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IRWINDOCUMENT NO.:NIMS/OX/PGJI/SW/136DOCUMENT TITLERADTRANSDOCUMENT NUMBER: NIMS/OX/PGJI/SW/136DOCUMENT STATUS SHEETISSUEREVDATEREASON FOR CHANGE1012/11/94New Software Release2019/12/94Addition of Scattering2120/3/95Addition of further features2230/7/96Major text revisions2323/10/98Long overdue revision23a13/1/00Minor corrections301/7/04Long overdue overhaul DISTRIBUTION LIST NAME NAME1P. IrwinOxford1N. TeanbyOxford1N. Bowles Oxford1C. WilsonOxford1C. TsangOxford1L. FletcherOxford1C. HowettOxfordTable of Contents0. Overview10.1 Reference Documents10.2 Defined fonts21. Introduction31.1 Location of code and reference files52. Atmospheric T,P and VMR Profile Files (.prf)72.1 Profile83. Dust/Aerosol Profiles114. Path134.1 Layers134.2 Paths154.3 Calculation Types164.4 Path File Format174.5 Running Path244.6 Changes in driver file format from Genlbl254.7 Non-LTE255. Radtrans265.1 Line by Line Models (ICONV<10)275.1.2 Line handling in Radtrans285.2 Band Models 9<ICONV<20285.2.1 Band Models using Line data (ICONV=10,11)285.2.2 Band Models using Band data (11<ICONV<20)305.2.3 Summary of Radtrans Band Models325.3 Correlated-K models 19<ICONV<30325.3.1 Correlated-K model using line data (ICONV=20)345.3.2 Malkmus-Lorentz Band Correlated-K (ICONV=21)345.3.3 Goody-Voigt Band Correlated-k (ICONV=22)365.3.4 Exponential Sum Models (ICONV=23)375.3.5 k-Distribution Look-up Table (ICONV=24)375.4 Running Radtrans376. Post Processing of Radtrans Output Spectra396.1 Conv_spec396.2 Li_spec406.3 Pl_spec406.4 Aground446.5 Diskav447. Setting up Spectral Data457.1 Line data457.1.1 Makedb457.1.2 Scan467.1.3 Check_index467.1.4 Li_lines467.1.5 Pl_lines467.1.6 Select467.1.7 Cp_lines487.1.8 Summary487.1.9 Merge497.1.10 Line data Strengths and Absorber Amounts Units497.2 Band Data497.2.1 Makeband517.2.2 Convert_data527.3 Correlated-k data537.4 Gas Continua538. Scattering548.1 Phase Functions and Normalisation548.1.1 Phase functions used in Radtrans558.2 Fourier Decomposition558.3 Doubling and adding568.3.1 Quadrature details588.4 Miscellaneous Calculation Details598.5 Calculation scattering properties608.5.1 Calculating scattering properties with Makephase608.5.2 Format of ‘.sca’ file62Appendix A Radtrans Gas ID Codes65OXFORD PLANETARY GROUPRadtransNIMS/OX/PGJI/SW/136Atmospheric, Oceanic and Planetary Physics, Oxford0. OverviewThis document describes the radiative transfer model Radtrans which has been developed over a number of years by the Planetary Group in Oxford for the modelling of radiances in planetary atmospheres.0.1. Reference Documents[R1]Atmospheric Radiation. Theoretical Basis 2nd Ed, R.M. Goody and Y.L.Yung (1989). Oxford University Press[R2]Integrated Absorption of a Spectral Line with the Voigt Profile, C.D.Rodgers and A.P.Williams (1974). J.Quant. Spectrosc. Radiat. Transfer 14 pp 319-323[R3]Approximate Methods of Calculating Transmission by Bands of Spectral Lines, C.D.Rodgers (1976). NCAR/TN-116+1A[R4]Spectral Parameters of Methane for Remote Sounding of the Jovian Atmosphere, E.K.Strong (1992). D.Phil.Thesis, Oxford[R5]AFCRL Atmospheric Absorption Line Parameters Compilation, McClatchey et al (1973). AFCRL-TR-73-0096[R6]A Description of the Correlated k Distribution Method for Modelling Nongray Gaseous Absorption, Thermal Emission, and Multiple Scattering in Vertically Inhomogeneous Atmospheres, A.A.Lacis and V.Oinas (1991). J.G.R. 96 pp 9027-9063[R7]The Correlated-k Method for Radiation Calculations in Nonhomogeneous Atmospheres, R.Goody, R.West, L.Chen and D.Crisp (1989), J.Quant. Spectrosc. Radiat. Trans. 42 pp 539-550[R8]Calculated Tabulations of H2O Line Broadening by H2O, N2, O2 and CO2 at High Temperature, C.Delaye, J-M Hartmann and J.Taine (1989), Appl. Opt. 28 pp 5080[R9]Estimation of Rotational Line Widths of Carbon Dioxide Bands, G.Yamamoto, M.Tanaka and T.Aoki (1969), J.Quant. Spectrosc. Radiat. Trans. 9 pp 371-382[R10]Oxford Planetary Group Radiative Transfer Models, P. Irwin (1994), NIMS/OX/PGJI/SW/133.[R11]Light Scattering in Planetary Atmospheres, J.E.Hansen and L.D.Travis (1974), Space Sci. Rev 16 527-610.[R12]Modelling of Pressure-Induced FIR Absorption spectra: Molecular Hydrogen Pairs, J.Borysow et al. (1985), Astrophys.J. 296 pp 644-654[R13]Collision-induced Rototranslational Absorption Spectra of H2_He pairs at temperatures from 40 to 3000K, J.Borysow et al. (1988), Astrophys.J. 326 pp 509-515[R14]Nemesis, P. Irwin (2004), CIRS/OX/TR/1392.[R15]Giant Planets of our Solar System, P.Irwin (2003), Springer-Praxis.[R16]Radtran Scattering Code, P. Irwin (1997) NIMS/OX/PGJI/SW/267[R17]NIMS Scattering Study, P. Irwin (1997), NIMS/OX/PGJI/SW/268.[R18]Multiple scattering of polarized light in planetary atmospheres. Part II. Sunlight reflected by terrestrial water clouds, Hansen, J. E (1971), J. Atm. Sci., 28, pp 1400-1426,[R19]Matrix operator theory of radiative transfer. 1: Rayleigh scattering, G.N. Plass et al. (1973), Appl. Opt., 12, pp 314- 3290.2. Defined FontsAs in [R14], in an attempt to make this document easier to read the following fonts are used to denote different objects.Executable programs are underlined. e.g. Radtrans Suites of codes in their own subdirectories are in copperplate font. e.g. RadtransSubroutine files are in courier font. e.g. genrads.fVariables defined within FORTRAN codes are capitalized. e.g. NCONV, IMOD.1. IntroductionThe Radtrans model calculates the transmission, absorption or thermal emission spectra of gaseous paths using one of three radiative transfer (RT) models: 1) line-by-line, 2) band or 3) correlated-k [R1]. In addition to transmission, absorption or thermal emission, Radtrans may compute multiple-scattered spectra, and hemispherically-averaged spectra. Depending on the RT model chosen, spectral information is read in either from line data bases, averaged band parameter, or k-distribution files. All the sub-models use identical methods for calculating the atmospheric gas paths and dust opacities and have identical outputs to allow easy intercomparison. The atmospheric profiles are read in from ‘.prf’ files which contain all the information required to model the atmosphere of any planet. The models are thus not limited to the Earth’s atmosphere like some but are intended to be general and simple to set up for any planet.Radtrans is a development from Genlbl, a general purpose line-by-line transmission calculation routine written by Simon Calcutt. Radtrans combines the LBL functions of Genlbl with faster, though less accurate, band and correlated-k models described in [R10]. The model takes as its input a ‘.drv’ driver file created by the program Path (which takes as its input a ‘.pat’ path definition file) and reads in the required spectral data files together with any additional files required by the particular RT model used (for example dust optical properties and g-intervals). An overview of the processing process is shown in Figure 1.1.Path file(.pat)Driver file(.pat)Key file(.key)PathCross-section file(.xsc)g-interval file(.gin)Scattering file(.sca)H4sIAAAAAAACC+1Uz0tUURT+7psBU0LGISVjlBlxMNMgoqBS8IGmCCoiLoZo0QgTCGqRgUKbt8qt i9qVmzbWv1ALt6IL9+1cuvI/eH7n3XPnXYdxEFzWge/d79577q9zzvcMgApSe5YFjrz+aRdQyADF l/PTgMFJG1DmeAaX7XMe2L0HHJIXDUBnjAonuHTEhAYF8hxhcgd/ZU0lsBDf18Si+g6EWdzWffu5 zvFBj5fCtjp/FAbJvtmkF01kQ9TnemD5XaJDz3fWrv3nXPiHbV59jfrrHsESP3PGjn+L49h/966x Lc/ML2MV66hhk69eYLvFdgnvOFbFBv5dM3WrFctejJcVYq+0Xo507suPnVDg5mRsrp5jay80b4ta Zw9ha+k+IbU2MzU7yfJCrOb8oX4V3VNq7gFPGtS8Sw2lp6S8I0TkfGQ/Tf0v+uzHQztTP8/GJksc uEWseO8sp7UUzfOz1qC3317f1WIJ52h2h8u8tblzKdnIv8OAcnnDtMYqp3HwtSNzd/Q9EstMci/b 79c4DCvv4r332DqtBFdoxfzXyjW1kuYvUJ0cE+PEJ+INk/G9QSturtvTSmN+thN9rOIt411l3D8w 5pvEWpKJ9+xLTmrMwcdkbVHrQ9BLPFadDil3bUF5rzc+6rUy1qf143Rfzdj7fm3yFjdnWrzF6f4p 4de0i1sna11q+In+E67QeWSR8mYavq5uh+V3cEPdttJn4OmzU/UJnRd+AZkX6BTQBwAA (Different format for LBL, band or c-k models)(correlated-k model only)(scattering model only)RadtransBinary output file(.out)Conv_specBinary averaged output file (.ave)Pl_specLi_specOutput ASCII filesFig. 1.1 Overview of Radtrans Processing SoftwareSpectra are calculated in wavenumber space only and the calculated spectra are written to binary ‘.out’ files. Hence these output files must be processed using one of the three post-processors Conv_spec, Li_spec and Pl_spec which are described later and which may transform the spectra to wavelength space if required and write the final output spectra in ASCII form. The basic procedure for calculating a spectrum is this:Construct the ‘.pat’ path file which defines which atmospheric profiles to use, which spectral information to include and the calculation type required.Run Path to create the ‘.drv’ driver file, for which the atmospheric layer properties (pressure, temperature, absorber amount etc.) have been calculated.Run Radtrans to compute the output binary spectra.Process the raw binary ‘.out’ files to the required output using either Conv_spec, Li_spec or Pl_spec (or in some cases Aground, Diskav)This document is laid out in same the order of these steps, except that a description of the atmospheric ‘.prf’ files is first described. Please note that reference ‘.prf’ files and also spectral databases are already available in the directories listed in section 1.1. New users of Radtrans should not need to generate reference ‘.prf’ and spectral database files from scratch, only the ‘.pat’ files.In summary:Section 2 describes the atmospheric temperature, pressure and vmr ‘.prf’ profiles.Section 3 describes the dust/aerosol ‘.prf’ profiles.Section 4 describes the ‘.pat’ path files and the program Path.Section 5 describes the detailed operation of the Radtrans program for the different spectral models available.Section 6 describes the details of the post-processing programs Conv_spec, Li_spec and Pl_spec.Finally Section 7 describes how line-by-line, band and correlated-k spectral databases are set up. Normally this will have already been done for you! In addition, Appendix A lists the Radtrans gas ID and ISO codes.1.1 Location of Code and Reference FilesAll source code is now under CVS management to maintain all versions of the software which might be released. Check document status sheet for issue of software described in this report. For an explanation of the CVS software, see the man pages on the UNIX systems. The central repository of Radtrans is currently based in /home/ahab/plan/irwin/cvsroot and there are three directories of stored programs/data: 1) radtran/ contains the Radtrans source code, 2) raddata/ contains data files accessed by some of the Radtrans routines and 3) radretrieve/ contains retrieval software based upon the Radtrans RT code suite. To access the CVS data you must add the linesetenv CVSROOT /home/ahab/plan/irwin/cvsroot to your .cshrc file and then ‘checkout’ the files you want.All path calculation source code is in the directory:/home/ahab/plan/irwin/cvsroot/radtran/pathAll spectral data calculation source code is in the directory:/home/ahab/plan/irwin/cvsroot/radtran/spec_dataAll Radtrans calculation source code is in the directory:/home/ahab/plan/irwin/cvsroot/radtran/radtranAll collision-induced-absorption source code is in the directory (OSF only):/home/ahab/plan/irwin/cvsroot/radtran/radtran/ciatableAll utility source code is in the directory:/home/ahab/plan/irwin/cvsroot/radtran/rtm_utilRelevant data files for a few routines are in the directory:/home/ahab/plan/irwin/cvsroot/raddataAll standard line data files are in the directory:/home/plan/linedataUseful planetary profile files (.prf files) are in the directory:/home/ahab/plan2/oxpln5/radtran/profilesUseful band data files (.ban files) are in the directory:/home/ahab/plan2/oxpln5/radtran/banddataUseful k-table files (.kta files) are in the directory:/home/ahab/plan2/oxpln5/radtran/ktablesThe code is currently compile-able under OSF using oxpln9, or using the Intel compiler on the newer architecture of departmental Linux machines. You will need to modify the provided makefiles to ensure you compile to your own directories.2 Atmospheric T,P and VMR Profile Files (.prf)Atmospheric profiles are read in from standard format ASCII ‘.prf’ files which contain the following information. The most common format listed below consists of 6 column blocks of data each with a descriptive header:IFORMIPLANET LATITUDE NP NVMR MOLWTID(1) ISO(1) : : : :ID(NVMR) ISO(NVMR)"H P T gas1 gas2 gas3"H(1) P(1) T(1) VMR(1,1) VMR(1,2) VMR(1,3) : : : : : : : : : : : :H(NP) P(NP) T(NP) VMR(NP,1) VMR(NP,2) VMR(NP,3)"Additional gas profiles 4 to ..."VMR(1,4) VMR(1,5) . .....VMR(1,NVMR) : : : : : :VMR(NP,4) VMR(NP,5) ...VMR(NP,NVMR)IFORMDefines the format of the atmospheric profile. Above is the default format with IFORM=0. If IFORM=1, then the pressure column is omitted but everything else is identical.IPLANETPlanet ID (3=Earth, 5=Jupiter etc)LATITUDEPlanet latitude (for calculating centripetal and non-spherical effects on gravity)NPNumber of points in the profile.NVMRNumber of gases whose volume mixing ratio (VMR) profiles are included in the file.MOLWTMean molecular weight of the atmosphere in grams.ID(1)Radtrans identification code of gas 1. See Appendix 1 for definitions of Gas Codes.ISO(1)Radtrans identification code of gas 1's isotope. 0 = all isotopes in standard terrestrial relative abundance.H(1)Height in km of point 1 above reference level (ground for terrestrial planets, usually 1-bar level for gas giants)P(1)Pressure in atm at point 1T(1)Temperature in K at point 1VMR(1,2)Volume mixing ratio of gas 2 at vertical point 1.Given the diverse sources for generating a planetary profile, it is usually necessary to generate new profiles off-line using bespoke software or an ASCII editor. However it is possible to initiate a new profile using Profile, a flexible manipulation program for the ‘.prf’ files which is now explained.2.1 ProfileThis is a general purpose manipulation program for ‘.prf’ files. At initiation, the program asks whether the user wishes to generate a new file or read in and adapt an existing file. If the user chooses to read in an existing file, the program will prompt for the filename and read in the data. If the user chooses to initiate a new file, the program will prompt for the appropriate data and generate the new profile. This first choice is really entirely up to you. For new profiles with only a few vertical points it is probably easier to enter the points manually using Profile. If there are many vertical points however, the user should probably familiarise himself with the ‘.prf’ format and generate a profile off-line. Should the user choose to enter the points manually however, the program will initially assume that you only know the temperature profile as a function of height (IFORM=1). Profile will prompt for the number of vertical points, the planetary mass and radius and the mean molecular weight of the atmosphere. It will then prompt for the altitude and temperature of each point and generate the new profile.Once a profile has been established, manipulation may begin. The program goes into a loop where at each stage the following menu is displayed: --------------------------------------------------- A - display summary of profiles B - add a VMR profile C - remove a VMR profile D - force VMR to saturation vapour pressure E - compute temperature profile from hydrostatic equil. F - compute pressure profile from hydrostatic equil. K - compute height profile from hydrostatic equil. H - output profiles and exit I - multiply pressure by const (e.g. scale bar-atm) P - output IDL compatable profile data M - multiply vmr profile by constant G - Map profile on to new pressure gridW - Set water vmr profile to pr-um V - output single gas VMR profile Q - quit--------------------------------------------------- command? These options are now described:A - display summary of profilesThis option simply displays a summary of the current profile to the screen. A typical output is: profiles contain 51 points, planetary nominal radius = 3400.000 km 5 volume mixing ratio profile(s) included gas: 1 identifier: 2 isotope: 0 gas: 2 identifier: 1 isotope: 0 gas: 3 identifier: 7 isotope: 0 gas: 4 identifier: 5 isotope: 0 gas: 5 identifier: 3 isotope: 0B - add a VMR profileThis option adds a gas volume mixing ratio to the profile. The new profile may be generated in one of three ways:1) read in from an external file. The format of the .vmr file is in default ASCII and must contain the following information:IDGASISOGASVMRH(1)VMR(1) : :VMRH(NV) VMR(NV)IDGAS and ISOGAS are as before and identify which gas the file contains. The next lines then contain the volume mixing ratio at any number of heights. The heights do not have to correspond to those in the existing temperature/ pressure file and the file does not have to have the same number of points. Profile reads in the data and automatically detects the end of the file. The program then interpolates the points and maps them onto the heights of the stored temperature/pressure file2) generate the new VMR profile assuming a constant mixing ratio with height which the program prompts for.3) generate the new VMR profile in the same manner as 1) except reading the data directly from the keyboard and terminating with -1,-1.C - remove a VMR profileSimply removes a VMR profile from the stored profile.D - force VMR to saturation vapour pressureThis option forces an existing VMR profile to be that of a saturated vapour pressure profile. The dependence of saturated vapour pressure (atm) on temperature (K) is assumed to be of the form:H4sIAAAAAAACC7t+9tgsBjCYySDMkABm/Q5nZOBkYGDWZmJgYGIQBYuxAjE3E4zFwyQMVM8CZLEw 8oJpPUYJMM3EyAhWwQlXy8j0//9/BmYgS46BC0iqsfED6f8gQTAAmf+b6QuUN4GRCcIQCMnMTS1W 8EstVwjKz03MA9kFxLqMDAwcQFqRlZmhuKyAgZeBkUEAzQSQM0Cs4MrcpPwcBiaIPkaw/g9AWXaw fkYGW6BuEQz7GQjaDzGHEe6O1AqQO+RI9gmmixKB5pgQ6R+EO2C6tYG6bajgiiSgOa4UhAvMHH2g OX5UcE8I0JwQikIlnmJXMDEkh/AyZFDkinIquCIF6IoGqDk/KYgbIyCrD+qbdyTnHA0GPmDswnia QN5ktLwNcRJInzrj///MYB4AqFLAdGwEAAA= \* mergeformatThe program prompts for the parameters a, b, c and d and then clips the VMR profile where required so that the partial pressure of the gas in question (PP = VMR(I,J)*P(I)) is always less than or equal to the saturated vapour pressure. A list of SVP parameters for commonly used gases may be