Optimize the Irrigation Water for Agriculture in the Proposed Kalugal Oya Reservoir in Ampara District

This study attempted to propose a methodology to optimize irrigation water with optimal cropping patterns and annual net profits to the proposed Kalugal Oya scheme, situated in Ampara District, Sri Lanka. The optimization approach was based on linear programming. Three models were formulated: 1) Maximize net profit, 2) Maximize irrigable area and 3) Maximize net profit in Maha and maximize irrigable area in Yala. The above models were analysed with three scenarios: Scenario I Multi crop cultivation, Scenario II OFC and Vegetable cultivation and Scenario III Paddy cultivation in Maha and OFC & Vegetables in Yala. Further, four major constraints were identified in the above models. The first constraint relates to the availability of land (L) for agriculture use. The second constraint defines the total amount of available water (W). Third major constraint is related to the internal crop consumption (Cio) of a crop for food security requirement. Maximum level of crop production (Si ) of a crop for local marketing capacity was considered as the fourth constraint. Considering agricultural year 2012, the total annual net profit gained from Scenario II of Model 1 is estimated to be 60 Million Rupees, which is almost two and half times greater than the profit obtained when traditional cropping patterns are used in these areas (26 Million Rupees). The highest annual net profit in Scenarios I and II of Model 1 achieved mainly from the cultivation of Kurakkan, Cowpea and Brinjal. However, to satisfy the need of internal crops consumption (Cio) of farmer families in these area, Paddy and Maize were recommended for cultivation though it is not profitable.


Introduction
One of the most important elements in the world is water and it constitutes the basis of human life (Qureshi et al., 2012). Nowadays, water crisis is the main problem in the world due to water scarcity.
Main area of water usage is in irrigated agriculture, industrial and other sectors. In many countries, effective water usage in irrigated agriculture often fails to compare with the other sectors. Therefore, comparatively, water usage in irrigated agriculture has many challenges not only in the developed countries but also in the developing countries.
The proposed Kalugal Oya scheme is located at latitude of 7 o 26'N and longitude of 81 o 33'E. Also, it is situated in Uhana DS Division (DSD), Ampara District in Sri Lanka. The Kalugal Oya stream, the main stream of the proposed tank, falls within the catchment of the Navakiri Tank which is under the purview of Navakiri Division in the Batticaloa Range (EIA, 2014). The area directly upstream of the Navakiri Tank in the Ampara District has no irrigation facilities for cultivation where it comes under the dry zone. More than 1000 farmer families living in these areas primarily depend on unpredicted rainfed chena cultivation and they face severe hardships during the dry season due to water scarcity (Feasibility study report, 2012).
MCM (10,000 Ac-Ft). Also, it is proposed to irrigate around 1215 ha (3000 acres) of land for agricultural activities. Proposed headwork and canal network in the schemes are as follows (Feasibility study report, 2012):  300 m long earth bund  Two tower sluices  Ogee type spillway  Rip rap protection  Toe filter  Internal and surface drainage  Two main canals, branch canals, distribution canals and field canals, with necessary turnouts, regulators, drop structures, check structures and other.
The major land use component in the Uhana DSD area is agriculture and the major cultivation is paddy, while other field crops (OFC) and vegetables etc. are grown in lesser quantities. Paddy cultivation is practiced only in the Maha season and other crops are mainly grown in the Yala season. However, Department of Agriculture and Land Use Division of Irrigation Department has recommended the wetland rice cultivation to be in the major rainy season, and upland annual crops in the minor rainy season and mid-season of the study area (Land Use Publication, 2017).
The lands in the study area have good potential for agriculture, including paddy, vegetables and other field crops etc (EIA, 2014). As water is scarce in this area, optimum use of water in the proposed Kalugal Oya scheme for irrigation and other needs is very much essential.

