Thomas Schartner$*$ Ingo Kirchner Institut für Meteorologie, Freie Universität Berlin

Version from June 14, 2016

$*$thomas.schartner@met.fu-berlin.de

This is only a brief documentation about the MiKlip Eady Growth Rate Plugin and is currently still under construction. Comments or any kind of feedback is highly appreciated. Please send an e-mail to the authors.

### 1 Introduction

In order to understand the process of baroclinic instability, the Eady Growth Rate will be used. The parameter describes how well deep pressure systems can develop in a weather situation over a specific area. It combines i.e. higher scaled weather situations with the development of extreme cyclones on the basis of theoretical derivations. In section 2, the methods of the calculation procedure are described [Hoskins and Valdes1990]. Sections 3 and 4 explain the input respectively the output of the Eady Growth Rate tool.

### 2 Methods

The Eady Growth Rate which assesses baroclinic instability through the vertical gradient in horizontal wind speed in the troposphere and a measure for static stability [Hoskins and Valdes1990],[Paciorek et al.2002]. The Eady Growth Rate is based on the Eady Model which makes several assumptions about the atmospheric state:

• The motion is on an $f$-plane.
• The stratification is uniform i.e. ${N}^{2}$ is constant. This is a reasonable approximation in the troposphere.
• The atmosphere is Boussinesq i.e. density variations are ignored except in the static stability.
• The motion is between two, flat, rigid horizontal surfaces. The upper surface may be considered to be the tropopause with the increase in static stability inhibits vertical motion
• There is a uniform vertical wind shear. By thermal wind balance this must be associated with a horizontal temperature gradient.

The Eady Model has two different modes, stable and unstable. For unstable modes the vorticity, vertical velocity, height and other atmospheric variables tilt westward with height, temperature tilt eastward. As a result, a poleward heat flux is observed with a positive feedback necessary for cyclognesis. The growth rate for the most unstable mode can be calculated by [Hoskins and Valdes1990]:

 ${\sigma }_{max}=0.31*\left(\frac{f}{N}\right)*|\frac{\delta \left(v,u\right)}{\delta z}|$ (1)

The result is the Eady Growth Rate. When horizontal temperature gradients exist on pressure surfaces it is possible that a sloping displacement of air parcels lowers the centre of gravity of the system while at the same time the buoyancy effects can allow the parcels to continue to move. There is thus a release of the available potential energy and a gain of kinetic energy by the disturbance.

### 3 Input

The calculation of the Eady Groth Rate is based on 6 hourly or daily temperature, velocity and geopotential height field in two different layers. Datasets with missing variables are sorted out for the time step.

 Outputdir Output Directory mandatory default: /scratch/user/evaluation_system/output/eady Cachedir Cache Directory mandatory default: /scratch/user/evaluation_system/cache/eady Cacheclear Option switch to NOT clear the cache. mandatory default: True Project Choose project, e.g. reanalysis, cmip5, baseline1, baseline0 mandatory Product Choose product, e.g. reanalysis, output mandatory Institute Choose institute of experiment, e.g. MPI-M, ECMWF mandatory Model Choose model of experiment, e.g. MPI-ESM-LR, IFS mandatory Experiment Choose experiment name, e.g. decadal1971, ERAINT mandatory Time frequency Choose frequency of choosen data, like mon or 6hr mandatory Ensemble Choose ensemble, e.g. r1i1p1, r2i1p1 or ”*” for all members mandatory default: * Firstyear Choose first year to be processed. Lastyear Choose last year to be processed. Level up Choose level [in Pa], e.g. 30000 mandatory default: 50000 Level down Choose level [in Pa], e.g. 50000 mandatory default: 85000 Makepic Set ”True” for make picture with tool movieplotter mandatory default: False Dryrun Set ”True” for just showing the result of find_files and set ”False” to process data. mandatory default: True Caption An additional caption to be displayed with the results

Table 1: Input options for Eady Growth Rate

At first, you have to specify your output (Outputdir) and cache (Cachedir) directories. The data paths of input files can be selected via the typical MiKlip data structure. Choose the Project, Product, Institute, Model and Experiment you want to process. Further, select ensemble member(s) in the Ensemble field and specify the variable (Variable) you want to analyze. In Firstyear and Lastyear you can choose the range of years which will be processed. The upper level (Level up) and bottom level (Level down) can be chosen. Finally, you have the option to visualize some results (Makepic), to remove the cache directories (Cacheclear) and to show the input file(s) from your input parameters based on freva - -databrowser (Dryrun).

### 4 Output

The processed files can be found in the selected Outputdir. The eady file contains the Eady Growth Rate. If selected, the Eady Growth Rate is also visualized

### References

Brian J Hoskins and Paul J Valdes. On the existence of storm-tracks. Journal of the atmospheric sciences, 47(15):1854–1864, 1990.

Christopher J Paciorek, James S Risbey, Valérie Ventura, and Richard D Rosen. Multiple indices of northern hemisphere cyclone activity, winters 1949-99. Journal of Climate, 15(13):1573–1590, 2002.