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

The immense computational cost of traditional numerical weather and climate models has sparked the development of machine learning (ML) based emulators. Because ML methods benefit from long records of training data, it is common to use data sets that are temporally subsampled relative to the time steps required for the numerical integration of differential equations. Here, we investigate how this often overlooked processing step affects the quality of an emulator's predictions. We implement two ML architectures from a class of methods called reservoir computing: (a) a form of Nonlinear Vector Autoregression (NVAR), and (b) an Echo State Network (ESN). Despite their simplicity, it is well documented that these architectures excel at predicting low dimensional chaotic dynamics. We are therefore motivated to test these architectures in an idealized setting of predicting high dimensional geophysical turbulence as represented by Surface Quasi‐Geostrophic dynamics. In all cases, subsampling the training data consistently leads to an increased bias at small spatial scales that resembles numerical diffusion. Interestingly, the NVAR architecture becomes unstable when the temporal resolution is increased, indicating that the polynomial based interactions are insufficient at capturing the detailed nonlinearities of the turbulent flow. The ESN architecture is found to be more robust, suggesting a benefit to the more expensive but more general structure. Spectral errors are reduced by including a penalty on the kinetic energy density spectrum during training, although the subsampling related errors persist. Future work is warranted to understand how the temporal resolution of training data affects other ML architectures. Plain Language Summary: The computer models that govern weather prediction and climate projections are extremely costly to run, causing practitioners to make unfortunate tradeoffs between accuracy of the physics and credibility of their statistics. Recent advances in machine learning have sparked the development of neural network‐based emulators, that is, low‐cost models that can be used as drop‐in replacements for the traditional expensive models. Due to the cost of storing large weather and climate data sets, it is common to subsample these fields in time to save disk space. This subsampling also reduces the computational expense of training emulators. Here, we show that this pre‐processing step hinders the fidelity of the emulator. We offer one method to mitigate the resulting errors, but more research is needed to understand and eventually overcome them. Key Points: Reducing training data temporal resolution by subsampling leads to overly dissipative small spatial scales in neural network emulatorsA quadratic autoregressive architecture is shown to be inadequate at capturing small scale turbulence, even when data are not subsampledSubsampling bias in Echo State Networks is mitigated but not eliminated by prioritizing kinetic energy spectrum during training [ABSTRACT FROM AUTHOR]