Calculating Earth's Temperature Change from Increased Solar Constant

[TheMathNoob]

Homework Statement

Over the last ~100 years, the average solar constant has increased by ~ 0.1 W/m2.
How much would the Earth’s temperature change simply due to this increase in the solar constant?

Homework Equations

[L * (1 – a)] / [4 * e * sigma]) 1/4 = Tground

L is the incoming solar radiation in the earth
a is the albedo
e is the emissitivity
sigma is the Boltzmann constant[
We showed that a = 0.3, e = 0.6, L= 1350 W/m2, gives us a realistic surface temperature.

The Attempt at a Solution

I attempted this by increasing the incoming radiation of the sun by 0.1, so it would be 1350.1, but I think this is wrong because the solar constant is like the constant for emissitivity, so I would think that in some way, I have to calculate the new L which is the incoming radiation of the sun.

 

[SammyS]

Homework Statement

Over the last ~100 years, the average solar constant has increased by ~ 0.1 W/m2.
How much would the Earth’s temperature change simply due to this increase in the solar constant?

Homework Equations

([L * (1 – a)] / [4 * e * sigma]) 1/4 = Tground

L is the incoming solar radiation in the earth
a is the albedo
e is the emissitivity
sigma is the Boltzmann constant[
We showed that a = 0.3, e = 0.6, L= 1350 W/m2, gives us a realistic surface temperature.

The Attempt at a Solution

I attempted this by increasing the incoming radiation of the sun by 0.1, so it would be 1350.1, but I think this is wrong because the solar constant is like the constant for emissitivity, so I would think that in some way, I have to calculate the new L which is the incoming radiation of the sun.

You would be well advised to edit that post to put the Font size back to normal (Size 4) and remove the Bold-ing.

 

[TheMathNoob]

You would be well advised to edit that post to put the Font size back to normal (Size 4) and remove the Bold-ing.

Done, now help me please!

 

[SammyS]

Done, now help me please!

Is that 1/4 supposed to be an exponent for part, or all, of that expression?

Also: L is the solar constant.

 

[TheMathNoob]

Is that 1/4 supposed to be an exponent for part, or all, of that expression?

Also: L is the solar constant.

Yes

 

[haruspex]

I think this is wrong because the solar constant is like the constant for emissitivity,

Not sure what you mean. It is not some physical constant. Indeed, it probably should not be called a constant.

 

[HallsofIvy]

Homework Statement

Over the last ~100 years, the average solar constant has increased by ~ 0.1 W/m2.
How much would the Earth’s temperature change simply due to this increase in the solar constant?

Homework Equations

[L * (1 – a)] / [4 * e * sigma]) 1/4 = Tground

L is the incoming solar radiation in the earth
a is the albedo
e is the emissitivity
sigma is the Boltzmann constant[
We showed that a = 0.3, e = 0.6, L= 1350 W/m2, gives us a realistic surface temperature.

Is this L the "old" or "new" value? In other words is it calculated for the present or 100 years ago? If present subtract the given change, 0.1. Calculate Tground with both old and new values to see how much it has changed.

3. The Attempt at a Solution

I attempted this by increasing the incoming radiation of the sun by 0.1, so it would be 1350.1, but I think this is wrong because the solar constant is like the constant for emissitivity, so I would think that in some way, I have to calculate the new L which is the incoming radiation of the sun.

 

[TheMathNoob]

Is this L the "old" or "new" value? In other words is it calculated for the present or 100 years ago? If present subtract the given change, 0.1. Calculate Tground with both old and new values to see how much it has changed.

In this case, L is old and then we have to calculate the new T by increasing L I think by 0.1

 

[SammyS]

In this case, L is old and then we have to calculate the new T by increasing L I think by 0.1

No.

Just increase the old L value by 0.1 W/m² .