  Advanced machine learning models have recently achieved high predictive
accuracy for weather and climate prediction. However, these complex models
often lack inherent transparency and interpretability, acting as "black boxes"
that impede user trust and hinder further model improvements. As such,
interpretable machine learning techniques have become crucial in enhancing the
credibility and utility of weather and climate modeling. In this survey, we
review current interpretable machine learning approaches applied to
meteorological predictions. We categorize methods into two major paradigms: 1)
Post-hoc interpretability techniques that explain pre-trained models, such as
perturbation-based, game theory based, and gradient-based attribution methods.
2) Designing inherently interpretable models from scratch using architectures
like tree ensembles and explainable neural networks. We summarize how each
technique provides insights into the predictions, uncovering novel
meteorological relationships captured by machine learning. Lastly, we discuss
research challenges around achieving deeper mechanistic interpretations aligned
with physical principles, developing standardized evaluation benchmarks,
integrating interpretability into iterative model development workflows, and
providing explainability for large foundation models.
