  Robust quantification of predictive uncertainty is critical for understanding
factors that drive weather and climate outcomes. Ensembles provide predictive
uncertainty estimates and can be decomposed physically, but both physics and
machine learning ensembles are computationally expensive. Parametric deep
learning can estimate uncertainty with one model by predicting the parameters
of a probability distribution but do not account for epistemic uncertainty..
Evidential deep learning, a technique that extends parametric deep learning to
higher-order distributions, can account for both aleatoric and epistemic
uncertainty with one model. This study compares the uncertainty derived from
evidential neural networks to those obtained from ensembles. Through
applications of classification of winter precipitation type and regression of
surface layer fluxes, we show evidential deep learning models attaining
predictive accuracy rivaling standard methods, while robustly quantifying both
sources of uncertainty. We evaluate the uncertainty in terms of how well the
predictions are calibrated and how well the uncertainty correlates with
prediction error. Analyses of uncertainty in the context of the inputs reveal
sensitivities to underlying meteorological processes, facilitating
interpretation of the models. The conceptual simplicity, interpretability, and
computational efficiency of evidential neural networks make them highly
extensible, offering a promising approach for reliable and practical
uncertainty quantification in Earth system science modeling. In order to
encourage broader adoption of evidential deep learning in Earth System Science,
we have developed a new Python package, MILES-GUESS
(https://github.com/ai2es/miles-guess), that enables users to train and
evaluate both evidential and ensemble deep learning.
