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User Manual for the LMD Martian Atmospheric General Circulation

1. 1 e e u u u u u u u Vi VL VL VL vi Vi VL 2 3 4 SE 6 7 e u u u EFX u u u u L A Vi Vi VL Vi Vi VL 8 9 1 1 1 1 ln T Ii T ial T e u VL Vi VL VL VL VL VL 1 1 1 17 1 1 i cL NL Cl vL vL vL vL vL v v rlatv 20 e e e e e e lt u u u u u u u T 4 boite grille scalaire rlonv 1 IM 1 rlonu Tj rlonv 1 IM 1 e e e rlatu 1 JM 1 u i 1 j u i j rlatv 1 JM v j e Figure 2 2 Dynamical and physical grids for a 6 x 7 horizontal resolution In the dy namical part but not in the physical part winds u and v are on a staggered dynamical grid The other variables are on the dynamical scalar grid The physical part uses the same grid for all the variables except for the points that are indexed in a single vector containing NGRID 2 JM 1 xIM points when counting from the north pole NB In the Fortran program the following variables are used iim IM iipl IM 1 jjm JM r jjpl JM 1 2 3 2 Vertical grids hybrid coordinates set to false hybrid coordinates set to true 25 layers 25 layers cA e T A T 1 H log nlayer preN km H log p nlayer pref km z
2. Figure 6 1 Example of temperature data at a given time using GrADS visualization 6 1 2 Graphic visualization of the NetCDF files using GrAds GrAdS The Grid Analysis and Display System is a graphic software developed by Brian Doty at the Center for Ocean Land Atmosphere COLA One of its functions is to enable data stored in NetCDF format to be visualized directly In figure 6 1 for example we can see the GrADS visualization of the temperature data at a given moment However unlike NetCDF GrADS only recognizes files where all the variables are stored on the same horizontal grid These variables can be in 1 2 3 or 4 dimensions X Y Z and t GrADS can also be obtained on the WWW http grads iges org grads 6 2 Input The 3D version of the GCM requires the input of two initialization files in NetCDF format start nc containing the initial states of the dynamic variables startfi nc containing the initial states of the physics variables Note that collections of initial states can be retreived at http www lmd jussieu fr forget datagcm Starts Extracting start nc and startfi nc from these archived requires using program newstart as described in section 4 8 To run the GCM also requires the three following parameter files ascii text files run def the parameters of the dynamical part of the program and the temporal integration of the model callphys def the parameters for calling the physical part Z2
3. Figure 2 3 Sketch illustrating the difference between hybrid and non hybrid coordinates The GCM was initially programmed using coordinates atmospheric pressure over surface pressure ratio which had the advantage of using a constant domain c 1 at the surface and 0 at the top of the atmosphere whatever the underlying topography However it became obvious that these coordinates significantly disturbed the stratospheric dynamical representation as the topography is visible in the coordinate system up to the top of the model An elegant solution to this problem has been found using the equivalent hybrid coordinates c nearer the surface and p for higher altitudes Figure 2 3 illustrates the importance of using these hybrid coordinates compared to the classical coordinates The distribution of the vertical layers is irregular to enable greater precision at ground level In general we use 25 levels to describe the atmosphere to a height of 80 km 32 levels for simulations up to 120 km or 50 levels up to thermosphere The first layer describes the first few meters above the ground whereas the upper layers describe several kilometers Figure 2 4 describes the vertical grid variables 2 4 Variables used in the model 2 4 1 Dynamical part The dynamical state variables are the atmospheric temperature surface pressure winds and tracer concentrations In practice the formulation selected to solve the equations in the dynamical pa
4. rcp tab 1 10 daysec tab cntrl 11 dtphys tab cntrl 12 O tab cntrl 13 O c Info sur la Planete Mars pour tab cntrl 14 year day tab cntrl 15 periheli tab cntrl 16 aphelie tab cntrl 17 peri day tab 1 18 obliquit c Couche limite et Turbulence tab cntrl 19 20 tab cntr1 20 lmixmin tab cntrl1 21 turb c propriete optiques des calottes albedice 1 albedice 2 emisice 1 tab cntrl 22 tab cntrl 23 tab cntrl 24 float ngridmx float nlayermx float idayref nombre de points de la grille physique nombre de couches jour 0 la dynamique et la physique rayon de mars m 3397200 vitesse de rotation rad s 1 gravite m s 2 3 72 Masse molaire de l atm g mol 1 43 49 r cp 70 256793 kappa dans dynamique duree du sol s 788775 pas de temps de la physique la physique uniquement duree de l annee sols dist min soleil mars Mkm 206 66 dist max soleil mars Mkm 249 22 date du perihelie sols depuis printemps Obliquite de la planete deg 723 98 7668 6 surface roughness m 70 01 longueur de melange 100 energie minimale 1 e 8 emissivite du sol Albedo calotte nord 0 5 Albedo calotte sud 0 5 Emissivite calotte nord et 70 95 39 tab_cntrl 25 emisice 2 Emissivite calotte sud 0 95 tab_cntrl 26 emissiv Emissivite du sol martien 95 tab cntrl 31 iceradius 1 mean scat radius of
5. up float cu latitude rlonu cu title Coefficient de passage pour U float cv rlatv longitude cv title Coefficient de passage pour V float aire latitude longitude aire title Aires de chaque maille float phisinit latitude longitude phisinit title Geopotentiel au sol float Time Time Time title Temps de simulation Time units days since 0 00 00 00 00 00 float ucov Time altitude latitude rlonu ucov title Vitesse U float vcov Time altitude rlatv longitude veov title Vitesse V float teta Time altitude latitude longitude teta title Temperature float q01 Time altitude latitude longitude qOl title Traceurs q01 float q02 Time altitude latitude longitude q02 title Traceurs q02 float masse Time altitude latitude longitude masse title C est quoi float ps Time latitude longitude ps title Pression au sol global attributes title Dynamic start file List of contents of a startfi file ncdump h startfi nc netcdf startfi dimensions index 100 physical points 3010 subsurface layers 10 variables float controle index controle title Parametres de controle float longitude physical points longitude title Longitudes de la grille physique float latitude physical points latitude title Latitudes de la grille physique float area physical points area title Aire des
6. etc the tracers ps surface pressure masse the atmosphere mass in each grid box Vectorial variables ucov and vcov are stored on staggered grids u and v respectively in the dynamical part see section 2 2 Scalar variables h q01 ps masse are stored on the scalar grid of the dynamical part For the physical part co2ice surface dry ice tsurf surface temperature tsoil temperatures at different layers under the surface emis surface emissivity q2 wind variance or more precisely the square root of the turbulent kinetic energy qsurf01 qsurf02 etc the surface tracer budget kg m 2 these variables are stored on the physical grid see section 2 2 The control variable Both the physical and dynamical headers of the GCM NetCDF files start with a controle variable This variable is a table with 100 reals the table called tab cntrl in the program which contains the program control parameters These parameters differ in the physical and dynamical parts and examples of both are listed below The contents of table tab_cntrl can also be seen by typing the command ncdump v controle The control variable in the header of a dynamical NetCDF file start 38 tab cntrl 1 FLOAT iim nombre de points en longitude tab cntrl1 2 FLOAT jjm nombre de points en latitude tab cntrl1 3 FLOAT llm nombre de couches tab cntrl 4 FLOAT idayref jour O
7. CO2 snow north tab cntrl 32 iceradius 2 mean scat radius of CO2 snow south tab cntrl 33 dtemisice 1 time scale for snow metamorphism north tab cntrl 34 dtemisice 2 time scale for snow metamorphism south C Proprietes des poussiere aerosol tab cntrl 27 tauvis profondeur optique visible moyenne tab cntrl1 28 0 tab cntrl 29 0 tab cntrl1 30 0 40 6 3 Output 6 3 1 NetCDF restart files restart nc and restartfi nc These files are of the exact same format as start and startfi nc 6 3 2 NetCDF file diagfi nc NetCDF file diagfi nc stores the instantaneous physical variables throughout the sim ulation at regular intervals set by the value of parameter ecritphy in parameter file run def Any variable from any sub routine of the physical part can be stored by calling subroutine writediagfi Visualization of the contents of a diagfi file using ncdump ncdump h diagfi netcdf diagfil dimensions Time UNLIMITED 366 currently index 100 rlonu 65 latitude 49 longitude 65 rlatv 48 interlayer 26 altitude 25 variables float Time Time Time long_name Time Time units days since 0000 00 00 00 00 00 float controle index controle title Parametres de controle float rlonu rlonu rlonu title Longitudes aux points float latitude latitude latitude units degrees_north latitude long na
8. CREER Beside 6 2 4 Initialization files start and startfi 6 3 Output ads MEER due Lt Ra lh i hadt 6 3 1 NetCDF restart files restart nc and restartfi nc 6 3 2 NetCDF file diagfinc 6 3 3 Stats fles uo SG EE Cash Malte ae EHE qe Zoomed simulations 7 1 To define the zoomed area 7 0 Making a zoomed initial state 7 3 Running a zoomed simulation and stability issue Water Cycle Simulation Photochemical Module 1D version of the Mars model 10 1 Gompilation sas xe ee eI AVE PRET ire 10 2 1 D runs and input files 10 3 Outputidata 222 A Sum UA Martian Calendar Utilities Bel concatnG a Xl Tug DANGER LA 25 B 2 ISI ao 2 05 9 2 uA os bed eR E RS vr gg nu B 3 Jocaltimes iu es A Ew Aet DIN LR RING Ta BA FIC east AS NA ULP Re AH ess ae Chapter 1 Introduction This document is a user manual for the General Circulation Model of the Martian atmo sphere developed by the Laboratoire de M t orologie Dynamique of the CNRS in Paris in collaboration with the Atmospheric and Oceanic Planetary Physics sub department in Oxford It corresponds to the version of the model available since November 2002 that includes the new dynamic code Imdz3 3 a
