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Brewer Weighting Coefficients

Brewer Weighting Coefficients. J S Rimmer University of Manchester. Introduction. Brewer calculates O3 and SO2 from ratios of UV intensities at 5 wavelengths. In fact, total extinction is measured including O3, SO2 and aerosol.

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Brewer Weighting Coefficients

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  1. Brewer Weighting Coefficients J S Rimmer University of Manchester 13th WMO-GAW Brewer Workshop, Beijing, 2011

  2. 13th WMO-GAW Brewer Workshop, Beijing, 2011

  3. Introduction • Brewer calculates O3 and SO2 from ratios of UV intensities at 5 wavelengths. • In fact, total extinction is measured including O3, SO2 and aerosol. • Have 3 unknowns but 5 Beer-Lambert eqns which can be solved simultaneously. • Weighting Coefficients applied to do this. 13th WMO-GAW Brewer Workshop, Beijing, 2011

  4. 13th WMO-GAW Brewer Workshop, Beijing, 2011

  5. Example 2x + y = 10 - (1) 4x + 6y = 44 - (2) Solve for y:- (1) * -2, (2) * 1, and add -2 and 1 are the weighting coefficients for y Solve for x:- (1) * -6, (2) * 1, and add -6 and 1 are the weighting coefficients for x Brewer uses 5 wavelengths – 5 equations – 5 weighting coefficients for each solution 13th WMO-GAW Brewer Workshop, Beijing, 2011

  6. How it works From Beer’s law: where j = 1 to 5. One equation for each wavelength. (Here we assume the Ij are corrected for Rayleigh scattering.) We have to mult iply each of the 5 equations by some number so that, when we add them up, two unknowns are eliminated leaving us with a solution for the remaining one. 13th WMO-GAW Brewer Workshop, Beijing, 2011

  7. Matrix form For O3, multiply by: 13th WMO-GAW Brewer Workshop, Beijing, 2011

  8. Note that weighting coefficients can be scaled! 13th WMO-GAW Brewer Workshop, Beijing, 2011

  9. Why ? • The intensity of the extra terrestrial solar spectrum may change, eg eccentricity of Earth’s orbit. • Responsivity of Brewer may change. • Any uniform variation in signal across Brewer wavelength range. 13th WMO-GAW Brewer Workshop, Beijing, 2011

  10. Assume uniform fractional change, s, across Brewer wavelength range. if 13th WMO-GAW Brewer Workshop, Beijing, 2011

  11. Calculation of O3 weighting coefficients • Choose k1 =0, strong S02 absorption. • Choose k2 = -1, strong O3 absorption and we can apply any scale. • Solve for remaining three coefficients with the three summation equations. 13th WMO-GAW Brewer Workshop, Beijing, 2011

  12. Weighting coefficients Depend on instrument 13th WMO-GAW Brewer Workshop, Beijing, 2011

  13. 13th WMO-GAW Brewer Workshop, Beijing, 2011

  14. Application • Weighting coefficients are to remove non-required unknowns from the solution. • Standard set of weighting coefficients widely adopted. (Hard coded). • Weighting coefficients should be determined for individual instruments. • What difference does it make? 13th WMO-GAW Brewer Workshop, Beijing, 2011

  15. Reprocessing • Re-evaluate ETC • Re-evaluate differential absorption coefficient. • Recalculate O3 from raw data • Difference should depend on levels of SO2 and aerosol. 13th WMO-GAW Brewer Workshop, Beijing, 2011

  16. Brewer MKIII 172 13th WMO-GAW Brewer Workshop, Beijing, 2011

  17. 13th WMO-GAW Brewer Workshop, Beijing, 2011

  18. 13th WMO-GAW Brewer Workshop, Beijing, 2011

  19. Summary • Correct weighting coefficients are important for more accurate data. • Effect may be different for different instruments • SO2 trends may affect ozone trends • ETC’s need to be recalculated via calibration history. 13th WMO-GAW Brewer Workshop, Beijing, 2011

  20. Thank You 13th WMO-GAW Brewer Workshop, Beijing, 2011

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