1. Clear Sky Forward Model & Its Adjoint Model
MURI Review April 27, 2004
leslie moy, dave tobin, paul van delst, hal woolf

2. Accomplishments: • Coefficients promulgated 2003.
Reproduce and Upgrade existing GIFTS/IOMI Fast Model
• Coefficients promulgated 2003.
• Greatly improved the dependent set statistics (esp. water vapor).
• SVD regression and optical depth weighting incorporated.
• Written in flexible code with visualization capabilities. Under CVS control.
Write the Corresponding Tangent Linear and Adjoint Code
• Tested to machine precision accuracy.
• User friendly “wrap-around” code complete.

3. Fast Model Production Flowchart:
Profile
Database
Fixed Gas
Amounts
Spectral line
parameters
Lineshapes
& Continua
Layering, l
Compute monochromatic
layer-to-space
transmittances
Reduce to sensor’s
spectral resolution
Effective Layer
Optical Depths, keff
Convolved
Layer-to-Space
Transmittances, tz (l)
Fast Model
Predictors, Qi
Fast Model
Regressions
Fast Model
Coefficients, ci
keff = -ln (teff ) = Si=1:N ci Qi

4. MURI model w/ OD weighted SVD OPTRAN, AIRS 281 channel set
GIFTS
OSS RMS upper limit*
Dependent Set Statistics: RMS(LBL-FM)
current model
MURI version
MURI model w/ OD weighted SVD
AIRS model c/o L. Strow, UMBC
OSS model c/o Xu Liu, AER, Inc.
OPTRAN, AIRS 281 channel set
c/o PVD

5. Profile of temperature,
User Input:
User Output:
Profile of temperature,
ozone, water vapor
at 101 levels
Profile perturbation
of temperature, ozone,
water vapor at 101 levels
Use to adjust
initial profile
Forward Model:
Adjoint Model:
Layer.m - convert 101 level values to
100 layer values
Predictor.m - convert layer values to
predictor values
Calc_Trans.m - using predictors and
coefficients calculate
level to space transmittance
Trans_to_Rad.m - calculate radiance
Layer_AD.m - layer to level sensitivities
Predictor_AD.m -
level to predictor sensitivities
Calc_Trans_AD.m - predictor to
transmittance sensitivities
Trans_to_Rad_AD.m - transmittance to
radiance sensitivities
User Output:
User Input:
Compare to
observations
Radiance Spectrum
Radiance Spectrum
perturbation

6. Simple Example: One Line Forward Model
Forward (FWD) model. The FWD operator maps the input state vector, X, to the model prediction, Y, e.g. for predictor #11:
Tangent-linear (TL) model. Linearisation of the forward model about Xb, the TL operator maps changes in the input state vector, X, to changes in the model prediction, Y,
Or, in matrix form:

7. Forward Model: TL Model: Testing subroutines:
Using the same procedure as in the Simple Model, build up the Tangent Linear Model.
Forward Model:
TL Model:
Layer.m - input: 101 level values of T,w,oz
output: 100 layer values
Predictor.m - input: layer values
output: predictor values
Calc_Trans.m - input: predictors, and
coefficients
output: transmittances
Trans_to_Rad.m - input: transmittances
output: TOA radiance
Layer_TL.m - input: d(level value)
output: d(layer value)
Predictor_TL.m - input d(layer value),
output: d(predictor), Calc_Trans_TL.m - input: d(predictor)
output: d(transmittance)
Trans_to_Rad_TL.m -
input: d(transmittance)
output: d(radiance)
Testing subroutines:
A range of Perturbations are added to a baseline input value. Plus&Minus 25%
The Forward output (less the baseline value) is compared to the TL output.

8. TL testing for Dry Predictor #6 (T2) vs Temp at layer 44
TL testing for Dry Predictor #6 (T2) vs Temp at layer 44. * TL results must be linear. * TL must equal (FWD-To) at dT=0.
TL results = blue, FWD-T0 results = red
Difference between TL and FWD
Input Temperature at Layer 44 were varied 25%.

9. TL testing for Dry Predictor #6 vs Temp at all layers
TL testing for Dry Predictor #6 vs Temp at all layers. Similar plots made for each subroutine’s variables.
D(dry.pred#6)
Layer no.
D(temp), %

10. Adjoint (AD) model. The AD operator maps in the reverse direction where for a given perturbation in the model prediction, Y, the change in the state vector, X, can be determined. The AD operator is the transpose of the TL operator. Using the example for predictor #11 in matrix form,
Expanding this into separate equations:

11. Adjoint code testing for Dry Predictor #6 vs Temperature layer
Adjoint code testing for Dry Predictor #6 vs Temperature layer. AD - TLt residual must be zero. Similar plots are produced for every subroutine’s variables.
AD - TLt residual
Output variable layer
Input variable layer

12. Adjoint for US Standard Profile, d(radiance)/d(ozone)
Pressure, -mbar
Wavenumber, cm-1

13. Adjoint for US Standard Profile, d(radiance)/d(water vapor)
Pressure, -mbar
Wavenumber, cm-1

14. Future Goals:
‘Reproduce and Upgrade existing GIFTS Fast Model’
• Increase the number and quality of training profiles (48); extend satellite zenith angle range;
further improve the dependent and independent set statistics.
• Breakout other gases.
• Steer research direction based on user feedback.
Corresponding Tangent Linear and Adjoint Code
• Improve code for speed and ease of use. Convert to a more efficient programming language.
• Investigator testing of code.

15. Sensitivity, d(P6)/d(T)
Adjoint code can be used for sensitivity analysis. d(Dry Predictor #6) / d(layer Temperature).
Sensitivity, d(P6)/d(T)
Output variable layer
Input variable layer