Abstract
 Top of page
 Abstract
 1. Introduction
 2. Basic Equations
 3. Participating Models
 4. Intercomparison Setup
 5. Line Shape Implementation Test (Exercise 0)
 6. Absorption Coefficient Intercomparison
 7. Radiative Transfer Intercomparison
 8. Lessons Learned, Summary
 9. Conclusion
 Appendix A: Relevant Details on the Forward Models
 Acknowledgments
 References
 Supporting Information
[1] We compare a number of radiative transfer models for atmospheric sounding in the millimeter and submillimeter wavelength range, check their consistency, and investigate their deviations from each other. This intercomparison deals with three different aspects of radiative transfer models: (1) the inherent physics of gaseous absorption lines and how they are modeled, (2) the calculation of absorption coefficients, and (3) the full calculation of radiative transfer for different geometries, i.e., uplooking, downlooking, and limblooking. The correctness and consistency of the implementations are tested by comparing calculations with predefined input such as spectroscopic data, line shape, continuum absorption model, and frequency grid. The absorption coefficients and brightness temperatures calculated by the different models are generally within about 1% of each other. Furthermore, the variability or uncertainty of the model results is estimated if (except for the atmospheric scenario) the input such as spectroscopic data, line shape, and continuum absorption model could be chosen freely. Here the models deviate from each other by about 10% around the center of major absorption lines. The main cause of such discrepancies is the variability of reported spectroscopic data for line absorption and of the continuum absorption model. Further possible causes of discrepancies are different frequency and pressure grids and differences in the corresponding interpolation routines, as well as differences in the line shape functions used, namely a prefactor of (ν/ν_{0}) or (ν/ν_{0})^{2} of the VanVleckWeisskopf line shape function. Whether or not the discrepancies affect retrieval results remains to be investigated for each application individually.
1. Introduction
 Top of page
 Abstract
 1. Introduction
 2. Basic Equations
 3. Participating Models
 4. Intercomparison Setup
 5. Line Shape Implementation Test (Exercise 0)
 6. Absorption Coefficient Intercomparison
 7. Radiative Transfer Intercomparison
 8. Lessons Learned, Summary
 9. Conclusion
 Appendix A: Relevant Details on the Forward Models
 Acknowledgments
 References
 Supporting Information
[2] During the past decades, numerous atmospheric radiative transfer models have been developed, i.e., computer programs that simulate the radiative transfer in the atmosphere. Most of them have been developed for specific purposes, typically for the analysis of data from specific sensors. Therefore they are typically suitable for, e.g., a limited wavelength range, or for a specific geometry as relevant for the sensor.
[3] Such models (commonly called “forward models”) are used to simulate the intensity of radiation that a sensor would measure for a given state of the atmosphere (pressure, temperature, constituent gases) and a given source of the radiation. The simulations are needed, e.g., when developing and designing new sensors, when retrieving atmospheric parameters (e.g., temperature, trace gas concentrations) from actual measurements, or when correcting measurements of the radiation from earth or space for the influence and contribution of the atmosphere.
[4] The aim of this paper is (1) to compare a number of forward models developed independently for atmospheric sounding, applicable in the millimeter and submillimeter wavelength range and for different geometries, including limblooking, and (2) to check their consistency and investigate their deviations from each other. Similar recent intercomparison studies are Tjemkes et al. [2003], von Clarmann et al. [2003b], Garand et al. [2001]. However, the studies by von Clarmann et al. [2003b] and Tjemkes et al. [2003] focused on the infrared wavelength range, and the study by Garand et al. [2001] focused exclusively on models for the Advanced Television Infrared Observation Satellite (TIROS) Operational Vertical Sounder (ATOVS) instruments flown on polar orbiting meteorological satellites (POES) of NASA.
[5] Section 2 reviews the basic equations relevant for this intercomparison study, sections 3 and 4 briefly present the forward models that participated in this study and the setup of this study. The subsequent sections deal with three different aspects of the radiative transfer models on which this study focuses: (1) the inherent physics of gaseous absorption lines and how they are modeled (section 5), (2) the calculation of absorption coefficients (section 6), and (3) the full calculation of radiative transfer for different geometries, i.e., downlooking, limblooking, and uplooking (section 7). Section 8 points out what has been learned not only by the results of this study, but also from performing it; section 9 gives a brief summary. Appendix A gives details about the radiative transfer models that participated in this study.
