When is reflectance actually reflectance?

[djhoese]

Problem

WARNING: I'm not a scientist.

This is related to #52, specifically the standard_name used for visible channel data returned by SatPy. We return visible channel data in the "reflectance" calibration with the standard_name of toa_bidirectional_reflectance. By CF definition this term should only be used for reflectance data that includes the normalization for the solar zenith angle (SZA). This normalization (as some may know) is applied by dividing by the cos(sza). While talking with @kathys, she mentioned that she has always referred to the data without this SZA adjustment as "normalized radiances" (normalized for the theoretical maximum energy entering the atmosphere from the sun, not for the angle of the sun).

The CF definition for toa_bidirectional_reflectance:

"Bidirectional_reflectance" depends on the angles of incident and measured radiation. Reflectance is the ratio of the energy of the reflected to the incident radiation. A coordinate variable of radiation_wavelength or radiation_frequency can be used to specify the wavelength or frequency, respectively, of the radiation. "toa" means top of atmosphere. toa_bidirectional_reflectance includes a factor to account for the cosine of the solar zenith angle but does not include any integration over solid angle.

So, I'm wondering if we should be listing the pre-sunz corrected reflectances as having a different standard_name. Thoughts?

Special Notes

• VIIRS SDRs already have the sunz correction done to them so toa_bidirectional_reflectance is actually correct for that reader
• Both pre-sza and post-sza adjustment data are unitless, so this can't be used to know which is which.
• I can't find a CF standard name that seems to apply to the pre-SZA adjustment reflectance data.

[adybbroe]

@djhoese Thanks for bringing it up.
First, I think the topic/name of the issue should be "When is reflectance actually a reflectance?" Right?
Then, I have always thought of and when discussing with my colleagues here in Sweden understood that when we say "normalised reflectance" it is the TOA Bi-directional reflectance, thus corrected for the sun zenith. So the uncorrected we usually sloppily just call "reflectance".

Concerning finding a suitable name for the reflectance when the sun-zenith correction has been omitted, I would thus lean towards something like "unnormalised reflectance". But I would be surprised if CF has that?

[adybbroe]

In the NWCSAF/PPS software we have intermediate level-1c files storing Tbs and Reflectances in netCDF. There we do:

        description = AVHRR ch_1
        id_tag = ch_r06
        long_name = Reflectance for 0.6 micro meter channel
        scale_factor = 0.01
        standard_name = toa_bidirectional_reflectance
        sun_earth_distance_correction_applied = TRUE
        sun_earth_distance_correction_factor = 0.94129384
        sun_zenith_angle_correction_applied = TRUE
        units = percent
        valid_range = 0,20000
        wavelength_range = 0.58,0.68

So, just to be VERY clear, what we mean! :-)

[frarue]

@djhoese @adybbroe Good to thoroughly discuss such stuff (and I really like your very clear NWCSAF/PPS netcdf statements also about the sun-earth distance correction). I currently work a lot on VIS recalibration and I always refer to Nicodemus et al. p. 12: "A reflectance factor is defined as the ratio of the radiant flux actually reflected by a sample surface to that which would be reflected into the same reflected-beam geometry by an ideal (lossless) perfectly diffuse (lambertian) standard surface irradiated in exactly the same way as the sample". That said I do not understand the definition of @kathys because the "theoretical maximum energy entering the atmosphere from the sun" cannot actually be determined without considering the sun-zenith angle. Or am I wrong?
Reflectance computation without SZA would be simply dividing the radiance by the solar irradiance. I cannot easily see the benefit of using this against radiance but: might be worth to consider what unit it would have: Assuming radiance comes in [Wm-2sr-1] and the solar irradiance in [Wm-2] ...it would then be [sr-1]? ...probably not a good idea to call this "unnormalized reflectance" then.
My suggestion would be to either do the full reflectance computation (apart from cos(sza): don't forget π!) and call it toa_bidirectional_reflectance or to keep the radiance. But maybe I'm missing something?

[mraspaud]

Dividing the radiance by the solar irradiance has been done and used a long time in different places, so that's probably why it's still in use today. But I concur that the visible channels should be sun normalised. However, as @adybbroe noted in an offline discussion, the cos(sza) has the problem of becoming zero at the day/night terminator, so for now this is smoothed out from 88 degrees onwards in satpy iirc. And this raises then the question: is the data then truly toa_bidirectional_reflectance ? Another aspect is that we are sometimes using another normalisation accounting for a better effective solar pathlength (Article from Li and Shibata 2006). Is the resulting dataset then a toa_bidirectional_reflectance ? For imagery, we maybe don't need to be really picky on what the physical meaning of the dataset is, but for data analysis purposes it is of utmost importance. So I'm wondering now if we should rename our modifier to make things a bit clearer, and take better care of the standard name and units.

[sfinkens]

On NOAA's GOES Calibration page they call the uncorrected value "reflectance factor" or "effective albedo" with the additional explanation:

The value of 1 corresponds to the radiance of a perfectly reflecting diffuse surface illuminated at normal incidence when the sun is at its annual-average distance from the Earth.

I guess that's what @kathys wanted to express. There is no standard name for effective albedo, though.

@frarue Regarding the units: On the NOAA page the reflectance factor A is computed as A = k*R where R is the radiance in W m-2 sr-1 um-1 and k is the calibration coefficient in m2 sr um W-1, so that A is indeed unitless. I agree that this quantity is not very useful for a proper quantitative analysis. But I could imagine that for a qualitative analysis (for example by a forecaster) a value between 0 and 1 might be easier to interpret than some W m-2 sr-1 um-1 - even if the value is not perfectly accurate.

[mraspaud]

Good point about the units @sfinkens, I would even add that radiances from differents sensors/platform have often different units (some have cm instead of um from example), which doesn't make it easy to compare.

[frarue]

@sfinkens Really...they simply set SZA=0. Interesting, thank you for pointing me there! So in summary the reason why A is useful is because it normalises the radiances to the max possible for the sensor's SRF and thus get's rid of the many different units for a human observer? A sensor-normalised radiance, so to say? How about storing it as radiance with the sensor's k as attribute? That would then be CF compliant, I guess?

[sfinkens]

@frarue I'm not sure there is such a factor for each sensor. In some places I have seen lookup tables being used for calibration.

What about making both datasets available: Something like calibration='reflectance_quick' without correction and - if possible - calibration='reflectance' with solar zenith and/or pathlength correction.

[frarue]

Just one last thought that crossed my mind: The spatial pattern of the image probably is rather comparable to radiance than to reflectance (as values decrease towards pixels with higher SZA). So maybe calibration='radiance_normalised' would be more accurate than reflectance_quick?