Advanced Torrential Loss Function for Precipitation Forecasting.

Area of Science:

• Meteorology and Climate Science
• Artificial Intelligence and Machine Learning

Background:

• Accurate precipitation forecasting is vital for climate change adaptation.
• Machine learning (ML) offers an alternative to traditional numerical weather prediction (NWP).
• Existing ML methods often use suboptimal loss functions like the critical success index (CSI).

Purpose of the Study:

• To develop a novel loss function for precipitation forecasting that overcomes limitations of the CSI.
• To enhance the performance of ML models in precipitation prediction, particularly during dry spells.

Main Methods:

• A penalty expression was formulated and reinterpreted as a quadratic unconstrained binary optimization (QUBO) problem.
• The QUBO formulation was relaxed into a differentiable advanced torrential (AT) loss function via approximation.
• The AT loss function's efficacy was evaluated against the CSI and through rigorous testing.

Main Results:

• The proposed AT loss function demonstrated superior performance compared to existing methods.
• Evaluations included Lipschitz constant analysis, forecast performance metrics, and consistency experiments.
• Ablation studies confirmed the AT loss's effectiveness when integrated with operational models.

Conclusions:

• The novel AT loss function provides a more robust and effective criterion for optimizing precipitation forecasting models.
• This advancement is particularly significant for improving predictions during extended dry periods.
• The study highlights the potential of QUBO-relaxed differentiable loss functions in meteorological ML applications.