Deep Learning (DL) models have become a game-changer approach for spatio-temporal modeling due to their ability to capture complex relations within data. However, their black-box nature hinders their widespread adoption in critical applications (e.g. environmental monitoring, natural hazard risk assessment, resource management, etc.). Explainable Artificial Intelligence (XAI) techniques have emerged to address this challenge, providing insights into model decisions and the learned influence of input features on predictions. Model-agnostic and perturbation-based approaches, which are particularly valuable due to their flexibility and independence from specific model architectures, are widely used for interpreting vector-based and image-based models. Among these, Local Interpretable Model-agnostic Explanations (LIME), SHapley Additive exPlanations (SHAP), and Randomized Input Sampling for Explanation (RISE) are three prominent methods. In this work, we extend and s RISE with adaptations of LIME, and SHAP for spatio-temporal deep learning models, enabling their application to geospatial image time series producing spatial, temporal, and spatio-temporal explanations. To assess the effectiveness of our approach, we apply the adapted methods to a real-world environmental case study: groundwater level prediction. Our findings demonstrate that RISE-based explanations provide different insights from LIME and SHAP ones, focusing on different aspects of the model behavior. Finally, we discuss the usefulness of producing a spatial, temporal, and spatio-temporal explanation. This comparative analysis highlights the strengths and limitations of each method in explaining deep learning models for dynamic environmental systems.