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GOME-202-2 slit function analysis PM2 Part 1: Retrieval Scheme R. Siddans, B. Latter, B. Kerridge RAL Remote Sensing Group 26 th June 2012 RAL. GOME-2 FM202-2: PM2 Slit function analysis. Overview of slit-function fitting method New results for FM202-2 (WP2100)

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GOME-2 FM202-2: PM2 Slit function analysis

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GOME-202-2 slit function analysisPM2Part 1: Retrieval SchemeR. Siddans, B. Latter, B. KerridgeRAL Remote Sensing Group26th June 2012RAL

gome 2 fm202 2 pm2 slit function analysis
GOME-2 FM202-2: PM2Slit 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 FM202-1
  • - FM202-2 1mm to FM202-2 0.5mm
  • 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)

FM3 1.0mm slit

FM2 0.5mm

(now 76-77.3)

FM2 1.0mm

Wavelength / nm

sfs measurements 2004

Detailed line-shape

    • Close to triangular
    • Presence of wings at few % level

Wavelength / nm

SFS Measurements (2004)
  • 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 analysis
SFS Analysis
  • 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
analysis procedure
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
      • 2nd 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
constraints on retrieval
Constraints on Retrieval
  • 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

  • Slit-function areas normalised to 1
  • 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

wavelength calibration
Wavelength calibration
  • 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.
normalisation constraint
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
retrieval of fringe intensity
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,NRi x Ci x i

radiance response



Fringe intensityW/cm2/sr

sum overdetector pixels

detector pixel spectral widthnm


Example early retrieval: Diagnosis of Ghost features


Fit residuals (measurement – model)


(colour scale to reveal structure away from main peak)

Fitted straylight

SFS power: Fitted (solid) First guess (dashed)

Retrieved slit-functions

Fully sampled pixels

Partially sampled pixels

Total reponse (radiometer constraint)

treatment of ghosts
Treatment of ghosts
  • Positions of Rowland ghosts modelled by equation:



  • with li=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
linear mapping
Linear mapping
  • Contribution functionDy= ( Sa + KtSy-1K )-1KtSy-1
  • Linear mapping of an error spectrum:( x’-x ) = Dy (y’-y)
  • Linear mapping of covariance in RTM or IM parameter:Sx:y = DySy:bDyt, butSy:b= KbSbKbt
  • Propagate errors onto slit function retrieval then O3 profile

x = State vector of (retrieved parameters)

y = Measurement vector (b = error considered)

K = Weighting function matrix (Kij = yj/xi)

Sa = a priori covariance

Sx = Estimate covariance of state after retrieval