Relationship between Reflectance and Albedo

[ecastro]

I have a question regarding the relationship between the reflectance and albedo of a material.

What I Know:
Both quantities are the ratio between the incoming and outgoing radiation from a material. Correct me if I am wrong, the reflectance of a material depends on the material while the albedo depends on which direction the outgoing radiation is viewed (and from what direction the incoming radiation strikes the material).

My Questions:
1. If I integrate the albedo along all directions, for both incoming and outgoing radiation, is it still albedo?
2. If I multiply albedo and reflectance, what quantity shall I get?

Thank you in advance.

 

[Andrew Mason]

Albedo usually applies to planets or other large astronomical bodies that receive radiation energy. It is a number between 0 and 1 that represents the fraction or the proportion of the total radiation energy incident on the body that is reflected back into space without being absorbed by the body. Since surfaces of astronomical bodies are generally round, the radiation that is reflected may be in all directions. Surface reflectance refers to the reflective efficiency of the surface with respect to radiation directly incident upon it. Reflectance is a function of the angle of incident radiation to the surface and the surface characteristics.

AM

 

[ecastro]

Thank you for your reply.

Albedo usually applies to planets or other large astronomical bodies that receive radiation energy.

I did read about the albedo being used in astronomical bodies, but I first encountered this term in a topic regarding the Earth's radiation budget, and on remote sensing. So I want to know its interpretation on terrestrial objects.

As an addition, I have encountered Lambert's Cosine Law, which states that the radiant energy reflected by a material is proportional to the cosine of the incident radiation with respect to the surface's normal direction.

Reflectance is a function of the angle of incident radiation to the surface and the surface characteristics.

This is a bit confusing, I have read that reflectance is only dependent on the material; the reflectance of a material being hit by the Sun's radiation should not change whether its morning or noon.

 

[Andrew Mason]

Thank you for your reply.

I did read about the albedo being used in astronomical bodies, but I first encountered this term in a topic regarding the Earth's radiation budget, and on remote sensing. So I want to know its interpretation on terrestrial objects.

Last time I checked the Earth was still a planet. The Earth albedo is very important in climate science. Radiation that is reflected from the clouds, ice and snow, roofs, etc. does not contribute to long wavelength blackbody radiation (which is surface radiation that is a function of surface temperatue) that can be absorbed by CO₂ and other gases in the atmosphere (and then partially reradiated back to the Earth surface). What the albedo tells us is the fraction of total incident solar radiation that does not contribute to surface temperature.

As an addition, I have encountered Lambert's Cosine Law, which states that the radiant energy reflected by a material is proportional to the cosine of the incident radiation with respect to the surface's normal direction.

This is a bit confusing, I have read that reflectance is only dependent on the material; the reflectance of a material being hit by the Sun's radiation should not change whether its morning or noon.

I am not distinguishing between your term "reflectance" and "reflectivity" which is the term used in physics. See: the hyperphysics page for example

Refectivity of a surface may depend on the angle of the incident radiation and with its wavelength. A surface may reflect from different layers or depths. For example, light reflected from one layer may encounter and destructively interfere with radiation reflected from other layers or with incoming radiation. The light path through the material varies with angle of incidence resulting in certain wavelengths being reflected and others not being reflected at different angles or depths. You can see this, for example, in the reflection of light from a surface of water covered with a thin film of oil.

AM

 

[ecastro]

The Earth albedo is very important in climate science. Radiation that is reflected from the clouds, ice and snow, roofs, etc. does not contribute to long wavelength blackbody radiation (which is surface radiation that is a function of surface temperatue) that can be absorbed by CO₂ and other gases in the atmosphere (and then partially reradiated back to the Earth surface). What the albedo tells us is the fraction of total incident solar radiation that does not contribute to surface temperature.

I think this indeed the case, but I am more concerned about the general term "albedo", or does albedo is concerned with long wavelength radiation? Is there no such thing as an albedo for visible or ultraviolet radiation?

Refectivity of a surface may depend on the angle of the incident radiation and with its wavelength. A surface may reflect from different layers or depths. For example, light reflected from one layer may encounter and destructively interfere with radiation reflected from other layers or with incoming radiation. The light path through the material varies with angle of incidence resulting in certain wavelengths being reflected and others not being reflected at different angles or depths. You can see this, for example, in the reflection of light from a surface of water covered with a thin film of oil.

I think what you are referring to as "reflectivity" is a coefficient from the Fresnel Equations. I am concerned with reflectance as shown by this figure:

From: http://gsp.humboldt.edu/OLM/Courses/GSP_216_Online/lesson2-1/reflectance.html

 

[Andrew Mason]

I think this indeed the case, but I am more concerned about the general term "albedo", or does albedo is concerned with long wavelength radiation? Is there no such thing as an albedo for visible or ultraviolet radiation?

Tell us what you questions you have and we will try to help you. I have explained what albedo is. It is the fraction of solar radiation (ie. all wavelengths of radiation from the sun) incident upon the Earth that is reflected back into space.

I think what you are referring to as "reflectivity" is a coefficient from the Fresnel Equations. I am concerned with reflectance as shown by this figure:
View attachment 235853
From: http://gsp.humboldt.edu/OLM/Courses/GSP_216_Online/lesson2-1/reflectance.html

Again if you have a specific question let us know.

AM

 

[anorlunda]

As stated, reflectivity normally applies to a surface, and it is a function of angle.

Albedo for an object in space includes absorbsion in the atmosphere. It is not a surface. The albedo also reflects the integral over all angles of incoming and emitted light.

 

[ecastro]

It is the fraction of solar radiation (ie. all wavelengths of radiation from the sun) incident upon the Earth that is reflected back into space.

The albedo also reflects the integral over all angles of incoming and emitted light.

This is one of the confusions I had, so if I integrate along all directions of the incoming and reflected radiation, it is the albedo? Is this correct?

If the Fresnel Coefficient "reflectivity" is indeed equal to the "reflectance" to what I had in mind before, does that mean that if I integrate these "reflectivity" coefficients along all directions, I will get albedo?

Again if you have a specific question let us know.

What I am actually trying to do is to form the intuition on how light interacts with the surface and the atmosphere. For example, a radiance $I_0$ hit the surface at an angle $\theta_0$ from the surface's normal and is reflected at all directions. Now I put a sensor at an angle $\theta$ from the surface's normal, I measured a radiance of $I$, so by dividing it by the initial radiance, I will have the reflectance, not the albedo? (Since I did not measure reflectance at all angles)