Rutherford Appleton Laboratory Remote Sensing Group GOME-202-2 slit function analysis PM2 Part 1:...
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Transcript of Rutherford Appleton Laboratory Remote Sensing Group GOME-202-2 slit function analysis PM2 Part 1:...
Rutherford Appleton Laboratory
Remote Sensing Group
GOME-202-2 slit function analysis
PM2Part 1: Retrieval Scheme
R. Siddans, B. Latter, B. KerridgeRAL Remote Sensing Group
26th June 2012RAL
Remote Sensing GroupGOME-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)
© 2010 RalSpace
Remote Sensing GroupSFS Measurements
© 2010 RalSpace
stim
ulu
s lin
e w
idth
/ n
mWavelength / nm
Remote Sensing Group
FM3 1.0mm slit
FM2 0.5mm(now 76-
77.3)
FM2 1.0mm
Wavelength / nm
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)
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
Remote Sensing GroupAnalysis 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
Remote Sensing GroupConstraints on Retrieval
1. Optical point spread function→ Smoothness of slit-function for given pixel
“Spot” dimension: 0.16nm in Ch 1&20.32nm 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
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
Remote Sensing Group
Remote Sensing GroupNormalisation 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
Remote Sensing GroupRetrieval 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 Ri x Ci x i
Fringe intensityW/cm2/sr
sum overdetector pixels
radiance response
(W/cm2/nm/sr)/(Counts/s)
detectorread-outCounts/s
detector pixel spectral width
nm
Remote Sensing Group
Example early retrieval:
Diagnosis of Ghost features
Measurements
Measurements(colour scale to reveal structure away from main peak)
Fitted straylight
Fit residuals (measurement – model)
Retrieved slit-functionsFully sampled pixelsPartially sampled pixelsTotal reponse (radiometer constraint)
SFS power: Fitted (solid) First guess (dashed)
Remote Sensing GroupTreatment 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
im
i
Remote Sensing Group
• Contribution function
Dy = ( 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 , but Sy:b= KbSbKb
t
• Propagate errors onto slit function retrieval then O3 profile
Linear mapping
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