# Climate Sensitivity math problem

1. Nov 23, 2013

### courtneywetts

1. The problem statement, all variables and given/known data

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

2. Relevant equations

3. 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

2. Nov 23, 2013

### haruspex

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

3. Nov 23, 2013

### courtneywetts

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

But how would I know the temperature difference?

4. Nov 23, 2013

### haruspex

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?

5. Nov 23, 2013

### courtneywetts

So would this mean I would do .5K x .06W/m^2 ?

6. Nov 23, 2013

### haruspex

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

7. Nov 23, 2013

### courtneywetts

So for the maximum forcing would I do

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

Is there more to this problem though?

8. Nov 23, 2013

### haruspex

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.)

9. Nov 23, 2013

### courtneywetts

What do you mean by the right units?

And how would I find this as a percentage?

10. Nov 24, 2013

### haruspex

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?

11. Nov 24, 2013

### courtneywetts

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%?

12. Nov 24, 2013

### haruspex

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.

13. Nov 24, 2013

### courtneywetts

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?

14. Nov 24, 2013

### haruspex

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.

15. Nov 24, 2013

### courtneywetts

How would I go about finding this then?

16. Nov 24, 2013

### haruspex

Finding what? .12 as a percentage of .9?

17. Nov 24, 2013

### courtneywetts

Would I put this into a ratio? If so how would I set this up?

18. Nov 24, 2013

### 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?