kCARTA : A fast pseudo line-by-line radiative transfer algorithm with analytic Jacobians, fluxes, Non-Local Thermodynamic Equilibrium and scattering for the infrared

A fast pseudo-monochromatic radiative transfer package using a Singular Value Decomposition (SVD) compressed atmospheric optical depth database has been developed, primarily for use with hyperspectral sounding instruments. The package has been tested extensively for clear sky radiative transfer cases, using field campaign data and satellite instrument data. The current database uses HITRAN 2016 line parameters and is primed for use in the spectral region spanning 605 cm−1 to 2830 cm−1 (with a point spacing of 0.0025 cm−1), but can easily be extended to other regions. The clear sky radiative trans5 fer model computes the background thermal radiation quickly and accurately using a layer-varying diffusivity angle at each spectral point; it takes less than 20 seconds (on a 2.8 GHz core using 4 threads) to complete a radiance calculation spanning the infrared. The code can also compute Non Local Thermodynamic Equilibrium effects for the 4 μm CO2 region, as well as analytic temperature, gas and surface jacobians. The package also includes flux and heating rate calculations, and an interface to a scattering model. 10

The bin of interest is at (-0.5,+0.5) cm −1 . Lineshapes whose line centers are within this bin (red) and within ± 1cm −1 of the bin edge (blue) are computed using high spectral resolution; line centers that are further out (green) have the lineshapes computed at medium resolution and then interpolated to a higher resolution; line centers even further away (not shown) are computed at coarse resolution. The black curve is the sum over all the line contributions within that bin.
The above steps are followed for almost all molecules. Modifications to the above steps are needed for water vapor (which 90 is separated into the traditional "basement" plus "continuum" contributions (Clough et al., 1980(Clough et al., , 1989) and CO 2 in the 4 and 15 µm region which needs line-mixing lineshapes (Strow and Pine, 1988;Tobin et al., 1996;Niro et al., 2005;Lamouroux et al., 2015). Other molecules have optical depths that are more easily modeled with the Van Huber lineshape, though recently the infrared absorption due to CH 4 has been modeled using line mixing (Tran et al., 2006). The UMBC-LBL optical depth computation for water vapor should be robust at all frequencies, and allows the addition of water continuum models such as 95 the recent MT-CKD 3.2 coefficients (Mlawer et al., 2012). Spectra from UMBC-LBL have been extensively compared against optical depths computed by models such as Line-by-line Radiative Transfer Model (LBLRTM) (Clough et al., 1992(Clough et al., , 2005 and the General line-by-line Atmospheric Transmittance and Radiance model (GENLN2) (Edwards, 1992). For example the optical depths of O 3 in the 10 µm region more closely resemble the reference monochromatic code MonoRTM than the LBLRTM code, which uses an accelerated algorithm for calculating the Voigt function (Mlawer, 2016).

