Distortion Representation of Forecast Errors

Forecast error is decomposed into three components, termed displacement error, amplitude error, mid residual error, respectively. Displacement error measures how much of the forecast error can be accounted for by moving the forecast to best fit the analysis. Amplitude error measures how much of the forecast error can be accounted for by changing the amplitude of the displaced forecast to best fit the analysis. The combination of a displacement and an amplification is called a distortion. The part of the forecast error unaccounted for by the distortion is called the residual error. The distortion must be large scale, in line with the basic premise that forecast errors are best described by reference to large-scale meteorological features. A general mathematical formalism for defining distortions and decomposing forecast errors into distortion and residual errors is formulated. The distortion representation of forecast errors should prove useful for describing forecast skill and for representing the statistics of the background errors in objective data analysis. Examples using nonstandard satellite data–SSM/I precipitable water and ERS-1 backscatter—demonstrate the detection and characterization of analysis errors in terms of position mid amplitude errors. In addition, a 48-h forecast of Northern Hemisphere 500-hPa geopotential height is decomposed. For this case a large-scale distortion is capable of representing the larger part of the forecast error field and the displacement error is predominant over the amplification error. These examples indicate the feasibility of implementing the proposed method in an operational setting.