Analysis of initial and model error in forecast errors of extended atmospheric Lorenz' 05 systems and the ECMWF system

If the error growth of initial conditions in numerical weather systems is scale-dependent, then micro or mesoscale significantly affects the accuracy of a cyclonic weather system prediction. Thus, as the forecast skill improves (by including smaller-scale phenomena and reducing the error of the initial conditions), we would reach an intrinsic limit of predictability that we have set for the forecast of mid-latitude synoptic phenomena (geopotential height 500 hPa) at about three weeks. For scale-dependent initial error growth, it may turn out that small-scale phenomena that contribute little to the forecast product significantly affect the ability to predict that product. It is reasonable to study whether omitting these atmospheric phenomena will improve the predictability of the final value. The topic is studied in the extended system of Lorenz (2005). This system shows that omitting small spatiotemporal scales will reduce predictability more than modeling it. In other words, a system with model error (omitting phenomena) will not improve predictability. Orrell's hypothesis is extended to explain and describe this behavior, whereby the difference between systems (model error) produced at each time step is treated as an error in the initial conditions. The resulting model error is then defined as the sum of the time evolution increments of the initial conditions so defined. The theory is compared to the fit parameters that define the model error in certain approximations of the average forecast error growth. Parameters are interpreted in this context, and the hypotheses are used to estimate the errors described in the theory. The results of the annual averages of the prediction error growth (geopotential height 500 hPa) of the ECMWF system from 1987 to 2011 are discussed.