Quantifying uncertainty for climate change and long-range forecasting scenarios with model errors. Part I: Gaussian models

Information theory provides a concise systematic framework for measuring climate consistency and sensitivity for imperfect models. A suite of increasingly complex physically relevant linear Gaussian models with time periodic features mimicking the seasonal cycle is utilized to elucidate central issues that arise in contemporary climate science. These include the role of model error, the memory of initial conditions, and effects of coarse graining in producing short-, medium-, and long-range forecasts. In particular, this study demonstrates how relative entropy can be used to improve climate consistency of an overdamped imperfect model by inflating stochastic forcing. Moreover, the authors show that, in the considered models, by improving climate consistency, this simultaneously increases the predictive skill of an imperfect model in response to external perturbation, a property of crucial importance in the context of climate change. The three models range in complexity from a scalar time periodic model mimicking seasonal fluctuations in a mean jet to a spatially extended system of turbulent Rossby waves to, finally, the behavior of a turbulent tracer with a mean gradient with the background turbulent field velocity generated by the first two models. This last model mimics the global and regional behavior of turbulent passive tracers under various climate change scenarios. This detailed study provides important guidelines for extending these strategies to more complicated and non-Gaussian physical systems.