found in /home/ahab/plan/irwin/cvsroot/raddata/SVP.datE - compute temperature profile from hydrostatic equil.Given the height and pressure profile, together with the mean atmospheric molecular weight, the temperature profile is calculated from hydrostatic equilibrium.F - compute pressure profile from hydrostatic equil.Program prompts for the pressure level of zero height and then computes all pressures at higher altitudes according to hydrostatic equilibrium using the temperature profile and mean molecular weight of the atmosphere.K - compute height profile from hydrostatic equil.Program prompts for the height level of 1atm pressure and then computes all pressures at higher altitudes according to hydrostatic equilibrium using the temperature profile and mean molecular weight of the atmosphere.H - output profiles and exitProgram prompts for a new profile filename and outputs modified data to a new .prf file.I - multiply pressure by a const.Self-explanatory! For example, pressures may be in bars and you want to convert them to atm. P - output IDL compatable profile dataOutputs plotting data to an ASCII file which is readable by IDL routines such as plotprf.pro.M - multiply vmr profile by constantMultiply a specified VMR column by a user-defined constant.G – Map profile on to new pressure gridSelf axplanatory.W – Set water vmr profile to pr-umNormalises water vapour VMR profile to the required column amount in units of precipitable microns.V - output single gas VMR profileOutput new profile to disk containing only the P, T, H information and a single VMR profile.3. Dust/Aerosol ProfilesDust/Aerosol profiles are read in from external ‘.prf’ files which have a similar format to temperature/pressure ‘.prf’ files. The dust ‘.prf’ profiles are defined in terms of specific concentration, i.e. number of dust particles per gram of atmosphere. Up to ten different dust particle profiles can be defined at present in a single ‘.prf’ file. The dust profiles may be written by the program Dust_profile or by hand. At present Dust_profile can generate homogeneous, steady state and simplified cloud model profiles. These are defined as follows:1. Homogeneous= Constant specific concentration with height2. Steady State=Developed for Mars, specific concentration isconstant at low altitudes and then falls off at arate depending on updraft/particle size etc.3. Simple Clouds=Define base height, specific concentration atbase and scale height of vertically extendedcloud.4. Better Clouds=Define base and cloud top pressures, fractionalscale height and required integrated optical depth of vertically extended cloud.Other distributions can be hacked in as necessary or by manually editing an existing dust ‘.prf’ file. Note that to generate the dust profiles, Dust_profile must read the corresponding temperature/pressure profile. The format of a dust ‘.prf’ file is as follows:NAMENPRO,NDUSTDUST(1,1) DUST(1,2) . . . DUST(1,10)DUST(2,1) DUST(2,2) . . . DUST(2,3) " " . . . " " " . . . "DUST(NPRO,1) DUST(NPRO,2) . . . DUST(NPRO,3)Where:NAMECHARname of the fileNPROINTnumber of vertical levelsNDUSTINTnumber of dust typesDUST(I,J)REALdust specific concentration of type J at level I.When Radtrans is run, it looks to see if any dust profiles have been read in and if so prompts the user for the name of the cross-section file. This file contains the extinction cross section of the particles in cm2 and the single scattering albedo for a number of wavelengths across the spectral interval. The value in each calculation bin is then determined by quadratic interpolation. The cross-section file may be written by either of the programs Write_xsec or Makephase or by hand. Makephase calculates the phase functions as well as the extinction x-sections of scattering particles. The spectral calculation programs then use the specific concentration profiles and cross-section spectra to calculate the optical thickness of each path due to dust for each spectral bin.N.B. The default units of Radtrans are that the aerosol concentrations in the ‘.prf’ files are in units of specific density (number of particles per gram) which is a hangover from Mars radiative transfer days and is not very friendly. The default units of the ‘.xsc’ cross-sections are cm2. When Path is run, the number density of dust per layer is calculated and converted to units of particles/cm2. At the end of the day the units are somewhat arbitrary since Radtrans multiplies the number of particles/cm2 in each layer by the particle cross-section to calculate the optical path and it’s only the optical path that really matters! It is thus often (very) convenient to use the fourth model of Dust_profile to normalise the specific density profile of the cloud such that the values in the associated ‘.xsc’ file then equate to total optical depth of the cloud at different wavenumbers rather than the extinction x-section (cm2) of each particle . 4. PathOnce the atmospheric profiles of the required planet have been defined for a radiative transfer calculation, the atmosphere must be split up into layers, so that mean properties can be evaluated. A number of paths through these layers must then be defined. The program which performs this function is Path which writes a driver file (.drv) which defines all the details of the calculation for Radtrans and later Pl_spec. Path takes as its input a ‘.pat’ file (described in this section) which contains the details of the atmosphere, layers and paths and computes the absorber amounts, pressures, temperatures etc. in all the layers and then in all the paths. Path also sets the calculation types which are discussed in section 4.3. Radtrans calculates the transmission, absorption or emission spectra of all the paths defined in the ‘.drv’ file and outputs these to a binary ‘.out’ file. The calculation types are only used by the post processor Pl_spec to control how the path calculations are combined to calculate, for example, the radiance seen in the sideband of a PMR or, as another example the weighting function.4.1 LayersTo perform radiative transfer calculations, the atmosphere in question must first be split into a number of vertical layers. Path reads the temperature/pressure/vmr profiles and the dust profile (if defined) and then using the subroutine layers.f splits the atmosphere into a number of discrete layers. It can do this in a number of ways:1) Split by equal changes in pressure through atmosphere2) Split by equal changes in log(pressure)3) Split by equal changes in height4) Split by equal changes in path length along viewing angle The viewing angle  is defined as the angle of the line of sight of the calculation with respect to the normal at the bottom of the lowest layer.The viewing angle is also used when calculating the mean properties of the layers. If the atmosphere is going to be used for a limb calculation, would be set at 90° and the layer properties calculated for a limb path to the bottom of the lowest layer. If the atmosphere is going to be used for a nadir calculation,  would be set at 0°. The path lengths through the layers are then determined in order that the mean properties of the layers may be calculated. This may be done in one of two ways:1) The mean temperature, pressures (for each gas) and specific dust concentration q (particles/g) are set at the interpolated values at the middle of the layers as seen along the viewing angle. The total absorber amounts in the layer as seen along the viewing angle is then calculated as:H4sIAAAAAAACC7t+9tgsBjBIZ5BhSACzuMIZGTgZGJhdmYAEgyhYjBWIuZlgLB4mGaB6FiCLhZEX TOsxSoBpJkZGsApOuFpGpv///wPNYWCQY+ACkmps/ED6P0gQDEDm/2b6AuVNYGSCMARCMnNTixX8 UssVgvJzE/NAdgGxLiMDAzuQVmRlZAhlEGRgZBBA0w9yBIgVXJmblJ/DwATRxQjW/QFJty1QNy+G 7QwEbYeYwwg1h4mhQ4GXQZJkX6C7h4khW0GQQZxI36C7gpFhC9A38hS7gpEhABjzWnBeCIMUgyYo LTD8YmJjgAWOEjwsQPErwsQLVANiCQNZhkT6gAmrD0xJjg+YD5jg5mgAzbElOSQw3RMMNMcJas5P CtxjyCDC4E52qOgCXeFHdrwyofgmnGTfYLrHCOibGCrEkibQPYlo5QHEGJBKdcb//5nBPAB4xJT0 oAQAAA== \* mergeformatwhere P is the mean pressure (atm), T is the mean temperature (K) and (S1-S2) is the viewing angle path length (km) through the layer. The calculated absorber amount units are in (molecule/cm2) and hence the modified Boltzman constant is calculated as:H4sIAAAAAAACC7t+9tgsBjD4xyDAkABmzQ9nZOBkYGCexczAwMQgChZjBWJuJhiLh0kAqJ4FyGJh 5AXTeowSYJqJkRGsghOulpHp////DECjGOQYuICkGhs/kP4PEgQDkPm/mb5AeRMYITSDQEhmbmqx gl9quUJQfm5iHsguINYFyrMDaUVWJoYOBU6guej6mQjoZwTTH5DMyVbgZWAE+h7DHWCjgitzk/Jz GJhgtkN0M0J1MzLYMvAC/UOqL9BdwchgCDRHGM7TA/IkGDjAPGYGA0NjIF+GbDduAeo2oNiNTAyG BrwMFlBzfpIQY+juMQWyXIj0DWZIgXzjTUa6QXUFxDfBUFf8JNkVukBWAhXCwgzISqEoLLKpFBbF JPsG0z2gmK2n2D2MDPpAf7VTnLcZgWHDy9BLUd6eRoW8bQ40ZwFK3l4KKmGBPFYGYxNjY0ugyEqK cvdJKuXuixSnaCYGIzN2hntUKJe9vXgZnhOZPzFDBZQ/v1IhRRsCWT/Rai6IMSCV6oz//zODeQA9 e1V2SgcAAA== \* mergeformatThe dust amount in the layer along the viewing angle (particles cm-2) for each particle type is calculated as:H4sIAAAAAAACC7t+9tgsBjDwYZBhSACzFMMZGTgZGJj9GBkYmBhEwWKsQMzNBGPxMMkA1bMAWSyM vGBaj1ECTDMxMoJVcMLVMjL9//+fgRnIkmPgApJqbPxA+j9IEAxA5v9m+gLlTWBkgjAEQjJzU4sV /FLLFYLycxPzQHYBsS7QTewgN7IyMrgwCALdJ4CmH+QIECu4MjcpP4eBCaKLEaz7A5JuW6BuXjJs h5jDCDenEGiOONmu2ALUrUAFV4QCzdGgyBUmVHCFLzDd2MF5fgxSDPaglMTwi4mNgRFiGoMSA8wV oNQhwsQLjAkQSxjI8kRLIRA9IPXqjP//M4N5AOzNSAmyAgAA \* mergeformatwhere q is the mean specific dust concentration (particles/g), U is the total atmospheric amount in the vertical layer (molecules/cm2), M is the mean molecular weight of the atmosphere in grams and N is Avogadro’s number.2) The mean temperature and pressure in the layer are calculated as the absorber amount weighted means along the viewing angle path. The integration is performed using Simpson’s rule with the layer split into 101 points along the path. The absorber amount and dust amount are similarly integrated along the line of sight.The paths through the layers are shown in Fig.4.1. z0z1z2s1s0Fig 4.1 Paths, Layers and Scaling FactorsReferring to that diagram, the first path s0 may be calculated from the cosine rule as:H4sIAAAAAAACC7t+9tgsBjCoYBBkSACzJMIZGTgZGJhbmRgYmBhEwWKsQMzNBGPxMAkC1bMAWSyM vGBaj1ECTDMxMoJVcMLVMjL9//+fgRnIkmPgApJqbPxA+j9IEAxA5v9m+gLlTWBkgjAEQjJzU4sV /FLLFYLycxPzQHYBsS4jAwM7kFZkZWSoYuCBuu8300+4fgYC+hnB9AckcwwZ+BnY4DwjMFsAzVUg r4FYwZW5Sfk5DEwwt0DMYoTrtgW6iZ9kP2G6CeQ3CZL9hukeA6BrZFH8Jkek3zDdpA10kyoZ8YXu pmKgOXpUiDeQ34xR/GZMdryB/GaN4TfS3WQENMeFCmEEin8vKoWRP5XiLJhK7okgOZwR7uEAm8PM kJwPclEcRnwzEZmWC4G689HKI4gzQCrVGf//ZwbzANXwa5sgBQAA \* mergeformatSolving the quadratic in s0:H4sIAAAAAAACC61UwUrDQBCdmbS11VpbjFgRtIpoe6hUj4J68urBCuLNqgULtqUEFMVfEDx58IO8 efY3BL2ohzizSRabLdjEBpKZ3byZvHk7mdeX5ydQ1yPYcKK89yOEDICVtfgBM2ovyfcEBV6WbMYn 2EvgpLLrWFSWEBUio7FIrutyHoAFGOfnamqKrSub6pL83/Thrx6QPCd/2Go3ndJ+87p00G03OvIt vqsIMMZ2KYngQA7Qj//U8fBHPCr79itPDQqQgnyIhxQjXv2mfdq9BAq+7kWjjt5mFjmjiugsypxl MYYaYT63nGdlBKpssCplvdqENFRia1RlTrXItZmcpLatyLWZfOTEd/pq2/3HCaZVHgucVof57Y2A nzCqG2rTQLVNlXrM4jhyPSaLCudpyCSAL0pBkGBZ1y9/t01ZmFXeNHtFjaYQmjR6zkcXYD6kZICR Nx4GeWZ4e4Ene+dD9iEZykgfXsT+x6ivD3uRz5kGTp6r2CdFuvPOujIL74bsGBrYMfeh6ezREOQa uq6lVj91/et1LgYAAA== \* mergeformatOther lengths are calculated in the same way. Once the mean pressures and temperatures of the layers, together with the gas absorber and dust absorber amounts have been calculated, the amounts are scaled back using the geometric scaling factor to simulate a vertical layer. For the example above, the scaling factor is:H4sIAAAAAAACC7t+9tgsBjCwZZBnSACzgsMZGTgZGJinMDIwMDGIgsVYgZibCcbiYZIHqmcBslgY ecG0HqMEmGZiZASr4ISrZWT6//8/AzOQJcfABSTV2PiB9H+QIBiAzP/N9AXKm8DIBGEIhGTmphYr +KWWKwTl5ybmgewCYl2gm9iBtCIrE0OwmyADI4MAmn6QI8C+qMxNys9hYILoYgTr/gDXzQh0vyCD EBm2Q8xhhJtTDAwrdag5P5FdgdccTPcYMPAw6FDBPVUMUgyyVHCPIdAURSJDF9MVukBXaJDsG0xX gHxjSLJvMN1jAPSNGShVM/xiYmOAGaAEtxeUUkWYeBlkwCxhIMsKLbVC9IDUqzP+/88M5gEA0zUU ST4DAAA= \* mergeformatApplying this scaling factor means that the layers can still be used for either nadir or limb calculations though of course it is better to calculate the layers in the manner closest to the majority of paths defined through the atmosphere. At this stage cell ‘layers’ are also defined which simply contain the mean pressures, temperatures and absorber amounts of any instrument cells (e.g.for simulating PMR or SCR instruments). These ‘layers’ can be combined with atmospheric layers into paths.4.2 PathsThe primary output from Radtrans are calculated transmission, absorption or emission spectra for a number of paths defined in the driver file. For atmospheric paths, once the layer properties have been calculated, paths are determined by the subroutine atm.f. The viewing angle, bottom layer height and number of the lowest layer are defined in the ‘.pat’ file and atm.f selects which layers (atmospheric and cell) are to be used in the path (and in what order) and calculates the appropriate scaling factor using the previous equations.Paths through cells may also be defined and combined as required with atmospheric paths to calculate PMR (Pressure Modulator Radiometer) or SCR (Selective Chopper Radiometer) outputs. The number of paths in a driver file may vary from one for a simple transmission calculation to many tens of paths for weighting function calculations. However, for each path a model identifier is defined which determines the output of Radtrans for that path. The model identifiers (IMOD) are defined as:0 = Transmission(Atmosphere)1 = Absorption (gives improved accuracy for low absorption)(Atmosphere)2 = Emission(Atmosphere)3 = Emission but uses source function at centre of current bin (much faster)(Atmosphere) 4 = The total transmission computed during the last emission calculation (so that surface radiance may be added)(Atmosphere)5 = Single cell transmission(Cell)6 = PMR sideband transmission(Cell)7 = The last cell output path multiplied by the last ‘Atmosphere’ output path(Combined) N.B. Radtrans won’t check to see if last calculation was an absorption or transmission.8 = The product of two previous outputs paths.(Combined)9 = The product of a single layer transmission and the output of the previous path (this is useful for speeding up calculation of transmission weighting functions)(Atmosphere)10 = As 2 but assumes transmissions calculated by single curtis-godson path(Atmosphere)11 = As 10 but uses source function at centre of bin(Atmosphere)12 = PMR Wideband transmission(Cell)13 = SCR Sideband transmission (1-Tc)(Cell)14 = SCR Wideband transmission (1+Tc)/2(Cell)15 = Scattering near-nadir calculation(Atmosphere)16 = Single-scattering calculation(Atmosphere)17 = Thermal emission into hemisphere(Atmosphere)18 = Thermal emission into hemisphere but using source function at centre of current bin(Atmosphere)19 = As 17 but using the Curtis-Godson approximation(Atmosphere)20 = As 18 but using the Curtis-Godson approximation(Atmosphere)21 = Scattering limb calculation(Atmosphere)4.3 Calculation TypesThe calculation types are defined by Path and are used only by Pl_spec to combine and plot the output of Radtrans. They are not used by the radiative transfer routines at all. Each ‘calculation’ is encoded in a single integer code ITYPE and passed via the driver file to Pl_spec. In general one bit in ITYPE corresponds to one of the logical variables where possible to simplify(!) evaluation of ITYPE. Calculation codes defined are:•Atmospheric Codes have bit 7 (128) zerobit 6 (64) 1 if limb pathbit 5 (32) 1 if reflecting path (down then up)bit 4 (16) 1 if transmission of single atmospheric pathbit 3 (8) 1 if Curtis Godsonbit 2 (4) 1 if weighting functionbit 1 (2) 1 if emission calculationbit 0 (1) 1 if calculate 1 minus transmission•Non atmosphere codes have bit 7 (128) 1128Single cell transmissions129PMR - two pressure, two temperature approximation130PMR File. Pressures/temperatures defined at a number of points in the cycle.131SCR•Combined cell/atmosphere codes160 is a combined cell and atmosphere - produces combined output161 is a reflecting path and cell - produces combined output•Reflecting layer atmosphere codes200 is a reflecting layer calculation with no cells201 is a reflecting layer calculation with cells(Both these calculations allow selection of paths in Pl_spec.)