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Attention-based Models for Snow-Water Equivalent Prediction

Krishu K. Thapa, Bhupinderjeet Singh, Supriya Savalkar, Alan Fern, Kirti Rajagopalan, Ananth Kalyanaraman

TL;DR

This study tackles the problem of predicting daily Snow Water-Equivalent (SWE) across locations and time in the Western U.S. by introducing attention-based models that separately capture spatial and temporal correlations, as well as an ensemble that combines both. Using a transformer-based framework, the authors demonstrate that spatial, temporal, and ensemble attention outperform traditional baselines (e.g., LSTM, linear regression) on 323 SNOTEL stations, with the ensemble approach delivering the strongest results. The work not only provides improved predictive performance but also offers insights into how spatial vs. temporal attention behave in SWE contexts and outlines a practical roadmap for deploying spatially complete SWE maps to support water management decisions. The proposed framework has implications for hydrological forecasting, enabling higher-resolution snowpack products and potentially reducing uncertainties in reservoir operations, drought planning, and irrigation scheduling. The study also highlights future directions, including spatiotemporal graph representations and process-based model coupling for interpretability and reliability.

Abstract

Snow Water-Equivalent (SWE) -- the amount of water available if snowpack is melted -- is a key decision variable used by water management agencies to make irrigation, flood control, power generation and drought management decisions. SWE values vary spatiotemporally -- affected by weather, topography and other environmental factors. While daily SWE can be measured by Snow Telemetry (SNOTEL) stations with requisite instrumentation, such stations are spatially sparse requiring interpolation techniques to create spatiotemporally complete data. While recent efforts have explored machine learning (ML) for SWE prediction, a number of recent ML advances have yet to be considered. The main contribution of this paper is to explore one such ML advance, attention mechanisms, for SWE prediction. Our hypothesis is that attention has a unique ability to capture and exploit correlations that may exist across locations or the temporal spectrum (or both). We present a generic attention-based modeling framework for SWE prediction and adapt it to capture spatial attention and temporal attention. Our experimental results on 323 SNOTEL stations in the Western U.S. demonstrate that our attention-based models outperform other machine learning approaches. We also provide key results highlighting the differences between spatial and temporal attention in this context and a roadmap toward deployment for generating spatially-complete SWE maps.

Attention-based Models for Snow-Water Equivalent Prediction

TL;DR

This study tackles the problem of predicting daily Snow Water-Equivalent (SWE) across locations and time in the Western U.S. by introducing attention-based models that separately capture spatial and temporal correlations, as well as an ensemble that combines both. Using a transformer-based framework, the authors demonstrate that spatial, temporal, and ensemble attention outperform traditional baselines (e.g., LSTM, linear regression) on 323 SNOTEL stations, with the ensemble approach delivering the strongest results. The work not only provides improved predictive performance but also offers insights into how spatial vs. temporal attention behave in SWE contexts and outlines a practical roadmap for deploying spatially complete SWE maps to support water management decisions. The proposed framework has implications for hydrological forecasting, enabling higher-resolution snowpack products and potentially reducing uncertainties in reservoir operations, drought planning, and irrigation scheduling. The study also highlights future directions, including spatiotemporal graph representations and process-based model coupling for interpretability and reliability.

Abstract

Snow Water-Equivalent (SWE) -- the amount of water available if snowpack is melted -- is a key decision variable used by water management agencies to make irrigation, flood control, power generation and drought management decisions. SWE values vary spatiotemporally -- affected by weather, topography and other environmental factors. While daily SWE can be measured by Snow Telemetry (SNOTEL) stations with requisite instrumentation, such stations are spatially sparse requiring interpolation techniques to create spatiotemporally complete data. While recent efforts have explored machine learning (ML) for SWE prediction, a number of recent ML advances have yet to be considered. The main contribution of this paper is to explore one such ML advance, attention mechanisms, for SWE prediction. Our hypothesis is that attention has a unique ability to capture and exploit correlations that may exist across locations or the temporal spectrum (or both). We present a generic attention-based modeling framework for SWE prediction and adapt it to capture spatial attention and temporal attention. Our experimental results on 323 SNOTEL stations in the Western U.S. demonstrate that our attention-based models outperform other machine learning approaches. We also provide key results highlighting the differences between spatial and temporal attention in this context and a roadmap toward deployment for generating spatially-complete SWE maps.
Paper Structure (18 sections, 4 equations, 6 figures, 1 table)

This paper contains 18 sections, 4 equations, 6 figures, 1 table.

Table of Contents

  1. Introduction
  2. Challenges:
  3. Contributions:
  4. Approach
  5. Spatial attention:
  6. Temporal attention:
  7. Ensemble attention:
  8. Model architecture
  9. Input:
  10. Output:
  11. Implementation and availability:
  12. Experimental setup
  13. Data description:
  14. Evaluation methodology:
  15. Experimental results
  16. ...and 3 more sections

Figures (6)

  • Figure 1: Spatial map showing the sparse spread of 822 SNOTEL locations across Western U.S., of which we used a subset of 323 stations based on data availability. The inset shows two SWE curves for a station (Albro Lake) for the 2007 SWE season. The blue curve is ground-truth (SNOTEL) and the red curve is the predicted curve obtained by our ensemble attention model.
  • Figure 2: SWE correlation between all location pairs as a function of their spatial distance and elevation difference product.
  • Figure 3: Spatial attention model architecture. This is easily adapted to also implement our temporal attention model.
  • Figure 4: The distribution of locations across five NSE groups for all models. The NSE metric is calculated for each location, with higher values (blue bars) indicating a better prediction. The left of the red dotted line corresponds to NSE $>$ 0.5.
  • Figure 5: Mean error (predicted - observed) in SWE (mm) for each location. Part (a) shows the errors in daily SWE across the 270 days of a SWE season. The range in each box plot corresponds to errors from 270 days $\times$ 323 locations. Part (b) shows a similar plot but for the annual maximum SWE predictions.
  • ...and 1 more figures