Time series modelling of monthly reference evapotranspiration for Bikaner, Rajasthan (India)
DOI:
https://doi.org/10.53550/Keywords:
Time series model, Monthly reference evapotranspiration, Mann-kendall test, Cube root transformation, Box-cox transformation, Stochastic modelsAbstract
Meteorological data were collected from Indian Meteorological Department (Pune) for Bikaner district of Rajasthan from the year 1961 to 2005 and monthly reference Evapotranspiration (ET ) was estimated using the Penman-Monteith 0 FAO-56 method. For smoothening data and to stablise the variance in the data series of monthly ET cube root transformation was applied. Monthly ET 0, 0 (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 ET 0 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) ET series. Hence, all 12 harmonics were 0 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 ) of independent stochastic component. Portmanteau test and t Box-Cox transformation was applied to series a for checking independence t 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 ET (cube root 0 transformation). Using the developed time series model, monthly ET were 0 forecasted for the year 2006 to 2050.
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