Spectral mapping with linearized Radiant Zhiming Kuang

1
Spectral mapping with linearized RadiantZhiming
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
Restrict spectral mapping to within each layer
Wavelength
scattering
An empirical function
absorption

• Using gas absorption and effects of
  cloud/aerosols/Rayleigh gives similar results

4
An O2-A band case
RMS 0.02 Before convolution
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.
5
A CO2 2.0um band case
RMS 0.02
6
O2 A-band
Table 1. Numbers of operations
Case of layer building (GR,GT) of adding/2
No spectral mapping 87681 79710
Current, no layer saving 815 31870
Current, with layer saving 815 7522
Table 2. Timing results
Function No spectral mapping no layer saving (total speedup4) Layer saving (speeduplt15)
GT,GR computation 34 26, 4.6 26
Global source 13 2.5, 18 10
Combine layers 14 2.5, 20 10
Linearized adding 33 2.5, 44 10
7
CO2 2um
Table 1. Numbers of operations
Case of layer building (GR,GT) of adding/2
No spectral mapping 6.0e5 5.4e5
Current, no layer saving 754 1.2e5
Current, with layer saving 754 18414
Table 2. Timing results
Function No spectral mapping no layer saving (total speedup6) Layer saving (speedup lt 40)
GT,GR computation 34 300, 3.6 300
Global source 13 4.5, 17 lt30
Combine layers 14 4.5, 17 lt30
Linearized adding 32 4.5, 43 lt30
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.