Blocking

 Andy Richling$*$ Chistopher Kadow, Sebastian Illing, Oliver Kunst Institut für Meteorologie, Freie Universität Berlin

Version from November 27, 2015

$*$andy.richling@met.fu-berlin.de

This is a brief documentation about the Freva Blocking Plugin and is currently still under construction. Please note the Plugin is originally developed for the northern hemisphere (NH), so that some features actually do not work well for the SH. Comments or any kind of feedback is highly appreciated. Please send an e-mail to the authors.

### 1 Introduction

Blocking anticyclones are synoptic-scale systems which have a crucial role in atmospheric low-frequency variability. In generally, blocking situations persist for multiple days to weeks and block the westerly flow. There exist two basic types of blocking, the dipole block and the omega block. In both of them, in the NH the jet stream is split up into a stronger, northern and a weaker, southern jet branch. The change of the flow in direction, intensity and position due to the characteristic geopotential height field during a blocking situation can be used to define blocking. The Blocking Plugin here is based on the instantaneous blocking index of Tibaldi and Molteni [1990] and will give you information, whether a longitude of a given day is instantaneous blocked or not.

In section 2, the methods of the calculation procedure are described. Sections 3 and 4 explain the input respectively the output of the Blocking Plugin.

### 2 Methods

#### 2.1 Instantaneous Blocked Longitude (IBL)

As mentioned above, blocking can be characterized by the distribution of large-scale geopotential height ($Z$) field. Basically, an area with high geopotential height values is located in the region where the path of the stormtrack (maximum of baroclinic activity) originally been placed. Tibaldi and Molteni [1990] use two geopotential height gradients to compute the instantaneous blocking – the southern geopotential height gradient (GHGS) relating to middle and the northern geopotential height gradient (GHGN) referring to high latitudes respectively.

 $GHGS=\frac{Z\left({\varphi }_{M}\right)-Z\left({\varphi }_{S}\right)}{\left({\varphi }_{M}-{\varphi }_{S}\right)},$ (1)
 $GHGN=\frac{Z\left({\varphi }_{N}\right)-Z\left({\varphi }_{M}\right)}{\left({\varphi }_{N}-{\varphi }_{M}\right)}.$ (2)

According to Barnes et al. [2012], a equation can be written to include the dependency of the meridional extent of blocks (${\delta }_{\varphi }$, here we use ${\delta }_{\varphi }=1{5}^{\circ }$) and the individual position of the local jet stream (${\varphi }_{C}$) to get the latitudes of ${\varphi }_{N}$, ${\varphi }_{M}$ and ${\varphi }_{S}$.

 ${\varphi }_{N}=\left({\varphi }_{C}+\frac{3}{2}{\delta }_{\varphi }\right)+\Delta$ (3)
 ${\varphi }_{M}=\left({\varphi }_{C}+\frac{1}{2}{\delta }_{\varphi }\right)+\Delta$ (4)
 ${\varphi }_{S}=\left({\varphi }_{C}-\frac{1}{2}{\delta }_{\varphi }\right)+\Delta$ (5)

Additionally, these definitions allow a northward and southward shift of $\Delta$ latitudes to catch blocks which are not directly located on ${\varphi }_{C}$. A simple schema in (fig. 1) from Barnes et al. [2012] shows the different latitude locations defining a blocking situation. Referring to fig. 1 a blocking situation can be described when GHGN is associated to a westerly flow north of the blocking anticyclone while GHGS defines an easterly wind equatorward of the blocking region. Relating to the definition of GHGN and GHGS respectively, the blocking criteria can be described as follow:

 $GHGS>{E}_{min},$ (6)
 $GHGN<{W}_{min}.$ (7)

Commonly, ${W}_{min}$ is set to -10 meters per degree latitude which is similar to a westerly geostrophic wind of approximately 8 m/s, while ${E}_{min}$ is set to 0 meters per degree latitude to reflect at least an easterly flow. In addition to these two criteria, a further criterion is used to define blocking. The individual geopotential height anomaly located on ${\varphi }_{M}$ must be positive [e.g. Barriopedro et al.2006Scaife et al.2010].

