Müller, A. and Névir, P. and Klein, R. (2017) Scale Dependent Analytical Investigation of the Dynamic State Index Concerning the QuasiGeostrophic Theory. SFB 1114 Preprint . pp. 138. (Unpublished)

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Abstract
The dynamic state index (DSI) is a scalar diagnostic field that quantifies local deviations from a steady and adiabatic wind solution and thus indicates nonstationarity and/or diabaticity. The DSIconcept has originally been developed through energyvorticity theory based on the full compressible flow equations without regard to the characteristic scaledependence of many atmospheric processes. Such scaledependent 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 scaledependent DSIlike indicators that distinguish the different levels of organization in precipitation systems. The example consists of (i) developing a DSI index for the quasigeostrophic model using energyvorticity 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 scaledependent precipitation information. A spinoff of the asymptotic analysis is a novel nonequilibrium 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:  30 Aug 2017 09:31 
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