As with the dynamical downscaling of RCMs, the methods described in this section rely on the concept that regional climates are largely a function of the large-scale atmospheric state. In empirical downscaling the cross-scale relationship is expressed as a stochastic and/or deterministic function between a set of large-scale atmospheric variables (predictors) and local/regional climate variables (predictands). Predictor and predictand can be the same variables on different spatial scales (e.g., Bürger, 1997; Wilks, 1999b; Widmann and Bretherton, 2000), but more commonly are different.

When using downscaling for assessing regional climate change, three implicit assumptions are made:

• The predictors are variables of relevance to the local climate variable being derived, and are realistically modelled by the GCM. Tropospheric quantities such as temperature or geopotential height are more skilfully represented than derived variables such as precipitation at the regional or grid scale (e.g., Osborn and Hulme, 1997; Trigo and Palutikof, 1999). Furthermore, there is no theoretical level of spatial aggregation at which GCMs can be considered skilful, though there is evidence that this is several grid lengths (Widmann and Bretherton, 2000).
• The transfer function is valid under altered climatic conditions (see Section 10.6.2.2). This cannot be proven in advance, as it would require the observational record to span all possible future realisations of the predictors. However, it could be evaluated with nested AOGCM/RCM simulations of present and future climate, using the simulation of present climate to determine the downscaling function and testing the function against the future time slice.
• The predictors fully represent the climate change signal. Most downscaling approaches to date have relied entirely on circulation-based predictors and, therefore, can only capture this component of the climate change. More recently other important predictors, e.g., atmospheric humidity, have been considered (e.g., Charles et al., 1999b; Hewitson, 1999).

A diverse range of downscaling methods has been developed, but, in principle, these models are based on three techniques:

• Weather generators, which are random number generators of realistic looking sequences of local climate variables, and may be conditioned upon the large-scale atmospheric state (Section 10.6.2.1);
• Transfer functions, where a direct quantitative relationship is derived through, for example, regression (Section 10.6.2.2);
• Weather typing schemes based on the more traditional synoptic climatology concept (including analogues and phase space partitioning) and which relate a particular atmospheric state to a set of local climate variables (Section 10.6.2.3).

Each of these approaches has relative strengths and weaknesses in representing the range of temporal variance of the local climate predictand. Consequently, the above approaches are often used in conjunction with one another in order to compensate for the relative deficiencies in one method.

Most downscaling applications have dealt with temperature and precipitation. However, a diverse array of studies exists in which other variables have been investigated. Appendix 10.4 provides a non-exhaustive list of past studies indicating predictands, geographical domain, and technique category. In light of the diversity in the literature, we concentrate on references to applications since 1995 and based on recent global climate change projections.

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