Influence of similarity measures on the performance of the analog method for downscaling daily precipitation C. Matulla Æ X. Zhang Æ X. L. Wang Æ J. Wang Æ E. Zorita Æ S. Wagner Æ H. von Storch Received: 2 March 2007 / Accepted: 22 May 2007 / Published online: 7 July 2007 Ó Springer-Verlag 2007 Abstract This study examines the performance of the analog method for downscaling daily precipitation. The evaluation is performed for (1) a number of similarity measures for searching analogs, (2) various ways to include the past atmospheric evolution, and (3) different truncations in EOF space. It is carried out for two regions with complex topographic structures, and with distinct climatic charac- teristics, namely, California’s Central Valley (together with the Sierra Nevada) and the European Alps. NCEP/NCAR reanalysis data are used to represent the large scale state of the atmosphere over the regions. The assessment is based on simulating daily precipitation for 103 stations for the month of January, for the years 1950–2004 in the California re- gion, and for 70 stations in the European Alps (January 1948–2004). Generally, simulated precipitation is in better agreement with observations in the California region than in the European Alps. Similarity measures such as the Euclidean norm, the sum of absolute differences and the angle between two atmospheric states perform better than measures which introduce additional weightings to princi- pal components (e.g., the Mahalanobis distance). The best choice seems dependent upon the target variable. Lengths of wet spells, for instance, are best simulated by using the angular similarity measure. Overall, the Euclidean norm performs satisfactorily in most cases and hence is a rea- sonable first choice, whereas the use of Mahalanobis dis- tance is less advisable. The performance of the analog method improves by including large-scale information for bygone days, particularly, for the simulation of wet and dry spells. Optimal performance is obtained when about 85– 90% of the total predictor variability is retained. 1 Introduction The analog method (AM) has been commonly used in weather prediction (Elliot 1951; Baur 1951; Lorenz 1969) and in seasonal forecasting (Livezey and Barnston 1988). Lorenz (1969) studied atmospheric predictability by the use of analogs but achieved poor results as the analogs were drawn from sparse weather archives (van den Dool 1994). Livezey et al. (1994) compared analog prediction systems, developed in the US (Livezey and Barnston 1988) and the former Soviet Union (Gruza and Ran’kova 1986) for the purpose of enhancing US seasonal temperature predictions. Even though seasonal forecasts are presently processed by ensemble forecasts of a number of general circulation models (GCMs), an analog prediction scheme still can act as a benchmark. Recently, Hamill and Whi- taker (2006) explored a set of analog techniques for the statistical correction of weather forecasts. A successful application of AM requires an extensive archive of obser- vations, and depends on the size and complexity of the considered region. In general it is more difficult to find a close match for an atmospheric state over a large region of complex structure than over a small, simply structured region. Zorita et al. (1995) and Zorita and von Storch (1999) introduced AM into the field of downscaling. One objective C. Matulla (&)  X. Zhang  X. L. Wang  J. Wang Climate Research Division, Environment Canada, 4905 Dufferin Street, Toronto, ON, Canada e-mail: Christoph.Matulla@ec.gc.ca E. Zorita  S. Wagner  H. von Storch Institute for Coastal Research, GKSS, Geesthacht, Germany 123 Clim Dyn (2008) 30:133–144 DOI 10.1007/s00382-007-0277-2