Forecasting temperature of the Saudi Arabian Province of Makkah using a discrete state–space modeling approach

Abstract

The maximum and minimum air temperature components (Tmax and Tmin) play a crucial role in science. This study proposes a discrete-time identified state-space modeling approach in which the temperature fluctuation was modelled as a state-space system with the temperature time series as inputs. We aim to provide a tool for projecting future scenarios of Tmax and Tmin. The current research employs a prediction-focused methodology to system identification, with the overarching goal of developing a realistic and dynamic system model. Data on the Tmin and Tmax recorded in the Saudi Arabian province of Makkah are used to test the accuracy and robustness of the proposed methodology. The proposed model was developed utilizing 120 years' (1901–2020) worth of historical monthly time series data on Tmax and Tmin. It was applied to anticipate future temperatures over the ensuing 60 years (up to 2080). For maximum temperature projections, the fit to the data or prediction focus was 87.04% and 85.14%, respectively for the identification (training) and validation phases of the model development. Akaike’s Final Prediction Error (FPE) and Mean Squared Error (MSE) values were observed to be 0.37 °C and 0.34 °C, respectively. The prediction focus during the identification and validation phases were 86.25% and 84.78%, respectively for the minimum temperature projection. The FPE and MSE values were 0.41 °C and 0.37 °C, respectively for this instance. The findings demonstrate that the recommended discrete state-space modeling approach may be utilized to predict temperature variations in the future.