Answers to rewiew by K. Gierens

Thank you very much for your useful comments. Please find below the point-to-point reply. In addition to your suggestions I also had to remove a sentence in the "code availability" section because it was not possible to submit the code as supplement to the paper as it is too large (only 50 MBytes are allowed). It is now only available from the libRadtran website, not as supplementary data.

Point-to-point reply line 105: aircraft corrected.

115: does the inclusion of Raman scattering affect the accuracy or rather raise the accuracy? Yes, this is right. Replaced "affects" by "improves"

125: new data on optical properties... corrected.

134: unclear. Do you mean: can be used to simulate the effect on radiation of variability in size distributions?

Changed the sentence to: "libradtran has also been rewritten to allow simulations with an arbitrary number of cloud and aerosol types - which can e.g. be used to take into account detailed particle size distributions (number densities for discretized size bins) that can be different in each layer. In earlier versions it was only possible to take into account parameterized size distributions such as gamma or log-normal distributions." Hope that it is now clear what we mean.

302 ff: In contrast to ... neither ... nor is it capable of ... Improved the sentence as suggested.

316: at the surface Corrected

327 ff: what does it mean: the atmosphere has to have a vertical resolution? Please reformulate. Reformulated as follows: "Note that in order to obtain a smooth signal, a fine vertical resolution of the model atmosphere is required. The vertical resolution should correspond to the range width of the simulated lidar instrument."

351: "Mystic is a physically correct model which does not include any approximations." This is a strong and bold statement! If you think, you need such a strong statement I would prefer to see some background information. In which way is it physically correct (what do you exactly mean with "physically correct"?). How sure are you that a Monte Carlo Simulation (that must necessarily be terminated somehow at 10^n photons) is NOT an approximation? I see, that we are entering philosophical discussions here, but strong statements usually evoke strong reactions. Some lines later it already sounds more modest, when speak of "uncertainty range". And again later, "the accuracy of MYSTIC depends only on...". I agree with this wording, but to my view it contradicts your first statement. Yes, I agree, the statement is too strong. What I meant is that it does not include approximations such as the cut-off of Legendre and Fourier series. This kind of approximations are included in the other solvers. The big advantage of MYSTIC is that the error (standard deviation) is known and the accuracy can be improved by simply running more photons. The error of other solvers can not be calculated and only be assessed by comparison to MYSTIC. I removed the statement in the beginning because I think it is not needed.

357: in 3D model domains. done

363: not accurate enough done

Table 2: correct word-wrap. Included some \newline to improve word-wrap.

Eq. 4 and text following it: is this effective radius r_eff indeed what it usually is in radiative transfer or is it just a parameter, unfortunately termed effective radius? Usually the effective radius can be computed as the ratio of two moments of the size distribution. If this is the r_eff in your eq. 4, then there is perhaps an inconsistency, because I would be very surprised if the ratio of these moments (mean volume divided by mean cross section, times a constant, see your eq. A3) would just result in r_eff, when r_eff is used in the definition of the gamma function and my surprise would even grow when this happens although you cut-off the integrals at arbitrarily chosen limits of 0.02 and 8 times r_eff. Please clarify.

We mean indeed the effective radius (ratio of the 3rd and the 2nd moment of the size distribution n(r) r^3 dr / int n(r) r^2 dr).

It may easily be calculated analytically for the size distribution using the following formulas: integral int_0^\infty x^(z-1) exp (-mu*x) = gamma(z)/mu^z, where gamma is the gamma function

A property of the gamma function is: gamma(x+1)=x*gamma(x)

With these formulas you find that the 3rd moment divided by the 2nd moment of the size distribution in Eq. 4 is exactly the effective radius.

You are right that the cut-off values introduce an inconsistency, however the deviation from the real effective radius is tiny for the mentioned cut-off values since the gamma distribution is narrow. We have tested the deviation and found that the real and prescribed reff's agree to 12 digits or more, for reff=1 micron as well as for reff=25 micron. So I think the term effective radius is absolutely correct here.

( You may use a simple gawk script and test this numerically: gawk 'BEGIN{reff=25;veff=0.1;alpha=1/veff-3;dr=0.1;for (r=0.02*reff;r<=8*reff;r+=dr) {n=r^alpha*exp(-r/reff/veff);sum3+=n*r*r*r*dr;sum2+=n*r*r*dr};printf("%.12f %.12f\n",reff,sum3/sum2)}' )

783: and that will be written... done Fig. 7, bottom: the lines are a bit flimsy, the colours can hardly be identified. Can you please improve.

The figure has been improved (different line styles to better identify the lines).

908: "the ozone band ... is colder". Please rewrite: "the ozone band... has lower brightness temperature..." or similar. Also a few lines later, "colder altitude" sounds ugly. Done.

937: Please avoid this sloppy language ("spectrum is colder"). Improved.

1102: radiative transfer simulations of the Earth atmosphere. (Evidently, all simulations are performed IN the atmosphere, unless some are performed on the ISS). Changed. Manuscript prepared for Geosci. Model Dev. with version 5.0 of the LATEX class copernicus.cls. Date: 12 April 2016

The libRadtran software package for radiative transfer calculations (Version 2.0.1)

Claudia Emde1, Robert Buras-Schnell5, Arve Kylling2, Bernhard Mayer1, Josef Gasteiger1, Ulrich Hamann4, Jonas Kylling2,3, Bettina Richter1, Christian Pause1, Timothy Dowling6, and Luca Bugliaro7 1Meteorological Institute, Ludwig-Maximilians-University, Theresienstr. 37, D-80333 Munich, Germany 2NILU – Norwegian Institute for Air Research, Kjeller, Norway 3Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Oslo, Norway 4MeteoSwiss, Radar, Satellite and Nowcasting Division, Via ai Monti 146, Locarno, Switzerland 5Schnell Algorithms, Am Erdapfelgarten¨ 1, 82205 Gilching, Germany 6Dept. of Physics & Astronomy, University of Louisville, KY 40292 USA 7Institut fur¨ Physik der Atmosphare,¨ Deutsches Zentrum fur¨ Luft- und Raumfahrt (DLR), Oberpfaffenhofen, 82234 Wessling, Germany

Correspondence to: Claudia Emde ([email protected])

Abstract. libRadtran is a widely used software package for 25 1 Introduction radiative transfer calculations. It allows to compute (polar- ized) radiances, irradiances, and actinic fluxes in the so- Radiative transfer modeling is essential for remote sensing lar and thermal spectral regions. libRadtran has been used of planetary atmospheres, but also for many other fields in 5 for various applications, including remote sensing of clouds, atmospheric physics: e.g., atmospheric chemistry which is aerosols and trace gases in the Earth’s atmosphere, climate largely influenced by photochemical reactions, calculation of studies, e.g., for the calculation of radiative forcing due to 30 radiative forcing in climate models, and radiatively driven different atmospheric components, for UV-forcasting, the dynamics in numerical weather prediction models. calculation of photolysis frequencies, and for remote sens- The libRadtran software package is a versatile toolbox 10 ing of other planets in our solar system. The package has which has been used for various applications related to at- been described in Mayer and Kylling (2005). Since then sev- mospheric radiation, a list of publications that have used the eral new features have been included, for example polar- 35 package can be found on the website http://www.libradtran. ization, Raman scattering, a new molecular gas absorption org, currently it includes more than 400 entries. Applications parameterization, and several new cloud and aerosol scat- include the following topics (the given references are taken 15 tering parameterizations. Furthermore a graphical user in- as examples out of the list of publications): terface is now available which greatly simplifies the usage of the model, especially for new users. This paper gives an – Analysis of UV-radiation measurements, from which overview of libRadtran version 2.0.1 with focus on new fea- 40 parameters like e.g. ozone concentrations, aerosol opti- tures. Applications including these new features are provided cal thickness, UV-index are derived. Since the libRad- tran package originally was a radiative transfer code for 20 as examples of use. A complete description of libRadtran and all its input options is given in the user manual included in the UV spectral range (the main executable is still called the libRadtran software package, which is freely available at uvspec), the model is well established in this research http://www.libradtran.org. 45 area and frequently used (e.g. Seckmeyer et al., 2008; Kreuter et al., 2014).

– Cloud and aerosol remote sensing using measure- ments in solar and thermal spectral regions. The devel- oped retrieval methods are for ground-based, satellite 2 C. Emde et al.: The libRadtran software package

50 and air-borne instruments which measure (polarized) ra- Since the publication of the first libRadtran reference pa- diances (e.g. Painemal and Zuidema, 2011; Bugliaro per (Mayer and Kylling, 2005) the model has been further et al., 2011; Zinner et al., 2010; Alexandrov et al., developed. It includes numerous new features which will be 2012). the focus of this paper. 100 One of the major extensions is the implementation of po- – Volcanic ash studies including remote sensing of ash larization in the radiative transfer solver MYSTIC (Emde 55 mass concentrations (e.g. Gasteiger et al., 2011; Kylling et al., 2010), which is important because an increasing num- et al., 2015) and visibility of ash particles from the pi- ber of polarimetric observations have been performed dur- lot’s perspective (e.g. Weinzierl et al., 2012). ing the last years and are planned for the future, from 105 ground, satellite, and air-craftaircraft. These observations – Remote sensing of surface properties; a model like ✿✿✿✿✿✿ include more information about optical and microphysical libRadtran is particularly important to develop atmo- properties of atmospheric particles than total radiances alone 60 spheric correction methods (e.g. Drusch et al., 2012; (Kokhanovsky et al., 2010; Mishchenko et al., 2007). An- Schulmann et al., 2015). other important reason for considering polarization is that in – Trace gas remote sensing, libRadtran can be used as 110 the short-wave spectral region (below about 500 nm) the ne- forward model for retrievals of O3, NO2 and BrO from glection of polarization can lead to large errors: more than DOAS (Differential Optical Absorption Spectroscopy) 10% for a molecular atmosphere and up to 5% for an atmo- 65 measurements (e.g. Theys et al., 2007; Emde et al., sphere with aerosol (Mishchenko et al., 1994; Kotchenova 2011). et al., 2006). 115 Moreover libRadtran now includes a solver to calculate ro- – Calculation of actinic fluxes in order to quantify pho- tational Raman scattering (Kylling et al., 2011) which affects

tolysis rates for atmospheric chemistry (e.g. Suminska-´ ✿✿✿✿✿✿✿improves✿the accuracy of trace gas retrievals. Further the Ra- Ebersoldt et al., 2012). man scattering signal can be used to estimate cloud top pres- sure from satellite measurements and aerosol properties from 70 – Determination of solar direct irradiance and global ir- 120 surface and satellite observations. radiance distributions in order to optimize locations of Numerous state-of-the-art parameterizations for aerosol solar energy platforms (e.g. Lohmann et al., 2006) and and ice cloud optical properties have been included (see calculation of circumsolar irradiance (Reinhardt et al., Secs. 5 and 6). These new parameterizations provide more 2014). accurate radiance calculations. In particular for polarized ra- 125 diative transfer, which requires not only a scattering phase 75 – Simulation of satellite radiances to be used for data function but the full scattering matrix, new optical properties assimilation in numerical weather prediction models data data on optical properties were required. In order to (Kostka et al., 2014). ✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿ improve the accuracy for highly peaked phase functions – – Validation of radiation schemes included in climate which are typical for ice clouds – an improved intensity cor- models (Forster et al., 2011), calculation of radiative 130 rection method has been developed and included into the 80 forcing of clouds and contrail cirrus (Forster et al., DISORT solver (Buras et al., 2011), and new variance re- 2012), impacts of aviation on climate (e.g. Lee et al., duction methods have been developed for the Monte Carlo 2010) solver MYSTIC (Buras and Mayer, 2011). libRadtran has also been rewritten to allow simulations with an arbitrary – Simulation of heating rates in three-dimensional atmo- 135 number of cloud and aerosol types – which can e.g. be spheres to develop fast radiation parameterizations for used to simulate variability in particle size distribution.

85 Large Eddy Simulation (LES) models (Klinger and ✿✿✿take✿✿✿✿into✿✿✿✿✿✿✿account ✿✿✿✿✿✿detailed✿✿✿✿✿✿✿particle✿✿✿✿size ✿✿✿✿✿✿✿✿✿✿distributions✿✿✿✿✿✿✿(number Mayer, 2014). ✿✿✿✿✿✿✿densities✿✿✿for✿✿✿✿✿✿✿✿✿✿discretized ✿✿✿✿size ✿✿✿✿bins)✿✿✿✿that✿✿✿✿can ✿✿be✿✿✿✿✿✿✿✿different✿✿in ✿✿✿✿each ✿✿✿✿✿layer. ✿✿In✿✿✿✿✿✿earlier✿✿✿✿✿✿✿✿versions ✿it✿✿✿✿was✿✿✿✿✿only ✿✿✿✿✿✿✿possible✿✿to✿✿✿✿take – Simulation of solar radiation during a total eclipse 140 ✿✿✿into✿✿✿✿✿✿✿account ✿✿✿✿✿✿✿✿✿✿✿✿parameterized ✿✿✿size✿✿✿✿✿✿✿✿✿✿✿distributions ✿✿✿✿such✿✿as✿✿✿✿✿✿gamma (Emde and Mayer, 2007). ✿✿or ✿✿✿✿✿✿✿✿✿log-normal✿✿✿✿✿✿✿✿✿✿✿distributions.✿ A new gas absorption parameterization for the solar and – Rotational Raman scattering, which explains the thermal spectral ranges has been developed (Gasteiger et al., 90 filling-in of Fraunhofer lines in the solar spectrum 2014). It is available in different spectral resolutions and can (Kylling et al., 2011). 145 be applied for the simulation of radiances and irradiances. – Estimation of background radiation affecting lidar It is particularly useful for efficient simulations of radiances measurements (e.g. Ehret et al., 2008) measured by satellite instruments (see Sec. 4.1). The DISORT radiative transfer solver has been translated – Remote sensing of planetary atmospheres (e.g. Ran- from FORTRAN77 to the C programming language. All vari- 95 nou et al., 2010) 150 ables were transferred from single to double precision. These C. Emde et al.: The libRadtran software package 3

changes improved the numerical stability of the code and re- The main tool of the libRadtran package is the uvspec ra- duced computational time significantly (for details see Buras 175 diative transfer model, which consists of the following parts: et al., 2011). The paper is organized as follows: Sec. 2 provides an 1. The atmospheric state (e.g. trace gas profiles, cloud liquid water content, cloud droplet size, aerosol concen- 155 overview of the uvspec radiative transfer model which is the core of the libRadtran package. Sec. 3 gives a short de- tration profiles, ...) needs to be provided as input to the scription of the radiative transfer solvers included in uvspec. model. Sec. 4 provides a summary of how molecules are han- 180 2. The user may select between various parameteriza- dled and outlines various ways to include molecular absorp- tions to convert the atmospheric state into optical prop- 160 tion. Moreover Rayleigh scattering parameterizations are de- erties, e.g. to convert from cloud liquid water content scribed. Sec. 5 summarizes the available parameterizations and effective droplet size to extinction coefficient, sin- for aerosol microphysical and optical properties. Sec. 6 gives gle scattering albedo and scattering phase function, or an overview of the parameterizations for water and ice clouds 185 phase matrix when polarization is considered. and also outlines how these were generated. In Sec. 7 avail- 165 able surface properties are described, including Lambertian 3. The optical properties are passed to a radiative transfer reflection, bidirectional distribution functions and fluorescent equation (RTE) solver, where again it is up to the user surfaces. In Sec. 8 we describe code and implementation im- to select the most appropriate one for the given applica- provements relevant for users. Sec. 9 introduces the graphical tion. Currently, more than a dozen different solvers are user interface for uvspec. Sec. 10 provides a short summary 190 included in uvspec. The six most used and maintained 170 of additional tools that come with the libRadtran package. RTE solvers are listed in Table 1 and briefly described in Finally Sec. 11 shows a few applications as examples of the Sec. 3. Among them are relatively simple and fast two- usage of libRadtran. stream solvers to compute irradiances, the widely used discrete ordinate solver DISORT and also the Monte 195 Carlo solver MYSTIC to compute (polarized) radiances or irradiances in three-dimensional geometry. 2 The uvspec radiative transfer model 4. The output of the RTE solver are radiation quantities as irradiance, actinic flux or (polarized) radiance. The quantities are normalized to the source function, i.e. the 200 solar irradiance in the solar spectral region. In order to Atmospheric Optical properties get physical quantities with corresponding units the out- description -Trace gas profiles Profiles of: put may be postprocessed. The uvspec output then cor- -Temperature profile Absorption - extinction coefficient responds to calibrated radiances or brightness tempera- - Pressure profile cross sections, - single scattering - Aerosol parameterizatios, albedo tures for a given instrumental filter function. It is also - Water clouds aerosol and - scattering phase 205 possible to obtain integrated solar or thermal irradiance. - Ice clouds cloud physics, function/matrix or ... - Surface properties Legendre polynomials The overall structure of the uvspec model is shown in Fig. 1. (albedo or BRDF) - reflectance function/ - Wind speed matrix The model was originally designed to compute UV- - ... radiation, therefore its name is uvspec. As said before it now covers the complete solar and thermal spectral range. Radiation quantities 210 The usage of the model is described in the user guide RTE which comes along with the package. The user guide in- uncalibrated radiance/Stokes vector, solver irradiance, actinic flux cludes descriptions of the RTE solvers, examples of use as well as detailed documentation of all options and respective Post- parameters. Below uvspec input options are put in teletype- processing 215 font, for example rte solver. The uvspec model may be run either from the command line using

Model output uvspec < input_file > output_file - calibrated radiance/Stokes vector, irradiance, actinic flux or from the Graphical User Interface (see Sec. 9). - integrated solar or thermal irradiance - brightness temperature - simulated measurements of satellite or ground based radiometers - ... 220 3 Radiative transfer equation solvers

The RTE for a macroscopically isotropic medium, i.e. ran- Fig. 1. Structure of the uvspec radiative transfer model. domly oriented particles and molecules, may be written as 4 C. Emde et al.: The libRadtran software package

Table 1. The radiative transfer equation solvers currently implemented in libRadtran.

RTE Geometry Radiation References Method solver quantities disort 1D, PP, PS E, F, L Stamnes et al. (1988, 2000); Buras et al. (2011); discrete ordinate, C-version Dahlback and Stamnes (1991) mystic 1D, 3D(a), PP, SP E, F, L, I Mayer (2009); Emde and Mayer (2007); Emde Monte Carlo et al. (2010); Mayer et al. (2010); Buras and Mayer (2011); Emde et al. (2011); Klinger and Mayer (2014) twostr 1D, PS E, F Kylling et al. (1995) two-stream, rodents 1D, PP E Zdunkowski et al. (2007) two-stream, plane-parallel sslidar 1D, PP ∗ single scattering lidar tzs 1D, PP L(TOA) thermal, zero scattering (a) 3D version not included in the free package; available in joint projects Explanation: PP, plane-parallel E, irradiance PS, pseudo-spherical F, actinic flux SP, fully spherical L, radiance 1D, one-dimensional L(TOA), radiance at top of atmosphere 3D, three-dimensional I is the Stokes vector (polarized radiance) ∗ sslidar: see section 3.4

(Chandrasekhar, 1950; Mishchenko et al., 2002) of the algorithm exhibited several numerical instabilities for certain combinations of geometries and optical properties. dI = −I + J (1) The FORTRAN77 code has been translated to C-code and βds is entirely in double precision (the FORTRAN77 version is 250 mostly in single precision) and includes dynamic memory al- 225 where the source function J is location (not possible in FORTRAN77). As such, the C ver- ω0 ′ ′ ′ sion is numerically stable and also faster than the original J = P(Ω,Ω )I(Ω )dΩ + (1 − ω0)Be(T ) (2) 4π Z FORTRAN77 version. We thus use the C version of the DIS- ORT algorithm by default. The original FORTRAN77 ver- Here I = (I,Q,U,V ) is the Stokes vector at location 255 sion may still be invoked by fdisort2. Both the C-code (x,y,z), β the volume extinction coefficient, ω0 the single and the FORTRAN77 version include the new intensity cor- scattering albedo, P(Ω,Ω′) the scattering phase matrix, and rection method for peaked phase functions by Buras et al. 230 Be(T ) = (B(T ),0,0,0) the emission vector including the (2011), which is used by default. Planck function B(T ). For most applications in the Earth’s For calculations with rotational Raman scattering, the C atmosphere, thermal emission can be neglected for wave- 260 version has been generalized so that arbitrary source func- lengths below about 3 µm. Polarization is also often ne- tions (not only a solar or thermal source function) can be han- glected, in this case the Stokes vector in Eqs. 1 and 2 is dled (Kylling and Stamnes, 1992; Kylling et al., 2011). Ro- 235 replaced by the radiance L, the phase matrix becomes the tational (inelastic) Raman scattering from other wavelengths scalar phase function p(Ω,Ω′) and the emission vector is just into the wavelength, for which the radiative transfer equation the Planck function B(T ). 265 is solved, is included into the source term. The uvspec model includes various methods to solve Eq. 1. The list of solvers which may be selected using the option 3.2 MYSTIC 240 rte solver is shown in Table 1. The most comprehensive solver in libRadtran is the Monte 3.1 DISORT Carlo model MYSTIC (Mayer, 2009), which may be used to calculate (polarized) radiances, irradiances and actinic The solver disort is used by default in libRadtran. DIS- 270 fluxes in the solar and thermal spectral regions. Within MYS- ORT (Stamnes et al., 2000) is based on discrete ordinates and TIC photons are traced through the atmosphere from the allows to compute radiances, irradiances and actinic fluxes in source towards the sensor or backwards, from the sensor to 245 plane-parallel geometry. The original FORTRAN77 version the source, which is much more efficient especially in the C. Emde et al.: The libRadtran software package 5

thermal wavelength region. One of the main applications of For the thermal irradiance, rodents also gives better re-

