Expanded downscaling for generating local weather scenarios

In an attempt to reconcile the capabilities of statistical downscaling and the demands of ecosystem modeling, the technique of expanded downscaling is introduced. Aimed at use in ecosystem models, emphasis is placed on the preservation of daily variability to the extent that possible climate change permits. Generally, the expansion is possible for any statistical model which is formulated by utilizing some form of regression, but I will concentrate on linear models as they are easier to handle. Linear statistical downscaling assumes that the local climate anomalies are linearly linked to the global circulation anomalies. In expanded downscaling, in contrast, I propose that the local climate covariance is linked bilinearly to the global circulation covariance. This is done by transforming the technique of unconstrained minimization of the error cost function into a constrained minimization problem, with the preservation of local covariance forming the side condition. A general normalization routine is included on the local side in order to perform the downscaling exclusively with normally distributed variables. Application of the expanded operator to the daily, global circulation works essentially like a weather generator. Using observed geopotential height fields over the North Atlantic and Europe gave consistent results for the weather station at Potsdam with 14 measured quantities, even for moisture-related variables. For GCM (general circulation model) scenarios, satisfactory results are obtained when the original variables are normally distributed. If they are not, strong sensitivity even to small input changes cause the normalization to produce large errors. Non-normally distributed variables such as most moisture variables are therefore strongly affected by even slight deficiencies of current GCMs with respect to daily variability and climatology. This marks the limit of applicability of expanded downscaling.