Analysis of model error in forecast errors of Extended Atmospheric Lorenz' 05 Systems and the ECMWF system

The 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 turns out that small scale phenomena, which contribute little to the forecast product, significantly affect the ability to predict this. 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 will reduce predictability more than modeling it. Generally, a system with model error (omitting phenomena) will not improve predictability. A theory 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 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. It is proposed how to distinguish increments to prediction error growth from small spatiotemporal-scales phenomena and model error. 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 theory, while over the same time, the instability of the system with respect to initial condition errors has grown.