1. The Spectral Mapping Atmospheric David Crisp, Jet Propulsion Laboratory ABSTRACT Spectrum-resolving multiple scattering models: Can provide a reliable description of the radiation field in a wide range of conditions in scattering, absorbing, emitting planetary atmospheres because they can include all available information about the wavelength and altitude dependent optical properties of the environment. Are often too computationally expensive for routine use in remote sensing and climate modeling applications that span the entire solar and/or thermal wavelength range. The Spectral Mapping Atmospheric Radiative Transfer (SMART) model maintains the versatility of conventional SRMS models, but provides large improvements in speed by reducing the number of monochromatic multiple scattering calculations needed to generate spectrally resolved radiances and fluxes in broad spectral regions. The SMART approach: Defines a spectral grid that completely resolves the wavelength-dependent optical properties of the surface and all gases, clouds, and aerosols that contribute to the radiation field throughout the atmospheric column Identifies spectral grid points that have similar optical properties along the entire surface/atmosphere optical path, Maps these grid points into a smaller number of quasi-monochromatic bins, Uses the multi-stream multiple scattering algorithm DISORT to calculate the angle- dependent radiances for each bin, maps these radiances back to their original spectral grid points to create a high-resolution spectrum. This approach typically reduces the number of multiple scattering calculations by a factor of ~100 to 1000 without introducing radiance or heating rate errors larger than 1% at spectral resolutions high as ~1 cm -1. Over the past decade the SMART model has enabled a broad range of radiative transfer and remote sensing applications in planetary atmospheres. Here, we describe these recent upgrades, including an efficient method for generating linearized “radiance Jacobians” or “weighting functions”, for use in remote sensing retrieval models. SMART reads input files containing the wavelength dependent optical properties for up to 50 absorbing gases, 10 different aerosol modes, and the surface BRDF. In general, these optical property files will have different spectral grids. SMART provides a spectrally-resolved description of the radiation field over broad spectral regions in realistic, vertically- inhomogeneous, scattering, absorbing, emitting planetary atmospheres. Specific products include: A high spectral resolution, angle dependent description of the radiance field throughout the atmosphere Radiance Jacobians (weighting functions) for use in remote sensing applications. Solar radiative heating rates and thermal cooling rates for use in climate models Objective and Approach Vertical variations in the thermal structure and optical properties are accounted for by dividing the atmosphere into a series of discrete levels (defined by a user-supplied table) The Atmosphere Structure Optically Active Gases Gas mixing ratios are read from files and interpolated to the level structure The log of the mixing ratio is assumed to vary linearly with log of pressure Clouds and Aerosols The vertical distribution of up to 10 discrete cloud and aerosol particle modes are read from files and interpolated to the vertical grid The differential optical depth and particle scale height at a reference wavelength are specified in each layers for each particle mode The scale height is used to interpolate particle number densities to the model grid. The vertical temperature structure of a 65 level tropical terrestrial atmosphere with a saturated alstostratus cloud. The trace gas distribution in a 65 level tropical terrestrial atmosphere with a saturated alstostratus cloud. Creating the Spectral Grid A very fine grid is needed to resolve narrow vibration-rotation absorption lines Our line-by-line model uses a non-uniform grid, with finer resolution near line centers and courser spacing elsewhere. Much coarser grids are adequate to resolve: Gas electronic transitions in the visible and UV Pressure-induced absorption by gases at infrared wavelengths The spectral dependence of the H 2 O (top) and CO 2 (bottom) absorption cross-sections are shown at 3 levels for a narrow spectral region in the near infrared near 2  m. A relatively course grid is also adequate to resolve The wavelength dependent single scattering optical properties of clouds and aerosols The wavelength dependent surface reflectance. The wavelength dependent single scattering optical properties for a fair weather cumulus cloud. To address the needs, SMART uses a "lowest common denominator" spectral grid, which preserves all of the spectral structure included in the input files. To implement this grid, it: Reads the spectrally-dependent input files sequentially as it marches through the spectrum, retaining the optical properties at the last two points in each file (for linear interpolation). If the last spectral grid point is at wavenumber o, it searches through the input files to identify the one with an input value that is at the smallest distance beyond this point. If this distance,  >10 -7 o, then, it defines the next spectral point at 1 = o + , and interpolates all spectral quantities to this point. Absorption and scattering cross-sections of gases and airborne particles Surface reflectance These properties are weighted by the absorber amount in each layer (N(z)×dz) to define the layer-integrated monochromatic optical depth, , single scattering albedo , and particle phase function P(  ). value o 1 Selecting the next grid point in the “lowest common denominator” monochromatic spectral grid.

