervals was taken as 14 days.

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Figure 3. Schematic layout for the Perkerra Irrigation scheme.

1999/2000 season

The daily water supply to the system for the 1999/2000 season, measuredusing the weir on the main canal (Figure 3) was aggregated into biweeklywater supply. The areas under crop, the actual yield and market prices foreach crop are presented in Table 1. The crop yield response factors shownin Table 2 were transformed into 14-day sensitivity index using graphicalmethod (Tsakiris 1982). When inputs such as fertilizers, pesticides, weedscontrol etc are at optimal levels, crops produce an absolute maximum possibleyield (Ymabs) when well watered. Often the above inputs are not at optimal

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Figure 4. 1999/2000 season cropping calendar with indication of the water shortage period.

Figure 5. Cropping calendar with indication of the water shortage period.

levels in the farmers’ fields and crop yield is limited. In this study, the yieldrealized for no water stress conditions in the farmers’ fields is referred tomaximum yield (Ym) under the given management conditions (Kipkorir etal. 2000). Ym (column 4, Table 1) was determined from Equation (2) usingthe observed actual yield Ya (column 3, Table 1) and the relative evapo-transpiration obtained by running soil water balance model with observedclimatic data and farmers’ actual irrigation schedules for 1999/2000 season.

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Table 1. Area under crop, actual yield, maximum yield under the given managementconditions and market prices for the 1999/2000 season (Source: NIB 2000).

Crop Area under Actual yield Maximum Market price

crop (ha) Ya (tons/ha) yield Ym (Ksh/Kg)

(Tons/ha)

Maize 344.0 2.1 3.1 29.0

Chili 22.8 1.5 2.8 18.7

Onion 22.1 4.0 12.4 24.5

Table 2. Length (days) and yield response factors (Ky) for the physiological growth stages(Source: Doorenbos & Kassam 1986).

Growth stage Length (days) Yield response factors (Ky)

Maize Chili Onion Maize Chili Onion

Establishment 21 28 49

Vegetative 28 35 28 0.4 1.1 0.45

Flowering 14 56 - 1.5 1.1 –

Yield formation 21 42 49 0.5 1.1 0.8

Ripening 14 21 21 0.2 1.1 0.3

The number of field groups NF considered in the system is 26. In 1999/2000season, one water shortage period that lasted for 18 weeks (week 21-39) wasobserved (Figure 4). The water content in the root zone at wilting point, fieldcapacity and saturation were measured as 21.8 vol%, 36.6 vol% and 52.2vol% respectively (Neijens 2001).

Sensitivity analysis

The hypothetical cropping calendar (Figure 5) is used for sensitivity analysis.The major factors considered in determining the cropping calendar are asfollows. Equal area under each crop, crops with high, medium and low yieldresponse factors and maximum possible crop returns per area. The areas un-der crop, Ym and market prices for each crop are presented in Table 3. Thecrop yield response factors are shown in Table 4. Climate data and soil datafor PIS is used. One water shortage period lasting for 14 weeks (week 19–33)was considered (Figure 5). The water shortage levels studied were 10%, 20%,30%, 40% and 50%. MIOS model was run in the two modes. The results fromthe two model runs, enables the four irrigation strategies to be compared for

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Table 3. Areas under crop, maximum yield under the given management conditions andmarket prices.

Crop Area under crop Maximum yield Market price

(ha) Ym (Tons/ha) (Ksh/Kg)

Maize 25 4.0 20.0

Sorghum 25 2.5 16.0

Watermelon 25 12.0 5.0

Table 4. Length (days) and yield response factors (Ky) for the physiological growth stages(Source: Doorenbos & Kassam 1986).

Growth stage Length (days) Yield response factors (Ky)

Maize Sorghum Watermelon Maize Sorghum Watermelon

Establishment 21 21 14

Vegetative 35 28 21 0.4 0.2 0.7

Flowering 21 21 21 1.5 0.55 0.8

Yield formation 35 42 21 0.5 0.45 0.8

Ripening 14 14 14 0.2 0.2 0.3

increasing water shortage and also the effect of crop production status on theoptimization model can be evaluated.