275 MYSTIC is to calculate radiances in cloudy atmospheres. sults at TOA (1.6%) and at✿✿✿✿the✿surface (1%) than twostr The sharp forward scattering of clouds and aerosols causes (3%). For irradiances within the atmosphere, no real prefer- numerical problems in Monte Carlo models. In order to avoid ence can be given. these, sophisticated variance reduction methods have been developed (Buras and Mayer, 2011). These are enabled using 325 3.4 Lidar and radar simulations 280 mc vroom on. Solar radiation is initially unpolarized and becomes polarized by molecular, aerosol or cloud scatter- In order to complement the instruments that can be sim- ing in the atmosphere. With the option mc polarisation ulated by libRadtran, a lidar simulator called sslidar (Emde et al., 2010) the full Stokes vector is calculated. For has been implemented. It only takes into account single 1D atmospheres MYSTIC may also be operated in spheri- scattering and reflection and is based on the lidar equa- 330 tion which is integrated over each range. Note that in or- 285 cal geometry using the option mc spherical (Emde and Mayer, 2007). der to obtain a smooth signal, a✿✿✿✿fine✿✿✿✿✿✿✿vertical✿✿✿✿✿✿✿✿✿resolution✿✿of The public version of MYSTIC allows calculations in ✿✿the✿✿✿✿✿✿model✿✿✿✿✿✿✿✿✿✿atmosphere✿✿✿is ✿✿✿✿✿✿✿✿required. ✿✿✿✿The ✿✿✿✿✿✿vertical✿✿✿✿✿✿✿✿✿resolution 1D (plane-parallel or spherical) geometry. A full 3D ver- ✿✿✿✿✿should✿✿✿✿✿✿✿✿✿✿correspond✿✿to✿the atmosphere normally has to have sion is also available for joint projects. The non-public ver- at least the same vertical resolution as the range width of✿ 335 the simulated lidar instrument. For radar simulations a stand- 290 sion includes several other features: Complex 3D topography ✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿ (Mayer et al., 2010) and efficient high spectral resolution cal- alone tool is available (see Sec. 10.2). culations using absorption lines importance sampling (Emde 3.5 Other solvers et al., 2011). The solver tzs (see Appendix B) is based on the zero scat- 3.3 Two-stream solvers tering approximation in the thermal spectral range. It may be 340 used for clear sky calculations of radiances at top of atmo- 295 For the calculation of irradiances, two fast two-stream solvers are available. sphere (TOA). It also calculates “black cloud” radiances for The first solver, twostr, is described in detail in Kylling the application of the CO2 slicing algorithm (Smith et al., et al. (1995). twostr is optimized for calculating actinic 1970; Chahine, 1974; Smith and Platt, 1978; Menzel et al., fluxes, and hence heating rates. It can be run in plane-parallel 1983; Eyre and Menzel, 1989) which may be used for the 345 determination of cloud top temperatures from passive remote 300 as well as in pseudo-spherical geometry. The second two-stream method available in libRad- sensing measurements in the thermal spectral range. sss tran is rodents, which is based on the delta-Eddington For the solar region a fast single scattering solver is two-stream described e.g. in Zdunkowski et al. (2007), available. These solvers may be used for fast but approximate Sec. 6.1–6.41. Based on a different two-stream approach than simulations of satellite measurements. 350 Several other RTE-solvers are included in uvspec for com- 305 twostr, it naturally yields different results. In contrast to twostr , neither the pseudo-spherical approximation is not patibility with earlier releases of the package. These include ✿✿✿✿✿✿ sdisort spsdisort implemented . Also is not implemented nor is rodents ca- (pseudospherical disort), (single ✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿ fdisort1 pable of calculating actinic fluxes. precision, pseudospherical disort), (version 1 of polradtran For actinic fluxes and atmospheric heating rates, twostr DISORT), and (Evans and Stephens, 1991). 355 While they may still be used, we do not recommend their use 310 is the better choice. However, for calculating solar irradi- ances, we recommend using rodents: For cases where as the other solvers listed in Table 1 perform better. the resulting irradiance is not negligible (larger than 2% 3.6 Accuracy of solvers of the extraterrestial irradiance), the difference between rodents and exact disort calculations is on average MYSTIC is a physically correct model which does not 315 5% (7%) for down(up)-welling irradiances. For twostr the include any approximations. It The✿✿✿✿✿✿✿✿✿✿✿MYSTIC ✿✿✿✿✿model✿has been values are 9% (11%). Especially in case the atmosphere is 360 validated in many international model intercomparison stud- only weakly absorbing, the average differences at top-of- ies, for radiance calculations with highly peaked phase func- atmosphere (TOA) and at the surface are only 2% (1%) tions (Kokhanovsky et al., 2010), for polarized radiance cal- for rodents, whereas they are 5% at TOA and even 13% culations (Emde et al., 2015), and for radiances and irradi- 320 (18%) at surface for twostr. ances in✿✿3D model domains (Cahalan et al., 2005). In all stud- 365 ies MYSTIC belongs to the core of models which produce 1Note that Zdunkowski et al. (2007) contains two misprints rele- equal results within their uncertainty range. MYSTIC agrees vant for the twostream solver: First, in Eq. 6.50, α12,Ed = −α21,Ed = 2 perfectly to DISORT for radiances and irradiances with only and α22,Ed −α11,Ed. Second, α2 in Eq. 6.88 should be α2. Also, the derivation in section 6.5 for thermal radiation does not work, a few exceptions, e.g. for circum-solar radiation, where the instead the equations need to be derived in analogy to the solar ra- second-order intensity correction included in DISORT is not

diation. 370 accurate ✿✿✿✿✿✿enough for highly peaked scattering phase functions 6 C. Emde et al.: The libRadtran software package

(Buras et al., 2011). In Emde et al. (2011), a comparison the ground, the mean parameterization error is in the range between DISORT and MYSTIC for a radiance spectrum in of 1%. The mean error is slightly larger than 1% for thermal the O2A-band is shown. The relative difference between the radiation at the surface. solvers is here less than 0.05%. All other solvers are ap- 425 The LOWTRAN band model adopted from from the SB- 375 proximations and hence less accurate: as mentioned before DART radiative transfer model (Ricchiazzi et al., 1998) is the two-stream solvers are only appropriate for irradiances also included in libRadtran. and the tzs solver only provides radiances in thermal atmo- For the simulation of radiances and irradiances we recom- spheres and neglects scattering completely. mend to use reptran because it is faster and more accurate The accuracy of MYSTIC depends only on the number of 430 than lowtran. 380 traced photons. The standard deviation of MYSTIC is cal- Several correlated-k parameterizations with different num- culated when the option mc std is enabled. The user may bers of bands, i.e. different accuracy, are included in libRad- run MYSTIC with many photons as reference for some cases tran. For the calculation of integrated solar and thermal irra- in order to check the accuracy of other solvers for specific diances and heating rates the correlated-k parameterizations applications. 435 by Kato et al. (1999) and Fu and Liou (1992, 1993) are rec- ommended. Also for the calculation of heating/cooling rates in the higher atmosphere (above 20 km) we recommend 385 4 Molecules these parameterizations because reptran and lowtran are affected by large errors. 4.1 Molecular absorption parameterizations 440 4.2 Molecular absorption cross sections Spectral ranges affected by molecular absorption comprising a complex line structure require parameterizations to reduce For the spectral region from 160 to 850 nm libRadtran the computational cost. Molecular absorption parameteriza- includes measured absorption cross sections of various 390 tions included in libRadtran are listed in Table 2. By default molecules in the atmosphere (see Table 3). Using the option the reptran parameterization is applied. Using the option mol abs param crs these cross sections are used instead mol abs param the user may select the most appropriate 445 of the default reptran parameterization. For wavelengths parameterization for the specific application. As an example below 500 nm reptran yields approximately the same re- Fig. 2 shows radiance calculations for nadir viewing direc- sults as mol abs param crs because the cross sections 395 tion at the top of the atmosphere using the parameterizations from HITRAN and the continua are very small at these wave- reptran and lowtran and line-by-line calculations. lengths and the same measured cross sections are relevant in The reptran parameterization (Gasteiger et al., 2014) 450 both cases. has recently been included in libRadtran. In reptran in- For O2 for instance the cross section data include the tegrals over spectral intervals, e.g. integrated over a narrow Schumann-Runge bands between 176 and 192.6 nm and the 400 spectral band or an instrument channel response function, are Herzberg continuum between 205 and 240 nm. Ozone ab- parameterized as weighted means over representative wave- sorption bands are for example the Huggins bands between lengths similar to the method described by Buehler et al. 455 320 and 360 nm and the Chappuis bands between 375 and (2010). The selection of an optimum set of representative 650 nm. Using the option crs model the user may spec- wavelengths is based on accurate line-by-line simulations for ify which cross section data should be used in the simula- 405 top of atmosphere radiances of a highly variable set of atmo- tions. Alternatively with crs file the users may specify spheric states. The ARTS model (Eriksson et al., 2011) in- their own absorption cross section data. cluding state-of-the-art continuum models and spectroscopic data from HITRAN 2004 (Rothman et al., 2005) were used 460 4.3 Line-by-line calculations to calculate the gas absorption properties. For wavelengths 410 below 1130 nm measured absorption cross sections of O3 In the shortwave infrared, thermal infrared and microwave (Molina and Molina, 1986), O4 (Greenblatt et al., 1990), region we find a huge number of absorption lines which and NO2 (Burrows et al., 1998) are included, as they are are due to vibrational or rotational transitions in molecules. not covered by HITRAN or the continua (see also Sec. 4.2). A line-by-line model is required in order to calculate spec- −1 −1 Three band resolutions (fine: 1 cm , medium: 5 cm , and 465 trally resolved radiances. Line-by-line models take the ab- −1 415 coarse: 15 cm ) are available in the solar and thermal spec- sorption line positions as well as line strength parameters tral range, as well as a number of instrument channels on the from spectral databases like HITRAN, calculate line broad- ADEOS, ALOS, EarthCARE, Envisat, ERS, Landsat, MSG, ening which depends on pressure and temperature in the at- PARASOL, Proba, Sentinel, Seosat, and SPOT satellites. The mosphere and finally obtain absorption optical thickness pro- parameterization has been validated by comparison to high 470 files. libRadtran does not include a line-by-line model but 420 spectral resolution calculations. For solar and thermal radia- it allows to specify absorption optical thickness profiles us- tion at the top of atmosphere, as well as for solar radiation at ing the option mol tau file abs. It is convenient to use C. Emde et al.: The libRadtran software package 7

0.06 300

290 0.05 280 0.04 270

0.03 260

250 0.02 240 normalized radiance 0.01

brightness temperature [K] 230

0.00 220 755 760 765 770 775 9000 9500 10000 10500 11000

0.06 300

0.05 290

0.04 280

0.03 270 reptran fine 0.02 260 reptran medium normalized radiance 0.01 250 reptran coarse

brightness temperature [K] lowtran 0.00 240 755 760 765 770 775 9000 9500 10000 10500 11000 wavelength [nm] wavelength [nm]

Fig. 2. Nadir top of the atmosphere radiance in the oxygen-A band around 760 nm (left) and in the IR window region (right) for the midlatitude-summer atmosphere of Anderson et al. (1986). All calculations were performed with the MYSTIC solver using the “absorption lines importance sampling” method (Emde et al., 2011). (Top) High spectral resolution calculation, based on line-by-line absorption cross sections calculated using ARTS (Eriksson et al., 2011); (bottom) pseudo-spectral calculations using the representative wavelengths band parameterizations (reptran) with different resolutions and lowtran. For comparison see also Fig. 3 in Mayer and Kylling (2005) which shows transmittances for genln2 line-by-line calculations and lowtran for the same spectral regions.

Table 2. Absorption parameterizations in libRadtran.

Name Description Application References reptran default setting; calculation of radiances, Gasteiger et al. (2014) bands parameterized using repr. wavelengths; simulation of satellite measure- fine (1cm−1), medium (5cm−1) and coarse ments (15cm−1) band resolutions available; based on HITRAN2004, MT CKD and mea- sured absorption cross section data of O3,O4, and NO2; solar and thermal region reptran channel satellite channels parameterized using fast and accurate simulations Gasteiger et al. (2014) representative wavelengths; for various satellite instruments lowtran LOWTRAN band model; pseudo-spectral calculations of solar and thermal region, resolution 20 cm−1 radiances Ricchiazzi et al. (1998); Pierluissi and Peng (1985) ✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿Pierluissi and Peng (1985) kato, kato2 correlated k distributions for solar region; calculation of integrated solar kato2.96, different versions available; irradiance Kato et al. (1999); Wandji Nyamsi et al. (2015) katoandwandji based on HITRAN96 or HITRAN2000; ✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿Wandji Nyamsi et al. (2015) 148 or 575 sub-bands fu correlated k distributions for solar (6 bands) calculation of integrated solar Fu and Liou (1992, 1993) and thermal (12 bands) regions; and thermal irradiance, optimized for climate models radiative forcing 8 C. Emde et al.: The libRadtran software package

Table 3. Absorption cross section data included in libRadtran, the non-default parameterizations are put in parantheses. PR(Θ) =

3 2 3 2 4 (1 + cos Θ) − 4 sin Θ 0 0 Molecule wavelength range [nm] reference 3 2 3 2  − 4 sin Θ 4 (1 + cos Θ) 0 0  BrO 312 – 385 Wahner et al. (1988) ∆ 3 0 0 2 cosΘ 0  ′  CO2 119 – 200 Yoshino et al. (1996)  0 0 0 ∆ 3 cosΘ  HCHO 300 – 386 Cantrell et al. (1990)  2  NO2 240 – 760 (Bogumil et al. (2003)) 1 0 0 0 231 – 794 Burrows et al. (1998)  0 0 0 0  +(1 − ∆) , O2 108 – 160 Ogawa and Ogawa (1975) 0 0 0 0 160 – 175 Yoshino et al. (2005)    0 0 0 0  175 – 204 Minschwaner et al. (1992)   205 – 240 Yoshino et al. (1988) 495 where O3 116 – 185 Ackerman (1971) 185 – 350 Molina and Molina (1986) 1 − δ ′ 1 − 2δ ∆ = , ∆ = , (3) 195 – 345 (Daumont et al. (1992))/ 1 + δ/2 1 − δ (Malicet et al. (1995)) 245 – 340 (Bass and Paur (1985)) and δ is the depolarization factor that accounts for the 240 – 850 (Bogumil et al. (2003)) anisotropy of the molecules, δ is also calculated according to 400 – 850 WMO (1986) Bodhaine et al. (1999). The Rayleigh phase matrix for δ=0 is O4 330 – 1130 Greenblatt et al. (1990) 500 shown in Fig 3. For calculations neglecting polarization only OClO 240 – 480 Wahner et al. (1987) the (1,1) element of the phase matrix which corresponds to SO 239 – 395 Bogumil et al. (2003) 2 the scattering phase function is required.

5 Aerosols

Besides the models by Shettle (1989) which are described 505 in Mayer and Kylling (2005), libRadtran now includes ad- the ARTS model (Eriksson et al., 2011) to generate spec- ditional aerosol properties based on the OPAC database trally resolved molecular absorption data because it outputs (Hess et al., 1998). OPAC provides the required parame- 475 the format required by libRadtran. ARTS includes a compre- ters for single scattering calculations: size distribution pa- hensive line-by-line module, it allows to use different spec- rameters, refractive indices, and the density of the mate- troscopic databases like HITRAN as input and it also in- 510 rial. Data are available for the spectral range from 250 nm cludes various state-of-the-art absorption continuum models. to 40 µm for the following basic aerosol types: insoluble The toolbox Py4CATS (Schreier and Bottger,¨ 2003; Schreier, (inso), water soluble (waso), soot (soot), sea salt accu- 480 2006; Schreier and Kohlert, 2008) which can be downloaded mulated (ssam), sea salt coarse mode (sscm), mineral nu- from www.libradtran.org also includes convenient command cleation mode (minm), mineral accumulated mode (miam), line programs to generate spectrally resolved absorption data. 515 mineral coarse mode (micm), mineral transported (mitr) The Py4CATS tools however do not include continuum mod- and soluble sulfate aerosol (suso). For the soluble aerosols els, hence it should only be used for simulations where the the parameters depend on humidity because the aerosol par- 485 continua are not relevant. ticles swell in humid air. Relative humidities of 0%, 50%, 70%, 80%, 90%, 95%, 98% and 99% are included in OPAC. 520 The option aerosol species file allows to define ar- bitrary mixtures of these basic types or to select pre-defined 4.4 Rayleigh scattering cross sections mixtures from OPAC like e.g. continental average, for which uvspec automatically uses the optical properties closest to the background humidity profile. The Rayleigh scattering cross sections are by default calcu- 525 Optical properties of all basic aerosol types were calcu- lated using Eqs. 22–23 of Bodhaine et al. (1999). Using the lated using libRadtran’s Mie tool (see Sec. 10.1). For mineral option crs model rayleigh the user may select Eq. 29 aerosols, which are highly aspherical, we additionally pro- 490 of Bodhaine et al. (1999) or the formulas proposed by Nico- vide optical properties calculated with the T-matrix method let (1984) and Penndorf (1957), respectively. The analytical (Mishchenko and Travis, 1998) assuming an aspect ratio dis- Rayleigh scattering phase matrix PR (Hansen and Travis, 530 tribution of prolate spheroids as described by Koepke et al. 1974) is (2015). C. Emde et al.: The libRadtran software package 9

P11 = P22 P12/P11 0.9 0.25 104 0.4 0.8 Rayleigh 0 2 103 . 0.7 0.20 waso 95% RH 0.0 0.6 102 ssam 95% RH 0.15 soot −0.2 0.5 1 10 0.4 cloud 10µm −0.4 0.10 100 0.3 −0.6 0.2 0.05 10−1 −0 8 . 0.1 scattering optical thickness absorption optical thickness 10−2 −1.0 0.0 0.00 0 20 40 60 80 100 120 140 160 180 0 20 40 60 80 100 120 140 160 180 300 400 500 600 700 800 300 400 500 600 700 800 P33/P11 P34/P11 wavelength [nm] wavelength [nm] 1.5 0.8 aerosol mixture name 1.0 0.6 continental_clean maritime_clean urban continental_average maritime_polluted desert 0.5 0.4 continental_polluted maritime_tropical antarctic

0.0 0.2

−0 5 0 0 . . Fig. 4. Absorption (left) and scattering (right) optical thick- −1.0 −0.2 ness for various aerosol mixtures specified using the option

−1.5 −0.4 aerosol species file. The aerosol optical properties as well 0 20 40 60 80 100 120 140 160 180 0 20 40 60 80 100 120 140 160 180 θ [ deg ] θ [ deg ] as the mixtures have been generated based on OPAC (Hess et al., 1998) parameters.

Fig. 3. Phase matrix elements for the basic OPAC aerosol types “water soluble” (waso), “sea salt accumulated mode” (ssam), and 555 For the simulation of irradiances and heating rates it is soot, for a water cloud with a droplet effective radius of 10 µm, normally sufficient to use a simple parameterization to con- and for Rayleigh scattering (with δ=0) at a wavelength of 350 nm. θ vert from cloud liquid water content and droplet effective is the scattering angle, i.e. the angle between incoming and scattered radius to the respective optical properties: extinction coeffi- directions. cient, single scattering albedo, and asymmetry parameter. For 560 this purpose libRadtran includes the parameterization gener- ated by Hu and Stamnes (1993). As an example Fig. 3 shows the phase matrix elements For the simulation of radiances more accurate optical of the basic OPAC aerosol types, of liquid cloud droplets properties are needed and the phase function should not be with an effective radius of 10 µm and the Rayleigh scat- approximated by a Henyey-Greenstein function as it is done 535 tering phase matrix. Note that for spherical particles only 565 in Hu and Stamnes (1993). Therefore, we have pre-calculated 4 elements of the 4x4 scattering phase matrix are indepen- cloud optical properties using libRadtran’s Mie tool assum- dent whereas for aspherical particles 6 elements are required ing that the cloud droplets are gamma distributed: (see e.g. Hansen and Travis, 1974). Fig. 4 shows the absorp- tion and the scattering optical thicknesses (integrated from α r 1 540 the surface to the top of the atmosphere) for the standard n(r) = Nr exp − ; α = − 3 (4)  reff · veff  veff aerosol mixtures in the spectral region from 300 to 800 nm. As expected, the optical thickness of the urban aerosol is Calculations have been performed for effective radii reff the largest and that of the antarctic aerosol the smallest. 570 from 1µm to 25µm with a step width of 1µm. The effec- In general the continental aerosol mixtures show a stronger tive variance was set to a value of veff = 0.1 and the constant 545 wavelength dependency than the maritime mixtures. N was determined by normalization. The size distributions The users may also provide their own optical properties were cut off at a minimum radius of 0.02·reff and a maximum data which may be generated using libRadtran’s Mie tool or radius of 8·reff . The size distribution bins are sampled on a 2πr 575 other external programs; more detailed instructions are pro- size parameter ( λ ) grid with a resolution of 0.003. This vided in the libRadtran user guide. fine resolution is necessary to obtain smooth phase matrices. The pre-calculated data includes the wavelength ranges from 250 nm to 2200 nm (solar) with a resolution of 10 nm and the 550 6 Clouds range from 2.2 µm to 100 µm (thermal) in 100 steps of equal 580 wavenumbers. The refractive index of water has been taken 6.1 Water clouds from Warren (1984). In the solar (thermal) region the phase matrices are computed from 5000 (500) Legendre polynomi- Table 4 summarizes the parameterizations of water cloud op- als. In the optical properties files 129 of the Legendre polyno- tical properties which may be selected in libRadtran using mials are stored, as well as the phase matrix elements, which the option wc properties. 585 are stored on scattering angle grids θ optimized such that 10 C. Emde et al.: The libRadtran software package

Table 4. Water clouds parameterizations in libRadtran.