kCompressed database
When applied toward any realistic Earth atmosphere simulation for an observing instrument, the UMBC-LBL calculations described above become impractically slow as they need to be performed for multiple gases in the atmosphere, over ∼ 100 atmospheric layers and encompassing a wide spectral range.
UMBC-LBL is therefore primarily used to generate an uncompressed database of look-up tables as described below. For 105 each gas other than water vapor, the spectra are computed using the US Standard Atmosphere temperature profile, as well as These 10000×100×11 optical depths intervals are then compressed using Singular Value Decomposition (SVD) to produce the kCompressed Database. Each compressed file will have a matrix of basis vectors B (size 10000 × N ), and compressed 115 optical depths D (size N × 100 × 11), where N is the number of significant singular vectors found. The prime denotes the compression worked more efficiently when the optical depths were scaled to the (1/4) power (Strow et al., 1998;Rodgers, 2000).
The self broadening of water is accounted for by generating monochromatic lookup tables for the reference water amount, multiplied by 0.1, 1.0, 3.3, 6.7 and 10.0 at the eleven temperature profiles specified above, meaning D for water will have an 120 extra dimension of length 5. Note that for the infrared we treat the HDO isotope (HITRAN isotope 4) as a separate gas from the rest of the water vapor isotopes.
The compressed optical depths D vary smoothly in pressure, meaning the user is not limited to only using the 100 AIRS layers. For an arbitrary pressure layering, the look-up tables are uncompressed using spline or linear interpolation in temperature and pressure, and scaled in gas absorber amount. Temperature interpolation of matrix D for an AIRS 100 layer atmosphere 125 therefore results in a matrix D of size N ×100, and the final optical depths (of size 10000×100) are computed using (BD ) 4 .
Both the spline and linear interpolations allow easy computation of the analytic temperature derivatives, from which kCARTA can rapidly compute analytic Jacobians (see Section 6). The cumulative optical depth for each layer in the atmosphere is obtained by a weighted sum of the individual gas optical depths, with accuracy limited by that of the compressed database (Strow et al., 1998). The interested reader is referred to (Vincent and Dudhia, 2017) for a further discussion of other RTAs that use 130 compressed databases.
The most recent kCompressed database uses line parameters from the HITRAN 2016 database (Rothman et al., 2013;Gordon et al., 2017), which together with the UMBC-LBL lineshape models, determine the accuracy of the spectral optical depths in this database. UMBC-LBL CO 2 line-mixing calculations use parameters that were derived a few years ago. Newer line-mixing models exist and we now use optical depths computed using LBLRTM v12.8 together with the line parameter database file 135 based on HITRAN 2012 (aer_v_3.6), and (a) CO 2 line mixing by (Lamouroux et al., 2010(Lamouroux et al., , 2015) and (b) CH 4 line mixing by (Tran et al., 2006).
In addition complete kCompressed databases for the IR using optical depths only from HITRAN 2012, LBLRTM v12.4 code and from GEISA 2015 (Husson et al., 2015) have been generated for comparison purposes. At compile time we usually point kCARTA to the HITRAN 2016 kCompressed database made by UMBC-LBL, but at run time we have switches that easily allow 140 us to swap in for example the CO 2 and CH 4 tables generated from LBLRTM.
The original lookup tables for the thermal infrared occupy hundreds of gigabytes, while the compressed monochromatic absorption coefficients are a much more manageable 824 megabytes (218 megabytes (water+HDO) + 76 megabytes (CO2) + 530 megabytes (about 40 other molecular and 30 cross section gases)). A general overview of some of the factors involved in compressing look-up tables for use in speeding up line-by-line codes is found in (Vincent and Dudhia, 2017), while more details 145 about the detailed testing and generation of the kCARTA SVD compressed database are found in (Strow et al., 1998). Appendix B discusses the extension of the database to span 15 cm −1 to 44000 cm −1 , though we note that kCARTA lacks built-in accurate scattering calculations in the shorter wavelengths. In order to resolve the narrow doppler lines at the top-of-atmosphere, the resolution of the spectral regions in Appendix B is adjusted according to δν ν 0 (T /m).
The default kCARTA mode is to use all 42 molecular gases in the HITRAN database, together with about 30 cross-section 150 gases. If the user does not provide the profiles for any of these gases, kCARTA uses the US Standard profile for that gas.
The user can also choose to only use a selected number of specified gases. While running kCARTA, the user can then define different sets of mixed paths, where some of the gases are either turned off or the entire profile is multiplied by a constant number, which is very useful when for example we want to include only certain gases when we parametrize optical depths for SARTA.