 $\phantom{\rule{1em}{0ex}}\left(Z\left({\varphi }_{M}\right)-\stackrel{?}{Z\left({\varphi }_{M}\right)}\right)>0.$ (8)

To get the Instantaneous Blocked Longitude (IBL), the geopotential height at each longitude on a given day is checked by the described criteria above. If all of the three criteria will be achieved, the individual longitude on the given day is flagged as ”blocked” and gets the value $IBL=1$, otherwise the longitude is not blocked and IBL is set to $IBL=0$. To seek for blocking near the originally positioned zonal flow, a northward and southward shift ($\Delta$ in equations 3-5) is allowed. An instantaneous blocked longitude is found, if at least one of the shifts achieves all three criteria. An example for detected blocking by this method is shown in figure 2.

#### 2.2 Central Reference Blocking Latitude (CRBL)

The Central Reference Blocking Latitude (CRBL) is identical to ${\varphi }_{C}$ in the equations above and represents the latitudinal position of the originally located stormtrack, which is blocked during a blocking situation. In the Blocking Plugin, CRBL can bet set to a constant latitude for all days of the year and each longitude (e.g. $CRBL=5{0}^{\circ }$N). Additionally, varying CRBL can be calculated from long-term geopotential height field for every calendar day and longitude. This is done similar to the approach in Barriopedro et al. [2010]. The CRBL is estimated by the latitudinal maximum of 5-day high-pass filtered daily geopotential height variance for each longitude, weighted by the cosine of individual longitude (fig. 3). A 61-day running window is applied to derive the variance for a given day (centered in that day). The resulting time series (one CRBL for each longitude and every calendar day) of the latitudinal maximum variance is spatially smoothed two times by using a 10-degree latitude window to avoid abrupt transition. Finally, the individual curve of each longitude is smoothed in time by applying a 11-day running mean. The final CRBL’s can be shown in a hovm?ller diagram (fig. 4).

### 3 Input

The calculation of Instantaneous Blocked Longitude (IBL) is based on hemispheric geopotential height field (temporal resolution higher equal 1-day) in a specific pressure level. Input fields with a higher temporal resolution than 1-day (e.g. 6-hourly data) can be averaged to a daily mean. Further note, a remapping of input grid to a regular longitude-latitude grid with spatial resolution defined by the user is applied.

 Outputdir Output directory mandatory default: /work/user/evaluation_system/output/blocking/timestemp Cachedir Cache directory mandatory default: /work/user/evaluation_system/cache/blocking/timestemp 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 Ensemble Choose ensemble, e.g. r1i1p1, r2i1p1 or ”*” for all members mandatory Time frequency Choose either ”6hr” or ”day” as time frequency mandatory Year range Choose range of years to be processed (comma separated). mandatory default: 1979,2010 Hemisphere Choose hemisphere, NH (SH) for northern (southern) hemisphere. mandatory default: NH Level Choose level [in Pa], e.g. 50000. mandatory default: 50000 Grid Specify a regular lon-lat grid (gridfile or grid description like r180x91). mandatory default: r180x91 Daymean Option to calculate daily mean of geopotential height before calculating IBL. Use the option if you have a higher temporal resolution than 1day in your input files. mandatory default: True Ghgn crit Criterion of GHGN (geopotential height gradient north (SH: south) of blocking high [in gpm/deg_north]). mandatory default: -10 Ghgs crit Criterion of GHGS (geopotential height gradient south (SH: north) of blocking high [in gpm/deg_north]). mandatory default: 0 Crbl const Option to set CRBL (Central Reference Blocking Latitude - latitudinal loaction of mean zonal flow which may be blocked) to a constant latitude location (for all seasons and longitudes). mandatory default: True Crbl constlat Constant latitudinal location of CRBL [in deg_north]. Use only if ”CRBL_const” is set ”True”!’ optional default: 50.0 Crbl calc Option to calculate seasonal (for every calendar day) and longitudinal varying CRBL. Use only if ”CRBL_const” is set ”False”! mandatory default: False Crbl file Option to input a file of seasonal (for every calendar day) and longitudinal varying CRBL. Use only if ”CRBL_const” and ”CRBL_calc” are set ”False”! The file format must be a NetCDF file including a variable named ”CRBL” with dimensions of [time=366, lat=1, lon=180, plev=1]. Save previous calculated CRBL files for multiple use. optional Delta Possible latitudinal northward and southward shifting of CRBL [in deg_lat], only positive values. mandatory default: 4.0 Geopcrit calc Option to calculate threshold criterion for geopotential height (long-term mean) at each grid point for every calendar day. Set ”False” to use an existing NetCDF file. mandatory default: True Geopcrit file Option to input file of threshold criterion for geopotential height. Use only if ”GEOPcrit_calc” is set ”False”. The file format must be a NetCDF file with regular $2.{0}^{\circ }$ x $2.{0}^{\circ }$ longitude-latitude grid of [time=366, lat=46, lon=180, plev=1] dimensions. Save previous calculated files for multiple use. optional Climyear range Choose range of years (comma separated) of long-term time period for calculation of CRBL and/or threshold criterion for geopotential height. Use only if ”GEOPcrit_calc” and/or ”CRBL_calc” are/is set ”True”. optional default: 1981,2010 Plot Option to plot some results. Note: Actually, only supported for NH. mandatory default: True Cacheclear Option switch to NOT cleard the cache. mandatory default: True Ntask Number of tasks. mandatory default: 24 Dryrun Set ”True” for just showing the result of find_files and set ”False” to process data. mandatory default: True

