Optimization of Irrigation Water Allocation Framework Based on Genetic Algorithm Approach

In a world where excessive use and degradation of water resources are threatening the sustainability of livelihoods dependent on water and agriculture, increased food production will have to be done in the face of a changing climate and climate variability. There is a need to make optimal use of the available water resource to maximize productivity. Climate-smart irrigation is aimed at increasing per unit production and income from irrigated cropping systems without having negative impacts on the environment or other water users and uses. This paper developed a water allocation model using Genetic Algorithm to equitably allocation available water to the various sectors in Kano River Irrigation Scheme yielding an optimal as well as equitable water release with a 96.44% demand met. An average relative supply of 0.94 was obtained indicating the there was even supply of water to all the sectors. The model is robust and relatively easy to apply and can be employed by farm managers to achieve equity and optimal use of the available water resource.


Introduction
Global water resources are under increasing pressure due to large-scale water abstraction for human needs [1] [2]. Agriculture is both a cause and victim of water scarcity, as the excessive use and degradation of water resources are threatening the sustainability of livelihoods dependent on water and agriculture [3]. Water scarcity is said to occur when demand for freshwater exceeds supply in a specified domain and of all sectors of the economy; agriculture is the most sensitive to water scarcity. Although the agricultural sector is sometimes viewed as a "residual" user of water, after domestic and industrial sectors, it accounts for 70 percent of global freshwater withdrawals, more than 90 percent of consumptive use [4]. About 70% of this water abstracted from freshwater systems is used for irrigation [5], yet, irrigation systems are under pressure to produce more food with lower supplies of water [6]. Although farmers have long adapted to environmental conditions, the severity of the predicted climate changes may be beyond many farmers' current ability to adapt and improve their agricultural production systems and livelihoods [7]; increased food production will have to be done in the face of a changing climate and climate variability [8]. The vulnerability of agriculture is increasing with the passage of time as climate change is badly affecting agriculture due to uncertainty in the availability and quality of natural resources [9]. However, there is an increasing interest focused on ensuring that both agriculture and irrigation become climate smart as a driven factor to ensure food security, improve rural livelihoods, and alleviate environmental risks for small-scale farmers [10].
Climate-smart agriculture (CSA) is the agriculture that sustainably increases productivity, enhances resilience, reduces or removes greenhouse gases where possible and enhances achievement of national food security [11]. The CSA has three concurrent objectives: 1) sustainably increasing farm productivity and income, 2) increasing adaptive capacity to climate change, and 3) reducing greenhouse gas emissions [12]. Climate-smart irrigation (CSI) is an important integral component of climate-smart agriculture. It is an irrigation approach for a given agro-climatic and societal context that may result directly or indirectly from the different aspects of climate change; it aims to increase per unit production and income from irrigated cropping systems without having negative impacts on the environment or other water users and uses (in space and time).
The performance of agricultural use of irrigation water in sub-Sahara Africa, as compared to Asia, has been characterized by inefficiency and poor management [13]. According FAO (2018) Sub-Saharan Africa (SSA) has the most significant potential for expanding irrigated agriculture in the world. But only one-fifth of the potential irrigable area has been developed despite its enormous land and water resources [14], of which the vast majority of this irrigated land is concentrated in just four countries: Madagascar, Nigeria, South Africa, and Sudan [15].
Irrigation practice in Nigeria has not achieved the set goals despite the huge investment involved. The available resources for agricultural and irrigation development are still underutilized including land, water resources, and other agricultural inputs [16]. Currently, the total arable land in the country is estimated at about 34.6 million ha; however, only 40% is under cultivation out of which less than 5% is irrigated [17] [18]. Notwithstanding the abundant land and water resources, the availability of land for crop production is under threat due to recently increased conflict of the resource among the farmers and the herders in some selected agro ecological zones of the country [19]. Although Nigeria irrigation system has recently started receiving due attention and there is an observed facelift in its development, there are still underline challenges that need to be adequately addressed such as inconsistent and unstable policies and inappropriate legal framework, funding constraint and farmers attitudes and awareness towards irrigation systems of crop production and lack of the farmers interested in the operation and maintenance of the large-scale irrigation facilities. [20] reported that poor knowledge of irrigation techniques among the farmers is one of the factors affecting their participation in large-scale irrigation scheme. Those that manage to participate are not equipped with the requisite knowledge for the operations and maintenance of the facilities. This problem is one of the current challenges being faced by the large-scale irrigation scheme in Nigeria. The participating farmers see the facilities as government properties which should be maintained by the government. These do not only make the equipment short-lived but has also resulted in the abandonment of irrigation scheme due to lack of irrigation equipment and infrastructure to make use of. Furthermore, in irrigation scheme like the Hadeja-Jama' are river project, the utilization of the project is just about 50% while the Zobe dam in Dutsin-Main Katsina, which was constructed 40 years ago, currently has very little irrigation activities. Also, at the Bakolori irrigation dam in Zamfara State, under the Sokoto Rima Water Project, the area cultivated is not commensurate with the amount of water in the dam [21].
Kano River Irrigation Project (KRIP) being one of the first, largest and said to be the best performing irrigation project in Nigeria, has been in existence for over four decades and has not met up to ten percent of the design capacity. The dominant problems as identified by [14] range from water distribution, water management, waterlogging, salinity, sodicity, reduced fertility, obliteration of the irrigation and drainage infrastructure. This paper is focused on addressing water management issues by developing an irrigation water allocation model that will ensure equity in water, ensure the proper management and distribution of water to the users.