•Scattering Calculation256Full doubling and adding scattering scheme4.4 Path File FormatPath takes as its input simple ASCII path files (.pat) which contain a series of keywords and parameters. The ‘.pat’ files are block structured, each block starting with a keyword and ending with a blank line. These path files may either be generated directly using an ASCII editor or generated interactively using the program Write_path which prompts for the appropriate inputs. An example of a typical ‘.pat’ file for Radtrans and an explanation of the possible keywords which may be processed by Path is given below. Note that the ‘interval’ and ‘line data’ formats have been slightly modified from [R10].interval1400 1495 5 51 1 5spec data~irwin/radtran/linedata/new/tim2model ~irwin/pmirr_cal/tim2dust model ~irwin/pmirr_cal/dustdust spectra testdustlayernlay 35layang 90.layht 20.laytyp 1layint 1atmlimb 1thermnowf nocgnoabsorbbinbbnobroadreflatmangles 45.0 30.0 8nocgnoabsorbcellgases 11 0 1.0length 10.pmr twop0.015449 292.00.020088 308.0Defining the wavenumber interval (essential keyword)The keyword is interval.The first parameter line is the wavenumber minimum, maximum, output spacing and resolution in wavenumbers. N.B. The final resolution parameter does not apply to LBL calculations (ICONV=0,1). For the adaptively integrated LBL model (ICONV=1) FWHM is hardwired to DELV as described in section 5.1.The second parameter line is the spectral model type ICONV followed by two parameters PAR1 and PAR2 which define additional information for the particular spectral model used. Defining the spectral data (essential keyword)The keyword is spec data. The only parameter is a spectral data key file name (line data, band data, or k data) (‘.key’ extension, though this may be omitted). The line data files are set up and manipulated by the programs: Makedb, Scan, Check_index, Li_lines, Pl_lines, Select, Cp_lines and Summary. These line data manipulation programs are described in section 7.The band data files may be set up with the program Makeband.The k data files may be set up with the program Calc_ntable.Defining an atmospheric model (essential for atmospheric calculations)The keyword is model and again the parameter is just the filename of the atmospheric model to use (‘.prf’ extension though again this may be omitted). In this case the filename is on the same line as the keyword. The model files are produced and manipulated with the program Profile and have the extension ‘.prf’. They contain the pressure, temperature and gas VMR profiles as a function of height. The profile files are described in section 2.Defining a dust or aerosol model (optional)The keyword is dust model followed by the name of the dust/aerosol profile. The dust/aerosol profiles are explained in section 3.Defining the dust optical properties (essential if dust is defined)The keyword is dust spectra followed by the name of the dust/aerosol cross section (‘.xsc’) file. This file has the following form:21900.001.0E-102.4E-100.50.12100.002.0E-103.0E-100.50.1The first line contains the number of dust types. It must be equal to the dust types defined in the dust model.Subsequent lines contain the cross-sections (cm2) for each particle type for as many wavenumbers as desired followed by the single scattering albedoes at the same wavenumber. The subroutine reading in the data automatically detects the end of the file.Calculating atmospheric layers (essential for atmospheric paths)The keyword is layer. Path splits the atmosphere into a number of layers. This is separate from calculations of the atmospheric paths so that you can have several paths through the same set of layers (e.g. for multiple tangent heights). There are multiple parameters on additional lines each defined by additional keywords. The keywords are:nlay followed by the number of layers to split the atmosphere into.layht followed by the height of the base of the lowest layer (km) relative to a reference level defined in the ‘.prf’ file.layang followed by the angle from the zenith for splitting into layers. For example you'd use 0º for nadir calculations but 90º for limb. The stored layer properties are scaled by the cosine of this angle so that they approximate to the nadir case. laytyp followed by an integer specifying the layering type.0=split by equal changes in pressure over layers1=split by equal changes in log pressure over layers2=split by equal changes in height over layers3=split by equal changes in path length at layang over layerslayint followed by an integer specifying how to integrate absorber amount, pressure and temperature vertically over the layer. 0=use values at centre of layer1=use curtis godson paths for a gas with constant mixing ratio. 1 is usually better but 0 is useful for intercomparisons.In the example above we have defined 35 layers starting from an altitude of 20km by splitting the atmosphere by equal changes in log(pressure). The mean pressure, temperature and absorber amounts of the layers are calculated using the Curtis-Godson approximation assuming that most of the paths will be limb-views to a tangent height of 20kmCalculating atmospheric layers with discrete cloud layersThe keyword is nlayer and the option is very similar to layer, but tailored fro cloudy atmospheres such as that of Jupiter’s. Subsequent keywords are:layint followed by an integer specifying how to integrate absorber amount, pressure and temperature vertically over the layer. 0=use values at centre of layer1=use curtis godson paths for a gas with constant mixing ratio. 1 is usually better but 0 is useful for intercomparisons.layang followed by the angle from the zenith for splitting into layers. For example you'd use zero for nadir calculations but 90 for limb. The stored layers are scaled by the cosine of this angle so that they're always similar to the nadir case. You might use layang=0 for multiple limb paths or for simulating someone elses code.nlaybot followed by the number of clear gas layers from the base of the profile to the bottom of the first cloud.nlayg followed by the number of clear gas between cloud layersnlaytop followed by the number of clear gas layers from the top of the last cloud layer to the top of the profile.layht followed by the height of the base of the lowest layer (km) relative to a reference level defined in the .prf file.ncloud followed by the number of main cloud decksSubsequent line contains the cloud base height (km), cloud top height (km) and number of intermediate cloud layers.Next lines contain the number of cloud particles per cm2 for a vertical path for each sub layer.Sequence then repeats for further cloud decks. E.g. : nlayerlayint 1layang 0nlaybot 8nlayg 8nlaytop 8layht -90.00ncloud 3 -45.00000 -44.00000 1.000000 1.1200000E+13 -15.00000 -14.00000 1.000000 2.9099999E+10 16.00000 17.00000 1.000000 7.7999997E+10If bi-modal clouds are required then instead of using nlayer, mlayer may be used which has an identical format with the exception that two columns now contain the number of cloud particles per cm2 for a vertical path for each particle type in each sub layer.Defining an atmospheric path (essential for atmospheric calculations)The keyword is atm. Additional parameters are defined on additional lines each defined by keyword. Most keywords can be negated by preceding them with a no. The keywords arelimb specifies a limb calculation and is followed by the number of the bottom layer to use. 1 is the bottom layer defined by layer above. Here paths are calculated to the tangent height and then beyond. nadir specifies a nadir, or near-nadir calculation and is followed by the angle from the zenith and the bottom layer to use. For an instrument looking vertically downwards, the angle is set to 0°. For an instrument on the surface looking upwards the angle is set to 180°. Here paths stop at the lowest layer.(no)therm specifies a thermal emission calculation.(no)hemisphere specifies a hemispherically-integrated thermal emission calculation using exponential integrals.(no)wf specifies a weighting function calculation. Note that this forces notherm.(no)cg specifies Curtis Godson paths are to be used.(no)scatter specifies a full doubling and adding scattering calculation. If scattering is defined then when Radtrans is run there must exist a ‘.sca’ file containing details of the scattering calculation. This will be explained more fully later.(no)absorb specifies that absorption rather than transmission is to be calculated for non thermal calculations. Needed for small absorptions when adaptive LBL integration (ICONV=1) is selected.(no)binbb specifies that the Planck function is to be computed at bin centres (see interval above) not each wavenumber which is much faster but less accurate.(no)broad specifies that an emission calculation is to be performed outside the RT calculation to simulate broad band calculations.The defaults are limb,nowf,nocg,therm,binbb,noabsorbIn the example atmosphere listed above we have defined the view path to be a limb path with a tangent height at the bottom of layer 1. We have specified a thermal radiance calculation where the Planck function is calculated for the centre of the bin only.Defining a reflected atmospheric pathThe keyword is reflatm. Additional parameters are defined on additional lines each defined by keyword. Most keywords can be negated by preceding them with a no. The keywords are:angles followed by the incident and reflected angles and the number of the layer from which the reflection occurs (reflection happens at base of layer)(no)cg Sets Curtis Godson flag as required(no)absorb Sets absorption flag as requiredDefining a gas cellThe keyword is cell. Additional keywords follow. These are:gases followed by the number of gases in the cell followed on subsequent lines by the identifier, isotope and volume mixing ratio of each gas. The identifier is NOT always the same as HITRAN and is listed in Appendix A. Isotope zero includes all isotopes at terrestrial ratios. The RT routines correct line strengths for explicitly specified isotopes as if they were 100%dop followed by a doppler shift for the cell (cm-1)length followed by the cell length (cm)sngl specifies single cells followed by the number of single cells.Subsequent lines hold the pressure (atm) and temperature (K) (in that order) for each cell.pmr twop specifies a Pressure Modulator Radiometer (PMR) calculation assuming a two pressure approximationThe next line holds the low pressure (atm) and associated temperature (K).The next line holds the high pressure and associated temperature.pmr file specifies that a PMR cycle is held in a fileThe next line holds the file name and the file contains pressure and temperature for each point in the cycle on separate lines. The format of the files is free-form and Path automatically detects the end of the file.scr specifies a Selective Chopping Radiometer (SCR) which alternately views the atmosphere directly or through a single cell. The next line holds the pressure and temperature of the cell.N.B. Cell calculations can only be done on LBL calculations. Radtrans does not explicitly pick this up.Defining single atmospheric pathsInstead of defining layers and atmospheres, single atmospheric paths may also be defined for various tests. Radtrans treats atmospheric and cell layers differently so this is not the same as defining single cell paths. 1.The keyword is sngatm followed optionally by a file name. If there is no file name the input is read from the subsequent lines. The first line should contain the keyword absorb or noabsorb as described earlier. The following line contains the number of gases, pressure (atm), and temperature (K). Each gas is defined on a subsequent line containing identifier, isotope, volume mixing ratio and amount (molecule cm-2). If the amount is < 1.e10 it is assumed to be a path length in km. The next line contains the number of dust types NCONT. If NCONT > 0 then the next lines contain the name of the dust cross-section file and the dust amount in the path (number of particles/cm2).Setting the error limit for adaptively integrated lbl calculationsThe keyword is error followed by the limit (%) on the same line. This is the limit for terminating adaptive integrations. The default is 1%.Defining how to process line data for lbl calculationsThe keyword is process followed by the gas id, isotope id and an integer IPROC to define how to do the processing. At present two options are available:IPROC=0DefaultAssume Voigt broadening for linesIPROC=1Assume Sub-Lorentzian line broadening (CO2)IPROC=2VanVleck-Weisskopf lineshape (far-IR)IPROC=3Rosenkrantz-Ben-Reuven lineshape for far-IR NH3IPROC=4Assume Lorentz-broadened linesNeeds Updating!!!Tidying the driver fileThe keyword is (no)clrlay and tells Path to remove any unused layers before creating the driver file. clrlay is the default.Combining atmospheric and cell pathsThe keyword is (no)combine and tells Path to add additional paths combining all combinations of atmospheric and cell paths that have been defined. combine is the default. The combination is always at the end so you can't just combine those defined so far.H4sIAAAAAAACC8VWXWgcVRT+zszsZjfZbJsmQSHWjjHVRttSFKFPPrSpjdjI2k3bN+M0O2lGsrvp 7CSt4IPUPBSkYJ+qViGRKlpf1EKL4lMkBbGiD5ZCRCj0QQtCpBSKtrCec2d2ktnO0o1QunD23Hvu ufd852fOvVd+uvgB1G+RrtJravTSAUIa0P9JAC14Tsl4iDbtGehqlNGu0iIZPDKoHcK30sOKa0RK I63VdpFWrVZ5H/AoWvn/ieQa5lURqt9aptvazWD2Lvkc5m67ZE9bUKduYWk788cS7dhvu54zak2Y uc3DJt7HINaolQ5YpYK5f2ivOemWx5wJu2Lic15Nq9UkNm2ddMf6v2FJC0vuaDVD/vnKY/yrJVGT 9wYrmtLvMeZxAe9gh4rHDhLPNjGlAqJgn4zXtfm08ifunmW+j6kRl9/Q8Mv5kVz+2W350/O+fT20 v5Ptb6+LoW81Lq6tyu8W5Pxo4FP8Ffoq/O/w5LN4hN7D9diTJTsb9SR66EPOsVART0PoFGM5hayy sha7jnq2W+Ks5MtT7qhdeZ5ttKq9Ono4aj04x/rnYpH6+UAkH3qQj0QYvVo+DGWzT0/wmbN4CCeZ n8QGxWfDnMm+Lu1NlsmoU5PVZiNXb+dj9vdLOEzCD6t51E4RPwd2RCPOToeKU3ctG2axXHDGuIw9 p1yqwMIbTSHZR2ewmz5jEj6r5lEkZzhTPhLRiEPify3rQiSTE2WvYsq3M4cCtanVNPJTxaLlOnYF X7E0ozJpcI1UcVHRtzjP1Azm65jDb/iESfhHah7FPMdn+ZhFIw5zSqEykLO88TQthXXs12+WuujO XfUbraZ6VH8iRYvIMAk3SOZRVCn6IkAlGv+3dkbIoFcoxSQcJPOoHYM6g4yJRrN2MioiGQy4zrTt mi9IJnU6TMvdruBO93eyJBqrbfQd/Y5xun9dbHBo13CfKOdOzy9HJBHad9j+q7S6eOpBx0rEVFcV i9A5Q8Jvq3k0vlVcCvIoGo3sBp3ykGsV8Qutr4tahwZaol/xoKLWoV3GEl1C7escsDxL5Ry6toH8 G/TGPW7QZBBDcM+UU3oh667qQGZ5zNxrFTzXKpkrKqryNb1dd2fUEF2mW/ieETV7e/u7k4EHrepL NlX/cTmuK+5oy+s/xhLfygnqpoP04wOL+wn28CAtBG+PLAYc1x71TLvgeE7p0HF6PPTngOt49gij H3dpY4OYHaGjsGn9qvrUAkp0AS6T8NdJ5tH6LvGpfn2LRlx9Z1X3TqCLjtBTil7k3iaUomZ62AJm +OTjTMLfIplHMczQsQDDTAMMtQiGr7fCVMUzr/BrrFbTy6+2P+56td1iSfSLBNv54b6+xpLRLXWV AdrJ9rcH/l8Lb7BrfDeGvZldHAmu2b6GVbGZ89dNvauqij3sYg5Z2sM0qDjqMtLNMh+RrMZlRPSf pGpVV7P/ABar5FsIDAAA Fig.4.2 Generation of Radtrans driver files using Path4.5 Running PathPath is invoked by simply typing 'Path'. The program prompts for the name of the path (.pat) file and outputs the generated driver (.drv) file together with a name (.nam) file which is useful for running Radtrans in background. For example if the path file is called surf.pat, Path will generate surf.drv and surf.nam, the latter file is usually just one line long and containing the name of the driver file. However in some case it may also contain extra parameters not easily passed elsewhere such as whether an equilibrium ortho:para H2 fraction is assumed or a deep 3:1 ratio [R15].4.6 Changes in driver file format from GenlblRadtrans has been designed to look as much as possible like the previous line-by-line model Genlbl in order that old calculations can be repeated using the same driver files. There are only three ways in which the driver files are different:1) Since the treatment of dust/aerosols has been changed, NCONT must be set to 0 if there is no dust instead of 1 as in Genlbl.2) If dust profiles are defined then an extra line follows the line containing ICONV and NCONT which contains the name of the dust extinction cross-section file.3) Dust amounts in the driver file are now in units of particles/cm2 instead of optical depth.The lines which contain details of any required filter profiles are still present and Radtrans will use them in the same way that Genlbl does if required. However it has only been left in to reduce the number of changes between the two systems and it is now recommended that this function should be performed as part of the post-processing in Conv_spec.4.7 Non-LTEUser specified NLTE parameters are also included in Radtrans. To use the facility the driver file must again be manually edited. Either before, after or instead of the hydrogen absorption parameters insert the line:NLTE 0The number specified is a code to indicate the type of NLTE required: At present there are two possibilities:0Perfect LTE1Assume NLTE is as that estimated by Glenn Orton for Saturn and Titan. Scaling for Planck function is:H4sIAAAAAAACC61Uy0rDQBQ9d9JGayotVMVFqNGFaSk+ipCdrtRVkaIFXbZiEcHYhYL4F679jn6D O8Gdv+HCjbqIdyZtKJ2FzWNgcs8M95w5ubmZj7fXF6hxDQddhbxzQgEw3gUgsKz28jwtMUZF4XB+ jlGOFlXcplUVBZHKKES5JIIggMGoigV+bpoljoHcVEPq/4qv0eqZRAjKnRu/f++c9B+d04Hfu5Nn 8dwiYI7jep5wjAr7K0/xpQmJzp78y8EtRMgixf6cYO8zu5jg9FCHIp02LKxpOvhHR/dTYx03hZ95 pWOg9+CzUiMDR3XWOZixvnpdhsw+TO1CoLlroTXS+Z5ZR/fjwcRFBlVpwsZK4qo0mF2N/ZV1F23W cWO/je6nxjo7KfxMdp2NvQwc1VnnKPFfPWR2K7UL2XU2OrG7Tvfjca905W2KH2FiLLARnStvyCVR 4iyJKoyupm7JkCPzXQoCQ63+AEv90aC2BQAA \* mergeformat5. RadtransAs outlined earlier in Section 1, Radtrans calculates transmission, absorption or emission spectra for the paths defined in a ‘.drv’ driver file constructed from a ‘.pat’ path definition file by the program Path. Spectra are calculated in wavenumber space only and the calculated spectra are written to binary ‘.out’ files. Hence the output files must be processed using one of the three post-processors Conv_spec, Li_spec and Pl_spec which are described later and which may transform the spectra to wavelength space (if required) and write the outputs in ASCII format. The spectral details of the calculation are given in the first line of the ‘.drv’ driver file where the wavenumber minimum, spacing, number of points and bin width are defined. The subsequent line contains two extra parameters PAR1 and PAR2 whose meaning depends on the spectral model required which is defined by the integer ICONV. Table 5.1 summarises the model options which are dealt with more fully in the following sections.Spectral ModelICONVPAR1PAR2Line-by-Line (LBL) CalculationsLine by line model - monochromatic0WINGVRELLine by line model - integrated1WINGVRELBand Model CalculationsNon-overlapping line model (linedata)10EquivW code-General random band model (linedata)11EW1Malkmus-Lorentz band (linedata)11EW2Goody-Lorentz band (linedata)11EW3Godson-Lorentz band (linedata)11EW4Malkmus-Lorentz band (band data)12--Goody-Lorentz band (band data)13--Godson-Lorentz band (band data)14--Goody-Voigt band (band data)15--Correlated-k CalculationsCorrelated-k model (linedata)20WINGVRELMalkmus-Lorentz Corrk (band data)211,2,3-Goody-Voigt Corrk (band data)220,1Exponential Sum model (not recommended)230,1-Correlated-k model (look-up table)24--Table 5.1 Radtrans Spectral ModelsHeavily shaded options not yet completed5.1 Line by Line ModelsICONV<10Here:PAR1=WINGPAR2=VRELThe spectral region defined in the path and driver files is extended to VMIN-VREL to VMAX+VREL, to cover line wings from lines outside the interval and divided into bins WING wavenumbers wide (Fig 5.2). Unlike Genln2, Radtrans ignores all lines outside the range VMIN-VREL to VMAX+VREL. Line data is stored in blocks corresponding to the WING-sized bins. At a particular wavenumber, the absorption by lines from the bin at that wavenumber and the two adjacent bins are treated explicitly. Absorption by lines from other bins is calculated by calculating the contribution to the middle and each end of the bin and fitting a quadratic since at this distance from the line centres it is assumed that we are in the Lorentzian (and thus quadratic) tail of the line shape (Figure 5.1). This greatly increases the calculation speed.H4sIAAAAAAACC7WWf2iVVRjHn+97f+xuc1ZzOrMl21rmBlfvagMLhevIphFSbrhyCmaYGnTHvcVm K/Va14HiykVIheyucBD+Ebf21/bP/hljzRXOZP2RS0OMjP64RSQt4fac877n8d7Xe4WIXng4z/dz znnO73Pe776e/Jj0dx2j2K29YAeomMgz7yMqombN2KVSawX5tbfIGsV1eNnzooxUugbLdWoBukSx ZWrBymQy5GFvpYpKC5afYDdJtbpOkGUpp5WBGJZihmqxwgrhPC1FEdNbHElFIKcsnCg+HUHlmCgW Lea0zuMjIIjV2g4D2oIwLal6FdYgqrW3hL1rsFkVBRyWQsApV0c3YNgNpz+m93ZEDyn6gDeJj6iX 4qK+YPWhqB9ZTVEJq1X+ezjN2EMiM/IavE7HcJR+YnsY+2Ss7pFFaBc+0HYSEW27kDuHx7h2LV7j