Atmospheric predictability at synoptic versus cloud-resolving scales

The limited atmospheric predictability has been addressed by the development of ensemble prediction systems (EPS) that are now routinely applied for medium-range synoptic-scale numerical weather prediction (NWP). With the increase of computational power, interest is growing in the design of high-resolution (cloud resolving) NWP models and their associated short-range EPS. This development raises a series of fundamental questions, espe cially concerning the type of error growth and the validity of the tangent-linear approximation. To address these issues, a comparison between perturbed medium-range (10 day) synoptic-scale integrations (taken from the operational ECMWF EPS with a horizontal resolution of about 80 km) and short-range (1 day) high-resolution simulations (based on the Lokal Modell of the Consortium for Small-Scale Modeling with a grid spacing of 2.2 km) is conducted. The differences between the two systems are interpreted in a nondimensional sense and illustrated with the help of the Lorenz attractor. Typical asymptotic perturbation-doubling times of cloud-resolving and synoptic-scale simulations amount to about 4 and 40 h, respectively, and are primarily related to convective and baro- clinic instability. Thus, in terms of growth rates, integrating a 1-day :1 Cloud- re solving forecast may be seen as equivalent to performing a 10-day synoptic-scale simulation. However, analysis of the prevailing linearity reveals that the two systems are fundamentally different in the following sense: the tangent-linear approximation breaks down at 1. 5 h for cloud resolving against 54 h for synoptic-scale forecasts. In terms of nonlinearity, a 10-day synoptic-scale integration thus corresponds to a very short cloud-resolving simulation of merely;about 7 h. The higher degree of nonlinearity raises questions concerning the direct application of standard synoptic-scale forecasting methodologies (e.g., optimal perturbations, 4D variational data assimilation, or targeted observations) to 1-day cloud-resolving forecasting.