The Study Area
The study area is located in the Kano State of Nigeria in Kano State between latitudes 11˚30'N and 12˚03'N and longitudes 8˚30'N and 9˚40'E. Kano River Irrigation Project, Phase I (KRIP I) is part of the Kano River Project which began in 1965 as a pilot project. It covers potentially irrigable land of 22,000 ha, which forms the study area. To this end, the area developed for irrigation is 16,500 ha while the area cropped ranges between 13,900 ha for dry season and 16,450 ha in wet seasons. KRIP I is a unique design, in that, the entire water distribution network operates on gravity owing to the elevation of 440 meters above sea level, with a minimum of the supply dam at 506.50 meters [14].
Tiga Dam is the source of irrigation water to the project site through the Ru-wan Kanya Reservoir and the 18 km long main canal II, which splits into West and East branch canals. These are then distributed to all sectors, to sector turnouts, to distributor canals, to field canals and siphoned to blocks or farmlands.
The excess is designed to be collected from the end of the field through field drains to collector drains and to main drains and back to the Kano River. The land is cultivated throughout the year (dry and wet season). Rainfall annual mean varies from about 884 mm to 600 mm in the north to 1200 mm in the south. Rain is more in five months (May-September) with August, recording the highest amount and mean annual temperature ranges from 26˚C -33˚C. The yearly rainfall amount in Kano is increasing, especially in July and August [22].

Determination of Crop Water Need (ET crop )
Steps for determining crop evapotranspiration, ET crop : 1) Identifying the crop growth stages, determining their lengths, and selecting the corresponding K c coefficients; 2) Adjusting the selected K c coefficients for frequency of wetting or climatic conditions during the stage; 3) Constructing the crop coefficient curve (allowing one to determine K c values for any period during the growing period); and 4) Calculating ET crop as the product of ET o and K c .
The general lengths for the four distinct growth stages and the total growing period for various types of climates and locations were employed as provided by FAO Irrigation and Drainage Paper No. 24 [26]. Crop water need was calculated based on the monthly reference crop evapotranspiration and the crop factor for each crop as shown in Equation (2) below based on FAO 56 standard.
where ET crop is crop water need and K c the crop factor. Crop factor varies for crops at various growth stages which include; initial, crop development, mid and late stages of growth.

