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 surface, 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 page
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
[http://web.bom.gov.au/eiab/publishing/images/bureau_logo.gif]
Observations & Infrastructure Division | Science & Engineering Section
Bureau of Meteorology
GPO Box 1289 Melbourne VIC 3001
Level 5, 700 Collins Street, Docklands VIC 3008
Tel: +61 3 9669 4080 | [email protected]
www.bom.gov.au
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