Forecasting Hydrological Time-Series with Uncertainty: An N-BEATS Approach for Low-Cost Sensor Data

Abstract Effective water resource management and flood prediction represent critical global challenges, frequently hampered by the prohibitive cost and sparse deployment of traditional hydrological monitoring systems. To address this persistent data gap, this study proposes and validates a comprehensive, complete system that synergizes a custom-developed low-cost ultrasonic sensor with an Advanced deep learning architecture for high-accuracy, multi-horizon river water level forecasting. This work leverages a deep N-BEATS (Neural Basis Expansion Analysis for Time Series Forecasting) model, trained on high-frequency (15-minute) sensor data, to predict water levels at 1-hour and 6-hour future horizons. The model's robustness is rigorously benchmarked against two other powerful architectures: a modern Temporal Convolutional Network (TCN) and a classic Long Short-Term Memory (LSTM) network. Crucially, its predictive uncertainty is quantified using the Monte Carlo (MC) Dropout technique, transforming single-point predictions into reliable probabilistic forecasts. The optimally tuned N-BEATS model exhibited outstanding performance, achieving a coefficient of determination (R2) of 0.82 on the test set for 15-minute ahead forecasts, significantly outperforming both the TCN (R2 = 0.72) and the LSTM (R2 = 0.66). Furthermore, the uncertainty analysis successfully captured the model's confidence, with prediction intervals dynamically widening during periods of high hydrological volatility, thereby adding a crucial layer of reliability to the forecasts. Ultimately, this study demonstrates that the integration of affordable sensing technology with advanced, uncertainty-aware, and interpretable deep learning provides a viable and scalable path toward more resilient and democratized water management.