A variational approach at uncertainty estimation in data-driven rainfall-runoff modeling

Abstract

Reliable uncertainty estimation is essential for decision making, evaluating model performance, and defining the limits of what can be inferred from data. While uncertainty estimation typically requires specifying prior assumptions about distributional form, we introduce an approach to learn the structure of uncertainty directly from data. Specifically, we introduce a variational long short-term

Summary

This paper introduces a novel variational Long Short-Term Memory network (vLSTM) for estimating uncertainty in rainfall-runoff modeling. Unlike traditional methods, the vLSTM learns the structure of uncertainty directly from data using variational inference and two distinct uncertainty propagation decoders, offering a more flexible and data-driven approach.

Key Insights

• •The vLSTM uses a variational layer to transform LSTM point predictions into probability distributions, enabling the model to learn uncertainty from data without pre-defined assumptions.
• •The authors propose two uncertainty propagation decoders: a Gaussian decoder, which produces Gaussian predictive distributions, and a dense decoder, which learns a complex, non-parametric relationship between noise and predicted streamflow using a dense layer.
• •The vLSTM, especially with the dense decoder, achieves state-of-the-art performance in log-likelihood on the CAMELS-US dataset, demonstrating its ability to learn uncertainty structures comparable to existing methods like Mixture Density Networks.

Practical Implications

• •The vLSTM provides a valuable tool for exploring uncertainty structures in hydrological modeling, particularly in situations where prior assumptions are difficult to justify, allowing for data-driven discovery of uncertainty patterns.
• •The authors suggest using the vLSTM to explore uncertainty structures before transitioning to more computationally efficient models, potentially informing the choice of appropriate distributional assumptions for simpler models.
• •Future research could focus on improving the computational efficiency of the vLSTM, particularly the dense decoder, and exploring alternative uncertainty propagation formulations to enhance its applicability in real-world scenarios.

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