9. The time dimension of the output can be sols or Ls note that in that latter case Ls values won t be evenly distributed and software like Grads may not be able to use and plot the data To obtain an evenly sampled Ls timescale you can use the 151 program described below The output file created by conctanc eis concat nc B 2 Islin This program is designed to interpolate data given in irregular Solar Longitude Ls into an evenly sampled linear time coordinate usable with Grads Input Netcdf files may be diagfi nc or concat nc files and the resulting output file is 1s1in nc lslin also create a 1slin ct1 file that can be read directly by grads gt xdfopen 1slin ctl1 to plot in Ls coordinate to avoid some problem with grads when Grads think that the time interval is too small B 3 localtime The localtime e program is designed to re interpolate data in order to yield values at the same given local time useful to mimic satellite observations or analyse day to day variations at given local time Input files may be of diagfi nc stats nc or concat nc type and the output file name is build from the input one to which LT nc is appened e g if the input file is myfile nc then output file will be myfile LT nc B 4 zrecast With this program you can recast atmospheric i e 4D dimentional longitude latitude altitude time data from outputs e g as given in diagfi nc concat nc and stats nc files onto either pressu
10. also used to create an initial state In practice we usually reuse an old initial state and modify it using newstart Like the GCM program newstart compiles to the required grid resolution For exam ple makegcm d 64x48x25 p mars newstart Then run newstart e The program then gives you two options A partir de quoi souhaitez vous creer vos etats initiaux 0 d un fichier start archive 1 d un fichier start e Option 1 allows you to read and modify the information needed to create a new initial state from thefiles start nc startfi nc e Option 0 allows you to read and modify the information needed to cre ate a new initial state from file start archive nc whatever the start archive nc gridresolution is If you use tracers make sure that they are taken into account in your start files either start or start archive For Option 0 the start archive nc find in SPATH1 LMDZ MARS deftank contains 12 martian seasons Then reply to the questions in the scroll menu These questions allow you to mod ify the initial state for the following parameters First set of questions Modifications of variables in tab cntrl day ini Jour initial 0 a Ls 0 z0 surface roughness m emin turb energie minimale lmixmin longueur de melange emissiv Emissivite du sol martien emisice Emissivite des calottes albedice Albedo des calotte iceradius mean scat radius of CO2 snow dtemisice time s
11. describes the input output data of the model The input files are the files needed to initialize the model state of the atmosphere at instant 0 as well as a dataset of boundary conditions and the output files are historical files archives of the atmospheric flow history as simulated by the model the diagfi files the stats files the daily averages etc The means to edit or visualize these files editor ncdump and the graphics software grads are also explained Chapter 8 explains how to run a simulation including the water cycle Chapter 9 illus trates how to run the model with the photochemical module Finally chapter 10 will help you to use a 1 dimensional version of the model which may be a simplier tool for some analysis work Chapter 2 Main features of the model 2 1 Basic principles The General Circulation Model GCM calculates the temporal evolution of the different variables listed below that control or describe the Martian meteorology and climate at different points of a 3D grid see below that covers the entire atmosphere From an initial state the model calculates the evolution of these variables timestep by timestep e At instant t we know variable X temperature for example at one point in the atmosphere e We calculate the evolution the tendencies 25 33 etc arising from each physical phenomenon calculated by a parameterization of each of these phe nomenon
12. for example heating due to absorption of solar radiation e At the next time step t t we can calculate X45 from X and This is the integration of the variables in time For example X 5 X t 2X Ox The main task of the model is to calculate these tendencies 55 arising from the different parameterized phenomenon 2 2 Dynamical Physical separation In practice the 3D model operates in two parts one dynamical part containing the numerical solution of the general equations for at mospheric circulation This part including the programming is common to the Earth and Martian model and in general for all atmospheres of the terrestrial type a second physical part that is specific to the planet in question and which calculates the forced circulation and the climate details at each point The calculations for the dynamical part are made on a 3D grid with horizontal ex changes between the grid boxes whereas the physical part can be seen as a juxtaposition of atmosphere columns that do not interact with each other diagram 2 1 The dynamical and physical parts deal with variables of different natures and oper ate on grids that are differently constructed The temporal integration of the variables is based on different numerical schemes simple such as the one above for the physical part and more complicated the Matsuno Leapfrog scheme for the dynamical part The timesteps are
13. kg m tsurf surface temperature K tsoil temperature at different layers under the surface K emis surface emissivity q2 wind variance or more precisely the square root of the turbulent kinetic energy qsurf01 qsurf02 etc tracer budget on the surface kg m 2 2 4 5 How tracers are handled The model may include different types of tracers dust particles which may have several modes chemical species which depict the chemical composition of the atmosphere co2 nqchem min co nqchem min 1 nqchem min 2 o 1d nqchem min 02 nqchem min 4 03 nqchem min 5 h nqchem min 6 h2 nqchem_min 7 oh nqchem_min 8 ho2 nqchem_min 9 h202 nqchem min 10 n2 nqchem min 11 ar nqchem min 12 If you choose not to handle dust particles general case then nqchem_min 1 10 photochemistry photochem thermochem es dust water ice water nqchem_min nqmx 1 nqmx dustbin q2 iceparty water Figure 2 5 tracers management water vapor and water ice particles h20 corresponds to the nqmx tracer nqmx is chosen when compiling with the option t nqmx If the option ice is chosen water ice corresponds to the nqmx 1 th tracer These tracers are managed with one unique vector by using different parameters Fig ure 2 5 describes this vector The inclusion of these tracers in the calculation can be con t
14. makefile which describes the compilation process is created automatically by the script create_make_gcm This utility program recreates the makefile file when necessary for example when a source file has been added or removed since the last compilation None of this is visible to the user To compile the model just run the command makegcm with adequate options e g makegcm d 62x48x32 p mars gom as discussed below and described in section 4 2 The nakegcm command compiles the model by calling the make utility detailed description of how it functions is given in the help manual below which will also be given by the makegcm h command Note that before compiling the GCM with makegcm you should have set the environment variable LIBOGCM to a path where intermediate objects and libraries will be generated In Cshell under Unix this would be achieved by the following command line setenv LIBOGCM users me put GCM objects there 23 1 Tnitialisation phyetad F surfini F iniorbit F initracer F solarlong F 1 5 Calculation of mean mass and cp and thermal conduction coeff concentration F Calculation of the radiative tendencies radiative transfer longwave and shortwave for CO2 and dust dustopacity F and callradite F 8 Gravity wave and subgrid scale topography drag calldrag noro F 10 Vertical diffusion turbulent mixing N vidfc F 12 Convective adjustment convadj F physiq F 14 Condensation and sublima
15. model can accumulate any variable from any subroutine of the physical part by calling subroutine wstat 42 This save is performed at regular intervals 12 times a day An average of the daily evolutions is calculated for example for 10 day run the averages of the variable values at OhTU 2hTU 4hTU 24hTU are calculated These data are stored in statistics file stats nc 43 Chapter 7 Zoomed simulations The LMD GCM can use zoom to enhance the resolution locally In practice one can increase the latitudinal resolution on the one hand and the longitudinal resolution on the other hand 7 1 To define the zoomed area The zoom is defined in run def Here are the variables that you want to set EAST longitude en degres du centre du zoom clon zoom center degree latitude en degres du centre du zoom clat zoom center degree N facteur de grossissement du zoom selon longitude grossismx Typically 1 5 2 or even 3 see below facteur de grossissement du zoom selon latitude grossismy Typically 1 5 2 or even 3 see below longitude en degres du centre du zoom clon Fonction f y hyperbolique si true sinon sinusoidale fxyhypb must be set to T for a zoom whereas it must be F usually extension en longitude de la zone du zoom dzoomx This is the total longitudinal extension of the zoomed region degree It is recommended that grossismx x dzoomx lt 200 extension en longitude de la zone du zoom dzoo
16. rad transfer is computed every iradia physical timestep callg2d Output of the exchange coefficient mattrix for diagnostic only F rayleigh Rayleigh scattering should be F for now F Tracer dust water ice and or chemical species options use if tracer T dustdevil DUST lifted by dust devils scavenging DUST Scavenging by CO2 snowfall sedimentation DUST WATERICE Gravitationnal sedimentation unes WATERICE includes water q nqmx 1 water must be T ie WATERICE Radiatively active transported atmospheric water ice 20 WATER Compute water cycle using q nqmx ee WATER current permanent caps at both poles T IS RECOMMENDED T caps T means Ncap is a source of water S pole is a cold trap photochem PHOTOCHEMISTRY chemical species included Thermospheric options relevant if tracer T callthermos call thermosphere thermoswater WATER included without cycle only if water F 32 dustbin DUST Transported dust if gt 0 uses q 1 to q dustbin 0 active DUST Radiatively active dust uses q 1 to q dustbin di DUST needs dustbin 1 use mass q 1 and number q 2 mixing ratio to predict dust size ut DUST lifted by GCM surface winds callconduct call thermal conduction matter only if callthermos T calleuv call EUV heating matter only if callthermos T callmolvis call molecular viscosity matter only if callthermos T cal
