1. Spectral mapping with linearized Radiant Zhiming Kuang Basic idea: Group wavelengths with similar optical properties into one “bin”, and approximate their RT solutions by that of this “bin”. Spectral mapping with the discrete- ordinate approach (SMART by Crisp) requires the optical properties are similar at all levels

2. The linearized hybrid model Radiant offers important advantages for spectral mapping No need to re-compute the GT and GR functions of individual layers when changes take place in other parts of the atmosphere. The analytical Jacobians can be used to make first order corrections thus to achieve better accuracy

3. Basic independent variables: Using gas absorption and effects of cloud/aerosols/Rayleigh gives similar results Wavelengthscattering Restrict spectral mapping to within each layer absorption An empirical function

4. Figure 1 An O2-A band spectrum and the percentage error relative to the continuum using the present approach. The RMS error is 0.02% relative to the continuum before convolution. An O 2 -A band case RMS 0.02% Before convolution

5. A CO 2 2.0um band case RMS 0.02%

6. Table 1. Numbers of operations Case # of layer building (GR,GT) # of adding/2 No spectral mapping8768179710 Current, no layer saving81531870 Current, with layer saving 8157522 Table 2. Timing results Function No spectral mapping no layer saving (total speedup~4) Layer saving ( speedup<15) GT,GR computation 34%26, 4.6%26 Global source13%2.5, 18%10 Combine layers14%2.5, 20%10 Linearized adding33%2.5, 44%10 O 2 A-band

7. Table 1. Numbers of operations Case # of layer building (GR,GT) # of adding/2 No spectral mapping6.0e55.4e5 Current, no layer saving7541.2e5 Current, with layer saving 75418414 Table 2. Timing results Function No spectral mapping no layer saving (total speedup~6) Layer saving (speedup < 40) GT,GR computation 34%300, 3.6%300 Global source13%4.5, 17%<30 Combine layers14%4.5, 17%<30 Linearized adding32%4.5, 43%<30 CO 2 2um

8. Further improvements For weak scattering cases (like OCO), the number of “bins” needed can be further reduced with single scattering correction in the same spirit as the Nakajima-Tanaka correction. Engineering: e.g. the overhead in the binned GR,GT calculations mostly comes from the copying of matrices.