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= CDXWRF: WRF module for CORDEX =
The `Coordinated Regional Climate Downscaling Experiment' ([http://www.cordex.org/ CORDEX]) is a scientific effort of the World Climate Research Program (WRCP) for the coordination of regional climate initiatives. In order to accept an experiment, CORDEX provides experiment guidelines, specifications of regional domains and data access/archiving. Data requirements are intended to cover all the possible needs of stake holders, and scientists working on climate change mitigation and adaptation policies in various scientific communities. The required data and diagnostics are grouped into different levels of frequency (sub-daily, daily, monthly and seasonal), priority (Core, Tier1, Tier2), and some of them even have to be provided as statistics (minimum, maximum, mean). Here is presented the development of a specialized module called <CODE>module_diag_cordex</CODE> (version 1.3) for the Weather Research and Forecasting (([http://www.mmm.ucar.edu/wrf/users/ WRF], Skamarok et al. 2008)) model, capable of outputting the required CORDEX variables. Additional diagnostic variables not required by CORDEX, but of potential interest to the regional climate modeling community, are also included in the module. `Generic' definitions of variables are adopted in order to overcome model and/or physics parameterization dependence of certain diagnostics and variables, thus facilitating a robust comparison among simulations. The module is computationally optimized, and the output is divided in different priority levels following CORDEX specifications (Core, Tier1, and additional) by selecting pre-compilation flags. This implementation of the module does not add a significant extra cost when running the model, for example the addition of the Core variables slows the model time-step by less than a 5%. The use of the module reduces the requirements of disk storage by about a 50%.


CORDEX requirements of data for stake holders and decision making community, push the output of the atmospheric models, which demands that usually require time consuming post-process of the standard model output. In order to avoid this time and effort consuming post-processing task, here is presented the implementation of a new module into the Weather and Forecasting Model ([WRF http://www.mmm.ucar.edu/wrf/users/], Skamarok et al. 2008) module called <PRE>module_diag_cordex</PRE> with which is expected to substantially limit the need of post-processing.
An article is available in `Geosciences Model Development' journal:


PDF version of this page here [[File:module_CORDEX_WRF.pdf]]
Lluís Fita, Jan Polcher, Theodore M. Giannaros, Torge Lorenz, Josipa Milovac, Giannis Sofiadis, Eleni Katragkou and Sophie Bastin, 2019: <I>CORDEX-WRF v1.3: development of a module for the Weather Research and Forecasting (WRF) model to support the CORDEX community</I>, Geosci. Model Dev., '''12''', 1029-1066, 2019, [https://www.geosci-model-dev.net/12/1029/2019/gmd-12-1029-2019.html https://doi.org/10.5194/gmd-12-1029-2019]


In order to get the code send an email to : lluis.fita [a] cima.fcen.uba.ar in order to keep a track and being able to inform of new versions/corrections.
It is recommend to contact Lluís Fita (lluis.fita [a] cima.fcen.uba.ar) in order to keep a track and being able to inform of new versions/corrections.


== CORDEX requirements ==
'''Disclaimer'''
<PRE>
Authors decline any responsibility of the possible unexpected consequence of the use of this software. This piece
of code is provided following the scientific spirit of sharing knowledge and technical advances. Please, use it
with the same intention and willingness.
</PRE>


CORDEX requirements of data must cover all the possible needs of stake holders, and scientists working on the adaptation and mitigation strategies. They are grouped in different levels of frequency and priority. A working copy of this list is available [here https://www.hymex.org/cordexfps-convection/wiki/doku.php?id=protocol] from the CORDEX convection permitting Flag Ship Pilot study.
There are four working versions of the code for WRFV3.7.1, WRFV3.8.1, WRFV3.9.1.1, WRFV4.0. :
* WRF-CORDEX module version 1.3 for WRFV3.7.1, L. Fita, [https://doi.org/10.5281/zenodo.1469639 DOI:zenodo.1469639]
* WRF-CORDEX module version 1.3 for WRFV3.8.1, L. Fita, [https://doi.org/10.5281/zenodo.1469645 DOI:zenodo.1469645]
* WRF-CORDEX module version 1.3 for WRFV3.9.1.1, L. Fita, [https://doi.org/10.5281/zenodo.1469647 DOI:zenodo.1469647]
* WRF-CORDEX module version 1.3 for WRFV4.0, L. Fita, [https://doi.org/10.5281/zenodo.1469651 DOI:zenodo.1469651]


Some of the variables are not directly computed in the WRF model which require to extend the model output in order to provide enough variables to post-process the variables.
'''GIT repository'''


The implementation of the module_diag_cordex module should allow to avoid the post-processing by computing
Recently all the code was uploaded to a GIT server. All new developments / updates / new WRF versions, will carried out only the GIT version of the codes. Please visit:
the CORDEX-required (Core & Tier) variables during model integration


'''NOTE: Be aware that any systematic checking process has been applied to this module. Use it and the
[https://git.cima.fcen.uba.ar/lluis.fita/cdxwrf/-/wikis/home https://git.cima.fcen.uba.ar/lluis.fita/cdxwrf/-/wikis/home]
variables therein at your own risk !! It has been tested on a 2-nested domain configuration with the inner
domain at cloud resolving resolution (< 5 km, without cumulus scheme), making use of restarts and on
pure distributed memory parallel environment'''


= CDXWRF in v7.1 =
It has been implemented in WRFv7.1 Lluís Fita's fork. Here the link to the announcement in the WRF-MPAS forum [https://forum.mmm.ucar.edu/threads/cdxwrf-module-in-wrfv7-1.23284/post-55849 #55940]


== module_diag_cordex ==
Although a pull of the WRF source code has been made and the module is currently being direclty added to the official source of the code of the model, and its final inclusion will be done by decission of the development team of the model.


The module is basically based on two modules:
'''NOTE:'''
* <PRE>phys/module_diag_cordex.F</PRE>: Main module which manages the calls to the variables and the accumulations for
Be aware that certain surface variables and their statistics (clWRF, Fita et al 2010) are retrieved from namelist configuration (from [http://
the means, ...
www2.mmm.ucar.edu/wrf/users/docs/user_guide_V3/users_guide_chap5.htm#_Description_of_Namelist WRF users web page])
* <PRE>phys/module_diagvar_cordex.F</PRE>: Module with the computation of all the variables
This module is accompanied with a new <PRE>Registry/registry.cordex</PRE> where the variables and a new section
in the <PRE>namelist.inpt</PRE> labeled cordex are defined. There are other necessary complementary modifications on
<PRE>phys/module_diagnostics_driver.F</PRE> encompassed by the pre-compilaton flag <PRE>CORDEXDIAG</PRE>, as well some modifications in the <PRE>main/depend.common</PRE> and <PRE>phys/Makefile</PRE>.
Output is provided by the auxiliary history output <PRE>#9</PRE> with a provisional file name: <PRE>wrfcordex_d<domain>_<date></PRE>
All that variables which are only required at output time step, are computed only at that exact time.


=== Additional: pressure levels interpolation ===
<PRE>
4. output_diagnostics = 1 in &time_control. Climate diagnostics. This option outputs 36 surface diagnostic variables:
maximum and minimum, times when max and min occur, mean value, standard deviation of the mean for T2, Q2, TSK, U10,
V10, 10 m wind speed, RAINCV, RAINNCV (the last two are time-step rain). The output goes to auxiliary output stream 3,
and hence it needs the following:


At the same time, WRF can output on pressure levels while integration. However, initial version of the module does
auxhist3_outname = “wrfxtrm_d<domain>_<date>”
not include required CORDEX variables: <PRE>wa</PRE> (vertical wind speed) and <PRE>hus</PRE> (specific humidity). Thus, code has also been modified and now, WRF output at pressure levels also provides wa and hus.
auxhist3_interval = 1440, 1440,
It has been accomplished after modifying the codes: <PRE>Registry/registry.diags</PRE>, <PRE>phys/module_diagnostics_driver.F</PRE>, <PRE>phys/module_diag_pld.F</PRE> and <PRE>dyn_em/start_em.F</PRE>. The three latest modifications are also encapsulated within precompilation flag <PRE>CORDEXDIAG</PRE>.
frames_per_auxhist3 = 100, 100,
See more details in how to activate this option in [WRF users http://www2.mmm.ucar.edu/wrf/users/docs/user_guide_V3/users_guide_chap5.htm#_Description_of_Namelist] web-page over the namelist section <PRE>diags&</PRE>.
io_form_auxhist3 = 2
</PRE>


=== Additional: water budget ===
In this page [[CDXWRFevolution]] one founds updates, bug fixes of the module.
It has been added also the components of the atmospheric water budget. They are accumulated internally and vertically
integrated allover the column. In order to provide this capability, a series of modifications have been introduced in
<PRE>dyn_em/solve_em.F</PRE>


== Installation ==
With this module, now all CORDEX variables (except `snow melt') are available with the files wrfxtrm, wrfpress and wrfcdx, except for the fied values such as 'areacella'. See [[CDXvariablestable]] for more detail


These steps must be followed prior the re-compilation of the WRF model and assuming that the process is started
= CORDEX requirements =
where the code resides (WRFV3)


# Untar the file
CORDEX requirements of data must cover all the possible needs of stake holders, and scientists working on the adaptation and mitigation strategies. They are grouped in different levels of frequency and priority. A working copy of this list is available [https://www.hymex.org/cordexfps-convection/wiki/doku.php?id=protocol here] from the CORDEX convection permitting Flag Ship Pilot study.
$ tar xvfz WRF_CORDEX.tar.gz
# It deflates all the required files and the modified orignal WRF files
main/depend.common
dyn_em/solve_em.F
dyn_em/start_em.F
phys/module_diagnostics_driver.F
phys/module_diag_cordex.F
phys/module_diagvar_cordex.F
phys/module_diag_pld.F
phys/Makefile
README.cordex
Registry/registry.cordex
Registry/registry.diags
# On the <PRE>Registry/Registry.EM</PRE> add the following line (after the line with include <PRE>registry.new3d_wif</PRE>)
include registry.cordex
# Clean the code (in order to avoid to run again configure one can make a copy of the <PRE>configure.wrf</PRE> and recover it after the clean, otherwise it is erased)
$ cp configure.wrf configure.cordex.wrf
$ ./clean -a
$ cp configure.cordex.wrf configure.wrf
# edit the <PRE>`configure.wrf'</PRE> and add the line (after the line <PRE>-DNETCDF</PRE>)
-DCORDEXDIAG
# compile as always
$ ./compile em_real >& compile.log


== Usage ==
Some of the variables are not directly computed in the WRF model which require to extend the model output in order to provide enough variables to post-process the variables.


These are the steps to use the module
The implementation of the <CODE>module_diag_cordex</CODE> module should allow to avoid the post-processing by computing the CORDEX-required (Core & Tier) variables during model integration. At the same time, some extra variables, which might be of interest to the community but not required by CORDEX, have also been added.
# One need to add to the <PRE>'namelist.input'</PRE> the auxiliar output number 9 (e.g. for output every 3 hours and
1-day files) at the <PRE>`&history'</PRE> section:
auxhist9_outname = "wrfcdx_d<domain>_<date>"
auxhist9_interval = 180, 180,
frames_per_auxhist9 = 8, 8,
io_form_auxhist9 = 2
# Also a new section should be added (assuming it will get complex and different implementations of the diagnostics
might be necessary...)
&cordex
output_cordex = 1
psl_diag = 1: sea-level pressure diagnostic following hydrostatic Shuell correction
        = 2: psl diagnostic following a target pressure
        = 3: psl diagnostic following ECMWF method (default)
psmooth  = 5: passes of neighborgh filtering (3x3-grid point mean) of psfc for psl_diag=2 (default 5)
ptarget  = 70000.: pressure [Pa] target to be used by psl_diag=2 (default 70000.)
wsgs_diag = 1: wind-gust diagnostic following Brasseur, 2001, MWR (default)
          = 2: wsgs folllowing heavy precipitation method
wsz100_diag = 1: wind extraoplation at z100m_wind using power-law method (default)
            = 2: wind extraoplation at z100m_wind using logarithmic method
            = 3: wind extraoplation at z100m_wind using Monin-Obukhov theory (NOT activated)
z100_wind  = 100.: height to extraplate winds (100. default)
zmlagen_dqv = 0.1: percentage of variation of mixing ratio to determine mixed layer depth used in zmla computation (0.1 default)
zmlagen_dtheta = 1.5: increment in K of potantial temperature from its minimum within the MLD used in zmla computation (1.5 default)
potevap_diag = 1: potential evapotranspiration following Penman-Monteith formulation after ORCHIDEE implementation
/


