Using Extreme Value Theory to Estimate Available Water in the Upper Awach-Kibuon Catchment in Nyamira County, Kenya

Abstract

In the management of water resources projects, water managers are often interested in quantifying the frequency and magnitude of floods that will occur at the management areas or units. The frequency analysis of these events is one of the most important aspects that define the relationship between the magnitude and the frequency of an event, for which that event is exceeded. Frequency analysis therefore find its usefulness in the design and implementation of water projects such as in irrigation water requirement where the interest is on how much water can be available from a water resource to support irrigation throughout the year. The objective of this paper therefore was to assess the available water, using the extreme value analyses methods, that can be put to other uses such as irrigation water demand, domestic water requirement after due consideration to the environmental flow. The available water was estimated by deducting the following from the 80% probable flows orQ80: i) Deduction of estimated existing/future abstractions- determined from available information on irrigation activities along the three rivers (upstream and downstream) and ii) Deduction of the environmental flow - taken as 30% of the Q95 probable flow based on monthly mean flows. In particular this research was biased towards supporting the water requirement for a proposed irrigation project in the study area. The area of study was Awach-Kibuon catchment of the Lake Victoria South Catchment Area. This river catchment drains parts of Nyamira County through the Awach-Kasipul sub-catchent (Nyabomite, Charachani and Eaka tributaries). Data used included daily rainfall and temperature data obtained from the Kenya Meteorological Department Headquarters in Nairobi while daily discharge or flow levels data from the three tributaries i.e. Nyabomite, Charachani and Eaka were obtained from the Water Resources Authority (Kisii sub-regional office). The flow levels from Nyabomite, Charachani and Eaka were converted to river discharge using appropriate rating curves. Rainfall data was used with the Curve Number method to estimate river discharge at Eaka where flow levels were hardly available. Flood frequency distributions (GEV, the Gumbel) with different methods of parameter estimations (moments, maximum likelihood, probability weighted moments) were then used to estimate flow magnitudes corresponding to specific return periods (Q50, Q80 and Q95) and generate flow duration curves. Results from the flood frequency analysis from the General Extreme Value and Extreme Value type 1 distribution using the methods of moments (mom), maximum likelihood (ML) and Probability Weighted Moments (PWM) indicated the best distribution to be EV1-PWM since it exibited the lowest standard error estimates. Based on the most suitable distribution (EV1-PWM), the probabilities of exceedance were computed and used to estimate the water available for irrigation purposes at the three target gauging stations in the sub-catchment.From the results, a larger volume of water is available for irrigation at Charachani, for example, lowest being 0.388 cumecs in the month of July compared to 0.147 cumecs for Nyabomite and 0.249 cumecs for Eaka.. The largest amount of water for irrigation is available during the months of May and November, with peaks corresponding to those of the rainy seasons. The months with the least available water for irrigation are December, January and February, which also corresponds with the dry seasons. These results were used to inform planning in setting up of flow control structures for irrigation project in the Charachani-Eaka-Nyabomite cluster in Nyamira County.