2. Basic Equations
 Top of page
 Abstract
 1. Introduction
 2. Basic Equations
 3. Participating Models
 4. Intercomparison Setup
 5. Line Shape Implementation Test (Exercise 0)
 6. Absorption Coefficient Intercomparison
 7. Radiative Transfer Intercomparison
 8. Lessons Learned, Summary
 9. Conclusion
 Appendix A: Relevant Details on the Forward Models
 Acknowledgments
 References
 Supporting Information
[6] Before going into the details of this intercomparison study, let us give a brief overview of the basic equations related to radiative transfer in the atmosphere in the millimeter and submillimeter wave domain. More details and derivations can be found in books by authors like, e.g., Goody and Yung [1989] or Janssen [1993].
[7] The radiation field is described in terms of the specific intensity I_{ν}, which is defined as the flux of energy in a given direction per second at a given frequency (ν) per unit frequency interval per unit solid angle per unit area.
[8] In the case of microwaves, scattering by air molecules is negligible (as compared to absorption), scattering by aerosols can be neglected as well, and scattering by cloud particles (droplets, ice particles) is neglected here since we only consider clear sky. In the case of local thermodynamic equilibrium, the integral form of the radiative transfer equation is then given by
where s is the coordinate along the line of sight; the observer (e.g., a radiometer) is at s = 0, the background is at s = s_{bg} and contributes the background radiation I_{ν}(s_{bg}). For uplooking and limblooking geometry, s_{bg} = ∞ and I_{ν}(s_{bg}) usually is the cosmic background, whereas for downlooking geometry, s_{bg} is finite and I_{ν}(s_{bg}) is the radiation emitted by the ground. The α_{ν} is the absorption coefficient, τ_{ν}(s) is the opacity defined as
and B_{ν}(T) is the Planck function defined as
Here, h is Planck's constant, c is the speed of light, k is Boltzmann's constant, and T is the physical temperature. The integral in equation (1) can be easily evaluated numerically, provided the absorption coefficient is known.
[9] The absorption coefficient α_{ν} for a specific gas absorption line can be written as
where n is the number density of the absorber molecule, S(T) is the line strength and F(ν) is the line shape function (∫F(ν) dν = 1). Spectroscopic databases (also called spectral line catalogs) contain the value of S at a reference temperature T_{0} for each spectral line. The conversion to other temperatures is done according to [Pickett et al., 1992]
where E_{l} is the lower energy level of the states between which the transition occurs, ν_{0} is the transition frequency, and Q(T) is the partition function. Spectral line catalogs contain E_{l} tabulated along with ν_{0} and S(T_{0}). Partition functions Q(T) for all molecular species are also available along with some spectral line catalogs, either in the form of tabulated values for a set of temperatures, or as polynomial approximations.
[10] In order to determine the line shape function F(ν) of atmospheric absorption lines, two effects have to be considered: Doppler or thermal broadening and collisional or pressure broadening. Doppler broadening is caused by the thermal motion of the gas molecules. Collisional broadening is caused by a perturbation of the energy levels by collisions of the molecules.
[11] Doppler broadening is dominant in the upper stratosphere and mesosphere for microwave frequencies. The Doppler line shape function is
where γ_{D} = . Here ν_{0} is the line center frequency, and m the mass of the respective molecule. The Doppler line shape is just a Gaussian, with the Doppler width γ_{D} giving the half width at 1/e maximum of the line shape function.
[12] Collisional broadening is more complicated than Doppler broadening. So far, it is not possible to calculate from basic principles a collisional line shape that is valid near the line center and in the far wing. All theoretical line shapes must rely on approximations that limit them to certain regions of the line profile. The most popular of these approximations is the impact approximation which states that the duration of the collisions is short compared to the time between collisions. That approximation allows the formulation of a simplified kinetic theory which yields the Lorentz line shape
where γ_{L} is the Lorentz line width which is a function of pressure and temperature. A generalization of the Lorentz line shape particularly for the microwave spectral region is the van VleckWeisskopf line shape [Van Vleck and Weisskopf, 1945]
which reduces to the Lorentz line shape for ∣ν − ν_{0})∣ ≪ ν_{0}. Note that this line shape function is an approximation and is not normalized [Rayer, 2001].
[13] Collision and Doppler broadening are taken into account simultaneously by the Voigt line shape, a convolution of the Lorentz line shape with a Doppler line shape:
This line shape is an approximation of the true line shape in the transition regime where both collisional broadening and Doppler broadening are significant. There is no analytical solution to the integral in equation (9), so one of several available approximation algorithms has to be used (see survey in the work of Schreier [1992]).
