optimizing cropping pattern to maximize water productivity · therefore, optimizing water...

Optimizing cropping pattern to maximize water productivity

M. N. ~ i r n a h ' , A. ~saibes ' , F. ~ l k a h l ~ , M. R. ~arwish ' & I. ash our' 1 American University of Beirut, Faculty of Agricultural and Food Sciences, Land and Water Resources Department. 2 American University of Beirut, Faculty of Architecture and Engineering, Engineering Management.

Abstract

Proper water management is becoming a must since shortage started to cause serious problems. The United Nations is stressing on the need to gradually produce more output andtor value per unit of water. The main purpose of this study is to improve water productivity. An optimization model was developed solved by linear programming utilizing the General Algebraic Modeling System to obtain the optimum cropping pattern that maximizes revenue per unit water taking into account crop evapotranspiration, land, market and water availability as constraints. A case study was conducted in Lebanon on an area of 6700 Hectares located in South Bekaa. It was found that the peak water productivity of 1306 L L / ~ ~ of water occurred at an available irrigation water volume of 26 MCM with a net revenue of $3,383 per hectare and a land use density of 180%, whereas, the peak total net revenue stabilized at 37 MCM with a net revenue of $3,834 per hectare, a water productivity of 1045 L L / ~ ~ and a land use density of 175%.

Transactions on Ecology and the Environment vol 60, © 2003 WIT Press, www.witpress.com, ISSN 1743-3541

l88 River Ba~itl Marragernctlr I 1

l Introduction

Irrigated agriculture expanded in Lebanon and neighboring countries, therefore water supplies became scarce at different localities in different seasons, the economical aspect of water supply systems were stressed [l]. Irrigation water for agriculture use in most of the arid and semi-arid regions has long been allocated by a variety of non-market mechanisms and recently, there have been several moves in the direction of a greater role for market forces in the allocation of water [2 ] . Therefore, optimizing water productivity (crop production per unit of water) and maximizing revenue is becoming essential in sustaining agriculture, conserving water, and meeting the increasing demand on food and fiber; in other words "getting more crop per drop" [3]. United Nations pointed out also the concept of "Virtual Water" which is a strategy concept developed by J.A. Allan [4] as being a prospective long-term solution for water-short Middle Eastern economies. The strategy consists of making water-short countries import water- intensive commodities and produce less water-consumptive commodities instead of importing large volumes of water for their production.

An optimal cropping pattern is the crop combination that matches available land and water supply to crop requirements, and at the same time maximizes economic benefits. Many studies have been conducted to serve the above objective. Matanga and Marino [5] developed an LP (Linear program) optimization model to determine the cropping pattern that would maximize the gross marginal profit from three crops under limiting water supply and rate of delivery. LP model was used to develop another model to derive estimates of financial and economic benefits of irrigation subject to different set of constraints on land and water availability as well as maximum allowable crop acreage based on market conditions [6], [7]. Bernardo [g] used an LP model in combination with a simulation model to determine the optimal intra-seasonal allocation of a limited amount of water. Eckert and Wang [9] examined the influence of various irrigation water supplies on the choice of different cropping patterns and on-farm irrigation technologies. Panda [l01 linked simulation and LP approaches for optimal allocation of water and land resources and return maximization. El-Awar [l l ] developed an LP model to determine the optimal cropping pattern that satisfies the existing climatic, agronomic, economic, and land and water availability constraints. Dynamic programming was also used in land and water allocation among crops to maximize profit. Kipkorir [l21 formulated a model that optimizes allocation of land and water under both full supply and deficit irrigation. Software programs based on LP models were developed, under the general objective of making optimum district planning, to optirnize land productivity taking into account physical, socio-economical and technological constraints like Kenya-AEZ software program [l 31, or predict the optimal allocation of land and water among crops like PSERM (Palestinian System for Environmental Resource Management) software program

A general objective of this study is to increase the efficiency and environmental sustainability of water use, therefore to improve the management


of water resources and to reduce impacts of water shortage. For this purpose a mathematical linear program was developed to maximize water productivity (revenue per unit water) that depends on optimum cropping pattern using an optimization model.

2 Optimization model formulation

Based on the new concept of allocating water based on a market mechanism, that is dealing with water as any other commodity allocated according to its demand and supply, a mathematical model was formulated to allocate water among different crops to get the maximum revenue out of each unit of it. The model implemented is a linear programming model with a linear objective function, subjected to a set of linear constraints, and it was developed using GAMS (General Algebraic Modeling System) software for mathematical model formulation [l 51.