Results and discussions

1999/2000 season

MIOS model has been applied to the Perkerra irrigation scheme in Kenya, andresults compared to the observed production in the system for the 1999/2000season. MIOS model calculations were done according to the four irrigationstrategies. Crop production for the 1999/2000 season, where the water supplywas 35% smaller than the demand, was increased by 2.0%, 8.4%, 8.7% and9.3% for maintaining equity strategy, equitable yield strategy, equitable be-nefit strategy and maximum benefit strategy respectively (Figure 6). From theresults it can be noticed that there is no significant difference in productionfor the strategies based on crop yield response to water. This is a result of thefact that one crop (maize) was grown in about 90% of the area (Figure 4).For a cropping calendar with crops having different prices and yield response

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Figure 6. Comparison of observed and optimization model production.

factors, difference between optimal simulations for the irrigation strategiesare expected to be large. Maintaining equity strategy is expected to be moreattractive to the managers of PIS, because the water fee paid by the farmersis fixed per unit area, while maximum benefit strategy might most like be at-tractive to a manager of a single owed system. There was an increase of 0.7%,0.4% and 0.3% in production for maximum benefit strategy, equitable benefitstrategy and equitable yield strategy respectively when crop production statusfactor (βj−1,i) was considered in the optimization model.

Sensitivity analysis

The results of sensitivity analysis for 40% water shortage are given in Fig-ure 7 and Figure 8 while for 20% water shortage are given in Figure 9 andFigure 10. The 20% water shortage results is a representative of the optim-ization model performance at low water shortage level while the 40% watershortage results is a representative of the optimization model performance athigh water shortage level.

The difference in system production when the four irrigation strategiesare applied with crop production status factor set to one is evident from theabove results (Figure 7 and Figure 9). If the equity strategy is taken as areference, at 20% water shortage level, it can be noted that the differences insystem production are +1.2%, +1.1% and –1.2% for equitable yield strategy,equitable benefit strategy and maximum benefit strategy respectively. Equiv-

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Figure 7. Comparison of optimization model productions at 40% water shortage level, foradjusted and non-adjusted crop production status conditions.

Figure 8. Comparison of optimization model relative crop yields at 40% water shortage level,for adjusted and non-adjusted crop production status conditions.

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Figure 9. Comparison of optimization model productions at 20% water shortage level, foradjusted and non-adjusted crop production status conditions.

Figure 10. Comparison of optimization model relative crop yields at 20% water shortagelevel, for adjusted and non-adjusted crop production status conditions.

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alent figures for 40% water shortage level are +7.3%, +11.5% and +13.3%for equitable yield strategy, equitable benefit strategy and maximum benefitstrategy respectively. From the above results it can be seen that, at high watershortage level, the strategies based on economic factors (maximum benefitstrategy and equitable benefit strategy) have high system production com-pared to equity strategy and equitable yield strategy. However at low watershortage levels this advantage is lost and the system production are nearlyequal (±1.2%) but the former tend to have lower production.

At a low water shortage level the equity strategy results in crop productionwhich is rather equal (Figure 10) compared to the other strategies based oncrop and economic factors. Therefore application of equity strategy can beadvantageous in systems with many farmers where social considerations maybe more important. For high water shortage level (Figure 7), improvement insystem production when the crop production status factor is adjusted in theoptimization model is +0.3% for maximum benefit strategy, +0.7% for equit-able benefit and +1.9% for equitable yield strategy. Equivalent figures forlow water shortage level (Figure 9) are +0.0% for maximum benefit strategy,–0.5% for equitable benefit and +0.0% for equitable yield strategy. From theabove results it can be noted that at low water shortage level there is no im-provement in system production or in individual crop production (Figure 10)when the crop production status factor is adjusted in the optimization model.However at a high water shortage level there is an improvement of about+1% in system production. This can be explained as follows. The optimiz-ation model allocate more water to more sensitive crops (watermelon andmaize) resulting in an increase in relative crop yields and allocate less waterto less sensitive crop (sorghum) resulting in reduction in relative crop yield(Figure 8). For further explanation, if equitable benefit strategy at high watershortage levels can be take as an example, there is an increase in productionof 4% and 2% for watermelon and maize respectively and a decrease of 7%in production for sorghum when crop production status is adjusted (Figure 8).

Conclusion

MIOS model, that determines optimal short-term decisions in function of aspecified irrigation strategy, was presented in this paper. The results indicatethat application of the model for real-time irrigation water management canprovide a benefit in crop production of up to 9%.

The sensitivity analysis results indicate that at high water shortage levelsmaximum benefit strategy can provide a benefit in crop production of upto 13% compared to equity strategy while at a low water shortage level thedifference in system production for the four strategies is very small. Socially,

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at a lower water shortage level the equity strategy performs better than theother three strategies. At a high water shortage level, if crop production statusis adjusted in the optimization model, there is a reduction in water allocationto less sensitive crops and an increase in water allocation to more sensitivecrops. These changes tend to cancel out resulting in very small improvementin system production when crop production status is adjusted. At a low watershortage level the adjustment of crop production status does not improvesystem production or individual crop production in the system.

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