[14] Finally, one can implement a hybrid line shape that behaves like a Van VleckWeisskopf line shape in the high pressure limit and like a Voigt line shape in the low pressure limit:
[15] Not related to the physics, but rather to the modeling of radiative transfer, is the way how to discretize functions of the vertical spatial variable (height h). Instead of taking point values at discrete heights, weighted means over layers can be taken, socalled CurtisGodson means. The CurtisGodson mean of a quantity X (e.g., pressure, temperature, or some volume mixing ratio) for layer j (between h_{j} and h_{j+1}) is defined by
where n(h′) is the number density of the atmosphere's molecules as a function of height h′, and X(h′) is the said physical quantity (e.g., pressure, temperature, or some volume mixing ratio) as a function of height h′.
3. Participating Models
 Top of page
 Abstract
 1. Introduction
 2. Basic Equations
 3. Participating Models
 4. Intercomparison Setup
 5. Line Shape Implementation Test (Exercise 0)
 6. Absorption Coefficient Intercomparison
 7. Radiative Transfer Intercomparison
 8. Lessons Learned, Summary
 9. Conclusion
 Appendix A: Relevant Details on the Forward Models
 Acknowledgments
 References
 Supporting Information
[16] The forward models which participated in this intercomparison study were as follows.
[17] 1. Atmospheric Radiative Transfer Simulator (ARTS), a public domain project which was initiated and developed jointly by the University of Bremen, Germany, and Chalmers University, Göteborg, Sweden [Buehler et al., 2005]. ARTS is used for the retrieval of atmospheric parameters from data from the limb sounder on board the Odin satellite, from the Advanced Microwave Sounding Unit (AMSU) on board the NOAA polarorbiting satellites, and from the groundbased Radiometer for Atmospheric Measurements (RAM) and the airborne Airborne Submillimeter Radiometer (ASUR) instruments. ARTS has further been used for instrument studies of Superconductive Submillimeter Limb Emission Sounder (SMILES) and MillimeterWave Acquisitions for Stratosphere/Troposphere Exchange Research/Submillimeter Observation of Processes in the Atmosphere Noteworthy for Ozone (MASTER/SOPRANO).
[18] 2. Bernese Atmospheric Model (BEAM), developed at the Institute of Applied Physics (IAP), University of Bern, Switzerland [Feist, 2001; Feist and Kämpfer, 1998; Feist, 1999a]. Today, BEAM is used for the data analysis of all the radiometric instruments at IAP as well as the ozone radiometer SOMORA at MeteoSwiss.
[19] 3. Earth Observation Research Center (EORC) model developed at EORC, National Space Development Agency (NASDA), Japan (for details see Table 1 and Appendix A). It is mainly intended as accurate and numerically efficient software for the L2 data processing of the planned Superconductive Submillimeter Limb Emission Sounder (SMILES) to be aboard the Japanese Experiment Module (JEM) of the International Space Station (ISS).
Table 1. Main Features of the Participating Radiative Transfer Models^{a}Model  Catalog^{b}  Partition Function^{c}  Line Shape^{d}  Continuum Absorption^{e}  Refraction^{f}  Geometry^{g} 


ARTS  J, H, O  poly.  Hy, Vo, VVW, Lo, Do  CKD, MPM, PWR, O  yes  D,L,U 
BEAM  J, H, O  JPL/int.  Vo, VVW  MPM93  no  L,U 
EORC  J, H  JPL/int., O  Vo, VVW, Lo, Do  MPM89,93  yes  D,L,U 
KMM^{h}  H  O  VVW  MPM89  yes  U 
MAES  J, H  JPL/int.  Vo, Lo, Do  MPM89,93  no  D,L,U 
MIRART  J, H, O  O  Hy, Vo, Lo  CKD2.2, O  yes  D,L,U 
MOLIERE/5  J, H, O  poly.  Hy, Vo, VVW, Lo, O  CKD,MPM93  yes  D,L,U 
SMOCO  J, H  JPL/int.  Vo, Lo, Do  MPM89,93  yes  D,L 
[20] 4. Karlsruhe MillimeterWave Forward Model (KMM) developed for groundbased millimeterwave radiometry at the Forschungszentrum Karlsruhe, Germany [Kopp, 2001]. It was used for the retrieval of ozone volume mixing ratio profiles from measurements of a 142 GHz radiometer and for the retrieval of ozone, ClO, HNO_{3} and N_{2}O profiles from measurements of the 268–280 GHz radiometer of the Forschungszentrum Karlsruhe. Since winter 2001/2002, the model has also been used for profile retrieval of the 200–228 GHz radiometer of the Swedish Institute of Space Physics (Institutet för Rymdfysik (IRF)) in Kiruna.