Name Description Application References hu Default setting. Simple parameterization, uses Irradiances, heating rates Hu and Stamnes (1993) Henyey-Greenstein phase function to approxi- mate Mie phase function echam4 Very simple two-band parameterization of Comparison of irradiances to Roeckner et al. (1996) ECHAM4 climate model results from ECHAM4 mie Optical properties calculated using Mie theory, (Polarized) radiances generated using Mie code by include full phase matrices Wiscombe (1980)

the error of the phase matrix – when interpolated linearly 625 For accurate radiance calculations the parameterizations in cosθ between the grid points – is smaller than 1%. As an by Baum et al. (2005a,b) (baum) and the newer one by example Fig. 3 shows the four phase matrix elements of a Heymsfield et al. (2013); Yang et al. (2013) and Baum et al. cloud droplet distribution with reff =10 µm at 350 nm. Here (2014) (baum v36) are available: baum includes full phase ◦ 590 the cloudbow at θ ≈140 is clearly visible in the P11 and functions for a mixture of particle shapes, the parameteri- P12/P11 elements of the phase matrix. P12/P11 corresponds 630 zation is based on single scattering properties of smooth ice to the degree of polarization in the principal plane after single crystals and on a large number of measured size distributions. scattering, it can be seen that the maximum in the cloudbow baum v36 includes full phase matrices and three different region is about 80%. The mystic solver uses the phase ma- habit models: a general habit mixture similar to baum but 595 trix stored on the θ-grid, whereas all other solvers use the for rough ice crystals, and the single habits solid-column and Legendre polynomials, except for the intensity correction in 635 aggregate, both of them severely roughened. disort which uses the phase function (see also Buras et al., We have generated two further parameterizations (hey 2011). and yang2013) for individual habits which also include the For specific applications, e.g. different size distributions, full phase matrices (see Appendix A): hey is available for 600 the user can easily generate optical properties using libRad- the wavelength region from 0.2 to 5 µm for smooth parti- tran’s Mie tool. 640 cles in the effective radius range from 5 to 90 µm. The full wavelength region from 200 nm to 99 µm is available for 6.2 Ice Clouds yang2013, effective radii may be in the range from 5 to 90 µm and a roughness parameter may also be specified, For ice clouds libRadtran includes a variety of parameteriza- ranging from smooth to severely rough. For the yang2013 tions (see Table 5) from which the user may select the most 645 parameterization, the single scattering properties of nine in- 605 appropriate one for a specific application by specifying the dividual ice crystal habits which are commonly observed in option ic properties. Ice clouds are more complex than ice clouds have been taken from the database by Yang et al. water clouds because they consist of ice crystals of different (2013). The hey parameterization was generated before this shapes. Some of the ice cloud parameterizations allow the database existed and it is based on single scattering data pro- crystal habit (ic habit) to be specified. 650 vided by Hong Gang who used the improved geometrical op- 610 As described in the previous section the exact phase matrix tics method (IGOM), the same method as used by Yang et al. is not needed when irradiances are calculated. For this pur- (2013). pose the parameterizations by Fu (1996); Fu et al. (1998) and Please refer to the libRadtran user guide for a list of avail- Key et al. (2002) are included in libRadtran. Fu (1996) and able habits for each parameterization. Fu et al. (1998) approximate the phase function by a Henyey- 655 Fig. 5 shows the phase matrix elements of ice crystal dis- 615 Greenstein function. Key et al. (2002) is slightly more ac- tributions with an effective radius of 40 µm at 550 nm wave- curate because it uses a double-Henyey-Greenstein function length. The red lines correspond to smooth crystals and the which represents the backscattering of ice crystals much bet- blue lines to severely rough crystals. The individual habits ter. The parameterization is based on single scattering cal- are for the yang2013 parameterization. General habit mix- culations for various ice crystal habits and on measured size 660 tures which are available for the hey parameterization based 620 distributions. It is available in the wavelength range from 0.2 on smooth crystals and for the baum v36 parameterization to 5 µm. Based on single scattering data provided by P. Yang based on severely rough crystals are also shown. For most and on the size distributions from J. R. Key we have extended smooth crystals and also for the general habit mixture ghm the original parameterization by Key et al. (2002) to the ther- of the hey parameterization scattering features of hexagonal mal wavelength region up to 100 µm. C. Emde et al.: The libRadtran software package 11

Table 5. Ice cloud parameterizations in libRadtran

Name Description Application References fu Default setting. Simple parameterization using Irradiances, heating rates Fu (1996); Fu et al. (1998) Henyey-Greenstein phase function. echam4 Very simple 2-band parameterization of Comparison of irradiances to Roeckner et al. (1996) ECHAM4 climate model. results from ECHAM4 key Parameterization using a double-Henyey- Irradiances, heating rates Key et al. (2002) Greenstein phase function, covers wavelength range from 0.2 µm to 5.0 µm. Available for various habits. yang Similar to key but based on different single Irradiances, heating rates Key et al. (2002), Yang et al. scattering calculations and extended to wave- (2005) lengths up to 100 µm. Below 3.4 µm equivalent to key. baum Bulk optical properties including phase func- Radiances Baum et al. (2005a,b) tions for a realistic mixture of habits. Covers wavelength range from 0.4 to 2.2 µm and from 3.1 to 100 µm. baum v36 Bulk optical properties including phase ma- (Polarized) radiances Heymsfield et al. (2013); Yang trices for three microphysical models: general et al. (2013); Baum et al. (2014) habit mixture, solid columns or rough aggre- gates. All models include severely rough par- ticles. Covers wavelength range from 0.2 to 99 µm. hey Bulk optical properties including phase matri- (Polarized) radiances Single scattering properties ces based on single scattering calculations for generated by Hong Gang using smooth crystals, covers wavelength range from the code by Yang et al. (2013), 0.2 to 5 µm, includes 6 habits and a habit mix- Appendix A ture. yang2013 Bulk optical properties including phase matri- (Polarized) radiances Yang et al. (2013), Appendix A ces for 9 habits and 3 degrees of roughness, cov- ers wavelength range from 0.2 to 99 µm.

◦ 665 ice crystals, the most prominent being the halo at 22 scatter- tional reflectance distribution functions. libRadtran provides ing angle, are visible in all phase matrix elements. The phase a variety of BRDFs, which are listed in table 6. matrices for severely rough crystals do not show halo fea- 680 Two parameterizations for land surfaces are available. tures and they are relatively similar for all habits. In reality The first is the “RPV” parameterization by Rahman et al. ice clouds are highly variable: There are situations when the (1993) with the extension by Degunther¨ and Meerkotter¨ 670 halo is visible, in this case obviously there must be regular (2000) for modelling snow-covered surfaces. The second is smooth ice crystals in the cirrus clouds. When no halo is vis- the “RossLi” BRDF first presented by Roujean et al. (1992). ible, the assumption of severely roughened crystals might be 685 The original RossLi BRDF is used in the AMBRALS (the more realistic. Algorithm for Modeling[MODIS] Bidirectional Reflectance Anisotropies of the Land Surface) BRDF Modeling Frame- work (Wanner et al., 1997), and consists of four different ker- 7 Surface nel combinations, of which the RossThickLiSparseRecipro- 690 cal combination was identified in several studies to be the model best suited for the operational MODIS BRDF/Albedo 675 7.1 Bidirectional reflectance distribution functions algorithm (see Schaaf et al., 2002). An additional factor for All solvers included in libRadtran may include Lambertian simulating the hot spot in vegetation canopies was added by surfaces, while disort and MYSTIC can also handle bidirec- Maignan et al. (2004). The version implemented in libRad- 12 C. Emde et al.: The libRadtran software package

Table 6. The surface reflection models currently implemented in libRadtran.

Option name BRDF type # of parameters References Solvers albedo Lambertian 1 All brdf cam Ocean BRDF 3+1 Cox and Munk (1954a,b); Nakajima and Tanaka (1983) D,M bpdf tsang Polarized ocean BRDF 1 Tsang et al. (1985); Mishchenko and Travis (1997) M brdf hapke Planetary & lunar surfaces 3 Hapke (1993) D,M brdf ambrals Ross-Li, MODIS Land Surface, 3 Roujean et al. (1992); Wanner et al. (1997); Lucht et al. D,M RTLSR (2000); Schaaf et al. (2002); Maignan et al. (2004) brdf rpv Land surfaces 3+3 Rahman et al. (1993); Degunther¨ and Meerkotter¨ (2000) D,M Explanation: D: DISORT M: MYSTIC RTLSR: RossThickLiSparseReciprocal model, optionally with hot spot parameterization

695 tran is the RossThickLiSparseReciprocal model as used in MODIS data, as presented in Lucht et al. (2000). The hot spot correction factor can be turned on on demand. As already stated in Mayer and Kylling (2005), but re- peated here for completeness, a parameterization of the 107 0.5 106 0.4 700 BRDF of water surfaces is also included which depends 105 0.3 104 0.2 mainly on wind speed and to a lesser degree on plankton 103 0.1 2 concentration and salinity. For the MYSTIC solver, also the

P11 10 0.0 1

10 P12/P11 0.1 100 0.2 wind direction can be set. In contrast to vegetation where -1 ◦ 10 0.3 the typical hot spot occurs in the 180 backscatter direction, 10-2 0.4 0 30 60 90 120 150 180 0 30 60 90 120 150 180 705 1.0 0.3 the main feature for water is specular reflection. The param- 0.8 0.2 eterization in uvspec was adopted from the 6S code (Ver- 0.6 0.4 0.1 mote et al., 1997) and is based on the measurements of Cox 0.2 0.0 0.0 and Munk (1954a,b) and the calculations of Nakajima and

P33/P11 0.2 P34/P11 0.1 0.4 Tanaka (1983). A vector version of the ocean parameteriza- 0.2 0.6 0.8 0.3 710 tion, developed by Tsang et al. (1985) and Mishchenko and 0 30 60 90 120 150 180 0 30 60 90 120 150 180 1.0 1.0 Travis (1997), is available for polarization calculations with 0.8 0.8 0.6 MYSTIC. The vector version uses only wind speed as a pa- 0.6 0.4 0.2 rameter and does not take into account plankton concentra- 0.4 0.0 tion, salinity or wind direction.

P22/P11 0.2 P44/P11 0.2 0.4 0.0 715 Finally, the parameterization of the surfaces of extrater- 0.6 0.2 0.8 restrial solid bodies such as the moon, asteroids or the inner 0 30 60 90 120 150 180 0 30 60 90 120 150 180 scattering angle [degrees] scattering angle [degrees] planets by Hapke (1993) is available. Ice crystal habit Only the ocean BRDF parameterizations depend directly solid_column (smooth) solid_column (sev. rough) column_8elements (smooth) column_8elements (sev. rough) on the wavelength. For all other BRDF models, the pa- plate (smooth) plate (sev. rough) 720 rameterization can either be given as being constant with HEY ghm baum_v36 ghm wavelength (by using e.g. the option brdf rpv), or as a file containing the parameters for each wavelength (using e.g. brdf rpv file). Fig. 5. Phase matrix elements of ice crystal distributions with an effective radius of 40 µm at 550 nm wavelength. The red 7.2 Fluorescence lines correspond to smooth and the blue lines to severely rough crystals, respectively. The individual habits (solid-column, 725 For vegetation covered surfaces, a weak solar-induced column-8elements and plate) are for the parameterization yang2013, and the general habit mixtures (ghm) are for hey in- chlorophyll fluorescence signal is emitted in the red and far- cluding smooth crystals and baum v36 including severely rough red spectral regions. The contribution of fluorescence to the particles. radiance leaving the bottom boundary is F Lg (µ,φ,λ) = F (λ), (5)

730 where F (λ) is the fluorescence source in the same units as the incoming solar flux at the top of the atmosphere (for ex- C. Emde et al.: The libRadtran software package 13

ample mW/(m2 nm sr)). The fluorescence source of radiation 9 Graphical User Interface is included in the disort solver. It may either be constant or vary as a function of wavelength. Additional surface bidi- The large number of input options available in the uvspec 735 rectional reflection of radiation may also be included. The model may appear overwhelming. To help the user to create flourescence source depends on the solar radiation impinging 785 uvspec input files a graphical user interface (GUI) has been the vegetation and the type of vegetation. Output from vege- developed. The GUI organizes the input options in logical tation fluorescence canopy models such as that described by groups such as “Molecular Atmosphere”, “Aerosol”, “Sur- Miller et al. (2005), may readily be used by uvspec. face” etc., see also the grey bar at the top in Fig. 6. Input options that are set by the user and ✿✿✿that✿will be written to the 790 given input files are shown in bold face (for example option 740 8 Implementation improvements rte solver in Fig. 6). Options that may be set are shown as normal characters, while options that are not compati- 8.1 Multiple atmospheric constituents ble with other set options are greyed (for example in Fig. 6 mc ipa is greyed since it is not possible to combine it with The previous versions of libRadtran were restricted to using 795 rte solver set to disort). at most four types of atmospheric constituents: molecules, On-line documentation of the options are available and aerosols, and water and ice clouds. Any user defined con- this is identical to the documentation in the libRadtran 745 stituent could only be included by replacing e.g. water clouds user manual. In Fig. 6 the documentation for the option with them. Also, it was not possible to use several types of number of streams is shown in the lower left corner. ice cloud habits at the same time. 800 The on-line help is activated by pointing the mouse at the A recent major internal restructuring of the libRadtran requested input variable. code has now made it possible to use any number of Input options that refer to input data files, such as wave- 750 atmospheric constituents for a radiative transfer simula- length dependent surface albedo, may be plotted from the tion. The number is only limited by computational mem- GUI. In the example in Fig. 6, the extraterrestrial flux (up- ory and time. The new input options needed for load- 805 per left subplot), the surface fluorescence spectrum (lower ing the additional constituents are profile file and left subplot) and surface albedo (lower right subplot) inputs profile properties. They work very similar to the are plotted. Note that the wavelength coverage (x-axis) dif- 755 cloud input options; merely the name of the constituent needs fers reflecting the different wavelength regions included in to be defined. the input data files. This option increases the flexibility of libRadtran in many 810 Once all wanted input options are set, they are saved to a ways. E.g. it can be used to load the optical properties for user specified file, and uvspec is run from within the GUI. each size bin of an aerosol or water or ice cloud. This way, the The output from the run may readily be plotted using the 760 size distribution may differ between the atmospheric layers. GUI. For example, in Fig. 6, the calculated nadir radiance at An example can be found in Kylling et al. (2013). the top of the atmosphere is shown in the upper right subplot. 8.2 Change of nomenclature and backward compatibil- 815 The GUI includes numerous working examples. Users may ity add more examples to the GUI specific to their interests.

As the number of input options had grown to more than 300 10 Other tools 765 over the years, we decided to restructure the language of the input options. The input options now have a largely consis- Several additional tools are included in the libRadtran pack- tent naming and their usage follows certain rules, making it age. An overview is given in Mayer and Kylling (2005, Tab. more easy to find related input options. 820 4). New tools are ssradar, a single scattering Radar simulator We have included a python script in order to provide (see below), and pmom, which calculates Legendre polyno- 770 backward compatibility for long-established libRadtran mials for a given phase function. users. The script can be found in the directory src py. By invoking the command 10.1 Mie calculations python translate.py input_file \ > new_input_file The tool for Mie calculations (mie) has been extended con- 775 input files written in the old nomenclature will be translated 825 siderably. The user may select between two Mie codes, to the new nomenclature automatically. Alternatively, the old MIEV0 by Wiscombe (1980) or bhmie by Bohren and Huff- input file can be sent directly to uvspec with the following man (1983). The tool allows to generate input optical proper- command: ties for uvspec calculations for arbitrary size distributions. It python translate.py input_file | uvspec generates full phase matrices which are stored on optimized 780 830 angular grids for a user-defined accuracy. The radiative trans- fer solvers MYSTIC and DISORT with the new intensity 14 C. Emde et al.: The libRadtran software package

Fig. 6. Screenshot of the Graphical User Interface for a spectral high-resolution simulation of the O2-B band including a fluorescence source. Plots of input and output data are included together with the help information for one option. See text for further explanation.

correction method (Buras et al., 2011) use the phase func- new users to create input files. Below some applications of tions/matrices rather than Legendre polynomials, which are libRadtran are described. calculated by the Mie codes. 11.1 uvspec and ARTS

835 10.2 Single scattering Radar simulator The high number of absorption lines in the shortwave in- Single scattering Radar (ssradar) is a stand-alone 1D pure 855 frared and the thermal infrared requires a line-by-line ap- Rayleigh-scattering cloud radar simulator that handles arbi- proach to resolve the spectral structure. Below is shown how trary cloud layers and droplet size distributions as well as molecular absorption data from ARTS may be combined tilted viewing angles and supercooled water droplets. The with uvspec to perform line-by-line calculations in both the solar and thermal parts of the spectrum. For both examples 840 radar reflectivity factor is calculated directly from the droplet 6 860 the spectral resolution, the molecules to be included and the distribution with Z = niD (Rinehart, 2010) where D is i i line function properties are specified in the input to ARTS. It the droplet diameter andP ni the distribution number density is noted that the same ambient atmospheric profile should be for the discrete interval Di,Di+1. Internally available distri- butions are gamma and lognormal, arbitrary distributions can used in both, ARTS and uvspec. 845 be entered using input files. 11.1.1 Solar source

865 Solar induced chlorophyll fluorescence is emitted in the 660 11 Some applications to 800 nm spectral region with two broad peaks at about 685 and 740 nm. In this spectral region are the O2-A and O2- The libRadtran package has been used for numerous appli- B bands which contain a large number of absorption lines. cations. Many of these are listed under the publications link Although the fluorescence signal is weak, especially the O2- at http://www.libradtran.org. The examples directory also 870 B region holds promise for retrieval of vegetation fluores- 850 includes a number input files that may be used especially by cence from spectrally high resolution space borne instru- C. Emde et al.: The libRadtran software package 15

ments (Guanter et al., 2010). In this spectral region the sur- 11.1.2 Thermal source face albedo is typically low while there is a fluorescence peak around 685 nm (see red line lower plot Fig. 7). The opti- 890 The Infrared Atmospheric Sounding Interferometer (IASI) on board the MetOp satellite measures the radiance from 645 to 2760 cm−1 (15.50-3.6 µm) with a spectral resolution of 1e13 −1 1.0 0.25cm . Its main purpose is high-resolution atmospheric 1.0 sounding of temperature and humidity, and trace gas column Transmittance 895 retrievals (Clerbaux et al., 2009; Hilton et al., 2011). It may 0.8

sr)] 0.8 Radiance also be used to detect volcanic ash (see Clarisse et al., 2013, 2 and references therein). 0.6 0.6 The left panel of Fig. 8 shows IASI spectra from a granule covering the ash cloud following the eruption of Mt. Kelud, 0.4 0.4 900

Transmittance Indonesia, in February, 2014. The spectra are classified as cloudless (green), ice cloud (blue), and volcanic ash (red). To

L [photons/(s nm cm nm L[photons/(s 0.2 0.2 investigate the realism of this identification the spectra were simulated with ARTS/uvspec. For all simulated spectra, the 0.0 0.0 675 680 685 690 695 700 surface emissivity was set equal to one which is representa- Wavelength [nm] 905 tive for water. The simulated spectra are shown in the right 1e13 0.2 plot of Fig. 8. With fluorescence 1.0 Without fluorescence The cloudless spectrum has brightness temperatures rep- Fluorescence source (*20) resentative for the ocean at these latitudes. The main molec-

sr)] Albedo

2 ular absorption features in this part of the spectrum are 0.8 910 water vapor lines throughout the spectrum, ozone (broad −1 0.1 band feature centered around 1050 cm ), and CO2 (fea- 0.6 −1

Albedo ture below 800 cm ). The data from ARTS include ab- sorption lines from these molecules. In the cloudless spec- −1 0.4 trum the ozone band around 1050 cm is colder has✿✿✿✿a L [photons/(s nm cm nm [photons/(s L 915 ✿✿✿✿✿lower ✿✿✿✿✿✿✿✿✿brigthness ✿✿✿✿✿✿✿✿✿✿temperature✿ than the radiation at lower and higher wavenumber, indicating that the radiation in the 0.2 0.0 675 680 685 690 695 700 ozone band was emitted at a higher and colder altitude Wavelength [nm] ✿✿✿✿✿✿altitude✿✿✿✿with✿✿✿✿✿lower✿✿✿✿✿✿✿✿✿✿temperature✿than the surface. Overall the ARTS/uvspec cloudless spectrum agrees well with the mea- Fig. 7. (Upper plot) The transmittance from ARTS output and ra- 920 sured spectrum. diance from uvspec. (Lower plot) The top of the atmosphere nadir For the simulation with an ice cloud, the ice cloud was lo- viewing radiance in the O2-B band with (blue black line) and with- cated between 12 and 13 km. Ice water content was set to ✿✿✿✿✿ 3 out (purple✿✿✿✿cyan line ✿✿✿with✿✿✿✿✿circles) a surface fluorescence source (red 1 g/m . The ice particles were assumed to consist of solid line ✿✿✿with✿✿✿✿✿✿✿triangles). The radiances have been convolved with a spec- columns with reff =40.0 µm. The ice cloud parameterization tral response function with FWHM of 0.3 nm. 925 ic properties yang was selected. The spectrum iden- tified as ice cloud (blue curve in left plot of Fig. 8) appears saturated for nearly all wavenumbers except for the ozone −1 875 cal depths from ARTS are input to uvspec which calculates band centered around 1050 cm . The rather low brightness the top of the atmosphere radiance (blue line, upper plot of temperature and wavenumber independent behaviour outside Fig. 7) including the fluorescence signal (red line, lower plot 930 the ozone band, indicates that this is an ice cloud and that it of Fig. 7), surface albedo (green line, lower plot of Fig. 7) and is opaque. The simulation with an ice cloud (blue curve in molecular scattering . Measurements may be made at a lower right plot of Fig. 8) agrees well with the measured spectrum. 880 spectral resolution. The lower plot of Fig. 7 shows radiance The higher temperatures in the ozone band implies that this spectra convolved with a triangular spectral response func- radiation was emitted at a higher altitude in the stratosphere tion with a full width at half maximum (FWHM) of 0.3 nm 935 where the temperature is higher than at the altitude of the using the conv tool of libRadtran. The spectral response func- cloud. tion was generated with the make slitfunction tool. Spectra The ash simulation included an ash cloud between 17 and 885 with (blue line) and without (purple line) fluorescence are 18 km. The ash particles were assumed to be made of an- presented. It is seen that the fluorescence signal is relatively desite, spherical and mono-disperse with a radius of 3 µm. larger when the surface albedo is low, below about 690 nm, 940 The refractive index of andesite was taken from Pollack et al. compared to larger wavelengths. (1973) and the optical properties were calculated using the 16 C. Emde et al.: The libRadtran software package

Measured (IASI) Simulated (ARTS/uvspec) Wavelength (µm) Wavelength (µm) 14 13 12 11 10 9 8 14 13 12 11 10 9 8

300 300

280 280

260 260

Processes included Classification Cloudless 240 240 Cloudless Volcanic ash

Brightness temperature (K) Volcanic ash Brightness temperature (K) Ice cloud Ice cloud Volcanic ash and ice cloud 220 220

200 200 700 800 900 1000 1100 1200 700 800 900 1000 1100 1200 Wavenumber (cm−1 ) Wavenumber (cm−1 )

Fig. 8. (Left plot) Brightness temperature spectra for different locations as measured by IASI on 15 February, 2014, 02:33 UTC, during the Mt. Kelud, Indonesia, eruption. Tentative classification of the spectra is given in the legend. See text for details. (Right plot) Simulated brightness temperature spectra using ARTS/uvspec. The atmospheric processes included in the simulations are given in the legend.

mie tool. The ash density was 1×10−3 g/m3 which corre- with both ash and ice is seen to well reproduce the measured sponds to a mass loading of 1 g/m2 for a 1 km thick cloud. ash spectrum in the left plot of Fig. 8. The red curve in the left plot of Fig. 8 is classified as 945 ash using the difference in brightness temperature method 11.2 Simulated satellite image described by Clarisse et al. (2010). This spectrum is colder

