Time series modelling of monthly reference evapotranspiration for Bikaner, Rajasthan (India)

Meteorological data were collected from Indian Meteorological Department (Pune) for Bikaner district of Rajasthan from the year 1961 to 2005 and monthly reference Evapotranspiration (ET₀) was estimated using the Penman-Monteith FAO-56 method. For smoothening data and to stablise the variance in the data series of monthly ET0, cube root transformation was applied. Monthly ET₀ (cube root transformation) data from the year 1961 to 2000 were taken for time series modelling and remaining data from the year 2001 to 2005 were used for model validation. Turning point and Mann-Kendall tests were used at 5% significant level for identifying trend component. A trend-free monthly ET0 series were used for modelling the periodic component using Fourier series analysis. First 12 harmonics explained total variance of 173.47% for monthly (cube root transformation) ET0 series. Hence, all 12 harmonics were considered. Before modelling stochastic dependent component, periodic component was removed from the time series and series was made stationary. For modelling dependent stochastic component autoregressive (AR)/moving average (MA)/autoregressive moving average (ARMA)/autoregressive integrated moving average (ARIMA) models were tried. ARIMA (12, 1, 1) model was fond the best fit model based on the minimum value BIC statistics. The dependent stochastic component was separated from the series to obtain new series (a_t) of independent stochastic component. Portmanteau test and Box-Cox transformation was applied to series a_t for checking independence and normalization, respectively. Time series models were developed by adding deterministic (trend and periodic) and stochastic (dependent and independent) components Model was evaluated with regards to several statistical measures. The correlation coefficient and Nash-sutcliffe coefficient also indicated high degree of models fitness to the observed data. Developed time series model was validated with 5 years values of monthly ET₀ (cube root transformation). Using the developed time series model, monthly ET0 were forecasted for the year 2006 to 2050.