155
3 kCARTA Clear sky radiative transfer algorithm As a stream of radiation propagates through a layer, the change in diffuse beam intensity R(ν) in a plane parallel medium is given by the standard Schwartschild equation (Liou, 1980;Goody and Yung, 1989;Edwards, 1992) where µ is the cosine of the viewing angle, k e is the extinction optical depth, ν is the wavenumber and J(ν) is the source 160 function. For a non-scattering "clear sky", the source function is usually the Planck emission B(ν, T ) at the layer temperature T , leading to an equation that can easily be solved for an individual layer. The general solution for a downlooking instrument measuring radiating propagting up through a clear-sky atmosphere can be written in terms of four components : which are the surface, layer emissions, downward thermal and solar terms respectively. In terms of integrals the expressions 165 can be written as (see e.g. (Liou, 1980;Dudhia, 2017 Figure 2. Viewing geometry for the sounders modeled by kCARTA. A is the satellite and point P is being observed by the satellite, while I is the sun where B(ν, T ) is the Planck radiance at temperature T , T s is the skin surface temperature, s , ρ s are the surface emissivity 170 and reflectivity; B (ν) is the solar radiance at TOA, θ is the solar zenith angle; θ is the satellite viewing angle, , τ i (ν, θ) is the transmission at angle θ while τ atm is the total atmospheric transmission.
In what follows we discretize Eqn. 2 so that layer i = 1 is the bottom and i = N (=100) the uppermost, schematically shown in Figure 2 for a clear sky four layer atmosphere, with O being the center of the Earth. A is the satellite while S is the satellite sub-point directly below it. Point P is the ground scene being observed by the satellite (slightly away from nadir), and N is the 175 local normal at P. ∠SAP is the satellite scan angle while ∠APN is the satellite zenith angle θ; ∠NPI is the solar zenith angle θ . Note that as the radiation propagates through the pressure layers from P to H 1 to H 2 to H 3 to H 4 to A, the local angle (between the radiation ray and the local normal at any of the concentric circles) keeps changing due to the spherical geometry of the layers (refraction effects can also be included).
The default mode of kCARTA assumes no variation of layer temperature with optical depth, uses a background thermal dif-180 fusive angle that varies with the layer-to-ground optical depth (instead of a constant value typically assumed to be cos −1 (3/5)) and does ray-tracing to account for the spherical atmospheric layers (but with no density effects). The f90 version of kCARTA allows the layer temperature to vary linearly with optical depth, and to choose alternate ways of computing the background term, which will be discussed in Section 7. The individual contributions to the upwelling radiance are computed as follows.
3.1 Surface emission 185 kCARTA requires the user to supply the spectrally varying emissivity (and surface reflectance). The kCARTA surface emission is given by

Layer emission
The atmospheric absorption and re-emission is modeled as : Layers with negligible absorption (τ i → 1) contribute negligibly to the overall radiance, while those with large optical depths weighting function W i of the layer.

Solar radiation 195
Letting the surface reflectance be denoted by ρ s (ν, θ, φ), then the solar contribution to the TOA radiance is given by Over ocean, if the wind speed and solar and satellite azimuth angles are known, the reflectance can be pre-computed using the Bi-directional Reflectance Distribution Function (BRDF) and input to kCARTA; see for example Appendix C in (Nalli et al., 2016). It is not easy to compute the BRDF over land, and the reflectance could be simply modeled as ρ s (ν) = 1− s(ν) π .
200 Ω = π(r s /d se ) 2 is the solid angle subtended at the earth by the sun, where r e is the radius of the sun and d se is the earthsun distance. The solar radiation incident at the TOA B (ν) comes from data files related to the ATMOS mission (Farmer et al., 1987;Farmer and Norton, 1989), and is modulated by the angle the sun makes with the vertical, cos(θ ) (day-of-year effects are not included in the earth-sun distance).

Background thermal radiation 205
The atmosphere also emits radiation downward, at all angles, in a manner analogous to the upward layer emission just discussed. The total background thermal radiance at the surface is an integral over all (zenith and azimuth) radiance streams propagating from the top-of-atmosphere (set to 2.7 K) to surface. This is time consuming to compute using quadrature, and one approximation is to use a single effective (or diffusivity) angle of θ dif f = cos −1 (3/5) at all layers and wavenumbers : The summation is from top-of-atmosphere to ground, and ρ s is the surface reflectance discussed above. Current sounders have channel radiance accuracy better than 0.2K, so while the above term is much smaller than the surface or upwelling atmospheric emission contributions, it has to be computed accurately. Section 7 includes a detailed discussion of how kCARTA improves the accuracy of this background term by using a look-up table to rapidly compute a spectrally and layer varying diffusive angle.

