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Kirstin Kober and George C. Craig

Abstract

Stochastic perturbations allow for the representation of small-scale variability due to unresolved physical processes. However, the properties of this variability depend on model resolution and weather regime. A physically based method is presented for introducing stochastic perturbations into kilometer-scale atmospheric models that explicitly account for these dependencies. The amplitude of the perturbations is based on information obtained from the model’s subgrid turbulence parameterization, while the spatial and temporal correlations are based on physical length and time scales of the turbulent motions. The stochastic perturbations lead to triggering of additional convective cells and improved precipitation amounts in simulations of two days with weak synoptic forcing of convection but different amounts of precipitation. The perturbations had little impact in a third case study, where precipitation was mainly associated with a cold front. In contrast, an unphysical version of the scheme with constant perturbation amplitude performed poorly since there was no perturbation amplitude that would give improved amounts of precipitation during the day without generating spurious convection at other times.

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Tobias Selz and George C. Craig

Abstract

The growth of small-amplitude, spatially uncorrelated perturbations has been studied in a weather forecast of a 4-day period in the summer of 2007, using a large domain covering Europe and the eastern Atlantic and with explicitly resolved deep convection. The error growth follows the three-stage conceptual model of Zhang et al., with rapid initial growth (e-folding time about 0.5 h) on all scales, relaxing over about 20 h to a slow growth of the large-scale perturbations (e-folding time 12 h). The initial growth was confined to precipitating regions, with a faster growth rate where conditional instability was large. Growth in these regions saturated within 3–10 h, continuing for the longest where the precipitation rate was large. While the initial growth was mainly in the divergent part of the flow, the eventual slow growth on large scales was more in the rotational component.

Spectral decomposition of the disturbance energy showed that the rapid growth in precipitating regions projected onto all Fourier components; however, the amplitude at saturation was too small to initiate the subsequent large-scale growth. Visualization of the disturbance energy showed it to expand outward from the precipitating regions at a speed corresponding to a deep tropospheric gravity wave. These results suggest a physical picture of error growth with a rapidly growing disturbance to the vertical mass transport in precipitating regions that spreads to the radius of deformation while undergoing geostrophic adjustment, eventually creating a balanced perturbation that continues to grow through baroclinic instability.

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Kirstin Kober, Annette M. Foerster, and George C. Craig

Abstract

Stochastic parameterizations allow the representation of the small-scale variability of parameterized physical processes. This study investigates whether additional variability introduced by a stochastic convection parameterization leads to improvements in the precipitation forecasts. Forecasts are calculated with two different ensembles: one considering large-scale and convective variability with the stochastic Plant–Craig convection parameterization and one considering only large-scale variability with the standard Tiedtke convection parameterization. The forecast quality of both ensembles is evaluated in comparison with radar observations for two case studies with weak and strong synoptic forcing of convection and measured with neighborhood and probabilistic verification methods. The skill of the ensemble based on the Plant–Craig convection parameterization relative to the ensemble with the Tiedtke parameterization strongly depends on the synoptic situation in which convection occurs. In the weak forcing case, where the convective precipitation is highly intermittent, the ensemble based on the stochastic parameterization is superior, but the scheme produces too much small-scale variability in the strong forcing case. In the future, the degree of stochastic variability could be tuned, and these results show that parameters should be chosen in a regime-dependent manner.

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