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Large and non-stationary spatial fields: Quantifying uncertainty in the pattern scaling of climate models

Pattern scaling has proved to be a useful way to extend and interpret Earth system model (i.e. climate) simulations. In the simplest case the response of local temperatures is assumed to be a linear function of the global temperature. This relationship makes it possible to consider many different scenarios of warming by using simpler climate models to infer global temperatures and then translating those results locally based on the scaling pattern deduced from a more complex model. This work explores a methodology using spatial statistics to quantify how the pattern varies across an ensemble of model runs. The key is to represent the pattern uncertainty as a Gaussian process with a spatially varying covariance function. We found that when applied to the NCAR/DOE CESM1 large ensemble experiment we are able to reproduce the heterogenous variation of the pattern among ensemble members. Also these data present an opportunity to fit a large, fixed-rank Kriging model (LatticeKrig) to give a global representation of the covariance function. The climate model output at 1 degree resolution has more than 50,000 spatial locations and so requires special numerical approaches to fit the covariance function and simulate files.聽 Much of the local statistical computations are embarrassingly parallel and the analysis can be accelerated by parallel tools within the R statistical environment.