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Neural networks are increasingly used in environmental science applications.Furthermore, neural network models are trained by minimizing a loss function,and it is crucial to choose the loss function very carefully for environmentalscience applications, as it determines what exactly is being optimized.Standard loss functions do not cover all the needs of the environmentalsciences, which makes it important for scientists to be able to develop theirown custom loss functions so that they can implement many of the classicperformance measures already developed in environmental science, includingmeasures developed for spatial model verification. However, there are very fewresources available that cover the basics of custom loss function developmentcomprehensively, and to the best of our knowledge none that focus on the needsof environmental scientists. This document seeks to fill this gap by providinga guide on how to write custom loss functions targeted toward environmentalscience applications. Topics include the basics of writing custom lossfunctions, common pitfalls, functions to use in loss functions, examples suchas fractions skill score as loss function, how to incorporate physicalconstraints, discrete and soft discretization, and concepts such as focal,robust, and adaptive loss. While examples are currently provided in this guidefor Python with Keras and the TensorFlow backend, the basic concepts also applyto other environments, such as Python with PyTorch. Similarly, while the sampleloss functions provided here are from meteorology, these are just examples ofhow to create custom loss functions. Other fields in the environmental scienceshave very similar needs for custom loss functions, e.g., for evaluating spatialforecasts effectively, and the concepts discussed here can be applied there aswell. All code samples are provided in a GitHub repository.

CIRA Guide to Custom Loss Functions for Neural Networks in Environmental Sciences -- Version 1