Table 1: Input options for Blocking Plugin

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 you want to process. Further, select ensemble member(s) in the Ensemble operator and specify the time frame (Time frequency) you want to analyze (only day and 6hr are available). In Year range you can choose the range of years which will be processed. Additionally, the hemisphere (Hemisphere) and pressure level (Level) of geopotential height field can be chosen. In Grid you can specify a regular lon-lat grid to remap the data. The option to calculate the daily mean of geopotential height before calculating IBL can be set in the Daymean parameter. The following parameters can be adjust to configure the calculation procedure. Referring to equations 6,7 you can specify ${E}_{min}$ (Ghgs crit) and ${W}_{min}$ (Ghgn crit). An option to use a constant CRBL or a varying CRBL in time and longitude can be selected in Crbl const. If Crbl const is TRUE, you have to specify a constant latitude of CRBL (Crbl constlat). If Crbl const is set to FALSE you have to choose in Crbl calc whether a varying CRBL file shall be calculated relating to section 2.2 or you want to input an own CRBL file (Crbl file), which was created by the Blocking Plugin previously. The CRBL file is a NetCDF file including a variable named ”CRBL” containing dimensions of [time=366, lat=1, lon, plev=1] where the longitude dimension depends on the specified Grid. The possible latitudinal northward and southward shift (see equations 3-?? in section 2.1) is specified in operator Delta. For the third blocking criterion (equation 8) there is an option (Geopcrit calc) to calculate the long-term mean of geopotential height. You also have the possibility to input an own file (Geopcrit file) of long-term geopotential height mean if Geopcrit calc is set FALSE. This file must be a NetCDF file for one hemispheric region (NH or SH) containing a variable named ”zg” with the same grid specified in Grid and dimensions of [time=366, lat, lon, plev=1]. To define the range of years which is used for the calculation of Crbl file and Geopcrit file the parameter Climyear range can be set.

Finally, you have the option to visualize some results (Plot), 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).

### 4 Output

The processed files can be found in the selected Outputdir. The IBL file contain the IBL (variable declared as ”IBL”), GHGS value (”GHGS”), GHGN value (”GHGN”) and the anomaly of geopotential height (”zg”) according to the (calculated or given) Geopcrit file. Additionally, calculated CRBL file (”CRBL”) and/or calculated GEOPcrit file (”zg”) will be saved. Output figures show the yearly averaged frequency of IBL based on chosen year range (figures 5,6 and 7). If selected, CRBL is also visualized.

### References

E. A. Barnes, J. Slingo, and T. Woollings. A methodology for the comparison of blocking climatologies across indices, models and climate scenarios. Clim. Dyn., 38: 2467–2481, 2012. doi: 10.1007/s00382-011-1243-6.

D. Barriopedro, R. Garc?a-Herrera, A. R. Lupo, and E. Hern?ndez. A Climatology of Northern Hemisphere Blocking. J. Climate, 19:1042–1063, 2006. doi: 10.1175/JCLI3678.1.

D. Barriopedro, R. Garc?a-Herrera, and R. M. Trigo. Application of blocking diagnosis methods to General Circulation Models. Part I: a novel detection scheme. Clim. Dyn., 35:1373–1391, 2010. doi: 10.1007/s00382-010-0767-5.

A. A. Scaife, T. Woollings, J. Knight, G. Martin, and T. Hinton. Atmospheric Blocking and Mean Biases in Climate Models. J. Climate, 23:6143–6152, 2010. doi: 10.1175/2010JCLI3728.1.

S. Tibaldi and F. Molteni. On the operational predictability of blocking. Tellus, 42A:343–365, 1990. doi: 10.1034/j.1600-0870.1990.t01-2-00003.x.