17. the same directory then type gcm e You might also want to keep all messages and diagnotics written to standard output i e the screen You should then redirect the output to some file e g gcm out gcm e gt gcm out 4 5 Visualizing the output files If you have never used the graphic software GrAds we strongly recommend spending half an hour to familiarize yourself with it by following the demonstration provided for that purpose The demo is fast and easy to follow and you will learn the basic commands To do this read file distrib local grads sample For example to visualize files diagfi nc and stats nc NetCDF files diagfi nc and stats nc can be accessed directly using GrAdS thanks to utility program gradsnc the user does not need to intervene To visualize the temperature card in the 5th layer using file diagfi nc for example Visualization using GrAdS grads return return opens a landscape window ga sdfopen diagfi nc ga query file displays info about the open file including the name of the stored variables Shortcut q file ga set z 5 fixes the altitude to the 5th layer ga set t 1 fixes the time to the first stored value 17 Creation of the initial state start_archive nc run def callphys def Z2sig def surface nc V startne startfi nc run def callphys def z2sig def Simulation 1 restart nc restar
18. 0 Appendix C2 e Calculation of the turbulent diffusion coefficients Forget et al 1999 3 3 2 Convection convadj See Hourdin et al 1993 13 3 3 3 Effects of subgrid orography and gravity waves calldrag_noro drag_noro See Forget et al 1999 and Lott and Miller 1997 3 4 Surface thermal conduction soil Thesis of Fr d ric Hourdin LMD Universit Paris 7 1992 section 3 3 equations and Appendix Numerical scheme 3 5 Condensation In Forget et al 1998 article published in Icarus Numerical method for calculating the condensation and sublimation levels at the surface and in the atmosphere newcondens explained in the appendix Description of the numerical scheme for calculating the evolution of snow emissivity co2 snow explained in section 4 1 3 6 Tracer transport and sources e Van Leer transport scheme used in the dynamical part tracvl and vlsplt in the dynamical part Hourdin and Armengaud 1999 Transport by turbulent diffusion in vdifc convection in convad j sedi mentation sedim dust lifting by winds dustlift see note Preliminary design of dust lifting and transport in the Model ESA contract Work Package 4 1998 available on the web Dust lifting by Dust devils dust devil Renno et al 1998 Dust transport by the Mass mixing ratio Number mixing ratio method for grain size evolution article by F Forget in pro
19. 02 316 1998 Y Fouquart and B Bonnel Computations of solar heating of the Earth s atmosphere A new parametriza tion Contrib Atmos Phys 53 35 62 1980 Hourdin J L Dufresnes Fournier and Hourdin Net exchange reformulation of radiative transfer in the CO2 15m band on mars Article in preparation 2000 F Hourdin A new representation of the 15 band for a Martian general circulation model J Geo phys Res 97 E11 18 319 18 335 1992 F Hourdin and A Armengaud Test of a hierarchy of finite volume schemes for transport of trace species in an atmospheric general circulation model Mon Wea Rev 127 822 837 1999 F Hourdin Le Van F Forget and Talagrand Meteorological variability and the annual surface pressure cycle on Mars J Atmos Sci 50 3625 3640 1993 S Lef vre S Lebonnois F Montmessin and F Forget Three dimensional modeling of ozone on Mars Journal of Geophysical Research Planets 109 E07004 2004 S R Lewis M Collins P L Read F Forget F Hourdin R Fournier C Hourdin O Talagrand and J P Huot A climate database for Mars J Geophys Res 104 24 177 24 194 1999 F Lott and M Miller A new sub grid scale orographic drag parametrization its formulation and testing J R Meteorol Soc 123 101 128 1997 F Montmessin F Forget P Rannou M Cabane and R M Haberle Origin and role of water ice clouds in the Martian water c
20. 2 390 190 598 630 339 356 155 72 683 395 193 596 635 342 082 160 74 925 400 196 618 640 344 783 165 71 168 405 199 662 645 347 461 170 79 413 410 202 729 650 350 116 175 81 661 415 205 818 655 352 748 180 83 912 420 208 927 660 355 357 185 86 167 425 212 056 665 357 945 669 0 Spring equinox N 190 88 427 430 215 203 670 0 512 193 47 90 Summer solstice N 195 90 693 435 218 368 675 3 057 200 92 965 440 221 549 680 5 583 205 95 245 445 224 746 685 8 089 210 97 532 450 227 955 690 10 577 215 99 827 455 231 177 695 13 046 220 102 131 460 234 409 700 15 498 225 104 446 465 237 650 705 17 933 230 106 770 470 240 898 710 20 351 235 109 107 475 244 151 715 22 755 240 111 455 480 247 408 720 25 143 53 Appendix B Utilities A few post processing tools which handle GCM outputs files diagfi nc and stats nc are available on the web at http www lmd jussieu fr forget datagcm Utilities The directory contains compiled executables e files of the tools decribed below along with some examples of input instruction def files and a README There is also a SOURCES directory which contains the Fortran sources of the codes if you should need to recompile them on your platform B 1 concatnc This program concatenates consecutive output files diagfi nc oreven stats nc files for a selection of variable in order to obtain one single big file
21. 48 e It has been found that when zooming in longitude on must set ngroup 1 in dyn3d groupeun F Otherwise the run is less stable e The very first initial state made with newstart e can be noisy and dynamically unstable It may be necessary to strongly increase the intensity of the dissipation and increase day step in run def for 1 to 3 sols and then use less strict values e If the run remains very unstable and requires too much dissipation or a too small timestep a good tip to help stabilize the model is to decrease the vertical extension of your run and the number of layer one generally zoom to study near surface process so 20 to 22 layers and a vertical extension up to 60 or 80 km is usually enough 45 Chapter 8 Water Cycle Simulation In order to simulate the water cycle with the LMD GCM e In callphys def set tracer to true tracer T Use the same options as below for the Tracer part the rest does not change compared to the basic callphys def The important parameters are wat er T to include water vapor tracer iceparty T to use water ice tracer and sedimentation T to allow sedimentation of water ice clouds Tracer dust water water ice and or chemical species options relevant if tracer T dustbin DUST Transported dust if gt 0 uses q 1 to q dustbin 0 active DUST Radiatively active dust uses q 1 to q dustbin F doubleq DUST needs dustbin 1 use mass q 1 and number q 2 mixing
22. B The latest version of the NetCDF package is available on the web at the following address http www unidata ucar edu packages netcdf faq html howtoget This package contains everything needed to create object library libnetcdf a the necessary 1include files h and to compile the basic NetCDF software nc dump and ncgen 15 To ensure that during compilation the model can find the library and include files that correspond to the type of machine used you should declare environment variables NCDFINC and NCDFLIB NCDFLIB Name of the directory containing the object library libnetcdf a and NCDFINC name of the directory containing the NetCDF include files netcdf inc for the different platforms setenv NCDFINC S PATH3 include setenv NCDFLIB PATH3 lib Install GrAdS For people working at LMD thanks to the brilliant Laurent Fairhead all you need to do to access GrAdS and its environment is to add the following to your cshrc this should already be in env_soft source distrib local grads grads env Copy compilation script makegcm into SHOME bin for example This script is avail able in SPATH1 LMDZ MARS or ask the LMD Finally make sure that you have access to all the executables needed for using the model and remember to set the corresponding pathes UNIX function 1make Fortran compiler f90 ncdump grads 4 20 Compiling the model Example 1 Compiling the Martian model at grid
23. KKKKKKKK Autre reglage possible e cc deltay deplacement en degres en de la zone du zoom cc dans xxx inigeom F xxx 6 2 2 callphys def General options tracer Run with or without tracer transport F diurnal Diurnal cycle if diurnal F diurnal averaged solar heating B Season Seasonal cycle if season F Ls stays constant like in start T lwrite want some more output on the screen F stats Saving statistics in file cumul T calleofdump Saving EOF profiles in file profiles for Climate Database 31 F Dust scenario Used if the dust is prescribed i e if tracer F or active F iaervar 1 Dust opt deph read in startfi 2 Viking scenario 3 MGS scenario 4 4 Mars Year 24 from TES assimilation iddist Dust vertical distribution 0 old distrib Pollack90 3 71 top set by topdustref 2 Viking scenario 3 MGS scenario topdustref Dust top altitude km Matter only if iddist 1 55 Physical Parameterizations callrad call radiative transfer callnlte call NLTE radiative schemes matter only if callrad T callnirco2 call CO2 NIR absorption matter only if callrad T calldifv call turbulent vertical diffusion calladj call convective adjustment callcond call CO2 condensation callsoil call thermal conduction in the soil calllott call Lott s gravity wave subgrid topography scheme Radiative transfer options iradia the
24. User Manual for the LMD Martian Atmospheric General Circulation Model Fran ois FORGET E Millour Dassas Christophe HOURDIN Fr d ric HOURDIN and Yann WANHERDRICK initial version translated by Gwen Davis LMD May 31 2007 Draft Contents Introduction Main features of the model 2 1 Basic Principles s seb RR RE due pc mes E hs 2 2 Dynamical Physical separation 2 3 Gnd 4 ge ESL I A oe de er eb 2 3 1 Horizontal ends 8 4 bow m Re SES 2 32 Vertical grids BALAI a aise 2 4 Variables used in the model 2 4 Dynamical parts lt i ban des eee dee ate Ee Ree 2 4 2 Physical mp ty SO P ee 243 How tracers are handled The physical parameterizations of the Martian model some references 3 1 General iso E c BS SE Bee LR ER S 3 2 Radiative transfer gt od amp poe eee ere Gals 3 2 1 gas absorption emission 3 3 Subgrid atmospheric dynamical processes 3 3 1 Turbulent diffusion in the upper layer 3 3 2 Convection LEA ee Pay 3 3 3 Effects of subgrid orography and gravity waves 3 4 Surface thermal conduction 3 5 Condensation 3 6 Tracer tr
