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GIFTS clear sky fast model, its adjoint, & the neglected reflected term

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##### GIFTS clear sky fast model, its adjoint, & the neglected reflected term

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**GIFTS clear sky fast model, its adjoint,& the neglected**reflected term MURI Hyperspectral Workshop Madison WI, 2005 June 7 bob knuteson, leslie moy, dave tobin, paul van delst, hal woolf**Outline of Talk**• Fast Model: Development & Status • Tangent Linear, Adjoint: Development & Status • Surface Reflected Term: Work in Progress**Fixed Gas**Amounts Spectral line parameters Lineshapes & Continua Reduce to sensor’s spectral resolution Fast Model Coefficients, ci Fast Model Regressions Profile Database Compute monochromatic layer-to-space transmittances Layering, l Convolved Layer-to-Space Transmittances, tz (l) Fast Model Predictors, Qi Effective Layer Optical Depths, keff Fast Model Production Flowchart:**RMS Error: water linesRed=before, Blue=after**Why the improvement? Mainly from SVD regression & Optical Depth Weighting.**RMS Error: water continuumRed=before, Blue=after**Why the improvement? Mainly from regressing nadir only Optical Depths and applying constant factors to off-nadir values.**------- GIFTS NeDT@296K**------- OSS RMS upper limit* Dependent Set Statistics: RMS(LBL-FM) Yr 2002 model MURI version MURI model w/ new regressions AIRS model c/o L. Strow, UMBC OSS model c/o Xu Liu, AER, Inc. OPTRAN, AIRS 281 channel set c/o PVD**User Input:**User Output: Profile of temperature, dry gases, water vapor at 101 levels Profileperturbation 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. Linearization 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:**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.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.AD - TLt residual must be zero.Similar plots are produced for every subroutine’s variables. 10 -18 x AD - TLt residual Output variable layer Input variable layer**I atmos**I surf reflect I surf emiss r, r I surf reflect = TtoaI(i,i) cos(i) sin(i) d(i) d(i) BDRF(r,r: i,i) Clear Sky Top of Atmosphere Radiance I TOA = I atmos + I surf emiss + I surf reflect =I atmos + Ttoa B(tempsurf ) surf + TtoaFluxsurf Reflectivity current fast model we write the expression more explicitly below This Term is often ignored because Refl < 10%. IF the term is calculated accurately enough, it can be exploited to derive surf and hence Tsurf**Approximations made & Their Associated Errors**I surf reflect = TtoaI(i,i) cos(i) sin(i) d(i) d(i) BDRF(r,r: i,i) Approx.1: Lambertian surface (reflection is independent of incident angle): BDRF = R(r,r) = 1-surf (r,r) Approx.2: Low Order Gaussian Quadrature technique for calculating flux # quadrature points needed? which table to use? (Abramowitz and Stegun, 1972) Approx.3: Resolution Reduction SRF {Ttoa2 I() d} {SRF Ttoa } {SRF 2 I() d} Approx.4: Calculating Downwelling Radiance from Upwelling Fast Model SRF I() (usingLBLRTM) (T GIFTSlayer to space convolved) B(templayer)**Expanding on Approx. 2:**2 /2 Downwelling flux = 0 0I(,) cos() sin() d d = 2 0 I() cos() sin() d substituting = cos (), = 2 0 I() d Diffusivity approximation, Low Order Gaussian Quadrature technique 0 I() d = wi I(i ) p.921, Abramozwitz & Stegun, 1972 n=1, 0.5 I(=48) n=2, 0.2 I(1=69°) + 0.3 I(2 =32°) In contrast to the 2-stream model application: -1 I() d = wi I(i ) p.916, Abramozwitz & Stegun, 1972 n=1, I(=54.73) /2 1 1 n i=1 1 n i=1**Approx 2: Error in Gaussian Quadrature Approximations**(difference from using 4 points) Using two points Difference, W/(cm2cm-1 ster) Using one point**Approx. 3: Convolution Error**Product of Convolution Minus Convolution of Products Difference, W/(cm2cm-1 ster)**1 point Gauss. Qaud.**Errors from 1 Point Gaussian Quad & Convolution Approximations Convolution Error Both approx.**2 point Gauss. Qaud.**Both approx. Errors from 2 Point Gaussian Quad & Convolution Approximations Convolution Error**Approx. 4: Using Fast Model Upwelling Level-2-space**Transmissivity to calculate Downwelling Radiance TOA radiance rad = rad + 0.5 (ba+bb) (1-Tb/ Ta) Ta layer trans level 2 space layer radiance emission Ta BOA radiance rad = rad + 0.5 (ba+bb) (1-Tb/ Ta ) (T1/ Tb) Tb T1 level 2 ground Close up of the window region Differences lblrtm - From Tran(lev2space) Comparison of Downwelling Radiance from Tran(lev2space) from lblrtm**Accomplishments:**Reproduce and Upgrade existing GIFTS/IOMI Fast Model • Coefficients promulgated 2003. • Greatly improved the dependent set statistics (esp. water vapor). • Water continuum regression made at nadir and applied to all angles. • 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. • Transferred code to FSU. Investigate Surface Reflected Radiance • Great improvement with two point Gaussian Quadrature (over 1 point). • Convolution order causes large errors – may be overcome with regression algorithm? • Depending on the application (micro-window or on/off line) using upwelling transmissivity for downwelling radiance may be reasonable.