CDXWRF

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, Skamarok et al. 2008) module called module_diag_cordex with which is expected to substantially limit the need of post-processing.

PDF version of this page here Archivo:module CORDEX WRF.pdf

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.

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 three working versions of the code for WRFV3.7.1, WRFV3.8.1 and WRFV3.9.1.1

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

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

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 pure distributed memory 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.inpt 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.

Additional: pressure levels interpolation

At the same time, WRF can output on pressure levels while integration. However, initial version of the module does not include certain required CORDEX variables:

• wa vertical wind speed [ms-1]
• hus specific humidity [1]
• uer Earth rotated x-compoment [ms-1]
• ver Earth rotated y-compoment [ms-1]
• ws wind speed [ms-1]

Thus, code has also been modified and now, WRF output at pressure levels also provides wa, hus, uer and ver

It has been accomplished after modifying the codes: Registry/registry.diags, phys/module_diagnostics_driver.F, phys/module_diag_pld.F and dyn_em/start_em.F. The three latest modifications are also encapsulated within precompilation flag CORDEXDIAG.

See more details in how to activate this option in WRF_users web-page over the namelist section diags&.

Additional: water budget

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 dyn_em/solve_em.F

Installation

These steps must be followed prior the re-compilation of the WRF model and assuming that the process is started where the code resides (WRFV3). NOTE: make sure that the already compiled version of WRF and the version of the module are the same!

1. Untar the file

$ tar xvfz WRFV[VERSION]_CORDEX.tar.gz

1. 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

1. On the Registry/Registry.EM add the following line (after the last line with include registry.bdy_perturb (on WRFV3.7.1, WRFV3.8.1), registry.new3d_wif (on WRFV3.9.1.1))

include registry.cordex

1. Clean the code (in order to avoid to run again configure one can make a copy of the configure.wrf and recover it after the clean, otherwise it is erased)

$ cp configure.wrf configure.cordex.wrf
$ ./clean -a
$ cp configure.cordex.wrf configure.wrf

1. edit the `configure.wrf' and add the line (after the line -DNETCDF)

                      -DCORDEXDIAG

1. compile as always

$ ./compile em_real >& compile.log

Usage

These are the steps to use the module

1. One need to add to the 'namelist.input' the auxiliar output number 9 (e.g. for output every 3 hours and 1-day files) at the `&history' section:

auxhist9_outname = "wrfcdx_d<domain>_<date>"
auxhist9_interval = 180, 180,
frames_per_auxhist9 = 8, 8,
io_form_auxhist9 = 2

1. 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
 output_wb          = 1: whether water-budget variables have to computed (1) or not (0, default)
 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)
 z100m_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)
 potevp_diag        = 1: potential evapotranspiration following Penman-Monteith formulation after ORCHIDEE 
                        implementation
 convxtrm_diag      = 0: diagnostic of extremes from convection indices: 0: No (default); 1: yes
 fogvisibility_diag = 1: diagnostic of visibility inside fog following Kunkel (1984)
                    = 2: RUC method (Smirnova et al., 2000)
                    = 3: FRAML 50% prob Gultepe and Milbrandt, (2010) (default)
 fogvars            = 1: variables to use to diagnose fog using 3D [qv, ta, pres] (default)
                    = 2: sfc [q2, tas, ps] (not available for Kunkel, 1984)
/

Pressure interpolation

Remember to activate section &diags 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.
/

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)

  - 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] (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]

  - ts: skin 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.

  - clt: total cloud cover [1]

  - cll: low-level cloud cover [1]

  - 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]

  - 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]

  - 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]

  - 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)

  - 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]

  • 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]
    • 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[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]

  - uer_pl: Earth-rotated wind x-component [ms-1]

  - ver_pl: Earth-rotated wind y-component [ms-1]

  - ws_pl: wind speed [ms-1]

clt: total cloudiness

This variable computes the total cloudiness above a grid point taking as input the cloud fraction of a given grid cell and level. NOTE:

cloud fraction in WRF is computed by the radiative scheme, which is called at a frequency given by radt. 
It should be taking into account when one gets any accumulation of any value retrieved from it. Otherwise, 
one could compute the cloud fraction at every time-step (using any of the subroutines from 
module_radiation_driver.F: cal_cldfra1, cal_cldfra2, cal_cldfra3), but then it will not be consistent in 
what was already considered whilst model integration

The most common implementation assumes 'random overlapping and its implemented in most of the global climate models. Here is considered to take the implementation from the GCM LMDZ (Hourdin et al., 2006). Calculation of the total cloudiness is done inside the subroutine newmicro.f90. Specific variable computation has already been extracted and implemented as a subroutine for the python utils PyNCplot.

cllmh: low, medium and high cloudiness

This variable computes the total cloudiness above a grid point at different vertical intervals (low: p ≥ 680hP a, medium: 680 < p ≥ 400 hP a, high: p < 400 HP a) taking as input the cloud fraction of a given grid cell.