✿✿✿has ✿a✿✿✿✿✿lower✿✿✿✿✿✿✿✿✿brigthness✿✿✿✿✿✿✿✿✿✿temperature✿than the cloudless spec- trum indicating a colder effective emitting temperature over- 975 Fig. 9 shows a simulated satellite image (top) and the corre- all. The general spectral shape is similar to the cloudless sponding observation (bottom). Three visible channels of the −1 −1 950 spectrum below 1000 cm . Above about 1200 cm the SEVIRI instrument on the MSG (Meteosat Second Genera- brightness temperature of the cloudless spectrum generally tion) satellite were simulated based on input data from the decreases with increasing wavenumber, while the converse operational COSMO-DE forecast (Baldauf et al., 2011) of is true for the ash spectrum. The simulated ash cloud spec- 980 Deutscher Wetterdienst for the 15th July 2012, 12 UTC. The trum (black curve in right plot of Fig. 8) differs from the spatial resolution of the simulation is 2.8 km×2.8 km, that 955 measured spectrum classified as ash. Both the simulated and of the SEVIRI observation is 3 km×3 km at the sub-satellite measured ash spectra increase in magnitude with increasing point. A false color composite was generated using the sim- wavelength above 1100 cm−1, but the simulated spectrum ulated radiance of the 1.6 µm channel for red, the 0.8 µm − increases more. Below about 900 cm 1 the spectral behav- 985 radiance for green and 0.6 µm radiance for blue. The simu- ior of the measured and simulated spectra differs. This may lations were performed using the one-dimensional disort 960 be due to either wrong assumptions about the ash type and solver. The MODIS surface albedo dataset was used (Schaaf hence refractive index and/or the mixing of ice with ash. Ice et al., 2002) to set the Lambertian surface albedo. The effec- clouds have an opposite effect of ash clouds on the bright- tive radii of liquid clouds were parameterized according to − ness temperature between 800-1000 cm 1, whereas above 990 Martin et al. (1994), and for the optical properties the mie 1075 cm−1 ice clouds have only a very weak dependence on parameterization was applied. Ice cloud effective radii were 965 wavenumber (see Fig. 2 of Gangale et al., 2010). To test if the parameterized according to Wyser (1998) and for the corre- presence of both ash and ice could reproduce the measured sponding optical properties the parameterization baum v36 spectrum, simulations were made with both an ash cloud and was used with the general habit mixture. Molecular absorp- an ice cloud. The altitude and thickness of the clouds were as 995 tion was included using the reptran parameterization. In above, but the ash cloud density was 2×10−4 g/m3 and the the false color composite water clouds appear white and −2 3 970 ice water content 1.5×10 g/m . The resulting spectrum is ice clouds appear blueish, because ice absorbs in the region shown in maroon in the right plot of Fig. 8. The mixed scene about 1.6 µm. The simulated image looks very similar to the observation. A major difference is that the ice clouds in the C. Emde et al.: The libRadtran software package 17

0

50

100 I Q

0.00 150 0.03

0.02 0.01 200 0.01 mol. atmosphere 0 100 200 300 400 0 0.00 0.02

0.01 0.12 50 0.03 0.08

100 0.05 0.04 ocean surface

0.07 0.00 150

0.00 0.09 200

0 100 200 300 400 0.01 0.08 aerosol desert

0.07 0.02 Fig. 9. Top: Simulation of MSG-SEVIRI image. False color com- posite, where red corresponds to the 1.6 µm channel, green to 0.00 0.8 µm and blue to 0.6 µm. The simulation was performed using 0.14 the disort solver with input data from the operational COSMO- 0.01 DE forecast for the 15th July 2012, 12 UTC. The axes correspond 0.12 to SEVIRI pixel. Bottom: Corresponding SEVIRI image.

liquid water cloud 0.02 0.10

0.01 1000 observation appear more blueish, the reason is that their real 0.14 optical thickness is larger than in the COSMO-DE forecast. 0.10 0.00

11.3 Polarization 0.06

ice cloud smooth 0.01 The MYSTIC solver can be applied to simulate multi- 0.02 angle multi-spectral polarized radiances using the option 0.00 1005 mc polarisation (Emde et al., 2010). Polarized radia- 0.06 tive transfer using MYSTIC has been validated in extensive model intercomparison projects (Kokhanovsky et al., 2010; 0.04 0.01 Emde et al., 2015). ice cloud rough 0.02 Fig. 10 shows an example for simulations at wavelengths 50 25 0 25 50 50 25 0 25 50 1010 of 443, 670 and 865 nm; these are measured by the POLDER viewing angle [ ◦ ] viewing angle [ ◦ ] (Polarization and Directionality of the Earth’s Reflectances) instrument onboard PARASOL (Polarization and Anisotropy Fig. 10. Stokes vector components I and Q at wavelengths of of Reflectances for Atmospheric Sciences coupled with Ob- 443 nm (blue solid lines), 670 nm (green dashed lines), and 865 nm (red dashed-dotted lines) for various atmospheric setups (see text servations from a Lidar) (Deschamps et al., 1994). All sim- ◦ for details). The radiances are calculated at the top of the atmo- 1015 ulations are for a solar zenith angle of 30 and show the re- sphere for viewing angles from -50◦ to 50◦, where 0◦ corresponds flected radiances (normalized to incoming solar irradiance) to the nadir direction. at the top of the atmosphere in the solar principal plane. The viewing angle of 30◦ corresponds to the exact backscattering direction. The angular resolution is 2◦. All simulations are 1020 for the US standard atmosphere. The figure shows the first and second components of the Stokes vector I and Q; the 18 C. Emde et al.: The libRadtran software package

components U and V are exactly 0 in the principal plane for has been used to determine the fraction of smooth crystals in symmetry reasons. ice clouds from POLDER measurements (Cole et al., 2014). The first row shows the results for a clear atmosphere, 1025 i.e. Rayleigh scattering and molecular absorption. Here I is 11.4 Fully spherical geometry largest for the shortest wavelength because the Rayleigh scat- tering cross section decreases with λ−4, where λ is the wave- MYSTIC can be operated in fully spherical geometry length. The absolute value of Q also increases with increas-1080 (mc spherical 1D). The implementation of 1D spheri- ing Rayleigh scattering cross section. A negative Q means cal geometry is described in Emde and Mayer (2007) where 1030 that Rayleigh scattering polarizes perpendicular to the scat- it has been used to simulate radiation in the umbral shadow of tering plane, which, for single scattering, corresponds to the a solar eclipse. A comparison to measurements during the to- principal plane for this geometry. tal eclipse in Greece in March 2006 (Kazantzidis et al., 2007) The second row of the figure shows the same simulation1085 showed a very good agreement for modeled and measured but with an underlying ocean surface, which is modelled ac- UV irradiances, which decreased during totality by 2 to 3 or- 1035 cording to Mishchenko and Travis (1997) (bpdf tsang). ders of magnitude depending on wavelength. Fully spherical geometry has also been used to simu- The wind speed was set to 2 m/s. I and Q clearly show the ◦ sun glint which has a maximum at a viewing angle of about late actinic fluxes at high solar zenith angles up to 92 -30◦ and which is highly polarized. The intensity of the sun-1090 (Suminska-Ebersoldt´ et al., 2012). glint increases with increasing wavelength since the incom- Another interesting application is the simulation of polar- 1040 ing radiance at the surface becomes less diffuse when there ized radiance at the surface at twilight, because polarized is less Rayleigh scattering in the atmosphere. radiance measurements at twilight can be used to retrieve The third row shows the result for desert aerosol as de- aerosol optical properties (e.g. Saito and Iwabuchi (2015)). 1095 As an example we calculated polarized clear sky radiances fined in the OPAC database (aerosol species file ◦ desert), with an underlying Lambertian surface albedo of for solar depression angles up to 9 for the US-standard at- 1045 0.3. I shows a backscatter peak at 670 and 865 nm. Q looks mosphere and default Rayleigh scattering and absorption set- similar as for Rayleigh scattering, however there are differ- tings. Fig. 11 shows the result as a function of viewing zenith angle. The relative azimuth angle between sun and observer ences mainly around the backscatter region. At wavelengths ◦ of 670 and 865 nm, Q has a minimum in the exact backscat-1100 is 0 which means that the observer looks into the direction of the sun. We see that the intensity decreases by about four ter direction and becomes positive for viewing angles around ◦ 1050 this direction. orders of magnitude for solar depression angles between 0 (sun at horizon) and 9◦ (sun 9◦ below horizon). The degree The fourth row shows a simulation including a water cloud ◦ (wc properties mie) in 2-3 km altitude with an optical of polarization (not shown) at a viewing angle of 5 is more thickness of 10 and an effective droplet radius of 10 µm. I1105 than 90%. All results agree to published results by Blattner¨ and Q show the glory about the backscatter direction and et al. (1974), which indicates that fully spherical geometry ◦ 1055 the rainbow at a viewing angle of about -10 corresponding works correctly in MYSTIC. to a scattering angle of 140◦. In Q the rainbow is more pro- nounced than in I because Q is less affected by multiple scat- 12 Summary tering. The angular resolution shown here is not sufficient to separate the glory from the backscattering peak in I. The sign We have presented the libRadtran software package (version 1060 of Q in the rainbow region is the same as for Rayleigh scat- 1110 2.0.1), which is a comprehensive and powerful collection of tering whereas it is opposite in the glory region, which means tools for radiative transfer simulations in ✿✿of✿the Earth’s at- that the rainbow is polarized perpendicular to the scattering mosphere. It is user-friendly, well-documented and is widely plane whereas the glory is polarized parallel to the scattering used in the scientific community. We have described vari- plane. ous new features and parameterizations which have been in- 1065 The last two rows show simulations with ice clouds, where 1115 cluded after the first publication of libRadtran in 2005. New we have used the yang2013 parameterization. An ice cloud features are for example a vector radiative transfer solver layer with an optical thickness of 2 was included at an alti- and a solver for rotational Raman scattering. The package in- tude from 9–10 km. The selected habit was solid column cludes state-of-the-art parameterizations for aerosol and ice and we performed simulations for smooth crystals and for cloud optical properties and a newly developed efficient ab- 1070 severely rough crystals respectively. The effective crystal 1120 sorption parameterization. radius in both simulations is 30 µm. The smooth crystals show a backscatter peak in I and a positive Q about the backscatter direction. Also there are some smaller features 13 Code availability in I and Q. The radiances (I and Q) for rough crystals are 1075 smooth functions of viewing angle. This different behaviour The libRadtran package was initiated about 20 years ago and is still under continuous development. Regularly up- C. Emde et al.: The libRadtran software package 19

500 nm 700 nm 100 100 References

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Wandji Nyamsi, W., Arola, A., Blanc, P., Lindfors, A. V., Cesnulyte, Appendix A V., Pitkanen,¨ M. R. A., and Wald, L.: Technical Note: A novel 1705 parameterization of the transmissivity due to ozone absorption1760 Ice crystal optical properties parameterizations in the k-distribution method and correlated-k approximation of Kato et al. (1999) over the UV band, Atmospheric Chemistry and The parameterization yang2013 is based on the single scat- Physics, 15, 7449–7456, doi:10.5194/acp-15-7449-2015, http:// tering data by Yang et al. (2013). It is available for nine habits www.atmos-chem-phys.net/15/7449/2015/, 2015. and three roughness parameters. It includes full phase matri- 1710 Wanner, W., Strahler, A., Hu, B., Lewis, P., Muller, J.-P., Li, X., ces for the spectral range from 200 nm to 99 m. 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A., Veira, A., Kueppers, U., and Schumann, U.: On the visi- In order to obtain bulk scattering properties (required by 1720 bility of airborne volcanic ash and mineral dust from the pi- the RTE solver) the single scattering properties need to be in- lot’s perspective in flight, Phys. Chem. Earth, 45-46, 87–102, tegrated over the particle size distribution. In reality the size doi:10.1016/j.pce.2012.04.003, 2012. 1775 distributions are highly variable, for radiative transfer sim- Wiscombe, W.: Improved Mie scattering algorithms, Appl. Opt., 19, 1505–1509, 1980. ulations they are often approximated by simple gamma dis- 1725 WMO: Atmospheric Ozone 1985, Tech. rep., WMO Report No. 16, tributions (e.g. Evans, 1998; Heymsfield et al., 2002; Baum 1986. et al., 2005a,b) or bi-modal gamma distributions (Mitchell et al., 1996; Ivanova et al., 2001). We assume a gamma size C. Emde et al.: The libRadtran software package 25

1780 distribution to compute the bulk scattering properties as for each scattering angle θ and for six matrix elements (denoted the water cloud properties (compare Eq. 4): by index i) needed to describe the scattering process by ran-

1 domly oriented nonspherical particles (see e.g. van de Hulst, b −3 re n(re) = Nre exp − (A1)1825 1981)):  ab Here r is a measure of the particle size (the radius in case Lmax e Lmin A(L)P (L,i,θ)ω0(L)Qext(L)n(L)dL hP (reff ,i,θ)i = of spherical particles) and N is the normalization constant R Lmax A(L) ω0(L)Qext(L)n(L)dL 1785 so that the integral over the distribution yields the number of Lmin particles in a unit volume. For spherical particles the param- R (A6) eters a and b correspond to the effective radius reff and to the Optical properties for a general habit mixture ghm have effective variance veff , respectively. Typical values of cirrus also been calculated for the hey parameterization following cloud size distributions for b are in the range between 0.1 and the mixing “recipe” suggested by Baum et al. (2005b). 1790 0.5 (Evans, 1998; Heymsfield et al., 2002). In the following we take a fixed value of b = 0.25. We define the effective par- ticle size re(L) for an individual ice crystal as follows (Yang1830 Appendix B et al., 2005): Description of TZS solver 3 V (L) re(L) = (A2) 4 A(L) This solver is based on the zero scattering approximation and can be used to calculate clear sky or “black cloud” radiances 1795 Here L is the maximum dimension of a nonspherical ice at the top of the atmopshere (TOA) in the thermal spectral crystal and A and V are the✿✿✿✿✿mean projected area and the vol- 1835 range. Without scattering the formal solution of the radiative ume of the particle, respectively. 2r (L) corresponds to the e transfer equation for the upward intensity (radiance) at TOA “effective distance”, i.e. the representative distance a photon at a given frequency reduces to travels through an ice crystal without experiencing internal Iν (τ = 0,µ,φ) ν 1800 reflections and refraction (Mitchell et al., 1996). The effec- ∗ ∗ Iν (τ = 0,µ,φ) = Iν (τ ,µ,φ)exp(−τ /µ) tive radius of a size distribution is generally defined as: τ ∗ Lmax dτ 1840 (B1) 3 Lmin V (L)n(L)dL + Bν (τ)exp(−τ/µ) . reff = (A3) Z µ 4 R Lmax 0 Lmin A(L)n(L)dL R Here we used the (vertical) absorption optical thickness τ In order to obtain bulk scattering properties which can be measured from top of atmosphere as the vertical coordinate used for radiative transfer calculations, we pre-calculate bulk such that τ = 0 at TOA and τ = τ ∗ at the surface. Variables 1805 optical properties on a specified equidistant effective radius 1845 µ and φ denote the cosine of the zenith angle and the azimuth grid including values from 5 to 90 µm in steps of 5 µm. angle respectively. Planck’s function at a given frequency ν Now using Eq. (A3) we iteratively find the parameter a of the is represented by Bν (τ) and its temperature dependence is size distribution which results in the desired effective radius. contained implicitly in τ. The bulk optical properties are then calculated by integration The first term on the right hand side in Eq. B1 represents 1810 over the gamma distributions with the parameters b=0.25 and1850 the contribution of the surface and the second one the con- the iteratively obtained a depending on the effective radius. tribution of the atmosphere. The surface contribution can be libRadtran requires the extinction coefficient normalized to written as 1 g/m3 ice: ∗ ∗ Lmax Iν (τ ,µ,φ) = ǫs Bν (τ )+ A(L)Qext(L)n(L)dL ∗ Lmin 1 τ ext eff (A4) hβ (r )i = Lmax R ρ V (L)n(L)dL ∗ Lmin 1855 + 2(1 − ǫs) Bν (τ)exp(−(τ − τ)/µ)dτdµ (B2) Z Z R 0 0 1815 Here Qext(L) is the extinction efficiency, ρ is the density of ice, and n(L) is the gamma size distribution which cor- with the first term representing the emission of the surface responds to the effective radius reff . The single scattering (ǫs=surface emissivity) and the second one the reflection at albedo hω0i is calculated as follows: the surface of the radiation emitted by the atmosphere toward 1860 the surface. The factor 2 comes from the integration over the Lmax Lmin A(L)ω0(L)Qext(L)n(L)dL azimuth angle φ. hω0(reff )i = (A5) R Lmax Under the approximation of Planck’s function B (τ) as a A(L)Qext(L)n(L)dL ν Lmin piecewise linear function in τ between two consecutive lev- R 1820 Finally, libRadtran requires the phase matrix hP (reff )i, els, both integrals can be solved as a function of the expo- −x −y which is computed according to the following equation for1865 nential integral Ei(x) = −∞ e /y dy. R 26 C. Emde et al.: The libRadtran software package

Acknowledgements. Numerous colleagues have contributed with software and comments to the package. We would like to thank K. Stamnes, W. Wiscombe, S.C. Tsay, and K. Jayaweera (disort), F. Evans (polradtran), S. Kato (correlated-k distribution), J.-M. Van- 1870 denberghe, F. Hendrick, and M. V. Roozendael (sdisort), T. Char- lock, Q. Fu, and F. Rose (Fu and Liou code), D. Kratz (AVHRR routines), B. A. Baum, P. Yang, L. Bi, H. Gang, J. Key, B. Rein- hardt, and A. Gonzales (ice cloud optical properties), P. Ricchiazzi (LOWTRAN/SBDART gas absorption), M. Hess (OPAC aerosol 1875 database), W. Wiscombe, C. F. Bohren, and D. Huffman (Mie codes), M. Mishchenko (water reflectance matrix), O. Engelsen (implementation of ozone cross sections), the ARTS community and Franz Schreier (line-by-line models), J. Betcke (implementa- tion of King Byrne equation). Thanks to all users for feedback and 1880 contributions, which helped to improve the software over the years. Thanks also to L. Scheck for providing the simulated satellite image

shown in Sec. 11.2. Finally we thank two anonymous reviewers and✿✿ ✿✿the✿✿✿✿✿✿topical ✿✿✿✿editor✿✿✿K. ✿✿✿✿✿✿Gierens for their useful comments. Part of the libRadtran development was funded by ESA (ESASLight projects 1885 AO/1-5433/07/NL/HE, AO/1-6607/10/NL/LvH). Point-to-point response to reviews

Answers to referee 1:

1. The paper should emphasis what is the added-value of this paper with respect to the user guide?

Certainly the most important point of the paper is that users need a reference for the model which they can use in their publications. The User Guide cannot serve as such a reference since it is grey literature which changes continuously. The previous libRadtran paper is more than 10 years old and it has been referenced close to 500 times, illustrating the need for a reasonably up-to-date reference. In addition to just documenting the parts of libRadtran, the papers explains a number of new and previously not documented features, e.g. how the optical properties of ice clouds were created. The paper, on the other hand, is no substitute for the User Guide which documents all 200 input options and has close to 200 pages. We feel that both are needed (and so do the users, obviously).

2. Information is lacking about the performance of this model when compared to other models for standard cases, or RTE solver between them.

This is a very important suggestion. A section on the "accuracy of solvers" has been included. Here references to a number of model intercomparison studies are provided which demonstrate the performance of libRadtran in comparison to a variety of other models. A reference to a comparison between the MYSTIC and the DISORT solver is also given. Further it is suggested to use MYSTIC as reference solver in order to estimate the accuracy of other solvers.

3. In Section 3.2, some parts of MYSTIC are not publicly available. Is it therefore appropriate to present them here?

The text has been slightly changed and the 3D version of MYSTIC is now only mentioned at the end of the section. It should be mentioned in the paper that there is the 3D version and that it is available in joint projects.

Answers to referee 2:

1) Section 3: The authors present the main features of the basic solvers used in libRadtran and the improvements that have been implemented in them. However, they do not provide a comparison with other codes/models. Moreover, it would very useful if they could provide a table containing the estimated uncertainties in the derived irradiances/radiances (possibly as a function of solar zenith angle), to help users select the right solver for their particular needs. This is a very good suggestion since libRadtran participated in various intercomparison studies where the uncertainties of the different solvers were assessed. A Subsection on the "accuracy of solvers" has been included in Section 3. References to model intercomparison studies are provided. A reference to a comparison between the MYSTIC and the DISORT solver is also given. Further it is suggested to use MYSTIC as reference solver in order to estimate the uncertainties of other solvers. A table has not been included because the range of applications is too large and there are too many parameters despite solar zenith angle that can influence the accuracy of the result (e.g. viewing angles, cloud optical properties, aerosol optical properties, surface properties ...).

2) Section 8.2: In the LibRadtran manual, it is mentioned that the "translate.py" function can be found under the directory "src_py/" but it is not clear at this point in the text.

The path has been included in Section 8.2.

3) Section 11: It would nice if the authors could provide the input files (possible as a supplement) so that the example presented here can be easily repeated by interested users. Moreover, the package itself includes a number of examples under the directory “examples/” that could be used (especially by new users) to create input files they would need.

The "examples" directory is now mentioned. Input files and python scripts to loop over various parameters are provided as supplement to the paper. Changes made in the manuscript:

• The most important changes are two new sections:

“Sec. 3.6 Accuracy of solvers” - this was requested by both reviewers

“Sec. 13 Code availability” - this is required for all GMD publications, as pointed out by A. Kerkweg

• Table 2 includes a new reference, which corresponds to an update of the Kato absorption parameterization. This update has been included in libRadtran after the publication of the discussion paper, for this reason we have also changed the version number of the software from 2.0 to 2.0.1.

• Other changes are only minor and can be seen in the marked-up manuscript. Manuscript prepared for Geosci. Model Dev. with version 5.0 of the LATEX class copernicus.cls. Date: 4 April 2016

The libRadtran software package for radiative transfer calculations

(Version 2.0.1✿✿)

Claudia Emde1, Robert Buras-Schnell5, Arve Kylling2, Bernhard Mayer1, Josef Gasteiger1, Ulrich Hamann4, Jonas Kylling2,3, Bettina Richter1, Christian Pause1, Timothy Dowling6, and Luca Bugliaro7 1Meteorological Institute, Ludwig-Maximilians-University, Theresienstr. 37, D-80333 Munich, Germany 2NILU – Norwegian Institute for Air Research, Kjeller, Norway 3Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Oslo, Norway 4MeteoSwiss, Radar, Satellite and Nowcasting Division, Via ai Monti 146, Locarno, Switzerland 5Schnell Algorithms, Am Erdapfelgarten¨ 1, 82205 Gilching, Germany 6Dept. of Physics & Astronomy, University of Louisville, KY 40292 USA 7Institut fur¨ Physik der Atmosphare,¨ Deutsches Zentrum fur¨ Luft- und Raumfahrt (DLR), Oberpfaffenhofen, 82234 Wessling, Germany

Correspondence to: Claudia Emde ([email protected])

Abstract. libRadtran is a widely used software package for 25 1 Introduction radiative transfer calculations. It allows to compute (polar- ized) radiances, irradiances, and actinic fluxes in the so- Radiative transfer modeling is essential for remote sensing lar and thermal spectral regions. libRadtran has been used of planetary atmospheres, but also for many other fields in 5 for various applications, including remote sensing of clouds, atmospheric physics: e.g., atmospheric chemistry which is aerosols and trace gases in the Earth’s atmosphere, climate largely influenced by photochemical reactions, calculation of studies, e.g., for the calculation of radiative forcing due to 30 radiative forcing in climate models, and radiatively driven different atmospheric components, for UV-forcasting, the dynamics in numerical weather prediction models. calculation of photolysis frequencies, and for remote sens- The libRadtran software package is a versatile toolbox 10 ing of other planets in our solar system. The package has which has been used for various applications related to at- been described in Mayer and Kylling (2005). Since then sev- mospheric radiation, a list of publications that have used the eral new features have been included, for example polar- 35 package can be found on the website http://www.libradtran. ization, Raman scattering, a new molecular gas absorption org, currently it includes more than 400 entries. Applications parameterization, and several new cloud and aerosol scat- include the following topics (the given references are taken 15 tering parameterizations. Furthermore a graphical user in- as examples out of the list of publications): terface is now available which greatly simplifies the usage of the model, especially for new users. This paper gives an – Analysis of UV-radiation measurements, from which 40 parameters like e.g. ozone concentrations, aerosol opti- overview of libRadtran version 2.0.1✿✿with focus on new fea- tures. Applications including these new features are provided cal thickness, UV-index are derived. Since the libRad- ✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿ tran package originally was a radiative transfer code for 20 ✿✿as ✿✿✿✿✿✿✿✿examples ✿✿of ✿✿✿use.✿A complete description of libRadtran and all its input options is given in the user manual included in the UV spectral range (the main executable is still called the libRadtran software package, which is freely available at uvspec), the model is well established in this research http://www.libradtran.org. 45 area and frequently used (e.g. Seckmeyer et al., 2008; Kreuter et al., 2014).