[21] 5. Millimeter Wave Atmospheric Emission Simulator (MAES), developed at the Communications Research Laboratory (CRL, now National Institute of Information and Communications Technology (NICT)), Tokyo, Japan (for details see Table 1 and Appendix A). MAES has been applied to data analyses of CRL groundbased millimeterwave radiometers [Ochiai et al., 2001] and to designing of the CRL Balloonborne Superconducting SubmillimeterWave LimbEmission Sounder (BSMILES) [Irimajiri et al., 2002] and space station–borne SMILES [SMILES Mission Team, 2002].
[22] 6. Modular Infrared Atmospheric Radiative Transfer (MIRART) developed at the Remote Sensing Technology Institute of the German Aerospace Center, Deutsches Zentrum für Luft und Raumfahrt (DLR) [Schreier and Schimpf, 2001; Schreier and Böttger, 2003]. It is used, e.g., for data analysis of the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) and for farinfrared heterodyne spectroscopy of the stratosphere.
[23] 7. Microwave Observation Line Estimation and Retrieval Code, Version 5 (MOLIERE/5) developed at the Observatoire de Bordeaux, France [Urban et al., 2004]. MOLIERE/5 is implemented in version 223 of the data processor used for the retrieval of vertical constituent profiles from limb observations of the submillimeter radiometer (SMR) on board the Odin satellite.
[24] 8. SMILES Observation Retrieval Code (SMOCO) developed by CRL (now NICT) in collaboration with Fujitsu FIP Corporation, Tokyo, Japan [SMILES Mission Team, 2002]. The main purpose of this model is to retrieve altitude profiles of molecular concentrations and of temperature from spectra measured by JEM/SMILES. SMOCO is the official retrieval code for the SMILES ground segment system for L1 and L2 processing.
[25] The main features and capabilities of the models are summarized in Table 1. Further relevant details are given in Appendix A.
5. Line Shape Implementation Test (Exercise 0)
 Top of page
 Abstract
 1. Introduction
 2. Basic Equations
 3. Participating Models
 4. Intercomparison Setup
 5. Line Shape Implementation Test (Exercise 0)
 6. Absorption Coefficient Intercomparison
 7. Radiative Transfer Intercomparison
 8. Lessons Learned, Summary
 9. Conclusion
 Appendix A: Relevant Details on the Forward Models
 Acknowledgments
 References
 Supporting Information
[27] The purpose of this exercise is to test the implementation of the Voigt line shape function. More precisely, the prescribed line shape for this exercise was the Voigt line shape with a quadratic prefactor:
[28] This was an arbitrary decision for the intercomparison, not a judgment that this is the best line shape to use. Other reasonable choices would have been the pure Voigt line shape of equation (9), or the hybrid line shape of equation (10). For the low frequency bands, the hybrid line shape would have been a more realistic choice, but it is not supported by most models except ARTS and MIRART. Note that KMM does not support the Voigt line shape, therefore this model could not participate in this exercise.
5.1. Calculations (Exercise 0)
[29] The absorption coefficient was calculated for just one line, the ozone line at 110.83 GHz, but for various pressure levels corresponding to altitudes between 0 and 55 km. Spectroscopic parameters were taken from the HITRAN line catalog. Two sets of calculations were carried out: (1) for constant temperature T = 296 K, chosen because the HITRAN line catalog provides line intensities for this temperature and (2) for constant temperature T = 250 K, which corresponds roughly to temperatures in the lower stratosphere, in order to test the implementation of the temperature dependence of the line strength (see equation (5)).
[30] Figure 1 shows the root mean square of the relative deviation of each model from ARTS for the two sets of calculations as a function of altitude. This is defined in the following way: Let α_{ARTS}(ν_{i}) and α_{other}(ν_{i}) be the absorption coefficient at frequency ν_{i}, calculated by ARTS and by another model, respectively; the frequency grid, {ν_{i}}, has N_{ν} elements in the given frequency band. The relative deviation of the other model from ARTS is
Note that here and throughout this study, ARTS was consistently chosen as the reference model just for the sake of convenience. Then the root mean square (RMS) of the relative deviation over the frequency band is
Although the actual vertical coordinate used in all calculations has been pressure, here and for all further plots, we always convert it into altitude which is a more intuitive quantity and therefore more suitable for discussion. The full results (i.e., the calculated absorption coefficient from each model as a function of frequency as well as its relative deviation from ARTS) for some specific altitudes are given in Figures 2 and 3.