25. also different The physical timestep is Iphysiq times longer than the dynam ical timestep as the solution of the dynamic equations requires a shorter timestep than the forced calculation for the physical part Dynamics Physics Dynamical tendencies 2 ql xy z T z T z 910 910 Tendencies due to radiative transfer condensation subgrid dynamics Physical fields Figure 2 1 Physical dynamical interface In practice the main program that handles the whole model gem F is located in the dynamical part When the temporal evolution is being calculated at each timestep the program calls the following 1 Call to the subroutine that handles the total tendency calculation 9x arising from the dynamical part caldyn F 2 Integration of these dynamical tendencies to calculate the evolution of the variables at the following timesteps subroutine integrd F 3 Every Tphysiq with the physical model physiq F that calculates the evolution of some of the purely physical variables ex Tsurf and returns the tendencies 2 arising from the physical part dynamic timestep a call to the interface subroutine calfis F 4 Integration of the physical variables subroutine addfi F 5 Similarly calculation then integration of the tendencies arising from the horizontal dissipation and the sponge layer etc Remark The physical par
26. ansport and sources 3 7 Thermosph ere dk Ue drag wes Running the model a practice simulation 4 1 Installing the model 4 2 Compiling the model 43 Input files initial state 44 Running the model 45 Visualizing the output files 4 6 Resuming simulation 47 Chansmulations ds ae eR du M LE Sud 4 8 Creating and modifying initial states 4 8 1 Using program newstart 4 8 2 Creating the initial start _archive nc file 4 8 3 Changing the horizontal or vertical grid resolution 10 Programming organization and compilation 5 1 Organization of the model source files 23 2 PropramMINE x 5 ev uo ee Be Ge but me E A 5 3 Model organization 5 4 Compiling the model Input Output 6 1 NetCDE format 2s 9 19 X 7e ER AOE 6 1 1 NetCDF file editor ncdump 6 1 2 Graphic visualization of the NetCDF files using GrAds 6 2 Inputs Sr LS SEE Kou ES ug ut ei te ee 6 2 1 gt TUNEL PR Ra UID Buts 6 2 2 callphys det c Mir b 9B Bane dex phe xs 0 28 Z2sig del i ean re EORR
27. artian solar days or sols 1 sols 88775 s from the northern spring equinox The following table gives the correspondence between sols and L calculated for the GCM using one Martian year 669 sols exactly 52 sol Ls sol Ls sol Ls 0 360 000 Spring equinox N 240 111 455 480 247 408 5 2 550 245 113 816 485 250 666 10 5 080 250 116 190 490 253 925 15 7 590 255 118 578 495 257 182 20 10 081 260 120 981 500 260 435 25 12 554 265 123 400 505 263 683 30 15 009 270 125 835 510 266 924 514 76 270 Winter solstice N 35 17 447 275 128 287 515 270 156 40 19 869 280 130 756 520 273 377 45 22 275 285 133 243 525 276 587 50 24 666 290 135 750 530 279 783 55 27 043 295 138 275 535 282 965 60 29 407 300 140 821 540 286 130 65 31 758 305 143 388 545 289 277 70 34 096 310 145 975 550 292 406 75 36 423 315 148 585 555 295 515 80 38 739 320 151 217 560 298 604 85 41 046 325 153 872 565 301 671 90 43 343 330 156 550 570 304 715 95 45 631 335 159 251 575 307 737 100 47 912 340 161 977 580 310 735 105 50 186 345 164 727 585 313 709 110 52 453 350 167 502 590 316 658 115 54 714 355 170 301 595 319 583 120 56 970 360 173 126 600 322 483 125 59 222 365 175 975 605 325 358 130 61 471 370 178 850 610 328 207 371 99 180 Autumn equinox N 135 63 716 375 181 750 615 331 032 140 65 959 380 184 675 620 333 831 145 68 201 385 187 624 625 336 606 150 70 44
28. cale for snow metamorphism tauvis profondeur optique visible moyenne obliquit planet obliquity deg peri day perihelion date sol since Ls 0 periheli min sun mars dist Mkm aphelie max sun mars dist Mkm 20 Second set of questions flat no topography aquaplanet bilball albedo inertie thermique uniforme coldspole sous sol froid et haut albedo au pole sud q 0 traceurs a zero ini q traceurs initialises pour la chimie ini q H20 idem sauf le dernier traceur H20 ini q iceH20 idem sauf ice et H20 watercapn H20 ice sur la calotte permanente nord watercaps H20 ice sur la calotte permanente sud wetstart start with a wet atmosphere igset give a specific value to tracer iq isotherm Temperatures isothermes et vents nuls co2ice 0 elimination des calottes polaires de CO2 ptot pression totale Program newstart e creates files restart nc restartfi nc that you generally need to rename for instance rename them in start0 nc and startfiO nc if you want to use run0 or run mcd starting with season 0 rename them in start nc and startfi nc if you just want to perform one run with gcm e 4 8 2 Creating the initial start archive nc file Archive file start archive nc is created from files start nc startfi nc by program start2archive Program start2archive compiles to the same grid resolution as the start nc and startfi nc grid resolution For example makegcm d 64x48x25 p mars star
29. d executable testphys1d e the compiled model in the directory from which you ran the makegcm command 10 2 1 runs and input files The 1 D model does not use an initial state file the simulation will be long enough to obtain a balanced state Thus to generate a simulation simply type gt testphysld e The following files are available in the same directory SPATH1 LMDZ MARS deftank copy them into your working directory first callphys def controls the options in the physical part just like for the 3D GCM Z2sig def controls the vertical discretization no change needed in general func tions as with the 3D GCM testphysld def controls the 1 D run The last file is specific to the 1 D model It contains the following 0 Initial day martian sol 0 at Ls 0 0 initial local time between 0 and 24 48 number of time step per day T Run duration sols 700 psurf Surface pressure Pa 0 2 tauref reference dust opacity at 700 Pa true tau taurefxpsurf 700 80 latitude degrees 50 Ded ground albedo under the ice 400 ground thermal inertia SI 10 composante vers l est du vent geostrophique u os composante vers le nord du vent geostrophique v 0 initial CO2 ice mass kg m 2 T Hybrid vertical coordinate T Hybrid F sigma Initial temperature profile 5 ichoice Kind of initial profile see below 200 tref reference temperature K used if ichoic
30. e 1 0 isin if isin 1 add a perturbation to profile 26 5220 pic pic perturbation gauss pour ichoice 6 ou 7 10 largeur de la perturbation gauss pour ichoice 6 ou 7 30 hauteur de la perturbation gauss pour ichoice 6 ou 7 differents profils d atmospheres T f z c ichoice 1 Temperature constante T tref c ichoice 2 profil Savidjari comme Seiff mais avec dT dz cte 1 3 Lindner profil polaire E ichoice 4 inversion c ichoice 5 Seiff profile standard base sur les entrees Viking 1 6 constante perturbation gauss level c ichoice 7 T constante perturbation gauss km c ichoice 8 Read in an ascii file profile 10 3 Output data During the entire 1D simulation you can obtain output data for any variable from any physical subroutine by using subroutine writegld This subroutine creates file gld nc that can be read by GRADS This subroutine is typically called at the end of subroutine physiq Example of a call to subroutine writegld requesting temperature output ngrid horizontal point nlayer layers variable pt called in K units CALL writegld ngrid nlayer pt T K 51 Appendix GCM Martian Calendar For Mars dates and seasons are expressed in Solar Longitude Lg in degrees or in radians counting from the northern hemisphere spring equinox In the GCM time is counted in M
31. effect but using an old numerical formulation Hourdin 1992 article 12 e At high altitudes parameterization of the thermal radiative transfer nltecool when the local thermodynamic balance is no longer valid e g within 0 1 Lopez Valverde et al 2001 Report for the ESA available on the web as CO2 non LTE cooling rate at 15 um and its parameterization for the Mars atmosphere Absorption of near infrared radiation nirco2abs e Forget et al 1999 3 2 2 Absorption emission and diffusion by dust Dust spatial distribution dustopacity e Vertical distribution and description of MGS and Viking scenarios in the ESA re port Mars Climate Database V3 0 Detailed Design Document by Lewis et al 2001 available on the web e For the MY24 scenario dust distribution obtained from assimilation of TES data is used and read via the readtesassim routine Thermal IR radiation lwmain e Numerical method 7oon et al 1989 e Optical properties of dust Forget 1998 Solar radiation swmain e Numerical method Fouquart and Bonel 1980 e Optical properties of dust see the discussion in Forget et al 1999 which quotes Ockert Bell et al 1997 and Clancy and Lee 1991 3 3 Subgrid atmospheric dynamical processes 3 3 1 Turbulent diffusion in the upper layer vdifc e Implicit numerical scheme in the vertical see the thesis of Laurent Li LMD Uni versit Paris 7 199
32. ep used for the dissipation If idissip is too short the model will lose time in the calculations But if idissip is too long the dissipation will not be parametrized correctly and the model will be more likely to diverge A check must be made in order of size that idissip tetagdiv xdaystep 88775 idem for tetagrot and tetatemp This is now tested automatically during the run iphysiq corresponds to the physical timestep In practice we normally set this time to the order of half an hour We therefore set iphysiq day_step 48 Contents of run def Nombre de jours d integration nday 9999 nombre de pas par jour multiple de iperiod ici pour dt 1 min day step 480 periode pour le pas Matsuno en pas iperiod 5 periode de sortie des variables de controle en pas iconser 120 periode d ecriture du fichier histoire en jour iecri 100 periode de stockage fichier histmoy en jour periodav 60 periode de la dissipation en pas idissip L choix de l operateur de dissipation star ou non star lstardis 29 T avec ou sans coordonnee hybrides hybrid T nombre d iterations de l operateur de dissipation nitergdiv 1 nombre d iterations de l operateur de dissipation nitergrot 2 nombre d iterations de l operateur de dissipation niterh temps de dissipation des plus petites long d ondes tetagdiv 3000 temps de dissipation des