– Cloud and aerosol remote sensing using measure- ments in solar and thermal spectral regions. The devel- oped retrieval methods are for ground-based, satellite 2 C. Emde et al.: The libRadtran software package

50 and air-borne instruments which measure (polarized) ra- Since the publication of the first libRadtran reference pa- diances (e.g. Painemal and Zuidema, 2011; Bugliaro per (Mayer and Kylling, 2005) the model has been further et al., 2011; Zinner et al., 2010; Alexandrov et al., developed. It includes numerous new features which will be 2012). the focus of this paper. 100 One of the major extensions is the implementation of po- – Volcanic ash studies including remote sensing of ash larization in the radiative transfer solver MYSTIC (Emde 55 mass concentrations (e.g. Gasteiger et al., 2011; Kylling et al., 2010), which is important because an increasing num- et al., 2015) and visibility of ash particles from the pi- ber of polarimetric observations have been performed during lot’s perspective (e.g. Weinzierl et al., 2012). the last years and are planned for the future, from ground, 105 satellite, and air-craft. These observations include more in- – Remote sensing of surface properties; a model like formation about optical and microphysical properties of at- libRadtran is particularly important to develop atmo- mospheric particles than total radiances alone (Kokhanovsky 60 spheric correction methods (e.g. Drusch et al., 2012; et al., 2010; Mishchenko et al., 2007). Another important Schulmann et al., 2015). reason for considering polarization is that in the short-wave – Trace gas remote sensing, libRadtran can be used as 110 spectral region (below about 500 nm) the neglection of polar- forward model for retrievals of O3, NO2 and BrO from ization can lead to large errors: more than 10% for a molecu- DOAS (Differential Optical Absorption Spectroscopy) lar atmosphere and up to 5% for an atmosphere with aerosol 65 measurements (e.g. Theys et al., 2007; Emde et al., (Mishchenko et al., 1994; Kotchenova et al., 2006). 2011). Moreover libRadtran now includes a solver to calculate ro- 115 tational Raman scattering (Kylling et al., 2011) which affects – Calculation of actinic fluxes in order to quantify pho- the accuracy of trace gas retrievals. Further the Raman scat- tolysis rates for atmospheric chemistry (e.g. Suminska-´ tering signal can be used to estimate cloud top pressure from Ebersoldt et al., 2012). satellite measurements and aerosol properties from surface and satellite observations. 70 – Determination of solar direct irradiance and global ir- 120 Numerous state-of-the-art parameterizations for aerosol radiance distributions in order to optimize locations of and ice cloud optical properties have been included (see solar energy platforms (e.g. Lohmann et al., 2006) and Secs. 5 and 6). These new parameterizations provide more calculation of circumsolar irradiance (Reinhardt et al., accurate radiance calculations. In particular for polarized ra- 2014). diative transfer, which requires not only a scattering phase 125 function but the full scattering matrix, new optical proper- 75 – Simulation of satellite radiances to be used for data ties data were required. In order to improve the accuracy for assimilation in numerical weather prediction models highly peaked phase functions – which are typical for ice (Kostka et al., 2014). clouds – an improved intensity correction method has been – Validation of radiation schemes included in climate developed and included into the DISORT solver (Buras et al., models (Forster et al., 2011), calculation of radiative 130 2011), and new variance reduction methods have been devel- 80 forcing of clouds and contrail cirrus (Forster et al., oped for the Monte Carlo solver MYSTIC (Buras and Mayer, 2012), impacts of aviation on climate (e.g. Lee et al., 2011). libRadtran has also been rewritten to allow simula- 2010) tions with an arbitrary number of cloud and aerosol types – which can e.g. be used to simulate variability in particle size – Simulation of heating rates in three-dimensional atmo- 135 distribution. spheres to develop fast radiation parameterizations for A new gas absorption parameterization for the solar and 85 Large Eddy Simulation (LES) models (Klinger and thermal spectral ranges has been developed (Gasteiger et al., Mayer, 2014). 2014). It is available in different spectral resolutions and can be applied for the simulation of radiances and irradiances. – Simulation of solar radiation during a total eclipse 140 It is particularly useful for efficient simulations of radiances (Emde and Mayer, 2007). measured by satellite instruments (see Sec. 4.1). The DISORT radiative transfer solver has been translated – Rotational Raman scattering, which explains the from FORTRAN77 to the C programming language. All vari- 90 filling-in of Fraunhofer lines in the solar spectrum ables were transferred from single to double precision. These (Kylling et al., 2011). 145 changes improved the numerical stability of the code and re- – Estimation of background radiation affecting lidar duced computational time significantly (for details see Buras measurements (e.g. Ehret et al., 2008) et al., 2011). The paper is organized as follows: Sec. 2 provides an – Remote sensing of planetary atmospheres (e.g. Ran- overview of the uvspec radiative transfer model which is 95 nou et al., 2010) 150 the core of the libRadtran package. Sec. 3 gives a short de- C. Emde et al.: The libRadtran software package 3

scription of the radiative transfer solvers included in uvspec. 2. The user may select between various parameteriza- Sec. 4 provides a summary of how molecules are han- 175 tions to convert the atmospheric state into optical prop- dled and outlines various ways to include molecular absorp- erties, e.g. to convert from cloud liquid water content tion. Moreover Rayleigh scattering parameterizations are de- and effective droplet size to extinction coefficient, sin- 155 scribed. Sec. 5 summarizes the available parameterizations gle scattering albedo and scattering phase function, or for aerosol microphysical and optical properties. Sec. 6 gives phase matrix when polarization is considered. an overview of the parameterizations for water and ice clouds and also outlines how these were generated. In Sec. 7 avail- 180 3. The optical properties are passed to a radiative transfer able surface properties are described, including Lambertian equation (RTE) solver, where again it is up to the user to select the most appropriate one for the given applica- 160 reflection, bidirectional distribution functions and fluorescent surfaces. In Sec. 8 we describe code and implementation im- tion. Currently, more than a dozen different solvers are provements relevant for users. Sec. 9 introduces the graphical included in uvspec. The six most used and maintained user interface for uvspec. Sec. 10 provides a short summary 185 RTE solvers are listed in Table 1 and briefly described in of additional tools that come with the libRadtran package. Sec. 3. Among them are relatively simple and fast two- stream solvers to compute irradiances, the widely used 165 Finally Sec. 11 shows a few applications as examples of the usage of libRadtran. discrete ordinate solver DISORT and also the Monte Carlo solver MYSTIC to compute (polarized) radiances 190 or irradiances in three-dimensional geometry. 2 The uvspec radiative transfer model 4. The output of the RTE solver are radiation quantities as irradiance, actinic flux or (polarized) radiance. The quantities are normalized to the source function, i.e. the solar irradiance in the solar spectral region. In order to Atmospheric Optical properties 195 description get physical quantities with corresponding units the out- -Trace gas profiles Profiles of: put may be postprocessed. The uvspec output then cor- -Temperature profile Absorption - extinction coefficient responds to calibrated radiances or brightness tempera- - Pressure profile cross sections, - single scattering - Aerosol parameterizatios, albedo tures for a given instrumental filter function. It is also - Water clouds aerosol and - scattering phase possible to obtain integrated solar or thermal irradiance. - Ice clouds cloud physics, function/matrix or ... - Surface properties Legendre polynomials (albedo or BRDF) - reflectance function/ 200 The overall structure of the uvspec model is shown in Fig. 1. - Wind speed matrix The model was originally designed to compute UV- - ... radiation, therefore its name is uvspec. As said before it now covers the complete solar and thermal spectral range. Radiation quantities The usage of the model is described in the user guide RTE 205 which comes along with the package. The user guide in- uncalibrated radiance/Stokes vector, solver irradiance, actinic flux cludes descriptions of the RTE solvers, examples of use as well as detailed documentation of all options and respective Post- parameters. Below uvspec input options are put in teletype- processing font, for example rte solver. 210 The uvspec model may be run either from the command line using Model output uvspec < input_file > output_file - calibrated radiance/Stokes vector, irradiance, actinic flux or from the Graphical User Interface (see Sec. 9). - integrated solar or thermal irradiance - brightness temperature - simulated measurements of satellite or ground based radiometers - ... 3 Radiative transfer equation solvers

215 The RTE for a macroscopically isotropic medium, i.e. ran- Fig. 1. Structure of the uvspec radiative transfer model. domly oriented particles and molecules, may be written as (Chandrasekhar, 1950; Mishchenko et al., 2002) The main tool of the libRadtran package is the uvspec ra- dI diative transfer model, which consists of the following parts: = −I + J (1) βds 170 1. The atmospheric state (e.g. trace gas profiles, cloud liquid water content, cloud droplet size, aerosol concen- where the source function J is

tration profiles, ...) needs to be provided as input to the ω0 ′ ′ ′ 220 J = P(Ω,Ω )I(Ω )dΩ + (1 − ω0)Be(T ) (2) model. 4π Z 4 C. Emde et al.: The libRadtran software package

Table 1. The radiative transfer equation solvers currently implemented in libRadtran.

RTE Geometry Radiation References Method solver quantities disort 1D, PP, PS E, F, L Stamnes et al. (1988, 2000); Buras et al. (2011); discrete ordinate, C-version Dahlback and Stamnes (1991) mystic 1D, 3D(a), PP, SP E, F, L, I Mayer (2009); Emde and Mayer (2007); Emde Monte Carlo et al. (2010); Mayer et al. (2010); Buras and Mayer (2011); Emde et al. (2011); Klinger and Mayer (2014) twostr 1D, PS E, F Kylling et al. (1995) two-stream, rodents 1D, PP E Zdunkowski et al. (2007) two-stream, plane-parallel sslidar 1D, PP ∗ single scattering lidar tzs 1D, PP L(TOA) thermal, zero scattering (a) 3D version not included in the free package; available in joint projects Explanation: PP, plane-parallel E, irradiance PS, pseudo-spherical F, actinic flux SP, fully spherical L, radiance 1D, one-dimensional L(TOA), radiance at top of atmosphere 3D, three-dimensional I is the Stokes vector (polarized radiance) ∗ sslidar: see section 3.4

Here I = (I,Q,U,V ) is the Stokes vector at location sion may still be invoked by fdisort2. Both the C-code (x,y,z), β the volume extinction coefficient, ω0 the single 250 and the FORTRAN77 version include the new intensity cor- scattering albedo, P(Ω,Ω′) the scattering phase matrix, and rection method for peaked phase functions by Buras et al. Be(T ) = (B(T ),0,0,0) the emission vector including the (2011), which is used by default. 225 Planck function B(T ). For most applications in the Earth’s For calculations with rotational Raman scattering, the C atmosphere, thermal emission can be neglected for wave- version has been generalized so that arbitrary source func- lengths below about 3 µm. Polarization is also often ne- 255 tions (not only a solar or thermal source function) can be han- glected, in this case the Stokes vector in Eqs. 1 and 2 is dled (Kylling and Stamnes, 1992; Kylling et al., 2011). Ro- replaced by the radiance L, the phase matrix becomes the tational (inelastic) Raman scattering from other wavelengths ′ 230 scalar phase function p(Ω,Ω ) and the emission vector is just into the wavelength, for which the radiative transfer equation the Planck function B(T ). is solved, is included into the source term. The uvspec model includes various methods to solve Eq. 1. The list of solvers which may be selected using the option 260 3.2 MYSTIC rte solver is shown in Table 1. The most comprehensive solver in libRadtran is the Monte 235 3.1 DISORT Carlo model MYSTIC (Mayer, 2009), which may be used to calculate (polarized) radiances, irradiances and actinic fluxes The solver disort is used by default in libRadtran. DIS- in the solar and thermal spectral regions. Within MYSTIC ORT (Stamnes et al., 2000) is based on discrete ordinates and 265 photons are traced through the atmosphere from the source allows to compute radiances, irradiances and actinic fluxes in towards the sensor or backwards, from the sensor to the plane-parallel geometry. The original FORTRAN77 version source, which is much more efficient especially in the ther- 240 of the algorithm exhibited several numerical instabilities for mal wavelength regionor if the radiance is only needed at a certain combinations of geometries and optical properties. specific location in a large 3D domain. One of the main appli- The FORTRAN77 code has been translated to C-code and 270 cations of MYSTIC is to calculate radiances in 3D geometry

is entirely in double precision (the FORTRAN77 version is including inhomogeneous clouds✿✿✿✿✿✿cloudy ✿✿✿✿✿✿✿✿✿✿✿atmospheres. The mostly in single precision) and includes dynamic memory al- sharp forward scattering of clouds and aerosols causes nu- 245 location (not possible in FORTRAN77). As such, the C ver- merical problems in Monte Carlo models. In order to avoid sion is numerically stable and also faster than the original these, sophisticated variance reduction methods have been FORTRAN77 version. We thus use the C version of the DIS- 275 developed (Buras and Mayer, 2011). These are enabled using ORT algorithm by default. The original FORTRAN77 ver- mc vroom on. Solar radiation is initially unpolarized and C. Emde et al.: The libRadtran software package 5

becomes polarized by molecular, aerosol or cloud scatter- 3.4 Lidar and radar simulations ing in the atmosphere. With the option mc polarisation (Emde et al., 2010) the full Stokes vector is calculated. For In order to complement the instruments that can be simulated 280 1D atmospheres MYSTIC may also be operated in spheri- by libRadtran, a lidar simulator called sslidar has been cal geometry using the option mc spherical (Emde and implemented. It only takes into account single scattering and Mayer, 2007). 325 reflection and is based on the lidar equation which is inte- The public version of MYSTIC allows calculations in 1D grated over each range. Note that in order to obtain a smooth

(plane-parallel or spherical) geometry, the ✿. ✿✿A✿full 3D ver- signal, the atmosphere normally has to have at least the same 285 sion is also✿✿✿✿available for joint projects. The non-public ver- vertical resolution as the range width. For radar simulations sion includes several other features: Complex 3D topography a stand-alone tool is available (see Sec. 10.2). (Mayer et al., 2010) and efficient high spectral resolution cal- culations using absorption lines importance sampling (Emde 330 3.5 Other solvers et al., 2011). The solver tzs (see Appendix B) is based on the zero scat- tering approximation in the thermal spectral range. It may be 290 3.3 Two-stream solvers used for clear sky calculations of radiances at top of atmo- sphere (TOA). It also calculates “black cloud” radiances for For the calculation of irradiances, two fast two-stream 335 the application of the CO2 slicing algorithm (Smith et al., solvers are available. 1970; Chahine, 1974; Smith and Platt, 1978; Menzel et al., The first solver, twostr, is described in detail in Kylling 1983; Eyre and Menzel, 1989) which may be used for the et al. (1995). twostr is optimized for calculating actinic determination of cloud top temperatures from passive remote 295 fluxes, and hence heating rates. It can be run in plane-parallel sensing measurements in the thermal spectral range. as well as in pseudo-spherical geometry. 340 For the solar region a fast single scattering solver sss is The second two-stream method available in libRad- available. These solvers may be used for fast but approximate tran is rodents, which is based on the delta-Eddington simulations of satellite measurements. two-stream described e.g. in Zdunkowski et al. (2007), Several other RTE-solvers are included in uvspec for com- 1 300 Sec. 6.1–6.4 . Based on a different two-stream approach than patibility with earlier releases of the package. These include twostr, it naturally yields different results. In contrast to 345 sdisort (pseudospherical disort), spsdisort (single twostr, the pseudo-spherical approximation is not imple- precision, pseudospherical disort), fdisort1 (version 1 of mented. Also rodents is not capable of calculating actinic DISORT), and polradtran (Evans and Stephens, 1991). fluxes. While they may still be used, we do not recommend their use 305 For actinic fluxes and atmospheric heating rates, twostr as the other solvers listed in Table 1 perform better. is the better choice. However, for calculating solar irradi- ances, we recommend using rodents: For cases where 350 3.6 Accuracy✿✿✿✿✿✿✿✿✿✿of ✿✿✿✿✿✿solvers the resulting irradiance is not negligible (larger than 2% of the extraterrestial irradiance), the difference between ✿✿✿✿✿✿✿✿MYSTIC ✿✿is✿✿a✿✿✿✿✿✿✿✿✿physically✿✿✿✿✿✿✿correct✿✿✿✿✿✿model✿✿✿✿✿✿which✿✿✿✿✿does ✿✿✿not 310 rodents and exact disort calculations is on average ✿✿✿✿✿✿include✿✿✿✿any✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿approximations. ✿✿It✿✿✿✿has✿✿✿✿✿✿been ✿✿✿✿✿✿✿✿validated✿✿✿in 5% (7%) for down(up)-welling irradiances. For twostr the ✿✿✿✿many✿✿✿✿✿✿✿✿✿✿✿✿international✿✿✿✿✿✿✿model ✿✿✿✿✿✿✿✿✿✿✿✿✿✿intercomparison✿✿✿✿✿✿✿✿studies, ✿✿✿for values are 9% (11%). Especially in case the atmosphere is ✿✿✿✿✿✿✿radiance ✿✿✿✿✿✿✿✿✿✿calculations✿✿✿✿✿with ✿✿✿✿✿✿highly✿✿✿✿✿✿peaked✿✿✿✿✿✿phase✿✿✿✿✿✿✿✿functions only weakly absorbing, the average differences at top-of- 355 ✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿(Kokhanovsky et al., 2010) , ✿✿✿✿✿for✿✿✿✿✿✿✿✿✿✿✿polarized ✿✿✿✿✿✿✿✿✿radiance atmosphere (TOA) and at the surface are only 2% (1%) ✿✿✿✿✿✿✿✿✿✿calculations ✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿(Emde et al., 2015) ,✿✿✿✿✿and ✿✿✿for✿✿✿✿✿✿✿✿✿radiances✿✿✿✿and 315 for rodents, whereas they are 5% at TOA and even 13% ✿✿✿✿✿✿✿✿✿irradiances ✿✿✿✿3D✿✿✿✿✿✿✿model ✿✿✿✿✿✿✿✿domains✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿(Cahalan et al., 2005) . (18%) at surface for twostr. ✿✿In ✿✿✿all ✿✿✿✿✿✿✿studies ✿✿✿✿✿✿✿✿MYSTIC✿✿✿✿✿✿✿✿belongs ✿✿to✿✿✿✿the✿✿✿✿✿core ✿✿of✿✿✿✿✿✿✿models For the thermal irradiance, rodents also gives better re- ✿✿✿✿✿which✿✿✿✿✿✿✿✿produce✿✿✿✿✿✿equal✿✿✿✿✿✿✿results ✿✿✿✿✿✿within✿✿✿✿✿✿their ✿✿✿✿✿✿✿✿✿✿uncertainty sults at TOA (1.6%) and surface (1%) than twostr (3%). 360 ✿✿✿✿✿range.✿✿✿✿✿✿✿✿MYSTIC✿✿✿✿✿✿agrees✿✿✿✿✿✿✿✿perfectly✿✿to✿✿✿✿✿✿✿✿DISORT✿✿✿for✿✿✿✿✿✿✿✿radiances For irradiances within the atmosphere, no real preference can ✿✿✿and✿✿✿✿✿✿✿✿✿✿irradiances✿✿✿✿✿with✿✿✿✿✿only✿✿a✿✿✿✿✿few ✿✿✿✿✿✿✿✿✿✿exceptions,✿✿✿✿✿e.g. ✿✿✿for 320 be given. ✿✿✿✿✿✿✿✿✿✿circum-solar✿✿✿✿✿✿✿✿✿radiation,✿✿✿✿✿✿where✿✿✿✿the ✿✿✿✿✿✿✿✿✿✿✿second-order✿✿✿✿✿✿✿✿intensity ✿✿✿✿✿✿✿✿correction✿✿✿✿✿✿✿✿included ✿✿in✿✿✿✿✿✿✿✿DISORT✿✿is✿✿✿✿not ✿✿✿✿✿✿✿accurate✿✿✿for✿✿✿✿✿✿highly ✿✿✿✿✿✿peaked ✿✿✿✿✿✿✿✿scattering✿✿✿✿✿✿phase✿✿✿✿✿✿✿✿functions✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿(Buras et al., 2011) . ✿✿In 365 Emde et al. (2011) , a comparison between DISORT and 1Note that Zdunkowski et al. (2007) contains two misprints rele- ✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿ ✿✿✿✿✿✿✿✿MYSTIC ✿✿for✿✿a ✿✿✿✿✿✿✿radiance✿✿✿✿✿✿✿✿spectrum ✿✿in ✿✿✿the ✿✿✿✿✿✿✿✿O2A-band✿✿is✿✿✿✿✿✿shown. vant for the twostream solver: First, in Eq. 6.50, α12,Ed = −α21,Ed = 2 The relative difference between the solvers is here less than and α22,Ed −α11,Ed. Second, α2 in Eq. 6.88 should be α2. Also, ✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿ the derivation in section 6.5 for thermal radiation does not work, ✿✿✿✿0.05%✿. ✿✿✿All ✿✿✿✿✿other ✿✿✿✿✿✿solvers ✿✿✿are✿✿✿✿✿✿✿✿✿✿✿✿✿approximations✿✿✿and✿✿✿✿✿✿hence ✿✿✿less instead the equations need to be derived in analogy to the solar ra- ✿✿✿✿✿✿✿accurate:✿✿✿as ✿✿✿✿✿✿✿✿✿mentioned✿✿✿✿✿✿before✿✿✿✿the ✿✿✿✿✿✿✿✿✿two-stream✿✿✿✿✿✿✿solvers✿✿✿are diation. 370 ✿✿✿✿only ✿✿✿✿✿✿✿✿✿✿appropriate ✿✿✿for ✿✿✿✿✿✿✿✿✿irradiances✿✿✿✿and✿✿✿✿the ✿tzs ✿✿✿✿✿solver✿✿✿✿only 6 C. Emde et al.: The libRadtran software package

