# 11.10.1.3 Empirical and Statistical Downscaling Methods

A complementary technique to RCMs is to use derived relationships linking large-scale atmospheric variables (predictors) and local/regional climate variables (predictands). The local/regional-scale climate change information is then obtained by applying the relationships to equivalent predictors from AOGCM simulations. The guidance document (Wilby et al., 2004) from the IPCC Task Group on Data and Scenario Support for Impact and Climate Analysis (TGICA) provides a comprehensive background on this approach and covers important issues in using SD applications. Statistical downscaling methods cover regression-type models including both linear and nonlinear relationships, unconditional or conditional weather generators for generating synthetic sequences of local variables, techniques based on weather classification that draw on the more skilful attributes of models to simulate circulation patterns, and analogue methods that seek equivalent weather states from the historical record; a combination of these techniques possibly being most appropriate. An extension to SD is the statistical-dynamical downscaling technique (e.g., Fuentes and Heimann, 2000), which combines weather classification with RCM simulations. A further development is the application of SD to high-resolution climate model output (Lionello et al., 2003; Imbert and Benestad, 2005).

Research on SD has shown an extensive growth in application, and includes an increased availability of generic tools for the impact community (e.g., SDSM, Wilby et al., 2002; the clim.pact package, Benestad, 2004b; the pyclimate package, Fernández and Sáenz, 2003); applications in new regions (e.g., Asia, Chen and Chen, 2003); the use of techniques to address exotic variables such as phenological series (Matulla et al., 2003), extreme heat-related mortality (Hayhoe et al., 2004), ski season (Scott et al., 2003), land use (Solecki and Oliveri, 2004), streamflow or aquatic ecosystems (Cannon and Whitfield, 2002; Blenckner and Chen, 2003); the treatment of climate extremes (e.g., Katz et al., 2002; Seem, 2004; X.L. Wang et al., 2004; Caires et al., 2006); intercomparison studies evaluating methods (e.g., STAtistical and Regional dynamical Downscaling of EXtremes for European regions (STARDEX), Haylock et al., 2006; Schmidli et al., 2006); application to multi-model and multi-ensemble simulations in order to express model uncertainty alongside other key uncertainties (e.g., Benestad, 2002a,b; Hewitson and Crane, 2006; Wang and Swail, 2006b); assessing non-stationarity in climate relationships (Hewitson and Crane, 2006); and spatial interpolation using geographical dependencies (Benestad, 2005). In some cases SD methods have been used to project statistical attributes instead of raw values of the predictand, for example, the probability of rainfall occurrence, precipitation, wind or wave height distribution parameters and extreme event frequency (e.g., Beckmann and Buishand, 2002; Buishand et al., 2004; Busuioc and von Storch, 2003; Abaurrea and Asin, 2005; Diaz-Nieto and Wilby, 2005; Pryor et al., 2005a,b; Wang and Swail, 2006a,b).

Evaluation of SD is done most commonly through cross-validation with observational data for a period that represents an independent or different ‘climate regime’ (e.g., Busuioc et al. 2001; Trigo and Palutikof, 2001; Bartman et al., 2003; Hanssen-Bauer et al., 2003). Stationarity, that is, whether the statistical relationships are valid under future climate regimes, remains a concern with SD methods. This is only weakly assessed through cross-validation tests because future changes in climate are likely to be substantially larger than observed historical changes. This issue was assessed in Hewitson and Crane (2006) where, within the SD method used, the non-stationarity was shown to result in an underestimation of the magnitude of the change. In general, the most effective SD methods are those that combine elements of deterministic transfer functions and stochastic components (e.g., Hansen and Mavromatis, 2001; Palutikof et al., 2002; Beersma and Buishand, 2003; Busuioc and von Storch, 2003; Katz et al., 2003; Lionello et al., 2003; Wilby et al., 2003; X.L. Wang et al., 2004; Hewitson and Crane, 2006). Regarding the predictors, the best choice appears to combine dynamical and moisture variables, especially in cases where precipitation is the predictand (e.g., Wilby et al., 2003).

Pattern scaling is a simple statistical method for projecting regional climate change, which involves normalising AOGCM response patterns according to the global mean temperature. These normalised patterns are then rescaled using global mean temperature responses estimated for different emissions scenarios from a simple climate model (see Chapter 10). Some developments were made using various versions of scaling techniques (e.g., Christensen et al., 2001; Mitchell, 2003; Salathé, 2005; Ruosteenoja et al., 2007). For example, Ruosteenoja et al. (2007) developed a pattern-scaling method using linear regression to represent the relationship between the local AOGCM-simulated temperature and precipitation response and the global mean temperature change. Another simple statistical technique is to use the GCM output for the variable of interest (i.e., the predictand) as the predictor and then apply a simple local change factor/scaling procedure (e.g., Chapter 13 of IPCC, 2001; Hanssen-Bauer et al., 2003; Widmann et al., 2003; Diaz-Nieto and Wilby, 2005).

Many studies have been performed since the TAR comparing various SD methods. In general, conclusions about one method compared to another are dependent on region and the criteria used for comparison, and on the inherent attributes of each method. For example, Diaz-Nieto and Wilby (2005) downscale river flow and find that while two methods give comparable results, they differ in responses as a function of how the methods treat multi-decadal variability.

When comparing the merits of SD methods based on daily and monthly downscaling models, in terms of their ability to predict monthly means, daily models are better (e.g., Buishand et al., 2004). In terms of nonlinearity in downscaling relationships, Trigo and Palutikof (2001) note that complex nonlinear models may not be better than simpler linear/slightly nonlinear approaches for some applications. However, Haylock et al. (2006) find that SD methods based on nonlinear artificial neural networks are best at modelling the interannual variability of heavy precipitation but they underestimate extremes. Much downscaling work remains unreported, as SD activities are often implemented pragmatically for serving specific project needs, rather than for use by a broader scientific community; this is especially the case in developing nations. In some cases, this work is only found within the “grey” literature, for example, the AIACC project (http://www.aiaccproject.org/), which supports impact studies in developing nations.