ForeSWE: Forecasting Snow-Water Equivalent with an Uncertainty-Aware Attention Model

TL;DR

ForeSWE addresses SWE forecasting in snow-dominant watersheds by integrating spatio-temporal attention with a Gaussian Process head to produce forecasts and principled uncertainty intervals. The model explicitly captures spatio-temporal correlations and attribute interactions via location embeddings, temporal aggregation, and a modified spatial attention mechanism, then yields predictive SWE distributions through a $ au$-component co-regionalized GP. Across 512 SNOTEL stations in the Western U.S., ForeSWE demonstrates improved daily and weekly forecasting accuracy and superior uncertainty calibration compared with baselines, with notable robustness in longer horizons where spatial dependencies dominate. The approach supports real-world decision making for reservoir operations, flood risk management, and water resource planning by providing reliable point estimates and well-calibrated prediction intervals, along with a clear deployment path with stakeholder engagement and interpretability considerations.

Abstract

Various complex water management decisions are made in snow-dominant watersheds with the knowledge of Snow-Water Equivalent (SWE) -- a key measure widely used to estimate the water content of a snowpack. However, forecasting SWE is challenging because SWE is influenced by various factors including topography and an array of environmental conditions, and has therefore been observed to be spatio-temporally variable. Classical approaches to SWE forecasting have not adequately utilized these spatial/temporal correlations, nor do they provide uncertainty estimates -- which can be of significant value to the decision maker. In this paper, we present ForeSWE, a new probabilistic spatio-temporal forecasting model that integrates deep learning and classical probabilistic techniques. The resulting model features a combination of an attention mechanism to integrate spatiotemporal features and interactions, alongside a Gaussian process module that provides principled quantification of prediction uncertainty. We evaluate the model on data from 512 Snow Telemetry (SNOTEL) stations in the Western US. The results show significant improvements in both forecasting accuracy and prediction interval compared to existing approaches. The results also serve to highlight the efficacy in uncertainty estimates between different approaches. Collectively, these findings have provided a platform for deployment and feedback by the water management community.

Figures (10)

• Figure 1: Spatiotemporal SWE forecasting with confidence interval for location $i$ over a horizon $h$, using $k$ days of historical observations with $f$ attributes. Each blue dot in the map is a SNOTEL location.
• Figure 3: Daily and Weekly forecasting models comparison: (a) The distribution of locations across five NSE groups for all models. NSE is calculated for each location, with higher values (blue bars) indicating a better prediction. Locations to the left of the red line have NSE $>0.75$. (b) Relative model performance (RMP) based on the NSE values. RMP chart: Each curve corresponds to a model; the closer and longer the line along the y-axis, the better the model performance. The X-axis shows the deviation of a model from the corresponding best performing model; Y-axis shows the fraction of locations with that deviation.
• Figure 4: Daily Forecasting: (a) ForeSWE model's relative bias, by the different months and location groups (with forecasting horizons ranging from 1 to 10 days). Groups 1 and 2 are blocked for May as the snow has melted completely at these locations. (b) Actual and ForeSWE Predicted SWE availability in different groups across the active SWE months. (c) (upper) Relative bias of ForeSWE model against a temporal model (LSTM) for Group 4 in May over different forecasting windows. (lower) Relative bias with the ensembling of ForeSWE and LSTM for Group 4 in May. The dotted lines in the plot mark $\pm$ 20%.
• Figure 5: (a) Group 3 daily relative bias with ForeSWE and LSTM model for May. (b) Group 3 weekly relative bias with ForeSWE and LSTM model for May. The dotted lines show the reference of relative bias between $\pm$ 20%. Findings --- LSTM model has consistent underprediction in its daily and weekly forecasts. Therefore, it is better to combine ForeSWE with LSTM only when it has significant overprediction or else can lead to reduced performance. For example, in (b) the combination pushed the median relative bias to -%20, even though it reduced the spread of the distribution.
• Figure 6: ForeSWE --- Prediction intervals for daily and weekly SWE forecasting starting Feb 1 (60 days or 8 weeks from Dec 1).