Advanced Analytical Methods for Climate Research: Overview

The aim of these lectures is to illustrate how uncertainty may be dealt with using probability-based methods. The lectures are based around Generalized Linear Models, which are designed for use in situations where we wish to assess how some variable (for example temperature or rainfall) is affected by a variety of other factors (such as seasonality, sea surface temperatures and large-scale atmospheric disturbances). These models have been used by statisticians for many years, and have enormous potential for climate researchers. They are powerful and flexible enough to cope with complex relationships in the atmosphere (unlike many statistical methods currently used in climate research). Uncertainty is dealt with by regarding any observation as being drawn from a probability distribution. Typically, the probability distributions are different for each observation in a dataset, but they vary in a systematic way according to the factors which influence the observations. Objective techniques are available for determining which factors are most important in influencing climate. The models are able to detect relatively weak signals in a noisy record. They also provide confidence intervals for the magnitude of any effect, taking other factors into account in deriving these.

Although Generalized Linear Models form the core of these lectures, it is also intended to give a broad introduction to the ideas of probability modelling in a wider sense. In particular, some of the issues involved in checking probability models will be discussed (interestingly, much of the pioneering work in this area was done by meteorologists wishing to monitor weather forecasts). Finally, there will be some discussion of how these ideas of probability modelling may be related to other techniques commonly used in climate research. The techniques will be illustrated using real datasets. An overview of these datasets may found on these pages.

The contents of the lectures are as follows:

Lecture 1: Probability and statistical modelling

This lecture introduces the fundamental ideas of probability modelling, motivated by problems in climate research. The aim is to give an accessible overview of the theory upon which the other two lectures are based. In particular, the link between probability models and statistical methods will be emphasised. The lecture will cover the following topics:

• Examples of problems in climate research
• The need to confront uncertainty
• Probability, and its application to climate research
• Simple distributions, and situations in which they arise
• Probability models and statistical methods
• Estimation and likelihood theory

Lecture 2: Generalized Linear Models

Here, we introduce Generalized Linear Models (GLMs). These provide a flexible means of incorporating climate relationships into probability distributions. Again, the aim is to give an overview of the important ideas, that is accessible to non-statisticians. The lecture will cover the following topics:

• Overview of linear regression
• The extension to Generalised Linear Models
• Simple examples of GLMs, illustrated by case studies.
• Common features of climate-related problems (autocorrelation in time, 2 types of spatial dependence, and nonlinearities), and suggestions for dealing with them
• Model checking and interpretation

Lecture 3: Applications, and alternatives

In the final lecture, we consider the case studies of Lecture 2 in more detail. An introduction to each of these studies is given here. The aim is to illustrate what can be achieved using GLMs in climate research. An attempt will also be made to put GLMs in context, by considering other methods that are commonly used by climate researchers. The lecture will cover the following topics:

• Detailed case studies
• Other statistical methods
• Relationship to physical and dynamical modelling
• Thoughts on the future