Reflectance standard name variations

[mraspaud]

Question

In our field (weather satellites), we often work with the toa_bidirectional_reflectance. Our understanding of that quantity is that it is the top of atmosphere radiance measured by the satellite instrument normalised by the solar irradiance, taking into account the solar zenith angle (see here for the formula for example).

However, reading files with these data, it is quite often so that we have arrays where the solar zenith angle normalisation (needed for the full fledged Reflectance) has not been applied, and thus we are looking for a possible standard name to propose to this community, but we can't agree on the naming.

Suggestions for standard names we have so far include:

• toa_bidirectional_reflectance_multiplied_by_cosine_solar_zenith_angle
• toa_bidirectional_pseudoreflectance
• toa_bidirectional_zenith_equivalent_reflectance

Would any of these be appropriate? are they following the expected forms for standard names? Are there extra guidelines (on top the already available standard name guidelines here) we can use to converge to a consensus?

[JonathanGregory]

Dear Martin @mraspaud

I think your first suggestion is best, because it includes the two existing standard names toa_bidirectional_reflectance and solar_zenith_angle, making it rather self-explanatory. Following the guidelines and existing standard names, we wouldn't say multiplied; instead it would be product_of_cosine_solar_zenith_angle_and_toa_bidirectional_reflectance (putting the factors in alphabetical order). Would this be all right?

We could say cosine_of_, like square_of_ and product_of_, but on the other hand we don't have of_ with ln_ and log10_ standard names. I think it's clear without of_. This will be the first standard name containing a trigonometric function!

In your reference there's π in the numerator, but there isn't in wikipedia. Can you explain this? I guess it's something to do with solid angle. I notice that the help for toa_bidirectional_reflectance says "does not include any integration over solid angle". Also the canonical unit is given as 1, whereas wikipedia says sr-1. I think the standard name description ought to be more informative. There may be subtle differences. I am not at all familiar with these quantities, as you can no doubt tell!

Best wishes

Jonathan

[djhoese]

I was discussing this with a coworker and he made a good point and I'm wondering if there are examples of this in CF:

The product_of_ and multiplied_by variants are being used to describe the simpler quantity by modifying a more complicated quantity. That is, the usual series of calculations here would be:

radiance -> "pseudoreflectance" -> reflectance

So we're taking the standard name of the reflectance (toa_bidirectional_reflectance) and back-stepping one of the calculations that was applied to get that reflectance quantity (/ cos(SZA)) so that we can describe the prior "pseudo" quantity. It seems odd. I can't think of another case like this but it's like saying a quantity is sqrt(x^2) rather than just x.

[mraspaud]

@JonathanGregory thanks a lot for your input!
product_of_cosine_solar_zenith_angle_and_toa_bidirectional_reflectance is working fine for us I think, I will of course consult with my colleagues before we make an official request for the standard name.

Regarding your question, my understanging is that the reflectance in our domain (earth-observation satellite remote-sensing) make the assumption of isotropic diffusion, and thus we can integrate over the half sphere. This assumption is of course wrong most of the times, but since we usually don't really know what we are looking at (what is the surface made of? what is the content of the atmosphere on this light path?), it's a compromise we make. Again, just my understanding of the question.

[JonathanGregory]

David @djhoese and Martin @mraspaud, thanks for your comments.

it's like saying a quantity is sqrt(x^2) rather than just x

That's a good point. It's quite often the case that there's more than one way you can describe something, which is what standard names do. We try to find a description which is simple, clear, and as consistent as possible with usual terminology (although that's less important than being self-explanatory). I am not sure I've understood this quantity. Would it be correct to describe it as the ratio of the shortwave flux (received at the instrument, per m2 perpendicular to the beam) to the TOA incoming shortwave flux (per m2 of Earth's surface)?