33. er concern the physical and dynamical grids They are the following the horizontal coordinates rlonu rlatu rlonv rlatv for the dynamical part lati long for the physical part the coefficients for passing from the physical grid to the dynamical grid cu cv only in the dynamical header and finally the grid box areas aire for the dynamical part area for the physical part Surface conditions The surface conditions are mostly given in the physical NetCDF files by variables phisfi for the initial state of surface geopotential albedodat for the bare ground albedo inertiedat for the surface thermal inertia zmea zstd zsig zgam and zthe for the subgrid scale topography For the dynamical part physinit for the initial state of surface geopotential 37 Remark variables phisfi and physinit contain the same information surface geopotential but physfi gives the geopotential values on the physical grid while physinit give the values on the dynamical grid Physical and dynamical state variables To save disk space the initialization files store the variables used by the model rather than the natural variables For the dynamical part ucov and vcov the covariant winds These variables are linked to the natural winds by ucov cu uandvcov x v teta the potential temperature or more precisely the potential enthalpy linked to temperature T by 0 K T va q01 q02
34. gress Watercycle see Montmessin et al 2004 Chemistry see Lef vre et al 2004 3 7 Thermosphere e See Angelats i Coll et al 2005 and Gonz lez Galindo et al 2005 14 Chapter 4 Running the model practice simulation This chapter is meant for first time users of the LMD model As the best introduction to the model is surely to run a simulation here we explain how to go about it you will need are files necessary to build the GCM all are in the LMDZ MARS directory as well as some initial states to initiate simulations see below Once you have followed the example given below you can then go on to change the control parameters and the initial states as you wish more detailed description of the model s organization as well as associated inputs and outputs are given in sections 5 and 6 4 1 Installing the model Copy the basic model directory LMDZ MARS into your files the contents of this direc tory are described in chapter 5 Set the environment variables for the model LMDGCM Directory path where you have stored the model full path setenv LMDGCM SPATH1 LMDZ MARS LIBOGCM Directory path you should create this directory 1ibo for example if that directory does not exist then makegcm will create it where the object libraries will be stored when you compile the model with makegcm setenv LIBOGCM SPATH2 libo Install NetCDF and set attribute environment variables NCDFINC and NCDFLI
35. gure 6 2 They contain a header with a control variable followed by a series of variables defining the physical and dynamical grid a series of non temporal variables that give information about surface conditions on the planet time variable giving the values of the different instants at which the temporal variables are stored a single time value t 0 for start as it describes the dynamical initial states and no time values for startfi as it describes only a physical state the model state variables on the grid corresponding to the different instants of the selected simulation adjustable by a timestep for the output files being simulated diagfi histmoy etc To visualize the contents of a start file using the ncdump editor ncdump h start nc netcdf start dimensions index 100 rlonu 65 latitude 49 longitude 65 34 DYNAMIQUE ex start Ent te PHYSIQUE ex startfi Ent te 1_ controle tab_cntrl 2 3 rlatu Informations 4 rlonv sur la grille 1_ controle tab cntrl 2 hor coor 3 vert coor Informations 4 vert2 coor sur la grille Conditions de surface Conditions de surface phisinit 1 phisfi 2 albedodat 4 zmea temps temps Valeur des instants auxquels sont stock es les variables Valeur des instants auxquels sont stock es les variables Stockage des variables temporelles Stockage des variables temporelle
36. ific case of hybrid coordinates such that aps 0 and bps P Ps Note that for the hybrid coordinates bps 0 above 50 km leading to pressure levels The user can choose whether to run the model using hybrid coordinates or not by setting variable hybrid in run def to True or False masse the atmosphere mass in each grid box ucov and vcov the covariant meridional and zonal waves These variables are linked to the natural winds by ucov cu u and vcov cv v where cu and cv are constants that only depend on the latitude 401 402 etc the tracer mixing ratio in the atmosphere typically kg kg ucov and vectorial variables are stocked on scalari grids and respectively in the dynamical part see section 2 2 theta q01 ps masse scalar variables are stocked on the scalar grid of the dynamical part 2 4 2 Physical part In the physical part the state variables of the dynamical part are transmitted via an interface that interpolates the winds on the scalar grid that corresponds to the physical grid and transforms the dynamical variables into more natural variables Thus we find winds u and v m s temperature T K the pressure field in the middle of the layers play Pa and at the level of the interlayers plev Pa tracers q01 q02 etc kg kg Furthermore the physical part handles the evolution of the purely physical state vari ables co2ice ice on the surface
37. in include files ccp that are located in directories that were not referenced by default Compiles the adjoint model to the dynamical code filter To select the longitudinal filter in the polar regions filter corresponds to the name of a directory located in The standard filter for the model is filtrez which can be used for a regular grid and for a grid with longitudinal zoom LMDGCM libf Ldirl lfilel Ldir2 lfile2 Adds link to libfilel a libfile2 a located in directories dirl If dirn is ad usr lib for example there is no need to specify Compilation 64 Frederic Hourdin bits for Sun FORTRAN libraries dir2 respectively irectory with an automatic path Ldirn hourdin lmd jussieu fr 26 Chapter 6 Input Output 6 1 NetCDF format GCM input output data are written in NetCDF format Network Common Data Form NetCDF is an interface used to store and access geophysical data and a library that pro vides an implementation of this interface The NetCDF library also defines a machine independent format for representing scientific data Together the interface library and format support the creation access and sharing of scientific data NetCDF was developed at the Unidata Program Center in Boulder Colorado The freely available source can be obtained from the Unidata website http www unidata ucar edu packages netcdf index html A data set in NetCDF format is a sing
38. ions can either be defined by default by editing the makegcm script or in interactive mode d imxjmxlm where im jm and lm are the number of longitudes latitudes and vertical layers respectively t ntrac Selects the number of tracers advected by the dynamical part In current versions of the Earth model ntrac 2 for water vapour and liquid for example Options d and t overwrite file SLMDGCM libf grid dimensions h which contains the 3 dimensions of the horizontal grid im jm lm plus the number of tracers passively advected by the dynamic ntrac in 4 PARAMETER FORTRAN format with a new file SLMDGCM libf grid dimension dimensions im jm lm tntrac f the file does not exist already it is created by the script SLMDGCM libf grid dimension makdim p PHYS Selects the physical parameterization set you require to compile the model The model is then compiled using the physical parameterization sources in directory SLMDGCM libf phyPHYS g grille Selects the grid type This option overwrites file SLMDGCM libf grid fxyprim h with file SLMDGCM libf grid fxy grille h the grid can take the following values 1 reg the regular grid 2 sin to obtain equidistant points in terms of sin latitude 3 new to zoom into a part of the globe O optimisation fortran where the fortran optimizations are the command f90 options include path 25 adjnt filtre link 64 Author Used if the subroutines conta
39. itialize the composition you can run newstart and use the options ini q the 15 tracers are initialized including water ice and vapor ini q h2o the 13 chemical species are initialized water ice is put to zero and water vapor is kept untouched ini g iceh2o the 13 chemical species are initialized water ice and vapor are kept untouched The initialization is done with the files atmosfera LMD may dat and atmosfera LMD min dat that should also be found in the data mars gcm directory Outputs The outputs can be done from the aeronomars calchim F routine for the 14 chemical species The variables put in the diagfi nc and stats nc files are labeled where name is the name of the chemical species e g co2 n name local density in molecule cm 3 dimensional field c name integrated column density in molecule cm 2 dimensional field 49 Chapter 10 1D version of the Mars model The physical part of the model can be used to generate realistic 1 D simulations one at mosphere column In practice the simulation is controlled from main program called testphys1d F which after initialization then calls the master subroutine of the phys ical part physiq F described in the preceding chapters 10 1 Compilation For example to compile the Martian model in 1 D with 25 layers type in compliance with the makegcm function manual described in section 5 4 makegcm d 25 p mars testphysid You can fin
40. le file as it is self descriptive 6 1 1 NetCDF file editor ncdump The editor is included in the NetCDF library By default it generates an ASCII representa tion as standard output from the NetCDF file specified at the input Main commands for ncdump ncdump diagfi nc dump contents of NetCDF file diagfi nc to standard output i e the screen ncdump c diagfi nc Displays the coordinate variable values variables which are also dimensions as well as the declarations variables and attribute values The values of the non coordinate variable data are not displayed at the output ncdump h diagfi nc Shows only the informative header of the file which is the declaration of the dimensions variables and attributes but not the values of these variables The output is identical to that in option c except for the fact that the coordinated variable values are not included ncdump v varl varn diagfi nc The output includes the specific variable values as well as all the dimensions variables and attributes More that one variable can be specified in the list following this option The list must be a simple argument for the command and must not contain any spaces If no variable is specified the command displays all the values of the variables in the file by default 27 90N 150 MA 160 4 Et 70 60N 30N 30S 60S 90S 180 120W 60W 0 60E 120E 180
