Stochastic Modelling of Great Letaba River Flow Process

Gislar E Kifanyi,Samuel N Odai,Julius M Ndambuki,Charles Gyamfi

doi:10.4236/gep.2019.76004

Abstract

A stochastic approach is presented in view that a time series modelling is achieved through an Autoregressive Moving Average (ARMA) model. The applicability of the ARMA model is then further presented using the Great Letaba River as a case study. River flow discharge for 25 years (1989-2014) for the Great Letaba River was obtained from the Department of Water and Sanitation, South Africa and analysed by Autoregressive (AR), Autoregressive Moving Average (ARMA) and Autoregressive Integrated Moving Average (ARIMA) models. Monte Carlo simulation approach was used to generate forecasts of the ARIMA error model for the next 25 years. Initial model identification was done using the Autocorrelation function (ACF) and Partial Autocorrelation function (PACF). The model analysis and evaluations provided proper predictions of the river system. The models revealed some degree of correlation and seasonality behaviour with decreasing river flow. Hence, in conclusion, the Great Letaba River flow has shown a decreasing trend and therefore, should be effectively used for sustainable future development.

Highlights

The hydrological modelling of a river system is complex and challenging because of increasingly anthropogenic influence on river flow and climate change coupled with lack of relevant data to characterise river systems
A stochastic approach is presented in view that a time series modelling is achieved through an Autoregressive Moving Average (ARMA) model
River flow discharge for 25 years (1989-2014) for the Great Letaba River was obtained from the Department of Water and Sanitation, South Africa and analysed by Autoregressive (AR), Autoregressive Moving Average (ARMA) and Autoregressive Integrated Moving Average (ARIMA) models

Summary

Introduction

The hydrological modelling of a river system is complex and challenging because of increasingly anthropogenic influence on river flow and climate change coupled with lack of relevant data to characterise river systems. Practical ways of modelling seasonal series must be envisioned and the appropriate order of such models specified It was Box and Jenkins (1976) who popularized the use of ARMA models through their establishment of methodological procedure for making the series stationary in both its mean and variance. They suggested the use of autocorrelations and partial autocorrelation coefficients for determining appropriate values of p and q and its seasonal equivalent P and Q when the series shows seasonality. The Autocorrelation function (ACF) and Partial Autocorrelation function (PACF) were used for initial model identification

Study Area

Theoretical Formulations and Statistical Procedures

Results and Discussion

Conclusion