Albedo equations giving different results

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In summary, the conversation discusses the difficulty in finding the albedo of the Earth using two different equations. The first equation, which combines the Stefan Boltzmann law with an equation for incoming power, gives the correct answer of 0.3 when solved for albedo. However, when using the second equation from a provided data booklet, the calculated albedo is incorrect. This may be due to a typo in the given value for power absorbed at the Earth's surface.
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Sabrewolf
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1. This question isn't so much a homework question per se, however I am having difficulty using certain equations to find the albedo of the Earth. In attempting to find the albedo, I am using two equations, shown below, however each equation gives a different answer. I am given the following variables:

- Power absorbed at the surface of the Earth is 240 W/m^2
- Solar Constant(S) is 1.37 kW/m^2
- Earth is assumed to be a perfect blackbody, thus emissivity is 1
- Temperature(T) on the Earth is assumed to be 255 kelvin
σ is Stefan Boltzmann constant, 5.67 x 10^-8
ε is emissivity of the Earth
α is albedo

Homework Equations



T = [tex]\sqrt[4]{\frac{S(1-\alpha)}{4\epsilon\sigma}}[/tex] <-- this is a given equation found by combining the Stefan Boltzmann law with an equation for incoming power.

albedo = total scattered power/total incident power <--this is from a provided data booklet

The Attempt at a Solution



The actual work isn't too hard, when the 1st equation is moved around to find the albedo, it reads:

[tex]\alpha[/tex] = -[tex]\frac{T^{4}4\sigma}{S}[/tex] + 1

This equation, when solved, gives the answer [tex]\alpha[/tex]=0.3, this is the correct response according to the book

When I use the second equation, I take the solar constant S as the total incident power. In order to find the total scattered power, I'm subtracting the amount absorbed (given as 240W/[tex]m^{2}[/tex]) from the solar constant because the difference isn't absorbed by the earth, meaning it is reflected into space or scattered. However I get this:

[[tex]\frac{1.37*10^{3} - 240}{1.37*10^{3}}[/tex] = 0.82

This value is incorrect and I'm not sure why, given a presumed correct equation, I'm getting a wrong answer. Am I misusing the equation somehow?
 
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  • #2
The given data are inconsistent. To match the rest of the data, the power absorbed should be 410W/m2. Maybe the 240 is a typo for 420.
 

Related to Albedo equations giving different results

What is albedo?

Albedo, also known as reflectance, is the measure of how much light is reflected off a surface. It is expressed as a percentage, with 0% being a completely black surface that absorbs all light, and 100% being a perfectly reflective surface that reflects all light.

Why do albedo equations give different results?

Albedo equations can give different results because they take into account different factors such as the type of surface, the angle of incidence of light, and the wavelength of light. Additionally, different methods of measurement or different units used can also contribute to varying results.

Which albedo equation is the most accurate?

There is no single albedo equation that is universally considered the most accurate. It is important to use an equation that is appropriate for the specific surface and conditions being measured. Additionally, taking multiple measurements and averaging the results can help to improve accuracy.

How can I ensure accurate results when using albedo equations?

To ensure accurate results when using albedo equations, it is important to use the equation that is most appropriate for the surface being measured. Taking multiple measurements and averaging the results can also help to improve accuracy. It is also important to carefully consider and account for any potential sources of error.

What are some applications of albedo measurements?

Albedo measurements are used in various fields, such as climate science, meteorology, and remote sensing. They can help to understand the Earth's energy balance, monitor changes in land and water surfaces, and study the effects of human activities on the environment. Albedo measurements can also be used in agriculture to optimize crop growth and in architecture to design more energy-efficient buildings.

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