SPGsSLcjtHGNN7SdRJs2d4RO9NA5VFASB6gS4xmbnsMl6kSUaT0qccQ1FntOCo+vHgn04zRmMYAt 6IG7V4cQxVltAzikLerqVT+TBrzDEU5xhO47Iuzh/OPaBrBHmztCF/dhGDVI4iDCvL9sOsw7uQtv M11vhfEe8o1LnYEWvQ9WswUcg7OPlV9ealv2p6ZATcK88tl6nDRb//nSr1fCoTJ/cUPf5r6bZU6P vbJvytFLf8lOU2k6K7eFc+thVIzVC8i3BqbECS4RlfKfsjouaozVJ6IushoV9QurWfzbFS+iftxP 3/JOasVCptCOLqEu1Gnr5xaUdbnWbRj76VWe/STGaT3K8+48c7N4XTeLl8zZjsvZjguLytmO4l72 /rb+cMZwyhzy6ta9kb3dL5rT7tNzWeOzqDv0Dd68rRpnECk497csyrkz/DILZkXNbASog5ZRO5tK O7U2eXH2Y8xiOm3XOvdWU3XsEakS+eYpoPvrpe3bNj3TSE849WKUcuptdDzFpoTlv7ncK5mi7TTO 98u4TndobfKm2B9jNqbTNq1z+67q2O2pEnfre8eWra1NNJK3T3asp8jjrOxWx6uwnhe2W9grwmLC 3hKWEPausNPChoR9JuxLYWPCJoTNCJsT9oOwn4WlhS0Is2DYIhhWIWylsFXCQsLWCWsR9rSwdmE7 hb0sLCLsoLC4sBPC3hd2RthZYZ8LG2Ev39ra5wjUTdP8WhvVSJuwWPIepYf4ZSp0j1TxG/+ktsOo 0hbEf7u3jd3M8pUdkZLVxbnn2it72tycDXxz3gf7HjvP/W/GGgxhLb8+lQ4dRB+/qGv5/bmCEf6P smkTlkOVT3LONJct9ALs4Pgb73rn1/CfR0DU46yqRT3Hap2oA6yeFXWU1f6859DuYZpmqRfz5OM9 nKaJgusyTWGktSV4JMrCrvu9FxP0G13gSPNZkbLvlTDmtCWQ0uaOsAGTNKT/TSbpMj14x5/ZVzyW FP3fu0F9EyXZu8G0v8DtX3X6OoQQNuB77msCl7m35rVchkF+35L8bzVC+2TPP0a/05yoJrrGO8So ZtrG/yuqrUeQyXh0+/8Ae4l9HtALAAA= Fig 5.1 Treatment of lines by Radtrans line-by-line code.Line-by-line calculations may either be performed monochromatically (ICONV=0) or integrated over square bins of width DELV using a cunning adaptively integrating Simpson’s rule scheme (ICONV=1). For the example path file given, Radtrans will integrate the spectrum over 5 cm-1 (i.e. DELV) wide regions centred on the required output wavenumber. The first region is thus from 1397.5 to 1402.5 cm-1 giving the average transmission or radiance at 1400 cm-1. [Note - the integration steps and the bin sizes are not related. Hence an integration may cover many bins or just one.]The adaptive integration scheme works by first performing a Simpson’s rule integration over the square bin of width DELV using 20 points. The number of intervals is then doubled and the integration evaluated again. The scheme tests for convergence by comparing the last two estimates. If they agree to within the convergence limit (set by error in the ‘.pat’ file and defaulting to 1%), the integration stops. Otherwise the number of integration steps is doubled and so on. 5.1.2 Line handling in RadtransPrevious releases of Radtrans included a program Radtran which used a clever line-binning scheme for LBL calculations to reduce the amount of data held in memory. However this scheme considerably increased the complexity of the code, making debugging and error analysis difficult. In addition, once the internal memory limit was exceeded a bin-swapping procedure was adopted which greatly increased the computation time. Hence it was decided to no longer support Radtran. Instead Radtrans has been developed which behaves exactly in the same way as Radtran, except that all the lines for all the bins are read in first. If the required calculation covers more than 10000 lines, which is currently the limit of Radtrans, the calculation range must be split up into separate spectral ranges. 5.2 Band Models9 < ICONV < 20Band models are useful for low- to medium-resolution spectral modelling. They represent a significant simplification over line-by-line models in that relative position of molecular absorption lines in a spectral interval is ignored. In the models included here it is assumed that the lines are randomly distributed across the interval and thus the equivalent widths of the lines (i.e. integrated absorptions) may simply be added. The models are generally not so accurate as line-by-line models but have the advantage that they are much faster and in some cases, where line data is not well known, are the only option available. While dust absorption is easily included, dust scattering is not possible with band models (since they must use the Curtis-Godson approximation), which is why the correlated-k models have also been developed. For a full discussion of band and correlated-k models, see [R1]. Two generic types of band models are included, those that use line data and those that use band data. 5.2.1 Band Models using Line data (ICONV=10, ICONV=11)For every central output wavenumber, each line in the integration range of width FWHM is read in and the equivalent width calculated before the mean transmission is calculated using a number of possible approximations. The equivalent width W of each line may be assumed to be that of: a) a Lorentz line only WL.b)a Lorentz line combined with a Doppler line using the equation H4sIAAAAAAACC7t+9tgsBjDYyiDBkABm3QlnZOBkYGA2ZWZgYGIQBYuxAjE3E4zFwyQBVM8CZLEw 8oJpPUYJMM3EyAhWwQlXy8j0//9/BqBRDHIMXEBSjY0fSP8HCYIByPzfTF+gvAmMTBCGQEhmbmqx gl9quUJQfm5iHsguINZlZGBgB9KKrIwM4QwCDIxAjKof5AgQK7gyNyk/h4EJoosRrPsDkm5boE5+ MmyHmMOI4goZqDk/iTYH0z0+DMIM6hjmMJDsHiNg6GqQHSraQJ36VAoVCyqEigswVJypFCrOZIeK LlCnN5VCJYJKaSWZSN9gumILUGcWyb7BdAXIN8Uk+wbTPaA4rsNwDwPJ7tEHuqed4lhiYgjOFWDo hYbuB5LTCijvhcB5mkDeHKqkXw6GhVA3vSLDTULA0h3hJiGGZVRwkyEDG8NKpNBnY1iL5F42hg1o 5T3ECpAp6oz//zODeQAYgDgagAYAAA== \* mergeformat to simulate Voigt lines. (Here S is the line strength and m is the absorber amount)c)interpolated from a Voigt width look-up table [R2].Both Lorentz and Doppler equivalent widths may be calculated using either the Weak or Strong assumptions or a combined width [R2].Once the line equivalent widths have been calculated, the path transmissions may be calculated using a) the non-overlapping line approximation where H4sIAAAAAAACC7t+9tgsBjBwYVBnSACzhMIZGTgZGJg3MDIwMDGIgsVYgZibCcbiYVIHqmcBslgY ecG0HqMEmGZiZASr4ISrZWT6//8/AzOQJcfABSTV2PiB9H+QIBiAzP/N9AXKm8DIBGEIhGTmphYr +KWWKwTl5ybmgewCYl2gm9iBtCIrI0MIgwwDI4MAmn6QI0Cs4MrcpPwcBiaILkaw7g9Ium2Bunkw bGcgaDvEHEa4OYZAc0TIdoUuULcMGWGA7opwBm4GE6g5P4k2B9M9mQx8DHZIPHEGbajf3hHwG6ab ngLNUiM7ZFwYVBl0KI4fJoYZCsoMZhiuYCLKFUwMpQqqwHAF5gaGX0xsDDDrleC2gVK4CJME0K0g ljCQ5YiWyiF6QOrVGf//ZwbzAADxeo12AwAA \* mergeformat b) the general random band model where H4sIAAAAAAACC6VTy0oDQRCs7jw0JiEBDUQ0MkZJTtlTBBFERK+KxEDwpkIOAWMEkehfeBQ/yJtn v8DHSTyIz8PaM/tw1z0kxIHZrhqmq6tndu5ub65hxh7q2DdotkVIATFi+aBg1hIy0+yhDNdlf1xQ nLImWlQ0kYnMjpS/l9i2bdEB5jAh30oyJ9HWi2Zo/W9+ddklsQPyzU63faq2233V6HUPjnUtmTUC xiTOJwhNlEDI/8nXJjTavege9o7AThaZ7JdA9qpkZyLVMbC6o0MYNzoxtM9PRKkwso+auLBGOAXP h6fTEp0NV+dzaJ2onw5y2AqwIlbc3p4H9Bb1dC9aSyOfzCYqWP7HDTk6jCu1iPWICx7KBeNMVbCm 3wO+OAmvfNmvpv/xKZ6We9RoUtDOkB1zxOmDSqPqsydlBdijmgmxcoC9qSwaPvuQvF/2rkohtiAs /A6dnrSXKtl2zLAf9FS1hxgEAAA= \* mergeformatc) the Malkmus Lorentz band model [R3]. Here H4sIAAAAAAACC61VTUtCQRQ9M5ZZKhkpCFFMUQmGhVFBC1sFbSKohFr2gZCQFQllixZBuyCCVgYu +yvtWvcP+ty0iEqFXnfGnAYNytd7MG/uedx75tyP997N9dUF1HWJKFaU9bHE0Aq4Tl10Q0g9a6bl 5VXLx6Pk30RWE/OrfZiF1c4ZUx6t2pdxy7KIB+hBG90H3e20W/KhuiR/mb98oTPGK0Ygmc6ksmIu tS8WtjOrW/IsWjEGtNDe28yQRBgMgZp4KUJaiweZte1N8EoUU9HPRnSCon11p+PX0ys8DB7F40Iq t0NMIds6YhQds1GFqo4qT5YUTH7xFP+cT72eUXgx9Y+6fPP0YqLhvOr17BNPQs4jStyNqpA+fa6c sSAPYlxZnWRNN6ye16mPU1fmG+wp19FDFL3sgIoxUrBuu4bcqGEA6YZng//QUy92HdCTpZ5uOKKn Cxk9AWt6AvZsdo7jVrRjVqN7IQx0J4IGehUdyGn0Tp45BzKK03flUKMRQkdGth4c255J+Z05cejN OLdd3wfhx4xGT2LAQI+i20BF8sxrVCbPb1Qiz7zRMy8iRs/6DXQnwgZ6Jc6C0bN+A72RZ6HmD1Up j8whwizLpdAn7Wva1zIHAAA= \* mergeformatwhereH4sIAAAAAAACC7t+9tgsBjDwYZBhSACzFMMZGTgZGJi3MgIJBlGwGCsQczPBWDxMMkD1LEAWCyMv mNZjlADTTIyMYBWccLWMTP///weaw8Agx8AFJNXY+IH0f5AgGIDM/830BcqbwMgEYQiEZOamFiv4 pZYrBOXnJuaB7AJiXaCb2EFuZGVkKGcQZGBkEEDTD3IEiBVcmZuUn8PABNHFCNb9AUm3LVA3L4bt DARth5jDCDfHEBhWMmS7woVBikGcYlcwMcxQkGBQxHAFE1GuYGIoVZBikAfFOcMvJjYGmPVKcNtA 8SjCxMsgBmYJA1lqJMcbE0bIBQNjwApqzk+izYG5ngluTiaDCIM9Ek+MwQwaEu8IxAemm54yCDNo kuw3TDflAv3mhJbeIeEKUqnO+P8/M5gHAIyhH06AAwAA \* mergeformat is the weak limit of the optical thickness and H4sIAAAAAAACC61UwUrDQBB9M20jUYuRRgm1SiyoJwU9qAh6Kh4LtoIgHqzQQ8HYQxHxLzyKH+TN s1/gVTx4UQ9xdjcJkhwaNQu7Mzt5M/N2ZjfPT48P0OMMDZxrbfOEYAOlDsuCOW2ryJziWJvmhuDL opWpquUGeVoykUbYCZY4DEOJAyxhUtZVa0ZkqIx6qPhf/B7t7oiN4hwPgv7Ib/dv/M4w6F2pXDLX CZgQuVwhjDALgpPyVySU1r0NLoaXYONF2vvth/e+eNuZ7Bib3cShJM6WRPH+zKKFOtx/s2Dc+x4W Myw4FwvGtV/Hguo5PtlCnL6ZZFN9dLmKmtZqojV/3TfOVK4rHTiI4nzkjhOz5yTOQCrYynn2LIue sDgsiEW7gKoEwucoqriD7ajiDnaS/nCqP5SgdyO0i73MTTEY9cVgLHkBxhZrynZaSCXm5VWYfryO eRHZ87/ILVtJ/SnMjVTINQrDkt59Azy8nBK6BAAA \* mergeformat is the strong limit.d) the Goody Lorentz band model [R3] whereH4sIAAAAAAACC7t+9tgsBjCoZpBgSACzhMIZGTgZGJhDmBgYmBhEwWKsQMzNBGPxMEkA1bMAWSyM vGBaj1ECTDMxMoJVcMLVMjL9//+fgRnIkmPgApJqbPxA+j9IEAxA5v9m+gLlTWBkgjAEQjJzU4sV /FLLFYLycxPzQHYBsS4jAwM7kFZkZWQIYeBnYGQQQNMPcgSIFVyZm5Sfw8AE0cUI1v0BSbctUDcP hu0MBG2HmMPIwAE2h5khtaIAaJIo2e7QBerWJiMUYO6AmVMONMcM6oqfZLiCk8Ee6oqfZIQGzBwj oDnOZIeFNtAPXlQIi2KgOcEUhUUklcIiFuqKdyS7QgOo0wjO0wTykoj0EaZLdBnYGNJI9hGmmwyB 5mTBefpAXi6Sb9kYCqAufEGyCzUYBBnUkXwryFCKVlpAnAvSp874/z8zmAcAkC3PVL4EAAA= \* mergeformat e) the Godson Lorentz band model [R3] where:H4sIAAAAAAACC7t+9tgsBjB4ziDGkABmNYQzMnAyMDBfYmFgYGIQBYuxAjE3E4zFwyQGVA+UZmBh 5AXTeowSYJqJkRGsghOulpHp////DMxAlhwDF5BUY+MH0v9BgmAAMv830xcobwIjE4QhEJKZm1qs 4JdarhCUn5uYB7ILiHUZGRjYgbQiKyNDCAMfAyODAJp+kCNArODK3KT8HAYmiC5GsO4PSLptgbp5 MGxnIGg7xBxGBg6wOcwMqRUFQJNEyXaHLlC3NhmhAHMHzJwKoDnGcF4qkGcHddNPMtzEweACddNP CtxUCTTHk2S/YbrHE+gbXwz3MJDsHgMGQYZAkuMc0z0aQPeEUSHOKoHmRFPBPZpAcxKITIGYrtAG 6k6ngiuMgOYUUBwqTAyVqXwM5RSl3SYqpd12KqXdCVRKu1OolHZnUintzqVS2l1MUdpdSaVY2kyF WDIExtJ2KsXSbirF0gEqxdIxaCy9JzmWohn4GbrhvFgg7xRF9eV5CuptREzxMVyHuuItya6oBvrB Es6rBfLuQM16TXLoaAB1qiOFtADDI7SWEsR7IH3qjP//M4N5AMt445u6CQAA \* mergeformatwhereH4sIAAAAAAACC7t+9tgsBjAwZJBjSACz4sIZGTgZGJh9GBkYmBhEwWKsQMzNBGPxMMkB1bMAWSyM vGBaj1ECTDMxMoJVcMLVMjL9//+fgRnIkmPgApJqbPxA+j9IEAxA5v9m+gLlTWBkgjAEQjJzU4sV /FLLFYLycxPzQHYBsS7QTexAWpGVkaGCQRjoPgE0/SBHgFjBlblJ+TkMTBBdjGDdH5B02wJ1c2PY zkDQdog5jHBzjIDmiGC4golIVxQAdUuTEQborigG+kUVas5Pon2D6R4jBjYGLSq4p5xBhkENlIoY fjGxMcAcogS3F5QyRJj4GVTALGEgSw8tdUD0gNSrM/7/zwzmAQB6ahKVrgIAAA== \* mergeformat and H4sIAAAAAAACC7t+9tgsBjAwYZBjSACzosMZGTgZGJgLGBkYmBhEwWKsQMzNBGPxMMkB1bMAWSyM vGBaj1ECTDMxMoJVcMLVMjL9//+fgRnIkmPgApJqbPxA+j9IEAxA5v9m+gLlTWBkgjAEQjJzU4sV /FLLFYLycxPzQHYBsS7QTexAWpGVkaGSQRjoPgE0/SBHgFjBlblJ+TkMTBBdjGDdH5B02wJ1c2HY zkDQdog5jHBzjIDmiGC4golIVxQAdUuREQborihn4GZQgZrzk2jfYLrHiIGNQZcK7ilmkGFQo4p7 xBi0QamR4RcTGwPMACW4vaAUJsLED/Q7iCUMZBmipTKIHpB6dcb//5nBPABvTLdV9gIAAA== \* mergeformatand I0 and I1 are Bessel functions.For these models, the path file parameter PAR1 contains the code for calculating the equivalent width WIDMOD. WIDMOD is an integer whose three digits when converted to base 3 are the codes COM_MOD, LOR_MOD and DOP_MOD respectively. For example, the number 7 is 021 in base 3 which sets COM_MOD=0, LOR_MOD=2 and DOP_MOD=1. These codes are identified below.COM_MOD. This code defines whether a voigt line shape is to be assumed and if so how:COM_MOD = 0, Equivalent width used is that of a Lorentz line onlyCOM_MOD = 1, Equivalent width used is that of a Lorentz line combined with a Doppler line using the equation \* mergeformat to simulate Voigt linesCOM_MOD=2, Equivalent width used is interpolated from a voigt width look-up table [R2].LOR_MOD. This code defines how the Lorentz equivalent width is to be calculated.LOR_MOD=0, Equivalent Lorentz width is assumed to be Weak.LOR_MOD=1, Equivalent Lorentz width is assumed to be StrongLOR_MOD=2, Equivalent Lorentz width is assumed to be intermediate between weak and strong as calculated by [R2]DOP_MOD. This code defines how the Doppler equivalent width is to be calculated.DOP_MOD=0, Equivalent Doppler width is assumed to be Weak.DOP_MOD=1, Equivalent Doppler width is assumed to be StrongDOP_MOD=2, Equivalent Doppler width is assumed to be intermediate between weak and strong as calculated by [R2]The band models are defined as follows:ModelICONVPAR1PAR2Non-overlapping Lines10EW codeUndefinedGeneral random band11EW code1Malkmus-Lorentz11EW code2Goody-Lorentz11EW code3Godson-Lorentz11EW code45.2.2 Band Models using Band data (11<ICONV<20)These models used band data generated off-line either by the program Makeband or from external sources. Radtrans uses these parameters to calculate the spectral transmission or radiance using one of four models [R4] (note that the absorber amount (in units of molecule-cm-2) must first be multiplied by the factor 10-20 to cancel the factor in H4sIAAAAAAACC7t+9tgsBjBQYhBiSACzHMMZGTgZGJi/ANlMDKJgMVYg5maCsXiYhIDqWYAsFkZe MK3HKAGmmRgZwSo44WoZmf7//8/ADGTJMXABSTU2fiD9HyQIBiDzfzN9gfImMDJBGAIhmbmpxQp+ qeUKQfm5iXkgu4BYl5GBgR1IK7IyMmQz8DAwMgiA9f9E1g82IrgyNyk/h4EJoosRrPsDku5SBn4g m3TbIeYwws0JAbpCEGoOwhUMBMzBdI8B0D0SUN98QDYHi28wXaEBdAUPnKcJZMuihTbESSB96oz/ /zODeQAaf47r/gEAAA== \* mergeformat). The available models are:ModelICONVMalkmus-Lorentz12Goody-Lorentz13Godson-Lorentz14Not completedGoody-Voigt15The additional parameters PAR1 and PAR2 are not used for these models.ICONV=12 Malkmus-Lorentz The Malkmus-Lorentz transmission of a single gas is given by:H4sIAAAAAAACC61UOy8EURT+7h3vd9jdkAh3FbtEltjoREFDISQIicprIx6LRLFUCoVCo6AgOqJQ +hE6tV/g3SjEsxjn3pm5O7sjYZZJZu75znznu+ece2auLi8Ooa5zRDCprOtxhmLAiBj0QFD58uku 5Y5VxiPEzyMrj5WrtY3VqpUzphjFmsu4aZqkAzSghJ6RgkpaTelUl9T/5M822mXcMqpG55OJNTGY SInhleTUstyL7hgDCmkN5zOMIgSGqqx4mYS0RjaS0ytL4FYUU9FPruhuii7z7I4fd7d0GIqUjoHE +iopBXPOI0bRsT/k4eh0kE6nRu2EulzvKjCgURyN6Pfdd2/mPaQzJCcFH7wATspNOkN5+gFejT5l 1ZA19ssucU91rVTPhO8uOTnzjE6kNGqmCpYy+rLquy/eXGVfUv+QawvpbNo677/W8eYTRx229Gks 6tPY9jmzPOM0dnxXyL+Z2QocaNRJ9e7nPJfp7HpJ50jXu6frPbZ9IczYvhBm9fzyrPnlmp2w2WHM ZX19Dke+sTgGFmyfY0nfSY5zz3EvyqkeBz2KsAs9iHoXeifmqUafxEyjD2Km0Y0oRVSjOyFc6FYE XOiFNM80eiNmGr2KIKHMP7o1ArKGKDNNQ6EvHx4mY2IGAAA= \* mergeformatwhere:H4sIAAAAAAACC7t+9tgsBjCwYeBnSACznMIZGTgZGJgjGRkYmBhEwWKsQMzNBGPxMPED1bMAWSyM vGBaj1ECTDMxMoJVcMLVMjL9//+fgRnIkmPgApJqbPxA+j9IEAxA5v9m+gLlTWBkgjAEQjJzU4sV /FLLFYLycxPzQHYBsS7QTexAWpGVkcERaA4TgwCafpAjQKzgytyk/BwGJoguRrDuD0i6bYG6eciw HWIOI9ycbKA5YlBX/EQ2hyhXlDLwMkhjuIKBZFdoAF2hSLJvMN0TAjRHlQru0QSao0sF9+QCzTFE SzcQ54BUqjP+/88M5gEAyz+k6sgCAAA= \* mergeformat, where m is the absorber amount andH4sIAAAAAAACC7t+9tgsBjBwYeBjSACzrMMZGTgZGJj9GRkYmBhEwWKsQMzNBGPxMPEB1bMAWSyM vGBaj1ECTDMxMoJVcMLVMjL9//+fgRnIkmPgApJqbPxA+j9IEAxA5v9m+gLlTWBkgjAEQjJzU4sV /FLLFYLycxPzQHYBsS7QTexAWpGVkcEJaA4TgwCafpAjQKzgytyk/BwGJoguRrDuD0i6bYG6eTB0 M2HVzQDVzQjXXQDULUay2zFd4Qg0R5ZsVyQCdatAXfGTAlf4MPAy6GL4hoFgTKC7Rx/oHlMifYPp ihSgbmu0NAJxBEilOuP//8xgHgCTke9EtAIAAA== \* mergeformatThe Lorentz width H4sIAAAAAAACC7t+9tgsBjAQYOBjSACz8sMZGTgZGJjbgGwmBlGwGCsQczPBWDxMfED1LEAWCyMv mNZjlADTTIyMYBWccLWMTP///2dgBrLkGLiApBobP5D+DxKE2svA8JvpC5Q3gZEJZCkQBFfmJuXn MDCBTNVlZGBgB9KKrIwMiUDdjGBX/Wb6iawLbFhIZm5qsYJfarlCUH5uYh7IhWD9jGD6A5I5Pgy8 QJNQXcQINgSkUp3x/39mMA8A2kkQJCIBAAA= \* mergeformatis found from the equation H4sIAAAAAAACC62Vz0sCURDHv++tVpampFEUxibRD8J+3Lp0EapLRaTUSdDAg6FJRJQRVHTpUOC5 fyfo1rn/IDp2kKg8bPOeuw/ZLXB1F3bfzOzMvM/MvmFfX54fIa8aEshJ6WmfIQBoWY0eGJY2P90D 3JKCPEH+PpJ8LCTXBTYqV86Y9AgoX8YNw6A8wAT66TndE6bVEEZ5Rehu8Lqp1RgFyth0tXxQKYGL rEkG9NI66WfIIwYmqRr8uzVKJssUy4UTfbtwpu9WyvkjQSjjmVw/WvJsYoQ47Lvjn92b0UxFrxLF UJvszr1FDeOua3BSiBqmHHnguhdLGFR56l3wHFNdi2321EkxT9ErDgq4pphFECmlLZO21jFTkqK3 POlMEHuua3PyzFGebBc8fTKPhvR6CnFsiDnHD++BhZJQO4vZjfEIdVJIUZJybXaR26g53vQQkVva uz7Won3qYZoHS/uid/mO6+OqTzvUp1KLFseh6znhf8yJTl/S6kxRdebUA+IMEd94whjGnSc8cdyq Wq9VrfemLYpz0xZFVZ0jbjtHXHlfmN5xXNpOt+Uj3jR9GK5MmyUJ24Pt/9FsjsgxwwxDk9ov4F5p l9AGAAA= \* mergeformatwhere q is the volume mixing ratio of the active gas and the temperature dependence exponent is assumed to be 1/2.The mean absorption for the conditions of the gas is given by H4sIAAAAAAACC7t+9tgsBjC4w6DGkABmdYczMnAyMDDvZAESDKJgMVYg5maCsXiY1IDqgdIMLIy8 YFqPUQJMMzEyglVwwtUyMv3//x9oDgODHAMXkFRj4wfS/0GCYAAy/zfTFyhvAiMThCEQkpmbWqzg l1quEJSfm5gHsguIdRkZGNiBtCIrI0M2gxgDI4MAWP9PZP1gI4Irc5PycxiYILoYwbo/IOkuZZAE stFtZyBoO8QcRrg5GkBX8JDsC0z3hADNEaSCezSB5khAQwXFHKJCxRaoW56MOEF3BShuNCmKGz0q xY0JleLGAmrOTwrcYwD0lz3J/sJ0DyiOXagQSyEMfAz+JPsL0z0GwJQbRhX3yDMEgsoehl9MbAww hyjB7QWVJyJMQgx+YJYwkBVFZEpnQnMzE8MzBX4GDzjvhYIMEu+bgiBDDJz3AygXgxFKxPqOCe67 QgYOhiSoOb+JNocJI7SLgOVnGtm5gwnoCpA5zAypFQXAdJQDN9cQyGuE8/SAvDa4WhNjSyC/i+Q4 xnS9K9CcuVQIzRxgXlpCcihguscQmAc2kp12mVDS7jqS8xITlrykxLAVntLXwVP6LiJTOqbLdIEh vpdKIXWCSiF1HO7D43AfnqcgL/MwLEfKy/JIvOcKwki8bwp8DBeQcrY8Eu+7gggS7yXQzDo477WC EhLvFbBEQPB+AlVeg/N+A1UieL+AKq+htXsgQQ/ygzrj///MYB4AukegsYgJAAA= \* mergeformat where qr is the rotational partition function which is 1.0 for linear molecules and 1.5 for non-linear polyatomic molecules [R5]If more than one gas contributes to the absorption, the lines are assumed to overlap randomly and thus the equivalent widths are simply added.Expressing H4sIAAAAAAACC7t+9tgsBjDwYJBjSACz1MMZGTgZGJhnMwIJBlGwGCsQczPBWDxMckD1LEAWCyMv mNZjlADTTIyMYBWccLWMTP///weawwA0nwtIqrHxA+n/IEEwAJn/m+kLlDeBkQnCEAjJzE0tVvBL LVcIys9NzAPZBcS6QDexA2lFVkaGEAYhBkYGATT9IEeAWMGVuUn5OQxMEF2MYN0fkHTbAnXzYNjO QNB2iDmMDBxgc5gZUisKgCaJku0OXWBo6JERCjB3wMwJB5pjSrYrXBikGQwoCA2IOUwMMxQkGSwx XMFElCuYGEoVpBnMQWmP4RcTGwPMeiW4baD0JMLEBwwzEEsYyLIn0sdMGC59psDNoA7nvVCQQOJ9 U+BlcITzfgDlHNHSLsRtIDPVGf//ZwbzALyw4J1MAwAA \* mergeformat , where W is the equivalent width, then in the weak limit:as H4sIAAAAAAACC7t+9tgsBjCwY+BnSACzHMIZGTgZGJgjGRkYmBhEwWKsQMzNBGPxMPED1bMAWSyM vGBaj1ECTDMxMoJVcMLVMjL9//+fgRnIkmPgApJqbPxA+j9IEAxA5v9m+gLlTWBkgjAEQjJzU4sV /FLLFYLycxPzQHYBsS7QTexAWpGVkSEbaA4jgwBY/09k/WAjgitzk/JzGJgguhjBuj8g6S5l4AWy 0W1nIGg7xBxGuDkaQFfwkOwLTPeEAM0RpIJ7NIHmSFDBPblAc2ShoYviHiyhi+mKdUDdGiT7BtMV BkBzzNHSDcQYkEp1xv//mcE8AP+2MS/IAgAA \* mergeformat , H4sIAAAAAAACC7t+9tgsBjDwYpBhSACz1MMZGTgZGJgvMQIJBlGwGCsQczPBWDxMMkD1LEAWCyMv mNZjlADTTIyMYBWccLWMTP///weaw8Agx8AFJNXY+IH0f5AgGIDM/830BcqbwMgEYQiEZOamFiv4 pZYrBOXnJuaB7AJiXaCb2IG0IisjQzjQlSwMAmj6QY4AsYIrc5PycxiYILoYwbo/IOl2YZACKhTF 1E3Adog5jFBzmBhmKEgw8GC4gokoVzAxlCpIAUMDGNoMv5jYGGDWK8FtA4WgCBMv0DAQSxjIEiTS x0xoLmVkWAfUK0pyeMPczAQ3JxtojgrUFT8J+BjTFaUMIgyaJIc7pis0gK7QJ9k3mO4JAZpjTAX3 aALNsaaCe3KB5tij5RSIc0Aq1Rn//2cG8wAmtNsFugMAAA== \* mergeformat If we assume randomly oriented lines, then in the weak limit: H4sIAAAAAAACC62Tv0oDQRDGv5lcItEEI8lJCEFPBRVBBfsgiGAjFiqkVSFFwDNFEPEtLMUHsrP2 CWzFwkZFNjN7fwx3hRvxYHdnl5lvvv3d3fPT4wPsc4g2zmy01CWUgcI3yQTfnhVlzHASVbgt+Z5E HlXtukVNuzKRzSinucTGGNEBFjAt82ppVlajh/ZR/S9+j3d3xFFQO+2HvWFw1LsJjgfh+ZX2krEp nqbUY5HQFZceapl6NaHRyW14MbgER1Vkq9/GqvfRkkQ/X/1L90iHYh3GfdBEJeeCnVwwroOW0BDa +OQSkvbLaTcl2OCqiGlUl2jO8caccUroSK0/Me/EM6c6ofhd+bML5R5MzD3rIuK+4cidc29Nua+n dBdTutv/wGconPdinQ9nnTypPho4GNvNYze+76vj1/7j6QV17GT+vwi6Zq6RMQW7GwEuxCsgEAQA AA== \* mergeformat In the strong Lorentz limit: as H4sIAAAAAAACC7t+9tgsBjBwZOBnSACz7MMZGTgZGJhtGBkYmBhEwWKsQMzNBGPxMPED1bMAWSyM