2.1 Objective function

The objective function determines the optimal combination of crop production in tons that maximizes the net return above production costs. It represents the net revenue out of a given combination of crops to be planted, that is their cost of production subtracted from their final selling price at the farm gate.

Max Z=C[(PX-CX-IX l i - C w ) * X i (WA)] i

Where Z is the net return in LL, I is the index of crop type, Pxi is the price of selling 1 ton of crop i in LL, Cx, the cost of producing 1 ton of crop i in LL. Ixi is the irrigation system cost per ton of crop i in LL, Cwi the cost of water needed to produce 1 ton of crop i in LL, and X.(WA)are the tons of crop i to be produced for a given water level (WA).

2.2 Constraints

The above objective function is subjected to the following constraints:

(1) Land constraint: This constraint insures that the total cropping area will not exceed the total available land for each month. Land productivity is defined as the area of land needed to produce one ton of a crop 'i'. When the model specifies the decision variable, that is the tons of crop 'i' to be produced, by multiplying this quantity by the land productivity, we get the total area of land to be planted with crop 'i'. The equation representing this constraint has the following general form:

X a ~ ~ , ~ x ~ ' LA. J l


190 River Ba~itl Marragernctlr I 1

Where a; is the area (m2) of land needed to produce 1 ton of crop I, sij is the land use for crop i in month j, and LA, is the total land available in month j in the study area (m2).

(2) Water productivity constraint: Water productivity constraint insures that production capacity won't exceed the water availability of the study area. Water productivity is the volume of water needed to produce 1 ton of crop 'i7 in one season. In the detailed formulation of the model, this volume will be divided among the different months where crop 'i' is planted and needs irrigation. The total water available for each month is nothing but the total water available in the study area minus the volume of water consumed in the previous months. The general form of the equation representing this constraint in the model is as follows:

Where bij is the water (m3) needed in month j to produce 1 ton of crop i (water productivity coefficient), eff the efficiency of water distribution and use, WA the total water available (m3), and WUK the total water used at month K (m3).

(3) Market constraint: This constraint is incorporated to insure that the production levels of any selected crop will be within the market absorption capacity or needs. Certain crops are essential for production and a minimum quantity is to be produced, while for other crops, a maximum quantity cannot be exceeded because the market cannot absorb it. The market demand in our study was expressed as a percentage of the total land available in each month. The formulation of this constraint came as follows:

a i s i , j X i I L A j * k o r a , s , , X , > L A * k J 1 j

Where k is the percentage of land corresponding to the maximum or minimum market demand. The sign in this equation can be either "greater or equal" or "less or equal" depending on crop type.

3 Study site and data needed

The data generated was specific for the South Bekaa region for an area specified as Phase 2 Area of the South Bekaa Irrigation Scheme Project. This area (6700 ha) (Fig.1). For the area defined above, the following input data were collected: Crops suitable to be planted in this area, crop planting and harvesting pattern over the year, yield of crop i (tonska), crop water requirements (rnrntmonth), cost of production of 1 ton of crop i (LL), selling price of 1 ton of crop i at the


farm gate (LL), water (LLIrn3), (m3).

cost of different irrigation systems per unit area (LL/m2), cost of crop market demand (tons), total available water over the year

Figure l : Project arealocation - Left Bank Phase 2 - 6700 ha

4 Results and discussion

The optimization model was run on GAMS using the CPLEX solver for linear programming. In the sections below, the different results obtained running first the initial model with its initial assumptions then the different scenarios representing the sensitivity of the model to the variation in the total water available, costs of production, selling prices and land productivity are shown.

4.1 Initial model

The input values of the variables used in the first model are presented in Table 1

Table 1. Input values used in the initial model formulated.

Variable Value

Total water available Price of one m3 of water Efficiency of vegetable irrigation Effkiency of fruit trees irrigation Efficiency of field crops irrigation

Total land available I 6700 ha 42 MCM 100 L U ~ ~

80% (Sprinkler) 90% (Trickle) 70% (Surface)



The value obtained for the objective function that maximizes net revenue was 38,716,653,666 LL ($2,569,1210) that is a net return of $3,834 per hectare. The land use density in the initial model was 175 % for a total area of 6700 hectares. Although the total water available was set at 42 MCM, only a total volume of 37.044 MCM was consumed. Table 2 below shows the quantities of crops to be produced and the percentage of land they occupy.

Table 2. Quantities and %planted area of crops obtained in the initial model

]crop 1 Quantity %Area

4.2 Water availability scenarios

Tomato 1 6864.8 5 Fruit trees

The change in the cropping pattern as the total available water increases is presented in Table 3. Vegetables like carrots, cauliflower, cucumber, eggplant, green beans, peas, radishl, squash, turnip, and water melon, fruit trees like apples, apricots, grapes, grenade, quince and walnut and field crops like barley and dry peas did not show up in any cropping pattern scenario.

