Appendix B

Vicarious Calibration
1

This appendix expands on the importance of a vicarious calibration. It provides the technical details associated with using Marine Optical Buoy (MOBY) for the ocean color vicarious calibration.

The following measurement equation is used to derive water-leaving radiance (Lw) (Franz et al., 2007):

Lt = [Lr + La + tdv(Lf + Lw)tgvtgs fp]

L: radiance;

t: transmittance;

Lt: spectral radiance at the satellite sensor;

Lr: Rayleigh contribution from the atmosphere;

La: aerosol contribution from the atmosphere (including Rayleigh-aerosol interactions);

Lf: sea-foam contribution;

tdv: diffuse transmittance along the satellite-to-surface path ;

tg: transmittance through gaseous absorption along the satellite-to-surface path;

ts: the transmittance along the sun-to-surface path; and

fp: accounts for the polarization dependence of the satellite sensor.

Sun glint is not included in the equation because these data would have been flagged under normal operations. All of these quantities depend on wavelength, and all but the Lw term can be determined from ancillary data (e.g., surface pressure is required to calculate Lr, wind speed for Lf, etc.) or, for La, through models combined with near-infrared measurements of the surface area that is being used for the vicarious calibration, in order to estimate the aerosol contribution at the blue-green spectral region of interest for the match-up dataset.

It is assumed that all quantities except Lw have zero uncertainty2 and propagate uncertainties according to the International Organization for Standardization’s (ISO) Guide to the Expression of Uncertainty in Measurement (GUM; ISO, 1993).

image

The approximation follows because Lw is small compared to Lt, e.g., about 5 percent, and no more than 15 percent. So to achieve a relative uncertainty of 5 percent in Lw we need the sensor to be producing Lt values with a relative uncertainty of » 0.3 percent (=5 percent × 5/95). However, this level of uncertainty on a satellite sensor in orbit is not possible at the present time. It requires pre-flight calibration of sufficient accuracy, complete and robust instrument characterizations, and the ability to monitor any change in the response upon launch. One limit is the uncertainty in the standards of spectral radiance supplied by National Institute of Standards and Technology (NIST), which typically have an uncertainty of 0.5 percent (k = 2) in the visible region of the spectrum.

A stringent vicarious calibration is required to overcome the inability to constrain the sensor’s uncertainty to 0.3 percent or less. To achieve this calibration, a natural source is selected as the surface reference site of Lw values, the site is instrumented with a robust, high-quality assured measurement facility, and the experiment is designed so as to

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1 Based on a white paper provided by C. Johnson, July 2010.

2 Uncertainty can be classified as arising from random or systematic effects. Uncertainty values from random effects can generally be reduced by increasing the number of measurements; they scale as 1/√N, where N is the number of measurements. For systematic effects, increasing the number of measurements has no impact whatsoever on the associated uncertainty values. Uncertainty values of either type are estimated as “standard uncertainties” corresponding to the estimated standard deviation (k = 1) and the combined uncertainty is the root-sum-square of the individual component values (assuming the values are uncorrelated). The GUM explains how to derive standard uncertainties for uncertainty estimates that can be evaluated statistically (Type A) and through other means (Type B).



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Appendix B Vicarious Calibration1 1 T his appendix expands on the importance of a vicarious uncertainty2 and propagate uncertainties according to the calibration. It provides the technical details associated International Organization for Standardization’s (ISO) Guide with using Marine Optical Buoy (MOBY) for the to the Expression of Uncertainty in Measurement (GUM; ocean color vicarious calibration. ISO, 1993). The following measurement equation is used to derive u(Lt) u(Lw) 1 ≅ u(Lw) Lw water-leaving radiance (Lw) (Franz et al., 2007): = Lt Lw Lr + La + tdv Lf Lw Lr + La + tdv Lf 1+ Lw Lt = [Lr + La + tdv(Lf + Lw)tgv tgs fp] L: radiance; The approximation follows because Lw is small compared to App B formula2.eps t: transmittance; Lt, e.g., about 5 percent, and no more than 15 percent. So to App B formula1_sm01.eps Lt: spectral radiance at the satellite sensor; achieve a relative uncertainty of 5 percent in Lw we need the Lr: Rayleigh contribution from the atmosphere; sensor to be producing Lt values with a relative uncertainty La: aerosol contribution from the atmosphere (including of » 0.3 percent (=5 percent × 5/95). However, this level of Rayleigh-aerosol interactions); uncertainty on a satellite sensor in orbit is not possible at the Lf: sea-foam contribution; present time. It requires pre-flight calibration of sufficient tdv: diffuse transmittance along the satellite-to-surface accuracy, complete and robust instrument characterizations, path ; and the ability to monitor any change in the response upon tg: transmittance through gaseous absorption along the launch. One limit is the uncertainty in the standards of spec- satellite-to-surface path; tral radiance supplied by National Institute of Standards and ts: the transmittance along the sun-to-surface path; and Technology (NIST), which typically have an uncertainty fp: accounts for the polarization dependence of the of 0.5 percent (k = 2) in the visible region of the spectrum. satellite sensor. A stringent vicarious calibration is required to over- come the inability to constrain the sensor’s uncertainty to Sun glint is not included in the equation because these 0.3 percent or less. To achieve this calibration, a natural data would have been flagged under normal operations. All source is selected as the surface reference site of Lw values, of these quantities depend on wavelength, and all but the Lw the site is instrumented with a robust, high-quality assured term can be determined from ancillary data (e.g., surface measurement facility, and the experiment is designed so as to pressure is required to calculate Lr, wind speed for Lf, etc.) or, for La, through models combined with near-infrared 2 Uncertainty can be classified as arising from random or systematic measurements of the surface area that is being used for the effects. Uncertainty values from random effects can generally be reduced by increasing the number of measurements; they scale as 1/√N, where N is vicarious calibration, in order to estimate the aerosol con- the number of measurements. For systematic effects, increasing the number tribution at the blue-green spectral region of interest for the of measurements has no impact whatsoever on the associated uncertainty match-up dataset. values. Uncertainty values of either type are estimated as “standard It is assumed that all quantities except Lw have zero uncertainties” corresponding to the estimated standard deviation (k = 1) and the combined uncertainty is the root-sum-square of the individual component values (assuming the values are uncorrelated). The GUM explains how to derive standard uncertainties for uncertainty estimates that 1 Based on a white paper provided by C. Johnson, July 2010. can be evaluated statistically (Type A) and through other means (Type B). 87