41. lmoldiff call molecular diffusion matter only if callthermos T thermochem call thermospheric photochemistry matter only if callthermos T solarcondate date for solar flux calculation 1985 lt date lt 2002 1993 4 Solar min 1996 4 ave 1993 4 max 1990 6 6 2 3 z2sig def z2sig def this version for 50 layers between and 400 km 10 00000 H atmospheric scale height km used as a reference only 0040 Typical pseudo altitude m for lst layer z H log sigma 018 wn EOS Glee eiu Rr oP orr 2nd layer eto 0400 1000 228200 460400 907000 73630 19040 54010 97780 5138 9666 0626 5527 369 369 369 369 369 369 369 369 369 369 37 37 37 37 37 37 33 37 37 S7 37 37 37 Cc 0 O1 O1 amp WWNE F ON co N o o B Q4 od GB Ga UA a UA a NS 101 108 115 122 129 136 143 150 157 164 TTE 178 185 192 BR DB DB DB BHA BB EE BA 33 199 437 206 437 213 437 220 437 227 437 234 437 241 437 248 437 255 437 262 437 269 437 276 437 283 437 290 437 297 437 304 437 311 437 318 437 325 437 332 437 339 437 346 437 353 237 360 437 367 437 374 437 381 437 388 437 395 437 6 2 4 Initialization files start and startfi Files start nc and startfi nc like all the NetCDF files of the GCM are con structed on the same model see NetCDF file composition fi
42. mailles float phisfi physical points phisfi title Geopotentiel au sol float albedodat physical points albedodat title Albedo du sol nu float inertiedat physical points 36 inertiedat title Inertie thermique du sol float ZMEA physical_points ZMEA title Relief moyen float ZSTD physical_points ZSTD title Ecartype du relief float ZSIG physical_points ZSIG title Relief parametre sigma float ZGAM physical_points ZGAM title Relief parametre gamma float ZTHE physical_points ZTHE title Relief parametre theta float co2ice physical points co2ice title CO2 ice cover float tsurf physical points tsurf title Surface temperature float tsoil subsurface_layers physical_points tsoil title Soil temperature float emis physical_points emis title Surface emissivity float q2 subsurface_layers physical points q2 title pbl wind variance float qsurfOl physical points qsurfOl title tracer on surface float qsurf02 physical points qsurf02 title tracer on surface global attributes title Fichier demarrage physique Physical and dynamical headers There are two types of headers one for the physical headers and one for the dynamical headers The headers always begin with a control variable described below that is allocated differently in the physical and dynamical parts The other variables in the head
43. me North latitude float longitude longitude longitude long name East longitude longitude units degrees east float altitude altitude altitude long name pseudo alt altitude units km altitude positive up float rlatv rlatv latv title Latitudes aux points float aps altitude aps title hybrid pressure at midlayers aps units h float bps altitude bps title hybrid sigma at midlayers bps units h float ap interlayer ap title hybrid pressure at interlayers ap units h float bp interlayer bp title hybrid sigma at interlayers bp units h float cu latitude rlonu cu title Coefficients de passage cov nature float cv rlatv longitude cv title Coefficients de passage cov lt gt nature float aire latitude longitude H 41 aire title Aires des mailles float phisinit latitude longitude phisinit title Geopotentiel au sol init float mtot Time latitude longitude mtot title total mass of water vapor mtot units kg m2 float icetot Time latitude longitude icetot title total mass of water ice icetot units kg m2 float rice Time altitude latitude longitude rice title ice radius rice units meter float rave Time latitude longitude rave title Mean ice radius rave units meter float co2ice Time latitude longitude co2ice title c
44. my This is the total longitudinal extension of the zoomed region degree It is recommended that grossismy x dzoomy lt 100 raideur du zoom en X taux 2 is for a smooth transition in longitude more means sharper transition raideur du zoom en Y taux 2 is for a smooth transition in latitude more means sharper transition 7 2 Making a zoomed initial state One must start from an initial state archive start archive noc obtained from previ ous simulation see section 4 8 Then compile and run newstart e using the def file designed for the zoom After running newstart e The zoomed grid should visualize using grads for in stance Here is a grads script that can be used to map the grid above a topography map set mpdraw off set grid off sdfopen restart nc set gxout grid set digsiz 0 set lon 180 180 d ps close 1 xxx replace the path to surface nc in the following line sdfopen u forget WWW datagcm datafile surface nc set lon 180 180 set gxout contour set clab off set cint 3 d zMOL 7 3 Running a zoomed simulation and stability issue e dynamical timestep Because of their higher resolution zoomed simulation requires a higher timestep Therefore in run def the number of dynamical timestep per day day step must be increased by more than grossismx or grossismy twice that if necessary However you can keep the same physical timestep 48 sol and thus increase iphysiqaccordingly iphysiq day step
45. nd the input and output data in NetCDF format The physical part has been available since June 2001 including the NLTE radiative transfer code valid at up to 120 km tracer transport the water cycle with water vapour and ice the double mode dust transport model and with optional photochemistry and extension in the thermosphere up to 250km A more general scientific description of the model without tracers can be found in Forget et al 1999 Chapter 2 of this document to be read before any of the others describes the main features of the model The model is divided into two relatively independent parts 1 The hydrodynamic code that is shared by all atmospheres Earth Mars etc that integrates the fluid mechanics equations in time and on the globe and 2 a set of Martian physical pa rameterizations including for example the radiative transfer calculation in the atmosphere and the turbulence mix in the upper layer It is followed by a list of references for anyone requiring a detailed description of the physics and the numerical formulation of the parameterizations of the Martian physical part Chapter 3 For your first contact with the model chapter 4 guides the user through a practice simulation choosing the initial states and parameters and visualizing the output files The document then describes the programming code for the model including a user computer manual for compiling and running the model Chapter 5 Chapter 6
46. o2 ice thickness co2ice units kg m 2 float tsurf Time latitude longitude tsurf title Surface temperature tsurf units K float ps Time latitude longitude ps title surface pressure ps units K float temp Time altitude latitude longitude temp title temperature temp units K float tau Time latitude longitude tau title tau tau units t float q02 Time altitude latitude longitude q02 title mix ratio q02 units kg kg float qsurf02 Time latitude longitude qsurf02 title qsurf qsurf02 units kg m 2 float 401 altitude latitude longitude q l title mix ratio q0l units kg kg float qsurf01 Time latitude longitude qsurfOl title qsurf qsurfOl units kg m 2 The structure of the file is thus as follows the dimensions variable time containing the time of the timestep stored in the file in Martian days since the beginning of the run variable control containing many parameters as described above from rhonu to phisinit a list of data describing the geometrical coordinates of the data file plus the surface topography finally all the 2D or 3D data stored in the run The frequency at which variables are stored in file diagfi nc is set by parameter ecritphy in file run def see section 6 2 1 6 3 3 Stats files As an option adjustable in callphys def the
47. ons in the header of runo e Copy start files start nc startfi nc and rename them start0 nc startfi0 nc e Type rund run0 runs a series of simulations that generate the indexed output files e g start1 startfil diagfil etc including files 1run1 lrun2 etc containing the redi rection of the display and the information about the run NOTE to restart a series of simulations after a first series for example starting from start5 and startfi5 just write the index of the initial files e g 5 in the file named num_run If num_run exists the model will start from the index written in num run If not it will start from startO and startfi O0 NOTE script is available for performing annual runs with 12 seasons at 30 solar longitude as it is in the database script run_mcd also found in directory deftank This script functions with script run0 Just set the number of simulations to 1 in Then copy run def into run def ref and set nday to 9999 in this file To start from startN c edit the file run mcd and comment with a the N months already created and describe N in num run Then run 19 4 8 Creating and modifying initial states 4 8 1 Using program newstart Several model parameters for example the dust optical depth are stored in the initial states NetCDF files start and startfi To change these parameters or to generally change the model resolution use program newstart This program is
48. plus petites long d ondes tetagrot 9000 temps de dissipation des plus petites long d ondes tetatemp 9000 coefficient pour gamdissip coefdis 0 gradiv nxgradrot divgrad pour u v gradiv pour u v nxgradrot pour h divgrad choix du shema d integration temporelle Matsuno ou Matsuno leapfrog purmats F avec ou sans physique physic T periode de la physique en pas iphysiq 10 choix d une grille reguliere grireg T frequence en pas de l ecriture du fichier diagfi ecritphy 120 longitude en degres du centre du zoom clon 63 latitude en degres du centre du zoom clat 0 facteur de grossissement du zoom selon longitude grossismx Ty facteur de grossissement du zoom selon latitude 30 grossismy T Fonction f y hyperbolique si true sinon sinusoidale fxyhypb F extension en longitude de la zone du zoom fraction de la zone totale dzoomx 0 extension en latitude de la zone du zoom fraction de la zone totale dzoomy 0 raideur du zoom en X taux 27 raideur du zoom en Y tauy 2 Fonction f y avec y Sin latit si TRUE Sinon y latit ysinus F Avec sponge layer callsponge T Sponge mode0 u v 0 model u umoy v 0 mode2 u umoy v vmoy mode_sponge 2 Sponge hauteur de sponge km hsponge 130 Sponge tetasponge secondes tetasponge 50000 KKKKKKKKKKKKKKKKKKKKK
