Time series prediction of aerosol optical depth across the northern Indian region: integrating PSO-optimized SARIMA-SVR based on MODIS data

Accurately predicting aerosol optical depth (AOD), a key parameter for characterizing atmospheric aerosols, is essential due to the increasing prevalence of air pollution and its detrimental effects. From existing literature on AOD time-series prediction, linear models like seasonal autoregressive integrated moving average (SARIMA) are commonly used, while nonlinear models such as machine learning (ML) and deep learning (DL) have gained popularity recently for their ability to handle nonlinear patterns. This study introduces a hybrid model, particle swarm optimization-seasonal autoregressive integrated moving average-support vector regression (PSOSARIMA-PSOSVR), which integrates linear and nonlinear modeling through residual modeling to significantly enhance AOD prediction accuracy. By combining these approaches, we aim to better handle the nonlinearities and overall variability in AOD data, leading to more accurate predictions. To address hyperparameter tuning challenges, including the risks of model misspecification and overfitting or underfitting, PSO is utilized for optimization. PSO’s evolutionary optimization ensures efficient tuning for optimal model performance. Monthly AOD data sourced from the moderate resolution imaging spectroradiometer (MODIS) satellite covering the northern Indian region from 2001 to 2019 is used for experiments. Performance metrics such as root mean square error (RMSE), mean absolute percentage error (MAPE), coefficient of determination ( \(R^2\) $R^2$ ), Nash-Sutcliffe efficiency (NSE), and root mean square error ratio (RSR) are employed to evaluate model accuracy and dependability. The results of this study illustrate that the proposed PSOSARIMA-PSOSVR model outperforms both standalone PSOSARIMA and PSOSVR models. Moreover, it consistently surpasses SARIMA, SVR, and long short-term memory (LSTM) in AOD prediction, effectively addressing non-stationarity and variability challenges in AOD data. This study suggests the hybrid model as a promising approach for improving the accuracy of AOD prediction.