We introduce a novel Graph Attention Autoencoder (GAE) with spatial regularization to address the challenge of scalable anomaly detection in spatiotemporal rainfall data across India from 1990 to 2015. Our model leverages a Graph Attention Network (GAT) to capture spatial dependencies and temporal dynamics in the data, further enhanced by a spatial regularization term ensuring geographic coherence. We construct two graph datasets employing rainfall, pressure, and temperature attributes from the Indian Meteorological Department and ERA5 Reanalysis on Single Levels, respectively. Our network operates on graph representations of the data, where nodes represent geographic locations, and edges, inferred through event synchronization, denote significant co-occurrences of rainfall events. Through extensive experiments, we demonstrate that our GAE effectively identifies anomalous rainfall patterns across the Indian landscape. Our work paves the way for sophisticated spatiotemporal anomaly detection methodologies in climate science, contributing to better climate change preparedness and response strategies.

Advances in neural architecture search, as well as explainability and interpretability of connectionist architectures, have been reported in the recent literature. However, our understanding of how to design Bayesian Deep Learning (BDL) hyperparameters, specifically, the depth, width and ensemble size, for robust function mapping with uncertainty quantification, is still emerging. This paper attempts to further our understanding by mapping Bayesian connectionist representations to polynomials of different orders with varying noise types and ratios. We examine the noise-contaminated polynomials to search for the combination of hyperparameters that can extract the underlying polynomial signals while quantifying uncertainties based on the noise attributes. Specifically, we attempt to study the question that an appropriate neural architecture and ensemble configuration can be found to detect a signal of any n-th order polynomial contaminated with noise having different distributions and signal-to-noise (SNR) ratios and varying noise attributes. Our results suggest the possible existence of an optimal network depth as well as an optimal number of ensembles for prediction skills and uncertainty quantification, respectively. However, optimality is not discernible for width, even though the performance gain reduces with increasing width at high values of width. Our experiments and insights can be directional to understand theoretical properties of BDL representations and to design practical solutions.

Current modeling approaches for hydrological modeling often rely on either physics-based or data-science methods, including Machine Learning (ML) algorithms. While physics-based models tend to rigid structure resulting in unrealistic parameter values in certain instances, ML algorithms establish the input-output relationship while ignoring the constraints imposed by well-known physical processes. While there is a notion that the physics model enables better process understanding and ML algorithms exhibit better predictive skills, scientific knowledge that does not add to predictive ability may be deceptive. Hence, there is a need for a hybrid modeling approach to couple ML algorithms and physics-based models in a synergistic manner. Here we develop a Physics Informed Machine Learning (PIML) model that combines the process understanding of conceptual hydrological model with predictive abilities of state-of-the-art ML models. We apply the proposed model to predict the monthly time series of the target (streamflow) and intermediate variables (actual evapotranspiration) in the Narmada river basin in India. Our results show the capability of the PIML model to outperform a purely conceptual model ($abcd$ model) and ML algorithms while ensuring the physical consistency in outputs validated through water balance analysis. The systematic approach for combining conceptual model structure with ML algorithms could be used to improve the predictive accuracy of crucial hydrological processes important for flood risk assessment.