✿✿✿✿✿✿✿provides✿✿✿✿✿✿✿✿✿radiances ✿✿in✿✿✿✿✿✿✿✿thermal ✿✿✿✿✿✿✿✿✿✿✿atmospheres ✿✿✿✿and ✿✿✿✿✿✿✿neglects For the simulation of radiances and irradiances we recom- ✿✿✿✿✿✿✿✿scattering ✿✿✿✿✿✿✿✿✿✿completely. mend to use reptran because it is faster and more accurate ✿✿✿The✿✿✿✿✿✿✿✿accuracy✿✿of✿✿✿✿✿✿✿✿✿MYSTIC ✿✿✿✿✿✿✿depends✿✿✿✿only✿✿✿on✿✿✿the✿✿✿✿✿✿✿number than lowtran. ✿✿of ✿✿✿✿✿traced✿✿✿✿✿✿✿✿photons.✿✿✿✿The✿✿✿✿✿✿✿✿standard✿✿✿✿✿✿✿✿deviation✿✿✿of ✿✿✿✿✿✿✿✿MYSTIC✿✿is 425 Several correlated-k parameterizations with different num-

375 ✿✿✿✿✿✿✿✿calculated✿✿✿✿✿when✿✿✿the ✿✿✿✿✿option✿mc std is✿✿✿✿✿✿✿✿enabled.✿✿✿✿The ✿✿✿✿user may✿✿✿ bers of bands, i.e. different accuracy, are included in libRad- ✿✿✿run ✿✿✿✿✿✿✿✿MYSTIC ✿✿✿✿with ✿✿✿✿✿many photons✿✿✿✿✿✿✿✿as✿✿✿✿✿✿✿✿reference✿✿✿for✿✿✿✿✿some ✿✿✿✿cases tran. For the calculation of integrated solar and thermal irra- ✿✿in ✿✿✿✿order✿✿✿to ✿✿✿✿✿check✿✿✿the✿✿✿✿✿✿✿✿accuracy✿✿of✿✿✿✿✿other✿✿✿✿✿✿✿solvers ✿✿✿for ✿✿✿✿✿✿specific diances and heating rates the correlated-k parameterizations ✿✿✿✿✿✿✿✿✿✿applications.✿ by Kato et al. (1999) and Fu and Liou (1992, 1993) are rec- 430 ommended. Also for the calculation of heating/cooling rates in the higher atmosphere (above 20 km) we recommend 4 Molecules these parameterizations because reptran and lowtran are affected by large errors. 380 4.1 Molecular absorption parameterizations 4.2 Molecular absorption cross sections Spectral ranges affected by molecular absorption comprising a complex line structure require parameterizations to reduce 435 For the spectral region from 160 to 850 nm libRadtran the computational cost. Molecular absorption parameteriza- includes measured absorption cross sections of various tions included in libRadtran are listed in Table 2. By default molecules in the atmosphere (see Table 3). Using the option 385 the reptran parameterization is applied. Using the option mol abs param crs these cross sections are used instead mol abs param the user may select the most appropriate of the default reptran parameterization. For wavelengths parameterization for the specific application. As an example 440 below 500 nm reptran yields approximately the same re- Fig. 2 shows radiance calculations for nadir viewing direc- sults as mol abs param crs because the cross sections tion at the top of the atmosphere using the parameterizations from HITRAN and the continua are very small at these wave- 390 reptran and lowtran and line-by-line calculations. lengths and the same measured cross sections are relevant in The reptran parameterization (Gasteiger et al., 2014) both cases. has recently been included in libRadtran. In reptran in- 445 For O2 for instance the cross section data include the tegrals over spectral intervals, e.g. integrated over a narrow Schumann-Runge bands between 176 and 192.6 nm and the spectral band or an instrument channel response function, are Herzberg continuum between 205 and 240 nm. Ozone ab- 395 parameterized as weighted means over representative wave- sorption bands are for example the Huggins bands between lengths similar to the method described by Buehler et al. 320 and 360 nm and the Chappuis bands between 375 and (2010). The selection of an optimum set of representative 450 650 nm. Using the option crs model the user may spec- wavelengths is based on accurate line-by-line simulations for ify which cross section data should be used in the simula- top of atmosphere radiances of a highly variable set of atmo- tions. Alternatively with crs file the users may specify 400 spheric states. The ARTS model (Eriksson et al., 2011) in- their own absorption cross section data. cluding state-of-the-art continuum models and spectroscopic data from HITRAN 2004 (Rothman et al., 2005) were used 4.3 Line-by-line calculations to calculate the gas absorption properties. For wavelengths below 1130 nm measured absorption cross sections of O3 455 In the shortwave infrared, thermal infrared and microwave 405 (Molina and Molina, 1986), O4 (Greenblatt et al., 1990), region we find a huge number of absorption lines which and NO2 (Burrows et al., 1998) are included, as they are are due to vibrational or rotational transitions in molecules. not covered by HITRAN or the continua (see also Sec. 4.2). A line-by-line model is required in order to calculate spec- Three band resolutions (fine: 1 cm−1, medium: 5 cm−1 , and trally resolved radiances. Line-by-line models take the ab- −1 coarse: 15 cm ) are available in the solar and thermal spec- 460 sorption line positions as well as line strength parameters 410 tral range, as well as a number of instrument channels on the from spectral databases like HITRAN, calculate line broad- ADEOS, ALOS, EarthCARE, Envisat, ERS, Landsat, MSG, ening which depends on pressure and temperature in the at- PARASOL, Proba, Sentinel, Seosat, and SPOT satellites. The mosphere and finally obtain absorption optical thickness pro- parameterization has been validated by comparison to high files. libRadtran does not include a line-by-line model but spectral resolution calculations. For solar and thermal radia- 465 it allows to specify absorption optical thickness profiles us- 415 tion at the top of atmosphere, as well as for solar radiation at ing the option mol tau file abs. It is convenient to use the ground, the mean parameterization error is in the range the ARTS model (Eriksson et al., 2011) to generate spec- of 1%. The mean error is slightly larger than 1% for thermal trally resolved molecular absorption data because it outputs radiation at the surface. the format required by libRadtran. ARTS includes a compre- The LOWTRAN band model adopted from from the SB- 470 hensive line-by-line module, it allows to use different spec- 420 DART radiative transfer model (Ricchiazzi et al., 1998) is troscopic databases like HITRAN as input and it also in- also included in libRadtran. cludes various state-of-the-art absorption continuum models. C. Emde et al.: The libRadtran software package 7

0.06 300

290 0.05 280 0.04 270

0.03 260

250 0.02 240 normalized radiance 0.01

brightness temperature [K] 230

0.00 220 755 760 765 770 775 9000 9500 10000 10500 11000

0.06 300

0.05 290

0.04 280

0.03 270 reptran fine 0.02 260 reptran medium normalized radiance 0.01 250 reptran coarse

brightness temperature [K] lowtran 0.00 240 755 760 765 770 775 9000 9500 10000 10500 11000 wavelength [nm] wavelength [nm]

Fig. 2. Nadir top of the atmosphere radiance in the oxygen-A band around 760 nm (left) and in the IR window region (right) for the midlatitude-summer atmosphere of Anderson et al. (1986). All calculations were performed with the MYSTIC solver using the “absorption lines importance sampling” method (Emde et al., 2011). (Top) High spectral resolution calculation, based on line-by-line absorption cross sections calculated using ARTS (Eriksson et al., 2011); (bottom) pseudo-spectral calculations using the representative wavelengths band parameterizations (reptran) with different resolutions and lowtran. For comparison see also Fig. 3 in Mayer and Kylling (2005) which shows transmittances for genln2 line-by-line calculations and lowtran for the same spectral regions.

Table 2. Absorption parameterizations in libRadtran.

Name Description Application References reptran default setting; calculation of radiances, simu- Gasteiger et al. (2014) bands parameterized using repr. wavelengths; lation of satellite measurements fine (1cm−1), medium (5cm−1) and coarse (15cm−1) band resolutions available; based on HITRAN2004, MT CKD and mea- sured absorption cross section data of O3,O4, and NO2; solar and thermal region reptran channel satellite channels parameterized using represen- fast and accurate simulations Gasteiger et al. (2014) tative wavelengths; for various satellite instruments lowtran LOWTRAN band model; pseudo-spectral calculations of Ricchiazzi et al. (1998); Pier- solar and thermal region, resolution 20 cm−1 radiances luissi and Peng (1985) kato, kato2 correlated k distributions for solar region; calculation of integrated solar Kato et al. (1999) ✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿Kato et al. (1999); Wandji Nyamsi kato2.96✿, different versions available; irradiance ✿✿✿✿✿✿✿✿✿✿✿katoandwandji based on HITRAN96 or HITRAN2000; 148 or 575 sub-bands fu correlated k distributions for solar (6 bands) calculation of integrated solar Fu and Liou (1992, 1993) and thermal (12 bands) regions; and thermal irradiance, radia- optimized for climate models tive forcing 8 C. Emde et al.: The libRadtran software package

Table 3. Absorption cross section data included in libRadtran, the where non-default parameterizations are put in parantheses. 1 − δ ′ 1 − 2δ 490 ∆ = , ∆ = , (3) 1 + δ/2 1 − δ

Molecule wavelength range [nm] reference and δ is the depolarization factor that accounts for the anisotropy of the molecules, δ is also calculated according to BrO 312 – 385 Wahner et al. (1988) Bodhaine et al. (1999). The Rayleigh phase matrix for δ=0 is CO2 119 – 200 Yoshino et al. (1996) shown in Fig 3. For calculations neglecting polarization only HCHO 300 – 386 Cantrell et al. (1990) 495 the (1,1) element of the phase matrix which corresponds to NO2 240 – 760 (Bogumil et al. (2003)) 231 – 794 Burrows et al. (1998) the scattering phase function is required. O2 108 – 160 Ogawa and Ogawa (1975) 160 – 175 Yoshino et al. (2005) 5 Aerosols 175 – 204 Minschwaner et al. (1992) 205 – 240 Yoshino et al. (1988) Besides the models by Shettle (1989) which are described O 116 – 185 Ackerman (1971) 3 in Mayer and Kylling (2005), libRadtran now includes ad- 185 – 350 Molina and Molina (1986) 195 – 345 (Daumont et al. (1992))/ 500 ditional aerosol properties based on the OPAC database (Malicet et al. (1995)) (Hess et al., 1998). OPAC provides the required parame- 245 – 340 (Bass and Paur (1985)) ters for single scattering calculations: size distribution pa- 240 – 850 (Bogumil et al. (2003)) rameters, refractive indices, and the density of the mate- 400 – 850 WMO (1986) rial. Data are available for the spectral range from 250 nm O4 330 – 1130 Greenblatt et al. (1990) 505 to 40 µm for the following basic aerosol types: insoluble OClO 240 – 480 Wahner et al. (1987) (inso), water soluble (waso), soot (soot), sea salt accu- SO2 239 – 395 Bogumil et al. (2003) mulated (ssam), sea salt coarse mode (sscm), mineral nu- cleation mode (minm), mineral accumulated mode (miam), mineral coarse mode (micm), mineral transported (mitr) The toolbox Py4CATS (Schreier and Bottger,¨ 2003; Schreier, 510 and soluble sulfate aerosol (suso). For the soluble aerosols 2006; Schreier and Kohlert, 2008) which can be downloaded the parameters depend on humidity because the aerosol par- 475 from www.libradtran.org also includes convenient command ticles swell in humid air. Relative humidities of 0%, 50%, line programs to generate spectrally resolved absorption data. 70%, 80%, 90%, 95%, 98% and 99% are included in OPAC. The Py4CATS tools however do not include continuum mod- The option aerosol species file allows to define ar- els, hence it should only be used for simulations where the 515 bitrary mixtures of these basic types or to select pre-defined continua are not relevant. mixtures from OPAC like e.g. continental average, for which uvspec automatically uses the optical properties 480 4.4 Rayleigh scattering cross sections closest to the background humidity profile. Optical properties of all basic aerosol types were calcu- The Rayleigh scattering cross sections are by default calcu- 520 lated using libRadtran’s Mie tool (see Sec. 10.1). For mineral lated using Eqs. 22–23 of Bodhaine et al. (1999). Using the aerosols, which are highly aspherical, we additionally pro- option crs model rayleigh the user may select Eq. 29 vide optical properties calculated with the T-matrix method of Bodhaine et al. (1999) or the formulas proposed by Nico- (Mishchenko and Travis, 1998) assuming an aspect ratio dis- 485 let (1984) and Penndorf (1957), respectively. The analytical tribution of prolate spheroids as described by Koepke et al. P Rayleigh scattering phase matrix R (Hansen and Travis, 525 (2015). 1974) is As an example Fig. 3 shows the phase matrix elements of the basic OPAC aerosol types, of liquid cloud droplets with an effective radius of 10 µm and the Rayleigh scat- PR(Θ) = tering phase matrix. Note that for spherical particles only 530 4 elements of the 4x4 scattering phase matrix are indepen- 3 2 3 2 4 (1 + cos Θ) − 4 sin Θ 0 0 dent whereas for aspherical particles 6 elements are required 3 2 3 2  − 4 sin Θ 4 (1 + cos Θ) 0 0  (see e.g. Hansen and Travis, 1974). Fig. 4 shows the absorp- ∆ 3 0 0 2 cosΘ 0 tion and the scattering optical thicknesses (integrated from  ′   0 0 0 ∆ 3 cosΘ  the surface to the top of the atmosphere) for the standard  2  535 aerosol mixtures in the spectral region from 300 to 800 nm. 1 0 0 0 As expected, the optical thickness of the urban aerosol is  0 0 0 0  +(1 − ∆) , the largest and that of the antarctic aerosol the smallest. 0 0 0 0   In general the continental aerosol mixtures show a stronger  0 0 0 0    wavelength dependency than the maritime mixtures. C. Emde et al.: The libRadtran software package 9

540 The users may also provide their own optical properties data which may be generated using libRadtran’s Mie tool or other external programs; more detailed instructions are pro- P11 = P22 P12/P11 104 0.4 vided in the libRadtran user guide. Rayleigh 103 0.2 waso 95% RH 0 0 2 . 10 ssam 95% RH 6 Clouds soot −0.2 101 cloud 10µm −0.4 545 100 6.1 Water clouds −0.6

−1 10 −0.8 Table 4 summarizes the parameterizations of water cloud op- 10−2 −1.0 0 20 40 60 80 100 120 140 160 180 0 20 40 60 80 100 120 140 160 180 tical properties which may be selected in libRadtran using P33/P11 P34/P11 the option wc properties. 1.5 0.8 For the simulation of irradiances and heating rates it is 1.0 0.6 550 normally sufficient to use a simple parameterization to con- 0.5 0.4 vert from cloud liquid water content and droplet effective

0.0 0.2 radius to the respective optical properties: extinction coeffi- cient, single scattering albedo, and asymmetry parameter. For −0.5 0.0 this purpose libRadtran includes the parameterization gener- −1.0 −0.2 555 ated by Hu and Stamnes (1993). −1.5 −0.4 0 20 40 60 80 100 120 140 160 180 0 20 40 60 80 100 120 140 160 180 For the simulation of radiances more accurate optical θ [ deg ] θ [ deg ] properties are needed and the phase function should not be approximated by a Henyey-Greenstein function as it is done Fig. 3. Phase matrix elements for the basic OPAC aerosol types in Hu and Stamnes (1993). Therefore, we have pre-calculated “water soluble” (waso), “sea salt accumulated mode” (ssam), and 560 cloud optical properties using libRadtran’s Mie tool assum- soot, for a water cloud with a droplet effective radius of 10 µm, ing that the cloud droplets are gamma distributed: and for Rayleigh scattering (with δ=0) at a wavelength of 350 nm. θ is the scattering angle, i.e. the angle between incoming and scattered r 1 n(r) = Nrα exp − ; α = − 3 (4) directions.  reff · veff  veff

Calculations have been performed for effective radii reff from 1µm to 25µm with a step width of 1µm. The effec- 565 tive variance was set to a value of veff = 0.1 and the constant N was determined by normalization. The size distributions

0.9 0.25 were cut off at a minimum radius of 0.02·reff and a maximum 0.8 radius of 8·reff . The size distribution bins are sampled on a 0.20 2πr 0.7 size parameter ( λ ) grid with a resolution of 0.003. This 0.6 570 fine resolution is necessary to obtain smooth phase matrices. 0.15 0.5 The pre-calculated data includes the wavelength ranges from 0.4 0.10 250 nm to 2200 nm (solar) with a resolution of 10 nm and the 0.3 range from 2.2 µm to 100 µm (thermal) in 100 steps of equal 0.2 0.05 0.1 wavenumbers. The refractive index of water has been taken scattering optical thickness absorption optical thickness 575 0.0 0.00 from Warren (1984). In the solar (thermal) region the phase 300 400 500 600 700 800 300 400 500 600 700 800 wavelength [nm] wavelength [nm] matrices are computed from 5000 (500) Legendre polynomi- aerosol mixture name als. In the optical properties files 129 of the Legendre polyno- continental_clean maritime_clean urban mials are stored, as well as the phase matrix elements, which continental_average maritime_polluted desert continental_polluted maritime_tropical antarctic are stored on scattering angle grids θ optimized such that 580 the error of the phase matrix – when interpolated linearly in cosθ between the grid points – is smaller than 1%. As an Fig. 4. Absorption (left) and scattering (right) optical thick- example Fig. 3 shows the four phase matrix elements of a ness for various aerosol mixtures specified using the option cloud droplet distribution with reff =10 µm at 350 nm. Here ◦ aerosol species file. The aerosol optical properties as well the cloudbow at θ ≈140 is clearly visible in the P11 and as the mixtures have been generated based on OPAC (Hess et al., 585 P12/P11 elements of the phase matrix. P12/P11 corresponds 1998) parameters. to the degree of polarization in the principal plane after single scattering, it can be seen that the maximum in the cloudbow region is about 80%. The mystic solver uses the phase ma- 10 C. Emde et al.: The libRadtran software package

Table 4. Water clouds parameterizations in libRadtran.

Name Description Application References hu Default setting. Simple parameterization, uses Irradiances, heating rates Hu and Stamnes (1993) Henyey-Greenstein phase function to approxi- mate Mie phase function echam4 Very simple two-band parameterization of Comparison of irradiances to Roeckner et al. (1996) ECHAM4 climate model results from ECHAM4 mie Optical properties calculated using Mie theory, (Polarized) radiances generated using Mie code by include full phase matrices Wiscombe (1980)

trix stored on the θ-grid, whereas all other solvers use the for rough ice crystals, and the single habits solid-column and 590 Legendre polynomials, except for the intensity correction in aggregate, both of them severely roughened. disort which uses the phase function (see also Buras et al., 630 We have generated two further parameterizations (hey 2011). and yang2013) for individual habits which also include the For specific applications, e.g. different size distributions, full phase matrices (see Appendix A): hey is available for the user can easily generate optical properties using libRad- the wavelength region from 0.2 to 5 µm for smooth parti- 595 tran’s Mie tool. cles in the effective radius range from 5 to 90 µm. The full 635 wavelength region from 200 nm to 99 µm is available for 6.2 Ice Clouds yang2013, effective radii may be in the range from 5 to 90 µm and a roughness parameter may also be specified, For ice clouds libRadtran includes a variety of parameteriza- ranging from smooth to severely rough. For the yang2013 tions (see Table 5) from which the user may select the most parameterization, the single scattering properties of nine in- appropriate one for a specific application by specifying the 640 dividual ice crystal habits which are commonly observed in 600 option ic properties. Ice clouds are more complex than ice clouds have been taken from the database by Yang et al. water clouds because they consist of ice crystals of different (2013). The hey parameterization was generated before this shapes. Some of the ice cloud parameterizations allow the database existed and it is based on single scattering data pro- crystal habit (ic habit) to be specified. vided by Hong Gang who used the improved geometrical op- As described in the previous section the exact phase matrix 645 tics method (IGOM), the same method as used by Yang et al. 605 is not needed when irradiances are calculated. For this pur- (2013). pose the parameterizations by Fu (1996); Fu et al. (1998) and Please refer to the libRadtran user guide for a list of avail- Key et al. (2002) are included in libRadtran. Fu (1996) and able habits for each parameterization. Fu et al. (1998) approximate the phase function by a Henyey- Fig. 5 shows the phase matrix elements of ice crystal dis- Greenstein function. Key et al. (2002) is slightly more ac- 650 tributions with an effective radius of 40 µm at 550 nm wave- 610 curate because it uses a double-Henyey-Greenstein function length. The red lines correspond to smooth crystals and the which represents the backscattering of ice crystals much bet- blue lines to severely rough crystals. The individual habits ter. The parameterization is based on single scattering cal- are for the yang2013 parameterization. General habit mix- culations for various ice crystal habits and on measured size tures which are available for the hey parameterization based distributions. It is available in the wavelength range from 0.2 655 on smooth crystals and for the baum v36 parameterization 615 to 5 µm. Based on single scattering data provided by P. Yang based on severely rough crystals are also shown. For most and on the size distributions from J. R. Key we have extended smooth crystals and also for the general habit mixture ghm the original parameterization by Key et al. (2002) to the ther- of the hey parameterization scattering features of hexagonal mal wavelength region up to 100 µm. ice crystals, the most prominent being the halo at 22◦ scatter- For accurate radiance calculations the parameterizations 660 ing angle, are visible in all phase matrix elements. The phase 620 by Baum et al. (2005a,b) (baum) and the newer one by matrices for severely rough crystals do not show halo fea- Heymsfield et al. (2013); Yang et al. (2013) and Baum et al. tures and they are relatively similar for all habits. In reality (2014) (baum v36) are available: baum includes full phase ice clouds are highly variable: There are situations when the functions for a mixture of particle shapes, the parameteri- halo is visible, in this case obviously there must be regular zation is based on single scattering properties of smooth ice 665 smooth ice crystals in the cirrus clouds. When no halo is vis- 625 crystals and on a large number of measured size distributions. ible, the assumption of severely roughened crystals might be baum v36 includes full phase matrices and three different more realistic. habit models: a general habit mixture similar to baum but C. Emde et al.: The libRadtran software package 11

Table 5. Ice cloud parameterizations in libRadtran

Name Description Application References fu Default setting. Simple parameterization using Irradiances, heating rates Fu (1996); Fu et al. (1998) Henyey-Greenstein phase function. echam4 Very simple 2-band parameterization of Comparison of irradiances to Roeckner et al. (1996) ECHAM4 climate model. results from ECHAM4 key Parameterization using a double-Henyey- Irradiances, heating rates Key et al. (2002) Greenstein phase function, covers wavelength range from 0.2 µm to 5.0 µm. Available for various habits. yang Similar to key but based on different single Irradiances, heating rates Key et al. (2002), Yang et al. scattering calculations and extended to wave- (2005) lengths up to 100 µm. Below 3.4 µm equivalent to key. baum Bulk optical properties including phase func- Radiances Baum et al. (2005a,b) tions for a realistic mixture of habits. Covers wavelength range from 0.4 to 2.2 µm and from 3.1 to 100 µm. baum v36 Bulk optical properties including phase ma- (Polarized) radiances Heymsfield et al. (2013); Yang trices for three microphysical models: general et al. (2013); Baum et al. (2014) habit mixture, solid columns or rough aggre- gates. All models include severely rough par- ticles. Covers wavelength range from 0.2 to 99 µm. hey Bulk optical properties including phase matri- (Polarized) radiances Single scattering properties ces based on single scattering calculations for generated by Hong Gang using smooth crystals, covers wavelength range from the code by Yang et al. (2013), 0.2 to 5 µm, includes 6 habits and a habit mix- Appendix A ture. yang2013 Bulk optical properties including phase matri- (Polarized) radiances Yang et al. (2013), Appendix A ces for 9 habits and 3 degrees of roughness, cov- ers wavelength range from 0.2 to 99 µm.