5.2. Discussion of Results (Exercise 0)
[31] ARTS, EORC model, SMOCO and MAES are almost identical, regarding both the values of the absorption coefficients and the line shapes; the root mean square of their relative deviation is below 0.1%. The same applies for MIRART at 296 K. The offset by 0.5% (in RMS) of MIRART in the calculation for 250 K (Figure 1 (right panel) and Figure 3) is caused by a different temperature conversion scheme of the line strength. MOLIERE/5 deviates (in RMS) by about 0.2%. In the line wings, it is below ARTS, SMOCO and EORC model with an almost constant offset of about 0.2% for all altitudes, but near the line center, it is above them. It was identified that this is caused by the intercomparison setup: MOLIERE/5 uses a slightly different line width since half widths are specified in MHz/Torr (Verdandi line catalog, cf. Appendix A) whereas HITRAN half widths are provided in cm^{−1}/atm. BEAM deviates by 1% to 1.5% (Figures 1–3); the line wings are higher and the line center is lower than the other models. This was caused by a unit conversion error of 1.3% in the line broadening coefficient that was unfortunately discovered too late for correction.
7. Radiative Transfer Intercomparison
 Top of page
 Abstract
 1. Introduction
 2. Basic Equations
 3. Participating Models
 4. Intercomparison Setup
 5. Line Shape Implementation Test (Exercise 0)
 6. Absorption Coefficient Intercomparison
 7. Radiative Transfer Intercomparison
 8. Lessons Learned, Summary
 9. Conclusion
 Appendix A: Relevant Details on the Forward Models
 Acknowledgments
 References
 Supporting Information
[49] The radiative transfer intercomparison was carried out for checking the implementation (exercise 3) and inspecting the variability (spread) among the models when input parameters were free (exercise 4). For each exercise the calculations were performed for three different configurations that correspond to three typical sensor types in atmospheric sounding: (1) a downlooking sensor like Advanced Microwave Sounding UnitB (AMSUB) [Vangasse et al., 1995], (2) a limblooking sensor like Millimeterwave Acquisitions for Stratosphere/Troposphere Exchange Research (MASTER) [Reburn et al., 2000], and (3) an uplooking sensor like RAM [Langer et al., 1996]. For each configuration and exercise, specific input was provided.
[50] In order to simulate the effect of the sensor, the characteristics of (1) the antenna, (2) the radiometer (particularly the mixer and receiver), and (3) the spectrometer were specified: The antenna pattern, the sideband ratio, and the spectrometer's channel response functions.
[51] The characteristics of the downlooking sensor were chosen to simulate AMSUB: The AMSUB channel characteristics are given in Table 5. The sensor was assumed to have a perfect antenna (i.e., the antenna pattern is a delta function), and to be a perfect double sideband receiver (both sidebands have equal weight). The spectrometer was assumed to have a perfect rectangular response function with a width equal to the bandwidth of the passband corresponding to each channel. The viewing angle, by which we shall always mean the zenith angle of the sensor's pointing direction, ranges from 130° to 180° (nadirlooking), in steps of 1°. The platform altitude was assumed to be 833 km, the ground temperature 271 K and the ground surface emissivity 1.0.
Table 5. AMSUB Channel CharacteristicsChannel  Center Frequency, GHz  Bandwidth of Passbands, MHz 

16  89.0 ± 0.9  1000 
17  150.0 ± 0.9  1000 
18  183.31 ± 0.9  500 
19  183.31 ± 3.0  1000 
20  183.31 ± 7.0  2000 
[52] The characteristics of the limblooking sensor were chosen as follows: The simulated antenna is assumed to have a Gaussian pattern, with a width of the main beam (full width at half maximum (FWHM) of the Gaussian function) of 0.07°. A perfect single sideband sensor was assumed, and a spectrometer where all 350 channels have the same Gaussian response function with a FWHM of 20 MHz, covering a frequency range from 498.5–506.25 GHz. The assumed platform altitude was 800 km, the tangent altitude range is 60–10 km in steps of 2 km. Surface temperature of the ground was assumed to be 272 K, ground surface emissivity 1.0.
[53] The characteristics of the uplooking sensor were chosen as follows: The sensor is assumed to have a perfect antenna (pencil beam), and be a perfect single sideband receiver. All 2400 channels of the spectrometer are assumed to have a Gaussian response function with a FWHM of 0.5 MHz, covering the frequency band from 141.58–142.78 GHz (O_{3} absorption line). Viewing (i.e., zenith) angles range from 0° (zenith) to 80°, in steps of 4°. The platform altitude was assumed to be 10 km (as for an airborne uplooking instrument).
