DISTORTION REPRESENTATION OF FORECAST ERRORS

Forecast error is decomposed into three components, termed displacemen t error, amplitude error, and residual error, respectively. Displaceme nt error measures how much of the forecast error can be accounted for by moving the forecast to best fit the analysis. Amplitude error measu res how much of the forecast error can be accounted for by changing th e amplitude of the displaced forecast to best fit the analysis. The co mbination of a displacement and an amplification is called a distortio n. The part of the forecast error unaccounted for by the distortion is called the residual error. The distortion must be large scale, in lin e with the basic premise that forecast errors are best described by re ference to large-scale meteorological features. A general mathematical formalism for defining distortions and decomposing forecast errors in to distortion and residual errors is formulated. The distortion repres entation of forecast errors should prove useful for describing forecas t skill and for representing the statistics of the background errors i n objective data analysis. Examples using nonstandard satellite data-S SM/I precipitable water and ERS-1 backscatter-demonstrate the detectio n and characterization of analysis errors in terms of position and amp litude errors. In addition, a 48-h forecast of Northern Hemisphere 500 -hPa geopotential height is decomposed. For this case a large-scale di stortion is capable of representing the larger part of the forecast er ror field and the displacement error is predominant over the amplifica tion error. These examples indicate the feasibility of implementing th e proposed method in an operational setting.