Top of Atmosphere BTs computed using different databases
For this section three spectral databases were used to compute TOA radiances (converted to BT) using kCARTA. A set of 49 regression profiles typically expected in the Earth atmosphere  were used throughout this paper for this and other studies. The profiles in this set include the US Standard temperature, pressure, and trace gas constituent fields (McClatchey et al., 1972), as well as the Mid-Latitude Summer/Winter, Polar Summer/Winter, Tropical profiles, and a set of 225 extreme and intermediate hot/cold/dry/humid profiles chosen from the Thermodynamic Initial Guess Retrieval (TIGR) database (Achard, 1991) to span the expected variablilty of profiles in the Earth's atmosphere . The results are shown in Figure 3. The HITRAN and GEISA databases are bundled with error indices associated with the individual spectroscopic line parameters.
The uncertainty codes in the HITRAN database (Rothman et al., 2005) are replicated in It is relatively straightforward to use these indices to include the associated uncertainty of any relevant line parameter for 255 most gases, and generate a new compressed database using UMBC-LBL. Exceptions arise because the HITRAN 1986 database edition did not have uncertainties and was populated with zeros, a few of which have not yet been updated (Gordon, 2018). In these cases the uncertainty index is 0 (for the left column of the table) or 0,1,2,3 (for the right part of the table). The value of 0 occurs for example, in many of the line strength uncertainties for the 10 µm O 3 isotopes 1,2; to remedy this we used 3% which is slightly lower than the 4% estimated in (Drouin et al., 2017;Birk et al., 2019). Similarly many of the strong 7.6 µm CH 4 260 lines (isotope 1) are assigned an intensity uncertainty code of 3; to our knowledge there is no other additional information and we used a maximum value of 20% (Gordon, 2018). We also used 0.1 cm −1 , 0.1 cm −1 /atm uncertainties for the line center and pressure shift when the uncertainty index was 0 (Gordon, 2018).
In Figures 4 and 5  strengths and broadening uncertainty indices that need to be updated (Gordon, 2018). A similar calculation where we assumed the uncertainties were independent of each other allowed us to randomize all perturbations to be within 0 and ±X (where X    is the maximum number corresponding to the error indices in Table 4.2); this roughly halves the largest errors shown in these two figures, so they are within ± 1 K in the CH 4 region.

Non Local Thermodynamic Equilibrium computations
During the daytime, incident solar radiation is preferentially absorbed by some CO 2 and O 3 infrared bands, whose kinetic temperature then differs from the rest of the bands or molecules. This leads to enhanced emission by the lines in these bands.
Limb sounders detect NLTE effects in the 15 µm CO 2 bands (and in other molecular bands for example O 3 ) due to the 280 extremely long paths involved, but these are not modeled in the package as kCARTA is designed for nadir sounders.
For a nadir sounder, the most important effects are seen in the CO 2 4 µm (ν 3 ) band. kCARTA includes a computationally intensive line-by-line Non Local Thermodynamic Equilibrium (NLTE) model to calculate the effects for this CO 2 band. The model requires the kinetic temperature profile and NLTE vibrational temperatures of the strong bands in this region, to compute the optical depths and Planck modifiers for the strong NLTE bands and the weaker LTE bands (Edwards et al., 1993(Edwards et al., , 1998; Retrievals of atmospheric profiles (temperature, humidity and trace gases) minimize the differences between observations and calculations, by adjusting the profiles using the linear derivatives (or jacobians) of the radiance with respect to the atmospheric parameters. This section describes the computation of analytic jacobians by kCARTA. For a downward looking instrument, for simplicity consider only the upwelling terms in the radiance equation (atmospheric layer emission and the surface terms).

295
Assuming a nadir satellite viewing angle, the solution to Equation 1 is: Differentiation with respect to the m-layer variable s m , (gas amount or layer temperature s m = q m(g) , T m ) yields where as usual, τ m (ν) = e −km(ν) , τ m→N (ν) = Π N j=m e −kj (ν) . The differentiation yields The individual Jacobian terms ∂km ∂s m(g) are rapidly computed by kCARTA, as follows. The gas amount derivative is simply ∂km ∂q m(g) = km q m(g) (with added complexity for water, to account for self broadening), and the temperature derivative ∂km ∂T is 305 cumulatively obtained while kCARTA is performing the temperature interpolations during the individual gas database uncompression.
The solar and background thermal contributions are also included in the Jacobian calculations. The thermal background Jacobians are computed at cos −1 (3/5) at all levels, for speed. This would lead to slight differences when comparing the Jacobians computed as above to those obtained using finite differences. The Jacobians with respect to the surface temperature 310 and surface emissivity are also computed, as are the weighting functions.

