TEMPERATURE FORECAST CONSIDERING THE IMPACT OF RAINFALL: A CASE STUDY ON BETWA RIVER BASIN AT BAIRAGARH STATION (BHOPAL)

Abstract

In climate impact studies, temperature forecasting has been considered as one of the most important factors on the sector of vegetation, irrigation, water resources and tourism. The main objective of this study is to forecast daily maximum and minimum temperature in Bairagarh station, Bhopal by employing auto-regressive integrated moving average (ARIMA) and the autoregressive integrated moving average with exogenous variables (ARIMAX) models. This study compares the two models and provide the best-fit prediction with the observed actual data. The daily maximum and minimum temperature observations between 1982 and 2012 were collected from NASA’s POWER data access viewer. ARIMA model was applied to the daily maximum and minimum temperature series to have the best-fit model however, ARIMA can capture the effect of rainfall by itself but introducing rainfall as exogenous variable will improve the efficiency. That is why ARIMAX was considered in this study. The Root Mean Square Error (RMSE), Mean Absolute Percentage Error (MAPE) and residual ACF serves as the error measures in evaluating the forecast ability of the models. The effect of (AIC) was tested. As compared to the ARIMA models, ARIMAX model performed well with lower error matrices, this effect was more significant in maximum temperature series. Which indicates that the rainfall factor was influential in the model. The results shows that the model with parameter greater than 1 and less than 3 would work better for Bairagarh station there is a significant correlation between rainfall and temperature, which is evident by the reduced error from ARIMAX modelling. For maximum temperature, ARIMA models (1, 1, 1), (2, 1, 1) and (1, 1, 2) have performed well compared to the other models at training stage with RMSE value of 1.325144, 1.319782, and 1.320031 and the AIC values were 12423.88, 12396.3, and 12397.67 and MAPE value of 2.953642, 2.939284 and 2.940243 respectively. At testing stage, model (1, 1, 2) have shown best results with RMSE=1.379335, AIC=1273.74, MAPE= 3.1285561. Whereas for minimum temperature, the ARIMA models (1, 1, 2), (2, 0, 2), (2, 1, 1), ( 3, 0, 0), and (3, 1, 0) at training stage with RMSE value of 1.287539, 1.286019, 1.287261, 1.303937, and 1.299155 and AIC values were 12215.74, 12216.6, 12214.16, 12315.47,and 12281.22 and MAPE value of 6.068753, 6.08717, 6.731284, 6.147745, and 6.090528 respectively. At validation stage vi model (2, 1, 1) have shown better results among all, with AIC = 1236.45, RMSE = 1.310559, and MAPE = 6.731284. For maximum temperature, ARIMAX models obtained for the considered station at training stage were (1, 1, 1), (2, 1, 1) and (1, 1, 2) have performed well compared to the other models with RMSE value of 1.3769, 1.3716, and 1.3714 and the AIC values were 1272.47, 1269.68, and 1269.57 respectively. At testing stage, model (1, 1, 2) have shown best results with RMSE=1.3714, AIC=1269.57, MAPE= 3.115147. Whereas for minimum temperature, the ARIMAX models (1, 1, 2), (2, 0, 2), (2, 1, 1), ( 3, 0, 0), and (3, 1, 0) at training stage with RMSE value of 1.285462, 1.283925, 1.285178, 1.301806, and 1.297123 and AIC values were 12205.94, 12206.69, 12204.34, 12305.52,and 12271.79 and MAPE value of 6.054431, 6.071131, 6.053243, 6.134001, and 6.077045 respectively. At validation stage model (2, 1, 1) have shown better results among all, with AIC = 1236.45, RMSE = 1.310558, and MAPE = 6.730814.