Thomas Schartner
Ingo Kirchner
Institut für Meteorologie, Freie Universität Berlin

Version from July 28, 2015

This is only a brief documentation about the MiKlip Stormtrack 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

The 500 mb geopotential height has a very large amount of low-frequency variability. If one were to construct the 500 mb root-mean-square (rms) geopotential height field, the result would be dominated by the low-frequency component. Many physically important, high-frequency components, such as those associated with developing baroclinic disturbances would be masked. In order to exhibit the higher frequency variability, one must resort to filtering. The method for filtering geopotential height is the expansion into spherical harmonics for the time scale of less than 10 days.

In section 2, the methods of the calculation procedure are described [Blackmon1976]. Sections 3 and 4 explain the input respectively the output of the stormtrack tool.

2 Methods

2.1 Spectral Analysis

As mentioned above, variability can be characterized by the expansion of the 500 mb geopotential height (Z) field into spherical harmonics. The spherical harmonics Y n,m are a complete, orthonormal set of functions with simultaneously satisfy the equations

2Y n,m = n(n + 1)Y n,m, (1)
2 λ2Y n,m = n2Y n,m, (2)

where 2 is the angular part of the Laplacian operator written in latitude and longitude. With a real basis, the conditions of the eigenvalues

m = 0,1,2,,integer (3)
n = 0,1,2,,integer (4)
n m. (5)

The functions Y n,m are written

Y n,0(e) = 2n + 1 4π Pn(sinϕ), (6)
Y n,m(e) = 2n + 1 2π (n m)! (n + m)!1 2 cosmλPnm(sinϕ), (7)
Y n,m(0) = 2n + 1 2π (n m)! (n + m)!1 2 sinmλPnm(sinϕ), (8)

where Pn(sinϕ) are Legendre polynomials and Pnm(sinϕ) are associated Legendre functions. The superscripts (e) and (0) specify the evenness and oddness of the functions under the substitution λ λ. The eigenvalue m is the longitudinal wavenumber. the difference n m gives the number of nodes from pole to pole and also determines the evenness (oddness) of the function Pnm(sinϕ), for n-m even (odd), under the substitution ϕ ϕ. Finally, n is the two-dimensional wavenumber appropriate for the spherical geometry and the basic functions. So, the geopotential height Z(ϕ,λ) has been expanded in a series of spherical harmonics

Z(ϕ,λ) = m=0 nm Cn,mY n,m(e)+ m=1 nm Sn,mY n,m(0) (9)

The expansion coefficients Cn,m and Sn,m are calculated using the orthogonality property of the spherical harmonics. Every field in the data set described above was expanded into a series of spherical harmonics. The series is truncated at

m n N = 18. (10)

Each field is therefore represented by 190 nontrivial expansion coefficients. The complete truncated field can be recovered using (9), where the upper limit of summation is m = n = 18. To construct the fields the summation is done over only part of the wavenumbers. Regime I is definied in wavenumber space to be those wavenumbers with

Regime I 0 n 6 0 m n . (11)

Regime I is called as the long waves ort the planetary-scale waves. Regime II is defined by

Regime II 7 n 12 0 m n . (12)

This regime contains the medium-scale waves. Finally, Regime III is defined by

Regime III 13 n 18 0 m n . (13)

This regime contains the short waves. The truncations used to define the total field and the wavenumber regimes are therefore total two-dimensional scale truncations. All three regimes defined above contain planetary-scale longitudinal harmonics m 5. These waves are distinguished by different latitudinal scales and consequently by different two-dimensional scales. The choice of the boundaries of the wavenumber regimes is somewhat arbitrary. Neverless, the bulk of the waves in each regime behaves differently from the bulk of waves in another regime. Each set of expansion coefficients, Cn,m(ti) or Sn,m(ti) for fixed n and m, forms a time series. To display the contributions to these time series comming from different frequency domains, a 31-point filters is used in form of

C¯n,m = a0Cn,m(ti) + p=115a p[Cn,m(ti+p) + Cn,m(tip)] (14)

to define new filtered coefficients correspoinding to a low-pass, a medium-pass and a high-pass filter. The medium-pass filter is sensitive to frequencies in the period 2.5 T 6days. So, the medium-pass filter is used for the stormtrack acitvies with the calculated coefficients in table 1.

a0 0.2776877534
a1 0.1433496840
a2 -0.1020097578
a3 -0.1947701551
a4 -0.0923257264
a5 0.0283041151
a6 0.0419335015
a7 0.0033466748
a8 0.0041075557
a9 0.0328072034
a10 0.0304306715
a11 -0.0020017146
a12 -0.0191709641
a13 -0.0096723016
a14 -0.0001341773
a15 -0.0030384857

Table 1: coefficients for data sets with a resolution of 12 hour

The result is the “Standard deviation of bandpassfiltered Sea Level Pressure anomalies” or the “Standard deviation of bandpassfiltered Geopotential Height anomalies”.

3 Input

The calculation of the stormtrack activity is based on at least 12 hourly geopotential height field in 500 hPa or air pressure at sea level (pmsl). Input fields with a higher temporal resolution than 12 hour (e.g. 6-hourly data) will be rejected.

Outputdir Output directory
mandatory default: /scratch/user/evaluation_system/output/stormtrack
Cachedir Cache directory
mandatory default: /scratch/user/evaluation_system/cache/stormtrack
Cacheclear Option switch to NOT clear the cache.
mandatory default: True
Variabel geopotential height (zg) or air pressure at sea level (psl).
mandatory default: zg
Project Choose project, e.g. reanalysis, cmip5, baseline1, baseline0
Product Choose product, e.g. reanalysis, output
Institute Choose institute of experiment, e.g. MPI-M, ECMWF
Model Choose model of experiment, e.g. MPI-ESM-LR, IFS
Experiment Choose experiment name, e.g. decadal1971, ERAINT
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 Choose level [in Pa], e.g. 50000 only reasonable for zg
mandatory default: 50000
Ntask Number of tasks.
mandatory default: 24
Accu type Set the accumulation type for Stormtrack - complete, monthly or seasonal
(for explanation see text)
mandatory default: complete
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 2: Input options for Stormtrack

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 of the geopotential height field or air pressure at sea level you want to process. Further, select ensemble member(s) in the Ensemble operator 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 pressure level(Level) of geopotential height field can be chosen. Finally, you have the option to visualize some results (Makepic), to remove the cache directories (Cacheclear), to specify the number of tasks (Ntask) and to show the found input file(s) from your input parameters based on solr_search (Dryrun). The Accu type defines the accumulation time. The accumulation time is the time period over which is averaged: complete - the whole time period is averaged, monthly - every month is averaged and seasonal DJF, MAM, JJA and SON is averaged.

4 Output

The processed files can be found in the selected Outputdir. The stormtrack file contain the stormtrack activity named as ”Standard deviation of bandpassfiltered Sea Level Pressure anomalies” or as “Standard deviation of bandpassfiltered Geopotential Height anomalies”. If selected, stormtrack activity is also visualized.


Figure 1: Example of Stormtrack activity with a complete accumulation for ERA-int (1979-1982).


Figure 2: Example of Stormtrack activity with a monthly accumulation for ERA-int (1979-1982).


Figure 3: Example of Stormtrack activity with a seasonal accumulation for ERA-int (1979-1982).


   Maurice L Blackmon. A climatological spectral study of the 500 mb geopotential height of the northern hemisphere. Journal of the Atmospheric Sciences, 33(8): 1607–1623, 1976.