Improved field reconstruction with the analog method:: searching the CCA space

The analog based downscaling method is revisited in an application to precipitation data for the northern coast of the Iberian Peninsula. Analog situations of a large-scale predictor are searched in the historical record and the regional-scale predictand is reconstructed by using the analog records found. The usual approach is insensitive to the predictand variable, and we present a new approach using Canonical Correlation Analysis (CCA), which consists in projecting the predictor field onto the spatial patterns obtained in a CCA between the predictor and predictand variables and searching for analogies in this dimension-reduced predictor. This approach is tested against the usual analog search, based on the projection onto the patterns derived from Principal Component Analysis (PCA), and the more commonly used linear CCA downscaling technique. In a projection space of the same dimension, the new approach performs better in reconstructing the precipitation (based on correlation and variance skill scores) than the PCA approach. The CCA linear method yields a similar correlation skill by comparison to our new approach, but reconstructs a much lower fraction of the variance. The non-normality of the probability density function inherent to the precipitation data is partly lost by the linear method, whereas it is preserved by the analog methods. A sensitivity analysis on several parameters of the analog search was also conducted. The improvement of the CCA approach over analogs seems to be related to the identification in the predictor field of the areas most closely connected to the predictand.