'''NOTE: '''
<PRE>Be aware that any systematic checking process has been applied to this module. Use it and the
variables therein at your own risk !! It has been tested on a 2-nested domain configuration with the
inner domain at cloud resolving resolution (< 5 km, without cumulus scheme), making use of restarts
and on serial, pure distributed memory and hybrid distributed/shared parallel environment
</PRE>


=== Pressure interpolation ===
= module_diag_cordex =
Remember to activate section <PRE>&diags</PRE> in order to get pressure-level vertical interpolation of state variables (g.e.: assuming 6 levels only and output every 3 hours)
&time_control
(...)
auxhist23_outname="wrfpress_d<domain>_<date>"
io_form_auxhist23 = 2,
auxhist23_interval = 180, 180,
frames_per_auxhist23 = 100, 100,
(...)
/
(...)
&diags
p_lev_diags = 1,
num_press_levels = 6,
press_levels = 100000, 92500, 85000, 70000, 50000, 20000
use_tot_or_hyd_p = 1
p_lev_missing = -999.
/


The module is basically based on two modules:
* <CODE>phys/module_diag_cordex.F</CODE>: Main module which manages the calls to the variables and the accumulations for the means, ...
* <CODE>phys/module_diagvar_cordex.F</CODE>: Module with the computation of all the variables
This module is accompanied with a new <CODE>Registry/registry.cordex</CODE> where the variables and a new section
in the <CODE>namelist.input</CODE> labeled cordex are defined. There are other necessary complementary modifications on
<CODE>phys/module_diagnostics_driver.F</CODE> encompassed by the pre-compilaton flag <CODE>CORDEXDIAG</CODE>, as well some modifications in the <CODE>main/depend.common</CODE> and <CODE>phys/Makefile</CODE>.
Output is provided by the auxiliary history output <CODE>#9</CODE> with a provisional file name: <CODE>wrfcordex_d<domain>_<date></CODE>
All that variables which are only required at output time step, are computed only at that exact time.


== Variables ==
Description of the installation process can be found here [[CDXWRFinstall]]
 
These are the different variables added and their implementations from the WRF point of view. There might be necessary to revise some of them, or even decide which version to use In case of accumulation/mean they are also be included
 
These variables are:
* Instantaneous diagnostics (only computed on output times)
*:- prw: Total water path
– clwvi: Total liquid water path (QCLOUD + QRAIN)
– clivi: Total ice water path (QSNOW+QICE+GRAUPEL+QHAIL)
– ua: 3D earth-rotated eastward wind [ms-1]
– va: 3D earth-rotated northward wind [ms-1]
– ws: 3D wind speed [ms-1]
– ta: 3D air-temperature [K]
– press: 3D air pressure [Pa]
– zg: 3D geopotential height [m]
– hur: 3D relative humidty [1]
– hus: 3D specific humidty [1]
– uas: 10m earth-rotated eastward wind [ms-1]
– vas: 10m earth-rotated northward wind [ms-1]
– wss: 10m wind speed [ms-1]
– hurs: 2m relative humidty [1]
– huss: 2m specific humidty [1]
– psl: sea level pressure [Pa] (three different ways)
– cape: Convective Available Potential Energy [Jkg-1]
– cin: Convective inhibition [Jkg-1]
– zlfc: Height at the Level of free convection [m]
– plfc: Pressure at the Level of free convection [Pa]
– li: Lifted index [1]
– mrso: total soil moisture content [kgm-2]
– slw: total liquid water content [kgm-2]
– zmla: pbl height following a generic method [m]
– ws100: 100m wind speed [ms-1]
– uz100: 100m wind x-direction [ms-1]
– vz100: 100m wind y-direction [ms-1]
– tauu, tauuv: components of the downward wind stress at 10 m [m2s-2]
– cdgen: generic drag coefficient [-]
• Accumulated or similar time dependency (computed at every time-step). They are initialized after each output
time-step. Thus, they represent statistics (mean, accumulation) only from between output time-steps.
– clt: total cloud cover [1]1
1 NOTE: CLDFRAC is computed by the radiative scheme thus, bear in mind to configure the namelist.input that: auxhist9_interval
> radt otherwise one obtains repeated values of clt, cll, clm, clh


Description of the usage of the model can be found here [[CDXWRFuse]]


CORDEX variables in WRF
Description of the additional pressure level interpolation variables can be found here [[CDXWRFpvars]]


9
Description of the `Core' variables can be found here [[CDXWRFcore]]


– cll: low-level cloud cover [1]
Description of the `Tier1' variables can be found here [[CDXWRFtier]]
– clm: mid-level cloud cover [1]
– clh: high-level cloud cover [1]
– cltmean: mean clt
– cllmean: mean cll
– clmmean: mean clm
– clhmean: mean clh
– wsgsmax: maximum surface wind gust [ms-1] (two different methods)
– ugsmax: eastward maximum surface gust wind direction [ms-1]
– vgsmax: northward maximum surface gust wind direction [ms-1]
– wsgspercen: percentage of times when grid point got gust wind [%]
– totwsgsmax: maximum surface wind gust [ms-1] (addition of different methods)
– totugsmax: eastward maximum surface gust wind direction [ms-1]
– totvgsmax: northward maximum surface gust wind direction [ms-1]
– totwsgspercen: percentage of times when grid point got total gust wind [%]
– wsz100max: maximum 100m wind [ms-1] (two different methods)
– uz100max: eastward maximum 100m wind direction [ms-1]
– vz100max: northward maximum 100m wind direction [ms-1]
– sund: sunshine length [s]
– rsds: mean surface Downwelling Shortwave Radiation [Wm-2]
– rlds: mean surface Downwelling Longwave Radiation [Wm-2]
– hfls: mean surface Upward Latent Heat Flux [Wm-2]
– hfss: mean surface Upward Sensible Heat Flux [Wm-2]
– rsus: mean surface Upwelling Shortwave Radiation [Wm-2]
– rlus: mean surface Upwelling Longwave Radiation [Wm-2]
– evspsbl: mean evaporation [kgm-2s-1]
– evspsblpot: mean potential evapotranspiration [kgm-2s-1]
– snc: mean snow area fraction [
– snd: mean snow depth [m]
– mrros: mean surface Runoff [kgm-2s-1]
– mrro: mean total Runoff [kgm-2s-1]
– mrsol: mean total water content of soil layer [kgm-2]
– pr: precipitation flux [kgm-2s-1]
– prl: large scale precipitation flux [kgm-2s-1]
– prc: convective precipitation flux [kgm-2s-1]
– snw: accumulated snow [ksm-2]
– Additionally added referred to the water budget in the atmosphere (not required by CORDEX):
∗ wbacdiabh: Water-budget vertically integrated accumulated of diabatic heating from microphysics [K]
∗ wbacpw, wbacpw[c/r/s/i/g/h]: Water-budget vertically integrated accumulated total tendency for
water vapour, cloud, rain, snow, ice, graupel, hail [mm]
∗ wbacf, wbacf[c/r/s/i/g/h]: Water-budget vertically integrated accumulated horizontal advection
for water vapour, cloud, rain, snow, ice, graupel, hail [mm]


Description of the `Additional' variables can be found here [[CDXWRFadditional]]


CORDEX variables in WRF
Description of the studies about optimization of the module can be found here [[CDXWRFopt]]


10
= Variables =


∗ wbacz, wbacz[c/r/s/i/g/h]: Water-budget vertically integrated accumulated vertical advection for
These are the different variables added and their implementations from the WRF point of view. There might be necessary to revise some of them, or even decide which version to use In case of accumulation/mean they are also be included
water vapour, cloud, rain, snow, ice, graupel, hail [mm]
∗ wbacdiabh{l/m/h}: Water-budget vertically integrated accumulated of diabatic heating from microphysics at low, medium and high levels (same as cloudiness) [K]
∗ wbacpw[v/c/r/s/i/g/h]{l/m/h}: Water-budget vertically integrated accumulated total tendency for
water vapour, cloud, rain, snow, ice, graupel, hail at low, medium and high levels (same as cloudiness)
[mm]
∗ wbacf[v/c/r/s/i/g/h]{l/m/h}: Water-budget vertically integrated accumulated horizontal advection for water vapour, cloud, rain, snow, ice, graupel, hail at low, medium and high levels (same as
cloudiness) [mm]
∗ wbacz[v/c/r/s/i/g/h]{l/m/h}: Water-budget vertically integrated accumulated vertical advection
for water vapour, cloud, rain, snow, ice, graupel, hail at low, medium and high levels (same as cloudiness) [mm]
• Pressure interplation
– hus_pl: specific humidity [1]
– w_pl: vertical wind speed [ms-1]


3.1
These variables are:
 
* Instantaneous diagnostics (only computed on output times)
clt: total cloudiness
** Core
 
*:- <CODE>prw:</CODE> Total water path
This variable computes the total cloudiness above a grid point taking as input the cloud fraction of a given grid cell
*:- <CODE>clwvi:</CODE> Total liquid water path (QCLOUD + QRAIN)
and level.
*:- <CODE>clivi:</CODE> Total ice water path (QSNOW+QICE+GRAUPEL+QHAIL)
NOTE:
*:- <CODE>uas:</CODE> 10m earth-rotated eastward wind [ms-1]
cloud fraction in WRF is computed by the radiative scheme, which is called at a frequency given by
*:- <CODE>vas:</CODE> 10m earth-rotated northward wind [ms-1]
radt. It should be taking into account when one gets any accumulation of any value retrieved from
*:- <CODE>wss:</CODE> 10m wind speed [ms-1]
it. Otherwise, one could compute the cloud fraction at every time-step (using any of the subroutines
*:- <CODE>hurs:</CODE> 2m relative humidty [1]
from module_radiation_driver.F: cal_cldfra1, cal_cldfra2, cal_cldfra3), but then it will not
*:- <CODE>huss:</CODE> 2m specific humidty [1]
be consistent in what was already considered whilst model integration
*:- <CODE>ws100:</CODE> 100m wind speed [ms-1]
The most common implementation assumes ‘random overlapping’ and its implemented in most of the global climate
*:- <CODE>uz100:</CODE> 100m wind x-direction [ms-1]
models. Here is considered to take the implementation from the GCM LMDZ (http://lmdz.lmd.jussieu.fr/?set_
*:- <CODE>vz100:</CODE> 100m wind y-direction [ms-1]
language=en{} Hourdin et al., 2006). Calculation of the total cloudiness is done inside the subroutine newmicro.f90.
*:- <CODE>tauu, tauuv:</CODE> components of the downward wind stress at 10 m [m2s-2] (might be zero if sf_sfclay_physics /= 1, 5)
Specific variable computation has already been extracted and implemented as a subroutine for the python utils
*:- <CODE>tauugen, tauuvgen:</CODE> generic components of the downward wind stress at 10 m [m2s-2]
PyNCplot (http://www.xn--llusfb-5va.cat/python/PyNCplot). The code is provided in the appendix A.1
*:- <CODE>cdcdx:</CODE> drag coefficient [-] (might be zero if sf_sfclay_physics /= 1, 5)
 
*:- <CODE>cdgen:</CODE> generic drag coefficient [-]
3.2
*:- <CODE>ps:</CODE> surface pressure [Pa]
 
*:- <CODE>psl:</CODE> sea level pressure [Pa] (three different ways)
cllmh: low, medium and high cloudiness
*:- <CODE>ts:</CODE> skin temperature [K]
 
*:- <CODE>zeroith:</CODE> 0-isotherm [m]
This variable computes the total cloudiness above a grid point at different vertical intervals (low: p ≥ 680hP a, medium:
*:- <CODE>mrsol:</CODE> moisture content of soil layer [kgm-2]
680 < p ≥ 400 hP a, high: p < 400 HP a) taking as input the cloud fraction of a given grid cell.
*:- <CODE>mrsos:</CODE> first layer soil moisture content (0-10 cm) [kgm-2]
As in the case of the ‘clt’ calculation from LMDZ has already been implemented as an independent subroutine.
*:- <CODE>mrso:</CODE> total soil moisture content [kgm-2]
See appendic B.1 for a snapshot of the code. See in figure 1 the result of the implementation
*:- <CODE>mrsll:</CODE> liquid water content of soil layer [kgm-2]
 
*:- <CODE>mrlso:</CODE> total liquid water content of soil layer [kgm-2]
3.3
*:- <CODE>mrlsos:</CODE> liquid water content in Upper Portion of soil column (0-10cm) [kgm-2]
 
*:- <CODE>mrsfl:</CODE> frozen water content of soil layer [kgm-2]
wsgsmax: Maximum Near-Surface Wind Speed of Gust
*:- <CODE>mrfso:</CODE> total frozen water content of soil layer [kgm-2]
 
