Evaluating Climate-Rainfall-Temperature Interactions and their Effects on Water Resource Sustainability (SDG 6) using ARIMA and ARIMAX Models
Ebenezer Tawiah Arhin *
Statistical Sciences Department, Tamale Technical University, Tamale, Ghana.
Karim Azumah
Statistical Sciences Department, Tamale Technical University, Tamale, Ghana.
Bashiru Imoro Ibn Saeed
Statistical Sciences Department, Tamale Technical University, Tamale, Ghana.
Caleb Nurideen Nambyn
Statistical Sciences Department, Tamale Technical University, Tamale, Ghana.
Amidu Abdul Hamid
Statistical Sciences Department, Tamale Technical University, Tamale, Ghana.
Salifu Hussein
Statistical Sciences Department, Tamale Technical University, Tamale, Ghana.
*Author to whom correspondence should be addressed.
Abstract
Aims: This study evaluated the interactions among climate, rainfall, and temperature and their implications for water resource sustainability in the Northern Region of Ghana, in line with Sustainable Development Goal 6 (SDG 6).
Study Design: The study employed a retrospective time series design.
Methodology: Annual average time series data from 2000 to 2024 were analyzed using Autoregressive Integrated Moving Average (ARIMA) and Autoregressive Integrated Moving Average with Exogenous Variables (ARIMAX) models, with rainfall variability serving as the primary proxy for water resource availability.
Results: The ARIMA (0,1,0) with drift model was identified as the best univariate fit for the rainfall series, while the ARIMAX model (0,1,1), which incorporated temperature and climate indices as exogenous variables, demonstrated superior predictive accuracy based on Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), and Mean Absolute Percentage Error (MAPE). Results revealed that climate variables exerted a stronger and statistically significant influence on rainfall variability compared to temperature, with climate indices showing significant positive coefficients (β = 4.278, p = 0.012) in the ARIMAX (0,1,1) framework. Forecasts from 2025 to 2034 indicated modest but consistent increases in rainfall and temperature, with a projected 10.91% rise in rainfall under a +1°C temperature scenario, signifying low climatic risk to water availability.
Conclusion: The study concludes that climatic factors, particularly composite climate indices, are the dominant drivers of rainfall variability and consequently water resource conditions in northern Ghana. The ARIMAX (0,1,1) model's superior performance underscores the importance of integrating exogenous climate variables into time-series frameworks for reliable hydrological forecasting and sustainable water resource planning.
Keywords: ARIMA, ARIMAX, time series, sustainable development goal 6