It is shown that as the available irrigation water decreases the cropping pattern tends to have more field crops, less vegetable and high water consuming trees. On the other hand, as the water becomes more available the cropping pattern shifts to crops that can increase the total revenue and that consume more water. Although the total net revenue increases as the water available increases, the water productivity shows an increase then a decrease with increasing water. The

Janarek Peach Pear Plum Field crops Alfalfa Lupine Wheat

3015.3 5 3997.6 5 4356.3 5 3633.4 5

1482.3 10 2243.8 5 1005.1 5


Table 3. Cropping pattern variation with varying water levels. (Values in cells represent the percent area planted).

Crop 27MCM 3 2 M C g 37MCM 42MCM*

Broad bean Cabbage Swisschardl Swisschard2 Garlic Okra Lettuce Melon Onion Early potato Late potato Radish2 Radish3 Spinach1 Spinach2 Tomato

land use density was highest at 184% which corresponds to the highest water productivity 1302 LLIm3 and 27 MCM water available. Then the changes in land use density decreases to 175% utilizing 37 MCM and did not change with more available water for irrigation.

Because water is not continuously abundant, different available water volumes were tested to detect the corresponding variation in the cropping pattern, the total net revenue, the water productivity, and the land use density. The available water volume that resulted in the peak water productivity and land use density was equal to 26 MCM while the total net revenue stabilized at a maximum volume of 37 MCM. The reason that the scenario at 37 MCM was chosen is that the water

Net ~ev . /wat& ( L L I ~ ~ ) Land use %

l188 1302 1183 1046 1045 146 184 170 175 175

*The maximum water volume co~isurned is 37.047 MCM out of the 42 MCM available


194 River Ba~itl Marragernctlr I 1

delivery system has to be designed based on the maximum water volume needed in case the irrigated area needed to be extended to utilize the allocated volume, and in order to better compare the hydraulic results of optimal model with the already designed scheme to test the sensitivity of the proposed model.

4.3 Scenarios with escalated selling prices, production costs and land productivity

The cropping pattern, total net revenue, water productivity, and land use density changes with the increase in the selling prices, production costs and land productivities of vegetables, fruits, and field crops are shown in Table 4.

Selling prices of agricultural food items are subject to intra-seasonal and inter- seasonal variation due to outside competition, to quality, and to market The same thing applies to production costs, where input costs can cause a variation in the final net revenue. In the scenarios tested in this study, fluctuations in the selling prices and production costs of crops were used to test the pattern of variation in the optimal cropping pattern, the total net revenue, and the water productivity. The increase in the selling prices of vegetables by 5% eliminated the production of peaches and increased the production of vegetables like spinach and tomato, while a 10% shifted ftom tomato to cucumber after that there was no change. The increase in the total net revenue and the water productivity was 8.7, 16.2, 22.6, and 28.4%, respectively and the increase in land use density was 5.4% at 5% increase in selling prices and stabilized at this level with increasing selling prices. Increase in selling prices of fruits did not cause any variation in the cropping pattern because of the market constraint imposed on fruit trees, moreover, the percent increase in the total net revenue and the water productivity was 2.1, 4.1, 6.0, and 7.9% respectively for the 5, 10, 15, and 20% increase in fruit selling prices. The increase in the field crops selling prices caused a change in the cropping pattern at 15% increase, where the land use density increased from 175 to 180%. The rate of total net revenue and water productivity increase is less than the increase in the selling prices and reached a maximum of 5.8% at 20% field crop price increase. The increase in the vegetable production costs caused a shift to field crop production at 20% increase. The decrease in the total net revenue and water productivity was 4.3, 9.0, 11.5 and 13.9% respectively. The increase in the production costs of fruits and field crops did not cause any change in the cropping pattern except when field crop costs increased by 20%.


Table 4. Net revenue, water productivity and land use density variation with different scenario

Water productivity ( L V ~ ) Land Use Density (?h)

1045

175

1000

175

951

170

925

160

900

160

1044

175

1038

175

1032

175

1026

175

1042

175

1039

175

1036

175

1033

175



The land productivity values (kglha) that were used in this study are average values subject to a lot of fluctuations.The increase in the vegetables productivity per unit land shifted the cropping pattern from peach to more tomato production at 5% land productivity decrease and a shift to cucumber production at 10% decrease and above. When, the land productivity of fruit trees and field crops was decreased, no cropping pattern shift was observed except when field cropland productivity was decreased by 15% causing lentil to be added to the crops. The total net revenue and water productivity increase linearly with the decrease in land productivity reaching 5% at a 20% decrease in productivity.

