Wavelet analysis and determination of the optimum probability distribution of hydrometeorological time series for Nyando river basin

Abstract

Perturbations in hydrologic time series have recently been witnessed in many parts of the world and knowledge of their occurrence is of great socio-economic significance. Various statistical techniques have been used in the past to analyse hydro-climatic series without revealing important frequency information. The main objective of this study was to analyse the trend, periodicity and frequency of the hydrometeorological time series for Nyando River basin. The specific objectives were to: determine trends investigate periodicity and determine the optimum probability distribution in rainfall and streamflow time series. Rainfall data of lengths ranging from of 41 - 100 years were obtained from Water Resources Authority, Kenya Meteorological Department and Finlay Kenya Limited. Streamflow data of lengths ranging from 45 – 60 years were obtained from Water Resources Authority. The datasets were first tested for homogeneity, normality and independence. This study used Wavelet Transform (WT) method in addition to Mann-Kendall (M-K) and Fourier Transform (FT) to investigate the rainfall and streamflow trend and periodicity in the basin. In trend detection, M-K computed the z-statistical values and declared trend or no trend at 95% confidence interval, while WT detected the peaks and disclosed the time-frequency information for the trends. Further, FT and WT techniques were used to estimate the power spectrum and to reveal the periodicities. To obtain the probability distributions, L-moment diagrams were generated to compare the L-skewness verses L-kurtosis relations of different distributions. The closest relationships were further confirmed using goodness-of-fit tests. The M-K results revealed minimal trend in rainfall but showed an overall increasing trend in streamflow. WT revealed overall increasing trends for both rainfall and streamflow. The dominant rainfall and streamflow periodicities were determined at 2-7 years, 2.7-3.3 years, 3.5-4 years, 5.6-6.5 years and 7-8 years. Based on the results, this study concluded that the Nyando River basin rainfall and streamflow exhibited increasing trends with periodic cycles over the last thirty years. Further, the study found that PE3 provides good approximation to the annual maximum floods in the basin. The study recommends that PE3 could be adopted for estimating the return periods of floods in the design of hydraulic structures for the Nyando River basin. Similar studies can be applied in other River basins in Kenya to determine the optimal probability distributions for the analysis of extreme rainfall and streamflow.