vGBaj1ECTDMxMoJVcMLVMjL9//+fgRnIkmPgApJqbPxA+j9IEAxA5v9m+gLlTWBkgjAEQjJzU4sV /FLLFYLycxPzQHYBsS7QTexAWpGVkSEbaA4jgwBY/09k/WAjgitzk/JzGJgguhjBuj8g6S5l4AWy 0W1nIGg7xBxGuDkaQFfwkOwLTPeEAM0RpIJ7NIHmSFDBPblAc2ShoYviHiyhi+mKdUDdGnDeUiDP HC32IV4D6VNn/P+fGcwDAC6YMlmOAgAA \* mergeformat , H4sIAAAAAAACC62Uz0rDQBDGv5n+kWqlkbQgSCWKVkXrqSdPHkRQxEMt9qgVi4iNLUgR38Kj+BA+ gkdvnn0ND16qhzi72URNDjbawGYnk5lvf7Obycvz0z301YODY23NNQk5IPXIckNJ+zIyJjiw8uxI fFqsNE3qeZ2m9cxEOiIXxhJ7nic6wCzG5V7JFmT2lFNfSv+D38zTLbFvWI1zt33l7LevnXrXbV2q tWRUCRhTjBlCE3nxWZF8BaGsgxv3pNsB+1mks1+/ZW+hLIGlePYvq/s6ZHQYd86McFjxKoagYPSd suyG7DbeOYtg+flwNbWDRbZETFm2WFNDVswRUsIDilJv0ooDZg51alJvdciK4xQ9ya4lPvU4xYXo bBiKQWKKPgrYHMFeLAvFduJq4jwN0dkdAc+K6NRHwOOKzmHCr/qLoiXZR4Zi8A+KPTmlsz9TnEqH 74QdtBZ2UMf4bCwYn43FsAc50oMcRldMdFlO/effIIhRb/wYwqrxBZbyuZE/oH/ASmOJPC+lnz4B 1FwMo5IFAAA= \* mergeformatAgain assuming randomly oriented Lorentz broadened lines:H4sIAAAAAAACC62UwUrDQBCG/52mlWqLLW2llGKjoFZBi95FEPHowYq9iS3kEGgsWER8C4/ie/gK 3jz7BF6lBy/qIc5ukq3tHkzUQLIzYWb2m38neX56vIe6LlHHubIaHYEskHogfqCi3qX5nqPIylGd 4y22LJFX65aoqpWEUBFZHSvI932uAyxilp+rmXlefflSXbL+J72F3q2gwCicuJ4ztI+ca/t44HUv 5F58bwpghteltECHKS0UpvIlhLTaN15v0AcFWUJlj75lH6DGgRUz+4fdgzoirEO4s6vIGRQUi4Jw ZddYDVYbH5RBtP2y3k0qWKY8F5NWia1izI5pilRgl3MriTuOmEnX2WHelV9TSN3tP1MEum/E1J2M U5O6N7W6Da1uK/E8mmTesIjDsM577DqmUi7KaCecrPEpdfm0T/+J4iykGMX8ysYUTabY1946ez2D CYmZtnkCHe212HMnprOfuG+T3MUC9sK+XxNP+QtKTDL5vwsalZFrwvdTyvsC7teWQoAFAAA= \* mergeformatThus equating the weak limits:H4sIAAAAAAACC7t+9tgsBjAIZZBhSACzLMIZGTgZGJhlmIAEgyhYjBWIuZlgLB4mGaB6FiCLhZEX TOsxSoBpJkZGsApOuFpGpv///wPNYWCQY+ACkmps/ED6P0gQDEDm/2b6AuVNYGSCMARCMnNTixX8 UssVgvJzE/NAdgGxLiMDAzuQVmRlZMhmEGRgZBAA6/+JrB9sRHBlblJ+DgMTRBcjWPcHJN2lDCJA NrrtDARth5jDCDdHA+gKHpJ9gemeEKA5glRwjybQFAloqKCYQ1So2AJ1y1PBFYbAFKRHtitcGKQY tCh2BRPDDAUJBhMMVxCXQpgYShWkwP5gYPjFxMYAs14JbhsodYsw8QJDHMQSBrIsSU4HTBghVwyM AR+oOT9JTk9McHMygek7EIknxuAJDYl3BOID001PGYQZrNFyLyQ8QCrVGf//ZwbzACi8FfhOBAAA \* mergeformatand equating the strong limits:H4sIAAAAAAACC62Vz0sCURDHv+/5IyzFKPudsRn0C+yH1CXoEBRdwiClugQZeZAyA5GQrkGHDtVF Ijr1h3Ts1rm/oOgUBhGZh232uT5/LMWuuLI7M+ubmc885s0+Pz3eQlz3CGBXaB9bDC7A9mCjB7rE OwfdbbysuXmA1ttJszOPkFOsV0jOmFjhkmsZV1WV4gBDaKXnqNNLUtVeiqud7iL/1K0rRo7CN5JN 7qUOwbWoQQa0kBx2MMTgAxNURV6o9hLBoolkPK2E4yfKRioZO9IIhT8TMl8VZw09xFGfHX9kL3kz 6b1IFB0m2Y259+FGUK+hJve/NRgp5uCnX6MUx+Q7YqDglikOKM6kTlGwTJGBgpkm7MU4UcxbrsbI E6U4C03gmaA4S9o5wg93ohwgIPNqZ8PH2zEotE7SVqRviPojYrI3uaGCZcq83nAFXI/DcaMMYNtk d9VTcGQUPzZllWFZ5U7DHcdlhWk6fRnLM8C4UwmaAVnTE6ieQptEp02iONMp8iYnEa/qex+d5ErX +XBuYIJlplnqwAtpTZN1WdOd15brNpIn0IekXve75S5/QTd9r6zN70pvvyoerErrTemvsr4UL3LS +qb/ck3Y0RCcuKv7ApbCaCvHmKrahPUL2byK9ZIHAAA= \* mergeformatICONV=13 Goody-LorentzThe Goody-Lorentz transmission is given by:H4sIAAAAAAACC6VUy0rDQBQ9c/vQ2hZbbaEby2jRLqSK4k5c+EDwQRe2oOBGhRQE0wouqn/h2g9y 59o/UJcuxOci3pkkY9os7COQzD13zj335kzI48P9HfTVRgknOpo9FEgAkT3iB/I6F+M7SX6UohLz oxxFRVqvC6KgVxJCMxKGK8hxHNYBihjj51x8nFdHJfWl9H/ozUO3gtwgUz+3rStZtdryoGWfNlUv visCGOF1OiZQ51qBTFe9GkJFtRv7rHUBcquErn4NVK9xdSrUHf92d3UERrVOBNb1JavkB56jwrWV IebwdZZYY8WgRUargb00qn07HZ51nc9w39P5GmLWZRRQU98YvikOX2DG9FXfTY6y2NXRJEdHPfpL oZnned7jgf2lDg8bfXsYnmeDPWyYN7TMG9peLscMN5fDpvGIujyCYW957CK2Q+fmctSOyyHseDk/ Urlmj952e0J4kkmUDXqRUwH0LLMB9C7TaBn0ycw/9CEnGHX+G9wDUv3KwnEiGv0CpRtgzawEAAA= \* mergeformatwhere A and B , the temperature dependencies of \* mergeformat and the mean absorption are all calculated in the same way as for the Malkmus-Lorentz model. However, here the statistical definition of \* mergeformat is different.Equating the weak limits we again obtain:\* mergeformatbut in the strong Lorentz limit: as \* mergeformat , H4sIAAAAAAACC62UzUrDQBDH/zP9kGqlkbYgSCSKVkXryYt48KB4URS0UI9WrOJHWkGK+BYepQ/h Y3jz7Gt48FI9xNnNdpHkYKMNJDuZzPz3Nzu7eXt96UJfV/Bwoq2NOiEHpLosD5S1LyP3GPetPHsS nxYrTeN6XKVJPTKRjsjZWOIgCEQHmMaoPCvZgoyBcupL6X/xh3l7JA4Np3bpN++8/ea9d9j2Gy01 l9xVAkZknMkQ6siLz4nkKwhlHT34p+0bcJhFOvv9R/Y2XAksx7N/mT3UIaPDePKmhMOJVzEABaPj ubIastr45Cz608/a2dQKltgRMWUVxZoYsGKOkBKeUZJ6k5Gyzb6VKquJuxWnuBadNUPRS0zRQQHr ibsWp1gUis3E1cR5aqKzNQSeJdHZHQKPLzoHA/Y4TtGQ7GND0fsHxZ50qfFnijM5mTt256/YnX9u fEXMGV8R8/bscOTskI2umGhXuh49xWGM+hLGEJaNr28p30XkzxU2WGksUBCk9Ns3RMweHkoFAAA= \* mergeformat which is equivalent to \* mergeformat for randomly distributed Lorentz lines. Thus equating the limits:H4sIAAAAAAACC62VzS8DQRjGn5lSKZoKrW8yGkElNDgKiUTCQYiPRNwQJEVVNI04OBAHiUtPIvw/ 4uLsLyBO0oOI6mG9O9ZYnZCdprvZnXm38z7ze7fPzD7c315DHjeIYlX27pYZAoDv1Ec3ROSzSrpq +HevlkdpfAX1KlhQtoOsWbacMTkioMYyblkW6QCdqKZ7jz9ErWU/lEcdXQX+6kRZRokyd/EouZ7a BbdVBxhQRW1XJcMawmCSqsDz7iwptpRIbqbF7OahWEgl1/ZsQpnPZJtz6cygiTiKZ8cfs39lM5U9 RhT1Htn1uTdQi34V7aODzoiu9W9FOtMOqXQ7THljpgwEYhoFjCn6iCJuXI3Os0Q6I2XgiZHOqO1n fHA/vgWial7bo2Feh3bZa6DeuModpv9pxqNHuFbBJM08XXIF3NHhuBJtmPfotWIKjozowJyqckpV uVyy47iqME2rYM94LepvKkFr8cDzTlBMYe8ImTJRHDsUOY87Anf5Poxtl+vCONGYYMw0RA48U1Gc ovNf7rwwrlsnT6AFW07dL8Yuf0QjVgz30R9vP4kgJlT0LFpd0ZsIIauid/otW4Y3Ogw/Lou+RF8y 9sheZlk+GX0CPuUbkhoHAAA= \* mergeformatWhich is a factor of 4 bigger than for the Malkmus-Lorentz model.ICONV=14 Godson-LorentzStill not completed! (and probably never will be!)ICONV=15 Goody-Voigt The Goody-Voigt transmission is given by the integral:H4sIAAAAAAACC61WPUwUQRT+Zg4O8dgAnpcgJJPFENDg+RcrE2KDhY0JitcqyhUGTkwI4UisbGws TGyMBaFRCwtDYiyksDE2hsLKhEqNESpFQ1A0Zn0zuzueO0Tu522yN+/Nve+bb+bNm523y6/uwzxN og+XjDVSEGgFUt1p+kHO9DXTm5Gx1Sb7KL7JoDzo9rDoMq0UwkS02lghgyAgHkBhN/32p9upDXSn eTT/L7kReXeEDI2O0aul4rR/tjjrn5sqjV3TY9GbF0ALtb3NAqOEFehI4LUIbZ2fK12emoQMUcKg 1yvQQ4Ruc0bHjqOHPAK7DE8KxfJ1YsnVrSNP2HwDOmKe48RxoubVdPVMEMfJaDZblTzbzMZVMYMu nKp5Nq6KA8Rxuo69kdSj98gZBj0HiWOEQU+JOC5YrwAP8yyr5eEhg7oy8Txm0HOIeBYZ9MwRzzOW 7HlYst4xOokmqqxXV9MgoadZ6kzhRgN11oubLDtH4RZLnSncZsmUwl2WOlO45+RYVnkmjxN6gUFF gXgeMWXpCUt9KzxlqW+F5yz1rfCCade8tN4R8l5XmXtX0xih30Sathqo72Gq0BWHp/bv+lH6oq4w nDe6Qtf0vQ4/ZRqxkP12XH1X2yt78M5YWbLe22iZiJY2+kMUrfAxMYM4Rv8TxmSxGvXFlu77EvV1 YjLq68R6zesmt1m3Hlxxztf/38qkRT9ABsUI/XkHtDv2N+zDxbpzFquQGC/n8LXKL1VShcQnP4MB 6635qsJb9fdUeJu+h9/W+0GRf73vfpa8f2/uYTr0eAMiCFLG+wPHrcEPSgwAAA== \* mergeformatwhereH4sIAAAAAAACC62WSy8DURTH//fUq0pKkHRj0mriESHYIvG2ICLqFSyUCEI9YoGthdhIrCwkErHy SeysfQaxsbBpLca5d6ZX9VrM1Ewyc8+59/zP/O45vZO+vjzfQV1PSGJdWbklgTAQGi7jB5rUXDnf EcpbNZTkeF5GmahVY7eIqZGEUBFhHSvItm3OA1io5mdrRZRHW06qS+b/ok/XuxHkGHXzu5mtk/jM 1ml87jCTPpDv4rtLAJU8JsoFzllLqCvSSwhppc4zG4f7IEcllPqjQD3I6mpDTX+q4aqFVqdRy3qH PeuZ3aSYZgLrHxRWIBRjSKBZ9hw5qoBw9GjRFZd9bKR6NCqrga2kx7qTwSzr3u5xx3lS+lX3Pt87 Nilk3fuNPPBYuR+eHlRhwONu6M/+9ZXcP/rVP/+7MXl6EOM8+W736m4P+T6lJuMsd26ywLMwHghx AlOaeFQTzwZAPI8arAXCGMWmyxjhrA5jBAv6xFHRiRM6etGNjmIZxV8BJ0auODECq+5c3pJz24FU wsKKrnJKV3lHRxzzW45K/iZ0svrM4PR/Gtv5N3ahvV72Lktm6mL1dQC1O+Y8t773ZvJ0cJ77f/BU qTwhpCZGuJtXupsXupsPJdaK8BaPYk977/HmAi/La4/a++K1x6L/AU4xZM42Ydsh5X0D0or1k5gI AAA= \* mergeformatThis function has to be integrated numerically.5.2.3 Summary of Radtrans Band ModelsThe band models available in Radtrans are:Spectral ModelICONVNon-overlapping Lines using line data10Random Band Models using line data11Malkmus-Lorentz band model (band data)12Goody-Lorentz band model (band data)13Godson-Lorentz band model (band data)14 (not complete)Goody-Voigt band model (band data)155.3 Correlated-K models 19 < ICONV < 30Correlated-k models share the same speed advantages of band models but may also be used for scattering calculations ([R1], [R6] and [R7]).As far as band transmission is concerned [R1], it is of no importance where in a frequency interval H4sIAAAAAAACC7t+9tgsBjAQYuBhSACz8sMZGTgZGJgbgWwmBgGwGCsQczPBWDxMPED1LEAWCyMv mNZjlADTTIyMYBWccLWMTP///2dgBrLkGLiApBobP5D+DxIEA5D5v5m+QHkTGMGWAkFwZW5Sfg4D E8hUXaAoO5BWZGVkcAHqZsTQxYRVFyPYTR+QdJcCdXOiuYMRbAZIpTrj///MYB4Aqee7hhgBAAA= \* mergeformat, a particular absorption coefficient occurs; it is sufficient to know what fraction of the frequency domain f(k)dk, is occupied by absorption coefficients between k and k+dk. It is thus possible to write the mean transmission function (where the transmission is a function of the absorber amount) for a homogeneous path in either of the two forms:H4sIAAAAAAACC7t+9tgsBjDoYZBhSACzHoYzMnAyMDA/YwISDKJgMVYg5maCsXiYZIDqWYAsFkZe MK3HKAGmmRgZwSo44WoZmf7//w80h4FBjoELSKqx8QPp/yBBMADaxPCLiY2BEcJlUAKbo8sI0S3C xA7UC2IJA1kcYNf8ZvoC1TuBkQnCEAjJzE0tVvBLLVcIys9NzAO5DGwKIwM7kFZkZWIIURAE2oGu n4GAfiYw/QFuDiODBoMg0P2kuwNiDhPcnFygOXxUcI8m0BxxBgFMc8BOCq7MTcrPYWDC5QpboG45 KrjCEBiPumS7woVBCugPAcwwxaIb0+5SoG4DaGrhBcYPJLXwMpiT7C+EyzjAZjMzpFYUAEPIk0if YbpNF6g7ngqpJRtoThrUFT/JCCERoAnUSbOFUFd8IDksQDknCiXdVmH4iPgUI85gT0F4iDM4Q3W/ I9nuT8CQtCI5NDFdkQIMgVoiUz2mK0qBupvRSlRIAgepVGf8/58ZzAMAtlWMKOIFAAA= \* mergeformatorH4sIAAAAAAACC7t+9tgsBjBoY5BgSACz3oczMnAyMDBPZQISDKJgMVYg5maCsXiYJIDqWYAsFkZe MK3HKAGmmRgZwSo44WoZmf7//w80h4FBjoELSKqx8QPp/yBBMADaxPCLiY2BEcJlUAKbo8sI0S0C lGEGs4SBLA6wa34zfYHqncDIBGEIhGTmphYr+KWWKwTl5ybmgVwGNoWRgR1IK7IyMYQoCADtQNfP QEA/E5j+ADeHkUGDQQDoftLdATGHCW5OLtAcPiq4RxNojjgQY5gDdlJwZW5Sfg4DEy5X2AJ1ypHs G0xXpAHNMSbZN5juAYWuJRXckw00x5YK7gGFrjMw3YF4zAypFQVAvgeKa6OIDHtMN+oCdcZRnJKY GLJzBYDhT52UVEIF96RkCzBUQM35SYF7DBjEGHSgofuT5JS9lIGNQQ+q+x3JcfOJQQQYu6jlFcQL IJXqjP//M4N5AKYJbfBABQAA \* mergeformatThe form of this last equation is a standard Laplace transform and thus we can define the mean transmission function of a path to be the Laplace transform of the absorption coefficient frequency distribution:H4sIAAAAAAACC7t+9tgsBjDwYxBgSACz9MMZGTgZGJiPMQIJBlGwGCsQczPBWDxMAkD1LEAWCyMv mNZjlADTTIyMYBWccLWMTP///weaw8Agx8AFJNXY+IH0f5AgGABtYvjFxMbACOEyKIHN0WWE6BZh YgTqBbGEgSwOsGt+M32B6p3AyARhCIRk5qYWK/illisE5ecm5oFcBjaFkYEdSCuyMjGEKHAD7UDX z0BAPxOY/gA3h5FBg4Eb6H7S3QExhwluTi7QHD4quEcTaI44MO4wzAE7KbgyNyk/h4EJlytsgbrl SPYNpit8gOZowHlpQJ4pyX7DdB0orK2o4LpsoDn2VHAPKKxdoWH9kUBYY7oimoGHQR/OiwXyPNFy BMRJIH3qjP//M4N5AGXqeUOiAwAA \* mergeformatSimilarly, the absorption coefficient frequency distribution may be defined as the inverse Laplace transform of the transmission function:H4sIAAAAAAACC7t+9tgsBjAIZRBiSACzzMIZGTgZGJjVmIAEgyhYjBWIuZlgLB4mIaB6FiCLhZEX TOsxSoBpJkZGsApOuFpGpv///wPNYWCQY+ACkmps/ED6P0gQDEDm/2b6AuVNYGSCMARCMnNTixX8 UssVgvJzE/NAdgGxLiMDAzuQVmRlZEhj4IG6D1k/AwH9jGD6A5I5GkBzOMlwB8QcRrg52UBzeKng Hk2gOcIMApjmgJ0UXJmblJ/DwITLFbZA3VIk+wbTFT5Ac1SgrvhJsit0GdgYtKCu+ElBWBgCzdED pUaGX0xsDDADlOBxAEphIkxMDOZgljCQZUuy35nQXM/EEKLAw2BGdkwyoaQse4rdw8iQCzTHmQru AaUsH2icviMQp5iuiAambiM4LxbIC0DL0RAngfSpM/7/zwzmAQB0H5uYYgQAAA== \* mergeformatLooking at the form of the equations it becomes apparent that the change of variable and integration space need not be restricted to evaluation of the transmission. In general if G is any analytic function where:H4sIAAAAAAACC61Uy0rDUBA9d/qQtgYbrfigSHTh+4HuBAUXlS4EF1boQgparCAaA0pRl/6Baz/I Xdf+hKiIG3URJ5OYRa9iU3MhmZmbOWfOnTvkoXV/B1k3KGJfvMeqQgZItIhfGJS9FD85+vZ6qcj5 SfaSyhC7qIbFklKSkQlzFbmuyzzAGLL8nkz3sXW9TVlcCR+UhvJDTAjPgvLRBf5C4g2wlxU1n/QW YG8V+U5+99huXFjbjUtrx7EPzjxlwqLQw3Y8RShbJtdox+MPPIl9CXkUpmEi14UOn4dCHpt58jHo mWGeEWbSeERS5dquO6eg31SsM9qKQcUy3+NS1ypKGMWchqYf0XrtJqNXgmkxMBtMi4HVGG6pzP3Z CqMTjqqBzvcudBZQi9xrXdM8q6hHPpuux5vAo+A0z5HvbA/9qIRRjSNH6ww67EwJQ9josK+6kiaj NwP0U+Tar9zJtRgm5ZC7ef6PGTZx1fZ/9EfDy5xSrpuQ6AvYX91ksAUAAA== \* mergeformatthen the following transformation applies:H4sIAAAAAAACC62Uv0oDQRDGv53kTpIoHhrlbOS08B8abGwEsZJgYxFFG4soRgjxksJCxJewtvdV 7Kx9CxERJFqss7PnFTkknNmF3ZldZn777RxzL89PD5BxhxBN8aZOFEpA4ZN4wYyceTwr9OuNU8jx RfaKakJsTYViSSmJKKWxirTWzAHmUeZ1yZ9kq82hDL4JX+RD2S0WhbOhbHaVPJB40+yVRc03fSS5 94qsExy149Z1dNC6iRq9+KxrlAlFYYztgkeoRwHfMZiPIfkk9i3lKKwgQOUfOiyHUk7MnMCBnlWm zPHMcETS4W183rsC/aVihzOj3K/Jqrhkzlbu12T1mOpuO9DTYc6uAz2munsO9NSZs++oPg1H9Tl2 oGedOacO9JhuaDr6Xu2R9RAuOgG6Cac/gp5NzKKWdGd/SHdmq/IInwk2+zV3b7+jirWBf659golc VloXZPcDArsSjgQGAAA= \* mergeformatHerein lies the principle advantage of k-distribution models, once the absorption coefficient frequency distribution of the gas absorption is determined, calculations such as multiple scattering may also be performed in k-space, and as we shall see, this space is much more amenable to efficient and fast calculations.We now define the cumulative frequency distribution g(k):H4sIAAAAAAACC7t+9tgsBjAIYJBgSACzLMMZGTgZGJh5mRgYmBhEwWKsQMzNBGPxMEkA1bMAWSyM vGBaj1ECTDMxMoJVcMLVMjL9//+fgRnIkmPgApJqbPxA+j9IEAxA5v9m+gLlTWBkgjAEQjJzU4sV /FLLFYLycxPzQHYBsS4jAwM7kFZkZWRIZxBgYMTQz0BAPyOY/oBkjgbQHHYy3AExhxFuTjbQHB4q uEcTaI4QEGOYA3ZScGVuUn4OAxMuV9gCdUqS7BtMV6QBzdEj2TeY7gGFrgkV3AMKXQsquAcUunYU u4eJISVbgMEJas5PCtxjwCDGoI5hDjnhwwb2G8icdySnmk8MIgzKaPkT4hmQSnXG//+ZwTwAkyay JzAEAAA= \* mergeformatSince f(k)dk represent fractions of the interval where the absorption coefficient lies between k and k+dk, the limit of this integral as k tends to infinity is unity. If we invert this function to express k as a function of g:H4sIAAAAAAACC7t+9tgsBjBwZBBgSACzFMIZGTgZGJiPMjIwMDGIgsVYgZibCcbiYRIAqmcBslgY ecG0HqMEmGZiZASr4ISrZWT6//8/AzOQJcfABSTV2PiB9H+QIBiAzP/N9AXKm8DIBGEIhGTmphYr +KWWKwTl5ybmgewCYl2gm9iBtCIrI0M2Aw8DI4Z+BgL6GcH0ByRzNIDmsJPhDog5jHBz0oHm8FDB PZpAU4SAsYFhDthJwZW5Sfk5DEy4XGEL1C1Jsm8wXQHyjTLUFT9JdoUuAxvQH6KYukl0hSHQHF2S wxTTPaA4NqRCqIDSnBkV3AOKYxu0/AAxBqRSnfH/f2YwDwCHK63toAMAAA== \* mergeformatThen the mean transmission may then be written:H4sIAAAAAAACC62UO07DQBCG/xknJuFpiUBcRYaCh0QQOQAVBV0KsISoeFoRIiYgCqDhDNQ5EB01 t0AI0QCFmR0HS8FCkbFX2p3Z9cy/386u/Pz02Ie2e7g4VK++R6gCVp9lwJyulaVP8I83ya7El8Qr 0ZTadXLVMpFGVJNY4iiKRAdoYFzGJXtGbGQWtclO+GQbFE+xqDpNirNr8sVSb1a8itJ88fsg94E4 dhz/LAyuvXZw4+30wqMLQ6YqhDGxC2WG7zmyx+98jMhnta+JDmEFjvBn54h1ONEJRWe6AJ5V0alL T+ko0u5deNzrgv+i2JTMRg6KiupYCG4vRak1VKWtf1M1JXM7c43TtTkXnXbm06V5zGn8Ang6orNf AI+584MCeMwbPCmIp5ubh3HacXA10PnIwbOBeawlsxZsfVFG9WXEW0zX6A01uf/hP1eMZCKXKYos nX0DZhxhvkoFAAA= \* mergeformatThe cumulative frequency distribution g(k) is a smooth monotonic function and we define its inverse to be the k-distribution which also varies monotonically and is thus easily integrated with comparatively rough quadrature. Dividing the space between g = 0,1 into N intervals such that the variation of k with g is sufficiently well sampled, the mean transmission of a path may be calculated from:H4sIAAAAAAACC61UPUsDQRB9M5fEOz8D51cVTgs9wVja2Qk2ksIcqNioGDTomYBITOsvsPYH2Vn7 C2zFwkYt1rm5y6EJEpLcwu3MLPPevp0Z7uX56RG62vBwrJ6/T3AA655lw5ye5eWb4I43yZ7k58TL 0ZTaDVpUy0Sa4aS5xMYY4QFKGJd9pTAj1kSHuuQmfHEBFIdYVp4yxehZdgQbea54tqr55o8E+0Ac O8WgHtZuvEqt5e01wpPrSJmyEMbELuUZgefKHd149MGz2veUh+DDFf2D64h5OOUJhWc6Az1rwrOA Yi+PSqq2w9PGFfg/FVuCLo2gwlYeC7W7pjBt/qnSztCqyoLeTfpvI0j6b+Nw4Lp314txKXNQTXg+ R+hfHfM4+BWVRHUnqqCA9eT1b31e39vRV1HnZzRhRxlN2NnQvdwW9MXIfSOcC08zo77ddv2J4qJE matkjKXRDxjFw7YaBQAA \* mergeformatwhere H4sIAAAAAAACC41PPQ8BURCc3fuQ4+QIEpUcBRU/RSESLYXiyFEo/A210o/Rqf0NhQbFs28fV6hs 8jKzm5nZfdfL+QitMuqYK1vNCBHgnYR7aOkskFfhL4u5LnpfmE9VxRG1FZlIFVGhJTbGSA7QEQ/Q DxNBY4dasglPDkGuRU9zhuTcTSbxWtYQVtJrXnz/eA/EjtSmWb7cpePlPp1s88XGXqYp1gN0A8Y6 jWWH8z/+9rPircghZEgQ/vzE3W6VAzLG0+4N+8AmTFoBAAA= \* mergeformat is the mean absorption coefficient in the ith g-interval.For band models, radiance calculations may only be performed using Curtis-Godson equivalent path approximation, thus precluding scattering. However when k-distribution models the Curtis-Godson approximation is not the only one that may be used. Referring to [R6], for an atmosphere split vertically into a number of layers, for a particular spectral interval there is a very good spectral correlation between the high and low absorption features of different layers. Hence, to a good approximation, the combined transmission of M layers may be calculated as:H4sIAAAAAAACC61UPUvDUBQ97/ZDa1osWEsrIq+Cdaqjk04K4mCHttDFwQ+KtDa2IFIFJwdnZ3+K P8DNwclf4MckDuLnEO97SWNJBtvUQHLvCfeed+7Je7m7ub6Evs6Rx5bObqsCMSB0RfzApH4X4dug bhanPNeHOQuLhI4LIqMjCaErYm6tIMuymAeYwRg/89FxjpZ6qS9eCV8UhbAhZjVPQdjdKYpzr8om OBvVar7p1em9EGQnyUrdrB3KYq0jSy1z+0Ap0ywCIxxzEUJFpnmNpKdfSVZZ+cTcaTVBdhfp7he3 W2AZaSR8q+PP1W0eYuWKJ4TacZuZ5gLrKHD3kuOMgbLjjIFqAGe62roO7bNDJYfns28er0ZCvZFl Pf1N6FUhsMoTbg48jd8pk3l2B57Gr6eBLJo9KId1F23w7l1zJn0e+FveI4OVgD4RHqSBRRc9SdmD HmWqB73JBNou+uDKX/TOle2hv7lAnX2ZdlGRfZnq0xe/48qXdOATovbP0dCnQWCPeU7/xZkszjx/ PvvHoSrnhWWFNPoBlRpEkooFAAA= \* mergeformatThis is the correlated-k approximation and the degree of correlation is in most cases exceptionally good, and usually better than the Curtis-Godson approximation. It should be noted that to use the correlated-k approach, the number and width of g-intervals must be the same for all layers.5.3.1 Correlated-k model using line data (ICONV=20)This option of Radtrans uses line-by-line routines to calculate the absorption coefficient spectrum of each layer and then numerically extracts a high-resolution k-distribution function which is then re-sampled to the required number and widths of the g-intervals.. This process is of a similar speed to a normal line-by-line transmission calculation but has the advantages of accurate determination of g(k) and the amenability of using the k-distributions for fast multiple scattering calculations. [To numerically calculated g(k), the absorption coefficient spectrum is basically analysed to evaluate what fraction of the spectral interval has absorption coefficients in the range k to k+dk.] 5.3.2 Malkmus-Lorentz Band Correlated-K (ICONV=21)The Malkmus-Lorentz model is particularly suitable for application of k-distribution methods since the k-distribution may be determined analytically from the band model parameters. Expressing the Malkmus-Lorentz band model in the form:H4sIAAAAAAACC61VTUwTQRR+M7ML9Ee6BQkxQa1NVP4qtuFKQguNHMAQW4LRkFJwg40sNIABNEYF A9zqyYMHw8FEL56MBxOihIM3z14RExX/MKbxB7R13my3S1shQNx2Z9++n+9782b2zauXL+6CuHor m2WwoORtJyiwKglAghVh5SJQQkDmT0LT6bTQnCAHhMZLCR9RslHISHbaLPdWlnPpWJEDqiCNQTAB CtcscvkZv12VACkOZMt42aEjOnYxPBlXAVwEk1nneOV6gtQtOD1Ex99PnxNNSOVc8hCULMhOdWsV 6yfItUEtqTcC4DYmSflPCU1qfcODQHQ8MVvwWdEHXarBYKhiJ9nOMKjI7WsBVk0Wa572WPRs56lm M3SrpYbusVPXHScjZRWC050GkxNZlXBMU0ddp9Vx15lhLTqUWRecgc5OeQUNdobr0uCDcYjAAtGx Sylx6Ng3UjvF3mpmjZxCRwVWI+8W1czYkUVFNHUi7vXCQ1iEc0UHSwyGeslm/V95+7J5l9JLBahk j5UOhDTokxc31cQNu8U2M7ZmsXFDh7VlYlYirOw959xKBDZVotuiFKLuYp/Hwcyw2bGV7T6ZLVYK 1/Gf36SRc24tPv1+XWqgLZEntlzr6i9mNaxuOluca11bM2PraYc91/r2+z3ZXD0m7ctaMZMmT52n XboidxUZPj6Wz/5h3WQPsHz2z39M9gGWz/7uh8l+Vsq3vv9pWm9K2/E+kLab9VJB7McNM3a5IPZL CmNXMt35KTG6c1fXIyLjErWGOsK8EZR3x4b8g4OB6Gisv2X4gtoZHVBHwSnn70gny6yyU24ZvjwS U0fQCE6pI+wKToyNRKEMSo40BBOtDYHOpOI4FfF3fjt8yN+ZrHD4IRlMHk0mAhEuKY4WfCSCydpI WzIhNM38eb2NC/7aSGskmMS/32EnfA8Syi8+I8L3FQOxt6yEn2fTYSgCJ6pQS2Faw3nfqcaBd24q zTRBE6VTKldMTeAQ585UOEszZW4Pw6MLX24tsjiPD4g3mPOJtsDQMQs+58WgOqgzgmCuETlDGeJc mJxEGD8/wYbZ6zAw1WCwWPVEhB69z+PQo4dfxeGa+M7MExbPYQLtQmucsMblznYi/StVoFjoF4QP