*:- <CODE>mrfsos:</CODE> frozen water content in Upper Portion of soil column (0-10cm) [kgm-2]
The wind gust accounts for the wind from upper levels that is projected to the surface due to instability within the
*:- <CODE>hus_pl:</CODE> Pressure level data, Specific humidity [1]
boundary layer. It can have different implementations. Winds are Earth-rotated.
*:- <CODE>w_pl:</CODE> Pressure level data, W wind [ms-1]
• Brasseur01: An implementation of a wind gust following Turbuelent Kinetic Energy (T KE) estimates and stability by virtual temperature (θv , see mainly equation 1) reproducing Brasseur (2001) from the clWRF (clWRF,
*:- <CODE>uer_pl:</CODE> Pressure level data, U wind Earth-Rotated [ms-1]
http://www.meteo.unican.es/wiki/cordexwrf/SoftwareTools/ClWrf Fita et al., 2010) [wsgs_diag = 1]
*:- <CODE>ver_pl:</CODE> Pressure level data, V wind Earth-Rotated [ms-1]
Z zp
*:- <CODE>ws_pl:</CODE> Pressure level data, wind speed [ms-1]
Z zp
*:- <CODE>qc_pl:</CODE> Pressure level data, cloud mixing ratio [kgkg-1]
1
*:- <CODE>qr_pl:</CODE> Pressure level data, rain mixing ratio [kgkg-1]
∆θv (z)
*:- <CODE>qs_pl:</CODE> Pressure level data, snow mixing ratio [kgkg-1]
T KE(z)dz ≥
*:- <CODE>qi_pl:</CODE> Pressure level data, ice mixing ratio [kgkg-1]
g
*:- <CODE>qg_pl:</CODE> Pressure level data, graupel mixing ratio [kgkg-1]
dz
*:- <CODE>qh_pl:</CODE> Pressure level data, hail mixing ratio [kgkg-1]
(1)
*:- <CODE>qv_pl_mc:</CODE> mass-conservative pressure level data, water vapour mixing ratio [kgkg-1]
zp 0
*:- <CODE>qc_pl_mc:</CODE> mass-conservative pressure level data, cloud mixing ratio [kgkg-1]
Θv (z)
*:- <CODE>qr_pl_mc:</CODE> mass-conservative pressure level data, rain mixing ratio [kgkg-1]
0
*:- <CODE>qs_pl_mc:</CODE> mass-conservative pressure level data, snow mixing ratio [kgkg-1]
 
*:- <CODE>qi_pl_mc:</CODE> mass-conservative pressure level data, ice mixing ratio [kgkg-1]
 
*:- <CODE>qg_pl_mc:</CODE> mass-conservative pressure level data, graupel mixing ratio [kgkg-1]
CORDEX variables in WRF
*:- <CODE>qh_pl_mc:</CODE> mass-conservative pressure level data, hail mixing ratio [kgkg-1]
 
11
 
Figure 1: Vertical distribution of cloud fraction and the different cloud types at a given point (top left): cloud fraction
(cldf ra, full circles with line in blue), mean total cloud fraction (cltmean, vertical dashed line), mean low-level cloud
fraction (cllmean p ≥ 680 hP a, dark green hexagon), mean mid-level (clmmean 680 < p ≥ 440 hP a, green hexagon),
mean high-level (clhmean p < 440 hP a, clear green hexagon). Temporal evolution of cloud types at the given point
(top right). Map of cltmean with colored topography beneath to show-up cloud extent (middle middle), map of
clhmean (middle right), map of clmmean (bottom middle) and map of cllmean (bottom right)
 
 
12
 
CORDEX variables in WRF
 
• WRF afwa diagnostics: Inside the WRF module module_diag_afwa.F there is an implementation of the calculation of the wind gust which only occurrs as a blending of upper-level winds (around 1km above ground zagl;
−1
zagl(k1000 ) ≥ 1000 m, see equation 2) above a given maximum precipitation inrensity of pratemm
hr ≥ 50 mmh
(see the code in appendix C.1) [wsgs_diag = 2]
va
~ 1km
 
= va(k
~ 1000 − 1) + [1000 − zagl(k1000 − 1)]
 
γ
 
=
 
va
~ blend
 
=
 
va(k
~ 1000 ) − va(k
~ 1000 − 1)
zagl(k1000 )
 
150 − pratemm
hr
100
vasγ
~ + va
~ 1km × (1 − γ)
 
(2)
 
These two methodologies have been implemented and can be switched by a new namelist.input parameter labeled
wsgs_diag (in cordex section). Its default value is 1
It comes out, that both methodologies provide wind gust estimation (WGE) from two different perspectives:
mechanic and convective. In order to take into account both winds gusts, another variable as the addition of both
estimations is provided as totwsgsmax, totugsmax, totvgsmax, totwsgspercen. On figure 2 is shown the different
outcomes applying each approximation
 
3.4
 
wsgsmax100: Daily Maximum Near-Surface Wind Speed of Gust at 100 m
 
The wind gust at 100 m is understood that should follow a similar implementation than for the wsgsmax, but at 100
m, since is understood than an extrapolation of such turbulent phenomena it would require a complete new set of
equations. This one is let to open discussion.
Instead as a way to overcome it, the estimation of maximum wind speed at 100 m is provided. Winds are Earthrotated. After PhD thesis of Jourdier (2015), two different methodologies are implemented to estimate the wind at
100 m above ground:
• Following power-law wind vertical distribution, as it is depicted in equation 3 using the upper-level atmospheric
<
>
wind speed below (k100
) and above (k100
) the height above ground of 100 m (zagl) [wsz100_diag = 1]
#αx,y
#
100.
>
(3)
va
~ 100 = va(k
~ 100
)
>
zagl(k100
)
>
<
ln(va(k
~ 100
)) − ln(va(k
~ 100
))
αx,y =
>
<
ln(zagl(k100 )) − ln(zagl(k100
))
• Following logarithmic-law wind vertical distribution, as it is depicted in equation 4 using upper-level atmospheric
<
>
wind speed below (k100
) and above (k100
) the height above ground of 100 m (zagl) [wsz100_diag = 2]
ln(z0 )
va
~ 100
 
>
<
<
>
va(k
~ 100
) ln(zagl(k100
)) − va(k
~ 100
) ln(zagl(k100
))
>
<
~ 100 )
va(k
~ 100 ) − va(k
ln(100.) − ln(z0 )
>
= va(k
~ 100
)
>
ln(zagl(k100
)) − ln(z0 )
 
=
 
(4)
 
• Following Monin-Obukhov theory is implemented and was tested, but it is not useful for heights larger than few
decameters (z > 80. m). However, the necessary code to extrapolate the wind at given height is left commented
just in case someone wants to use it.
These two methodologies have been implemented and can be switched by a new namelist.input parameter labeled
wsz100_diag (in cordex section). Its default value is 1. Even one can select another height for the estimation by
providing the new parameter z100m_wind with a different value than 100 m (default value)
On figure 3 is shown the different outcomes applying each approximation. There are some problems on MoninObukhov application under certain stable conditions (too small Obukhov length)
 
 
CORDEX variables in WRF
 
13
 
Figure 2: near surface wind gust estimates. 3h-maximum total wind gust strength (wsgsmaxtot , top left), percentage
of wsgsmaxtot due to Brasseur’s application (wsgsmaxb01 , top middle), percentage due to AFWA-heavy precipitation
implementation (wsgsmaxhp , top right), percentage of time-steps where grid point got total wind gust (bottom left),
percentage of time-steps where grid point got wsgsmaxb01 (bottom middle), percentage due to wsgsmaxhp (bottom
right)
 
 
CORDEX variables in WRF
 
14
 
Figure 3: 100 m wind estimates. Comparison between upper-level winds and estimation at a given point and moment
(upper left): 3h-maximum eastward wind (red) at 100 m by power-law (uzmaxpl , star), Monin-Obukhov theory
(uzmaxmo , cross) by logarithmic law (uzmaxll , sum) 10-m wind value (uas, filled triangle) and upper-level winds
(ua, filled circles with line), also for the northward component (green). Temporal evolution of wind speed (top right)
with all approximations and upper-level winds at the closest vertical level at 100 m (on log-y scale). Maps of both
estimations (bottom left and middle) with the blue cross showing the point of previous figures. Wind rose at the given
point (bottom right)
 
 
15
 
CORDEX variables in WRF
 
Figure 4: On a given point (left): water path (prw, vertical straight line), vertical profile of water vapour (qv, line
with full circles), water pat at each level (line with crosses). Map of water path (right), red cross shows where the
vertical is retrieved
 
3.5
 
prw: precipitable water or water vapor path
 
This variable accounts for the column integrated amount of water vapor.
This one is already implemented in a old WRF tool for vertical interpolation called p_interp.F. It was modified
by L. Fita when he was as post-doc at the ‘Universidad de Cantabria’ related to the clWRF. The general equation
following WRF standard variables as:
prw =
 
e_vert
mu + mub X
QV AP OR[iz](dnw[iz + 1] − dnw[iz])
g
iz=1
 
(5)
 
where mu: perturbation dry air mass in column, mub: base-state dry air mass in column, g: gravity, e_vert: total
number of vertical levels, qvapor: mixing ratio of water vapour, dnw: full-sigma eta-layer height. See an example on
figure 4
 
3.6
 
clwvi: condensed water path
 
This variable provides similar information, but for the liquid condensed water species. It is the same calculation as in
5, but replacing QV AP OR by QCLOU D + QRAIN
 
3.7
 
clivi: ice water path
 
This variable provides similar information, but for the liquid condensed water species. It is the same calculation as in
5, but replacing QV AP OR by QICE + QSN OW + QGRAU P EL + QHAIL
 
3.8
 
clgvi: graupel water path
 
This variable provides similar information, but for the liquid condensed water species. It is the same calculation as in
5, but replacing QV AP OR by QGRAU P EL
 
 
16
 
CORDEX variables in WRF
 
3.9
 
clhvi: hail water path
 
This variable provides similar information, but for the liquid condensed water species. It is the same calculation as in
5, but replacing QV AP OR by QHAIL
 
3.10
 
psl: sea level pressure
 
This accounts for the pressure at the sea level (extrapolation of the pressure at the level of the sea). That means the
pressure that might be without the presence of orography.
Three different methodologies have been implemented
• One using hydrostatic-Shuell method already implemented in the the module phys/module_diag_afwa.F (assuming a constant lapse-rate of 6.5 ◦ km−1 , see appendix D.1) [psl_diag = 1]
• Using smoothed surface pressure and a target upper-level pressure, already implemented in p_interp.F90 (see
appendix D.3) [psl_diag = 2]
• ECMWF method taken from LMDZ from the module pppmer.F90, following the methodology by Mats Hamrud
and Philippe Courtier from ECMWF (see appendix D.2) [psl_diag = 3]
These three methodologies have been implemented and can be switched by a new namelist.input parameter
labeled psl_diag (in cordex section). Its default value is 3. Even, on using the ‘ptarget’ method (psl_diag = 2) one
can select the degree of smoothing of the surface place by the selecting the number of times that the smoothing (as
the mean of the point and its surrounding 8 neighbors) has to be applied (psmooth, default 5) and the upper pressure
to be used as target (ptarget, default 70000 P a).
On figure 5 is shown the different outcomes applying each approximation. There are some problems with the
ptarget methodology in both psl estimate and borders for each parallel process on applying the smoothing
 
3.11
 
cape: convective available potential energy
 
This variable accounts for all the energy that convectively might be released.
From AMS glossary is described as: (http://glossary.ametsoc.org/wiki/Convective_available_potential_
energy)
On a thermodynamic diagram this is called positive area and can be seen as the region between the lifted
parcel process curve and the environmental sounding, from the parcel’s level of free convection to its level
of neutral buoyancy. CAPE may be expressed as follows:
Z pn
CAP E =
Rd (Tvp − Tve )d ln p
(6)
pf
 
where Tvp is the virtual temperature of a lifted parcel moving upward moist adiabatically from the level
of free convection to the level of neutral buoyancy, Tve is the virtual temperature of the environment, Rd
is the specific gas constant for dry air, pf is the pressure at the level of free convection, and pn is the
pressure at the level of neutral buoyancy. The value depends on whether the moist-adiabatic process is
considered to be reversible or irreversible (conventionally irreversible, or a pseudoadiabatic process in which
condensed water immediately falls out of the parcel) and whether the latent heat of freezing is considered
(conventionally not). It is assumed that the environment is in hydrostatic balance and that the pressure
of the parcel is the same as that of the environment. Virtual temperature is used for the parcel and
environment to account for the effect of moisture on air density.
It has been at this stage only the calculation already implemented in WRF inside the module module_diag_afwa.F
via the function Buoyancy, which at the same time it provides: Convective inhibition (CIN), Height at the Level of
free convection (ZLFC), Pressure at the Level of free convection (PLFC) and Lifted index (LI)
 