4.4 Scenarios with changing water prices

According to different studies done in the study area regarding water price, [l l], it was found the most feasible water price is ~ O O L L / ~ ~ . In this study we tried to quantify the net revenue per unit water changes with increasing prices.

Figure 2: Net revenue per unit water with changing water levels and prices

As expected, the net revenue per unit water decreased with increasing water price, however, the decrease was not linear as in the case of water levels 32, 37 and 42 MCM (Fig. 2). It is also noticed that the values of the net revenue per unit water at a given unit water price increased as the water volume decreased until it reaches 27MCM and decreased there after. The cost of water was not included in the production costs because it was tested separately. In this initial model study, a water price of 100 L L / ~ ~ was used but a sensitivity analysis was done to check the trend of the model output variation with changing water prices. Water prices were varied from 0 to 500 LLJrn3. Increasing the unit water price at a specific available water volume did not affect the cropping pattern significantly, whereas, the effect was pronounced on the total revenue and water productivity. The rate of decrease was 0.775 at the 22 and 27 MCM. But at higher volumes the decrease was not linear in the range of the water prices tested.


In this study, the allocation of water and land was on a monthly basis rather than on a yearly basis. The monthly allocation of water permitted us to determine the maximum irrigation water volume available for each month. The same applies to the land constraint where land was allocated on a monthly basis which allowed multiple cropping and a land use density greater than 100%. This is a modification on Kipkorir [l31 study that allocated land on a yearly basis and water on a seasonal basis.

5 Summary

This study was conducted to optirnize usage of irrigation water by maximizing water productivity and minimizing water distribution system costs. This model aimed at maximizing total net revenue and water productivity by allocating the monthly available land and water among three groups of crops: Vegetables, h i t trees, and field crops.

References

[l] Iramy, S. 1954. "Calcul Economique des Reseaux de Distribution d'Eaun. La ffouille Blanche. 9: 135.

[2] Hooker, M.A., Alexander, W.E. 1998. Estimating Demand for Irrigation Water in the Central Valley of California. Journal of the American Water Resources Association. 34 (3): 497-505.

[3] United Nations. 2000. Sustainable Agriculture and Rural Development: Linkage between Agriculture, Land and Water. Economic and Social Council, Commission on Sustainable Development, eighth session, 24 April - 5 May.

[4] Allan, J.A. 1997. "Virtual Water": A Long-Term Solution for Water-Short Middle Eastern Economies? Water Issues Group, Place: School of Oriental and African Studies (SOAS), London: University of London.

[5] Matanga, G. B., and Marino, M. A. 1979. Irrigation planning I: Cropping pattern. Water Resources Research. 15 (3): 672-678.

[6] Bowen, R. L., and R. A. Young. 1985. Financial and economic irrigation net benefit functions for Egypt's Northern Delta. Water Resources Research 21 (9): 1329-1335.

[7] Zhenmin, Z. 1995. Optimization of water allocation in canal systems of Chengai irrigation area. Technical Sessions about Irrigation Water Delivery Models, FAO.

[8] Bemardo, D. J., N. K. Whittlessey, K. E. Saxton, and D. L. Bassett. 1988. Irrigation optimization under limited water supply. Transactions of the ASAE 31 (3): 712-719.

[9] Eckert, J. B., and Wang, E. 1993. Effects of irrigation water supply variations on limited resource fanning in Conejos County, Colorado. Water Resources Research 29 (2): 229-235.



[l01 Panda, S. N., Khepar, S. D., and Kaushal, M. P. 1996. Intraseasonal irrigation system planning for waterlogged sodic soils. J. Irrig. and Drainage Eng. 122 (3): 135-144.

[l l] El-Awar, F.A., Darwish, M.R., Mteirik, R.M., Nimah, M.N. 2001. Optimal Cropping Pattern for Limited Water Supply: A Case Study in Lebanon. Applied Engineering in Agriculture. American Society of Agricultural Engineers (ASAE). 17 (3): 39 1-397

[l21 Kipkorir, E.C., Sahli A., Raes D., Tollens E. Optimal Irrigated Cropping Pattern of a Multiple System under Water Scarcity Constraints. Water Resources Management. WIT Press. 2001.

[l31 Food and Agriculture Organization (FAO) of the United Nations. 1994. Making Land Use Choices for District Planning. Rome, Italy: FAO.

[IS] Brooke, A., Kendrick, D., Meeraus, A., Rarnan, R. 1998. CAMS A User's Guide. Washington DC, USA: GAMS Development Corporation.


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