49. ratio to predict dust size F lifting DUST lifted by GCM surface winds F dustdevil DUST lifted by dust devils F Scavenging DUST Scavenging by CO2 snowfall F sedimentation DUST WATERICE Gravitationnal sedimentation T iceparty WATERICE Water cycle includes water ice mixing ratio q nqmx 1 T activice WATERICE Radiatively active transported atmospheric water ice water WATER Compute water cycle using q nqmx T caps WATER put the current permanent caps at both poles T photochem PHOTOCHEMISTRY chemical species included Thermospheric options relevant if tracer T callthermos call thermosphere F thermoswater WATER included without cycle only if water F F callconduct call thermal conduction matter only if callthermos T F calleuv call EUV heating matter only if callthermos T F callmolvis call molecular viscosity matter only if callthermos T 46 F callmoldiff call molecular diffusion matter only if callthermos T thermochem call thermospheric photochemistry matter only if callthermos T F solarcondate date for solar flux calculation 1998 Compilation You need to compile with at least 2 tracers If you don t have dust dustbin 0 or other chemical species photochem F compilation is done with the command lines makegcm d 64x48x25 t 2 p mars newstart makegcm d 64x48x25 t 2 p mars gcm Run Same as usual Just make s
50. re or altitude above areoid vertical coordinates Since integrating the hydrostatic equation is required to recast the data the input file must contain surface pressure and atmospheric temperature as well as the ground geopotential If recasting data onto pressure coordinates then the output file name is given by the input file name to which P nc will be appened If recasting data onto altitude above areoid coordinates then a nc will be appened 54 Bibliography 10 11 12 13 14 15 16 17 Clancy and W Lee new look at dust and clouds in the Mars atmosphere Analysis of emission phase function sequences from global Viking IRTM observations Icarus 93 135 158 1991 J L Dufresne Fournier Hourdin and F Hourdin Net Exchange Reformulation of Radiative Transfer in the CO2 15 um Band on Mars Journal of Atmospheric Sciences 62 3303 3319 2005 F Forget Improved optical properties of the Martian atmospheric dust for radiative transfer calculations in the infrared Geophys Res Lett 25 1105 1109 1998 F Forget F Hourdin Fournier C Hourdin Talagrand M Collins S Lewis P L Read and J P Huot Improved general circulation models of the Martian atmosphere from the surface to above 80 km J Geophys Res 104 24 155 24 176 1999 F Forget F Hourdin and Talagrand snow fall on Mars Simulation with a general circulation model Icarus 131 3
51. resolution 64x48x25 for example type in compliance with the manual for the makegcm function given in section 5 4 makegcm d 64x48x25 p mars gcm You can find executable gem e the compiled model in the directory where you ran the makegcm command Example 2 Compiling the Martian model with 2 tracers water vapour and ice makegcm d 64x48x25 t 2 p mars gcm Example 3 Compiling the the Martian model to check for table overflow debugging warning the model compiles very slowly makegcm d 64x48x25 p mars 0O C gcm 16 4 3 Input files initial state In directory SPATH1 LMDZ MARS deftank you will find parameter file run def described in section 6 2 needed for the model For the Martian model you will also need files callphys def and z2sig def The parameters are attributed using the usual values and we recommend running the first simulation without changing them Copy files start nc and startfi nc described in section 6 2 to the same directory You can extract such files from start archive banks of initial states ie files which contain collections of initial states from stndard scenarios and which can thus be used to check if the model is installed correctly stored on the LMD website at http www lmd jussieu fr forget datagcm Starts See section 4 8 for a description of how to proceed to extract start files from start archives 4 4 Running the model Move program gcm e and the input files into
52. roled by setting coresponding options in the callphys def file see Section 6 2 2 The combination of theses options lead to including all or only part of the tracers 11 Chapter 3 The physical parameterizations of the Martian model some references 3 1 General The Martian General Circulation Model uses large number of physical parameterizations based on various scientific theories and some generated using specific numerical methods A list of these parameterizations is given below along with the most appro priate references for each one Most of these documents can be consulted at http www lmd jussieu fr mars html General references Two documents attempt to give a complete scientific description of the current version of the GCM a version without tracers e Forget et al 1999 article published in the JGR e Updated Detailed Design Document for the Model ESA contract Work Package 6 1999 available on the web which is simply a compilation of the preceding article with a few additions that were published separately 3 2 Radiative transfer The radiative transfer parameterizations are used to calculate the heating and cooling ratios in the atmosphere and the radiative flux at the surface 3 2 1 gas absorption emission Thermal IR radiation lwmain e New numerical method solution for the radiative transfer equation Dufresne et al 2005 e Model validation and inclusion of the Doppler
53. rt is optimised using the following less natural variables theta potential temperature linked to T the temperature by 0 T P Pref with k R C note that is called kappa in the dynamical code and rcp in the physical code We take Pref 610 Pa on Mars ps surface pressure DYNAMIQUE PHYSIQUE variables ap bp niveaux de pression ap llm 1 0 bp llm 1 0 x xxekkexk ke XX KK KKK plev nlayer 1 0 aps llm bps llm sso lm elus nlayer play nlayer ap 11m bp 11m OK kk kk plev nlayer aps llm 1 bps llm 1 nlayer 1 play nlayer 1 ap llm 1 bp 1lm 1 plev nlayer 1 2 bps 2 use 2 2 bp 2 1 2 aps 1 bps 1 Laver play 1 ap 1 1 plev 1 Psurf Figure 2 4 Vertical grid description of 11m nlayer atmospheric layers in the programming code 11m is the variable used in the dynamical part and nlayer is used in the physical part Variables ap bp and ap s bp s indicate the hybrid levels at the interlayer levels and at middle of the layers respectively Pressure at the interlayer is Plev l 1 bp I x Ps and pressure in the middle of the layer is defined by Play l aps l bps l x Ps where Ps is surface pressure Sigma coordinates are merely a spec
54. s t 1 C co2ice C tsurf D h tsoil 5 1 1 2 gt q ucov 2 co2ice 5 C VCOV D tsurf 2 C tsoil D D D 23 CR A D i Ucov D co2ice b VCOV 2 tsurf P E h 1501 Figure 6 2 Organization of NetCDF files rlatv 48 altitude 25 interlayer 26 Time UNLIMITED 1 currently variables float controle index controle title Parametres de controle float rlonu rlonu rlonu title Longitudes des points U float rlatu latitude rlatu title Latitudes des points U float rlonv longitude rlonv title Longitudes des points V float rlatv rlatv rlatv title Latitudes des points V float ap interlayer ap title Coef A hybrid pres levels float bp interlayer bp title Coef B hybrid sigma level float aps altitude aps title Coef AS hybrid pressure in midlayer float bps altitude bps title Coef BS hybrid sigma midlayer float presnivs altitude float latitude latitude latitude units degrees_north latitude long_name North latitude float longitude longitude longitude long_name East longitude longitude units degrees_east float altitude altitude altitude long_name pseudo alt altitude units km altitude positive
55. sig def the parameters for the vertical distribution of the layers Examples of these parameter files can be found in the LMDZ MARS deftank directory 6 2 1 run def A typical run def file is given as an example below The choice of variables to be set is simple e g nday integration time while the others do not need to be changed for normal 28 use However the following explanations may be helpful e day step the number of steps per day is governed by the stability criterion called CFL which depends on the horizontal resolution of the model On Mars in the ory the GCM can run with day_st ep 400 using the 64x48 grid but model sta bility improves when this figure is higher day_st ep 960 is recommended using the 64x48 grid According to the CFL criterion day_step should vary in propor tion with the resolution for example day_st ep 480 using the 32 x24 horizontal resolution day_step must also be divisible by iperiod tetagdiv tetagrot tetatemp control the dissipation intensity It is better to limit the dissipation intensity tetagdiv tetagrot tetatemp should not be too low However the model diverges if tetagdiv tetagrot tetatemp are too high especially if there is a lot of dust in the atmosphere Example used with nitergdiv 1 and nitergrot niterh 2 using the 32 24 grid tetagdiv 6000 s tetagrot tetatemp 30000 s using the 64x48 grid tetagdiv 3000 s tetagrot tetatemp 9000 s idissip is the time st
56. t can be run separately for a 1 D calculation for a single column using program testphysld F 2 3 Grid boxes Examples of typical grid values are 64x48x25 64x48x32 or 32x24x25 These are the number of points in longitude latitude and altitude Thus we obtain horizontal grid boxes to the order of 200x200 kilometers near the equator 2 3 1 Horizontal grids Each part uses a different grid Figure 2 2 shows the numbering of the physical and dy namical grids as well as the different possible positions of the variables on these grids To identify the coordinates of a variable at one grid point up down right or left we use coordinates rlonu rlatu rlonv rlatv longitude and latitude in radians For the dynamical grid we repeat values i 1 at i IM 1 periodicity in longitude As for the values at the poles they are duplicated IM 1 times However on the physical grid there is only one value at the poles and there is no periodicity in longitude In practice the calculations are made for a series of NGRID atmospheric columns with NGRID IM x JM 1 2 e grille scalaire de la dynamique Exemple IM 6 JM 4 grille physique 1 IM IM 1 1 2 3 4 5 6 j 1 2 3 JM 4 JM 1 5
57. t2archive Then run start2archive e You now have a start_archive nc file for one season that you can use with newstart If you want to cumulate other initial states for other seasons rerun start2archive e with the start nc and startfi nc corresponding to your new season The new initial state will automatically be added to the start archive nc file present in your directory 4 8 3 Changing the horizontal or vertical grid resolution For example to create initial states at grid resolution 32x24x25 from NetCDF files start and startfi at grid resolution 64x48x32 e Create file start_archive nc with start2archive e compiled at grid resolu tion 64x48x25 using old file z2sig def used previously e Create files newstart nc newstartfi nc with newstart e compiled at grid resolution 32x24x25 using new file z2sig def If you want to create starts files with tarcers for 50 layers using a start_archive nc file done for 32 layers do not forget to use the ini qoption in newstart in order to correctly initialize tracers value for layer 33 to layer 50 You just have to answer yes to the question on thermosphere initialization if you want to initialize the thermosphere part only 1 33 to 1 50 and no if you want to initialize tracers for all layers 1 0 to 1250 21 Chapter 5 Programming organization and compilation The LMD model is organized in basic directory This directory is associated with en vironment variable LMDGCM The example belo