7 Surface nel combinations, of which the RossThickLiSparseRecipro- cal combination was identified in several studies to be the 7.1 Bidirectional reflectance distribution functions 685 model best suited for the operational MODIS BRDF/Albedo algorithm (see Schaaf et al., 2002). An additional factor for simulating the hot spot in vegetation canopies was added by 670 All solvers included in libRadtran may include Lambertian surfaces, while disort and MYSTIC can also handle bidirec- Maignan et al. (2004). The version implemented in libRad- tional reflectance distribution functions. libRadtran provides tran is the RossThickLiSparseReciprocal model as used in a variety of BRDFs, which are listed in table 6. 690 MODIS data, as presented in Lucht et al. (2000). The hot Two parameterizations for land surfaces are available. spot correction factor can be turned on on demand. As already stated in Mayer and Kylling (2005), but re- 675 The first is the “RPV” parameterization by Rahman et al. (1993) with the extension by Degunther¨ and Meerkotter¨ peated here for completeness, a parameterization of the (2000) for modelling snow-covered surfaces. The second is BRDF of water surfaces is also included which depends the “RossLi” BRDF first presented by Roujean et al. (1992). 695 mainly on wind speed and to a lesser degree on plankton The original RossLi BRDF is used in the AMBRALS (the concentration and salinity. For the MYSTIC solver, also the 680 wind direction can be set. In contrast to vegetation where Algorithm for Modeling[MODIS] Bidirectional Reflectance ◦ Anisotropies of the Land Surface) BRDF Modeling Frame- the typical hot spot occurs in the 180 backscatter direction, work (Wanner et al., 1997), and consists of four different ker- the main feature for water is specular reflection. The param- 12 C. Emde et al.: The libRadtran software package

Table 6. The surface reflection models currently implemented in libRadtran.

Option name BRDF type # of parameters References Solvers albedo Lambertian 1 All brdf cam Ocean BRDF 3+1 Cox and Munk (1954a,b); Nakajima and Tanaka (1983) D,M bpdf tsang Polarized ocean BRDF 1 Tsang et al. (1985); Mishchenko and Travis (1997) M brdf hapke Planetary & lunar surfaces 3 Hapke (1993) D,M brdf ambrals Ross-Li, MODIS Land Surface, 3 Roujean et al. (1992); Wanner et al. (1997); Lucht et al. D,M RTLSR (2000); Schaaf et al. (2002); Maignan et al. (2004) brdf rpv Land surfaces 3+3 Rahman et al. (1993); Degunther¨ and Meerkotter¨ (2000) D,M Explanation: D: DISORT M: MYSTIC RTLSR: RossThickLiSparseReciprocal model, optionally with hot spot parameterization

700 eterization in uvspec was adopted from the 6S code (Ver- mote et al., 1997) and is based on the measurements of Cox and Munk (1954a,b) and the calculations of Nakajima and Tanaka (1983). A vector version of the ocean parameteriza- tion, developed by Tsang et al. (1985) and Mishchenko and 107 0.5 106 0.4 705 Travis (1997), is available for polarization calculations with 105 0.3 104 0.2 MYSTIC. The vector version uses only wind speed as a pa- 103 0.1 2 rameter and does not take into account plankton concentra-

P11 10 0.0 1

10 P12/P11 0.1 100 0.2 tion, salinity or wind direction. 10-1 0.3 Finally, the parameterization of the surfaces of extrater- 10-2 0.4 0 30 60 90 120 150 180 0 30 60 90 120 150 180 710 1.0 0.3 restrial solid bodies such as the moon, asteroids or the inner 0.8 0.2 planets by Hapke (1993) is available. 0.6 0.4 0.1 Only the ocean BRDF parameterizations depend directly 0.2 0.0 0.0 on the wavelength. For all other BRDF models, the pa-

P33/P11 0.2 P34/P11 0.1 0.4 rameterization can either be given as being constant with 0.2 0.6 0.8 0.3 715 wavelength (by using e.g. the option brdf rpv), or as a 0 30 60 90 120 150 180 0 30 60 90 120 150 180 1.0 1.0 file containing the parameters for each wavelength (using 0.8 0.8 0.6 e.g. brdf rpv file). 0.6 0.4 0.2 0.4 0.0

P22/P11 0.2 P44/P11 0.2 7.2 Fluorescence 0.4 0.0 0.6 0.2 0.8 0 30 60 90 120 150 180 0 30 60 90 120 150 180 For vegetation covered surfaces, a weak solar-induced scattering angle [degrees] scattering angle [degrees] 720 Ice crystal habit chlorophyll fluorescence signal is emitted in the red and far- solid_column (smooth) solid_column (sev. rough) red spectral regions. The contribution of fluorescence to the column_8elements (smooth) column_8elements (sev. rough) radiance leaving the bottom boundary is plate (smooth) plate (sev. rough) HEY ghm baum_v36 ghm

F Lg (µ,φ,λ) = F (λ), (5) Fig. 5. Phase matrix elements of ice crystal distributions with an effective radius of 40 µm at 550 nm wavelength. The red lines correspond to smooth and the blue lines to severely rough where F (λ) is the fluorescence source in the same units as crystals, respectively. The individual habits (solid-column, 725 the incoming solar flux at the top of the atmosphere (for ex- column-8elements and plate) are for the parameterization ample mW/(m2 nm sr)). The fluorescence source of radiation yang2013, and the general habit mixtures (ghm) are for hey in- is included in the disort solver. It may either be constant cluding smooth crystals and baum v36 including severely rough or vary as a function of wavelength. Additional surface bidi- particles. rectional reflection of radiation may also be included. The 730 flourescence source depends on the solar radiation impinging the vegetation and the type of vegetation. Output from vege- tation fluorescence canopy models such as that described by Miller et al. (2005), may readily be used by uvspec. C. Emde et al.: The libRadtran software package 13

8 Implementation improvements options that are set by the user and will be written to the given input files are shown in bold face (for example option 735 8.1 Multiple atmospheric constituents 785 rte solver in Fig. 6). Options that may be set are shown as normal characters, while options that are not compati- The previous versions of libRadtran were restricted to using ble with other set options are greyed (for example in Fig. 6 at most four types of atmospheric constituents: molecules, mc ipa is greyed since it is not possible to combine it with aerosols, and water and ice clouds. Any user defined con- rte solver set to disort). stituent could only be included by replacing e.g. water clouds 790 On-line documentation of the options are available and 740 with them. Also, it was not possible to use several types of this is identical to the documentation in the libRadtran ice cloud habits at the same time. user manual. In Fig. 6 the documentation for the option A recent major internal restructuring of the libRadtran number of streams is shown in the lower left corner. code has now made it possible to use any number of The on-line help is activated by pointing the mouse at the atmospheric constituents for a radiative transfer simula- 795 requested input variable. 745 tion. The number is only limited by computational mem- Input options that refer to input data files, such as wave- ory and time. The new input options needed for load- length dependent surface albedo, may be plotted from the ing the additional constituents are profile file and GUI. In the example in Fig. 6, the extraterrestrial flux (up- profile properties. They work very similar to the per left subplot), the surface fluorescence spectrum (lower cloud input options; merely the name of the constituent needs 800 left subplot) and surface albedo (lower right subplot) inputs 750 to be defined. are plotted. Note that the wavelength coverage (x-axis) dif- This option increases the flexibility of libRadtran in many fers reflecting the different wavelength regions included in ways. E.g. it can be used to load the optical properties for the input data files. each size bin of an aerosol or water or ice cloud. This way, the Once all wanted input options are set, they are saved to a size distribution may differ between the atmospheric layers. 805 user specified file, and uvspec is run from within the GUI. 755 An example can be found in Kylling et al. (2013). The output from the run may readily be plotted using the GUI. For example, in Fig. 6, the calculated nadir radiance at 8.2 Change of nomenclature and backward compatibil- the top of the atmosphere is shown in the upper right subplot. ity The GUI includes numerous working examples. Users may As the number of input options had grown to more than 300 810 add more examples to the GUI specific to their interests. over the years, we decided to restructure the language of the 760 input options. The input options now have a largely consis- 10 Other tools tent naming and their usage follows certain rules, making it more easy to find related input options. Several additional tools are included in the libRadtran pack- We have included a python script in order to provide age. An overview is given in Mayer and Kylling (2005, Tab. backward compatibility for long-established libRadtran 4). New tools are ssradar, a single scattering Radar simulator 765 users. ✿✿✿The✿✿✿✿✿script✿✿✿✿can ✿✿be✿✿✿✿✿✿found ✿✿in ✿✿✿the ✿✿✿✿✿✿✿✿directory src py.✿By 815 (see below), and pmom, which calculates Legendre polyno- invoking the command mials for a given phase function. python translate.py input_file \ > new_input_file 10.1 Mie calculations input files written in the old nomenclature will be translated 770 to the new nomenclature automatically. Alternatively, the old The tool for Mie calculations (mie) has been extended con- input file can be sent directly to uvspec with the following siderably. The user may select between two Mie codes, command: 820 MIEV0 by Wiscombe (1980) or bhmie by Bohren and Huff- python translate.py input_file | uvspec man (1983). The tool allows to generate input optical proper- ties for uvspec calculations for arbitrary size distributions. It

775 generates full phase matrices which are stored on optimized angular grids for a user-defined accuracy. The radiative trans- 825 fer solvers MYSTIC and DISORT with the new intensity 9 Graphical User Interface correction method (Buras et al., 2011) use the phase func- tions/matrices rather than Legendre polynomials, which are The large number of input options available in the uvspec calculated by the Mie codes. model may appear overwhelming. To help the user to create uvspec input files a graphical user interface (GUI) has been 10.2 Single scattering Radar simulator 780 developed. The GUI organizes the input options in logical groups such as “Molecular Atmosphere”, “Aerosol”, “Sur- 830 Single scattering Radar (ssradar) is a stand-alone 1D pure face” etc., see also the grey bar at the top in Fig. 6. Input Rayleigh-scattering cloud radar simulator that handles arbi- 14 C. Emde et al.: The libRadtran software package

Fig. 6. Screenshot of the Graphical User Interface for a spectral high-resolution simulation of the O2-B band including a fluorescence source. Plots of input and output data are included together with the help information for one option. See text for further explanation.

trary cloud layers and droplet size distributions as well as with uvspec to perform line-by-line calculations in both the tilted viewing angles and supercooled water droplets. The solar and thermal parts of the spectrum. For both examples radar reflectivity factor is calculated directly from the droplet the spectral resolution, the molecules to be included and the 6 835 distribution with Z = i niDi (Rinehart, 2010) where D is 855 line function properties are specified in the input to ARTS. It the droplet diameter andP ni the distribution number density is noted that the same ambient atmospheric profile should be for the discrete interval Di,Di+1. Internally available distri- used in both, ARTS and uvspec. butions are gamma and lognormal, arbitrary distributions can be entered using input files. 11.1.1 Solar source

Solar induced chlorophyll fluorescence is emitted in the 660 840 11 Some applications 860 to 800 nm spectral region with two broad peaks at about 685 The libRadtran package has been used for numerous appli- and 740 nm. In this spectral region are the O2-A and O2- cations. Many of these are listed under the publications link B bands which contain a large number of absorption lines. at http://www.libradtran.org. The examples directory also Although the fluorescence signal is weak, especially the O2- ✿✿✿✿ ✿✿✿✿✿✿✿✿✿✿✿ B region holds promise for retrieval of vegetation fluores- ✿✿✿✿✿✿✿includes ✿a✿✿✿✿✿✿✿number ✿✿✿✿input✿✿✿✿files✿✿✿✿that ✿✿✿✿may ✿✿be✿✿✿✿used✿✿✿✿✿✿✿✿✿especially ✿✿by 865 cence from spectrally high resolution space borne instru- 845 ✿✿✿new✿✿✿✿✿users✿✿to✿✿✿✿✿✿create ✿✿✿✿input✿✿✿✿✿files.✿Below some applications of libRadtran are described. ments (Guanter et al., 2010). In this spectral region the sur- face albedo is typically low while there is a fluorescence peak 11.1 uvspec and ARTS around 685 nm (see red line lower plot Fig. 7). The opti- cal depths from ARTS are input to uvspec which calculates The high number of absorption lines in the shortwave in- 870 the top of the atmosphere radiance (blue line, upper plot of frared and the thermal infrared requires a line-by-line ap- Fig. 7) including the fluorescence signal (red line, lower plot 850 proach to resolve the spectral structure. Below is shown how of Fig. 7), surface albedo (green line, lower plot of Fig. 7) and molecular absorption data from ARTS may be combined molecular scattering . Measurements may be made at a lower C. Emde et al.: The libRadtran software package 15

The left panel of Fig. 8 shows IASI spectra from a granule 1e13 1.0 covering the ash cloud following the eruption of Mt. Kelud, 1.0 Indonesia, in February, 2014. The spectra are classified as Transmittance 0.8 895 cloudless (green), ice cloud (blue), and volcanic ash (red). To

sr)] 0.8 Radiance 2 investigate the realism of this identification the spectra were

0.6 simulated with ARTS/uvspec. For all simulated spectra, the 0.6 surface emissivity was set equal to one which is representa-

0.4 0.4 tive for water. The simulated spectra are shown in the right Transmittance 900 plot of Fig. 8.

L [photons/(s nm cm nm L [photons/(s 0.2 0.2 The cloudless spectrum has brightness temperatures rep- resentative for the ocean at these latitudes. The main molec- 0.0 0.0 675 680 685 690 695 700 ular absorption features in this part of the spectrum are water Wavelength [nm] vapor lines throughout the spectrum, ozone (broad band fea- −1 905 1e13 ture centered around 1050 cm ), and CO2 (feature below 0.2 −1 With fluorescence 800 cm ). The data from ARTS include absorption lines 1.0 Without fluorescence from these molecules. In the cloudless spectrum the ozone Fluorescence source (*20) band around 1050 cm−1 is colder than the radiation at lower sr)] Albedo 2 0.8 and higher wavenumber, indicating that the radiation in the 910 ozone band was emitted at a higher and colder altitude than 0.1 0.6 the surface. Overall the ARTS/uvspec cloudless spectrum Albedo agrees well with the measured spectrum. For the simulation with an ice cloud, the ice cloud was lo- 0.4 L [photons/(s nm cm nm [photons/(s L cated between 12 and 13 km. Ice water content was set to 3 915 1 g/m . The ice particles were assumed to consist of solid 0.2 0.0 675 680 685 690 695 700 columns with reff =40.0 µm. The ice cloud parameterization Wavelength [nm] ic properties yang was selected. The spectrum iden- tified as ice cloud (blue curve in left plot of Fig. 8) appears saturated for nearly all wavenumbers except for the ozone Fig. 7. (Upper plot) The transmittance from ARTS output and ra- −1 920 band centered around 1050 cm . The rather low brightness diance from uvspec. (Lower plot) The top of the atmosphere nadir temperature and wavenumber independent behaviour outside viewing radiance in the O2-B band with (blue line) and without (purple line) a surface fluorescence source (red line). The radiances the ozone band, indicates that this is an ice cloud and that it have been convolved with a spectral response function with FWHM is opaque. The simulation with an ice cloud (blue curve in of 0.3 nm. right plot of Fig. 8) agrees well with the measured spectrum. 925 The higher temperatures in the ozone band implies that this radiation was emitted at a higher altitude in the stratosphere spectral resolution. The lower plot of Fig. 7 shows radiance where the temperature is higher than at the altitude of the 875 spectra convolved with a triangular spectral response func- cloud. tion with a full width at half maximum (FWHM) of 0.3 nm The ash simulation included an ash cloud between 17 and using the conv tool of libRadtran. The spectral response func- 930 18 km. The ash particles were assumed to be made of an- tion was generated with the make slitfunction tool. Spectra desite, spherical and mono-disperse with a radius of 3 µm. with (blue line) and without (purple line) fluorescence are The refractive index of andesite was taken from Pollack et al. 880 presented. It is seen that the fluorescence signal is relatively (1973) and the optical properties were calculated using the − larger when the surface albedo is low, below about 690 nm, mie tool. The ash density was 1×10 3 g/m3 which corre- 2 compared to larger wavelengths. 935 sponds to a mass loading of 1 g/m for a 1 km thick cloud. The red curve in the left plot of Fig. 8 is classified as ash 11.1.2 Thermal source using the difference in brightness temperature method de- scribed by Clarisse et al. (2010). This spectrum is colder than The Infrared Atmospheric Sounding Interferometer (IASI) the cloudless spectrum indicating a colder effective emitting 885 on board the MetOp satellite measures the radiance from 645 940 temperature overall. The general spectral shape is similar to 2760 cm−1 (15.50-3.6 µm) with a spectral resolution of to the cloudless spectrum below 1000 cm−1. Above about 0.25cm −1. Its main purpose is high-resolution atmospheric 1200 cm−1 the brightness temperature of the cloudless spec- sounding of temperature and humidity, and trace gas column trum generally decreases with increasing wavenumber, while retrievals (Clerbaux et al., 2009; Hilton et al., 2011). It may the converse is true for the ash spectrum. The simulated ash 890 also be used to detect volcanic ash (see Clarisse et al., 2013, 945 cloud spectrum (black curve in right plot of Fig. 8) differs and references therein). from the measured spectrum classified as ash. Both the sim- 16 C. Emde et al.: The libRadtran software package

Measured (IASI) Simulated (ARTS/uvspec) Wavelength (µm) Wavelength (µm) 14 13 12 11 10 9 8 14 13 12 11 10 9 8

300 300

280 280

260 260

Processes included Classification Cloudless 240 240 Cloudless Volcanic ash

Brightness temperature (K) Volcanic ash Brightness temperature (K) Ice cloud Ice cloud Volcanic ash and ice cloud 220 220

200 200 700 800 900 1000 1100 1200 700 800 900 1000 1100 1200 Wavenumber (cm−1 ) Wavenumber (cm−1 )

Fig. 8. (Left plot) Brightness temperature spectra for different locations as measured by IASI on 15 February, 2014, 02:33 UTC, during the Mt. Kelud, Indonesia, eruption. Tentative classification of the spectra is given in the legend. See text for details. (Right plot) Simulated brightness temperature spectra using ARTS/uvspec. The atmospheric processes included in the simulations are given in the legend.

ulated and measured ash spectra increase in magnitude with 0 increasing wavelength above 1100 cm−1, but the simulated spectrum increases more. Below about 900 cm−1 the spectral 50 950 behavior of the measured and simulated spectra differs. This may be due to either wrong assumptions about the ash type and hence refractive index and/or the mixing of ice with ash. 100 Ice clouds have an opposite effect of ash clouds on the bright- −1 ness temperature between 800-1000 cm , whereas above 150 −1 955 1075 cm ice clouds have only a very weak dependence on wavenumber (see Fig. 2 of Gangale et al., 2010). To test if the 200 presence of both ash and ice could reproduce the measured spectrum, simulations were made with both an ash cloud and 0 100 200 300 400 0 an ice cloud. The altitude and thickness of the clouds were as −4 3 960 above, but the ash cloud density was 2×10 g/m and the ice water content 1.5×10−2 g/m3. The resulting spectrum is 50 shown in maroon in the right plot of Fig. 8. The mixed scene with both ash and ice is seen to well reproduce the measured 100 ash spectrum in the left plot of Fig. 8.