Background thermal and temperature variation in a layer
In this section we take a closer look at the computation of downwelling background thermal radiation, and layer temperature variation.

Background thermal radiation 315
The contribution of downwelling background thermal to top-of-atmosphere upwelling radiances is negligible in regions that are blacked out as the instrument cannot see surface leaving emission. Similarly in layers/spectral regions where there is very little absorption and re-emission, the contribution is negligible as the effective layer emissivity (denoted by ∆τ i (ν) below) goes to zero. The background contribution thus needs to be done most accurately in the window regions (low but finite optical depths) ; depending on the surface reflectance in the window regions, in terms of BT this term contribute as much as 4 K of the 320 total radiance when reflected back up to the top of the atmosphere.
The contribution at the surface by a downwelling radiance stream propagating at angle (θ, φ) through layer i, is given by to-ground optical depths x. This equation can be rewritten as An integral over (θ, φ) would give the contribution from the layer. The total downwelling spectral radiance at the surface would be a sum over all i layers (and the downwelling flux at the surface would be the integral over all wavenumbers).
The integral over the azimuth is straightforward (assuming isotropic radiation), but the integral over the zenith is more 330 complex. Since the reflected background term is much smaller than the surface or atmospheric terms, a single stream at the effective angle θ dif f = cos −1 (3/5) (Liou, 1980) is often used as an approximation, at all layers and wavenumbers.
We have refined the computation as follows. Recall that ∆R(ν) in Equation 12 depends on the layer-to-ground optical depth x. Letting µ = cosθ the integral over the zenith ( The area under the E 3 (x) curve would be the total flux coming all optical depths (0 ≤ x ≤ ∞); over 77% of this area comes from the range 0 ≤ x ≤ 1.

335
Applying the Mean Value Theorem for Integrals (MVTI) to E 3 (x), we can write Eq. 12 in terms of two effective diffusive with the effective angles varying as a function of the layer to ground space optical depth of that layer, and the layer immediately 340 below it. Numerical solutions to the MVTI show that when x → 0 then µ d → 0.5 (or θ d → 60 • ). Similarly as x → ∞ then θ d → 0 • , but this optically thick atmosphere means an instrument observing from the TOA cannot see the surface, so we use a lower limit (of 30 • ) for the diffusive angle. Finally when x = 1.00 we find the special case µ d = 0.59274 (3/5). For "optically thin" regions, the layers closest to the ground contribute most to R th (ν).
With today's high speed computers, kCARTA uses an effective diffusive angle θ d tabulated as a function of layer to ground 345 optical depth x, as follows. For each 25 cm −1 interval spanning the infared the layer L above which cos −1 (3/5) can be safely used was determined; below this layer, the lookup table is used. The table has higher resolution for x ≤ 0.1 and becomes more coarse as x increases, with the effective diffusive angle cutoff at 30 • when the optical depths are larger than about 15.
We have tested this method of computing the background thermal against both 20 point Gauss-Legendre quadrature and the 3 point exponential Gauss-quadrature (used by LBLRTM flux computations), and found the method to very accurate and fast, 350 both in terms of the downwelling flux at the surface, and also the final TOA computed radiance, even when the emissivity is as low as 0.8 (which means a significant contribution from the reflected thermal). At this low emissivity value, the constant acos(3/5) diffusivity angle model produces final TOA BT which differ from the Gauss-Legendre model by as much as 1.3 K (for the tropical profile) at for example 900 cm −1 , while the exponential quadrature and our model have errors smaller than 0.005 K.

