Error growth and estimates of predictability from the ECMWF forecasting system

Abstract

Examination has been made of the skill of ECMWF forecasts of the 500 hPa height field produced daily out to ten days ahead, verifying in the period from 1 December 1980 to 31 May 1994. Over this time accuracy has been improved substantially over the first half of the forecast range. The systematic (seasonal-mean) component of the error has been greatly reduced at all forecast times, but there has been little reduction in the non-systematic (transient) component later in the range.The simple model proposed by Lorenz for the intrinsic growth of forecast error has been applied to the evolution of differences between consecutive forecasts. The implied growth-rates of small forecast errors have increased significantly since 1981. They do not show much variation with season, and are a little lower in the southern than in the northern hemisphere. The most recent error-doubling times are around 1.5 days for the northern hemisphere and 1.7 days for the southern hemisphere. Error saturation levels are at present similar to or greater than those of the 1981 version of the model, having been significantly lower in intermediate years. The accuracy of recent short-and early medium-range forecasts and realism of the climatology of the forecast model support the view that estimates of intrinsic error-growth parameters from the current forecasting system are more reliable than those obtained earlier. Forecast accuracy later in the medium range may thus not have benefited fully from improvements earlier in the range because of the faster error-growth associated with a more active, though more realistic, forecast model. Overprediction of variance may nevertheless detrimentally affect present levels of skill and estimates of predictability in all seasons other than summer.The error-growth model currently indicates that it is possible, in principle, to make deterministic mediumrange forecasts for the extratropical 500 hPa height field of the northern hemisphere that are as accurate five days ahead as present forecasts are three days ahead, provided the one-day forecast error can be reduced by the same factor in the future as has actually been achieved in the years since 1981. The level of error currently reached at day seven would then be reached at around day ten. The scope for improvement of forecasts for the southern hemisphere appears to be rather larger. Improvements seem to be possible throughout the spectral range studied, up to total wave-number 40. This is found also for the rotational and divergent wind components at 850 and 200 hPa. For these components, particularly the divergent component, there is a quite pronounced error in the representation of the largest scales.

Horizontal resolution impact on short- and long-range forecast error

“…As in Simmons et al (1995), Eq. (1) has been written in a discretized form, and the three parameters (α, β, γ ) have been estimated by a least-squares fit of the root-meansquare differences between consecutive forecast errors E j for j = 1,17, with t 1 = 0 and t 17 = 360 hours.…”

“…Forecast-error growth has been studied applying the Simmons et al (1995) version of the error growth model of Dalcher and Kalnay (1987), who included in the Lorenz (1982) model both the systematic and the random error components, and nonlinear error saturation.…”

“…The forecast-error growth model used to estimate the predictability limits was first proposed by Lorenz (1982), then used and slightly modified by Dalcher and Kalnay (1987) and by Simmons et al (1995). Accordingly to this model, the time evolution of the forecast error E is given by the following equation:…”

“…, N, t is equal to 12 hours, E j = (E j+1 − E j ) is the forecast-error increase between steps j and (j + 1), and E j = 0.5(E j + E j+1 ) is the average forecast error between the two steps. As in Lorenz (1982) and Simmons et al (1995), the three parameters (α, β, γ ) of Eq. (A1) can be estimated by a least-square fit of the root-mean-square differences between consecutive forecast errors E j for j = 1,17, with t 1 = 0 and t 17 = 360 hours.…”

Optimal Evolutionary Window for the Nonlinear Local Lyapunov Exponent

“…The last approach "is partly dynamical and partly empirical" as noted by Lorenz (1969b) and takes errors of different scales into account (1969c). Up to now, most studies concerning the limit of predictability are based upon models (Lorenz 1965;Leith 1983;Simmons et al 1995;Mu et al 2002). Recently, several studies have shown that the limit of predictability achieved through models would depend on the calculation, the accuracy of computers and the numerical model itself (Feng et al 2001;Li et al 2000;Li et al 2001;Li et al 2006) In view of the limitations of quantifying the predictability limit by models as mentioned above, a theoretical approach based upon the nonlinear error growth dynamics was introduced.…”