# e-book Computational Statistics in Climatology

This lecture contains basic information about atmospheric circulation, climate, and climate change. The role of greenhouse gases and other forcings is emphasized. Climate movie. L96Sens The basic equations of fluid dynamics are described, and their application to climate systems. The implementation of computer models to solve the equations is described with a view to helping a statistical audience understand the strengths and weaknesses of such physically based models. Scenarios i. Global climate models are relatively coarse, and in order to make regional projections it is necessary to develop regional models, or use other forms of downscaling global models to a finer resolution.

Smoothers File. Spatial processes and geophysical data Geophysical data typically come as spatio-temporal fields living on at least approximately a rotating sphere. Among the tasks for the statistician is estimation e. The processes involved are nonstationary in space and time, and usually space and time are not separable, and our statistical models need to take this into account. File updated. R code 1. R code 2. North American data. What is a spline? Common tasks in statistical climatology are estimation of trends in space and time.

Linear models are common in climate science, but nonparametric nonlinear smoothers are better descriptions of the complicated functional forms of these trends. There are many classes of splines, many defined as solutions to constrained optimization problems. Some large sample theory for Kriging and splines The large sample theory for Kriging and splines were developed by Stein and Wahba, respectively. The theory makes clear what assumptions are most important in spatial analysis and unifies the methods of kernel smoothing, variational methods and Kriging.

Mesquita slides. Spatial models for large data sets For large data sets the statistical computations to estimate parameters, form spatial predictions and to quantify the uncertainty may not be feasible given current computational resources. There are different approaches to deal with this problem, such as developing sparse matrix approximations to the covariances, or using Markov random field approaches. In either case these practical solutions modify the spatial model and it is important to understand how they change the statistical assumptions. Introduction to Linear Regression Analysis.

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## Computational statistics in climatology

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