r6I7NDk6pmpGZ2HZbsCE31+mvK7zTggAAA== (where H4sIAAAAAAACC7t+9tgsBjAwZOBnSACz/MMZGTgZGJhNGRkYmBhEwWKsQMzNBGPxMPED1bMAWSyM vGBaj1ECTDMxMoJVcMLVMjL9//+fgRnIkmPgApJqbPxA+j9IEAxA5v9m+gLlTWBkgjAEQjJzU4sV /FLLFYLycxPzQHYBsS7QTexAWpGVkSEYaA4jgwCafpAjQKzgytyk/BwGJoguRrDuD0i6bYG6ucmw HWIOI9ycbKA5IlBX/EQ2hyhXlDLwMkhhuIKBZFdoAF0hT7JvMN0TAjRHhQru0QSao40W3xBjQCrV Gf//ZwbzAHfudOiAAgAA \* mergeformat and H4sIAAAAAAACC7t+9tgsBjCwYeBjSACznMMZGTgZGJgNGBkYmBhEwWKsQMzNBGPxMPEB1bMAWSyM vGBaj1ECTDMxMoJVcMLVMjL9//+fgRnIkmPgApJqbPxA+j9IEAxA5v9m+gLlTWBkgjAEQjJzU4sV /FLLFYLycxPzQHYBsS7QTexAWpGVkcEJaA4TgwCafpAjQKzgytyk/BwGJoguRrDuD0i6bYG6eTBs ZyBoO8QcRrg5JkBzxDBcwUSkKxKBumWgrvhJQhigu8KHgZdBlWTfYLpHH+geXSJ9g+mKFKBuY7RY hjgCpFKd8f9/ZjAPAKw3ANt2AgAA \* mergeformat) then the absorption coefficient frequency absorption is given by:H4sIAAAAAAACC7t+9tgsBjA4x6DAkABmzQ9nZOBkYGA+wQwkGETBYqxAzM0EY/EwKQDVswBZLIy8 YFqPUQJMMzEyglVwwtUyMv3//x9oDgODHAMXkFRj4wfS/0GCYAAy/zfTFyhvAiMThCEQkpmbWqzg l1quEJSfm5gHsguIdRkZGNiBtCIrI0MagzDUfcj6GQjoZwTTH5DM0QCaw0mGOyDmMMLNyQaaw0sF 92gCzRFmEMA0B+yk4MrcpPwcBiZcrrAF6pWigisMGbgZVOE8IwYZIA+YKhh+MbExwIxTgocFKKZF mPgZVMAsYSBLi+QQZcIaorrQkPhJICRgPmCC69YFxoYJ1BU/iQ4JTFcYA80xh/P0gTxrpHDhZbAj 2afobmVicAoWZvCA+vQTAZ9iuhCUgp1R0k8Yyf7GDD9DBh6GSCR/8zDEIvmbB1hakJrKEC7nAJvD zJBaUQB0bRpGamciMo4LgKm0jgopzQloTivZuQbhHhNgPmmC54ZaeG7oQQo5YYYpROZuTHfqAnXP pTi9MTIEA/27HCmfyQB5MFcvg7t6LUXu3EgFd2YD3bkbydUyQB7Mnbvg7jxIpjuZGJ4p8DD0wXkv FCSReN8U+BgOwXk/gHII3kugvgo477WCDBLvlYI4Eu8nUOUJOO83UCWC9wuo8gRarQhJdCB3qjP+ /88M5gEA+gblxqYHAAA= \* mergeformatwith a peak value at:H4sIAAAAAAACC61VS2gTQRj+Z2aTNg/No1YUq9YFpbbEmNSTUDBpg7VYCSZFQSRdbdDQJilNpWkv llbUgxDxUIp49WDx4q2HHnLSkwVP3rz5LEKRxUcLxn9ms7t52EKsSzLzz//4/m/+eb19/fIxiK/o BSvYuPRmgHCBMQlAgnfCiiJQQsCCPaGlUkloTpD9QhOgBFsuOSiUJScFa9HbgtIxqwvaoMSDIA9u ngvlJfzPegGW0NlR9nLCoDJ5Mz49ngSIEk5mA/FaNIJUFjl9RMPfQ4HJEpdaUApadd2TZl333M4l G2dENetBsri7FaVNKpc00IdEwwZ3PJVO5tovJKfaL2bTSqY8Zx/O2Yl90M7dGJ+rPwhTkIAVomHe I/OORjGp6NeJqHMZmwcFDdQi+wqNM9VQaQ3jtJKHZ6AY2Bl6WdKwZ3/vlHE3ptBQh9m5XY2imozt BipfrkDgPdNxH0gDtv/PNkP3WWpRyT+yjYUfSWYVTkOjuFuxHQWzBid3wLYaNVxRg4Vmdz0q5aix 6fS17BiQ7RmOVzBsk7ayLZMZq7t+Bf+SZ6sKf/414tDRZOptqrZ++F6yGjzoap11r7GXOtiMtdr6 ZcNEHmbrtPrk9HT5IGVbM+LnWG3ujz/M3K/Yap3VzB2QtotdlLZjtizVIn/6aSLLFm+dtaIillrk tU2O/K58574g+p07NPSUWPgS9MUG46fwDr2UyoTGxsJKLnW9NzuSjCo3kjnwWGp3nIeVV9Fj6c3e mkglJ7gRPNJgvD2Sn5xQwAvNR/yRQp8/HFXdrrOJUPTb4UOhqNrqCoEaUY+qhXACJberl3eFiNqZ 6FcLQnMG+9v9KIQ6E32JiMp/IZeT4B4jFD+cEcF9w0DsHTvB8fwoDg/gq4IDOpdGzZzCmzxuTAJ2 Kt3tgR7GHx3ufb+bh8TEQLpTZOM4Cov1ZxwU/1Wdo9axjCFqu9DBm+M8uI3nJ8IYRBvP2gVdOAps 7RjgLP2VIV7ZZ4Rc4c1VcX7M95K/qgTOC63+XuqfbNwv2ulzQ5PQrwgfrJ4cm85NJtP6jcGMU86E 3x+TVc8SHAgAAA== The cumulative frequency distribution may also be expressed analytically as:H4sIAAAAAAACC7VWb2hbVRQ/9768/kkT89Ku080l7cvWrrakXWo/iFho0gTHXEu0mQpWsnS+daV/ SSu2KNPZICJChx9E/FRF5gSRTWYRjaz4QfwyED8oiNiBIzArTCVQYmPjOe+9+7K96GhxvuTc+3vn nvs7555zL+9+f+Wrt0F/lluvSlBL6NHnGQHpoAxQA02MdA4UzhigChgvlUq6ppPt0TUhTkaE6jiY yMWvSsutDYhaqzywD0o0CeZBQc0q4k9RjrcCvCXhLNPKBQOpuVOJhRkNbXSWWuLjhHbxF/ggo9mb vHbrZz3ms+SW408ZWpgcmZ4ARlEFUUsL6XaSDZm0mTERxxW+PQ6mr/C3Cq77wND8iZE1GKnjARB+ DS/Av3UQakC0IgtrsFlz05rxyy7Dep3lTJTh/W4D3YAPLPTGXdWIigYXB5NHMuORdTWlWXhwwF7s D0h1kHUV2e+uNRZ1D/N33TlkIinABXcBBtwZ/iDKj64N9qWrmtuj+0IR0V1TRHRhr4jpfQudrbd7 /UwpshvKGot4h/myN4cWJAX4yFuAR7wZ/gDKD8oGW1XsXs/xU06jTvG/bl8n2awT+9ean+PZ+u1x iZrL/1Bze4X7GkWFD+y2ZyzoExlL+ETGLvpEnu72CwRN9oy1+4os6VtjH/uGueLPoQVJAfz+Anzu y/DzKEd8G+yQr7JOIVV4fVIVXj9Rha97AwI59tu9dqpFdkJdYyvqMN8VyKEFSQECgQJcVjP8Q5RB dYP1qJV1+m7vnavTof3/vU4G1xS75mjUuV7agjIXsSmJsUlttnlQe675senJ1JRV23KETouVjloo NKWAZPAe5/NVO+UtR7vb4qUmpKVPdunNr+w8nIbT/CenQMLf69Ivd2wd3d3ldVxiX7cYvIGS4GXb XsetWY9AlonsHAV7tGzb0d5jsdL3YHQ8NT6iiwbvsD21l3gn/4Zlse/B/nFeXklbi1K5kh3smhkr /hq+JSuV2b7tbnZbXKS5XrheiLrbpSPu8o5ZlhTLpgqlNxjsCHasSK9V98nvYSssH5K25FvZ1jfX NwUbfYfpG3k/F9/IY8cOcpkWFR0aSPTg2X5ibCo8MRFJzY6d6J9+RounRrVZ8Mr2zHslcy1euX/6 2fSYlqZB8DoGEs2x+bl0CuqhRu2KLUW7IvG84nk4GY7/0eQPx/ONnjDkY/mW/FIkiUjx9FO3FMu3 Jw/nl3RNH/YvHkYQbk9Gk7E8/cMeF8NMM44PppJh1iTQq+Fk+L44Sq+kQTxO6X6zjRo8zdzxSi/0 SrQhaPTVkNl3Y3IkkCShRbv6QJDDGQ3fz6SpOXkTaQqbl7tQ4QTLSx2dDzFvcaRyEEfLgVD3FDVP 60F1QMf/GhTy7zQoWNTQfJ9uhjMcmVVpBpURYx+Xb1h0D2NwVNfabibWvYHBTfcM66RWgXE2FH0U IKuPY1UDQwuzc9qksKu2zpmk2/0NxGhiTmQKAAA= where H4sIAAAAAAACC7t+9tgsBjBwY5BhSACztMMZGTgZGJiTGYEEgyhYjBWIuZlgLB4mGaB6FiCLhZEX TOsxSoBpJkZGsApOuFpGpv///wPNYWCQY+ACkmps/ED6P0gQDEDm/2b6AuVNYGSCMARCMnNTixX8 UssVgvJzE/NAdgGxLtBN7EBakZWRIZFBkIGRQQBNP8gRIFZwZW5Sfg4DE0QXI1j3ByTdtkDdXBi2 MxC0HWIOI9wcQ2BYicJ5RgxSQB4w9Bh+MbExwIxTYoC5AhQiIky8DCJgljCQJY3hAyasPmDC8EEB 0AdKZIQfxBwmqDlMDE7BggyaUFd8IhCOmK7QALpCFs7TBPLMoG76SXKoMiGFKheDFZynD+TZIYUx F4MjWlqCWAEyRZ3x/39mMA8AlMrM3dwCAAA= \* mergeformat, H4sIAAAAAAACC7t+9tgsBjDwZ5BhSACzlMIZGTgZGJhXMwIJBlGwGCsQczPBWDxMMkD1LEAWCyMv mNZjlADTTIyMYBWccLWMTP///weaw8Agx8AFJNXY+IH0f5AgGIDM/830BcqbwMgEYQiEZOamFiv4 pZYrBOXnJuaB7AJiXaCb2IG0IisjQxKDIAMjgwCafpAjQKzgytyk/BwGJoguRrDuD0i6bYG6uTBs ZyBoO8QcRrg5hsCwEoXzjBikgDxg6DH8YmJjgBmnxABzBShERJh4GUTALGEgSxrDB0xYfcCE4YMC oA8UyQg/iDlMcHOcgOZokBwSmO7RB5pjRAX3BAPNsYSGyicC8YrpCg2gblk4TxPIs4e66SfJscyE FMtcDM5IPuVicEeKcy4GT7S0DbECZIo64///zGAeAPiiV6hsAwAA \* mergeformat and where erf(z) is the error function:H4sIAAAAAAACC61UTUsDMRB9mW2rVYsLVlkRZPXgF1SlnlQEvYkHxS88eFCLWxBcK7Ug9uRP8OwP 8ubZfyEiXmoP6ySbXbFBuq0GsjOTvLy8zCT78vz0CNWqcHCqvLEjgSxg3RN/MKzG0tz7KfIGyGF8 ir2UyCk7LxxlSQiFyMZYQUEQMA8wjj7+TmUG2QZyUDXJ36QPHT2I0MI+uPC9G3fbu3X3Kv7ZldyL e4Hne9lOpC141TJsCPSoWGCGI9vgozZ8Qtk35o146syS70JXyPOtZ5Z5RrkbPErS/p1fqlyCflOx xivdf1BRZJ65OFrgaMnQRAk1XfPKDXk38EkZRGIm471lvfOUw7LyhthbidHUgqYYvarRNp/55yki jJwJMWms67HIk2ObHVedjDx5fLZDnZlGwmpRvLrAd/pYq2j8QUWNeU40TzNx1U09RfZKhh50rGcR I9jp+Fymnjoy2NXZfW2TXVPFO7/Hra5fdqSCcF6zUW75C4VJkchpEQSWir4A/hv8wRYFAAA= \* mergeformatUnfortunately, no analytical solution for the k-distribution which is the inverse of g(k) exists and so this must be found by iteration.As mentioned earlier, once g-intervals have been defined, the mean absorption coefficient is most easily determined as the arithmetic mean. However when this is done the resultant mean transmission is not exactly that of the equivalent band model but depends on the number and width of the g-intervals. However the mean transmission can be forced to be exactly the same as the equivalent band model if we use the cumulative transmission function h(k) which is dependent on the particular path being calculated: H4sIAAAAAAACC7t+9tgsBjDoZpBgSACzHoUzMnAyMDB/ZmJgYGIQBYuxAjE3E4zFwyQBVM8CZLEw 8oJpPUYJMM3EyAhWwQlXy8j0//9/BmYgS46BC0iqsfED6f8gQTAAmf+b6QuUN4GRCcIQCMnMTS1W 8EstVwjKz03MA9kFxLqMDAzsQFqRlZEhg0GAgRFDPwMB/Yxg+gOSORpAc9jJcAfEHEa4OdlAc3io 4B5NoDlCQIxhDthJwZW5Sfk5DEy4XGEL1ClJsm8wXZEGNEePZN9gugcUusZE+gbdFUwMixQEGOwo jhsmhmygORZUihtHBg4wj5khtaIAyHdH8WsE2TGnC9QZg+LzLIrjEeLzFLgduUA7cqgQq6BwKKVC KksBmlNFZohBwqiNSmHUADXnJwWhYsAgxqCOYQ7poZLNwAYOYZA570hOR58YRBiU0cpaiGdAKtUZ //9nBvMA5ULJIPwFAAA= \* mergeformatFor the Malkmus-Lorentz distribution, this function exists in a closed form:H4sIAAAAAAACC7VWb0xbVRQ/976WQmnX9/ijsCzQ1pYwmkIgMzGLLCvQuA+yNNJpohis+DYQSllB gbgAk4o6Z1CncxoTP2xZ9mlGsxjnyEJiMj8YNSYkxk+QmJAsmPgnTUgFV895r/cVXucGCbY99/3e uef+zjn3nAv35+9vfQzaZ7pxWYISQidHGAFJKgIohnZGOgsKZwys+GQ8m81qmkZWrWmaORkRKuWQ Qw6+LE03liOqK3LBPsjSIhgHGTULiL9COdwIcEHCVTkrB3TGRvuiE8Mq2mgsJcTHCVXwU9zHaPU6 L7nzqxbzO+SW41fumog/nxgERlEFUUuJtNjJhkzqczERx0W+PQ6mZfhHAdd+0DV/Y2Tl+tZxLwi/ uhfgVyyEyhGdtQprMFnznDXjHzh061U2n0MpXu3U0e8wZaC+PTZEGzoXhxyPlIvHqqlpm4UHC+zF p08qhfccG+xbxxLb6+zm484VZCLJwKwzAw85U1xG+cKxxi44bNwc3euyiO6qLKIrVURMJw30dJnZ a0reYNflJeZQuvmLygpakGRgXMlApZLiHOWSvMbOyGavl/khu16nyD/3rpM1Vyf2nzW/zGfLtscl am69S823VriWKRV63rXspwrRW7bK7fXW/WM+xRcf2Fmf3i1m0Y2fVYluPFdtru4nblHdb9yium6P qOmsgRJec3U/cm+wH9xLzOPp5lOeFbQgycDbngw0eFL8QZTr7jX2qbuwp973Ca83fMJrlV/4mjTQ iTqz13d9G+yWb4lV+7v5mH8FLUgy8Jo/A15/irtQPvetsQ99hT0Vrtm9njpXt/s9td4geupGQPTB n4Hd66mbwd3qqSH2taVS45q+A3kuYpOj/XF1xH1UHXM/kYjHhow88xHaDVb6U9bcbKsASed9jh8t 2ilvPtoqg5f+ozSryeNN2tAEv7ErMAmTfGyPQA/bhc+z0sKu5dLSks/lGgvs13m9WcHLtp3L1p1v g3kmduggmKNl2462xmB1ofQNxAZ6B6JxGtVoHN5k1SXX+AF+k3XwZdaK+CDiJ/l3+JbP6q16uTCr HXTRsJFLMV+0yoU7f8/udhpcpLmduZ15xPlj0SFnvoNelmTDBq8w0BoMBoKBL6Uztl+KL+EoLB+V Fq1b2VbXV9cFG9176E7yChd3kmPHEtxKSXV0dUYP4Dl9qn8oNDjYFhvp721PvKBGYifUEVCs5ioo Ui4XxdqeeCnZryZpEhRLZ9QdHh9NxqAMij1N4bmOprZIWnY91hOK/FVbE4qkK10hSIfT/vRcWw8i 2dVOj7lwuqHnSHpO0xzG59QRBKGGno6ecJp+IZeD4U4zjh/cSoa7JoFWDTvD95k+eiUN4gHa7vP1 NODp5pbZVmiV6PjQ7BvNuWcLbo6EN0KhRbsyb5DDaRXfTydpOL6JNIbDq02osIPhpZTOilg301s4 ibP5QOjxDA3P0r1zJoqFVDY5iJujDkDgf40a+XcaNcyoaL5PM8MVltSCNIzKNtDWoKP75gWbb8Z0 f2bwuKY13SiN+x6DTfdD4/QXgX7GZG0WYF6bx+7wdk2MjKpxYWczzquk2f0L3dqFhhwMAAA= where \* mergeformat, H4sIAAAAAAACC7t+9tgsBjDIZJBhSACzWMIZGTgZGJiFmIAEgyhYjBWIuZlgLB4mGaB6FpBaRl4w rccoAaaZGBnBKjjhahmZ/v//DzSHgUGOgQtIqrHxA+n/IEEwAJn/m+kLlDeBkQnCEAjJzE0tVvBL LVcIys9NzAPZBcS6jAwM7EBakZWRIZlBkIGRQQBNP8gRIFZwZW5Sfg4DE0QXI1j3ByTdtkDdXBi2 MxC0HWIOI9wcQ2BYicB5RgxSQB4w9Bh+MbExwIxTYoC5AhQiIky8DMJgljCQJYXhAyasPmDC8EEB 0AeKZIQfxBwmuDlOQHM0SA4JTPfoA80xpIJ7goHmWBAZr5iu0AbqdiQ7XhGuMAGa40WybzDdkws0 JxDqm08EfIPpCg2gbhk4TxPIi4K66ScFMWUITPmxSPHGxZCIlIK5GFLQcirECpAp6oz//zODeQB2 H9oNOgQAAA== \* mergeformat and where H4sIAAAAAAACC62QvQ4BQRSFz73rby1WgtCQpfBT8CgKkWiJbKFYCoXXUHsgndo7qBQqinH3Dlto RGKS2XNmcs83J3s+HQ/Q1YSPubrljOACzkW8g5repWV7/HYF9mU+JS5FRdURNVSZSCfcZJbYGCMc oIW8fLsZX9TEl7rkJdw5A7JHdJQzJJuuMkk2dhVxOW3z4Nsruye2pjxdReE2GIe7YLKJFuu4mVII WdF2mjENPHnjM48veVa9JhxCH570/72H5XDCiYRT+kOfgXDqH3/WYuLJHhnj6OkJq9NAN+oBAAA= \* mergeformat is Malkmus-Lorentz transmission function. Once the limits of k are found for each interval of g, the mean absorption coefficients are defined as transmission weighted averages:H4sIAAAAAAACC62Wy0rDQBSG/5m2SrTaSrUGlBLFSyq9UVEREd0o6EJFC67EC0aoaezChfgWrn0g d659CxHppnYRTyZprGZhQyYlmZNkzj/fzPmH9O315RniaKCKCxGVTxkUIHYepwsmxLMEncO8GyV5 lfrTa8TZiGhLTBUtZ0z0UPy+jNu2TTpADkN0XRhIUWs7D8Xh6Hd4y7t7YtwN0rW6ZdxrB8aDdty0 Lu+csegsMmCQ2pkEg4FpMKRFftvPdyCc6OTRumo2wN0sJrI/erKLyFJM88QXHwBz0zHrj+Kwj/M0 kiLKUDTqsbb7ZuXeqMwblcPUsqTo6nT61unSc5++DhWpyDwMFq3CmLeGrT7X8IdikyowFbqCQYob mstqQAehV0UnnQ0JPCbpbEvgyZPOrgQeg3T2Qzqd9zhdwZEM71oKaqFn85eH49pM4UyCd03SWJKy lyZpjWTwJFCQwHNLUcWr9vs/1Q5SfCKD+chVcvakjq3QeyDIo9NvRwKPSTp7EnjypHMoxcW6vxui uaaEZSkurmBNCk8OK1JcrGE9gosLKHvfYBVz3jdYpVn+/g/hGsDJXmS2HRN33wwYlv3UCAAA \* mergeformatorH4sIAAAAAAACC61UPUsDQRB9M5ecRD3MkYgfiJwKfoAfpLPRKpWFQhQCVioEDeaSwiL4L6z9QXbW /o0UNmqxzs5drrgr9JJb2J03e/tm37yF+3h/e4WOG6zJtMNrEyqAc8GyYFH3yjLneIzm2Z4tCSqR p/GQljUykZ6oJGeJjTFSB1jHrKzb7oJEYzd1yE34ZhcUpdjUOgcUsevyxVFUEzSjan74M+a+EEeg etUNO0/BeWcYtAbhbd8q0yokHGCjzHgMfLkj4n/9m88aR0kdQhd1uKimdNjWLbp8Du8GPfD49ojN CfsEPrxMF8itoiG+rUzgRlpPiFUsxU57MaoJCqbWyOj1fWxN7FRTnGrk7jDr1L3UOc797lk99t1P C3i5I9HTnMqVswJceZA6rYJcacfdjP7oJqtiV1TsJ9meZNepf0RksOXtkDGOZr/ijha9tAQAAA== \* mergeformatSince the mean absorption coefficients defined here are weighted averages for a specified absorber amount, the resulting histogram of absorption coefficients is necessarily absorber dependent. Because of this, the transmission computed by\* mergeformatremains equal to the Malkmus-Lorentz transmission regardless of the number of g-intervals used. This removes any errors in the calculation due to fitting k-distributions to band models. However the number and width of the g-intervals obviously affects the accuracy of any multiple scattering calculations. In practice it is best to use g-intervals which are unequal in width but which provide approximately equal ratios in absorption coefficient strength. In the case of multiple scattering and vertical inhomogeneity then for a given number of intervals, optimum accuracy is obtained when the g-intervals are more closely spaced near g = 0 and the strong absorption end near g = 1.The additional parameter PAR1 here defines further details of how the Malkmus-Lorentz correlated-k model is to be calculated:PAR1=1 a) The mean absorption of each sub-interval is the simple arithmetic mean of the absorption coefficient in the interval.b) Overlapping gases in the intervals are combined using the weak and strong limits.This second part may be explained as follows. To determine the B and S Malkmus-Lorentz parameters of the interval when there is more than one active gas, the B and S parameters for each gas are combined in a manner which is consistent with the band model assumption of uncorrelated randomly overlapping absorption lines. Consider, for example, two overlapping gases that are characterised by band model parameters Ba, Sa and absorber amount ua, and Bb, Sb, and ub respectively. The statistical parameter definitions of these parameters in the weak and strong limits imply:H4sIAAAAAAACC7t+9tgsBjBIYeBnSACzpMIZGTgZGJh5mRgYmBhEwWKsQMzNBGPxMPED1bMAWSyM vGBaj1ECTDMxMoJVcMLVMjL9//+fgRnIkmPgApJqbPxA+j9IEAxA5v9m+gLlTWBkgjAEQjJzU4sV /FLLFYLycxPzQHYBsS4jAwM7kFZkZWQIBprDyCCAph/kCBAruDI3KT+HgQmiixGs+wOSblugbm4y bIeYw4jiChGoOT+JNgfTPYkMvAxSVHBPKdA9clRyjwqGexhIdo8+0D3aJPsL0z0gfxkSGduYrtAG 6rai2BVMDMGlXAzOJIcupnuSgKHrT3LoYoYKKHTDqJRqYtHyJ8Q5IJXqjP//M4N5AA/ah/cwBAAA \* mergeformatandH4sIAAAAAAACC7t+9tgsBjDYxyDMkABm3QlnZOBkYGB+y8zAwMQgChZjBWJuJhiLh0kYqJ4FyGJh 5AXTeowSYJqJkRGsghOulpHp////DECjGOQYuICkGhs/kP4PEgQDkPm/mb5AeRMYmSAMgZDM3NRi Bb/UcoWg/NzEPJBdQKzLyMDADqQVWZkYnIJ5GdgYBMD6P8H1gxwBYgVX5ibl5zAwQXQxgnV/gOtm ZNBg4GVghPM0gTwRqFt+IptFwC0QUxHmGAJdJA7n6QN50nCeEZAnB3XvF5Ldawt0oRoZoYXuQieg OSYYPiVkDqZ7EoE+saKCe4KB7rGnkntcqOCeUqB7PKjkHj8M95CeovSB7gkl2V+Y7gH5Kxqa+j4Q SH2YrgDlFn2U3JJEcm7BdJMhsIRIRfIpK0MmUm5hZcghMrdgulcb6MJiKoQaKLc0kpwaMN2TBPRJ OxXcA8otPVRyz0QqpaqpVHLPbJJzC6Z7QLllEZVKgRVE5hbsdUsNSm5ZT5W6hZVhE0pu2YaSW3ai 1a8QK0CmqDP+/88M5gEAH08ah/AHAAA= \* mergeformatPAR1=2 a) The mean absorption of each sub-interval is the absorber amount weighted mean using the cumulative transmission function.b) Overlapping gases in the intervals are combined using the weak and strong limits.PAR1=3 a) The mean absorption of each sub-interval is the absorber amount weighted mean using the cumulative transmission function.b) Overlapping gases in the intervals are combined by summing the optical depths.Combining the band parameters statistically is reasonable if the absorption of the overlapping gases is comparable with similar degree of saturation. However in the extreme situation where one is strongly absorbing and the other is weakly absorbing, the square root dependence of the product SB can lead to greatly overestimated values of B. In these situations it is better to add the effective Malkmus-Lorentz optical depths of the two gases calculated with:H4sIAAAAAAACC7t+9tgsBjCYwSDDkABmfQ1nZOBkYGDOZQYSDKJgMVYg5maCsXiYZIDqWYAsFkZe MK3HKAGmmRgZwSo44WoZmf7//w80h4FBjoELSKqx8QPp/yBBMBAA4t9MX6C8CYxAjWC9wZW5Sfk5 DEwgU3UZGRjYgbQiKyNDCYMgAyPYVb+ZfiLrAhsWkpmbWqzgl1quEJSfm5gHciFYPyOY/oBkTiaD CJCNbjsDDtshuhnhum2BruAl0u2YdhcAw1cC6ocvRPsB0xVOQHPkqRIWPAxqGO5hINk9RgxSDLKg tMPwi4mNAWaAEtxeUHoQYeJlEAezhIEsDbheQ2CIGhEZH0wYPtAG6rYk2wdMcHNMgOY4kxwzmO4J BprjSXLMYLoHlEr9qeCeUqB7AqnknnCSwxnTPfpA98QSnffRXVEA1J1MhVBxApqTRaVQKYD65gPJ aVcD6Ao9OE8TyCvBcBPpKdkQmA/LkcKbk6EaKZ9yMtSRndd0gS5spUJeA+X4XqgrXpDsimhgmGvB ebFA3mS0+gXiJJA+dcb//5nBPAAjbFtM8AYAAA== \* mergeformatand then use the equation:H4sIAAAAAAACC5VTPUsDQRB9M0lOYqIJnJ+gIQbRpDhBGwsRxMZCUDABWxVSBDwjaBD/hXV+kJ21 /0JEbKLFOrt3WeQ2kLuF3X2zzHvz9mbv/e11CDM6qOHKoINLQhHIfZAsWDRnBZklHqMy1yQ/LyhP c2bfoRWzM5HJKNpcYqWU6ED0Z2Xd8iqyK31ohtb/5e84eiGOQLXTC7sP9bPuU/2iH17f6VoyA/E0 I/tGgXAMH4xqgq9NaNR+Dm/6t+CIRYb9+Y99KOyyw+aJbMRssuxHlLAcex+l9u666GEe644Opn6D pJ89eKKT7jaui3usYVX3HD/sYVy+YavpPi5wBUsG+YIamfvGCc+M9sBHK2P/2HoOpH/7KW/ME/rn 4yhmf2Wu3RT2po1aEp3EWqMpWq6TQF7haeYX4HraFZ3zxB8WyejMbVIqZ6I/2d5Nb/IDAAA= \* mergeformatto determine B. The S parameters, which add linearly, are not adversely affected by the absorber mismatch.In all three cases, the integral over g is performed by the simple sum solution. 