1. GSICS SEVIRI-IASI Inter-Calibration Uncertainty Evaluation Tim Hewison1
The regression propagates these variances to estimate the uncertainty on the corrected radiance, which provides a Quality Indicator for the inter-calibration product. The uncertainties are analysed through a measurement model of the process for case studies.
Each process of the inter-calibration algorithm is considered and the uncertainties evaluated on key variables due to random and systematic effects. These uncertainties are then combined to produce an error budget giving a Type B evaluation of the uncertainty on the inter-calibration bias. The random component of this is then compared to the statistics of the standard bias and recommendations made for adjustments of the inter-calibration algorithm to produce more consistent uncertainty estimates.
The collocation criteria represent trade-offs between the errors on each collocation and the number of collocations available. The uncertainty analysis presented here allows these trade-offs to be reviewed quantitatively to make recommendations to further improve the inter-calibration products.
Abstract
Methodology for Random Errors
Methodology for Systematic Errors
This paper presents an analysis of the uncertainties in the Global Space-based Inter-Calibration System (GSICS) products for the infrared channels of Meteosat/SEVIRI using Metop/IASI as a reference. It is based on the Guide to the Expression of Uncertainty in Measurement (GUM) and aims to provides guidance for users of these GSICS products as well as future evaluations of other products.
The inter-calibration algorithm is based on the selection of observations from the monitored instrument (Meteosat/SEVIRI) and the reference instrument (Metop/IASI) that are collocated in space, time and viewing geometry. The collocated observations are transformed to be comparable on spatial scale and spectral coverage and compared using a weighted regression. Each collocated observation is allocated a weighting based on its measured spatial variance and the specified radiometric noise of each channel.
Various processes introduce random errors in each collocated radiance
Their magnitude is estimated from typical range of each variable
And the sensitivity of radiances to perturbations of each variable
Regression process used to generate GSICS Correction coefficients
Reduces impact of random errors on each collocation
Repeat regression many times for randomly perturbed datasets
To estimate uncertainty on corrected radiances
A Monte Carlo-like approach
For processes introducing random errors:
Each collocated radiance is perturbed by random amount
Where zi is a random number drawn from distribution consistent with characteristic difference ∆xr
Repeat regression nk times gives modified functions, gj,k’(L)
Each evaluation is used to calculated corrected radiances:
Standard deviation of over the Monte Carlo ensemble is calculated to provide an estimate of the uncertainty on corrected radiances due to each random process, j :
Collocation criteria designed to minimise systematic errors
By ensuring samples systematically distributed
But in reality small residual differences remain
Sampling differences introduce radiance errors in each collocation
These introduce systematic errors in end product,
According to its sensitivity to each variable,
Which is estimated from statistics of cases studies
Use actual sampling distribution
Or assume uniform distribution between threshold limits
For processes introducing systematic errors:
Each collocated radiance is perturbed by
Recalculated regression gives modified function, g’(L)
Evaluate for range of scene radiances
Compare to unmodified function, g(L)
To estimate uncertainty on corrected radiance,
Due to systematic errors introduced by process j:
Global Space-based Inter-Calibration System
What is GSICS?
Initiative of CGMS and WMO
An effort to produce consistent, well-calibrated data from the international constellation of environmental satellites
What are the basic strategies of GSICS?
Best practices/requirements for prelaunch characterisation (with CEOS WGCV)
Improve on-orbit calibration by developing an integrated inter-calibration system
Initially by LEO-GEO Inter-satellite/ inter-sensor calibration
This will allow us to:
Improve consistency between instruments
Produce less bias in Level 1 and 2 products
Retrospectively re-calibrate archive data
Better specify future instruments
Temporal Mismatch
Temporal Variability
Uniform distribution over ±∆tmax= 300 s equivalent to r.m.s. difference, ∆t = ∆tmax/√3 ≈ 173 s.
Temporal Variability of typical SEVIRI images evaluated as RMSD between radiances sampled over different time intervals
Calculate sensitivity from RMSD between radiances sampled at 21:30 and 21:45 over target area
Uniform distribution over ±∆tmax=300 s with n ~30000 collocations gives mean time difference ∆t = 2∆tmax/√(3n) ≈ 2 s.
But mean difference in sampling time of collocations, ∆t=30s due to deficiencies in orbital selection
Calculate sensitivity from mean rate of change of radiances from time series of observations
Much worse using 09:30 overpasses!
R.M.S. differences in Meteosat μm brightness temperatures with time intervals from Rapid Scanning Meteosat data (red diamonds) and with spatial separation in North-South direction (black pluses) and West-East direction (black stars)6
Time series of mean rate of change of radiances calculated from Meteosat-9 observations on over (30°W-30°E)x(30°S-30°N)
[1mW/m2/st/cm-1/hr ~ 1K/hr]
Introduction
This analysis follows QA4EO guidelines1
Based on Guide to the Expression of Uncertainty in Measurement (GUM)2
To be read in conjunction with the Algorithm Theoretical Basis Document3
Uncertainties provide Quality Indicators for the inter-calibration products
Evaluate uncertainties for key variables in each process of ATBD due to
Random and
Systematic effects
Combined to produce error budget
(Type B evaluation of combined uncertainty)
Used to make recommendations for ATBD adjustments
To produce more consistent uncertainty estimates
Combining all Random Errors
Combining all Systematic Errors
All uncertainties due to random processes, added in quadrature: .
