Model Selection: Using Information Measures from Ordinal Symbolic Analysis to Select Model Subgrid-Scale Parameterizations

Abstract

Abstract The use of information measures for model selection in geophysical models with subgrid parameterizations is examined. Although the resolved dynamical equations of atmospheric or oceanic global numerical models are well established, the development and evaluation of parameterizations that represent subgrid-scale effects pose a big challenge. For climate studies, the parameters or parameterizations are usually selected according to a root-mean-square error criterion that measures the differences between the model-state evolution and observations along the trajectory. However, inaccurate initial conditions and systematic model errors contaminate root-mean-square error measures. In this work, information theory quantifiers, in particular Shannon entropy, statistical complexity, and Jensen–Shannon divergence, are evaluated as measures of the model dynamics. An ordinal analysis is conducted using the Bandt–Pompe symbolic data reduction in the signals. The proposed ordinal information measures are examined in the two-scale Lorenz-96 system. By comparing the two-scale Lorenz-96 system signals with a one-scale Lorenz-96 system with deterministic and stochastic parameterizations, the study shows that information measures are able to select the correct model and to distinguish the parameterizations, including the degree of stochasticity that results in the closest model dynamics to the two-scale Lorenz-96 system.