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The immense computational cost of traditional numerical weather and climatemodels has sparked the development of machine learning (ML) based emulators.Because ML methods benefit from long records of training data, it is common touse datasets that are temporally subsampled relative to the time steps requiredfor the numerical integration of differential equations. Here, we investigatehow this often overlooked processing step affects the quality of an emulator'spredictions. We implement two ML architectures from a class of methods calledreservoir computing: (1) a form of Nonlinear Vector Autoregression (NVAR), and(2) an Echo State Network (ESN). Despite their simplicity, it is welldocumented that these architectures excel at predicting low dimensional chaoticdynamics. We are therefore motivated to test these architectures in anidealized setting of predicting high dimensional geophysical turbulence asrepresented by Surface Quasi-Geostrophic dynamics. In all cases, subsamplingthe training data consistently leads to an increased bias at small spatialscales that resembles numerical diffusion. Interestingly, the NVAR architecturebecomes unstable when the temporal resolution is increased, indicating that thepolynomial based interactions are insufficient at capturing the detailednonlinearities of the turbulent flow. The ESN architecture is found to be morerobust, suggesting a benefit to the more expensive but more general structure.Spectral errors are reduced by including a penalty on the kinetic energydensity spectrum during training, although the subsampling related errorspersist. Future work is warranted to understand how the temporal resolution oftraining data affects other ML architectures.

Temporal Subsampling Diminishes Small Spatial Scales in Recurrent Neural Network Emulators of Geophysical Turbulence