A New Generic Method for Quantifying the Scale Predictability of Fractal Atmosphere Xingqin Fang and Ying-Hwa Kuo University Corporation for Atmospheric Research and National Center for Atmospheric Research, Boulder, CO 80307 Abstract We revisit the issue the predictability of a flow which possesses many scales of motion raised by Lorenz (1969), and apply the general systems theory of Selvam (1990) to error diagnostics and predictability in the fractal atmosphere. We then introduce a new generic method to quantify the scale predictability of the fractal atmosphere following the assumptions of the intrinsic inverse power law and the upscale cascade of error. In this method, the whole-scale eddies are extracted against the instant zonal mean without the need of auxiliary information, and the ratio of noise (domain-average square of error amplitudes) to signal (domain-average square of total eddy amplitudes), referred to as noise-to-signal ratio (NSR), is used as a measure of forecast skill. The time limit of useful predictability for any wavenumber of the fractal atmosphere can be determined by the criterion , where is the Golden Ratio. By definition, the NSR is flow-dependent. In addition, the time series of the logarithm with base of NSR, , have consistent stable variations in different ranges of forecasts, thus have strong stationarity, which is advantageous for model verification. An important advantage of this new NSR method over the widely used anomaly correlation coefficient (ACC) method is that it can detect the successive scale predictability of different wavenumbers without the need to perform scaledecomposition explicitly. As a demonstration, the NSR method is used to examine the scale predictability of the National Center for Environmental Prediction (NCEP) Global Forecast System (GFS) 500 hPa geopotential height. With the ability to reveal the predictive skills on different scales as well as the model error growth between scales, the NSR method can be used for model inter-comparison to provide useful insights on the relative performance of different global models (e.g., NCEP GFS vs. ECMWF) on different scales. Key words: noise-to-signal ratio; scale predictability; fractal atmosphere; general systems theory; model inter-comparison.