Statistical Analysis Of Water Level, Temperature And Humidity Using Cointegrated Vector Autoregression (VAR) Models

Abstract

The leading climate factors influencing availability of water are; temperature, relative humidity, precipitation, and evaporation. Water and agricultural production cycles are indisputably influenced by temperature and relative humidity. Temperature and relative humidity projections can therefore proficiently be employed in making decisions when optimal usage of water resources is of interest. Thus, the current study explored both the “long-run” and “short-run” impact of both temperature and relative humidity on water level through cointegrated VAR models with specific application to the Akosombo Dam water level. The quarterly averages of the daily Akosombo water level, temperature and humidity of its surrounding was computed from the daily data obtained and it spanned the period January 1980 to December 2014. Seasonal ARIMA models ARIMA(0,1,1)(0,1,1)4 , ARIMA(1,0,1)(1,1,1)4 and ARIMA(2,1,1)(1,1,1)4 were estimated using values of AIC, AICc and BIC for Akosombo Dam water level, temperature, and humidity respectively. Also, water level was observed to granger causes both temperature and relative humidity whiles relative humidity also granger causes both water level and relative humidity. In addition, both water level and temperature responded positively to the impulse of humidity. The VAR model outperformed the SARIMA model in forecasting water level, temperature, and relative humidity. Finally, water level and relative humidity were cointegrated whiles a cointeration relation was observed between temperature and relative humidity. The rate of adjustment to equilibrium observed by temperature was very high among the three variables.