150 965 11.2 Simulated satellite image

200 Fig. 9 shows a simulated satellite image (top) and the corre- sponding observation (bottom). Three visible channels of the 0 100 200 300 400 SEVIRI instrument on the MSG (Meteosat Second Genera- tion) satellite were simulated based on input data from the Fig. 9. Top: Simulation of MSG-SEVIRI image. False color com- 970 operational COSMO-DE forecast (Baldauf et al., 2011) of posite, where red corresponds to the 1.6 µm channel, green to Deutscher Wetterdienst for the 15th July 2012, 12 UTC. The 0.8 µm and blue to 0.6 µm. The simulation was performed using spatial resolution of the simulation is 2.8 km×2.8 km, that the disort solver with input data from the operational COSMO- of the SEVIRI observation is 3 km×3 km at the sub-satellite DE forecast for the 15th July 2012, 12 UTC. The axes correspond point. A false color composite was generated using the sim- to SEVIRI pixel. Bottom: Corresponding SEVIRI image. 975 ulated radiance of the 1.6 µm channel for red, the 0.8 µm C. Emde et al.: The libRadtran software package 17

radiance for green and 0.6 µm radiance for blue. The simu- lations were performed using the one-dimensional disort solver. The MODIS surface albedo dataset was used (Schaaf et al., 2002) to set the Lambertian surface albedo. The effec- 980 tive radii of liquid clouds were parameterized according to I Q Martin et al. (1994), and for the optical properties the mie parameterization was applied. Ice cloud effective radii were 0.00 0.03 parameterized according to Wyser (1998) and for the corre- sponding optical properties the parameterization baum v36 0.02 0.01 985 was used with the general habit mixture. Molecular absorp- 0.01

tion was included using the reptran parameterization. In mol. atmosphere the false color composite water clouds appear white and 0.00 0.02

ice clouds appear blueish, because ice absorbs in the region 0.01 about 1.6 µm. The simulated image looks very similar to the 0.12 0.03 990 observation. A major difference is that the ice clouds in the 0.08

observation appear more blueish, the reason is that their real 0.05 0.04 optical thickness is larger than in the COSMO-DE forecast. ocean surface 0.07 0.00 11.3 Polarization 0.00 0.09 The MYSTIC solver can be applied to simulate multi- 995 0.01 angle multi-spectral polarized radiances using the option 0.08

mc polarisation (Emde et al., 2010). Polarized radia- aerosol desert

tive transfer using MYSTIC has been validated in extensive 0.07 0.02 model intercomparison projects (Kokhanovsky et al., 2010;

Emde et al., 2015). 0.00 0.14 1000 Fig. 10 shows an example for simulations at wavelengths of 443, 670 and 865 nm; these are measured by the POLDER 0.01 0.12 (Polarization and Directionality of the Earth’s Reflectances) instrument onboard PARASOL (Polarization and Anisotropy liquid water cloud 0.02 0.10 of Reflectances for Atmospheric Sciences coupled with Ob- 1005 0.01 servations from a Lidar) (Deschamps et al., 1994). All sim- 0.14 ulations are for a solar zenith angle of 30◦ and show the re- flected radiances (normalized to incoming solar irradiance) 0.10 0.00

at the top of the atmosphere in the solar principal plane. The 0.06 ◦ viewing angle of 30 corresponds to the exact backscattering ice cloud smooth 0.01 ◦ 0.02 1010 direction. The angular resolution is 2 . All simulations are for the US standard atmosphere. The figure shows the first 0.00 and second components of the Stokes vector I and Q; the 0.06 components U and V are exactly 0 in the principal plane for symmetry reasons. 0.04 0.01 1015 The first row shows the results for a clear atmosphere, ice cloud rough 0.02 i.e. Rayleigh scattering and molecular absorption. Here I is 50 25 0 25 50 50 25 0 25 50 largest for the shortest wavelength because the Rayleigh scat- viewing angle [ ◦ ] viewing angle [ ◦ ] tering cross section decreases with λ−4, where λ is the wave- length. The absolute value of Q also increases with increas- Fig. 10. Stokes vector components I and Q at wavelengths of 443 nm (blue solid lines), 670 nm (green dashed lines), and 865 nm 1020 ing Rayleigh scattering cross section. A negative Q means (red dashed-dotted lines) for various atmospheric setups (see text that Rayleigh scattering polarizes perpendicular to the scat- for details). The radiances are calculated at the top of the atmo- tering plane, which, for single scattering, corresponds to the sphere for viewing angles from -50◦ to 50◦, where 0◦ corresponds principal plane for this geometry. to the nadir direction. The second row of the figure shows the same simulation 1025 but with an underlying ocean surface, which is modelled ac- cording to Mishchenko and Travis (1997) (bpdf tsang). The wind speed was set to 2 m/s. I and Q clearly show the sun glint which has a maximum at a viewing angle of about 18 C. Emde et al.: The libRadtran software package

-30◦ and which is highly polarized. The intensity of the sun- Another interesting application is the simulation of polar- 1030 glint increases with increasing wavelength since the incom- ized radiance at the surface at twilight, because polarized ing radiance at the surface becomes less diffuse when there radiance measurements at twilight can be used to retrieve is less Rayleigh scattering in the atmosphere. 1085 aerosol optical properties (e.g. Saito and Iwabuchi (2015)). The third row shows the result for desert aerosol as de- As an example we calculated polarized clear sky radiances fined in the OPAC database (aerosol species file for solar depression angles up to 9◦ for the US-standard at- 1035 desert), with an underlying Lambertian surface albedo of mosphere and default Rayleigh scattering and absorption set- 0.3. I shows a backscatter peak at 670 and 865 nm. Q looks tings. Fig. 11 shows the result as a function of viewing zenith similar as for Rayleigh scattering, however there are differ-1090 angle. The relative azimuth angle between sun and observer ences mainly around the backscatter region. At wavelengths is 0◦ which means that the observer looks into the direction of 670 and 865 nm, Q has a minimum in the exact backscat- of the sun. We see that the intensity decreases by about four ◦ 1040 ter direction and becomes positive for viewing angles around orders of magnitude for solar depression angles between 0 this direction. (sun at horizon) and 9◦ (sun 9◦ below horizon). The degree ◦ The fourth row shows a simulation including a water cloud1095 of polarization (not shown) at a viewing angle of 5 is more (wc properties mie) in 2-3 km altitude with an optical than 90%. All results agree to published results by Blattner¨ thickness of 10 and an effective droplet radius of 10 µm. I et al. (1974), which indicates that fully spherical geometry 1045 and Q show the glory about the backscatter direction and works correctly in MYSTIC. the rainbow at a viewing angle of about -10◦ corresponding ◦ to a scattering angle of 140 . In the rainbow is more pro- 500 nm 700 nm Q 100 100 nounced than in I because Q is less affected by multiple scat-

tering. The angular resolution shown here is not sufficient to 10-1 10-1 1050 separate the glory from the backscattering peak in I. The sign

of Q in the rainbow region is the same as for Rayleigh scat- 10-2 -2 ◦ 10-2 ◦ -2 ◦ tering whereas it is opposite in the glory region, which means 0 0 ◦ 2 ◦ 2 ◦ that the rainbow is polarized perpendicular to the scattering -3 -3 10 10 ◦ 3 ◦ 3

plane whereas the glory is polarized parallel to the scattering L ◦ ◦ π 4 4 1055 plane. 10-4 10-4 5 ◦ ◦ The last two rows show simulations with ice clouds, where 5 ◦ 6 6 ◦ we have used the yang2013 parameterization. An ice cloud 10-5 10-5

layer with an optical thickness of 2 was included at an alti- 8 ◦ 8 ◦ tude from 9–10 km. The selected habit was solid column 10-6 10-6 9 ◦ 9 ◦ 1060 and we performed simulations for smooth crystals and for severely rough crystals respectively. The effective crystal 10-7 10-7 20 0 20 40 60 80 100 20 0 20 40 60 80 100 radius in both simulations is 30 µm. The smooth crystals θ [ ◦ ] θ [ ◦ ] show a backscatter peak in I and a positive Q about the backscatter direction. Also there are some smaller features Fig. 11. Twilight radiance at 500 nm and 700 nm calculated using fully spherical geometry for the US-standard atmosphere. The lines 1065 in I and Q. The radiances (I and Q) for rough crystals are smooth functions of viewing angle. This different behaviour are for different solar depression angles. The x-axis corresponds to the viewing zenith angle. has been used to determine the fraction of smooth crystals in ice clouds from POLDER measurements (Cole et al., 2014).

11.4 Fully spherical geometry 12 Summary

1070 MYSTIC can be operated in fully spherical geometry1100 We have presented the libRadtran software package (version

(mc spherical 1D). The implementation of 1D spheri- 2.0.1✿), which is a comprehensive and powerful collection of cal geometry is described in Emde and Mayer (2007) where tools for radiative transfer simulations in the Earth’s atmo- it has been used to simulate radiation in the umbral shadow of sphere. It is user-friendly, well-documented and is widely a solar eclipse. A comparison to measurements during the to- used in the scientific community. We have described vari- 1075 tal eclipse in Greece in March 2006 (Kazantzidis et al., 2007)1105 ous new features and parameterizations which have been in- showed a very good agreement for modeled and measured cluded after the first publication of libRadtran in 2005. New UV irradiances, which decreased during totality by 2 to 3 or- features are for example a vector radiative transfer solver ders of magnitude depending on wavelength. and a solver for rotational Raman scattering. The package in- Fully spherical geometry has also been used to simu- cludes state-of-the-art parameterizations for aerosol and ice ◦ 1080 late actinic fluxes at high solar zenith angles up to 92 1110 cloud optical properties and a newly developed efficient ab- (Suminska-Ebersoldt´ et al., 2012). sorption parameterization. C. Emde et al.: The libRadtran software package 19

13 ✿✿✿✿Code✿✿✿✿✿✿✿✿✿✿availability References

The libRadtran package was initiated about 20 years ago Ackerman, M.: UV-solar radiation related to mesospheric pro- and is still under continuous development. Regularly up-1130 cesses, D. Reidel Publishing Company, edited by G. Fiocco, 1115 dated versions of the package are available from http://www. 1971. libradtran.org. Alexandrov, M. D., Cairns, B., Emde, C., Ackerman, A. S., and The website includes all released versions of the package. van Diedenhoven, B.: Accuracy assessments of cloud droplet ✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿ size retrievals from polarized reflectance measurements by the The latest release is version 2.0.1 and includes the source ✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿1135 research scanning polarimeter, Remote Sens. Environ., 125, 92– ✿✿✿✿code,✿✿✿✿✿✿✿✿example✿✿✿✿✿input✿✿✿✿✿files, ✿✿✿✿✿✿several✿✿✿✿✿tests,✿✿✿✿and ✿✿✿the✿✿✿✿✿✿✿✿graphical 111, doi:10.1016/j.rse.2012.07.012, 2012. 1120 ✿✿✿user✿✿✿✿✿✿✿✿✿interface. ✿✿✿✿✿✿✿✿✿Additional✿✿✿✿data✿✿✿✿✿✿✿✿packages✿✿✿✿✿✿✿✿✿containing✿✿✿✿✿✿optical Anderson, G., Clough, S., Kneizys, F., Chetwynd, J., and Shettle, ✿✿✿✿✿✿✿✿properties✿✿✿of ✿✿✿✿✿✿clouds ✿✿✿and✿✿✿✿✿✿✿✿aerosols ✿✿✿✿and ✿✿✿the✿✿✿✿✿✿✿✿✿✿REPTRAN✿✿✿gas E.: AFGL atmospheric constituent profiles (0-120 km), Tech. ✿✿✿✿✿✿✿✿absorption✿✿✿✿✿✿✿✿✿✿✿✿✿✿parameterization✿✿✿are✿✿✿✿also✿✿✿✿✿✿✿✿available.✿✿✿✿✿✿✿✿✿✿✿Alternatively Rep. AFGL-TR-86-0110, Air Force Geophys. Lab., Hanscom Air ✿✿✿✿✿✿version✿✿✿✿✿2.0.1✿✿✿✿and✿✿✿✿the✿✿✿✿✿✿✿✿✿additional✿✿✿✿✿data✿✿✿✿are✿✿✿✿✿✿✿✿available✿✿✿as1140 Force Base, Bedford, Mass., 1986. ✿✿✿✿✿✿✿✿✿supplement✿✿to✿✿✿✿this ✿✿✿✿✿model✿✿✿✿✿✿✿✿✿✿description ✿✿✿✿✿paper.✿✿✿✿The✿✿✿1D✿✿✿✿✿✿version Baldauf, M., Seifert, A., Forstner,¨ J., Majewski, D., Raschendorfer, M., , and Reinhardt, T.: Operational convective-scale numerical 1125 ✿✿of ✿✿✿✿✿✿✿✿MYSTIC✿✿is✿✿✿✿part ✿✿of✿✿✿the✿✿✿✿✿✿✿✿✿libRadtran✿✿✿✿✿✿public✿✿✿✿✿✿✿release. ✿✿✿✿✿Please weather prediction with the COSMO model: description and sen- ✿✿✿note✿✿✿✿that✿✿✿✿the✿✿✿3D✿✿✿✿✿✿✿version✿✿✿of ✿✿✿✿✿✿✿✿MYSTIC✿✿✿is ✿✿✿not✿✿✿✿part✿✿✿of✿✿✿the sitivities, Monthly Weather Review, 139, 3887–3905, 2011. ✿✿✿✿✿✿✿✿libRadtran✿✿✿✿✿✿public✿✿✿✿✿✿release,✿✿it✿✿is✿✿✿✿✿✿✿✿available ✿✿in ✿✿✿✿joint ✿✿✿✿✿✿✿projects.✿ 1145 Bass, A. M. and Paur, R. J.: The ultraviolet cross–section of ozone, I, The measurements, in: Atmospheric Ozone: Proceedings of the Quadrennial Ozone Symposium, edited by Zerefos, C. S. and Ghazi, A., pp. 601–606, D. Reidel, Norwell, Mass., 1985. Baum, B., Heymsfield, A., Yang, P., and Bedka, S.: Bulk scattering 1150 models for the remote sensing of ice clouds. Part 1: Microphysi- cal data and models, J. of Applied Meteorology, 44, 1885–1895, 2005a. Baum, B., Yang, P., Heymsfield, A., Platnick, S., King, M., Hu, Y.- X., and Bedka, S.: Bulk scattering models for the remote sensing 1155 of ice clouds. Part 2: Narrowband models, J. of Applied Meteo- rology, 44, 1896–1911, 2005b. Baum, B. A., Yang, P., Heymsfield, A. J., Bansemer, A., Merrelli, A., Schmitt, C., and Wang, C.: Ice cloud bulk single-scattering property models with the full phase matrix at wavelengths from 1160 0.2 to 100 µm, J. Quant. Spectrosc. Radiat. Transfer, special Is- sue ELS-XIV, 2014. Blattner,¨ W. G., Horak, H. G., Collins, D. G., and Wells, M. B.: Monte Carlo Studies of the Sky Radiation of Twilight, Appl. Opt., 13, 534–547, 1974. 1165 Bodhaine, B. A., Wood, N. B., Dutton, E. G., and Slusser, J. R.: On Rayleigh optical depth calculations, J. Atm. Ocean Technol., 16, 1854–1861, 1999. Bogumil, K., Orphal, J., Voigt, S., Spietz, P., Fleischmann, O. C., Vogel, A., Hartmann, M., Kromminga, H., Bovensmann, H., Fr- 1170 erick, J., and Burrows, J. P.: Measurements of molecular ab- sorption spectra with the SCIAMACHY pre-flight model: instru- ment characterization and reference data for atmospheric remote- sensing in the 230-2380 nm region, J. Photochem. and Photobio. A: Chem., 157, 167–184, 2003. 1175 Bohren, C. F. and Huffman, D. R.: Absorption and Scattering of Light by Small Particles, John Wiley & Sons, 1983. Buehler, S., John, V., Kottayil, A., Milz, M., and Eriksson, P.: Ef- ficient radiative transfer simulations for a broadband infrared ra- diometer - combining a weighted mean of representative frequen- 1180 cies approach with frequency selection by simulated annealing, JQSRT, 111, 602–615, 2010. Bugliaro, L., Zinner, T., Keil, C., Mayer, B., Hollmann, R., Reuter, M., and Thomas, W.: Validation of cloud property retrievals with simulated satellite radiances: a case study for SEVIRI, Atmos. 1185 Chem. Phys., 11, 5603–5624, doi:10.5194/acp-11-5603-2011, 2011. 20 C. Emde et al.: The libRadtran software package

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Wandji Nyamsi, W., Arola, A., Blanc, P., Lindfors, A. V., Cesnulyte, Appendix A V., Pitkanen,¨ M. R. A., and Wald, L.: Technical Note: A novel 1695 parameterization of the transmissivity due to ozone absorption1750 Ice crystal optical properties parameterizations in the k-distribution method and correlated-k approximation of Kato et al. (1999) over the UV band, Atmospheric Chemistry and The parameterization yang2013 is based on the single scat- Physics, 15, 7449–7456, doi:10.5194/acp-15-7449-2015, http:// tering data by Yang et al. (2013). It is available for nine habits www.atmos-chem-phys.net/15/7449/2015/, 2015. and three roughness parameters. It includes full phase matri- 1700 Wanner, W., Strahler, A., Hu, B., Lewis, P., Muller, J.-P., Li, X., ces for the spectral range from 200 nm to 99 m. The hey Barker Schaaf, C., and Barnsley, M.: Global retrieval of bidi- µ rectional reflectance and albedo over land from EOS MODIS1755 (Hong, Emde, Yang) parameterization is available for six in- and MISR data: Theory and algorithm, J. Geophys. Res., 102, dividual smooth habits and includes the full phase matrices 17 143–17 161, 1997. for the wavelength region from 0.2 to 5 µm. The single scat- 1705 Warren, S. G.: Optical constants of ice from the ultraviolet to the tering properties for the six ice crystal habits have been gen- microwave, Applied Optics, 23, 1206–1225, 1984. erated by Hong Gang based on the improved geometrical op- Weinzierl, B., Sauer, D., Minikin, A., Reitebuch, O., Dahlkoet-1760 tics method (IGOM), the same which is applied in Yang et al. ter, F., Mayer, B., Emde, C., Tegen, I., Gasteiger, J., Petzold, (2013). A., Veira, A., Kueppers, U., and Schumann, U.: On the visi- In order to obtain bulk scattering properties (required by 1710 bility of airborne volcanic ash and mineral dust from the pi- the RTE solver) the single scattering properties need to be in- lot’s perspective in flight, Phys. Chem. Earth, 45-46, 87–102, tegrated over the particle size distribution. In reality the size doi:10.1016/j.pce.2012.04.003, 2012. 1765 distributions are highly variable, for radiative transfer sim- Wiscombe, W.: Improved Mie scattering algorithms, Appl. Opt., 19, 1505–1509, 1980. ulations they are often approximated by simple gamma dis- 1715 WMO: Atmospheric Ozone 1985, Tech. rep., WMO Report No. 16, tributions (e.g. Evans, 1998; Heymsfield et al., 2002; Baum 1986. et al., 2005a,b) or bi-modal gamma distributions (Mitchell et al., 1996; Ivanova et al., 2001). We assume a gamma size C. Emde et al.: The libRadtran software package 25

1770 distribution to compute the bulk scattering properties as for each scattering angle θ and for six matrix elements (denoted the water cloud properties (compare Eq. 4): by index i) needed to describe the scattering process by ran-

1 domly oriented nonspherical particles (see e.g. van de Hulst, b −3 re n(re) = Nre exp − (A1)1815 1981)):  ab Here r is a measure of the particle size (the radius in case Lmax e Lmin A(L)P (L,i,θ)ω0(L)Qext(L)n(L)dL hP (reff ,i,θ)i = of spherical particles) and N is the normalization constant R Lmax A(L) ω0(L)Qext(L)n(L)dL 1775 so that the integral over the distribution yields the number of Lmin particles in a unit volume. For spherical particles the param- R (A6) eters a and b correspond to the effective radius reff and to the Optical properties for a general habit mixture ghm have effective variance veff , respectively. Typical values of cirrus also been calculated for the hey parameterization following cloud size distributions for b are in the range between 0.1 and the mixing “recipe” suggested by Baum et al. (2005b). 1780 0.5 (Evans, 1998; Heymsfield et al., 2002). In the following we take a fixed value of b = 0.25. We define the effective par- ticle size re(L) for an individual ice crystal as follows (Yang1820 Appendix B et al., 2005): Description of TZS solver 3 V (L) re(L) = (A2) 4 A(L) This solver is based on the zero scattering approximation and can be used to calculate clear sky or “black cloud” radiances 1785 Here L is the maximum dimension of a nonspherical ice at the top of the atmopshere (TOA) in the thermal spectral crystal and A and V are the projected area and the volume of 1825 range. Without scattering the formal solution of the radiative the particle, respectively. 2r (L) corresponds to the “effec- e transfer equation for the upward intensity (radiance) at TOA tive distance”, i.e. the representative distance a photon trav- at a given frequency reduces to els through an ice crystal without experiencing internal re- Iν (τ = 0,µ,φ) ν 1790 flections and refraction (Mitchell et al., 1996). The effective ∗ ∗ Iν (τ = 0,µ,φ) = Iν (τ ,µ,φ)exp(−τ /µ) radius of a size distribution is generally defined as: τ ∗ Lmax dτ 1830 (B1) 3 Lmin V (L)n(L)dL + Bν (τ)exp(−τ/µ) . reff = (A3) Z µ 4 R Lmax 0 Lmin A(L)n(L)dL R Here we used the (vertical) absorption optical thickness τ In order to obtain bulk scattering properties which can be measured from top of atmosphere as the vertical coordinate used for radiative transfer calculations, we pre-calculate bulk such that τ = 0 at TOA and τ = τ ∗ at the surface. Variables 1795 optical properties on a specified equidistant effective radius 1835 µ and φ denote the cosine of the zenith angle and the azimuth grid including values from 5 to 90 µm in steps of 5 µm. angle respectively. Planck’s function at a given frequency ν Now using Eq. (A3) we iteratively find the parameter a of the is represented by Bν (τ) and its temperature dependence is size distribution which results in the desired effective radius. contained implicitly in τ. The bulk optical properties are then calculated by integration The first term on the right hand side in Eq. B1 represents 1800 over the gamma distributions with the parameters b=0.25 and1840 the contribution of the surface and the second one the con- the iteratively obtained a depending on the effective radius. tribution of the atmosphere. The surface contribution can be libRadtran requires the extinction coefficient normalized to written as 1 g/m3 ice: ∗ ∗ Lmax Iν (τ ,µ,φ) = ǫs Bν (τ )+ A(L)Qext(L)n(L)dL ∗ Lmin 1 τ ext eff (A4) hβ (r )i = Lmax R ρ V (L)n(L)dL ∗ Lmin 1845 + 2(1 − ǫs) Bν (τ)exp(−(τ − τ)/µ)dτdµ (B2) Z Z R 0 0 1805 Here Qext(L) is the extinction efficiency, ρ is the density of ice, and n(L) is the gamma size distribution which cor- with the first term representing the emission of the surface responds to the effective radius reff . The single scattering (ǫs=surface emissivity) and the second one the reflection at albedo hω0i is calculated as follows: the surface of the radiation emitted by the atmosphere toward 1850 the surface. The factor 2 comes from the integration over the Lmax Lmin A(L)ω0(L)Qext(L)n(L)dL azimuth angle φ. hω0(reff )i = (A5) R Lmax Under the approximation of Planck’s function B (τ) as a A(L)Qext(L)n(L)dL ν Lmin piecewise linear function in τ between two consecutive lev- R 1810 Finally, libRadtran requires the phase matrix hP (reff )i, els, both integrals can be solved as a function of the expo- −x −y which is computed according to the following equation for1855 nential integral Ei(x) = −∞ e /y dy. R 26 C. Emde et al.: The libRadtran software package

Acknowledgements. Numerous colleagues have contributed with software and comments to the package. We would like to thank K. Stamnes, W. Wiscombe, S.C. Tsay, and K. Jayaweera (disort), F. Evans (polradtran), S. Kato (correlated-k distribution), J.-M. Van- 1860 denberghe, F. Hendrick, and M. V. Roozendael (sdisort), T. Char- lock, Q. Fu, and F. Rose (Fu and Liou code), D. Kratz (AVHRR routines), B. A. Baum, P. Yang, L. Bi, H. Gang, J. Key, B. Rein- hardt, and A. Gonzales (ice cloud optical properties), P. Ricchiazzi (LOWTRAN/SBDART gas absorption), M. Hess (OPAC aerosol 1865 database), W. Wiscombe, C. F. Bohren, and D. Huffman (Mie codes), M. Mishchenko (water reflectance matrix), O. Engelsen (implementation of ozone cross sections), the ARTS community and Franz Schreier (line-by-line models), J. Betcke (implementa- tion of King Byrne equation). Thanks to all users for feedback and 1870 contributions, which helped to improve the software over the years. Thanks also to L. Scheck for providing the simulated satellite im-

age shown in Sec. 11.2.✿✿✿✿✿Finally✿✿✿we✿✿✿✿thank✿✿✿two✿✿✿✿✿✿✿✿✿anonymous✿✿✿✿✿✿✿reviewers ✿✿for✿✿✿✿their✿✿✿✿✿useful ✿✿✿✿✿✿✿✿comments.✿Part of the libRadtran development was funded by ESA (ESASLight projects AO/1-5433/07/NL/HE, AO/1- 1875 6607/10/NL/LvH).