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Rutherford Appleton Laboratory Remote Sensing Group GOME slit function analysis PM2 Part 1: Retrieval Scheme R. Siddans, B. Latter, B. Kerridge RAL Remote Sensing Group 26 th June 2012 RAL

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Remote Sensing Group GOME-2 FM202-2: PM2 Slit function analysis Overview of slit-function fitting method New results for FM202-2 (WP2100) - use of new angular parameters from TNO - modification of source line shape to match commissioning measurements Comparisons of results: - FM202-2 to FM FM mm to FM mm Error analysis for FM202-2 Discussion re next steps, date of next meeting (FP) AVHRR/GOME-2 co-location, spatial aliasing and geo- referencing (Ruediger Lang) © 2010 RalSpace

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Remote Sensing Group SFS Measurements © 2010 RalSpace stimulus line width / nm Wavelength / nm

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Remote Sensing Group FM3 1.0mm slit FM2 0.5mm (now ) FM2 1.0mm Wavelength / nm

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Remote Sensing Group Detailed line-shape –Close to triangular –Presence of wings at few % level Wavelength / nm Spectral ghosts & straylight –Broad-band stray-light –Rowland ghosts –symmetric about peak –Additional “straylight” ghost for FM3 Limited knowledge of –Wavelength calibration –Source intensity SFS Measurements (2004)

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Remote Sensing Group Problem: –deconvolution from a signal which also includes –the spectral shape of the stimulus –radiometric response of the instrument –random and systematic errors (e.g. straylight). –stimulus width is not negligible: –solution requires a priori knowledge Optimal estimation (OE) used here: –Physical model of measurement system –Quantitative incorporation of a priori knowledge –Not necessary to define ad-hoc functional slit-shapes –Quantitative description of errors SFS Analysis

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Remote Sensing Group Analysis Procedure Optimal Estimation Retrieval –Uses physical “forward” model (FM) of the SFS measurement process –Optimise model parameters including slit functions to get consistent fit to measurements Measurement vector : –GOME-2 signals (dark-corrected BU/s) within interval +/- 0.3x order spacing of a fringe pk State-vector: –Slit-function –Piece-wise linear representation at 0.01 or 0.02nm spacing –Stray-light –2 nd order polynomial –Amplitudes of Rowland ghosts –Spectrally-integrated order intensity at each Echelle angle Resulting Key-data: –Retrievals for “fully-sampled” pixels (including estimated errors) –Linear interpolation to other pixels

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Remote Sensing Group Constraints on Retrieval 1.Optical point spread function →Smoothness of slit-function for given pixel “Spot” dimension: 0.16nm in Ch 1&2 0.32nm in Ch 3&4 2.Slit-function areas normalised to 1 3.Slit-function values at any given input wavelength sum to 1 –input delta-fn is distributed across detector pixels but GOME conserves total intensity (after radiometric calibration) 4.Tikhonov smoothing (weak) from pixel to pixel

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Remote Sensing Group Assume SFS wavelength calibration is highly accurate –based on grating theory with angles optimised by TPD scheme Slit-function wavelength grid defined relative to nominal wavelength of each pixel according to the SLS key-data wavelength calibration –SLS -calibration has known deficiencies where lines sparse (NB Huggins bands) Retrieval scheme will offset slit-function centre-of-mass as necessary –will be offset where SLS calibration erroneous No attempt is made to re-centre slit-functions before delivery –off-centre slit-functions provide implicit correction for SLS wavelength calibration errors when used to simulate L1 spectra by convolving high-resolution reference spectra. Wavelength calibration

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Remote Sensing Group

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Normalisation constraint By definition slit-functions should be normalised after application of the GOME-2 radiance response function. Errors in prior knowledge of fringe intensity and GOME-2 radiance response mean slit-functions should not be assumed normalised without fitting source intensity Slit-functions constrained to be normalised within “a priori” error of 0.01% Fringe intensity retrieved for given order at every echelle step –No a priori constraint –First guess from TPD derived value

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Remote Sensing Group Retrieval of fringe intensity Further constraint is required to give stable solution Need to assume intensity in the fringe (at each echelle step) = total intensity recorded by all the detector pixels (after radiometric calibration and removal of straylight) I.e. by adding response in all detector pixels, GOME-2 behaves as perfect radiometer, and conserves total input energy (after accounting for radiance response): P = i=1,N R i x C i x i Fringe intensity W/cm 2 /sr sum over detector pixels radiance response (W/cm 2 /nm/sr)/(Counts/s) detector read-out Counts/s detector pixel spectral width nm

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Example early retrieval: Diagnosis of Ghost features Measurements (colour scale to reveal structure away from main peak) Fitted straylight Fit residuals (measurement – model) Retrieved slit-functions Fully sampled pixels Partially sampled pixels Total reponse (radiometer constraint) SFS power: Fitted (solid) First guess (dashed)

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Remote Sensing Group Treatment of ghosts Positions of Rowland ghosts modelled by equation: with l i =0.205,0.29,0.47 based on analysis of data by TPD Intensity of each ghost line is retrieved (assuming symmetric about peak) Choose to always fit measurements in detector pixels with +/- 0.3 fractional order of main peak Over this range, after fitting ghosts, remaining straylight linear with wavelength im i

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Remote Sensing Group Contribution function D y = ( S a + K t S y -1 K ) -1 K t S y -1 Linear mapping of an error spectrum: ( x’-x ) = D y (y’-y) Linear mapping of covariance in RTM or IM parameter: S x:y = D y S y:b D y t, but S y:b = K b S b K b t Propagate errors onto slit function retrieval then O 3 profile Linear mapping x = State vector of (retrieved parameters) y = Measurement vector (b = error considered) K = Weighting function matrix (K ij = y j / x i ) S a = a priori covariance S x = Estimate covariance of state after retrieval

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