 
CORDEX variables in WRF
 
17
 
Figure 5: sea level pressure estimates. Following hydrostatic-Shuell method at a given time-step (pslshuell , upper left),
p-target (pslptarget , upper middle) and ECMWF (pslecmwf , upper right). Differences between methods pslshuell −
pslptarget (bottom left), pslshuell − pslecmwf (bottom middle) and pslptarget − pslecmwf (bottom right)
 
 
18
 
CORDEX variables in WRF
 
3.12
 
cin: convective inhibition
 
This variable accounts for the process which inhibits the convection. Already provided by the implementation of the
AFWA’s CAPE calculation
From AMS glossary is described as: http://glossary.ametsoc.org/wiki/Convective_inhibition)
The energy needed to lift an air parcel upward adiabatically to the lifting condensation level (LCL) and
then as a psuedoadiabatic process from the LCL to its level of free convection (LF C).
For an air parcel possessing positive CAP E, the CIN represents the negative area on a thermodynamic
diagram. The negative area typically arises from the presence of a lid, or the amount of kinetic energy
that must be added to a parcel to enable that parcel to reach the LF C. Even though other factors may be
favorable for development of convection, if convective inhibition is sufficiently large, deep convection will
not form. The convective inhibition is expressed (analogously to CAP E) as follows:
Z
 
pf
 
CIN = −
 
Rd (Tvp − Tve )d ln p
 
(7)
 
pi
 
where pi is the pressure at the level at which the parcel originates, pf is the pressure at the LF C, Rd
is the specific gas constant for dry air, Tvp is the virtual temperature of the lifted parcel, and Tve is the
virtual temperature of the environment. It is assumed that the environment is in hydrostatic balance and
that the pressure of the parcel is the same as that of the environment. Virtual temperature is used for the
parcel and environment to account for the effect of moisture on air density.
 
3.13
 
sund: duration of sunshine
 
This variable accounts for the time where short-wave radiation is above 120 W m−2 .
It is already implemented in a advance version of the clWRF http://www.meteo.unican.es/wiki/cordexwrf/
SoftwareTools/ClWrf. But here will directly computed using XIOS (http://forge.ipsl.jussieu.fr/ioserver/)
See results of the variable in figure 6
 
3.14
 
hur: relative humidity
 
Relative humidity can be obtained following the Clausius-Clapeyron formula and its approximation from the AugustRoche-Magnus formula of saturated water vapor pressure es
17.625∗tempC
 
es = 6.1094 ∗ e tempC+243.04
0.622 ∗ es
ws =
presshP a − es
q
hur =
ws ∗ 1000.
 
(8)
(9)
(10)
 
being tempC: temperature in Celsius degree (◦ C), presshP a: pressure in hP a, es : saturated water vapor pressure,
ws : saturated mixing ratio kgkg −1 , q: mixing ratio kgkg −1
 
3.15
 
hus: specific humidity
 
From the AMS glossary http://glossary.ametsoc.org/wiki/Specific_humidity
q=
where rv : mixing ratio
 
rv
rv + 1
 
(11)
 
 
CORDEX variables in WRF
 
19
 
Figure 6: Temporal evolution (left) of shortwave downward radiation (swdown, red line, left y-axis) and sunshine
duration (sund, stars, right y-axis. sund map at a given time (right))
 
 
20
 
CORDEX variables in WRF
 
3.16
 
zg: geopotential height
(12)
 
zg = P H + P HB
where P HB, WRF base geopotential height, P , WRF perturbation geopotential height
 
3.17
 
press: air-pressure
(13)
 
press = P + P H
where P B, WRF base pressure, P , WRF perturbation pressure
 
3.18
 
ta: air-temperature
#
ta = (T + 300)
 
P + PB
p0
 
#R/Cp
 
(14)
 
where T , WRF temperature (which is as potential temperature), P B, WRF base pressure, P , WRF perturbation
pressure, p0: pressure reference 100000 P a
 
3.19
 
ua/va: air-wind Earth oriented
#
 
ua = Uunstg ∗ COSALP HA − Vunstg ∗ SIN ALP HA
va = Uunstg ∗ SIN ALP HA + Vunstg ∗ COSALP HA
 
(15)
 
where Uunstg , unstaggered WRF eastward wind, Vunstg , unstaggered WRF northward wind, COSALP HA, local
cosine of map rotation, SIN ALP HA, local sine of map rotation
 
3.20
 
cdgen
 
Drag coefficient at surface. Computation of drag coefficient depends on selected surface scheme. In order to avoid this
scheme dependency, a general calculation of the coefficient has been introduced as it is shown in equation 16, after
Garratt (1992).
#
Cd =
 
u∗
wss
 
#2
 
(16)
 
Being, u∗ : from similarity theory, wss 10 m wind speed
 
3.21
 
tauuv
 
Surface Downdward wind stress at 10m.
It is implemented following the equation 17, begin CD drag coefficient. Winds are Earth-rotated. The generic drag
coefficient cdgen is used to compute these variables.
tauv = CD uas2 , CD vas2
 
#
 
(17)
 
 
21
 
CORDEX variables in WRF
 
3.22
 
evspsblpot
 
Potential evapotranspiration is computed following its computation from ORCHIDEE model (Organising Carbon
and Hydrology In Dynamic Ecosystems, http://orchidee.ipsl.fr/). The implementation is retrieved from the
module src_sechiba/enerbil.f90 and basically consists no an implementation of the Penman-Monteith formulation
(Monteith, 1965). It is a simple formulation (see equation 18)
potevap = ρ(1) ∗ qc ∗ (q2sat − qv(1))
p
qc = Cd uas2 + vas2
 
(18)
(19)
 
where qc: surface drag coefficient, q2sat : Saturated air at 2m (can be assumed to be q2 == qsf c?), uas, vas: 10 m
wind components.
Up to now there is only one implementation and it is selected via namelist parameter potevap_diag, up to now
only with value 1 for the ORCHIDEE implementation
 
3.23
 
rsus
 
Surface Upwelling Shortwave Radiation, is understood as the shortwave radiation from land. It is provided accumulated
by radiation schemes CAM and RRTMG (sw_ra_scheme = 3,4) in variable swupb. However, it might be re-calculated
(if necessary) in a generic way as the reflected shortwave radiation due to albedo as it is shown in equation 20
rsus = −alebdo ∗ swdown
 
(20)
 
Being, albedo: albedo, sdown: downward at surface shortwave radiation
 
3.24
 
rlus
 
Surface Upwelling Longwave Radiation, is understood as the longwave radiation from land. It is provided accumulated
by radiation schemes CAM and RRTMG (sw_ra_scheme = 3,4) in variable slupb. However, it might be re-calculated
(if necessary) in a generic way as the longwave radiation due to surface temperature following black body formulation
as it is shown in equation 21
rlus = CtBoltzxman ∗ skt4
Being, CtBoltzman: albedo, skt: skin temperature
 
(21)
 
 
22
 
CORDEX variables in WRF
 
4
 
Additional variables
 
Some other variables not required by CORDEX, but might be interesting for other purposes will be also added
 
4.1
 
Water vapor balance terms
 
These covers the different column integrated terms of the water balance equation. The equation of the water vapour
budget:
T ENq
∂qq
∂t
 
= HORq + V ERq + M Pq
~ q − w ∂qq + SOq − SIq
= −Vh ∇q
∂z
 
(22)
 
Where q stands for either of the five water species concentration (vapor, snow, ice, rain and liquid), V h stands
for horizontal wind speed, w stands for the vertical wind speed and M P for the loss or gain of water due to cloud
microphysical processes. The term in the left-hand side of the equation represents the water species tendency (T EN
or ‘PW’), referring to the difference between q at the model previous time step and at the end of the actual time step,
divided by the time step. T EN equals to the horizontal advection (HOR or ‘F’, first term in right-hand side of the
equation), the vertical advection (V ER or ‘Z’, second term in right-hand side) and the sources (SO) or sink (SI) of
atmospheric water due to microphysical processes (M P ). All terms are expressed in kgkg −1 s−1 . However, SO, and
SI ca not be provided because they are micro-physics dependent an make difficult to provide a general formula for
them.
In order to obtain the total column mass of water due to each term (in units of mm), it is applied to each term of
eq. 22 (similarly as in 5):
 
−
 
1
g
 
Z
 
ptop
 
dp
 
(23)
 
psf c
 
Following the methodology of Huang et al. (2014) and Yang et al. (2011), Fita and Flaounas (2017) implemented
the water budget terms in a new module in WRF in order to allow the computation of the terms during model
integration. For the CORDEX module, only the vertically integrated variables will be implemented. Microphysics
processes depends on the micro-physics scheme used during model run. It is know the the budget is closed, thus,
residual of the terms must be the micor-phsyics term. Due to the complexity of each micro-physics scheme and the
impossibility to generalize the calculation, the accumulation of diabatic heating from the micro-physics scheme is
provided as a proxy.
All water species decomposition is shown in figures 7 and 8
It has also been grouped by vertical levels as it is done with the clouds: p ≥ 68000 P a, 40000 ≤ p < 68000 P a,
p < 40000 P a. Decomposition of each term is shown for water vapour qv and snow in figures from 9 to 12.
 
 
CORDEX variables in WRF
 
23
 
Figure 7: Water budget 3h-accumulated vertically integrated total tendency ‘PW’ at a given time, for water vapour
(qv, top left), cloud (qc, top middle), rain (qr, top right), water condensed species (qc + qr, middle left), snow (qs,
middle middle), ice (qi, middle right), water solid species (qs + qi + qg, bottom left), graupel (qg, bottom middle), hail
(qh, bottom right). Number on low left corner of the figure correspond to the standard deviation (σ in mm) value
used for the normalization
 
 
CORDEX variables in WRF
 
24
 
Figure 8: As in 7, but for Water budget 3h-accumulated vertically integrated horizontal advection ‘F’ at a given time
 
 
CORDEX variables in WRF
 
25
 
Figure 9: Water budget evolution at a given point for water vapour of vertically integrated water-budget terms: total
tendency ‘PW’ (∂t qv, red), horizontal advection ‘F’ (advh qv, green), vertical advection ‘Z’ (advz qv, green), residual
PW - F -Z (res(∂t qv), gray dashed) and diabatic heating from micro-physics (Qd , pink) (top left), only high-level
vertically integrated values (p < 440 hP a, top right), high/mid/low-level (degree of color intensity) decomposition of
partialt qv (red) and Qd (pink) and their respective residuals as dashed lines (middle left), only mid-level vertically
integrated values (680 > p ≤ 440 hP a, middle right), high/mid/low-level (degree of color intensity) decomposition
of advh qv (green) and advz qv (blue) and their respective residuals as dashed lines (bottom left) and only low-level
vertically integrated values (p ≥ 680 hP a, bottom right)
 
 
CORDEX variables in WRF
 
26
 
Figure 10: water vapour water budget maps of each component and diabtic heating from micro-physics at a given
time and the percentual contribution at each different vertically integrated layer respective the total. total tendency
‘PW’ (∂t qv, first column), horizontal advection ‘F’ (advh qv, second col), vertical advection ‘Z’ (advz qv, third col.) and
diabatic heating from micro-physics (Qd , 4th col). Percentage contribution of high level (p < 440 hP a) integration
to the total (second row), percentage for mid level (680 > p ≥ 440 hP a) integration to the total (third row) and
percentage of low-level (p ≥ 680 hP a) integration (bottom row)
 
 
27
 
CORDEX variables in WRF
 
Figure 11: The same as in figure 9, but for snow
 
 
28
 
CORDEX variables in WRF
 
Figure 12: The same as in 10, bur for snow
 
 
CORDEX variables in WRF
 
4.2
 
29
 
zmlagen: generic boundary layer height
 
Boundary layer height is a clear example of model dependence and even scheme dependence of how a diagnostic is
computed. Each pbl scheme has its own assumptions and has to be compiled in a specific way.
However, one could try to find a general definition as it was done in (García-Díez et al., 2013) after (NielsenGammon et al., 2008). The method consists in searching for the first level where potential temperature exceeds the
minimum potential temperature reached in the mixed layer (ML) by more than 1.5 K. It has been implemented as it
is shown below
1. Mixed layer depth (kM LD ) first layer at which the variation of mixing ratio upwards from first layer value achieves
LD )−qv(1)|
> δqv (here applied a δqv = 0.1)
a given percentage: |qv(kMqv(1)
2. Minimum potential temperature within the MLD: θminM LD = min(θ(1), ..., θ(kM LD ))
3. Boundary layer level (kzmla ) first level where: θ(kzmla ) + δθ > θminM LD (here δθ = 1.5 K)
4. Boundary layer height (zmla) height above ground (zagl): zmla = zagl(kzmla )
Comparison of this implementation with the zmla directly provided by WRF’s pbl scheme is shown in figure 13.
No general rule has been applied to determine the correct value of δqv used to determine depth of mixed layer. They
can be determined by the namelist.input parameters zmlagen_dqv for δqv (default value 0.1) and zmlagen_dtheta
for δθ (default value 1.5 K)
 
