I made a significant mistake in my post today. When I defined the BRF I should have called it the "bidirectional reflectance factor" rather than "bidrectional reflectance function". Apologies for the confusion.
Ian Grant
________________________________
From: Ian Grant
Sent: Thursday, 9 July 2015 6:11 PM
To: cf-metadata at cgd.ucar.edu
Subject: Re: [CF-metadata] New reflectance standard names [SEC=UNCLASSIFIED]
Dear all,
Ted Kennelly's proposals for new reflectance standard names (initially
http://mailman.cgd.ucar.edu/pipermail/cf-metadata/2013/056462.html, and discussed and refined in
http://mailman.cgd.ucar.edu/pipermail/cf-metadata/2013/056464.html and
http://mailman.cgd.ucar.edu/pipermail/cf-metadata/2013/056481.html) aim to fill a need but I believe they need to be modified or replaced to be consistent with existing, carefully devised nomenclature schemes. I only became aware of this forum a week ago when alerted by a colleague. This contribution is rather long, but I will describe prior literature on related standardisation in this area, then give my proposals, and finally comment on Ted's proposals and the subsequent discussion.
The nomenclature of radiometric quantities relating to reflection was set out by Nicodemus et al. (1977) for physical sciences in general. That nomenclature was applied to remote sensing, with an emphasis on the Earth's surface, by Schaepman-Strub et al. (2006) and Martonchik et al. (2000). I see a gap in the naming of the TOA observations made by satellites in reflective bands that are presented as reflectance-like quantities rather than radiances. I suggest that such TOA quantities should continue and be consistent with this naming scheme for surface reflectance.
To discuss the variables involved, I define the symbols
L = Radiance observed by the satellite
d = Earth-Sun distance in astronomical units (au)
mu0 = Cosine of the solar zenith angle
E0,d = In-band solar irradiance on a plane normal to the solar beam for the Earth-Sun distance d pertaining to the observation
E0,1au = In-band solar irradiance on a plane normal to the solar beam for d = 1 au
The bidirectional reflectance function (BRF), as defined in the above references, is the observed radiance divided by the radiance that would be observed from a perfect diffuse (Lambertian) horizontal surface:
R = (pi L) / (mu0 E0,d)
I propose standard names for two quantities:
1) scaled_radiance (canonical units: 1)
L* = (pi L) / (E0,1au) = (mu0 / d^2) R
The mapping from radiance L to L* is fixed; it does not change with mu0 or d. L* represents the radiance but normalises out the in-band solar irradiance. For an unchanging target, L* will increase as mu0 increases and as d decreases, just as the radiance does. L* is effectively the BRF for the sun at the target zenith and unit Earth-sun distance.
2) toa_bidirectional_reflectance_factor (canonical units: 1)
This is the BRF (R) defined above. This is L* normalised to remove the effects of varying mu0 and d. For an unchanging target, R does not vary as d and mu0 vary, and thus characterises the reflective properties of the target.
I have not provided formally worded definitions yet, while the broad approach of my proposals and their relationship to Ted's proposals is under discussion.
Discussion on the name ?scaled_radiance?: An alternative and accurate name for L* would be ?bidirectional_reflectance_factor_multiplied_by_cosine_solar_zenith_angle_and_divided_by_earth_sun_distance_squared? but this is unwieldy. While this quantity is often discussed in the literature on calibration of satellite reflective bands, there does not appear to be an agreed name for it. ?Scaled radiance? has been used by the International Satellite Cloud Climatology Project (ISCCP,
http://isccp.giss.nasa.gov/docs/calib.html). To my mind, the word ?scaled? conveys that the quantity is proportional to radiance by a fixed factor, although I would agree that it does not comprehensively describe the relationship. This quantity has at times been inappropriately called ?reflectance? or ?albedo?, terms which are inconsistent with the nomenclature schemes described above.
Note that the GRIB tables controlled by the World Meteorological Organisation (WMO) (
http://www.wmo.int/pages/prog/www/WMOCodes/WMO306_vI2/LatestVERSION/WMO306_vI2_GRIB2_CodeFlag_en.pdf) include a name ?scaled radiance? with a different meaning, namely the radiance mapped to a numeric range to enable display as an image. My group at the Australian Bureau of Meteorology (ABoM) recently proposed the name ?scaled radiance? for L* in a different section of the WMO GRIB tables.
The two quantities for which I propose names are both useful forms into which to transform radiance in reflective bands, relieving the user of needing to know and apply one or more of E0,1au, d and mu0.
