Tree approximation of the long wave radiation parameterization in the NCAR CAM global climate model

The computation of Global Climate Models (GCMs) presents significant numerical challenges. This paper presents new algorithms based on sparse occupancy trees for learning and emulating the long wave radiation parameterization in the NCAR CAM climate model. This emulation occupies by far the most significant portion of the computational time in the implementation of the model. From the mathematical point of view this parameterization can be considered as a mapping R220→R33R220→R33 which is to be learned from scattered data samples (xi,yi)(xi,yi), i=1,…,Ni=1,…,N. Hence, the problem represents a typical application of high-dimensional statistical learning. The goal is to develop learning schemes that are not only accurate and reliable but also computationally efficient and capable of adapting to time-varying environmental states. The algorithms developed in this paper are compared with other approaches such as neural networks, nearest neighbor methods, and regression trees as to how these various goals are met.