 
CORDEX variables in WRF
 
30
 
Figure 13: Vertical characteristics of the atmosphere at a given point (top left): potential temperature vertical profile
(θ K, red line), vertical profile of mixing ratio (qv kgkg −1 , blue line), mixed layer depth (M LD, dashed horizontal
line at 323.522 m), derived boundary layer height (zmla, horizontal dashed line at 107.122 m and WRF derived pbl
scheme value (W RF zmla at 903.017 m). Comparison of temporal evolutions (top right) between derived zmla (yellow
stars) and WRF’s pbl scheme (blue line). Map of differences between derived and WRF simulated (zmla − zmlaW RF ,
bottom left), zmla map (bottom middle) and zmlaW RF (bottom right)
 
 
CORDEX variables in WRF
 
5
 
31
 
Work done
 
Following similar experiencies like clWRF, the implementation would be done as follows:
1. Introduce the new variables in the registry.cordex
2. Reproduce the structure of any of the diagnostics module (e.g. phys/module_diag_cl.F) and introduce each
computation from the different sources.
3. This accounts for a lot of additional variables, thus all the module related will be activated on computation by
a pre-compilation flag called DIAGCORDEX
4. Introduction of a new namelis.input section for that variables with more than one option
5. Output these variables in a new output file wrfcdx_d<domain>_<date>
6. As an additional work, all the instantaneous variables used for the different accumuluations and extremes, can
also be retrieved. It is only necessary to:
• Give an output unit on the registry.cordex (see instructions at the end of the file)
• Uncomment in the code (phys/module_diagnostics_dirver.F and module_diag_cordex.F), the commented lines with the key word: INSTVALS
• re-compile WRF
 
 
32
 
CORDEX variables in WRF


6
** Tier1 (CDXWRF=1)
*:- <CODE>zmla:</CODE> pbl height following a generic method [m]
*:- <CODE>clgvi:</CODE> Total graupel path (QGRAUPEL)
*:- <CODE>clhvi:</CODE> Total hail path (QHAIL)
*:- <CODE>colmax:</CODE> high-frequency maximum radar reflectivity in the column [dBz] (on auxhist18, wrfhfcdx)


Missing variables
** INSTVALS
Only if <CODE>INSTVALS</CODE> modifications are made in the code
*:- <CODE>cape:</CODE> Convective Available Potential Energy [Jkg-1]
*:- <CODE>cin:</CODE> Convective inhibition [Jkg-1]
*:- <CODE>zlfc:</CODE> Height at the Level of free convection [m]
*:- <CODE>plfc:</CODE> Pressure at the Level of free convection [Pa]
*:- <CODE>lidx:</CODE> Lifted index [1]


There are certain variables which could not be introduced (yet?)
** Additional (CDXWRF=2)
*:- <CODE>ua:</CODE> 3D earth-rotated eastward wind [ms-1]
*:- <CODE>va:</CODE> 3D earth-rotated northward wind [ms-1]
*:- <CODE>ws:</CODE> 3D wind speed [ms-1]
*:- <CODE>ta:</CODE> 3D air-temperature [K]
*:- <CODE>press:</CODE> 3D air pressure [Pa]
*:- <CODE>zg:</CODE> 3D geopotential height [m]
*:- <CODE>hur:</CODE> 3D relative humidty [1]
*:- <CODE>hus:</CODE> 3D specific humidty [1]


6.1
** Only via changes in the registry
'''NOTE:''' CLDFRAC is computed by the radiative scheme thus, bear in mind to configure the `namelist.input` that:
<PRE>
auxhist19_interval > radt
</PRE>


wsgsmax100: Daily Maximum Near-Surface Wind Speed of Gust at 100 m
*:- <CODE>clt:</CODE> total cloud cover [1]
*:- <CODE>cll:</CODE> low-level cloud cover [1]
*:- <CODE>clm:</CODE> mid-level cloud cover [1]
*:- <CODE>clh:</CODE> high-level cloud cover [1]
*:- <CODE>cape:</CODE> Convective Available Potential Energy [Jkg-1]
*:- <CODE>cin:</CODE> Convective inhibition [Jkg-1]
*:- <CODE>zlfc:</CODE> Height at the Level of free convection [m]
*:- <CODE>plfc:</CODE> Pressure at the Level of free convection [Pa]
*:- <CODE>li:</CODE> Lifted index [1]
*:- <CODE>tds:</CODE> 2m dew point temperature [K]


The wind gust at 100 m is understood that should follow a similar implementation than for the wsgsmax, but at 100
* Accumulated or similar time dependency (computed at every time-step). They are initialized after each output time-step. Thus, they represent statistics (mean, accumulation) only from between output time-steps.
m, since is understood than an extrapolation of such turbulent phenomena it would require a complete new set of
** Core
equations. This one is let to open discussion.
*:- <CODE>cltmean:</CODE> mean clt
*:- <CODE>cllmean:</CODE> mean cll
*:- <CODE>clmmean:</CODE> mean clm
*:- <CODE>clhmean:</CODE> mean clh
*:- <CODE>wsgsmax:</CODE> maximum surface wind gust [ms-1] (two different methods)
*:- <CODE>ugsmax:</CODE> eastward maximum surface gust wind direction [ms-1]
*:- <CODE>vgsmax:</CODE> northward maximum surface gust wind direction [ms-1]
*:- <CODE>wsgspercen:</CODE> percentage of times when grid point got gust wind [%]
*:- <CODE>totwsgsmax:</CODE> maximum surface wind gust [ms-1] (addition of different methods)
*:- <CODE>totugsmax:</CODE> eastward maximum surface gust wind direction [ms-1]
*:- <CODE>totvgsmax:</CODE> northward maximum surface gust wind direction [ms-1]
*:- <CODE>totwsgspercen:</CODE> percentage of times when grid point got total gust wind [%]
*:- <CODE>wsz100max:</CODE> maximum 100m wind [ms-1] (two different methods)
*:- <CODE>uz100max:</CODE> eastward maximum 100m wind direction [ms-1]
*:- <CODE>vz100max:</CODE> northward maximum 100m wind direction [ms-1]
*:- <CODE>sund:</CODE> sunshine length [s]
*:- <CODE>rsds:</CODE> mean surface Downwelling Shortwave Radiation [Wm-2]
*:- <CODE>rlds:</CODE> mean surface Downwelling Longwave Radiation [Wm-2]
*:- <CODE>hfls:</CODE> mean surface Upward Latent Heat Flux [Wm-2]
*:- <CODE>hfss:</CODE> mean surface Upward Sensible Heat Flux [Wm-2]
*:- <CODE>rsus:</CODE> mean surface Upwelling Shortwave Radiation [Wm-2]
*:- <CODE>rlus:</CODE> mean surface Upwelling Longwave Radiation [Wm-2]
*:- <CODE>rsusgen:</CODE> mean generic surface Upwelling Shortwave Radiation [Wm-2]
*:- <CODE>rlusgen:</CODE> mean generic surface Upwelling Longwave Radiation [Wm-2]
*:- <CODE>evspsbl:</CODE> mean evaporation [kgm-2s-1]
*:- <CODE>evspsblpot:</CODE> mean potential evapotranspiration [kgm-2s-1]
*:- <CODE>evspsblpotgen:</CODE> mean generic potential evapotranspiration [kgm-2s-1]
*:- <CODE>snc:</CODE> mean snow area fraction [%]
*:- <CODE>snd:</CODE> mean snow depth [m]
*:- <CODE>mrros:</CODE> mean surface Runoff [kgm-2s-1]
*:- <CODE>mrro:</CODE> mean total Runoff [kgm-2s-1]
*:- <CODE>mrsol:</CODE> mean total water content of soil layer [kgm-2]
*:- <CODE>pr:</CODE> precipitation flux [kgm-2s-1]
*:- <CODE>prl:</CODE> large scale precipitation flux [kgm-2s-1]
*:- <CODE>prc:</CODE> convective precipitation flux [kgm-2s-1]
*:- <CODE>prsh:</CODE> shallow-cumulus precipitation flux [kgm-2s-1]
*:- <CODE>prsn:</CODE> solid precipitation flux [kgm-2s-1]
*:- <CODE>snw:</CODE> accumulated snow [ksm-2]
*:- <CODE>rsdt:</CODE> Top Of the Atmosphere incident shortwave radiation [kgm-2]
*:- <CODE>rsut:</CODE> TOA outgoing shortwave radiation [kgm-2]
*:- <CODE>rlut:</CODE> TOA outgoing Longwave radiation [kgm-2]
*:- <CODE>mrsolmean:</CODE> mean moisture content of soil layer [kgm-2]
*:- <CODE>mrsosmean:</CODE> mean first layer soil moisture content (0-10 cm) [kgm-2]
*:- <CODE>mrsomean:</CODE> mean total soil moisture content [kgm-2]
*:- <CODE>mrsllmean:</CODE> mean liquid water content of soil layer [kgm-2]
*:- <CODE>mrlsomean:</CODE> mean total liquid water content of soil layer [kgm-2]
*:- <CODE>mrlsosmean:</CODE> mean liquid water content in Upper Portion of soil column (0-10cm) [kgm-2]
*:- <CODE>mrsflmean:</CODE> mean frozen water content of soil layer [kgm-2]
*:- <CODE>mrfsomean:</CODE> mean total frozen water content of soil layer [kgm-2]
*:- <CODE>mrfsosmean:</CODE> mean frozen water content in Upper Portion of soil column (0-10cm) [kgm-2]


6.2
** Tier1 (CDXWRF=1)
*:- <CODE>capemin:</CODE> minimum CAPE [Jkg-1] (activated if convxtrm_diag =1)
*:- <CODE>cinmin:</CODE> minimum CIN [Jkg-1] (activated if convxtrm_diag =1)
*:- <CODE>zlfcmin:</CODE> minimum height at LFC [m] (activated if convxtrm_diag =1)
*:- <CODE>plfcmin:</CODE> minimum Pressure at LFC [Pa] (activated if convxtrm_diag =1)
*:- <CODE>lidxmin:</CODE> minimum Lifted index [1] (activated if convxtrm_diag =1)
*:- <CODE>capemax:</CODE> maximum CAPE [Jkg-1] (activated if convxtrm_diag =1)
*:- <CODE>cinmax:</CODE> maximum CIN [Jkg-1] (activated if convxtrm_diag =1)
*:- <CODE>zlfcmax:</CODE> maximum height at LFC [m] (activated if convxtrm_diag =1)
*:- <CODE>plfcmax:</CODE> maximum Pressure at LFC [Pa] (activated if convxtrm_diag =1)
*:- <CODE>lidxmax:</CODE> maximum Lifted index [1] (activated if convxtrm_diag =1)
*:- <CODE>capemean:</CODE> mean CAPE [Jkg-1] (activated if convxtrm_diag =1)
*:- <CODE>cinmean:</CODE> mean CIN [Jkg-1] (activated if convxtrm_diag =1)
*:- <CODE>zlfcmean:</CODE> mean height at LFC [m] (activated if convxtrm_diag =1)
*:- <CODE>plfcmean:</CODE> mean Pressure at LFC [Pa] (activated if convxtrm_diag =1)
*:- <CODE>lidxmean:</CODE> mean Lifted index [1] (activated if convxtrm_diag =1)
*:- <CODE>prflux:</CODE> high-frequency precipitation flux [kgm-2s-1] (on auxhist18, wrfhfcdx)


ic_lightning, cg_lightning, tot_lightning: intra-cloud, ground and total lightning
** Additional (not required by CORDEX) CDXWRF=2
flashes
*:- <CODE>tfog:</CODE> time of presence of fog [s]
*:- <CODE>fogvisbltymin:</CODE> minimun visibility inside fog [km]
*:- <CODE>fogvisbltymax:</CODE> maximun visibility inside fog [km]
*:- <CODE>fogvisbltymean:</CODE> mean visibility inside fog [km]
*:- <CODE>tdsmin:</CODE> minimum 2m dew point temperature [K]
*:- <CODE>tdsmax:</CODE> maximum 2m dew point temperature [K]
*:- <CODE>tdsmean:</CODE> mean 2m dew point temperature [K]