7.1. Exercise 3: Radiative Transfer Implementation
[54] The aim of this exercise is to investigate the differences between the models due solely to the numerical solution of the radiative transfer equation (1). The three geometries, limb, up, and down looking, were considered. For each geometry of concern a standard set of absorption coefficient spectra was used as input, calculated by using the HITRAN database, H_{2}O and N_{2} continuum model by Liebe [1989], O_{2} continuum model by Rosenkranz [1993]. The atmospheric scenario, again, was midlatitude winter [Anderson et al., 1986].
[55] For given specifications, the precalculated absorption spectra were used to derive the spectra of pencil beam monochromatic brightness temperature (“monochromatic (pencil beam) spectra”) for a set of viewing directions specific to each geometry, and the spectra as would be recorded by the sensor with given characteristics (antenna pattern, spectrometer response, sideband ratio). Two sets of calculations were performed, one with the input absorption coefficients given on a coarse grid (45 pressure grid points corresponding to altitudes between 0 and 95 km, spaced about 1 to 5 km apart), the other with the input absorption coefficients given on a fine grid (264 pressure grid points corresponding to altitudes between 0 and 95 km, spaced about 160 to 750 m apart). Refraction of the radiation by the atmosphere was not considered.
7.2. Discussion of Results (Exercise 3)
7.2.1. DownLooking (AMSUB Type)
[56] Participating models: ARTS, MAES, MOLIERE/5, MIRART. Monochromatic pencilbeam spectra for the extreme viewing angles of 130° and 180° (nadir) are shown in Figure 12, and the “spectra” as would be recorded by the sensor AMSUB (here just an average over each band), for various viewing angles, are shown in Table 6. In the two window channels (16 and 17), all models are well within less than 1 K of each other. In the three water vapor channels (18 to 20), they are even closer, except for MAES which deviates by up to 4 K. The cause is very likely to be in the radiative transfer calculations, for MAES was very close to ARTS in the line shape implementation test (exercise 0) and the absorption calculation test (exercise 1 and 2). Note that all results shown here are from calculations on the fine grid. The spectra calculated on the coarse grid were not significantly different.
Table 6. Exercise 3, DownLooking Geometry^{a}Zenith Angle, deg  Model 

MAE  MIR  MOL 


Channel 16 
130  −0.04  −0.95  −0.64 
140  −0.02  −1.01  −0.69 
150  −0.02  −1.05  −0.71 
160  −0.01  −1.06  −0.72 
180  −0.01  −1.07  −0.73 

Channel 17 
130  −0.26  −0.74  −0.50 
140  −0.15  −0.84  −0.58 
150  −0.11  −0.89  −0.61 
160  −0.09  −0.92  −0.63 
180  −0.08  −0.94  −0.64 

Channel 18 
130  −3.92  −0.58  −0.07 
140  −3.54  −0.56  −0.05 
150  −3.30  −0.57  −0.04 
160  −3.16  −0.55  −0.04 
180  −3.06  −0.54  −0.05 

Channel 19 
130  −3.70  0.02  −0.08 
140  −3.29  0.01  −0.07 
150  −3.03  −0.00  −0.07 
160  −2.86  0.00  −0.08 
180  −2.74  −0.00  −0.08 

Channel 20 
130  −2.39  −0.06  −0.11 
140  −1.86  −0.15  −0.16 
150  −1.56  −0.22  −0.19 
160  −1.38  −0.25  −0.22 
180  −1.26  −0.29  −0.24 
7.2.2. LimbLooking (Master Type)
[57] Participating models in this exercise are ARTS, EORC, MAES, MIRART, MOLIERE/5 and SMOCO.
7.2.2.1. Monochromatic PencilBeam Spectra
[58] Figure 13 displays the root mean square of the absolute deviation from ARTS calculations as a function of tangent altitude. Figure 14 shows the brightness temperature, and the absolute deviation from ARTS for two particular tangent altitudes (16 km and 46 km).
[59] ARTS and MOLIERE/5 almost exactly match (difference less than 0.02 K). SMOCO results are also close to ARTS results. The only notable deviation appears at only one altitude around 11 km; the deviation from ARTS at other altitudes is less than 0.08 K. The EORC model and MIRART deviate by at most 0.2 K (at 11 km), but less than 0.01 K (EORC model) and 0.1 K (MIRART) at altitudes above 25 km. MAES shows a noteworthy deviation of about 0.7 K only at the lowest altitudes; otherwise, it is within 0.1 K of ARTS. Note that in the used atmospheric scenario (midlatitude winter from AFGL data base, see section 6.1), the sharp tropopause is at about 10.5 km, which explains the large deviations at 11 km.