Determination of Crop Water Requirement (CWR)
Crop water requirement is the amount of water required to compensate the evapotranspiration loss from the cropped field. Crop water requirement for the various sectors on weekly bases were computed for the crop water needs and the area of each sector as shown in Equation (3) crop CWR ET A = × where CWR is the crop water requirement, ET crop is crop water need and A is the area of each sector.

Determination of Relative Water Supply (RWS)
The relative water supply is the ratio of supply water to demand. The relative water supply of the irrigation scheme is in Equation (4).
( ) volume of water allocated Relative water supply RWS crop water requirement = (4)

Model Formulation
A number of alternative objective function formulations are possible for the water allocation problem. The most appropriate function has been found to be of the form [27]: ( ) where n is the number of irrigation schemes, i d the irrigation demand for scheme i and i x the irrigation supply to scheme i. The Genetic Algorithm flow chart for the water allocation is shown in Figure 1. The above equation is subject to canal capacity constraints, and supply constraints defined mathematically as: where i is the number of weeks, j is the number of sectors and Q is the weekly available water, subject to the constraint which states that the allocated supply to each sector should not exceed the minimum of either the weekly demand of each sector or the total weekly available supply was evaluated accordingly as in Equation (7).

Results and Discussion
The result of the reference evapotranspiration of Kano computed using the Penman-Monteith method is shown in Table 1. The average monthly reference evapotranspiration ranges from 4.33 mm/day in August to 7.39 mm/day in April.
This is partly accordance with the findings of [28], observed that evapotranspiration for Kano is very low in rainy season having lowest value in August and high during dry season with its highest value in February, although in the case of the study, the evapotranspiration was highest in April.
The crop water need (ET crop ) was computed for each crop from Equation (2).
The crops were planted at various weeks based on FAO 56 standard. The irrigation duration was for 36 weeks, when planting started in week 40 through week 23 of the next year.
Other details of the crops are presented in Table 2. It was observed that rice had the highest crop water need of 1124.71 mm although rice did not have the longest growth duration while maize had the lowest crop water need of 520.33 mm although maize did not have the longest growth duration. The crop water need is largely dependent on the crop factor of the crops at the different growth stages that the growth duration of the crops.
The crop water requirement for the entire irrigation scheme was then computed based on the crop water need based and cropping pattern of the Kano River Irrigation Project. The result of the crop water requirement is shown in Table 3.    The total crop water requirement for Kano River Irrigation Project was estimated to be 119.51 MCM with peak demand of 4.964 MCM obtained in week 11. At full canal capacity, the weekly available water is 5.184 MCM. The weekly demand and the optimized release during the entire group period are shown in Figure 3. It was observed that the optimized release was very close to the demand for all the weeks during the entire growth period, supplying just what is needed by the crops. Table 4 shows the demand vs supply of all the 38 sectors in KRIP, it also shows the relative water supply of each sector. It was observed that the water allocated was closely matched with the demand (crop water requirement). Resulting to a 96.44% demand met. The GA Parameters used for the water allocation model are outlined in Table 5.
An overall optimized relative water supply of 0.96 was obtained for KRIP, with 0.94 and 0.99 as the minimum and maximum relative water supply respectively. The optimized relative water supply for Kadawa sector, Azore sector and Karfi sector where compared with those measured in the 90's in a study by [29]. Figures 4-6 show the minimum and maximum relative water supply for the three sectors respectively.     It was observed that the measured relative water supplies indicates uneven supply of water during the planting season and also tail end problem, while the optimized relative water supplies indicates fairly uniform relative water supplies during the planning season also eliminating tail end problem.

Conclusion
The optimisation approach developed to minimize the gap between supply and crop water requirement based on the Genetic Algorithm optimization technique is robust and relatively easy to apply. Applying it to a real-time irrigation scheme, it has proven to be an effective tool in decision making tool for effective water allocation as the water allocation model yielded an optimal as well as equitable water release with a 96.44% demand met. An average relative supply of 0.94 was obtained indicating that there was even supply of water to all the sectors. The model can be employed by farm managers to achieve equity and optimal use of the available water resource.