Statistical downscaling of an air quality model using Fitted Empirical Orthogonal Functions

Downscaling is a technique that is used to extract high-resolution information from regional scale variables produced by coarse resolution models such as Chemical Transport Models (CTMs). Statistical downscaling methods in geophysics often rely on Empirical Orthogonal Functions (EOFs). EOFs are spatial Principal Components (PCs) that display space-time modes of variability of a quantity over a region. Here we present a novel statistical downscaling method that employs Fitted Empirical Orthogonal Functions (F-EOFs) to provide local forecasts. F-EOFs differ from EOFs in that they represent space-time variations associated with a particular location through the use of inverse regression. We illustrate our downscaling method, for ozone levels over the US, with the Regional chEmical trAnsport Model (REAM) whose outputs are over 70 by 70 km grid cells. We use ground level ozone observations from monitoring stations within the south-eastern US region to downscale REAM. We select the first leading F-EOFs and regress our observations on the corresponding F-EOF loadings. We also compare our results to linear regression and PC regression. The regression on F-EOFs shows the best predictive ability. To examine the consistency of our results we repeat the analysis for different fitting and validation periods. Furthermore, in our application, PFC regression also outperforms PC regression as a dimension reduction technique.