Mathematical Modeling and Deep Learning for Early Prediction of Fluid Hazards in Mountain Communities

Abstract

Mountain communities are increasingly exposed to rapidly evolving fluid hazards, including flash floods, rainfall-triggered debris flows, glacial lake outburst floods (GLOFs), and flood–landslide cascades. Their short response times, complex terrain, sparse observational networks, and changing hydro-climatic conditions limit the generalizability of conventional threshold-based warning systems. This study develops a hybrid research framework that integrates physically interpretable mathematical modeling with deep learning for the early prediction of fluid hazards in mountain environments, with particular relevance to Nepal. The proposed framework integrates rainfall, snow and glacier indicators, soil moisture, terrain attributes, river stage and discharge, surface deformation, and historical hazard observations. A rainfall–runoff and threshold-based component provides physical constraints, while LSTM and CNN-LSTM models capture nonlinear temporal and spatial relationships. A probabilistic decision layer then translates model outputs into actionable warning levels while explicitly representing predictive uncertainty. Model performance is evaluated using precision, recall, F1-score, false-alarm ratio, probability of detection, critical success index, lead time, and calibration. Evidence considered in the study indicates that LSTM models can outperform conceptual rainfall–runoff models in some mountainous catchments in Nepal, while community-based warning systems can substantially extend warning lead time when forecasts are effectively integrated with local response mechanisms. The study further identifies sensor limitations, domain shift, rare-event imbalance, communication failures, model interpretability, and institutional coordination as major implementation challenges. The proposed framework contributes an explainable and community-oriented architecture for data-scarce mountain regions by combining physical process representation, machine-learning-based hazard probability estimation, uncertainty communication, and locally meaningful warning dissemination. It provides a basis for developing next-generation early-warning systems in which mathematical models constrain prediction, machine learning updates hazard probabilities, and communities receive timely and actionable warnings.