Predictability as a function of scale

Abstract

The forecast skill of the Canadian Meteorological Centre (CMC) operational global forecast/analysis system is assessed as a function of scale for the traditional forecast variable of 500‐hPa geopotential height using results from January 2002. These results are compared to an earlier analysis of forecasts from the European Centre for Medium‐range Weather Forecasts (ECMWF) which indicated unexpectedly enhanced skill at high wavenumbers (small scales) especially in the mean forecast component identified with local topographical structures. The global rms error for the CMC forecasts is dominated by the transient component compared to the mean and continues to grow with time during the six days of the forecast. Geographically the transient error grows most rapidly in middle and high latitude regions of large natural variability. The relative error behaves differently and grows most rapidly initially in tropical regions and is inferred to exhibit both climatological and flow‐dependent error growth.

In terms of spherical harmonic two‐dimensional wavenumber n, low wavenumber (large scale) 500‐hPa geopotential height structures are dominated by the mean component but beyond wavenumber 10 to 15 the transient component dominates and exhibits an approximately n–5 spectral slope consistent with a quasi‐two dimensional turbulence enstrophy cascading subrange. Error grows slowly for the large scales dominated by mean climatological structures but these are not of interest for daily weather forecasting. Transient error grows rapidly at small scales and penetrates toward larger scales with time in keeping with the expected predictability behaviour. An expression of the form f(n, τ) = 1 – e–^τ/^τp(n) is fitted to the growth of relative error as a function of wavenumber and forecast range and gives a scale dependent predictability timescale for the transient component that varies as τ_p ? n^?3/2, although the generality of the relationship is not known.

The mean component at intermediate/high wavenumbers exhibits an apparent region of enhanced skill in the CMC system apparently connected to the topography. The result supports the possibility that some small‐scale mean flow structures, although containing only a minor amount of variance, are maintained in the face of errors in other scales. The results do not support the level of enhanced skill found in an earlier analysis of ECMWF results suggesting them to be an artefact of the analysis/forecast system in use at the time.