As in the case of the ‘clt’ calculation from LMDZ has already been implemented as an independent subroutine. See in figure 1 the result of the implementation

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)

wsgsmax: Maximum Near-Surface Wind Speed of Gust

The wind gust accounts for the wind from upper levels that is projected to the surface due to instability within the boundary layer. It can have different implementations. Winds are Earth-rotated.

• Brasseur01: An implementation of a wind gust following Turbuelent Kinetic Energy (TKE) estimates and stability by virtual temperature (θv , see mainly equation 1) reproducing Brasseur (2001) from the clWRF (clWRF Fita et al., 2010) [wsgs_diag = 1]

• 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 mm [wsgs_diag = 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

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)

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]

• 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]

• 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)

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)

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:

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

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

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 QVAPOR by QCLOUD + QRAIN

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 QVAPOR by QICE + QSNOW + QGRAUPEL + QHAIL

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 QVAPOR by QGRAUPEL

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 QVAPOR by QHAIL

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 K km-1) [psl_diag = 1]
• Using smoothed surface pressure and a target upper-level pressure, already implemented in p_interp.F90 [psl_diag = 2]
• ECMWF method taken from LMDZ from the module pppmer.F90, following the methodology by Mats Hamrud and Philippe Courtier from ECMWF [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 Pa). 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

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)

cape: convective available potential energy

This variable accounts for all the energy that convectively might be released. From AMS glossary is described as: (CAPE)

"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:

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)

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: CIN) "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 CAPE) as follows:

where pi is the pressure at the level at which the parcel originates, pf is the pressure at the LFC, 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."

sund: duration of sunshine

This variable accounts for the time where short-wave radiation is above 120 Wm-2 .

It is already implemented in a advance version of the clWRF. See results of the variable in figure 6

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))

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

being tempC: temperature in Celsius degree (◦ C), presshPa: pressure in hPa, es: saturated water vapor pressure, ws: saturated mixing ratio kgkg-1 , q: mixing ratio kgkg-1

hus: specific humidity

From the AMS glossary hus

zg: geopotential height

where PHB, WRF base geopotential height, PH, WRF perturbation geopotential height

press: air-pressure

where PB, WRF base pressure, P, WRF perturbation pressure

ta: air-temperature

where T, WRF temperature (which is as potential temperature), PB, WRF base pressure, P, WRF perturbation pressure, p0: pressure reference 100000 Pa

ua/va: air-wind Earth oriented

where Uunstg, unstaggered WRF eastward wind, Vunstg, unstaggered WRF northward wind, cosa, local cosine of map rotation, sina, local sine of map rotation

tauuv

Surface Downdward wind stress at 10m. It is implemented following the equation 16, begin CD drag coefficient. Winds are Earth-rotated. The generic drag coefficient cdgen is used to compute these variables.

evspsblpot

Potential evapotranspiration is computed following its computation from ORCHIDEE model (Organising Carbon and Hydrology In Dynamic Ecosystems, ORCHIDEE). 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 17)

where qc: surface drag coefficient, q2sat: Saturated air at 2m (can be assumed to be q2 = qsfc?), 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

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.

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.

tds

Dew point temperature following August-Roche-Magnus approximation as it is shown in equation 18

where tas: 2m temperature, hurs: 2m relative humidity

Statistical values are provided in the output: minimum, maximum and mean within output time-steps

pr

Total precipitation flux is computed as the sum of all the types of precipitation as it is shown in equation 19

where prc: convective precipitation, prl: large-scale precipitation, prsh: shallow-cumulus precipitation

prsn

Solid precipitation flux accounts for all the precipitation which is frozen. Depending on the micro-physics scheme it might account for the precipitation of: snow, graupel and hail. It is computed as it is shown in equation 20

where pr: total precipitation, sr: fraction of solid precipitation (variable included in WRF).

Additional variables

Some other variables not required by CORDEX, but might be interesting for other purposes will be also added

Water vapor balance terms

These covers the different column integrated terms of the water balance equation. The equation of the water vapour budget:

Where q stands for either of the five water species concentration (vapor, snow, ice, rain and liquid), Vh stands for horizontal wind speed, w stands for the vertical wind speed and MP 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 (TEN 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. TEN equals to the horizontal advection (HOR or 'F', first term in right-hand side of the equation), the vertical advection (VER or 'Z', second term in right-hand side) and the sources (SO) or sink (SI) of atmospheric water due to microphysical processes (MP). All terms are expressed in kgkg-1s-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):

Following the methodology of Huang et al. (2014) and Yang et al. (2011), Fita and Flaounas (2018) 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.

