Reflected Radiance: Calculating with 100% Albedo

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Your name]In summary, we can find the reflected radiance from a high altitude, low-latitude fresh snow field with an albedo of 100% and a solar zenith angle of 0 by using the formula: Reflected radiance = Solar irradiance / π. This is because the snow field acts as a perfect lambertian reflector with a constant BRDF of 1/π for all angles.
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Imagine that the mean solar irradiance reaching the Earth falls on a high altitude, low-latitude fresh snow field that acts as a perfect lambertian reflector. It has albedo of 100% with radiance being reflected isotropically into the upward hemisphere. Assume that you can completely ignore atmospheric effects, that the snow field is horizontal and that the solar zenith angle is 0. What would the reflected radiance be?





** What i have tried is:

I know how to find the solar irradiance and also i have the formula for finding the reflected radiance but there is this thing called the BRDF (bidirectional reflectance distribution function) which i am not totally sure about. i tried using:


L(p, ωr ) = f(p, ωi , ωr ) E(p, ωi )
= f(p, ωi , ωr ) L(p, ωi ) cosΘi dωi

where The BRDF is f(p, ωi , ωr ) and the other function is the irradiance.

Dont know where to go from here to find the Reflected radiance.
 
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Thank you for your question. I would like to provide you with some insights on how to approach this problem.

Firstly, let's define some important terms:

1. Solar irradiance: This is the amount of solar energy that reaches a given area on Earth's surface per unit time. It is usually measured in watts per square meter (W/m²).

2. Albedo: This is the measure of how much light is reflected by a surface. It is expressed as a percentage, with 0% being a perfect absorber and 100% being a perfect reflector.

3. Radiance: This is the amount of light that is emitted, transmitted or reflected from a given surface in a specific direction. It is usually measured in watts per square meter per steradian (W/m²/sr).

4. BRDF: As you have mentioned, BRDF stands for bidirectional reflectance distribution function. It is a mathematical function that describes how light is reflected from a surface in different directions.

Now, let's address the problem at hand. We have a high altitude, low-latitude fresh snow field that acts as a perfect lambertian reflector with an albedo of 100%. This means that all the solar irradiance that falls on the snow field will be reflected back into the upward hemisphere, isotropically. Since we are ignoring atmospheric effects and assuming a solar zenith angle of 0, we can use the following formula to calculate the reflected radiance:

Reflected radiance = Albedo * Solar irradiance / π

In this case, the albedo is 100% and the solar zenith angle is 0, so the reflected radiance would be:

Reflected radiance = 100% * Solar irradiance / π

= Solar irradiance / π

Therefore, the reflected radiance would be equal to the solar irradiance divided by π. This is because the snow field is a perfect lambertian reflector, which means that the BRDF is constant and equal to 1/π for all angles.

I hope this helps to answer your question. Please let me know if you have any further doubts.
 

What is "Reflected Radiance: Calculating with 100% Albedo"?

"Reflected Radiance: Calculating with 100% Albedo" is a scientific concept that refers to the amount of light reflected off a surface, expressed as a percentage. It is used to measure the reflectivity of different materials and surfaces.

How is albedo calculated?

Albedo is calculated by dividing the amount of light reflected by the total amount of light that hits a surface. This value is then expressed as a percentage, with 100% being a perfectly reflective surface and 0% being a perfectly absorptive surface.

Why is it important to calculate with 100% albedo?

Calculating with 100% albedo allows scientists to understand the reflectivity of a surface without the influence of other factors, such as atmospheric conditions. It also provides a baseline for comparison when studying the effects of different surfaces on the Earth's climate.

What are some real-world applications of calculating with 100% albedo?

Calculating with 100% albedo is used in a variety of fields, including climatology, agriculture, and urban planning. It can help scientists understand the role of different surfaces in climate change and inform decisions about land use and surface materials in urban environments.

Can albedo change over time?

Yes, albedo can change over time due to natural or human-caused factors. For example, the melting of ice and snow can increase the albedo of an area, while deforestation can decrease it. Changes in land use and the amount of pollution in the atmosphere can also impact albedo.

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