Accurate numerical weather predictions (NWP) are considered important over mountainous regions, where the hydrological and meteorological risks associated with heavy precipitation are especially acute. Quantitative precipitation forecasting (QPF) is unfortunately a very challenging task and traditional limited-area or global NWP models tend to exhibit low predictive skills. In recent years, promising prospects have emerged with the development of next-generation NWP models characterized by grid spacings of some few kilometers (O(1 km)). These allow the quasi-explicit treatment of moist convective processes and a better representation of orography and surface fields. Also, due to the chaotic nature of the atmospheric dynamics and motivated by the success of ensemble prediction systems (EPS) at the synoptic scale, interest is growing in the design of cloud-resolving EPS. This development raises a series of fundamental questions concerning the predictability of the simulated weather phenomena.
This study aims at investigating aspects of mesoscale predictability relevant for high-resolution (cloud-resolving) quantitative precipitation forecasting over complex topography. Emphasis is set on predictability limitations arising at the mesobeta-scale (20-200 km) due to the growth and amplification of mesogamma-scale (2-20 km) initial uncertainties. Real-case ensemble simulations are performed with the NWP model COSMO integrated on a convection-resolving grid of 2.2 km. The approach uses perturbed initial conditions but assumes perfect predictability on the synoptic scale (identical lateral boundaries).
Numerical experimentations conducted within MAP and afterwards have demonstrated that predictability limitations arising from the growth and amplification of cloud-scale uncertainties present in the initial conditions of a cloud-resolving model are highly relevant for mesoscale quantitative precipitation forecasting and flood forecasting, even when assuming a perfect model and perfect lateral boundary conditions (see e.g., Walser et al. 2004a,b, Hohenegger et al. 2006 and Fig. 1). The resulting predictability limitations exhibits a strong case-to-case variability (see Fig. 1 left versus Fig. 1 right). Losses of predictability are primarily associated with moist processes and convective instability. However, due to the limited spatial extent of moist convective unstable regions, we also found that significant error growth only occurs if the flow regime sustains upstream propagation of perturbations (Hohenegger et al. 2006). Since moist convection acts as triggering mechanism, amplification of cloud-scale initial uncertainties can be extremely fast. Combined with an effective propagation through sound and gravity waves, hot spots of error growth can quickly (1-2 h) develop far remote from initial perturbations (Hohenegger et al. 2007b).
Contrasting the resulting fundamental properties characterizing cloud-resolving short-rang (1 d) simulations to the well-known behavior of synoptic-scale medium-range (10 d) weather forecasts, the following conclusions could be drawn concerning predictability and applicability of synoptic-scale NWP strategies onto cloud-resolving scales (see Hohenegger et al. 2007a). Consistent with the higher power of convective versus baroclinic instability, error growth rates are about ten times larger on cloud-resolving scales than on synoptic-scales. In this sense, integrating a 10-d synoptic-scale forecast equates to performing a 1-d cloud-resolving simulation. However, analyzing the linearity characterizing the two systems, we found that the tangent-linear assumption already breaks down at 1.5 h for cloud-resolving against 54 h for synoptic scale integrations. Hence, in terms of nonlinearity, a 10-d synoptic-scale forecast only corresponds to a 7-h cloud-resolving simulation, which is much shorter than the anticipated lead time of 1 day. This actually questions the direct application of certain synoptic-scale ensemble, data assimilation, and targeting techniques relying on the tangent-linear assumption to short-range cloud-resolving NWP. The meaning of these differences in tangent-linear time scales between the two systems may be also illustrated by considering the Lorenz model and the related sensitivity to its initial conditions in terms of X=f(Xo,t) (see Fig. 2). Using the scaling associated with the tangent-linear time scale, the integration of synoptic-scale NWP to 5 days and of cloud-resolving NWP to 12 h (half of lead times) gives 2.2 and 8 nondimensional time units. The corresponding more advanced fragmentation of the phase space revealed by Fig. 5f versus Fig. 5d implies a much weaker relationship between initial and future states, which would in principle reduce the optimal performance of certain synoptic-scale NWP analysis methodologies at cloud-resolvng scales for the assumed lead time (see Hohenegger et al. 2007a).
Hohenegger, C., D. Lüthi, and C. Schär, 2006: Predictability mysteries in cloud-resolving models, Mon. Wea. Rev., 134, 2095-2107.
Hohenegger, C., and C. Schär, 2007a: Atmospheric predictability at synoptic versus cloud-resolving scales, Bull. Amer. Meteor. Soc., in press.
Hohenegger, C., and C. Schär, 2007b: Predictability and error growth dynamics in cloud-resolving models, J. Atmos. Sci., in press.
Walser, A., and C. Schär, 2004: Convection-resolving precipitation forecasting and its predictability in Alpine river catchments. J. Hydrol., 288, 57-73.
Walser, A., D. Lüthi, and C. Schär, 2004: Predictability of precipitation in a cloud-resolving model, Mon. Wea. Rev., 132, 560-577.
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