58. tab cntrl 5 FLOAT anneeref annee 0 tab cntrl 6 rad rayon de mars m 3397200 tab cntrl 7 omeg vitesse de rotation rad s 1 tab cntrl1 8 g gravite m s 2 3 72 tab cntrl 9 cpp tab cntrl 10 kappa r cp 70 256793 rcp dans physique tab cntrl 11 daysec duree du sol s 788775 tab cntrl 12 dtvr pas de temps de la dynamique s tab cntrl 13 etotO energie totale tab cntrl 14 ptotO pression totale tab cntrl 15 ztot0 enstrophie totale tab cntrl 16 stotO enthalpie totale tab cntrl 17 angO moment cinetique tab cntrl1 18 pa tab cntrl 19 preff pression de reference 7670 tab cntrl1 20 clon longitude en degres du centre du zoom tab cntrl 21 clat latitude en degres du centre du zoom tab cntrl1 22 grossismx facteur de grossissement du zoom selon longitude tab cntrl1 23 grossismy facteur de grossissement du zoom selon latitude tab 1 25 dzoomx extension en longitude de la zone du zoom tab 1 26 dzoomy extension en latitude de la zone du zoom tab 1 28 taux raideur du zoom en x tab cntrl1 29 raideur du zoom en y The controle variable in the header of a physical NetCDF file startfi nc c Info sur la grille physique tab cntrl 1 tab cntrl 2 tab cntrl 3 c Info sur la Planete Mars pour tab cntrl 5 rad tab_cntrl 6 omeg tab cntrl 7 g tab cntrl1 8 mugaz tab cntrl 9
59. tains the longitudinal filter sources applied in the upper latitudes where the Courant Friedrich Levy stability criterion is violated aeronomars contains the Martian chemistry and thermosphere sources 5 2 Programming The model is programmed in FORTRAN 77 and FORTRAN 90 e The program sources are written in file F files The extension F is the standard ex tension for a FORTRAN file These files must be preprocessed by aC preprocessor such as cpp before compilation Most FORTRAN compliers recognize this exten sion automatically A source file generally corresponds to FORTRAN program or a subroutine or sometimes to a small group of coherent subroutines Constants are placed in COMMON declarations located in the common include files file h In general variables are passed from subroutine to subroutine as arguments and never as COMMON e In some parts of the code for historical reasons we apply the following rule in any subroutine the variables ex name passed as an argument by the calling program are given the prefix p ex pname while the local variables are given the prefix z ex zname As a result several variables change their prefix and thus their name when passing from a calling subroutine to a called subroutine 5 3 Model organization Figure 5 1 describes the main subroutines called by physiq F 5 4 Compiling the model The model is compiled using the UNIX utility program make The file
60. ted atmospheric water ice water WATER Compute water cycle using q nqmx T caps WATER put the current permanent caps at both poles T photochem PHOTOCHEMISTRY chemical species included T Thermospheric options relevant if tracer T callthermos call thermosphere F thermoswater WATER included without cycle only if water F F callconduct call thermal conduction matter only if callthermos T F 48 calleuv call EUV heating matter only if callthermos T F callmolvis call molecular viscosity matter only if callthermos T F callmoldiff call molecular diffusion matter only if callthermos T F thermochem call thermospheric photochemistry matter only if callthermos T F solarcondate date for solar flux calculation 1998 You will need the up to date file jmars yyyymmdd e g jmars 20030707 which contains the photodissociation rates You should find it in the data mars gocm directory of your arborescence Compilation You need to compile with 15 tracers if you don t have dust dustbin 0 13 chemical species q01 to q13 co2 co o o 1d 02 03 h h2 oh ho2 h202 n2 ar water ice last but one tracer water vapor last tracer Compilation is done with the command lines makegcm d 64x48x25 t 15 p mars newstart makegcm d 64x48x25 t 15 p mars gcm Run Same as usual Just make sure that your start files contains the correct num ber of tracers If you need to in
61. tfi nc stats nc es ae run def Simulation 2 2 GCM Boa calphys def a gt Z2sig def Figure 4 1 Input output data 18 ga query dims indicates the fixed values for the 4 dimensions Shortcut q dims ga display temp displays the temperature card for the 5th layer and for the first time value stored Shortcut d T ga gt clear clears the display Shortcut c ga gt set gxout shaded nota contour plot but a shaded one ga gt display temp ga gt set gxout contour returns to contour mode to display the levels ga gt display temp superimposes the contours if the clear command is not used 4 6 Resuming a simulation At the end of a simulation the model generates restart files that contain the final state of the model as shown in figure 4 1 these files of same format as the start files can be used as initial states for a new simulation The restart files just need to be renamed mv restart nc start nc mv restartfi nc startfi nc and running a simulation with those will in fact resume it from where the previous run had ended 4 7 Chain simulations In practice we recommend running chain of simulations lasting several days or longer or hundreds of days at low resolution To do this a script named run0 is available in SPATH1 LMDZ MARS deftank Utilization e Set the length of each simulation in run def e Set the maximum number of simulati
62. tion of carbon dioxide newcondens F 7 TRACERS 6a water and water ice watercloud F 6b call for photochemistry when tracers are chemical species callchim F 6c other scheme for tracer dust transport lifting sedimentation dustdevil F callsedim F 6d updates CO2 pressure variations surface budget 19 Thermosphere thermosphere F 85 Surface and sub surface temperature calculations soil F 9 Writing output files startfi histfi if it s time physdem4 F saving statistics if callstats true wstats F dumping eof if calleofdump true eofdump F output any needed variables in diagfi writediagfi F Figure 5 1 Organigram of subroutine function physiq F 24 Help manual for the makegcm function By default the makegcm command 1 compiles a series of subroutines located in the S LMDGCM libf sub directories The subroutines are then stored in the FORTRAN libraries at S LIBOGCM 2 next makegcm compiles program prog f located by default at SLMDGCM libf dyn3d and makes the link with the libraries Variable LMDGCM must be initialized in your cshrc file or directly in the makegcm file The makegcm command is used to control the different versions of the model in parallel compiled using the compilation options and the various dimensions without having to recompile the whole model The FORTRAN libraries are stored in directory S LIBOGCM OPTIONS The following opt
63. ure that your start files contains the initial states for water with an initial state for water vapor and water ice particles 47 Chapter 9 Photochemical Module The LMD GCM now includes a photochemical module which allows to compute the at mospheric composition e 14 chemical species are included CO background gas CO OC D H HO H209 H20 e In callphys def set tracer to true tracer T Use the same options as below for the Tracer part the rest does not change compared to the basic callphys def You need to set photochem T and to include the water cycle water T iceparty T sedimentation T see Chapter 8 because composition is ex tremely dependent on the water vapor abundance Tracer dust water water ice and or chemical species options relevant if tracer T dustbin DUST Transported dust if gt 0 uses q 1 to q dustbin 0 active DUST Radiatively active dust uses q 1 to q dustbin F doubleq DUST needs dustbin 1 use mass q 1 and number q 2 mixing ratio to predict dust size F lifting DUST lifted by GCM surface winds F dustdevil DUST lifted by dust devils F scavenging DUST Scavenging by CO2 snowfall F sedimentation DUST WATERICE Gravitationnal sedimentation T iceparty WATERICE Water cycle includes water ice mixing ratio q nqmx 1 T activice WATERICE Radiatively active transpor
64. w shows the attribution of this variable using Cshell in UNIX for the model reference version at the LMD setenv LMDGCM users lmdz SOURCES LMDZ MARS Here is a brief description of the directory contents LMDZ MARS libf 11 the model FORTRAN Sources F for cpp and include files h organised in sub directories physics phymars dynamics dyn3d filters filtrez data mars gcm All the surface data topography albedo thermal inertia and initialization files for the chemistry and the troposphere create make Executable used to create the makefil This command is run automatically by makegcm see below deftank A collection of parametrization files required for the run examples of run def 5 1 Organization of the model source files The model source files are stored in various sub directories in directory libf These sub directories correspond to the different parts of the model grid mainly made up of dimensions h file which contains the parameters that define the model grid i e the number of points in longitude IIM latitude JJM and altitude LLM as well as the number of tracers NQMX advected in the dynamical part for example 2 for water vapour and liquid in the basic version of the Earth model dyn3d contains the dynamical subroutines 22 bibio contains some generic subroutines used by all the parts phymars contains the Martian physical sources filtrez con
65. ycle as inferred from a general circulation model Journal of Geophysical Research Planets 109 E18 10004 2004 M E Ockert Bell J F Bell III C McKay J Pollack and F Forget Absorption and scattering properties of the Martian dust in the solar wavelengths J Geophys Res 102 9039 9050 1997 N Rennd M L Burkett and M P Larkin A simple thermodynamical theory for dust devils J At mos Sci 55 3244 3252 1998 O B Toon C P McKay T P Ackerman and K Santhanam Rapid calculation of radiative heating rates and photodissociation rates in inhomogeneous multiple scattering atmospheres J Geophys Res 94 16 287 16 301 1989 55

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