355
7.2 Variation of layer temperature with optical depth LBLRTM (Clough et al., 1992(Clough et al., , 2005) has been extensively tested and shown to be very accurate, in its computation of optical depths, radiances and fluxes. In the computation of radiances, the main difference between the kCARTA and LBLRTM codes is that for each spectral point, the former defaults to a "constant in τ " layer temperature variation, while the latter uses a "linear in τ " layer temperature variation. Here we summarize the relevant equations, and briefly discuss the computed differences using 360 kCARTA. For an individual layer, with lower and upper boundary temperatures T L , T U , the "linear in τ " approximation leads to the following expression for the radiance at the top of the layer (re-written from Equation 13 in (Clough et al., 1992)) where the optical depth τ includes the view angle τ = τ layer /cos(θ) and transmission T = exp(−τ ). I 0 (ν) is the radiation incident at the bottom of the layer, B av (ν) is the Planck radiance corresponding to the average layer temperature, while B u (ν) 365 is the Planck radiance corresponding to the upper boundary. For large τ , T → 0 and I(ν) → B u (ν). For small τ → 0 the expression can be further expanded as follows Comparing to the top of layer radiance in the "constant in τ " model, 370 one sees the expressions are identical if there is no temperature variation ie (B u (ν) = B av (ν)). The default kCARTA model layers are approximately 0.25 km thick (or a temperature spread of about 1.5 K for a 6K/km lapse rate) at the bottom of the atmosphere, and about 2 km thick in the stratosphere (a temperature difference of 10 K). However the gaseous absorption in these upper layers is typically negligible, except deep inside the strongly absorbing 15 µm and 4 µm CO 2 bands. Differences in BTs computed using the "constant" versus "linear" models will be expected to be greatest in these regions. The US Standard,

375
Tropical, Mid Latitude and Polar Summer/Winter profiles were used to evaluate the differences between the "constant" versus At 0.0025 cm −1 resolution the kCARTA and RRTM-LW heating rates differ by less than 0.2 K/day on average for altitudes below 40 km, but at higher altitudes the differences were much larger, and could be 1.5 K/day. This was attributed to the default spectral resolution of kCARTA in the 15 µm region. To test this, we generated a database of resolution 0.0005 cm −1 spanning 400 605-1205 cm −1 for H 2 O, CO 2 and O 3 which are by far the dominant absorbers in this spectral region, especially at higher altitudes. This significantly improved the results, with heating rate differences dropping to about 0.2 K/day almost everywhere. Figure 6 shows the heating rate differences between kCARTA and RRTM. The left panel shows differences between kCARTA and RRTM, with the mean and standard deviation being solid and dashed respectively; the right panel shows mean calculations as a function of height. The blue curves were done at default 0.0025 cm −1 resolution while the red curves were done at higher 405 0.0005 cm −1 resolution. While the agreement is better than 0.05 K/day in the lowest 30 km, Figure 6 shows the heating rates using the low resolution begin to differ noticeably above 45 km (blue curve); conversely the high resolution heating rates (red curves) are within 0.2 K/day till about 65 km. 9 Scattering package included with f90 kCARTA The daily coverage of hyperspectral sounders provides us with information pertaining to the effects of cloud contamination on measured radiances. Ignoring these effects can negatively impact retrievals used for weather forecasting and climate modeling. scheme (Chou et al., 1999) has been interfaced into f90 kCARTA (see Appendix C). The implementation allows kCARTA to compute radiances very quickly in the presence of scattering media such as clouds or aerosol. For a given scattering species and assumed particle shape and distribution, the extinction coefficients, single scattering albedo and asymmetry parameters needed by the scattering code are stored in tables as a function of wavenumber and effective particle size (for a particle amount of 1 g/m 2 ). In addition one can easily use kCARTA to output monochromatic optical depths that can be imported into well 420 known scattering packages. More details about PCLSAM and our cloud representation models are found in Appendix C.