Previous Studies
Irrigation water allocation of a reservoir for water optimization requires a comprehensive understanding of irrigation water demand, cropping pattern, designated area and reservoir operation (Hamideh et al., 2012

Data Collection
Data collection was carried out in the field level and also by contacting various governmental and nongovernmental organizations. Continuous field investigations were conducted to observe the present status of the study area, including agriculture practices, soil structure and climatic conditions. Also, crop cutting survey was carried out to collect data on the crop yield, total cost of crop production, farm gate price of crops and domestic crop consumption etc.
During the reconnaissance survey, Agrarian Development Officer and staff, Divisional Secretary, Grama Niladari's, Agricultural Officers, Agriculture Research and Production Assistants (ARPA), Irrigation Engineers, professional staff and farmers were consulted and interviewed to gather relevant information and for data collection.
Much effort has been taken for surveys and also to review different documents collected from various places to check the reliability and consistency of data, including climatic data (rainfall, monthly evaporation and monthly average wind speed), crop factors and crop growth stages as well. Figure 1 illustrates the methodology used in this study. by Food and Agriculture Organization (FAO) was used to compute crop water requirement (CWR) and total gross irrigation water requirement (IWR) for different crops considered in this study. The software calculates the CWR and IWR for given climatic, soil and crop data. Procedures for calculation of the CWR and IWR are mainly based on the methodology presented in FAO, Irrigation and Drainage paper No. 24 (Doorenbos and Pruitt., 1977).

Data Analysis
b. Analysis of the commencement date of cultivation Based on the available climatic and crop data, the total gross irrigation for a crop can be calculated according to the respective commencement date of cultivation.
By varying the date of commencement of cultivation, different total gross irrigation water requirements were computed for each crop (Dharmasena, 1990). The critical month of commencement for cultivation is identified as the one that gives the minimum total gross irrigation water requirement for the cultivation season.

c. Determination of annual gross irrigation water requirement IR (Wi) for each crop
Based on the aforementioned minimum total gross irrigation with respect to the critical date, optimum gross irrigation water requirement (IR) for each crop in both Maha and Yala seasons were computed and shown in Table 1.

Model formulation
Three models were formulated and analysed using a linear programming technique. These models are: Internal crop consumption requirement for food security Local marketing capacity requirement  (1). Equation (1) gives the objective function of the model, which is to maximize the net profit (Z). Four major constraints were identified. The first constraint relates to the availability of land (L) for agriculture use. The second constraint defines the total amount of available water (W). Third major constraint is related to the internal crops consumption (Coi) of a crop for food security requirement. Maximum level of crop production ( i S ) of a crop for local marketing capacity was considered as the fourth constraint.
The model assesses and identifies possible solutions with respect to these limits in order to achieve the optimum objective function (Anon., 2001). Four major constraints of the model are generally expressed as follows: The expansion of the above expression for n number of decision variables (6 number of crops) and respective constraints are defined as Land constraint: Where, L = 1215 ha Water constraint: Where, W = 6 MCM (readily available water) for both seasons.
Internal crop consumption requirement for food security:

3.4Model simulations for different scenarios
The above three models were analyzed with the following three scenarios to study different cropping patterns:

Microsoft
Excel Solver (http://www. economicsnetwork.ac.uk) was used in this study to solve the above linear programming models developed for different scenarios. This analysis considered only six types of crops proposed in the study area, namely, paddy, manioc, kurakkan, cowpea, brinjal and maize.

4.1Model 1: Maximize Net Profit in Both Maha and Yala Seasons
Results of this analysis are summarized in Tables 2, 3 and 4 for Scenarios I, II and III,  respectively. In these Tables, crop types Results of all optimization models for Scenarios  I, II and III are summarized in Table 11. Results of this analysis indicate that (See Table  11), if the objective function is to maximize net profit (Model 1), the maximum total annual net profit is 60 Million Rupees from Scenario II of Model 1. But, total annual net profit of the same model from Scenario I is lower than Scenario II (47 Million Rupees).

