Rutherford Appleton Laboratory Remote Sensing Group GOME-202-2 slit function analysis PM2 Part 1: Retrieval Scheme R. Siddans, B. Latter, B. Kerridge RAL.

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