A Question about Radiance, Solar Flux and Reflectance

[ecastro]

I stumbled upon this equation for a Lambertian uniform target:

##\rho^{*} = \frac{\pi L}{\mu_s E_s}##,

where ##\rho^{*}## is the reflectance, ##L## is the measured radiance, ##E_s## is the solar flux at the top of the atmosphere, and ##\mu_s## is the cosine of the sun zenith angle, ##\theta_s##.

The equation confuses me if I were to consider a monochromatic reflectance of the target, i.e. the reflectance of the target at a specific wavelength. What should be the measured reflectance for this case, is it the spectral radiance, should its units be ##\frac{W}{m^2 nm^2 sr}##? How about the solar flux (I considered it to be equivalent to the irradiance of the source at the target), should it be spectral irradiance, which I can calculate by the black-body radiation equation?

 

[eljose79]

Thank you for sharing this equation for a Lambertian uniform target. I can understand your confusion regarding the monochromatic reflectance of the target. In this case, the measured reflectance should indeed be the spectral radiance, with units of ##\frac{W}{m^2 nm^2 sr}##. This is because the reflectance of a target is dependent on the amount of light it reflects at a specific wavelength, which is represented by the spectral radiance.

As for the solar flux, it is indeed equivalent to the irradiance of the source at the target. However, instead of using the black-body radiation equation, it would be more accurate to use the solar spectral irradiance data from a reputable source, such as the National Solar Radiation Database or the Solar Spectral Irradiance (SSI) dataset from the Solar Radiation and Climate Experiment (SORCE) mission.

I hope this helps clarify any confusion you may have had. Keep up the great work in your research!