Repository: Freie Universität Berlin, Math Department

Scale Dependent Analytical Investigation of the Dynamic State Index Concerning the Quasi-Geostrophic Theory

Müller, A. and Névir, P. and Klein, R. (2017) Scale Dependent Analytical Investigation of the Dynamic State Index Concerning the Quasi-Geostrophic Theory. SFB 1114 Preprint . pp. 1-38. (Unpublished)



The dynamic state index (DSI) is a scalar diagnostic field that quantifies local deviations from a steady and adiabatic wind solution and thus indicates non-stationarity and/or diabaticity. The DSI-concept has originally been developed through energy-vorticity theory based on the full compressible flow equations without regard to the characteristic scale-dependence of many atmospheric processes. Such scale-dependent information is often of importance, however, and particularly so in the context of precipitation modelling: Small scale convective events are often organized in storms, clusters and “Großwetterlagen” across a wide range of scales. A concrete example shows that, by combining the DSI concept with ideas of scale analysis, one can derive new scale-dependent DSI-like indicators that distinguish the different levels of organization in precipitation systems. The example consists of (i) developing a DSI index for the quasi-geostrophic model using energy-vorticity theory, (ii) showing that it is asymptotically consistent with the original index for the primitive equations, and (iii) evaluating both indices for meteorological reanalysis data to demonstrate that they capture systematically different scale-dependent precipitation information. A spin-off of the asymptotic analysis is a novel non-equilibrium time scale combining potential vorticity and the DSI indices. Its ramifications for turbulence modelling across a wide range of atmospheric scales is briefly discussed.

Item Type:Article
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics > Geophysical Fluid Dynamics Group
ID Code:2101
Deposited By: Silvia Hoemke
Deposited On:30 Aug 2017 09:29
Last Modified:08 Dec 2017 08:02

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