Comparison of Different Scenarios Based on Annual Net Profits
On the other hand, if the objective function is to maximize irrigable area (Model 2), the maximum total annual net profit shown in Table 11 is 57 Million Rupees from Scenario II and 40 Million Rupees from Scenario I of Model 2.
Results of analysis for Model 3 indicate that total annual net profit is smaller than for Model 1 and equal to Model 2 except for Scenario II (See Table 11).
If the existing (Agriculture year 2012) traditional cropping pattern (%) is applied to the entire irrigable area (1215 ha) while considering other parameters and the constraints are same, the total annual net profit from this cropping pattern in both Maha and Yala seasons can be estimated around 26 Million Rupees. Table 12 and Table 13 present the volume of water consumption in the proposed reservoir and added values of one cubic metre of water in all the models for Scenarios I, II and III. The added value of one cubic metre of water in this table is computed based on annual water consumption in the proposed reservoir and total annual net profit from each scenario. Table  13 illustrates the added value of one cubic metre of water used by agriculture for different cropping patterns. Results of this analysis indicate (See Table 13) that Scenario II of Model 1 will offer the maximum added value which is 36.4 Rupees per cubic metre of water. Comparison of total annual net profit versus added value of one cubic metre of water is indicated in Table 14. From Table 14, it should be noted that the maximum total annual net profit (60 Million Rupees) and the maximum added value of one cubic metre of water (36.4 Rupees) will be achieved only in Scenario II of Model 1.

Comparison of Different Scenarios Based on Irrigation Water Usage
On the other hand, if objective function is to maximize irrigable area (Model 2), the maximum annual net profit and the added values of one cubic metre of water are fairly reduced compared to Model 1.

Conclusions
The linear programming model is suitable for the analysis of different scenarios in managing available water in the proposed Kalugal Oya reservoir, resulting in optimal cropping patterns, showing the water requirement and annual net profits.
Considering agricultural year 2012, the total annual net profit gained from Scenario II of Model 1 is estimated to be 60 Million Rupees, which is almost two and half times greater than the profit obtained when traditional cropping patterns are used in these areas (26 Million Rupees).
Further, the highest annual net profit in Scenarios I and II of Model 1 was achieved mainly from the cultivation of Kurakkan, Cowpea and Brinjal. Moreover, the annual net profit from the cultivation of paddy and Manioc are very small compared to Brinjal. Also, Maize cultivation in this model consumes more water and provides only a negative value as an annual net profit which indicates that the farmers will not get any returns other than a loss. However, to satisfy internal crop consumption (Cio) of farmer families in these areas, the above crops were recommended for cultivation though it is not profitable.
Similarly, the highest annual net profit of Model 2 is also achieved from the cultivation of Kurakkan, Cowpea and Brinjal. However, total annual net profit in this model slightly decreases due to the Maize cultivation. In Model 3, the total annual net profit gained from Scenarios I and II are smaller compared to Model 1 and equal to Model 2 except for Scenario II (See Table 11).
Maize cultivation in Scenarios I, II and III of each model provides only negative values as annual net profits, which imply that cultivation of Maize is not advisable. Similarly, cultivation of paddy during Yala season also provides the same outcome in each model. Therefore, paddy can be recommended only during Maha season to satisfy their internal crop consumption by the farmer families as well as for marketing purposes.
It is also concluded that the maximum added value per cubic meter of water usage is 36.4 Rupees which is gained only from Scenario II of Model 1. On the other hand, Scenario III of each model was equal (2.1 Rupees) compared to others.

Recommendation for Further Studies
 In this study three models were formulated and analyzed. The output of the above models suggests the optimum irrigation water to be applied over a given period. However, from a practical point of view, it is better providing the appropriate irrigation schedule rather than only proposing the amount of water to be used. This suggests integrating the current models with a mathematical scheduling model.
 Further, the above models were analyzed with three scenarios to study different cropping patterns. However, this study did not account for climate change which is usually important for crop water requirement. Future studies can consider climate change impacts on the cropping system too.
 The capacity of the proposed reservoir is 12 MCM. After the reduction of conveyance losses and dead storage only 6 MCM has been taken into account as readily available water whole year. However, from a practical point of view, discharging amount of water from a reservoir is larger compared to the actual capacity due to seasonal changes of inflow.
 Only four major constraints were considered in this model. Therefore, several additional constraints can be added to enrich the model and to account for realistic restrictions in the system such as type of soil etc.