Regarding your question, my understanding is that the reflectance in our domain (earth-observation satellite remote-sensing) make the assumption of isotropic diffusion, and thus we can integrate over the half sphere

Ah, I see. Is that perhaps why it's called "bidirectional reflectance", depends on two angles and is dimensionless, whereas the object described by wikipedia is the "bidirectional reflectance distribution function", which depends on four angles and is in srad-1?

[gerritholl]

Hi @JonathanGregory . A good and widely cited reference on terminology is this paper:

Schaepman-Strub, G., M. E. Schaepman, T. H. Painter, S. Dangel, and J. V. Martonchik. 2006. "Reflectance Quantities in Optical Remote Sensing-Definitions and Case Studies.", Remote Sensing of Environment 103 (1): 27-42. doi:10.1016/j.rse.2006.03.002, https://www.sciencedirect.com/science/article/pii/S0034425706001167

Following Schaepman-Strub et al. (2006), toa_bidirectional_reflectance is not a measurable quantity, but can only be estimated using assumptions (as Martin was already writing). The quantity that can be almomst unambiguously calculated from measurements is hemispherical–conical reflectance: radiation reflects from all sources and enters the field of view of the detector (a cone). If we neglect the difference between hemispherical-conical reflectance and conical-conical reflectance (i.e. we neglect any daytime irradiance not coming from our own Sun), then this quantity can be unambiguously calculated from measurements. Following this, the correct name might be product_of_cosine_solar_zenith_angle_and_hemispherical_conical_reflectance or
product_of_cosine_solar_zenith_angle_and_hemispherical_conical_toa_reflectance or product_of_cosine_solar_zenith_angle_and_conical_conical_reflectance or product_of_cosine_solar_zenith_angle_and_conical_conical_toa_reflectance. However, in practice, the terms hemispherical-conical reflectance or conical-conical reflectance are rarely used, and the calibrated quantity is normally called toa_bidirectional_reflectance, even though calibration to toa_bidirectional_reflectance involves isotropy assumptions but hemispherical_conical_reflectance would not.

[pdebuyl]

Hello @JonathanGregory , all,

I have some extra ideas about this (after some discussion in a satpy meeting). The back-stepping mentioned by @djhoese makes sense for my intuition. What is measured is the toa radiance within the instrument's spectral band (say L). Then, L is normalized by the incoming solar irradiance (in the same spectral band), and that is always between 0 and 1. But we also know that L will be proportional to the cosine of the solar zenith angle and can divide by it to neutralize (or try to as atmospheric effects are still left out) the geometry dependence.

From this point of view, we take the ratio of "toa_outgoing_radiance_per_unit_wavelength" by "solar_irradiance_per_unit_wavelength". But that maybe a bit long. Note: those quantities are both defined in CF :-)

In GOES files for instance, you can find the following quantities:

            Rad:standard_name = "toa_outgoing_radiance_per_unit_wavenumber" ;
            esun:standard_name = "toa_shortwave_irradiance_per_unit_wavelength" ;

I hope that this helps to move forward for this issue.

[djhoese]

So the psuedo-reflectance being discussed here is equal to toa_outgoing_radiance_per_unit_wavenumber / toa_shortwave_irradiance_per_unit_wavelength?

Edit: Or are there other factors/constants or variables involved?

[pdebuyl]

There are factors. One can look at https://github.com/pytroll/satpy/blob/main/satpy/readers/abi_l1b.py#L133 for instance. Note that the

Units of Rad: "mW m-2 sr-1 (cm-1)-1"

Units of esun: "W m-2 um-1"

There is one "pi" for the angular part, but also the fact that the solar irradiance needs to be scaled by the square of the earth-sun distance (in astronomic units, so that it is unitless). Also, one needs to check the "per unit wavelength" and "per unit wavenumber" to convert them properly :-)

[JonathanGregory]

Dear all

We agreed that the quantity we want to name equals the TOA bidirectional reflectance multiplied by the cosine of the solar zenith angle.