There is lightning scheme implementation in WRF. (lightning_option among other from namelist.input). It might
** CDXWRF=3
require some adjustment prior it’s use.
*:- <CODE>tashurstreshighres:</CODE> high resolution of simultaneous temporal residence of 2-meter temperature and relative humidity
It does not sees to provide cloud/ground discrimination
*:- <CODE>tashurstreslowres:</CODE> low resolution of simultaneous temporal residence of 2-meter temperature and relative humidity
*:- <CODE>wbdswsstres:</CODE> simultaneous temporal residence of 10-meter wind direction (from where it blows) and wind speed


6.3
** CDXWRF=4
* Additionally added referred to the water budget in the atmosphere:
*:- <CODE>wbacdiabh:</CODE> Water-budget vertically integrated accumulated of diabatic heating from microphysics [K]
*:- <CODE>wbacpw, wbacpw[c/r/s/i/g/h]:</CODE> Water-budget vertically integrated accumulated total tendency for water vapour, cloud, rain, snow, ice, graupel, hail [mm]
*:- <CODE>wbacf, wbacf[c/r/s/i/g/h]:</CODE> Water-budget vertically integrated accumulated horizontal advection for water vapour, cloud, rain, snow, ice, graupel, hail [mm]
*:- <CODE>wbacz, wbacz[c/r/s/i/g/h]:</CODE> Water-budget vertically integrated accumulated vertical advection for water vapour, cloud, rain, snow, ice, graupel, hail [mm]
*:- <CODE>wbacdiabh{l/m/h}:</CODE> Water-budget vertically integrated accumulated of diabatic heating from microphysics at low, medium and high levels (same as cloudiness) [K]
*:- <CODE>wbacpw{l/m/h}[v/c/r/s/i/g/h]:</CODE> Water-budget vertically integrated accumulated total tendency for water vapour, cloud, rain, snow, ice, graupel, hail at low, medium and high levels (same as cloudiness) [mm]
*:- <CODE>wbacf{l/m/h}[v/c/r/s/i/g/h]:</CODE> Water-budget vertically integrated accumulated horizontal advection for water vapour, cloud, rain, snow, ice, graupel, hail at low, medium and high levels (same as cloudiness) [mm]
*:- <CODE>wbacz{l/m/h}[v/c/r/s/i/g/h]:</CODE> Water-budget vertically integrated accumulated vertical advection for water vapour, cloud, rain, snow, ice, graupel, hail at low, medium and high levels (same as cloudiness) [mm]


praccmov
= Missing variables =
There are certain variables from CORDEX `Core' and/or `Tier1' which could not yet be introduced


Moving accumulated precipitation values for different temporal thresholds (τ ): 30 minutes, 1 hour, 3 hour, 6 hours
== snw: snow melt ==
and 24 hours.
Accumulation of melted snow
This variable might be useful for the impact studies on infrastructures like bridges. The idea would be to provide
its maximum between output times (tout ) as it is suggested in the equation 24


praccmovτ (t)
== wsgsmax100: Daily Maximum Near-Surface Wind Speed of Gust at 100 m ==
The wind gust at 100 m is understood that should follow similar processes that the wind gust at the surface (like in wsgsmax). At this version of the module there has not been considered to be included in the search for the right equations and approximations.


=
== ic_lightning, cg_lightning, tot_lightning: intra-cloud, ground and total lightning flashes ==
There is lightning scheme implementation in WRF. (lightning_option among other from namelist.input). It might require some adjustment prior it's use.
It does not sees to provide a wolrdwide cloud/ground discrimination


t
Accordingly to the value given to the pre-compilation variable CDXWRF one obtains:
X
* Without adding the variable: all CORDEX 'Core' variables
* <code>CDXWRF=1</code> CORDEX 'Tier' variables: clgvi, clhvi, zmla, [cape/cin/zlfc/plfc/lidx]{min/max/mean}
* <code>CDXWRF=2</code> The same as with CDXWRF=1 and additional variables: ua, va, ws, ta, press, zg, hur, hus, tfog, fogvisblty{min/max/mean}, tds{min/max/mean} and the Water-Budget relarted ones: wbacdiabh, wbacpw, wbacpw[c/r/s/i/g/h], wbacf, wbacf[c/r/s/i/g/h], wbacz, wbacz[c/r/s/i/g/h], wbacdiabh{l/m/h}, wbacpw{l/m/h}, wbacpw{l/m/h}[c/r/s/i/g/h], wbacf{l/m/h}, wbacf{l/m/h}[c/r/s/i/g/h], wbacz{l/m/h}, wbacz{l/m/h}[c/r/s/i/g/h]


pr(it)
Simultanesouly, one needs to modify the <code>Registry/registry.cordex</code> accordingly to the value of <code>CDXWRF</code>:
* Without adding CDXWRF, nothing needs to be changed
* Adding <code>CDXWRF=1</code>, one needs to remove the comment <code>##CDXWRF1##</code> at the beginning of the line of the definition of certain variables
* Adding <code>CDXWRF=2</code>, one needs to remove the comment <code>##CDXWRF1##</code> and <code>##CDXWRF2##</code> at the beginning of the line of the definition of certain variables


(24)
Additionally, now interpolation of 3D fields to pressure levels is only done at the same frequency as the output of the <code>wrfpress</code> file.
 
it=t−τ
 
maxpraccmovτ
 
= max [praccmovτ (tout + δt), ..., praccmovτ (tout )]
 
(25)
 
 
CORDEX variables in WRF
 
7
 
33
 
Others


= Others =
It will be some other hard work to do related to it.
It will be some other hard work to do related to it.


7.1
== New variables ==
 
Pretty sure that as we get closer to stake-holders, decision makers, impact and mitigation communities more variables will arise... keep in touch !?
New variables
 
Pretty sure that as we get closer to stake-holders, decision makers, impact and mitigation communities more variables
will arise... keep in touch !?
 
7.2
 
CF-compilant file
 
WRF does not provide a real CF-compilant file format. It would be necessary to add at least at the output (at least
on the wrfcdx_d<domain>_<date> file):
• time variable: CF-version of variable with times in the file
• atrtributes: WRF does not provide variables with standard attributes like: standar_name, long_name, ...
 
7.3
 
Optimization


Avoid the use of namelist options and got the variables/method directly without the introduction of ifs which might
== CF-compilant file ==
make WRF run slowly. This could be done directly via pre-compilation flags, using for example, the namelist options
The module provides almost all the required all the CORDEX variables. However, user still needs to perform some postprocessing of the output data in order to meet CORDEX standards. Mainly:
as pre-compilation options?
* Computation of the required different statistical values as daily, monthly and seasonal extremes (minimum, maximum, accumulations, means)
Acknowledgements All the coders of WRF, LMDZ, ORCHIDEE are acknowledged for their work on the developing and maintaining of the models. M. A. Jiménez from Universitat de les Illes Balears is acknowledged by her
* Cmorization of the output understood as: 1 file per variable, right metadata and attributes and general CF-compilant standard specifications
explanations on certain PBL calculations. J. Milovac from U. Hohenheim for her comments is also acknowledged.


References
WRF output does not fully follows CF-conventions. Thus a huge coding effort needs to be done in order to provide a full CF-compliant output directly from it. User still needs to process the output of the model in order to provide data following all the CORDEX guidelines. Due to uncovered steps of the CF-standard, a user of the WRF model still needs to: concatenate files, change names and attributes of variables, calculate temporal statistics over different periods (daily, monthly, seasonal) and provide the right time-variables in order to fully reach the CF-standard which followed by CORDEX. However, these steps are computationally lighter and easier to perform in comparison to the computation of the different diagnostics and the vertical pressure interpolation already introduced in the module.
Brasseur, O. (2001). Development and application of a physical approach to estimating wind gusts. Monthly Weather
Review, 129(1):5–25.
Fita, L., Fernández, J., and García-Díez, M. (2010). Clwrf: Wrf modifications for regional climate simulation under
future scenarios. Proceedings of 11th WRF Users’ Workshop.
Fita, L. and Flaounas, E. (2017). Medicanes as subtropical cyclones: the december 2005 case from the perspective of
surface pressure tendency diagnostics and atmospheric water budget. Q. J. Royal Met. Soc., under revision.
García-Díez, M., Fernández, J., Fita, L., and Yagüe, C. (2013). Seasonal dependence of wrf model biases and sensitivity
to pbl schemes over europe. Q. J. of Roy. Met. Soc., 139:501–514.
Garratt, J. (1992). The Atmospheric Boundary Layer. Cambridge Univ. Press, Cambridge, U.K.
Hourdin, F., Musat, I., Bony, S., Braconnot, P., Codron, F., Dufresne, J.-L., Fairhead, L., Filiberti, M.-A., Friedlingstein, P., Grandpeix, J.-Y., Krinner, G., LeVan, P., Li, Z.-X., and Lott, F. (2006). The lmdz4 general circulation
model: climate performance and sensitivity to parametrized physics with emphasis on tropical convection. Clim.
Dyn., 27(7-8):787–813.
Huang, H.-L., Yang, M.-J., and Sui, C.-H. (2014). Water budget and precipitation efficiency of typhoon morakot
(2009). J. Atmos. Sci., 71:112–129.
Jourdier, B. (2015). Ressource éolienne en france métropolitaine : méthodes dâĂŹévaluation du potentiel, variabilité
et tendances. Climatologie: École Doctorale Polytechnique, 2015. Français. ph:+33 01238226, pages 1–229.
Monteith, J. L. (1965). Evaporation and environment. the state and movement of water in living organisms. 19th
Symp. Soc. Exp. Biol, pages 205–234.


The incompatibility between WRF output and CF-convention can be overcame with the use of a complementary dedicated I/O library. This has been done for example in the [[https://sourcesup.renater.fr/wiki/morcemed/Home RegIPSL]] platform (which uses WRF as atmospheric model) which uses [[http://forge.ipsl.jussieu.fr/ioserver XIOS]] libraries to manage the I/O.


CORDEX variables in WRF
== Instantaneous values ==
As an additional work, all the instantaneous variables used for the different accumuluations and extremes, can also be retrieved. It is only necessary to:
# Give an output unit on the <CODE>registry.cordex</CODE> (see instructions at the end of the file)
# Uncomment in the code (<CODE>phys/module_diagnostics_dirver.F</CODE> and <CODE>module_diag_cordex.F</CODE>), the commented lines with the key word: <CODE>INSTVALS</CODE>
# re-compile WRF after cleaning all the code (due to the modification in the <code>Registry</code>)


34
= WRF output names =
Open page for the list of variables added with the module [[CDXWRFout]]


Nielsen-Gammon, J. W., Powell, C. L., Mahoney, M. J., Angevine, W. M., Senff, C., White, A., Berkowitz, C.,
= Acknowledgements =
Doran, C., and Knupp, K. (2008). Multisensor estimation of mixing heights over a coastal city. Journal of Applied
All the coders of WRF, LMDZ and ORCHIDEE models are acknowledged for their hard work on the developing and maintaining of the models. M. A. Jiménez from Universitat de les Illes Balears is acknowledged by her explanations on certain PBL calculations. D. Argüeso from UIB. V. Galligani, J. Ruiz and M. Sebastián from CIMA are also acknowldeged by their commentaries. A. Sörensson and E. Borrell are also acknowledged by their assistance. Implementation tests where performed in CIMA HPC resources ‘hydra’ cluster supported by the High Performance Computing National System (SNCAD) of Argentina L. Fita thanks the CIMA-IT support for their work. E. Katragkou and I. Sofiadis acknowledge the technical support and provision of resources from the Scientific Computing Center of [[https://it.auth.gr/el AUTH]] and the [[https://hpc.grnet.gr/ GRNET]] National HPC infrastucture. J.Milovac gratefully acknowledge the support by the German Science Foundation (DFG) through project FOR 1695 and the supercomputing center HLRS in Stuttgart Germany for granting the computing time necessary for the test simulations. T. Lorenz acknowledges the support from the Research Council of Norway and its basic institute support of their strategic project on Climate Services. The simulations were performed on resources provided by UNINETT Sigma2 - the National Infrastructure for High Performance Computing and Data Storage in Norway. Figures were produced with python (except performarnce tests drawn with GNUplot) and L. Fita thanks the development of matplotlib above which he developed and make available a suite in python for netCDF management and plotting purposes called [[http://www.xn--llusfb-5va.cat/python/PyNCplot PyNCplot]]. Authors thank the commentaries of the topical editor (J. Kala) which remarkably improve the manuscript.
Meteorology and Climatology, 47(1):27–43.
Skamarock, W. C., Klemp, J. B., Dudhia, J., Gill, D. O., Duda, D. M. B. M. G., Huang, X.-Y., Wang, W.,
and Powers, J. G. (2008). A description of the advanced research wrf version 3. NCAR TECHNICAL NOTE,
475:NCAR/TNÂŋ475+STR.
Yang, M. J., Braun, S. A., and Chen, D.-S. (2011). Water budget of typhoon nari (2001). Mon. Wather Rev.,
139:3809–3828.

