A novel heuristic method for detecting overfit in unsupervised classification of climate model data

Unsupervised classification is becoming an increasingly common method to objectively identify coherent structures within both observed and modelled climate data. However, in most applications using this method, the user must choose the number of classes into which the data are to be sorted in advance. Typically, a combination of statistical methods and expertise is used to choose the appropriate number of classes for a given study; however, it may not be possible to identify a single “optimal” number of classes. In this work, we present a heuristic method, the ensemble difference criterion, for unambiguously determining the maximum number of classes supported by model data ensembles. This method requires robustness in the class definition between simulated ensembles of the system of interest. For demonstration, we apply this to the clustering of Southern Ocean potential temperatures in a CMIP6 climate model, and show that the data supports between four and seven classes of a Gaussian mixture model.