7.2.2.2. Spectra As Would Be Recorded by the Sensor
[60] Figure 15 displays the root mean square of the absolute deviation from ARTS as a function of tangent altitude. Figure 16 shows the brightness temperature and the absolute difference for two tangent altitudes (14 km and 46 km). The agreement between all models except MIRART at low altitudes is rather good, with differences below 0.1 K, up to tangent altitudes of 30 km. Above 30 km the deviation of all the models from ARTS and EORC model is increasing with increasing altitude (Figure 15), MAES, MOLIERE/5, and SMOCO reaching a value of about 0.5 K at altitudes of 50 km. MIRART deviates slightly more, up to 1.3 K at 40 km, and 3 K at the lowest altitudes. Investigating the deviation as a function of frequency, we found a maximum of 15 K for MIRART at only a few grid points resulting from the use of a different frequency grid internally in MIRART. The deviation of MIRART at 14 km (Figure 16, left plot) is probably caused by the different numerical quadrature scheme MIRART uses (see Appendix A) for calculating the radiative transfer, i.e., the Schwarzschild equation; similar deviations have been found between results calculated with just one model, MIRART, but using different quadrature schemes.
[61] Apart from that, MIRART matches well as is seen from the root mean square deviation mentioned above. In this sense the root mean square deviation is a better measure for the overall agreement of two models than the maximum deviation that is possibly only found at a few frequency grid points.
7.2.3. UpLooking (RAM Type)
[62] The models participating in this exercise are ARTS, KMM, MAES, MIRART and MOLIERE/5. Figure 17 shows the brightness temperature and the absolute difference with respect to ARTS for two particular viewing angles (0° = zenith, 80°); Figure 18 shows the root mean square of the absolute deviation of the monochromatic pencilbeam spectra from ARTS as a function of viewing angle, i.e., zenith angle, and Figure 19 shows the root mean square of the absolute deviation of the spectra as would be recorded by the sensor (RAM), as a function of viewing angle.
[63] All the participating models agree very well for all viewing angles. The differences from the reference model ARTS are very small and mostly at the line centers. As a general feature, the deviation from ARTS increases with increasing viewing angle (or, in other words, ARTS deviates from the other models with increasing viewing angle). However, the deviation is generally below 0.2 K. The simulations also show that maximum difference between the models occurs close to the line center and then diminishes toward the line wings.
7.3. Exercise 4: Model Differences
[64] The aim of this exercise is to inspect the variability (spread) among the models when they use their standard inputs: The radiative transfer calculations were carried out for given atmospheric conditions corresponding to the midlatitude winter [Anderson et al., 1986], and for given sensor characteristics, but all other parameters (spectroscopic data, line shape, line selection, continuum absorption model) were not fixed. As in exercise 2, the spread of the results among the models gives a rough idea about the discrepancy between models under realistic conditions.
[65] The comparison was carried out for all three configurations mentioned above (exercise 3), i.e., AMSUB type (downlooking), MASTER type (limblooking), and RAM type (uplooking) with the same sensor characteristics as in exercise 3. For a given set of viewing directions, the spectra as they would be recorded by the sensors were calculated. In contrast to exercise 3, refraction was to be taken into account.
[66] The calculations with BEAM, EORC, KMM, and SMOCO used the same setup as in exercise 2 (see section 6.5, Table 4). MAES used the same setup except for a different threshold altitude for the switch from Lorentz to Voigt line shape: The threshold altitude was set to the altitude where the pressure broadening width γ_{L} becomes twice the Doppler broadening width γ_{D}. The Lorentz line shape function is used at altitudes below the threshold.
[67] ARTS used the same setup as in exercise 2 except for the continuum model for N_{2} for up and downlooking geometry: Here, the model by Rosenkranz [Janssen 1993, chapter 2] was used.
[68] The setup for MIRART: HITRAN line catalog; Voigt line shape function with a prefactor of (ν/ν_{0})^{2} and a linewing cutoff at 10 cm^{−1}. For H_{2}O lines: a cutoff at 25 cm^{−1} and subtraction of F_{Voigt}(25 cm^{−1})) was used, appropriate for the CKD continuum absorption model (cf. Appendix A).