Revisión actual - 12:22 3 sep 2025

The `Coordinated Regional Climate Downscaling Experiment' (CORDEX) is a scientific effort of the World Climate Research Program (WRCP) for the coordination of regional climate initiatives. In order to accept an experiment, CORDEX provides experiment guidelines, specifications of regional domains and data access/archiving. Data requirements are intended to cover all the possible needs of stake holders, and scientists working on climate change mitigation and adaptation policies in various scientific communities. The required data and diagnostics are grouped into different levels of frequency (sub-daily, daily, monthly and seasonal), priority (Core, Tier1, Tier2), and some of them even have to be provided as statistics (minimum, maximum, mean). Here is presented the development of a specialized module called module_diag_cordex (version 1.3) for the Weather Research and Forecasting ((WRF, Skamarok et al. 2008)) model, capable of outputting the required CORDEX variables. Additional diagnostic variables not required by CORDEX, but of potential interest to the regional climate modeling community, are also included in the module. `Generic' definitions of variables are adopted in order to overcome model and/or physics parameterization dependence of certain diagnostics and variables, thus facilitating a robust comparison among simulations. The module is computationally optimized, and the output is divided in different priority levels following CORDEX specifications (Core, Tier1, and additional) by selecting pre-compilation flags. This implementation of the module does not add a significant extra cost when running the model, for example the addition of the Core variables slows the model time-step by less than a 5%. The use of the module reduces the requirements of disk storage by about a 50%.

An article is available in `Geosciences Model Development' journal:

Lluís Fita, Jan Polcher, Theodore M. Giannaros, Torge Lorenz, Josipa Milovac, Giannis Sofiadis, Eleni Katragkou and Sophie Bastin, 2019: CORDEX-WRF v1.3: development of a module for the Weather Research and Forecasting (WRF) model to support the CORDEX community, Geosci. Model Dev., 12, 1029-1066, 2019, https://doi.org/10.5194/gmd-12-1029-2019

It is recommend to contact Lluís Fita (lluis.fita [a] cima.fcen.uba.ar) in order to keep a track and being able to inform of new versions/corrections.

Disclaimer 

Authors decline any responsibility of the possible unexpected consequence of the use of this software. This piece 
of code is provided following the scientific spirit of sharing knowledge and technical advances. Please, use it 
with the same intention and willingness.

There are four working versions of the code for WRFV3.7.1, WRFV3.8.1, WRFV3.9.1.1, WRFV4.0. :

GIT repository

Recently all the code was uploaded to a GIT server. All new developments / updates / new WRF versions, will carried out only the GIT version of the codes. Please visit:

https://git.cima.fcen.uba.ar/lluis.fita/cdxwrf/-/wikis/home

CDXWRF in v7.1

It has been implemented in WRFv7.1 Lluís Fita's fork. Here the link to the announcement in the WRF-MPAS forum #55940

Although a pull of the WRF source code has been made and the module is currently being direclty added to the official source of the code of the model, and its final inclusion will be done by decission of the development team of the model.

NOTE: Be aware that certain surface variables and their statistics (clWRF, Fita et al 2010) are retrieved from namelist configuration (from [http:// www2.mmm.ucar.edu/wrf/users/docs/user_guide_V3/users_guide_chap5.htm#_Description_of_Namelist WRF users web page]) 

4. output_diagnostics = 1 in &time_control. Climate diagnostics. This option outputs 36 surface diagnostic variables:
maximum and minimum, times when max and min occur, mean value, standard deviation of the mean for T2, Q2, TSK, U10, 
V10, 10 m wind speed, RAINCV, RAINNCV (the last two are time-step rain). The output goes to auxiliary output stream 3, 
and hence it needs the following:

auxhist3_outname = “wrfxtrm_d<domain>_<date>”
auxhist3_interval = 1440, 1440,
frames_per_auxhist3 = 100, 100,
io_form_auxhist3 = 2

In this page CDXWRFevolution one founds updates, bug fixes of the module.

With this module, now all CORDEX variables (except `snow melt') are available with the files wrfxtrm, wrfpress and wrfcdx, except for the fied values such as 'areacella'. See CDXvariablestable for more detail

CORDEX requirements

CORDEX requirements of data must cover all the possible needs of stake holders, and scientists working on the adaptation and mitigation strategies. They are grouped in different levels of frequency and priority. A working copy of this list is available here from the CORDEX convection permitting Flag Ship Pilot study.

Some of the variables are not directly computed in the WRF model which require to extend the model output in order to provide enough variables to post-process the variables.

The implementation of the module_diag_cordex module should allow to avoid the post-processing by computing the CORDEX-required (Core & Tier) variables during model integration. At the same time, some extra variables, which might be of interest to the community but not required by CORDEX, have also been added.

NOTE: 

Be aware that any systematic checking process has been applied to this module. Use it and the
variables therein at your own risk !! It has been tested on a 2-nested domain configuration with the 
inner domain at cloud resolving resolution (< 5 km, without cumulus scheme), making use of restarts 
and on serial, pure distributed memory and hybrid distributed/shared parallel environment

module_diag_cordex

The module is basically based on two modules:

  • phys/module_diag_cordex.F: Main module which manages the calls to the variables and the accumulations for the means, ...
  • phys/module_diagvar_cordex.F: Module with the computation of all the variables

This module is accompanied with a new Registry/registry.cordex where the variables and a new section in the namelist.input labeled cordex are defined. There are other necessary complementary modifications on phys/module_diagnostics_driver.F encompassed by the pre-compilaton flag CORDEXDIAG, as well some modifications in the main/depend.common and phys/Makefile. Output is provided by the auxiliary history output #9 with a provisional file name: wrfcordex_d<domain>_<date> All that variables which are only required at output time step, are computed only at that exact time.

Description of the installation process can be found here CDXWRFinstall

Description of the usage of the model can be found here CDXWRFuse

Description of the additional pressure level interpolation variables can be found here CDXWRFpvars

Description of the `Core' variables can be found here CDXWRFcore

Description of the `Tier1' variables can be found here CDXWRFtier

Description of the `Additional' variables can be found here CDXWRFadditional

Description of the studies about optimization of the module can be found here CDXWRFopt

Variables

These are the different variables added and their implementations from the WRF point of view. There might be necessary to revise some of them, or even decide which version to use In case of accumulation/mean they are also be included

These variables are:

  • Instantaneous diagnostics (only computed on output times)
    • Core
    - prw: Total water path
    - clwvi: Total liquid water path (QCLOUD + QRAIN)
    - clivi: Total ice water path (QSNOW+QICE+GRAUPEL+QHAIL)
    - uas: 10m earth-rotated eastward wind [ms-1]
    - vas: 10m earth-rotated northward wind [ms-1]
    - wss: 10m wind speed [ms-1]
    - hurs: 2m relative humidty [1]
    - huss: 2m specific humidty [1]
    - ws100: 100m wind speed [ms-1]
    - uz100: 100m wind x-direction [ms-1]
    - vz100: 100m wind y-direction [ms-1]
    - tauu, tauuv: components of the downward wind stress at 10 m [m2s-2] (might be zero if sf_sfclay_physics /= 1, 5)
    - tauugen, tauuvgen: generic components of the downward wind stress at 10 m [m2s-2]
    - cdcdx: drag coefficient [-] (might be zero if sf_sfclay_physics /= 1, 5)
    - cdgen: generic drag coefficient [-]
    - ps: surface pressure [Pa]
    - psl: sea level pressure [Pa] (three different ways)
    - ts: skin temperature [K]
    - zeroith: 0-isotherm [m]
    - mrsol: moisture content of soil layer [kgm-2]
    - mrsos: first layer soil moisture content (0-10 cm) [kgm-2]
    - mrso: total soil moisture content [kgm-2]
    - mrsll: liquid water content of soil layer [kgm-2]
    - mrlso: total liquid water content of soil layer [kgm-2]
    - mrlsos: liquid water content in Upper Portion of soil column (0-10cm) [kgm-2]
    - mrsfl: frozen water content of soil layer [kgm-2]
    - mrfso: total frozen water content of soil layer [kgm-2]
    - mrfsos: frozen water content in Upper Portion of soil column (0-10cm) [kgm-2]
    - hus_pl: Pressure level data, Specific humidity [1]
    - w_pl: Pressure level data, W wind [ms-1]
    - uer_pl: Pressure level data, U wind Earth-Rotated [ms-1]
    - ver_pl: Pressure level data, V wind Earth-Rotated [ms-1]
    - ws_pl: Pressure level data, wind speed [ms-1]
    - qc_pl: Pressure level data, cloud mixing ratio [kgkg-1]
    - qr_pl: Pressure level data, rain mixing ratio [kgkg-1]
    - qs_pl: Pressure level data, snow mixing ratio [kgkg-1]
    - qi_pl: Pressure level data, ice mixing ratio [kgkg-1]
    - qg_pl: Pressure level data, graupel mixing ratio [kgkg-1]
    - qh_pl: Pressure level data, hail mixing ratio [kgkg-1]
    - qv_pl_mc: mass-conservative pressure level data, water vapour mixing ratio [kgkg-1]
    - qc_pl_mc: mass-conservative pressure level data, cloud mixing ratio [kgkg-1]
    - qr_pl_mc: mass-conservative pressure level data, rain mixing ratio [kgkg-1]
    - qs_pl_mc: mass-conservative pressure level data, snow mixing ratio [kgkg-1]
    - qi_pl_mc: mass-conservative pressure level data, ice mixing ratio [kgkg-1]
    - qg_pl_mc: mass-conservative pressure level data, graupel mixing ratio [kgkg-1]
    - qh_pl_mc: mass-conservative pressure level data, hail mixing ratio [kgkg-1]
    • Tier1 (CDXWRF=1)
    - zmla: pbl height following a generic method [m]
    - clgvi: Total graupel path (QGRAUPEL)
    - clhvi: Total hail path (QHAIL)
    - colmax: high-frequency maximum radar reflectivity in the column [dBz] (on auxhist18, wrfhfcdx)
    • INSTVALS

Only if INSTVALS modifications are made in the code

  • - cape: Convective Available Potential Energy [Jkg-1]
    - cin: Convective inhibition [Jkg-1]
    - zlfc: Height at the Level of free convection [m]
    - plfc: Pressure at the Level of free convection [Pa]
    - lidx: Lifted index [1]
    • Additional (CDXWRF=2)
    - ua: 3D earth-rotated eastward wind [ms-1]
    - va: 3D earth-rotated northward wind [ms-1]
    - ws: 3D wind speed [ms-1]
    - ta: 3D air-temperature [K]
    - press: 3D air pressure [Pa]
    - zg: 3D geopotential height [m]
    - hur: 3D relative humidty [1]
    - hus: 3D specific humidty [1]
    • Only via changes in the registry