5.3.3 Goody-Voigt Band Correlated-K(ICONV=22)For calculations in the Jovian atmosphere, the spectral properties of methane are important. Unfortunately the line data for CH4 is not very reliable in the near-IR (although is improving steadily) and so band models are often used where the band parameters are fitted to laboratory measurements of methane spectra. [R4] found that the best fit to the laboratory measurements was the Goody-Voigt band and to use this data in a scattering model of Jupiter's atmosphere requires a Goody-Voigt correlated-k model. Unfortunately, k(g) cannot be determined analytically from the Goody-Voigt parameters but must be determined from a numerical Laplace transform of the transmission spectrum. This may be done in one of two ways:PAR1 = 0, k(g) is the mean absorption coefficient over the intervalPAR1 = 1,k(g) is weighted by the cumulative transmission function to get close agreement between correlated-k and band calculations5.3.4 Exponential Sum Model(ICONV=23)Not been updated fro some time – use with caution! Performs least squares fit to the transmission functions calculated with band models to derive the exponential sum k-coefficients directly. This is usually better done off-line with the program, Band_ktable and the k-tables then used with the ICONV=24 model below. There are two models depending on PAR1:PAR1 = 0,k(g) calculated from Malkmus-Lorentz transmission curvePAR1 = 1,k(g) calculated from Goody-Voigt transmission curveModel only still exists for historical completeness. Recommend using ICONS=24 instead.5.3.5 k-Distribution Look-up Table(ICONV=24)Identical to ICONV=20, except the k-coefficients are calculated for each gas BEFOREHAND over a representative grid of pressures and temperatures using either Calc_ntable for line data, or Band_ktable for band data. Overlapping gases are combined as per [R8]. Look-up tables calculated with Calc_ntable and Band_ktable may be inspected using the program Read_table.5.4 Running RadtransTo run the program Radtrans, the atmospheric information in the ‘.prf’ profile files and spectral details must be combined into a driver file (.drv) using the program Path as previously described in Section 4. If the driver file has the name ‘surf.drv’ then Radtrans is invoked (in background) using the line:Radtrans < surf.nam > surf.prc &The binary output spectra are sent to the file surf.out while any processing information is sent to surf.prc. In addition a log file is written, called in this case surf.log which contains a full listing of the run details for reference. An overview of the processing software was shown earlier in Fig. 1.1:If one of the correlated-k models has been selected then there must also exist a ‘.gin’ file which contains the desired g-ordinates and weights for a Gauss-Legendre integration. This file has the same name as the driver. A typical ‘.gin’ file has the following format:10 1.3046736E-023.3335671E-02 6.7468315E-027.4725673E-02 0.1602952 0.1095432 0.2833023 0.1346334 0.4255628 0.1477621 0.5744371 0.1477621 0.7166977 0.1346334 0.8397048 0.1095432 0.9325317 7.4725673E-02 0.98695333.3335671E-02where the first integer is NG, the number of g-ordinates and the subsequent columns contain the g-ordinates and weights respectively.Finally if a scattering path is defined, then a ‘.sca’ file must also be present whose format is described in Section 8.5.2.6. Post Processing of Radtrans Output SpectraThree main programs are available for processing the binary output data of Radtrans:Conv_specLi_spec Pl_specIn addition, the programs Aground and Diskav may also be used to produce more specific output (described below).6.1 Conv_specThe program Conv_spec convolves the output spectra with user specified instrument functions . The program is very similar to Conv described in [R10] but slightly more general and manipulable. The output from Radtrans are binary spectra with interval DELV cm-1 where the calculated quantities are either averages over a square bin of width FWHM centred the output wavenumber, or for ICONV=0, pure monochromatic spectra. For example, if ICONV 0, if VMIN = 2000 cm-1, DELV = 5 cm-1 and FWHM = 5 cm-1 then the first output at 2000 cm-1 will be the average from 1997.5 to 2002.5cm-1. Conv_spec, takes these spectra and applies one of the following functions:1Square bin convolution2Triangular bin convolution3Multiplication by a Filter profile followed by square bin convolution4Sinc function convolutionThe convolutions shapes are of user-specified widths and may be applied in either wavelength or wavenumber space. Conv_spec limits the convolution to wavenumbers where the convolution shape is within the originally defined interval so output ‘.ave’ spectra always contain less points than the original .out spectra. The centres of these convolution shapes is at the same wavenumbers as the output spectra and Conv_spec determines the average of the convolution shape over each bin and calculates the weighted mean. If the convolution shape covers half a bin, then an appropriate fraction of the bin is added. This of course assumes that the absorption is evenly spread over the bin which may or may not be a good idea. In general it is better not to use fractions of bins so if you want to calculate an output spectra with triangular convolution of FWHM=10cm-1, for example, set DELV = 6.666 and FWHM = 6.666 cm-1 .A typical input sequence is shown below: driving file name? :testc1 enter FWHM, wavespace [0=wavenumber, 1=microns]:10,0 Enter ICONV [1=square, 2=triangle, 3=filter, 4=sinc ] :26.2 Li_specThe program Li_spec reads in either a direct output or convolved spectrum and writes the data to the screen or an ASCII file. The user is guided interactively through its operation.6.3 Pl_specThe program Pl_spec again reads in either a direct output or convolved spectrum and outpots spectra to a an ASCII file suitable for display by the IDL routine plot_radtran.pro. After the spectrum has been read in, the program gives the user the following options:A - display calculationsB - display pathsC - display layersD - plot a spectrum for a pathE - plot results of a calculationQ - quitTo illustrate the effects of the above options, consider the spectrum generated using the following driver file: original name of this file: testc1.drv 1900.000 5.00000 21 5.000 :Vmin dV Npoints FWHM (BAND) 0.000 2.000 : Additional codes PAR1 and PAR2 5jupiter5 12 0 : type of convolution/model & NCONT 1 1 1 : number of layers, paths and gases 6 : identifier for gas 1 1 0 : isotope ID and process parameterformat of layer data layer baseH delH baseP baseT totam pressure temp doppler absorber amounts and partial pressures continuum points if any 1 0.000 0.000 0.00000E+00 0.000 0.36717E+25 0.10000E+01 296.000 0.0000 0.36717E+25 0.10000E+01 1 0 0.10000E-01 : Nlayers, model & error limit, path 1 1 1 0.000 0.10000E+01 : layer or path, emision temp, scale 1 : number of filter profile points 0.00000E+00 0.000 : filter profile point 1 testc1.out 1 :number of calculations 128 2 0 0 :type and # of parameters for calc 1 1 1A - display calculationsThis option simply outputs to the screen the number of different calculations being done and the number and value of the parameters defining it. The output in this case is: there are 1 calculations -------------------------------------------------- Calculation : 1 Cell calculation Single cell calculations Number of cells = 1Path: 1 Layer: 1 --------------------------------------------------From the driver file, the first calculation has ITYP=128 which corresponds to a single cell transmission.B - display pathsThis option summarises the paths for which spectra have been calculated. The output in this case is: path: 1 model type: 0, 1layers included 1 ---------------------------------------------------Thus this driver contains just one path which is a cell path for which the transmission is calculated (IMOD = 0) and comprises just one layer, LAYER=1.C - display layersThis options summarises the layers used in the spectral calculations and the number of gases used. The output in this case is: there are 1 gases gas: 1 identifier: 6 isotope id: 1 -------------------------------------------------- layer: 1 pressure: 0.10000E+01bars temp: 296.00K gas amounts 0.36717E+25 --------------------------------------------------D - plot a spectrum for a pathThis option plots the calculated spectra for any of the paths. The option has an interactive input to define which path spectrum to output and in what form. A sample session for the ‘.drv’ file above is shown below. absorbtion plot? [1-output] :y Plot against wavenumber (1) or microns (2) :1 log plot? [Y/N] :n 1945.000 1900.000 wavenumber ( x ) limits are: 1900.000 2000.000 y limits are: 0.00000E+00 0.88040E+00 force plotting axes? [y/n] :nDifferent options appear for different spectral calculations, e.g. brightness temperatures may be plotted for radiance calculations. E - plot results of a calculationThis option plots the results of calculations defined by the ITYPE integers. In most cases, the calculation output is simply one of the calculated path spectra. However, this option also plots the PMR transmissions/emissions and weighting functions. This is the option which should be most commonly used. An example input session is shown below.there are 1 calculations plot which one? :1 ------------------------------------------ Cell calculation Single cell calculations Number of cells = 1 Path: 1 Layer: 1 ------------------------------------------ Cell calculation Single cell transmission There are 1 paths : 1 Enter desired path :1 absorbtion plot? [1-output] :y Plot against wavenumber (1) or microns (2) :1 log plot? [Y/N] :n 1945.000 1900.000 wavenumber ( x ) limits are: 1900.000 2000.000 y limits are: 0.00000E+00 0.88040E+00 force plotting axes? [y/n] :nAs can be seen, the option first prints the details of the calculation in the same way as for option A.A typical input sequence if the calculation is for reflecting layers is:there are 5 calculations plot which one? :5 ------------------------------------------ Reflecting Layer Calculation Pure atmospheric pathsNumber of atmosphere calculations = 1Number of reflected atmosphere calcs = 3 Atmospheric calculations are: 4 Reflection Atmosphere calculations are: 1 2 3 ------------------------------------------ Cell calculation Reflecting layers calculation Pure atmosphere pathsNumber of atmosphere calculations = 1Number of reflected atmosphere calcs = 3 Atmospheric calculations are: 4 Reflection Atmosphere calculations are: 1 2 3 Enter required number of reflecting calcs :3 Enter reflecting atmosphere calc :1 Enter albedo of layer :0.9 Enter reflecting atmosphere calc :2 Enter albedo of layer :0.5 Enter reflecting atmosphere calc :3 Enter albedo of layer :0.1 Enter required number of atmospheric calcs :1 Enter atmosphere calc :4 Enter distance from sun (AU) :5 Enter surface temperature of Sun (K) :6000 plot brightness temperature? :y Plot against wavenumber (1) or microns (2) :1 log plot? [Y/N] :n 1998.850 1700.000 wavenumber ( x ) limits are: 1700.000 2299.850 y limits are: 0.00000E+00 0.26876E+03 force plotting axes? [y/n] :nThe reflecting atmosphere calculations correspond to reflatm in the path file and the atmosphere calculations correspond to atm. The calculated radiance spectra in this case are determined as:H4sIAAAAAAACC7t+9tgsBjBYw6DAkABm/Q1nZOBkYGDWZmFgYGIQBYuxAjE3E4zFw6QAVA+UZmBh 5AXTeowSYJqJkRGsghOulpHp////DMxAlhwDF5BUY+MH0v9BgmAAMv830xcobwIjE4QhEJKZm1qs 4JdarhCUn5uYB7ILiHUZGRjYgbQiKyNDEIMw1H3I+hkI6GcE0x+QzNEAmsMJ5TExzFAQZBAAQgxX gR0WXJmblJ/DwARzC8QsRrjuUgVhBj4quEkT6CYxDFcwEOUKRgZboG4ZkkMW0xWgEFaHmvOThBhC d08i0C+6VIopI5SYsqQopsypFFN2ZMeUNlC3K5F+wLS7BKg7hgrxkwmMnyQknhyDP9RNPwn4CNNN tkDdQRhuYiDZTYZAc8JI9hume/wY2IDugfjmHcnx8xToAj8qpdxUlJSbQ1HKzaJSyi0io/xFDyNH oDnlVIgpUCqspYJ7PIHuaSA5BWK6xwDonhaSwxnTPaC470SJ+wlk5nhI3PdRwU2guJ8G5+kDeXPI LoUKgLoXo9XtECeBVKoz/v/PDOYBAK5aGElsCAAA \* mergeformatwhere:Ra is the calculated thermal radiance from the atmosphere alone.ti is the transmission from the sun to the ith reflecting layer and back to the instrument.A is the albedo of the reflection layerI0 is the incident solar flux:H4sIAAAAAAACC61UyUoDQRB9VVkkJiFRIxHB0CpoBDdEvIgIIogIHkxAFA9GSEBwjAsi/oVH8YO8 iUf/QDx6EHE5jNU9SRMzQhamobuqeqpev6qerufHh3uYcQGFQ6ON7xJiQOiJZcGg2YvIjHNdS7AS /7BoYUoaOUtDRjKR8YhZX2LXdQUHyKFX1oloSqSrN83Q+D/8XrNuiT0lXTx2ypdqu3ytdqpO6VSf JXOGgB6RoxHCJjLgWvyXjUeLeDLyrQFnHllEfTzQkoeHQxYnL3ziNYtxp/rRh7Q/O5Ng4cY5qp6A /+fEuFIZpALgNCWcsj4WaIsFYUWic13cUDOLNcHJd5yNn4+u8NyfCi+1WeFmTl6FFwPgNC2clgOo UVFwVgPgo298o8uqEM4kesta50hgP5AXlkIpgBqtYwQHujfhm6OoExmz5+p+k+E09ow2IFq5zX+f fS/wRSVRsNarGm6wPlQKFWt9yrdKx1WqZ8c2uwXpQk5Tj/RgtOckuW7IWL/e5cmntAUAAA== \* mergeformatwhere 0 is the angular radius of the sun at 1 A.U. and D is the distance from the sun in A.U.6.4 AgroundAdds ground emission spectrum multiplied by an atmospheric transmission spectrum to an atmospheric emission spectrum. Assumes .out file contains both the atmospheric thermal emission and the transmission spectrum to the ground and combines them appropriately given the surface temperature. This program basically does the same job as the old Addground program without the use of intermediate ASCII files.6.5 DiskavProgram for numerically simulating disk-averaged spectra. The Radtrans ‘.out’ file is assumed to contain thermal emission spectra calculated at a number of emission angles from a .pat file written by Write_diskpat. A Guassian Quadrature over emission angle is assumed with the angles and weights defined by getquad.f. Diskav simply combines the output spectra (which may also include ground radiances) using the weights specified by getquad.f to generate disk-averaged spectra. This program has been somewhat superseded by the introduction of the analytical exponential-integral method of achieving the same result.7 Setting up Spectral Data7.1 Line dataA number of programs are available for setting up and manipulating direct access line data bases. An overview of the software is shown in Fig.7.1.H4sIAAAAAAACC8VVzWtcVRT/nTcfbToTtdZU40d9Lf1CMGJCK1aysAnVwqSNhrbCNE3fvLmJj5lM 7MwkbUQpzSyyEGkWglqNUlACgmBXFgO6ESGL7grtpgu1f4CIq9gynnvuey95kwmmCeILJ+f+7j33 /H73zP24deOXK5Bvjo7SWWl9eYrQAsS+SgBJHJA+biJlpZGSVto6SnMU51acWqF9Bz0h3iKSiBYr mEVWvV5HjFs7sIn/37PIEEr88wyYC4tWEkH/Ln+EJP6peA1dlMGveITR39afdRM1E4Tbr6mSmnCC fBa2sd+ZeBIZr6TyTtWx3xwbr3K7Yh+fUOUJT51fxDS2cNTe5MPs61qgfIbhr39hiIn/g5lahCmJ Pqeg8rlh1HzFBVzHW7jQwGHSbZE5m1ndUFGLaodLQV9/0fQdgOP3bcLA+OioU55EP4bIZH8Wn1Ea WR+9wmh/iE4y6mHUbHWB2gFVVG71Kob9OXM856MVc5bUNuYJ1Pa8Y9T+iLN+pp8507UHyJSWTCn0 vK3cwpBXyqsLKGDQz3YO39KZB8i2WbLFMeA6pWkU/SwfsqZ3V8liZsRQUJPoxl20Cm6FU3E9z857 Za6TjdM8YpSm4biuqlRs2VZF7g84c05FvcfY1DgBs5aP8bu/I3pxHy/yHjboCyTpA0b6bB0mfUr2 +2q0EZbUPZoytvzTC/6G/Qm21TxHXVz+F5yNgP83VnO7aRVTsoIWvwZjZRt9aEewG1XOzXuujUHu C369ijo3rkpVzynaGOX+IIPeHFIpvM+9wWkPzo5RMsXVPYzt/1slpvA486ew1j1mbjBEbrB45D5Y tBKhtl3hnfQQ+92xBM7DgQfFpv2g4OC20/MesxxkpbXN0hFr1dXIc4vzLjDPgvhBwY0810OehaY8 Jq4NPWTi5rm1Fu4staGP2tm03yo4yr2UU0esd42naR7H6Cc27b8XHOWZR2+o/di6ebI0yyqvsmn/ qeAoz2y4ntkNrCdLNZ49zab9RcFRnlrIU9tQ3Ua4GgU27V3BUZ4RfnENz8iG6pZhlf1s2r8uOMqT CdeT2dB6OlnlQTbtOwRHeTrDfdC5ynp0rj2c6wr9gK/FbvKLoO3SsrHP8Z3YHXRB29Sa9HVxjpdw mf1lvCD+UoO+T7jP6NOj661DN+t5FTPsZ/Cy+KkVPN0+jx5txtMmd/cOlDpyHXZ/eWyk7IxWbKfM F7kqjVVV3s5NHrL30htyE+5MEGwcZLRdkA1bvl79PA57RbVi6hGODV4CcwM/R4foaXqm6c3yX74K YfSyVyHhazpBe6iLNUXfrKXRIzy6u+k+0pH7qF6PCfoHH5p1Nl4LAAA= Fig. 7.1. Overview of Linedata Manipulation Software7.1.1 MakedbThis is the central program of the system and transcribes sequential-access line data bases (eg HITRAN or GEISA) from files as copied from tape into direct access files containing one transition per record. The records are in FORTRAN character format as in the original data base and conversion to ASCII from EBCDIC is allowed. An index file is also produced consisting of one record corresponding to each record (transition) in the data base. This record contains a pointer to the data base record holding the next transition for this species (of any isotope). The program also produces a key file summarising the following information:the name of the data base filethe name of the index filethe name of the file describing the gases known to the Radtrans softwarethe name of the file containing the translation between isotope identifiers in the data base used and those used by RadtranThus only this key file has to be specified to identify the data base. Since HITRAN and GEISA use slightly different gas identifiers, Makedb and all the subsequent Radtrans software uses its own identification system, based on HITRAN so that both data formats can be transcribed. The gas identification system used is shown in Appendix A. The local gas identifier agrees with HITRAN IDs as far as possible (Jan 1988) with extra IDs for gases not in the HITRAN compilation e.g. those in the GEISA compilation. Isotope identifiers also agree as far as possible with HITRAN identifiers. Similar (1,2,3...n) identifiers have been defined for additional gases. Makedb also converts the sequential files output by Select and Cp_lines into direct access data bases.7.1.2 ScanThis program opens a line data base specified by an input key file name and lists the line data records directly to screen. The program prompts for a starting wavenumber and then lists all transitions from that point in the storage format until told to abort.7.1.3 Check_indexCheck_index opens a line data base specified by an input key file name and lists the index file records directly to screen. The program prompts for a starting wavenumber and then lists all transitions from that point in the storage format until told to abort.7.1.4 Li_linesThis program opens a line data base specified by an input key file name and lists selected line data directly to screen. The line data is read in by the subroutine lines.f which in turn reads in line data records with the subroutine rdline.f. To avoid numerical underflow when passing line strengths between these subroutines, the strengths are multiplied by the factor 1047 in rdline.f. Before listing the strengths therefore, Li_lines multiplies the returned strengths by 10-47 so that the strengths are listed in units of cm-1/(molecule cm-2) as defined in the line data bases (see section 2.1). The program prompts for the required gases and the wavenumber range and then lists main line data parameters for these gases.7.1.5 Pl_linesPl_lines plots out line details for a particular spectral region ASCII format, suitable for display using the IDL routine pl_alines.pro. The program prompts for line data key, gas identifiers, wavelength range and plotting details and then plots out line strengths versus wavenumber. The same scaling and de-scaling of the line strengths by the factor 1047 is applied as in Li_lines.7.1.6 SelectThis a line data manipulation/editing program which opens a line data base created by Makedb (e.g. HITRAN or GEISA) specified by an input key file name and copies a specified subset of the line data base to a new sequential ASCII file. This file may then be modified and perhaps merged with new spectral lines before being turned back into a new direct access data base using Makedb. All lines or only selected lines between given wavenumber limits are copied. Selection can be performed by gas ID, isotope, and line strength limit. The strength limit for a particular gas or isotope is set so that the sum of strengths of omitted lines is less than n% of the total sum of strengths. This criteria is calculated by finding the number of lines in each decade of strength. Note that the strength limit can be set independently for each isotope or can be set for all of the isotopes to be included. In the latter case terrestrial isotopic abundances are assumed, i.e the strengths are used uncorrected. The logic behind this is that if the isotopic abundance may vary you want to treat them independently anyway. The line data may also be modified to have, for example, different line widths for comparison with other programs or to check details of the line data itself.Example input sequence:Enter wavenumber limits :1400,1450Enter bin size :10Enter error limit [%] :0Enter new file name :testset self broadened width to air broadened? :nmultiply H2O air broadened width by 1.3? :nreplace H2O air b. by delaye CO2-broadened data? :ngenerate linedata using PMR2 assumptions? :ngenerate linedata using Wedads assumptions? :ngenerate linedata using Brunos assumptions? :ngenerate linedata using all PMIRR assumptions? :nH2-He broaden PH3 for Jupiter? :n--------------------------------------------------enter gas detailsenter gas id and isotope [0=all isotopes]ALL includes all gases, GO starts execution,? gives summaryID ISO ? :1,0ID ISO ? :GOAs can be seen, the new sequential file is called 'test' and contains linedata between 1400 and 1450 cm-1 for all isotopes of water vapour only. The program may then perform a number of modifications to the line