Comments on Ted Kennelly's proposals and the subsequent discussion:
- ?lambertian_equivalent_reflectance? or ?lambertian_equivalent_albedo? appear intended to mean the BRF but are not standard or in general use. The BRF is exactly appropriate here. Ted?s initial proposal objected that BRF "implies a directional dependence of the radiation". However, the observation is indeed dependent on the direction of the illumination (sun direction) and the direction of the reflected radiation (satellite view direction), even if the variation is only implicit in a single observation. In general for an unchanging target the radiance observed will be different when observed from different view directions and will also vary with sun direction beyond just the mu0 factor. This is due to anisotropic effects, often referred to as BRDF effects, such as changing viewed and illuminated fractions of soil and vegetation, 3D effects of clouds and their shadows, different atmospheric path lengths, etc. The normalisation by the radiance that would be reflected from an ideal lambertian sur
face, as when deriving the BRF, does not change this: the radiance from the lambertian reflector is independent of direction but that from the actual TOA target, in general for realistic cases, is not.
- The term ?reflectance? without being followed by ?factor? refers to a ratio of reflected to incident radiative flux (power), where the reflected power is considered over the whole outward-going hemisphere of solid angle, and so is not appropriate here. Similarly, ?albedo? is not appropriate here since it is also a ratio of powers, for the special case where both the incident and reflected powers are taken over the incoming and outgoing hemispheres respectively.
- If a quantity that is a function of wavelength or frequency (units W m-2 sr-1 m-1) is meant then the word ?spectral? should appear in its name (reference needed).
- It is unclear what quantity Ted wants to name. He describes one of them by the equation ?rho = PI * L/ mu / E?. It is critical to know whether this E means for Earth-Sun distance with the value d at the time of the observation or for d = 1 au. If "E" is E0,d then Ted?s rho is the BRF R. Whereas if "E" is E0,1au then his rho is R / d^2.
- Related to the previous point, Ted in his initial proposal says the GOES-R imagery products "represent the signal measured at the top of the atmosphere". Does this mean one of them has a fixed relationship to observed radiance that is independent of variations in mu0 and d?
- The reference that Karl provided,
http://www.princeton.edu/~achaney/tmve/wiki100k/docs/Reflectivity.html describing the difference between reflectance and reflectivity is useful but I think it has been misapplied in this discussion by suggesting that "reflectivity" be used for the satellite observation. According to the reference, reflectivity is a property of the material, determined by measurement of an optically thick sample of the material. While remote sensing deals with an optically thick target (the radiation does not originate from the other side of the Earth), the TOA reflectance is concerned with only the consolidated reflectance of the Earth-atmosphere system from a fictitious surface at the TOA, irrespective of the optical properties of the individual materials underlying that surface. Consider, for instance, a land target that comprises soil covered (possibly partially) by optically thin vegetation that is in turn overlayed by the (optically thin) atmosphere. The Princeton web pag
e quantifies the reflection from this composite system by "reflectance", which term is consistent with Nicodemus et al. and the other references given in my second paragraph above. When the last sentence of the reference says ?reflectance is the fraction of electromagnetic power reflected from a specific sample? this could be paraphrased to the satellite observation case as ?? from a specific target?.
References
Martonchik, John V., Carol J. Bruegge, and Alan H. Strahler. ?A Review of Reflectance Nomenclature Used in Remote Sensing?. Remote Sensing Reviews 19, no. 1?4 (2000): 9?20. doi:10.1080/02757250009532407.
Nicodemus, F. E. et al. ?Geometrical Considerations and Nomenclature for Reflectance?. Vol. 160. US Department of Commerce, National Bureau of Standards Washington, D. C., 1977.
http://graphics.stanford.edu/courses/cs448-05-winter/papers/nicodemus-brdf-nist.pdf.
Schaepman-Strub, G., M.E. Schaepman, T.H. Painter, S. Dangel, and J.V. Martonchik. ?Reflectance Quantities in Optical Remote Sensing?definitions and Case Studies?. Remote Sensing of Environment 103, no. 1 (2006): 27?42. doi:10.1016/j.rse.2006.03.002.
Regards,
Ian
Ian Grant | Satellite Specialist
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Observations & Infrastructure Division | Science & Engineering Section
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Tel: +61 3 9669 4080 | i.grant at bom.gov.au
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Received on Thu Jul 09 2015 - 04:47:14 BST