NOTE: CLDFRAC is computed by the radiative scheme thus, bear in mind to configure the `namelist.input` that: 

 auxhist19_interval > radt
  • - clt: total cloud cover [1]
    - cll: low-level cloud cover [1]
    - clm: mid-level cloud cover [1]
    - clh: high-level cloud cover [1]
    - cape: Convective Available Potential Energy [Jkg-1]
    - cin: Convective inhibition [Jkg-1]
    - zlfc: Height at the Level of free convection [m]
    - plfc: Pressure at the Level of free convection [Pa]
    - li: Lifted index [1]
    - tds: 2m dew point temperature [K]
  • Accumulated or similar time dependency (computed at every time-step). They are initialized after each output time-step. Thus, they represent statistics (mean, accumulation) only from between output time-steps.
    • Core
    - cltmean: mean clt
    - cllmean: mean cll
    - clmmean: mean clm
    - clhmean: mean clh
    - wsgsmax: maximum surface wind gust [ms-1] (two different methods)
    - ugsmax: eastward maximum surface gust wind direction [ms-1]
    - vgsmax: northward maximum surface gust wind direction [ms-1]
    - wsgspercen: percentage of times when grid point got gust wind [%]
    - totwsgsmax: maximum surface wind gust [ms-1] (addition of different methods)
    - totugsmax: eastward maximum surface gust wind direction [ms-1]
    - totvgsmax: northward maximum surface gust wind direction [ms-1]
    - totwsgspercen: percentage of times when grid point got total gust wind [%]
    - wsz100max: maximum 100m wind [ms-1] (two different methods)
    - uz100max: eastward maximum 100m wind direction [ms-1]
    - vz100max: northward maximum 100m wind direction [ms-1]
    - sund: sunshine length [s]
    - rsds: mean surface Downwelling Shortwave Radiation [Wm-2]
    - rlds: mean surface Downwelling Longwave Radiation [Wm-2]
    - hfls: mean surface Upward Latent Heat Flux [Wm-2]
    - hfss: mean surface Upward Sensible Heat Flux [Wm-2]
    - rsus: mean surface Upwelling Shortwave Radiation [Wm-2]
    - rlus: mean surface Upwelling Longwave Radiation [Wm-2]
    - rsusgen: mean generic surface Upwelling Shortwave Radiation [Wm-2]
    - rlusgen: mean generic surface Upwelling Longwave Radiation [Wm-2]
    - evspsbl: mean evaporation [kgm-2s-1]
    - evspsblpot: mean potential evapotranspiration [kgm-2s-1]
    - evspsblpotgen: mean generic potential evapotranspiration [kgm-2s-1]
    - snc: mean snow area fraction [%]
    - snd: mean snow depth [m]
    - mrros: mean surface Runoff [kgm-2s-1]
    - mrro: mean total Runoff [kgm-2s-1]
    - mrsol: mean total water content of soil layer [kgm-2]
    - pr: precipitation flux [kgm-2s-1]
    - prl: large scale precipitation flux [kgm-2s-1]
    - prc: convective precipitation flux [kgm-2s-1]
    - prsh: shallow-cumulus precipitation flux [kgm-2s-1]
    - prsn: solid precipitation flux [kgm-2s-1]
    - snw: accumulated snow [ksm-2]
    - rsdt: Top Of the Atmosphere incident shortwave radiation [kgm-2]
    - rsut: TOA outgoing shortwave radiation [kgm-2]
    - rlut: TOA outgoing Longwave radiation [kgm-2]
    - mrsolmean: mean moisture content of soil layer [kgm-2]
    - mrsosmean: mean first layer soil moisture content (0-10 cm) [kgm-2]
    - mrsomean: mean total soil moisture content [kgm-2]
    - mrsllmean: mean liquid water content of soil layer [kgm-2]
    - mrlsomean: mean total liquid water content of soil layer [kgm-2]
    - mrlsosmean: mean liquid water content in Upper Portion of soil column (0-10cm) [kgm-2]
    - mrsflmean: mean frozen water content of soil layer [kgm-2]
    - mrfsomean: mean total frozen water content of soil layer [kgm-2]
    - mrfsosmean: mean frozen water content in Upper Portion of soil column (0-10cm) [kgm-2]
    • Tier1 (CDXWRF=1)
    - capemin: minimum CAPE [Jkg-1] (activated if convxtrm_diag =1)
    - cinmin: minimum CIN [Jkg-1] (activated if convxtrm_diag =1)
    - zlfcmin: minimum height at LFC [m] (activated if convxtrm_diag =1)
    - plfcmin: minimum Pressure at LFC [Pa] (activated if convxtrm_diag =1)
    - lidxmin: minimum Lifted index [1] (activated if convxtrm_diag =1)
    - capemax: maximum CAPE [Jkg-1] (activated if convxtrm_diag =1)
    - cinmax: maximum CIN [Jkg-1] (activated if convxtrm_diag =1)
    - zlfcmax: maximum height at LFC [m] (activated if convxtrm_diag =1)
    - plfcmax: maximum Pressure at LFC [Pa] (activated if convxtrm_diag =1)
    - lidxmax: maximum Lifted index [1] (activated if convxtrm_diag =1)
    - capemean: mean CAPE [Jkg-1] (activated if convxtrm_diag =1)
    - cinmean: mean CIN [Jkg-1] (activated if convxtrm_diag =1)
    - zlfcmean: mean height at LFC [m] (activated if convxtrm_diag =1)
    - plfcmean: mean Pressure at LFC [Pa] (activated if convxtrm_diag =1)
    - lidxmean: mean Lifted index [1] (activated if convxtrm_diag =1)
    - prflux: high-frequency precipitation flux [kgm-2s-1] (on auxhist18, wrfhfcdx)
    • Additional (not required by CORDEX) CDXWRF=2
    - tfog: time of presence of fog [s]
    - fogvisbltymin: minimun visibility inside fog [km]
    - fogvisbltymax: maximun visibility inside fog [km]
    - fogvisbltymean: mean visibility inside fog [km]
    - tdsmin: minimum 2m dew point temperature [K]
    - tdsmax: maximum 2m dew point temperature [K]
    - tdsmean: mean 2m dew point temperature [K]
    • CDXWRF=3
    - tashurstreshighres: high resolution of simultaneous temporal residence of 2-meter temperature and relative humidity
    - tashurstreslowres: low resolution of simultaneous temporal residence of 2-meter temperature and relative humidity
    - wbdswsstres: simultaneous temporal residence of 10-meter wind direction (from where it blows) and wind speed
    • CDXWRF=4
  • Additionally added referred to the water budget in the atmosphere:
    - wbacdiabh: Water-budget vertically integrated accumulated of diabatic heating from microphysics [K]
    - wbacpw, wbacpw[c/r/s/i/g/h]: Water-budget vertically integrated accumulated total tendency for water vapour, cloud, rain, snow, ice, graupel, hail [mm]
    - wbacf, wbacf[c/r/s/i/g/h]: Water-budget vertically integrated accumulated horizontal advection for water vapour, cloud, rain, snow, ice, graupel, hail [mm]
    - wbacz, wbacz[c/r/s/i/g/h]: Water-budget vertically integrated accumulated vertical advection for water vapour, cloud, rain, snow, ice, graupel, hail [mm]
    - wbacdiabh{l/m/h}: Water-budget vertically integrated accumulated of diabatic heating from microphysics at low, medium and high levels (same as cloudiness) [K]
    - wbacpw{l/m/h}[v/c/r/s/i/g/h]: Water-budget vertically integrated accumulated total tendency for water vapour, cloud, rain, snow, ice, graupel, hail at low, medium and high levels (same as cloudiness) [mm]
    - wbacf{l/m/h}[v/c/r/s/i/g/h]: Water-budget vertically integrated accumulated horizontal advection for water vapour, cloud, rain, snow, ice, graupel, hail at low, medium and high levels (same as cloudiness) [mm]
    - wbacz{l/m/h}[v/c/r/s/i/g/h]: Water-budget vertically integrated accumulated vertical advection for water vapour, cloud, rain, snow, ice, graupel, hail at low, medium and high levels (same as cloudiness) [mm]

Missing variables

There are certain variables from CORDEX `Core' and/or `Tier1' which could not yet be introduced

snw: snow melt

Accumulation of melted snow

wsgsmax100: Daily Maximum Near-Surface Wind Speed of Gust at 100 m

The wind gust at 100 m is understood that should follow similar processes that the wind gust at the surface (like in wsgsmax). At this version of the module there has not been considered to be included in the search for the right equations and approximations.

ic_lightning, cg_lightning, tot_lightning: intra-cloud, ground and total lightning flashes

There is lightning scheme implementation in WRF. (lightning_option among other from namelist.input). It might require some adjustment prior it's use. It does not sees to provide a wolrdwide cloud/ground discrimination

Accordingly to the value given to the pre-compilation variable CDXWRF one obtains:

  • Without adding the variable: all CORDEX 'Core' variables
  • CDXWRF=1 CORDEX 'Tier' variables: clgvi, clhvi, zmla, [cape/cin/zlfc/plfc/lidx]{min/max/mean}
  • CDXWRF=2 The same as with CDXWRF=1 and additional variables: ua, va, ws, ta, press, zg, hur, hus, tfog, fogvisblty{min/max/mean}, tds{min/max/mean} and the Water-Budget relarted ones: wbacdiabh, wbacpw, wbacpw[c/r/s/i/g/h], wbacf, wbacf[c/r/s/i/g/h], wbacz, wbacz[c/r/s/i/g/h], wbacdiabh{l/m/h}, wbacpw{l/m/h}, wbacpw{l/m/h}[c/r/s/i/g/h], wbacf{l/m/h}, wbacf{l/m/h}[c/r/s/i/g/h], wbacz{l/m/h}, wbacz{l/m/h}[c/r/s/i/g/h]

Simultanesouly, one needs to modify the Registry/registry.cordex accordingly to the value of CDXWRF:

  • Without adding CDXWRF, nothing needs to be changed
  • Adding CDXWRF=1, one needs to remove the comment ##CDXWRF1## at the beginning of the line of the definition of certain variables
  • Adding CDXWRF=2, one needs to remove the comment ##CDXWRF1## and ##CDXWRF2## at the beginning of the line of the definition of certain variables

Additionally, now interpolation of 3D fields to pressure levels is only done at the same frequency as the output of the wrfpress file.

Others

It will be some other hard work to do related to it.

New variables

Pretty sure that as we get closer to stake-holders, decision makers, impact and mitigation communities more variables will arise... keep in touch !?

CF-compilant file

The module provides almost all the required all the CORDEX variables. However, user still needs to perform some postprocessing of the output data in order to meet CORDEX standards. Mainly:

  • Computation of the required different statistical values as daily, monthly and seasonal extremes (minimum, maximum, accumulations, means)
  • Cmorization of the output understood as: 1 file per variable, right metadata and attributes and general CF-compilant standard specifications

WRF output does not fully follows CF-conventions. Thus a huge coding effort needs to be done in order to provide a full CF-compliant output directly from it. User still needs to process the output of the model in order to provide data following all the CORDEX guidelines. Due to uncovered steps of the CF-standard, a user of the WRF model still needs to: concatenate files, change names and attributes of variables, calculate temporal statistics over different periods (daily, monthly, seasonal) and provide the right time-variables in order to fully reach the CF-standard which followed by CORDEX. However, these steps are computationally lighter and easier to perform in comparison to the computation of the different diagnostics and the vertical pressure interpolation already introduced in the module.

The incompatibility between WRF output and CF-convention can be overcame with the use of a complementary dedicated I/O library. This has been done for example in the [RegIPSL] platform (which uses WRF as atmospheric model) which uses [XIOS] libraries to manage the I/O.

Instantaneous values

As an additional work, all the instantaneous variables used for the different accumuluations and extremes, can also be retrieved. It is only necessary to:

  1. Give an output unit on the registry.cordex (see instructions at the end of the file)
  2. Uncomment in the code (phys/module_diagnostics_dirver.F and module_diag_cordex.F), the commented lines with the key word: INSTVALS
  3. re-compile WRF after cleaning all the code (due to the modification in the Registry)

WRF output names

Open page for the list of variables added with the module CDXWRFout

Acknowledgements

All the coders of WRF, LMDZ and ORCHIDEE models are acknowledged for their hard work on the developing and maintaining of the models. M. A. Jiménez from Universitat de les Illes Balears is acknowledged by her explanations on certain PBL calculations. D. Argüeso from UIB. V. Galligani, J. Ruiz and M. Sebastián from CIMA are also acknowldeged by their commentaries. A. Sörensson and E. Borrell are also acknowledged by their assistance. Implementation tests where performed in CIMA HPC resources ‘hydra’ cluster supported by the High Performance Computing National System (SNCAD) of Argentina L. Fita thanks the CIMA-IT support for their work. E. Katragkou and I. Sofiadis acknowledge the technical support and provision of resources from the Scientific Computing Center of [AUTH] and the [GRNET] National HPC infrastucture. J.Milovac gratefully acknowledge the support by the German Science Foundation (DFG) through project FOR 1695 and the supercomputing center HLRS in Stuttgart Germany for granting the computing time necessary for the test simulations. T. Lorenz acknowledges the support from the Research Council of Norway and its basic institute support of their strategic project on Climate Services. The simulations were performed on resources provided by UNINETT Sigma2 - the National Infrastructure for High Performance Computing and Data Storage in Norway. Figures were produced with python (except performarnce tests drawn with GNUplot) and L. Fita thanks the development of matplotlib above which he developed and make available a suite in python for netCDF management and plotting purposes called [PyNCplot]. Authors thank the commentaries of the topical editor (J. Kala) which remarkably improve the manuscript.

Obtenido de «http://wiki.cima.fcen.uba.ar/index.php?title=CDXWRF&oldid=3699»