data which are historical in nature. The first three possible operations are self-explanatory, the data for the third operation coming from [R8]. It should also be noted that the third option replaces the transmission probability column with the temperature dependence of the self-broadening since this column is not normally used by Radtrans (This data is not used in version 1.1). The last three operations are more obscure.PMR2 Assumptions - This operation generates linedata equivalent to that used by PMR2, a non-overlapping line model developed by J.T.Schofield. Modifications are:H2OMultiply air broadening coefficient by 1/1.013246Set self-broadening to 6.5 times air broadeningSet temperature dependancies to 0.5.Replace transition probability column with the temperature dependence of the self-broadeningCO2Set the air and self broadened widths to those calculated by Yamamoto [R9] multiplied by the empirical factor 1.1/1.013246.Set the temperature dependancies to those calculated by Yamamoto.Replace transition probability column with the temperature dependence of the self-broadeningWedad Assumptions - This operation generates linedata equivalent to that used by Wedad Adbou at JPL for some of the PMIRR intercomparison tests. Modifications are:H2OMultiply air broadening coefficient by 1/1.013246Set self-broadening to 6.5 times air broadeningSet temperature dependancies to 0.5.Replace transition probability column with the temperature dependence of the self-broadeningCO2If the self broadened width is listed as zero, set it to that calculated by Yamamoto [R9] multiplied by 1/1.013246.Set the temperature dependancies to those calculated by Yamamoto.Replace transition probability column with the temperature dependence of the self-broadeningBruno Assumptions – Various modifications to linewidths etc. for CIRS Jovian radiative transfer tests. PMIRR Assumptions - These are the assumptions that would have been used to generate the final transmittance tables for PMIRR. Modifications are:H2OReplace air broadened width and temperature dependence of water with Delaye calculated CO2 broadened valueReplace transition probability column by temperature dependence of self broadening calculated from DelayeIf self broadening is set to zero, substitute Delaye calculated value.CO2Leave air broadened CO2 unchangedIf self broadening is listed as zero, set it to that calculated by Yamamoto/1.013426Replace air broadened temperature dependence with that calculated by YamamotoReplace transition probability column by temperature dependence of self broadening calculated from YamamotoH2-He broaden PH3 for Jupiter – self-explanatory.7.1.7 Cp_linesCp_lines opens a line data base created by Makedb (eg HITRAN or GEISA) specified by an input key file name and copies a specified subset of the line data base to a new sequential ASCII file just like Select. Unlike Select however, it copies all lines between given wavenumber limits rather than selecting them by gas, isotope and strength.7.1.8 SummaryThis program opens a line data base specified by an input key file name and prompts for a wavelength range and bin width. Summary then producues an ASCII output file called "summary.out" which summaries the content of the datebase for each gas for each bin in the specified range. The first few lines of a typical summary file are listed below: data base: hitran92 from DB file: /vol/local/linedata/hitran92.asc as defined in key: hitran92.key-------------------------------------------------------- BIN: 1 1400.000 - 1410.000 cm-1 id iso smin smax nlines H2O 1 1 0.47000E-26 0.27800E-19 29 H2O 1 2 0.28800E-25 0.55200E-22 11 H2O 1 3 0.52400E-26 0.10300E-22 11 H2O 1 4 0.10370E-26 0.96180E-23 29 total of 80 H2O lines id iso smin smax nlines CO2 2 3 0.94910E-26 0.70040E-25 40 CO2 2 4 0.50400E-26 0.19980E-25 13 total of 53 CO2 lines id iso smin smax nlines O3 3 1 0.10200E-24 0.29100E-23 280 total of 280 O3 lines7.1.9 MergeThis program takes two sequential access line data base files and then merges them together in order of wavenumber. This program is very useful for adding extra lines to existing line data bases.7.1.10 Line data Strengths and Absorber Amounts UnitsThis area causes a lot of confusion! When Radtrans reads in line data from one of the data bases set up by Makedb, they do so using the subroutine lines.f which in turn uses the subroutine rdline.f. The units of line strength in the line databases are the standard ones of cm-1/ (molecule cm-2) and as such have rather small exponents. In order to avoid numerical underflow when passing small strengths between the subroutines, rdline.f multiplies the strengths by the factor 1047. Thus when the final calculation routines get hold of the strengths, they must be converted back to their correct units using the factor 10-47. This number is too small to be applied in one go using real*4 numbers and so is applied in two stages. The factor 10-27 is applied directly and the factor 10-20 is applied to the absorber amounts which are defined in the units of (molecule cm-2).7.2 Band DataRadtrans contains some spectral models which use band data instead of line data. When these routines are used, the spectral data must be read in from a band parameter file which has a ‘.ban’ suffix. This band data file may be generated either by statistical analysis of line data in the HITRAN or GEISA databases or calculated from low resolution laboratory experiments. For every ‘.ban’ file there must also be a .key file which contains the location of the ‘.ban’ file and the gas identifier filesA typical ‘.ban’ file has the following format: ------------------------------------------------------------------------------ Original file name : 5jupiter5.ban Originator : Pat Irwin Date : 25/10/94 Data sources : Gas : 6 1 HITRAN92 Gas : 11 0 " Gas : 6 3 " Gas : 28 0 " Gas : 33 0 " Gas : 1 0 " Corrected line treatment in Makeband ******************************************************* VMIN = 1800.00 DELV = 5.00 FWHM = 5.00 NPOINT = 61 NGAS = 6 Gas : 6 1 Gas : 11 0 Gas : 6 3 Gas : 28 0 Gas : 33 0 Gas : 1 0 ------------------------------------------------------------------------------ Band data for gas : 6 1 V0 dV Kv(T0) delta/AD0 y0 El SFB 1800.00 5.00 0.52856E-03 0.88439E+03 0.26271E+03 0.14892E+04 0.13373E+01 1805.00 5.00 0.11291E-02 0.91134E+03 0.27025E+03 0.14911E+04 0.13193E+01 1810.00 5.00 0.12633E-03 0.11360E+04 0.45271E+03 0.16362E+04 0.13533E+01 1815.00 5.00 0.38263E-03 0.12947E+04 0.37365E+03 0.16080E+04 0.13393E+01 1820.00 5.00 0.89474E-03 0.93499E+03 0.25684E+03 0.15506E+04 0.13320E+01The first half of the header contains information on the data sources, who generated the file and when. The second half contains the spectral details of the file and the number of gases contained. The data itself contains the following columns for each spectral bin defined for each gas:H4sIAAAAAAACC7t+9tgsBjDgZuBlSACzysMZGTgZGJjbgGwmBlGwGCtIBROMxcPEC1TPAmSxMPKC aT1GCTDNxMgIVsEJV8vI9P//fwZmIEuOgQtIqrHxA+n/IEEwAJn/m+kLlDeBEUIzCIRk5qYWK/il lisE5ecm5oHsAmJdoDw7kFZkZWKYocAJNFcATT8TyNFAEFyZm5Sfw8AE0cUI1v0BSXepAjcDI5qL IJaDVKoz/v/PDOYBAFaAFWQiAQAA \* mergeformatH4sIAAAAAAACC7t+9tgsBjAQYuBlSACz8sIZGTgZGJiXAtlMDKJgMVYg5maCsXiYeIHqWYAsFkZe MK3HKAGmmRgZwSo44WoZmf7//8/ADGTJMXABSTU2fiD9HyQIBgJA/JvpC5Q3gRFsKRAEV+Ym5ecw MIFM1QWKsgNpRVZGBhcGbgZGsKvQdIENC8nMTS1W8EstVwjKz03MA7kQrJ8RTH+Am8PEMEOBE2gS uu1MOGyH6GaE6y5V4AaGEap/II4AqVRn/P+fGcwDAIauOF5gAQAA \* mergeformat\* mergeformatH4sIAAAAAAACC7t+9tgsBjBQZBBgSACzHMIZGTgZGJjfAtlMDKJgMVYg5maCsXiYBIDqWYAsFkZe MK3HKAGmmRgZwSo44WoZmf7//8/ADGTJMXABSTU2fiD9HyQIBgJA/JvpC5Q3gZEJZCkQBFfmJuXn MDCBTNVlZGBgB7mRlZEhhYGHgRHsKmRdDFDDQjJzU4sV/FLLFYLycxPzQC4E62cE0x+QzNEHmsNN tO0Q3Yxw3YlA3YJQV/xE1k2iK1wY+BmkMMwh5BtM9xgwsAHNQQ1fiDEgleqM//8zg3kAewYUxPAB AAA= \* mergeformatH4sIAAAAAAACC7t+9tgsBjDgYeBnSACzisIZGTgZGJi7gWwmBlGwGCsQczPBWDxM/ED1LEAWCyMv mNZjlADTTIyMYBWccLWMTP///2dgBrLkGLiApBobP5D+DxIEA5D5v5m+QHkTGJkgDIGQzNzUYgW/ 1HKFoPzcxDyQXUCsy8jAwA6kFVkZGSqB5jBB9f+E62cgoJ8RTH9AMseAgRfIRnUbxBiQSnXG//+Z wTwAgzwIJiwBAAA= \* mergeformatElSFBwhere:\* mergeformat is the central wavenumber of the bin\* mergeformat is the width of the bin in wavenumbers\* mergeformat is 1020 H4sIAAAAAAACC7t+9tgsBjDgYuBkSACzisIZgWwG5iQgm5FBACzGCsTcTDAWDxMnUD0LkMXCyAum 9RglwDQTIyNYBSdcLSPT////GZiBLDmgHgYGNTZ+IP0fJAgGIPN/M32B8iYwggwBsYIrc5PycxiY QKbqAkXZgbQiKyPDFgYOoKtQTWIE6wWpVGf8/58ZzAMAauy0xtoAAAA= \* mergeformat the mean absorption coefficient at H4sIAAAAAAACC7t+9tgsBjDgZeBnSACzisMZGTgZGJi7gWwmBlGwGCsQczPBWDxM/ED1LEAWCyOE 1mOUANNMjIxgFZxwtYxM////Z2AGsuQYuICkGhs/kP4PEgQDkPm/mb5AeRMYmSAMgZDM3NRiBb/U coWg/NzEPJBdQKzLyMDADqQVWRkZQoDmMEL1/4TrZyCgnxFMf0AyxwDoFw40t0GMAalUZ/z/nxnM AwARxzTDLAEAAA== \* mergeformat = 296K (units of absorption are (molecule cm-2)-1)\* mergeformat is the mean line spacing H4sIAAAAAAACC12MsQ4BYRCEZ/a/I8cvlCqJhoqXUWjloiRKubdQeyCd2ovoFGv/CQqbbGZ2M988 7rcrNANk7OTOW6IBUhuemOhXxw7t67LlyFfhKo6ka06lRirR/LI0d0cKNwsGWPTGoV6emtL/sufn ujBAsZvu2J4OsNK6ItAPndfEPmj+NVFsSS7pnnS9AepYKNraAAAA \* mergeformat over the mean Doppler width coefficient H4sIAAAAAAACC7t+9tgsBjAQAMIEMKswnJGBk4GBeRWQzcQgChZjBWJuJhiLhwmkmgXIYmHkBdN6 jBJgmomREayCE66Wken///8MzECWHAMXkFRj4wfS/0GCUHsZGH4zfYHyJjAygSwFguDK3KT8HAYm kKm6jAwM7EBakZWRIZGBh4ER7KrfTD+RdYENC8nMTS1W8EstVwjKz03MA7kQrJ8RTH9AMseFAeQO dHMYCJjDADWHEW6OAQMb0BxUn0GMAalUZ/z/nxnMAwDJYKILagEAAA== \* mergeformat.H4sIAAAAAAACC7t+9tgsBjCwYxBkSACz4sIZGTgZGJjnMDIwMDGIgsVYgZibCcbiYRIEqmcBslgY ecG0HqMEmGZiZASr4ISrZWT6//8/AzOQJcfABSTV2PiB9H+QIBiAzP/N9AXKm8DIBGEIhGTmphYr +KWWKwTl5ybmgewCYl2gm9iBtCIrI0MlAw/Ufb+ZfsL1MxDQzwimPyCZY8DAD2QLoLkD5BkQK7gy Nyk/h4EJZjtENyNcty3QFfwYupmw6sa0OxGoWwLDD4TDAN0VPkA3KFIlLNjg5nwh2hxM9+gD/aVJ UajoUyFUXIChYkGlULFAS70QY0Aq1Rn//2cG8wCDeN0fTgMAAA== \* mergeformat is the mean self-broadened Lorentz width at \* mergeformat, H4sIAAAAAAACC7t+9tgsBjDgY+BnSACzCsIZGTgZGJi7gWwmBlGwGCsQczPBWDxM/ED1LEAWCyMv mNZjlADTTIyMYBWccLWMTP///2dgBrLkGLiApBobP5D+DxIEA5D5v5m+QHkTGJkgDIGQzNzUYgW/ 1HKFoPzcxDyQXUCsy8jAwA6kFVkZGQKA5jBB9f+E62cgoJ8RTH9AMseAgZeBA81tEGNAKtUZ//9n BvMA4YLRASwBAAA= \* mergeformat (= 1 atm) over the mean doppler width coefficient.El is the mean lower state energy (cm-1)SFB is the mean self-to-foreign broadening ratio.\* mergeformat is the Doppler width coefficient for the bin which depends only on the mean wavenumber of the bin and the molecular mass. The Doppler width at temperature T is then found from: H4sIAAAAAAACC7t+9tgsBjCwYxBgSACz4sMZGTgZGJirGIEEgyhYjBWIuZlgLB4mAaB6FiCLhZEX TOsxSoBpJkZGsApOuFpGpv///wPNYWCQY+ACkmps/ED6P0gQDASA+DfTFyhvAiNQI1hvcGVuUn4O AxPIVF2gS9iBtCIrI0MiAw8DI9hVv5l+IusCGxaSmZtarOCXWq4QlJ+bmAdyIVg/I5j+gGSOCwPI Hei2M+CwHaKbEa7bFugKYSLdjmk3yA8yJPsB0xUgP6himMNAclgYMLDBzflCgXtCgP4yAaUdhl9M bAwwhyjB7QWlBxEmTgYdMEsYyNKFq2ZCU80EV60HVc0DdCeqD2BqQDIQNYwMxlAxGAskZo2W8iAu A5mhzvj/PzOYBwAdJiD7CgMAAA== \* mergeformatA typical ‘.key’ file has the following format:5jupiter5.ban/home/plan/linedata/gas_info.dat7.2.1 MakebandThe data in the ‘.ban’ files may come either from laboratory experiments or from analysis of line data bases. The program which performs this latter function is Makeband which also generates a ‘.key’ file. The band parameters defined above are derived from the linedata as follows:From [R4], the mean absorption in a spectral interval is given by:H4sIAAAAAAACC61UTUtCQRQ9c/0IS8nISpLqZWAmaLkLwl2LFiGRgtuUXFiahIn0L1pG/6Vtu9b9 grbRoo21eN037znoG0GfNTDv3hnmnHvuB+/t9eUJct0hgwvp7VcEQoDvmfiDFXkX4L1AAy9MGX7v Z88vItLmRFxaEkK+CKm3gkzTZB5gE/P8TQUX2ZrWpVwW/w99OacHQbYTLTda9Y5RrPeM83aremPF 4p0VwBzb7YDANbYgEJX4/jBeUpTuW7V2E2SjhER/DqG7SLLvjo6J0W0eoXjSrCLsOQtdT5l5lhye /h/0HHBecc956Xr2WM+GU90RnjHV1VUUGL3zDyryPIn5GWbEraeIda4MTzW+KYiBkKSKa01qjCLI SW+ZvUOF7XBfTrXOTNJAWi4NxHA2dFrFiVPfjynrSwr9zlxHWnfGz76u5JKntuDknEDWyTmBksd+ 00i/K577pCvrYQ31mVUcc141z1PnVkF4NFJoTlldtwpC10jjSlW3qqp76/r/2cIs9K4wTZ88/QKz CLovkAUAAA== \* mergeformatwhereH4sIAAAAAAACC7t+9tgsBjAwYBBmSACzgsIZGTgZGJi/ANlMDKJgMVYg5maCsXiYhIHqWYAsFkZe MK3HKAGmmRgZwSo44WoZmf7//8/ADGTJMXABSTU2fiD9HyQIBiDzfzN9gfImMDJBGAIhmbmpxQp+ qeUKQfm5iXkgu4BYl5GBgR1IK7IyMpQz8DAwMgig6Qc7GgiCK3OT8nMYmCC6GMG6PyDptgXq5iXD dog5jHBzioHmqEPN+Um0OZjuyWTgZ9BG4gkyKEP99o6A3zDd9JSBj0EMLbQZwWaAVKoz/v/PDOYB AA0x8b3+AQAA \* mergeformat is the sum of the line strengths and the mean line spacing is defined as H4sIAAAAAAACC7t+9tgsBjDQYJBjSACz3MMZGTgZGJjZGBkYmBhEwWKsQMzNBGPxMMkB1bMAWSyM vGBaj1ECTDMxMoJVcMLVMjL9//+fgRnIkmPgApJqbPxA+j9IEAwEgPg30xcobwIjE8hSIAiuzE3K z2FgApmqC3QJO5BWZGVkSGEQZmDE0MWAVRcj2E0fkHTbAnVzw3kuQLYY2IdoZoEdFpKZm1qs4Jda rhCUn5uYB/It1C0QUxmh5jAxzFDgYlAg0ifobmJiKFXgBoaNKKZuklzByODHIMMgBYo5hl9MbAww bygxwOwFxYYIEz/QJhBLGMhSRYsRiB6QenXG//+ZwTwAwc2dmSICAAA= \* mergeformat.The mean Doppler width coefficient depends on the mean wavenumber and absorber molecular weight (g) only through the equation:H4sIAAAAAAACC61TPUsDQRB9s/nQGI8YTkUhmtMiqS5cUBDUCEpKY6GCCBZGSSEYU4iI/8JS/B3+ Bjtr/4ZFmpjinJ3sHfEiaGIOdufj3rx7s7fz/vb6DHkukce5eNYJIQXEKoo3zEkuwSutAm9a5Rkf Zy9OltgSLYhVRIJIhVhSvu8zD7CMKd4LyQxbXyflmeHVVW0TPRIXSu3RQ/OidQ2lWV0CJtiuJAh1 2CBR1VWd/iohO75qNm6dg8a9c9hq1m+0QqknsR99PFXMs44oD37hgeGhkMeDxTzRLvBjF4MqKtyN bVS0R1ah8ORk+f/97SyjKhTuHBtL/1ZBWEcaxTAqceRiUqIY1rwyx97IJ/XC1dUxnFTZS2PfqOgM rcJFEqdjuDUbzHM20M3wt7iGHPb0tOJTJREIWQ2/qydwVi1iUzybva0QrSJoFaK3DTqHnUgHAUa/ 6WGy2DW5wNO5msllUDC5DE/u9/nvqdW8RfL9mERfs6UB45AEAAA= \* mergeformatIn Section 5 we saw that the Goody and Malkmus distributions have different definitions of \* mergeformat with the Malkmus value being 4 times smaller. Using the Goody definition the mean self-broadened half-width at T0, P0 may be calculated to be:H4sIAAAAAAACC61UwUrDQBB9M2kjtZaKteJBbSNi7cEq9qQgguBNPGjBqxV7EI0VShH/wrMf5M2z v+Ghl9rDOjumoSSCDWZgM7PLzJv3Jtl8vL+9Qu0EHq40Kl8ScoCzzwCjrGdZWXkeR3PsSX5GogwV 1DdoWT0TaUYuzCU2xsCRaA2z8tx0i+KNPVSblzXiQbB7IW0qdvHsX3fvwRZ1m4AZ8V6W0EYJpKxG PJysUrDWrd/pVc86T9Xzrt9+sAy1ntR/TuCcYkl4RHHwBw4CHApxdlEQnKgK/KoizuJQ1CxMPYNo 7xvkUQs0DP4xi57gNFKYxR5cNKdUE2fxiBWsJlYTZ3EnOBsBi2FiFn1UUI+xSD6LLWGxk8K7aQlO M5XvtIKDxLrifOrC58j+H/DFLsYA62Ffe+cXuShZNipJdBy59z81Nr9Gxji6+wZHMeamiAQAAA== \* mergeformatwhere H4sIAAAAAAACC7t+9tgsBjCIY5BhSACzjMMZGTgZGJgDmIAEgyhYjBWIuZlgLB4mGaB6FiCLhZEX TOsxSoBpJkZGsApOuFpGpv///wPNYWCQY+ACkmps/ED6P0gQDEDm/2b6AuVNYGSCMARCMnNTixX8 UssVgvJzE/NAdgGxLiMDAzuQVmRlZChmEGRgZBBA0w9yBIgVXJmblJ/DwATRxQjW/QFJty1QNyeG 7QwEbYeYwwg3xwhoigTZrnBhkGIQodgVTAwzFCQYZDFcwUSUK5gYShWkGKRBcc7wi4mNAWa9Etw2 UDyKMPEyCINZwkCWEsnxxoQRcqD4s4Ka85Noc2CuZ4KbkwkMQTsi/Y7pikSgKxyp5ApPJL9xM3hB 3fSOQKrAdJMGgxCDGZynCeT5UcWFYsDUSq6bngJjXxXDFQwku8KQgYMhCM7TB/LCkPISB0MEWikB sQJkijrj///MYB4AGjNEjbYEAAA= \* mergeformat. When using this table to calculate Malkmus bands, the value of H4sIAAAAAAACC7t+9tgsBjAQAMIEMKswnJGBk4GBeRWQzcQgChZjBWJuJhiLhwmkmgXIYmHkBdN6 jBJgmomREayCE66Wken///8MzECWHAMXkFRj4wfS/0GCUHsZGH4zfYHyJjAygSwFguDK3KT8HAYm kKm6jAwM7EBakZWRIZGBh4ER7KrfTD+RdYENC8nMTS1W8EstVwjKz03MA7kQrJ8RTH9AMseHAeQO dHMYCJjDADWHEW6OAQMb0BxUn0GMAalUZ/z/nxnMAwBw5xJfagEAAA== \* mergeformat must thus first be divided by 4.The mean self/foreign broadening ratio and mean lower state energy are simply the mass weighted means:H4sIAAAAAAACC7t+9tgsBjBIYlBkSACzjMIZGTgZGJhfMDIwMDGIgsVYgZibCcbiYVIEqmcBslgY ecG0HqMEmGZiZASr4ISrZWT6//8/AzOQJcfABSTV2PiB9H+QIBiAzP/N9AXKm8DIBGEIhGTmphYr +KWWKwTl5ybmgewCYl2gmziAtCIrM0OwmxODGAMjgwCaCSBngFjBlblJ+TkMTBB9jGD9H4Cy7GD9 jAy2QN2SZNgPMYcRbk4xAw+DCdScn0Sbg+meTAZ+BksM3zBh9Q2mKxKBrrCmkiuckfzGzuCCEUYM JIeRPtB13kT6DdNNIL8Fkuw3TFeA/BYJ56UBWdFIcoIMhlAXviM5LT0FmqxChbRUziAPTJfA3Mfw i4mNARbQSvDYAuUoESYhBmUwSxjIikfLVRA9IPXqjP//M4N5AKrjVW/mAwAA \* mergeformatH4sIAAAAAAACC7t+9tgsBjBwZFBkSACzBMMZGTgZGJhnMzIwMDGIgsVYgZibCcbiYVIEqmcBslgY ecG0HqMEmGZiZASr4ISrZWT6//8/AzOQJcfABSTV2PiB9H+QIBiAzP/N9AXKm8DIBGEIhGTmphYr +KWWKwTl5ybmgewCYl2gm9iBtCIrI4MrgxjUfb+ZfhKtnxFMf0AyJ4dBEuhfATR3gDwDYgVX5ibl 5zAwwWyH6GaE67YFuoKfZF9guqKYgYdBi2TfYLonE+gafSq4xxXoHiOK3cPEkJPJz2CJ5DpBBnVo WL8jENaYbnoK9JsUGSkGPYzKGeQZNEBpnOEXExsDI0Q/gxI8LEDpVoRJCJguQCxhIMsOLe1C9IDU qzP+/88M5gEAWKuq1kwDAAA= \* mergeformatMakeband is a user-interactive program which is fairly self-explanatory. The input session used to create the band parameter file in the example is shown below. N.B. Gas Ids are Radtrans IDs. Enter name of lbl key file :/home/oxpln3/plan/linedata/hitran92 38 gases recognised by software 32 gases in data base Enter wavenumber range and spacing. Enter Vmin, Vmax, DelV, FWHM :1800,2100,5,5 Enter number of gases :6 Gas : 1 Enter Gas ID and ISO :6 1 Gas : 2 Enter Gas ID and ISO :11 0 Gas : 3 Enter Gas ID and ISO :6 3 Gas : 4 Enter Gas ID and ISO :33 0 Gas : 5 Enter Gas ID and ISO :28 0 Gas : 6 Enter Gas ID and ISO :1 0 Enter name of output file :5jupiter5 %writing output Enter Originator :Pat Irwin Enter Date :15/10/94 Enter source of data for gas 6 1HITRAN92 Enter source of data for gas 11 0" Enter source of data for gas 6 3" Enter source of data for gas 33 0" Enter source of data for gas 28 0" Enter source of data for gas 1 0" Enter any additional header informationCorrected line treatment in Makeband %calculation completeIn this example the spacing of the points and the bin width is the same so that the bins do not overlap. Hence the resultant spectra are under-sampled. Nyquist sampling (at least!) is usually recommended. DELV and FWHM are independent of each other and can be set at will.7.2.2 Convert_dataThe routines written by Kim Strong for fitting band parameters to laboratory measurements produce an output which is similar but not identical to the .ban format used by Radtrans. The output from Kim’s routines can be converted using Convert_data.Unfortunately, Kim’s files do not specify which parameter is which so that the correspondence between this output and the ‘.ban’ format has to be hard-coded into Convert_data. In particular, Convert_data is currently set up to convert the fits made of Simon Calcutt’s NH3 data by Kam Sihra which do not include an SFB parameter. Thus the code will have to be modified to cope with any subsequent changes to the output from Kim’s routines.7.3 Correlated-k dataRadtrans may also operate with pre-calculated correlated-k tables. These are created by the program Calc_ntable (line data) and Band_ktable (band data) and may be inspected using the program Read_table. 7.4 Gas ContinuaCollision-induced absorption by Hydrogen-Helium has now been incorporated into Radtrans [R12,13]. Additional CIA coefficients for N2, CH4 have also been incorporated.