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

Figure 8: As in 7, but for Water budget 3h-accumulated vertically integrated horizontal advection 'F' at a given time

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)

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)

Figure 11: The same as in figure 9, but for snow

Figure 12: The same as in 10, bur for snow

tfog: time of presence of fog

A diagnostic of visibility has been introduced. From it, one can define fog as that moment where the visibility is lower than 1 km.

tfog accounts for the time in which the grid point has visibility lower than 1 km (see equation 23)

where N_fog: number of time steps where visibility was below 1 km. δt: model time step (s)

fogvisblty: visibility inside fog

A diagnostic of visibility is introduced in order to provide a diagnostic for fog. Three different methods have been introduced:

• K84: Visibility is computed by means of liquid water (QCLOUD) and ice (QICE) concentrations. Following (Bergot et al., 2007) fog appears when there are liquid and/or ice water species at the lowest level. Visibility using (see equation 24, Kunkel 1984) formula is computed on that grid points where fog appeared. Method selected with visibility_diag = 1

where qc: liquid water (cloud) mixing ratio (kgkg-1), qi: ice mixing ratio (kgkg-1). Visibility values are in km

• RUC: Visibility is computed using relative humidity (hur) as it is implemented in the RUC model (see equation 25, Smirnova et al. 2000). Method selected with visibility_diag = 2

where rh: relative humidity (1) and can be from surface or first model layer. Visibility values are in km

• FRAM-L: Visibility is computed using relative humidity (hur) after (see equation 26, Gultepe and Milbrandt, 2010). In this work, it is proposed a probabilistic approach to the computation of the visibility in three different bins: 95% , 50% and 5% of probability to get certain visibility (for rh > 30%). As a matter of compromise, the calculation for the 50% of probability has been chosen as the preferred one. Thus, this method provides the visibility that might be with a 50% of probability. Method selected with visibility_diag = 3 (default)

where rh: relative humidity (1) and can be from surface or first model layer. Visibility values are in km

Provided values in the output are the minimum, maximum and mean values within output time-steps

Different choices are controlled throughout namelist.input variables: visibility_diag method of visibility computation, fogvars source of the relative humidity. From first model layer (hur) fogvars=1 (default), surface (hurs) fogvars=2.

It is known that certain methods of visibility relay on numerical adjustments on certain observational data taken under certain circumstances and places. It would be desirable to provide a more generic all places/purposes (if possible) approach. Take this value with certain care

Generic variables

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 (kMLD) first layer at which the variation of mixing ratio upwards from first layer value achieves a given percentage: > δqv (here applied a δqv = 0.1)
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)

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-zmlaWRF ,bottom left), zmla map (bottom middle) and zmlaW RF (bottom right)

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 27, after Garratt (1992).

Being, u∗: from similarity theory, wss: 10 m wind speed

tauuvgen: generic surface downdward wind stress

Generic surface downdward wind stress at 10m.

It is implemented following the equation 28, begin CDgen generic drag coefficient (see equation 28). Winds are Earth-rotated

rsusgen

Surface Upwelling Shortwave Radiation, is understood as the shortwave radiation from land. It is calculated in a generic way as the reflected shortwave radiation due to albedo as it is shown in equation 29

Being, albedo: albedo, sdown: downward at surface shortwave radiation

rlusgen

Surface Upwelling Longwave Radiation, is understood as the longwave radiation from land. It is calculated in a generic way as the longwave radiation due to surface temperature following black body formulation as it is shown in equation 30

where CtBoltzman: Boltzman constant, skt: skin temperature

Missing variables

There are certain variables which could not be introduced (yet?)

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.

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

praccmov

Moving accumulated precipitation values for different temporal thresholds (τ ): 30 minutes, 1 hour, 3 hour, 6 hours and 24 hours. 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 31

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

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, ...

Optimization

Avoid the use of namelist options and got the variables/method directly without the introduction of ifs which might make WRF run slowly. This could be done directly via pre-compilation flags, using for example, the namelist options as pre-compilation options?

Instantaneous valuess

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, ORCHIDEE are acknowledged for their work on the developing and maintaining of the models. M. A. Jiménez from Universitat de les Illes Balears (UIB) is acknowledged by her explanations on certain PBL calculations. J. Milovac from U. Hohenheim for her comments is also acknowledged. D. Argüeso from UIB. E. Katragkou from U. Thesaloniki, T. Μ. Giannaros from National Observatory of Athens, T. Lorenz from Uni Research, the Bjerknes Centre and J. Milovac from U. Hohenheim for their assistance in the additional tests. V. Galligani, J. Ruiz and M. Sebastián from CIMA.

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