SEVIRI-IASI Inter-calibration Uncertainty Evaluation

1. SEVIRI-IASI Inter-calibration Uncertainty Evaluation Tim Hewison

2. Introduction • Following guidelines provided by QA4EO • Based on Guide to the Expression of Uncertainty in Measurement (GUM) • To be read in conjunction with the Algorithm Theoretical Basis Document • Uncertainties provide Quality Indicators for the inter-calibration products • Each process of ATBD is considered: • Uncertainties evaluated for key variables 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

3. Method – Introduction • 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 • But some are included here, to illustrate their magnitude

4. Method – Systematic Errors • 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

5. Method – Random Errors • Similarly, different 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

6. Method – Combining Errors • Method may be refined for dominate processes.

7. General Methodology • 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,

8. Methodology for Systematic Errors • 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:

9. Temporal Mismatch • Uniform distribution over ±∆tmax=300 swith n~30000 collocations gives mean time difference ∆t = 2∆tmax/√(3n) ≈ 2 s. • But mean difference in sampling time of collocations, ∆t=30sdue to deficiencies in orbital selection • Calculate sensitivity from mean rate of change of radiances from time series of observationsMuch worse using 09:30 overpasses! Time series of mean rate of change of radiances calculated from Meteosat-9 observations on 2009-09-20 over (30°W-30°E)x(30°S-30°N) [1mW/m2/st/cm-1/hr ~ 1K/hr]

10. Summary of Systematic Errors’ Perturbations and Sensitivities • Table 1 summarises the magnitude of typical perturbations, ∆xj, of processes introducing systematic errors in the collocated radiances and the sensitivity of the 8 infrared channels of SEVIRI to these perturbations, dLj/dx. Table 1 Summary of Systematic Errors’ Perturbations and Sensitivities

11. Combining all Systematic Errors • All uncertainties due to systematic processes, added in quadrature: • 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 coverage

12. Methodology for Random Errors • For processes introducing random errors: • each collocated radiance is perturbed by • where ziis a random number drawn from distribution consistent with characteristic difference ∆xr • Repeat regression nktimes 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 :

13. 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 R.M.S. differences in Meteosat-8 10.8 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)

14. Summary of Random Errors’ Perturbations and Sensitivities • Table 3 summarises the characteristic difference, ∆xrj, of processes introducing random errors in the collocated radiances and the sensitivity of the 8 infrared channels of SEVIRI to these perturbations, dLj/dx. Table 3 Summary of Random Errors’ Perturbations and Sensitivities

15. Combining all Random Errors • All uncertainties due to random processes, added in quadrature: • Random variability in space and time dominate the total random uncertainty for all channels • * 300s matches 3km well • Other terms negligible • => Could relax geometric collocation threshold!

16. Compare with Quoted Uncertainty • 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

17. Combining Systematic and Random Errors • Total uncertainties due to random and systematic processes: • Random components dominate total errorin most conditions • Uncertainties increase rapidly for low Tb (fewer collocations) • Errors much lower in WV channels

18. Recommendations • Geometric collocation criteria could be relaxed by a factor of 10 • Would give more collocations and reduce random error • 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!