All uncertainties due to random processes, added in quadrature: .
Basic Method
ATBD uses weighted linear regression to compare collocated radiances
from monitored and reference instruments
weightings based on spatial variance of radiances + radiometric noise
Regression propagates these variances
to estimate uncertainty on corrected radiance
But these are only 2 processes introducing uncertainty to final product
Full dynamic error propagation of all processes could be prohibitive
Analysis reviews uncertainties based on measurement model of processes
for case studies, which are assumed to be typical
Define IASI as inter-calibration reference = Truth
IASI errors should not contribute to uncertainty of products
For each process:
Estimate typical differences in sampling variables, ∆x
between monitored and reference instruments
Estimate sensitivity of radiances to perturbations in x: ∂L/∂x
where Li is radiance of each collocation, i
Uncertainty on Li due to process, j:
Regression of collocated radiances => GSICS Correction, g(L)
Perturb observed radiances Li by u(Li)
Recalculated regression gives modified function, g’(L)
Gives different corrected radiances,
Random variability in space and time dominates total random uncertainty – for all channels
Space/Time threshold (3km/300s) match well
Other terms negligible
=>Relax geometric collocation threshold?
Systematic mismatches in time and space dominate the total systematic uncertainty due to finite gradients
But, IR3.9 dominated by spectral correction to compensate for IASI’s incomplete coverage11
Recommendations
Combining Systematic and Random Errors
Geometric collocation criteria could be relaxed by a factor of 10
Should give more collocations and reduce random error
But found to also change bias significantly
=>So only implement for Rapid Scan Service to give more collocations
=>ATBD should be revised to account for correlations when estimating uncertainty on GSICS Correction
Or inflate uncertainty from regression by a factor of ~2
Analysis assumes published SRFs are correctly interpreted
Misinterpretation would dominate systematic errors
=>Need clear guidance in the application of published SRFs
=>Should repeat this analysis for all GSICS Products!
Total uncertainties due to random and systematic processes:
Random components dominate total error in most conditions
Uncertainties increase rapidly for low Tb scenes (fewer collocations)
Errors much lower in water vapour channels
Validating Random Component
This total random uncertainty is 1-4x larger than quoted values
=> ATBD does not include important random processes
Time series of Standard Biases shows higher variability
=> Implies there are real instrument calibration changes
References
Nigel Fox, 2010: A guide to expression of uncertainty of measurements, QA4EO Guideline QA4EO-QAEO-GEN-DQK-006.
Tim Hewison, 2009: Quantifying the Impact of Scene Variability on Inter-Calibration, GSICS Quarterly, Vol. 3, No. 2.
B. Tournier and Co-Authors, 2007: IASI on MetOp-A – Radiometric and spectral performances measured during commissioning. First IASI Conference, Anglet, France, November 2007,
JCGM 2008: Evaluation of measurement data – Guide to the expression of uncertainty in measurement,
EUMETSAT, 2007: Typical Radiometric Accuracy and Noise for MSG-1/2, EUM/OPS/TEN/07/0314.
EUMETSAT, 2006: MSG-2 SEVIRI Modulation Transfer Function Characterisation, EUM/MSG/TEN/06/0010.
Denis Blumstein, 2008: MetOp-A IASI Level 1 Cal/Val at IASI TEC, GSICS Quarterly, Vol. 2, No. 2, 2008.
Tim Hewison, 2010: ATBD for EUMETSAT’s Inter-Calibration of SEVIRI-IASI, EUM/MET/REP/08/0468.
Denis Blumstein, 2007: In-flight performance of the infrared atmospheric sounding interferometer (IASI) on Metop-A, Proc. of SPIE, Vol. 6684, 66840H-1, doi: /
Tahara, Yoshihiko and Koji Kato, 2009: New Spectral Compensation Method for Intercalibration Using High Spectral Resolution Sounder, JMA Meteorological Satellite Center Technical Note No. 52, 1-37.
EUMETSAT, 2007: Typical Geometrical Accuracy for MSG-1/2, EUM/OPS/TEN/07/0313.
IASI L1 Cal/Val Team, 2007: Presentation of the IASI Level 1 Cal/Val Results, 23/10/2007, EUMETSAT, Darmstadt
1: EUMETSAT, Eumetsat-Allee 1, D Darmstadt, Germany
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EUM/MET/VWG/11/0399 EUMETSAT Meteorological Satellite Conference, Oslo, Norway, 5-9 Sept 2011