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Advanced Analytical Methods for Climate Research
Case study 3: Monthly temperatures in the United States

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This case study is an example of the use of GLMs with very large datasets. It also illustrates how two GLMs can be joined together to model the mean and variance of a probability distribution separately. Technically, this is the most sophisticated of the four case studies.


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    Background to the study

    This case study was originally motivated by a request from a reinsurance company. Their business is such that they will suffer financially as a result either of unusally hot summers or of unusually cold winters, anywhere in the United States. In the context of this lecture series, the case study serves as a good example of how the GLM approach can be applied to the modelling of climate at a continental scale. The problem considered here is to model monthly mean temperatures at any location in the USA. The data available are monthly mean temperatures from 2600 weather stations, for a 50-year period - the dataset has a total of one and a half million observations.

    An interesting feature of monthly temperature data is that its variance changes systematically with factors such as latitude and season. This needs to be modelled explicitly. This can be achieved using a combination of two GLMs. The approach, which is quite a sophisticated application of the theory, will be described in the lectures.

    The figure above gives an example of information that can be extracted from a GLM. It shows the systematic regional variations in temperature in the United States, at different times of year. Such maps can be produced straightforwardly once models have been fitted. In this case, the result is not particularly interesting from a scientific point of view. However, it does show how the structure of a GLM may subsequently be interpreted. The ability to produce maps such as this is particularly useful for many climatological applications. For example, it is possible to produce maps showing the effect of phenomena such as ENSO, over a large area, at different times of year. Of course, these maps just show average effects. Differences in extremal behaviour may be much larger than this, but can be quantified by simulation if necessary.

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    Questions of interest

    This case study is primarily included as an example of a large dataset, and to illustrate how the GLM approach may be used to study monthly temperature data. The key questions that are of interest here are:
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    Page last updated: 26th April 2001.