Earlier, I asked whether the TOA bidirectional reflectance is the ratio of the shortwave flux (received at the instrument, per m2 perpendicular to the beam) to the TOA incoming shortwave flux (per m2 of Earth's surface).

The help for toa_bidirectional_reflectance says "bidirectional_reflectance depends on the angles of incident and measured radiation". I think the angle of incidence is the solar zenith angle. What happens to the angle of reflection? The help says "toa_bidirectional_reflectance ... does not include any integration over solid angle." What does that mean? Is it correct? Is the instrument measuring radiation from one direction (i.e. a radiance in W m-2 srad-1), or an entire hemisphere (i.e. a radiative flux in W m-2)? Perhaps this is the same as asking whether the Earth fills the entire hemisphere of view of the instrument (because it's in low orbit) or appears as a remote source in one direction (because it's in high orbit)?

@pdebuyl writes that the quantity we want to name is calculated as the ratio of toa_outgoing_radiance_per_unit_wavelength to solar_irradiance_per_unit_wavelength. This raises the same question about angles, because outgoing radiance (in W m-2 srad-1) has a direction, whereas solar irradiance is a flux (in W m-2). The ratio of these two quantities wouldn't be dimensionless.

As you see, I'm not clear about these concepts yet. More explanation and insight would be useful. 😃

Best wishes

Jonathan

[mraspaud]

I like @pdebuyl 's proposal, but I'll let the scientists here answer the unit question.

[gerritholl]

The instrument measures radiation from a small solid angle (a cone) that is much smaller than the solid angle for the entire Earth disc. The radiation from one direction would be, in the limit, zero. We integrate over the solid angle and it becomes dimensionless.

Borrowing an image from Schaepman-Scrub et al. (2006):

From an entire hemisphere would be the bihemispherical case, but what we have in practice is the biconical case (in practice equal to hemispherical-conical). Both the nominator and denominator integrate over the solid angle so the ratio is again dimensionless.

[JonathanGregory]

Thanks for the diagram, but I'm sorry, I don't understand this yet, not having the background. Could we talk about it?

[pdebuyl]

Hello all, update on the units:

1. I checked the units of Rad for a thermal band (above, in "mW m-2 sr-1 (cm-1)-1"). The visible bands have Rad in "W m-2 sr-1 um-1" so the unit issue is moot for ABI data;
2. The units for FCI visible bands in the product user guide are consistently in "mW / (m2 cm-1)" and for ABI in "W m-2 um-1" (with a 1/sr appearing consistently in the radiance and not in the incident energy).
3. EUMETSAT's FCI product user guide refers specifically to Schaepman-Strub "BRF / Bidirectional Reflectance Factor" and states "BRF = pi BRDF". (I believe that there is then a missing pi in the document). The BRF then includes the cos(SZA) correction, which suggests that this quantity (the BRF) is indeed CF's toa_bidirectional_reflectance as it "includes a factor to account for the cosine of the solar zenith angle" (from CF standard names).

So, CF's toa_bidirectional_reflectance is "Rad * pi * d**2 * cos(SZA) / esun" (d is here unitless).

Dropping the cosine, we have "Rad * pi * d**2 / esun" or in full words "toa_outgoing_radiance_per_unit_wavelength times divided by the solar_irradiance_per_unit_wavelength. If a scalar distance_from_sun is included in the dataset, the quantity solar_irradiance_per_unit_wavelength can be considered distance corrected.

So we have "ratio of product of toa_outgoing_radiance_per_unit_wavelength and pi by solar_irradiance_per_unit_wavelength". Now, there is the issue of conical vs directional but I believe that we are in fact in "case 1" (so, directional, as is the canonical BRDF in the paper) unless there is a specific geometric information (i.e. conical angle of the measurement or whatever, which we don't have in the imager measurements. If there is such a geometric consideration it is taken into account in the radiance calibration and not visible to the data users).