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

Abstract. Forecast error growth as a function of lead time of atmospheric phenomena is caused by initial and model errors. When studying the initial error growth, it may turn out that small-scale phenomena, which contribute little to the forecast product, significantly affect the ability to predict this product. The question under investigation is whether omitting these atmospheric phenomena will improve the predictability of the resulting value. The topic is studied in the extended Lorenz (2005) system. This system shows that omitting small spatiotemporal scales that significantly affect prediction ability will reduce predictability more than modeling it. In other words, a system with model error (omitting phenomena) will not improve predictability. A hypothesis explaining and describing this behavior is developed, with the difference between systems (model error) produced at each time step seen as the error of the initial conditions. The resulting model error is then defined as the sum of the increments of the time evolution of the initial conditions so defined. The hypothesis 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 approximations are used to estimate the errors described in the hypothesis. A method is proposed to distinguish increments of prediction error growth from small-spatiotemporal-scale phenomena and model errors. Results are presented for the error growth of the ECMWF system, where a 40 % reduction in model error between 1987 and 2011 is calculated based on the developed hypothesis, while over the same period the instability (error growth rate) of the system with respect to initial condition errors has grown.