This work is a substantive application of data science to the analysis of climate model experiments. 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 a simpler, global climate model and combining them with the scaling pattern from a more complex model. This work explores methodologies 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. When applied to the NCAR/DOE CESM1 large ensemble experiment this approach can reproduce the heterogenous variation of the pattern among ensemble members . The climate model output at one degree resolution has more than 50,000 spatial locations. The size of these “big data” break conventional spatial methods and so motivates the development of approximate methods that are computationally feasible. A fixed-rank Kriging model (LatticeKrig) exploiting Markov random fields is presented that gives a global representation of the covariance function on the sphere and provides a route to quantifying the uncertainty in the pattern. Much of the local statistical computations are embarrassingly parallel and the analysis can be accelerated by parallel tools within the R statistical environment.
References for background reading:
Nychka, Douglas, Soutir Bandyopadhyay, Dorit Hammerling, Finn Lindgren, and Stephan Sain. “A multiresolution Gaussian process model for the analysis of large spatial datasets.” Journal of Computational and Graphical Statistics 24, no. 2 (2015): 579-599.
Alexeeff, Stacey E., Doug Nychka, Stephan R. Sain, and Claudia Tebaldi. “Emulating mean patterns and variability of temperature across and within scenarios in anthropogenic climate change experiments.” Climatic Change (2016): 1-15.