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88 APPENDIX B minimize sources of bias and improve the data return (e.g., would be to have a precise, stable dataset so that the number consideration of cloud cover probabilities). of observations required to produce the asymptotic value of The MOBY site has been used to calibrate ocean color the random uncertainty component is as small as possible. sensors in the post-Coastal Zone Color Scanner (CZCS) era, The Ocean Biology Processing Group (OBPG) studied the and the requirements for ocean color vicarious calibration effect of sample size on the uncertainty in the vicarious gain have been well documented (NASA, 2003). Here, we present coefficient using MOBY for SeaWiFS; it concluded 45 to 60 the concept of random and systematic uncertainty and the samples would be required for reliable vicarious calibration measurement equation to support the role of a MOBY-like of a stable sensor such as SeaWiFS (see Figure B.1). facility in ocean color research. First, in order to have accept- Second, in order to have acceptable values for the able values for the random components of uncertainty one systematic components of uncertainty, one needs a robust, can either have a broad distribution, or a narrow, well-defined well-characterized, high-quality assured dataset. Spectral distribution. The latter requires fewer samples to achieve the biases cannot be tolerated at any level, because the bio- same uncertainty value. The well-defined, narrow distribu- optical algorithms rely on band ratios. Unidentified or tion is found at the MOBY facility, with its stable marine difficult to quantify bias introduced by the “atmospheric atmosphere, central Pacific location, uniform oligotrophic correction” (e.g., the process of estimating all the terms waters, and robust instrument design that results in good in the measurement equation except Lw) are mitigated by measurement precision. An example of a broader distribu- selecting sites where the atmospheric conditions and the tion would be the BOUSSOLE or Aeronet-OC (Bailey et al., marine environment are as simple as possible, the necessary 2008). It can be argued that the best technical approach for ancillary data are available, and the models can be verified vicariously calibrating a new satellite sensor such as VIIRS and improved upon. Likewise, the in situ instrument must be FIGURE B.1 Mean vicarious gains, g, derived for SeaWiFS B.1.eps 555, and 765 nm based on calibration samples between Sep - bands at 443, tember 1997 and March 2006. Individual gains from the mission-long set of calibration match-ups were randomly sampled; growing the sample set one case at a time and averaging to show the effectbitmap of increasing sample size on g. Vertical error bars show the standard error on the mean at each sample size. SOURCE: Franz et al., 2007; used with permission from the Optical Society.

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89 APPENDIX B fully characterized and supply values that are SI-traceable. A case could be made for additional sites, including coastal The more robust this procedure, the more reliable is the sites, with a MOBY-like site producing the basic calibra- final product. The MOBY project has gone to great effort to tion and the other equally robust sites, serving to explore meet these objectives by incorporation of check standards, the intricacies of the atmospheric correction methods, dark repeat calibrations, close linkage with NIST, expert and pixel assumptions, and the satellite sensor characterization dedicated staff, good instrument design, and so forth. The functions themselves. evidence of the degree of the stability and precision of the In conclusion, study of the measurement equation and MOBY products and the atmospheric correction procedures robust experimental design establishes that the MOBY is demonstrated in Franz et al. (2007). approach and its uncertainty values are necessary for produc- The MOBY site was selected to represent the majority tive ocean color research. An examination of the uncertainty of the observed natural sources—the open oceans. Coastal in upwelling spectral radiance for MOBY is given in Brown regions exhibit variations in Lw and the other terms in the et al. (2007), where the Type A random uncertainty was measurement equation on many different temporal and estimated to be 1 percent. Franz et al. (2007) state that with- spatial time scales compared to the MOBY site off Lanai, out the vicarious calibration provided by MOBY, the bias Hawaii. The sensor measures Lt, the proper interpretation of in Lwn resulting from the errors in the pre-flight calibration these data depend on thorough understanding of the sensor for SeaWiFS would have been 25 percent at 490 nm and 75 characterization (linearity, polarization, spectral out of band, percent at 412 nm and the mean Ca retrieval would be biased etc.) and response to this top of the atmosphere radiant flux. low by 25 percent.