2. Radiative Transfer (SMART) Model California Institute of Technology Given the wavelength dependent monochromatic optical properties of the surface and atmosphere, spectral mapping methods gain their efficiency by: Identifying grid points with similar optical properties at all points along the optical path Mapping these optical properties into a small number of quasi-monochromatic bins Performing monochromatic multiple scattering calculation to derive the angle dependent radiance field for each bin Spectral Binning Cartoon showing differential optical depths,  (z) for 3 bins (blue, green, red). The mean value (solid line) and allowed range of values (dashed lines) are shown for each bin. The  values for a candidate monochromatic segment are also shown (dotted black line).  Altitude (km) Given the level-dependent monochromatic optical properties in each layer, j, for a given sounding at wavenumber, n, x n =[  i (z),  i (z), g i (z), a], SMART compares these values to the values in existing bins. Each Spectral Bin is defined by a mean value and a range of acceptable values at each atmospheric level and at the surface: Mean Values: x b = [  b (z),  b (z), g(z), a b ] Range:  b (z),  b (z),  g(z),  a b Set by the user at run time A monochromatic sounding is included in a bin if it satisfies the following criteria at all levels:  (z) = (1   )×  b (z)  (z),= (1   )×  b (z) g(z) = (1   )×g b (z),  a = (1   )×a b If the sounding fits in a bin, the bin number is recorded on a “Spectral Map” Radiative Transfer Calculations If a sounding does not fit in an existing bin, a new bin is defined with by its optical properties Once the all (~1024) bins are allocated multiple scattering calculations are performed to derive the radiation field for each of these bins. If the maximum number of bins does not accommodate the variability across the spectral interval of interest, the bins are reinitialized and the process is repeated. Differential optical depths for a ~2.5 km thick layer ~10 km above the Martian surface for spectral region in the wing of a weak CO 2 band (left) are shown along with bin indices stored in the spectral map created by SMART (right). SMART uses the DISORT algorithm to perform multi-level, multi-stream monochromatic multiple scattering calculations for each spectral bin. Early versions of SMART: Performed only one multiple scattering calculation for the mean optical properties in each bin Mapped these values directly back to the high resolution grid This approach maximizes the efficiency, but it can introduce errors and biases Radiance % Error -5 0 5 10 15 20 4650.224650.23 Wavenumber (cm -1 ) Direct Mapping of radiances derived from mean optical properties in each bin can produce systematic errors that are most obvious where optical properties are varying monotonically The spectral mapping scheme in current version of SMART has been modified to improve the accuracy and efficiency: Radiances are assumed to vary linearly with optical property variations within each bin SMART finds radiances for: The mean optical properties of each bin Perturbed values:  x b (z) +  x b ’ (z) Radiance fields for mean and perturbed cases are used to estimate the radiance Jacobians: (  r i /  x j ) which specify the rate of change of the radiances, r, at any level, i, with respect to changes in optical property, x, at level, j. Radiance Jacobians improve the accuracy of the process for mapping radiances for each bin back to the original spectral grid. A simplified version of the “Adding Method” is used to estimate the radiance Jacobians: The radiance at any angle at the interface of two layers, r(z j, ,  ), consists of a “transmitted” component, T(z j, ,  ) and a “source”, S(z j, ,  ). The transmitted component is approximated by the layer’s diffuse transmittance The source, S, includes contributions from all radiation scattered into angle ( ,  ) from other angles, as well as internal sources. The source is approximated as follows: S(x,z j, ,  ) = r(x,z j, ,  ) - r(x,z j-1, ,  )×T(x,z j, ,  ) (up) S(x,z j, ,  ) = r(x,z j, ,  ) - r(x,z j, ,  )×T(x,z j+1, ,  ) (down) Similar results are derived for the perturbed optical properties (x + x’) and the partial derivatives of S are derived as follows:  S/  x i = (S(x i,z j, ,  ) - S(x i +x i ’,z j, ,  )) / x i ’ Before binned radiances are mapped back to the original spectral grid, linear interpolation is used to correct layer-dependent S values for differences between the binned values of the optical properties, x b, and the monochromatic values at each wavenumber, x n ( n ): S( n,x n, ,  ) = S(x b ,  ) +  S(x b ,  ) /  x (x n – x b ) The T ( n,x n, ,  ) values are interpolated from pre-computed tables. The simplified adding method is then used to find the radiances at each level at each point on the original monochromatic grid, e.g.: r( n,z j, ,  )=S( n,x n, ,  )+r( n,z j, ,  ) T ( n,x n, ,  ) This mapping approach usually produces radiance errors no larger than ~0.1 to 1%, while reducing the number of multiple scattering calculations by 100 to 1000. This enables a broad range of radiance calculations in realistic, scattering, absorbing planetary atmospheres. The accuracy and efficiency of the linearized method for mapping the binned values back to the original spectral grid also provides and efficient method for generating Jacobians for use in remote sensing retrieval algorithms. Back-Mapping Radiances Temperature Jacobians (weighting functions) are shown for the 15-  m CO 2 band in the Earth’s atmosphere. Jacobians (weighting functions) for HCl (left) and H 2 O are shown for the 1.74-  m atmospheric window on the night side of Venus. Jacobians like these will be used to analyze Venus Express observations of the Venus atmosphere to assess the abundances of trace gases below the planet- encircling sulfuric acid cloud deck. This work was supported by the NASA Astrobiology Institute’s Virtual Planetary Laboratory (VPL)