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

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.

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

MURI model w/ OD weighted SVD OPTRAN, AIRS 281 channel set ------- GIFTS NeDT@296K ------- 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

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

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:

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.

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%.

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), %

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:

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

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

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

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.

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