[69] The setup of MOLIERE/5 is the same as in exercise 2, except for different selection criteria of the absorption lines included in the calculations: For the limblooking (MASTERE type) configuration, all lines between 477 and 527 GHz having a minimum contribution of 10 mK to the target interval (496.9 to 507.1 GHz) were selected; cosmic background was taken into account. For the downlooking (AMSUB type) configuration (three separate frequency ranges, see Table 5), lines between 69 and 89 GHz, between 130 and 150 GHz, and between 163.31 and 183.31 GHz having 10 mK sensitivity with respect to target intervals (87.6 to 88.6 GHz, 148.6 to 149.66 GHz, and 175.31 to 182.66 GHz, respectively, and corresponding image bands) were selected; the ground was treated as a blackbody at the temperature of the lowest atmospheric layer. For the uplooking (RAM type) configuration, lines between 122.175 and 162.175 GHz having 10 mK sensitivity with respect to target interval (141.57 to 142.78 GHz) and the corresponding image band were selected; cosmic background was taken into account.
7.4. Discussion of Results (Exercise 4)
7.4.1. DownLooking
[70] Data from ARTS, MAES, MIRART and MOLIERE/5 are available in this exercise. The absolute deviation of the results from ARTS is shown in Table 7. The highest deviations of about 4 K occur at channel 19 and 20 for MAES, and at channel 16 for MOLIERE/5. Deviations are the larger, the more offnadir the viewing angle (i.e., the longer the path through the atmosphere). They are probably caused by differences in the continuum absorption modeling.
Table 7. Exercise 4, DownLooking Geometry^{a}Zenith Angle, deg  Model 

MAE  MIR  MOL 


Channel 16 
130  0.80  −5.76  −4.72 
180  0.89  −3.31  −2.51 

Channel 17 
130  −0.29  −3.81  −2.65 
180  0.37  −2.32  −1.39 

Channel 18 
130  −3.71  −0.20  −0.42 
180  −2.71  −0.04  −0.13 

Channel 19 
130  −4.25  −0.90  −1.70 
180  −3.10  −0.63  −1.20 

Channel 20 
130  −3.32  −2.38  −2.46 
180  −1.74  −1.73  −1.58 
7.4.2. LimbLooking
[71] The models which participated in this exercise are ARTS, EORC model, MAES, MIRART, MOLIERE/5 and SMOCO. The RMS deviations of the different models from ARTS are shown in Figure 20. The results for tangent altitudes of 12 km and 52 km are shown in Figure 21.
[72] At low altitudes the smallest deviations are found in the line centers and the largest deviations are found in the wings. This can be mainly explained by the different continuum absorption models which have been used to calculate the absorption coefficients. Absolute deviations are around 20 K. MOLIERE/5 is 20 K higher than ARTS, MIRART is 20 K lower. EORC model and MAES and SMOCO are very similar.
[73] At higher altitudes both a shift in the line center frequency and a difference in the line intensities are seen. These are explained by the different spectroscopic data which have been used. For example, at 22 km, in most parts of the spectrum, MOLIERE/5 is about 5 K higher than ARTS, whereas MIRART is about 3 K lower than ARTS. The biggest deviation of about 40 K (MAES) can be seen at 52 km at about 500.44 GHz (Figure 21, right panel). It is probably caused by a shift of the line found at this frequency: The line is so narrow that it will be sampled differently by the frequency grid, resulting in a different peak value. Since the spike is very narrow, it does not have much weight in the root mean square plot (Figure 20). Note that, for limblooking geometry, neither differences in continuum absorption modeling nor frequency shifts cause much harm in retrieval, as explained below (section 8.6). However, discrepancies coming from the radiative transfer calculations or the instrument model can cause large systematic retrieval errors.
7.4.3. UpLooking
[74] The models participating in this exercise are ARTS, KMM, MAES, MIRART, and MOLIERE/5. The results for viewing angles of 0° (i.e., zenith) and 60° are shown in Figure 22.
[75] The largest deviation of several K from ARTS is shown by MAES at a viewing angle of 60° where a shift in the line center can be seen (Figure 22, right panel). The different line center frequency is explained by the different line catalogs used by different models. The same feature is observed for MOLIERE/5: a shift in the line center frequency. In addition, MOLIERE/5 is about 3 K higher in the far wings. The deviation in the line wings can be explained by the different continuum absorption models, (N_{2}, O_{2}, and H_{2}O) and the line selection of the far outofband lines. Apart from that, all differences are of the order of 1 K.