Summary. In this chapter we present examples of hypothesis tests in the contexts of confirming, or validating, Atmospheric General Circulation Models (AGCMs) (Section 7.1, see also [1.2.7]) and the analysis of paired sensitivity experiments (Section 7.2, see also [1.2.7]). Similar applications in the literature include [105, 132, 134,135,161,393]. See also Frankignoul's review of the topic [130], and the recurrence analysis examples presented in Sections 6.9 and 6.10. An application of the Hotelling test is described in Section 7.3 and an example of the anthropogenic CO2 signal is discussed in Section 7.4.

Validating a General Circulation Model

The Problem. Climate models in general, and AGCMs specifically, are mathematical representations of the climate that are built from first principles. On short time scales they simulate the day-to-day variations in the weather, ideally in such a way that the statistics of the observed climate are reproduced when the model is run for a long period of time. A careful strategy is needed to determine, even partly, whether a model has achieved this goal. The problem is complex because, in principle, we would need to compare the statistics of a state vector that characterizes all aspects of the thermo- and hydrodynamics of the atmosphere. The statistics should include time averaged fields of various variables at various levels, and temporal and spatial cross-covariances of different variables on different scales.