Conclusions
We have described the details of a very fast and accurate pseudo-monochromatic code, optimized for the thermal infrared spectral region used by operational weather sounders for thermodynamic retrievals. It is much faster than line-by-line codes, and the accuracy of its spectroscopic database has been extensively compared against GENLN2 and more recently to LBLRTM. 425 Updating the spectroscopy in a selected wavenumber region for a specified gas is as simple as updating the relevant file(s) in the database : for example, our custom UMBC-LBL enables us to re-build entire databases within weeks of the latest HITRAN release.
The computed clear sky radiances includes a fast, accurate estimate of the background thermal radiation. Analytic temperature and gas amount Jacobians can be rapidly computed. Early in the AIRS mission, comparisons of AIRS observations against 430 by kCARTA. A number of Matlab based readers can then be used to further process the kCARTA output as needed. More information is found at http://asl.umbc.edu/pub/packages/ kcarta.html.
Appendix B: Available spectral regions and f90 kCARTA features 465 The UMBC-LBL line-by-line code has been used to generate optical depths in the spectral regions seen in Table B1. The 605-2830 cm −1 band is marked with an asterisk, since our work focuses on this spectral region. The current database in this spectral region uses lineshape parameters from HITRAN 2016. The Van Vleck and Huber lineshape is used for all HITRAN molecules from ozone onwards; water vapor uses the "without basement" plus MT-CKD 3.2, and CO 2 ,CH 4 use line-mixing optical depths generated from LBLRTM v12.8. Note that in the important 4.3 µm temperature sounding region, the f90 version 470 can also include the N 2 /H 2 O and N 2 /CO 2 Collision Induced Absorption (CIA) effects modeled in (Hartmann et al., 2018;Tran et al., 2018), which depend on CO 2 ,H 2 O and N 2 absorber amounts.
A clear-sky radiance calculation in the infrared takes about 20 seconds, using a 2.8 GHz 32 core multi-threading Intel machine. The run-time goes to 120 seconds if Jacobians are also computed (for 9 gases). A full radiance calculation from 15 to 44000 cm −1 takes less than 5 minutes.
475 Table B2 lists a number of the features of kCARTA, with the ones marked by a asterisk only available in the f90 version.
Note that the tables defaults to describing the spectroscopy for the infrared region.  , 2010), to modeling the effects of clouds on sounder data (Matricardi, 2005;Vidot et al., 2015). This scattering model changes the extinction optical depth from k(ν) to a parametrized number k scatterer ef f.extinction (ν) (Chou et al., 1999), and is designed for cases of the single scattering albedo ω being much less than 1, such as in the thermal infrared, where ω for cirrus and water droplets and aerosols is typically on the order of 0.5.
Since k scatterer ef f.extinction (ν) is now effectively the absorption due to the cloud or aerosol, for each layer i that contains scatterers 485 we replace the gas absorption optical depth with the total absorption optical depth k total (ν) = k gases atm (ν) + k scatterer ef f.extinction (ν) where (Chou et al., 1999) k scatterer ef f.extinction (ν) = k scatterer extinction (ν) × (1 − ω(ν))(1 − b(ν))) and the backscatter b(ν) = (1 − g(ν))/2. Using this for every layer containing scatterers, the radiative transfer algorithm is now the same as clear sky radiative transfer, with very little speed penalty. This allows for non unity fractions for up to two clouds, so that radiative transfer then assumes the total radiance is a sum of four radiance streams (clear, cloudy 1, cloud 2 and the cloud overlap) weighted appropriately : r(ν) = c overlap r (12) (ν) + c 1 r (1) (ν) + c 2 r (2) (ν) + f clr r clr (ν) With this model kCARTA allows the user to specify upto two types of scatterers in the atmosphere (ice/water, ice/dust, 495 water/dust or even ice/ice, water/water, dust/dust); the two scatterers are placed in separate "slabs" which occupy complete AIRS layers and are specified by cloud top/bottom pressure (in millibars), cloud amount (in g/m2), cloud effective particle diameter (in µm). After the computations are done, all five radiances are output when two clouds are defined (overlap, two clouds separately, clear, and the weighted sum), and three radiances if only one cloud is defined (one cloud, clear, weighted sum).

500
Analytic jacobians for temperature, gas amounts, and cloud micro-physical parameters (effective size and loading) can also be computed, as can be fluxes and associated heating rates, though the slab boundaries could introduce spikes in the heating rate profiles.