# Climate Sensitivity math problem

## Homework Statement

Using a climate sensitivity of 0.5K per watt per square meter, estimate how much of the .9 c global temperature increase since 1900 could be due to solar forcing who value is the range of .06 to .24 w/m2

## The Attempt at a Solution

I am not sure how to start this problem. I know the solar constant is 239 w/m^2 but don't know what to do with the rest.

I need help getting started

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haruspex
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What is the minimum value for solar forcing since 1900?
What temperature difference would that account for?

What is the minimum value for solar forcing since 1900?
What temperature difference would that account for?
The minimum value for solar forcing would be .06 right?

But how would I know the temperature difference?

haruspex
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The minimum value for solar forcing would be .06 right?

But how would I know the temperature difference?
You are told climate sensitivity of 0.5K per watt per square meter.
That means, for each extra watt per square meter the temperature rises 0.5K.
If the solar forcing has been 0.6 watt per square meter, how much would that have increased the temperature?

You are told climate sensitivity of 0.5K per watt per square meter.
That means, for each extra watt per square meter the temperature rises 0.5K.
If the solar forcing has been 0.6 watt per square meter, how much would that have increased the temperature?
So would this mean I would do .5K x .06W/m^2 ?

haruspex
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So would this mean I would do .5K x .06W/m^2 ?
More precisely (tracking the units) .5K(Wm-2)-1 x .06(Wm-2) = .5 x .06 K
Now what about the maximum forcing?

More precisely (tracking the units) .5K(Wm-2)-1 x .06(Wm-2) = .5 x .06 K
Now what about the maximum forcing?
So for the maximum forcing would I do

.5K x .24 W/m^2?

Is there more to this problem though?

haruspex
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So for the maximum forcing would I do

.5K x .24 W/m^2?
Please try to get the units right.
Is there more to this problem though?
So how much of the .9C of warming can solar forcing explain? (Might be they're expecting it as a percentage - hard to know.)

Please try to get the units right.

So how much of the .9C of warming can solar forcing explain? (Might be they're expecting it as a percentage - hard to know.)
What do you mean by the right units?

And how would I find this as a percentage?

haruspex
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What do you mean by the right units?
See post #6. You wrote .5K x .24 W/m^2. The sensitivity is not .5K, it's .5K/(W/m2), which could also be written .5K(Wm-2)-1 or .5Km2W-1. When you multiply by solar forcing in units Wm-2 then Wm-2 cancels (Wm-2)-1 to give an answer in K.
And how would I find this as a percentage?
You don't know how to find one number as a percentage of another?

See post #6. You wrote .5K x .24 W/m^2. The sensitivity is not .5K, it's .5K/(W/m2), which could also be written .5K(Wm-2)-1 or .5Km2W-1. When you multiply by solar forcing in units Wm-2 then Wm-2 cancels (Wm-2)-1 to give an answer in K.

You don't know how to find one number as a percentage of another?
Would I do .06 W/m^2 x .5K =.03K

and .24 W/m^2 x .5K= .12 K

and then do .03K/.12 K= .25K or 25%?

haruspex
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Would I do .06 W/m^2 x .5K =.03K

and .24 W/m^2 x .5K= .12 K
No. You are given:
Climate sensitivity = .5K per W per m2. That means .5 K(Wm-2)-1, or more simply .5 KW-1m2.
Solar forcing = .24 Wm-2.
Climate sensitivity * Solar forcing = .5 KW-1m2 * .24 Wm-2, which simplifies to (.5 * .24) K. That's reasonable because the answer should be a temperature.
You wrote .24 W/m2 x .5K. That would give the result (.5 * .24) KWm-2, which is not a temperature.
Do you see the difference?
and then do .03K/.12 K= .25K or 25%?
No. You have calculated the minimum and maximum temperature rises that could have come from solar forcing. You are asked what portion of the observed .9 C rise could be a result of solar forcing, i.e. the largest possible portion.

No. You are given:
Climate sensitivity = .5K per W per m2. That means .5 K(Wm-2)-1, or more simply .5 KW-1m2.
Solar forcing = .24 Wm-2.
Climate sensitivity * Solar forcing = .5 KW-1m2 * .24 Wm-2, which simplifies to (.5 * .24) K. That's reasonable because the answer should be a temperature.
You wrote .24 W/m2 x .5K. That would give the result (.5 * .24) KWm-2, which is not a temperature.
Do you see the difference?

No. You have calculated the minimum and maximum temperature rises that could have come from solar forcing. You are asked what portion of the observed .9 C rise could be a result of solar forcing, i.e. the largest possible portion.

So I would use the maximum amount to find the ration? This would be .12K right?

How would I then use the .9 C. This is also in Celsius so would I need to convert?

haruspex
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So I would use the maximum amount to find the ration? This would be .12K right?

How would I then use the .9 C. This is also in Celsius so would I need to convert?
The .12K and the .9C are both changes in temperature. The K and C scales only differ by a constant, so a change of some number of degrees C is a change of the same number of degrees K. No conversion to be done.

The .12K and the .9C are both changes in temperature. The K and C scales only differ by a constant, so a change of some number of degrees C is a change of the same number of degrees K. No conversion to be done.
How would I go about finding this then?

haruspex
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How would I go about finding this then?
Finding what? .12 as a percentage of .9?

Finding what? .12 as a percentage of .9?
Would I put this into a ratio? If so how would I set this up?

haruspex
You don't now how to find a percentage? If you invest $100 and get back$105 you've made \$5 profit. What percentage did you earn?