On MichaelCrow’s Analysis of Climate Sensitivity

I’ve been arguing with MichaelCrow on Twitter around climate sensitivity and thought I’d put together a more detailed rebuttal using an analogy.

Michael’s analysis of climate sensitivity is interesting and unique and I can understand how someone might think it’s relevant.

I admit I haven’t downloaded his code and his blog post is a bit light on details but in summary he looks at the daily change in temperate then divides this by the daily change in daily solar input to get a climate sensitivity.

This kind of sounds reasonable. As the seasons change in the extra-tropics the temperatures are obviously going to respond to the change in solar input as the days get shorter or longer.

So why can’t you calculate climate sensitivity this way? Well first off it just isn’t done by any scientists. Climate sensitivity is supposed to be the temperature response to a forcing after the perturbation to the system has ended. It is the new equilibrium that detarmines the sensitivity. I can’t find good numbers on this but it seems most scientists believe it can take decades to centuries for the system to return to equilibrium.

Michael claims there is only a few hours worth of heat in the atmosphere so a daily time period is sufficient. I’m not sure how the oceans are supposed to fit in but that’s an argument for another day.

For now let’s forget all that and look at a system we know a little more about – metabolism. Well maybe only slightly more. Regardless I think this can make a good analogy.

Lets say we have Bob who is a 40 year old male. His height is 5’10” and his weight is 180 lbs. He eats 2700 calories a day. Now let’s say we want to determine what would happen to his weight if he consumed an extra 100 calories a day.

To do this we need to determine his “caloric sensitivity”. We figure out how much weight he gains for each calorie and times by 100 – easy!

We can start by doing the obvious. 180 pounds divided by 2700 calories is .067 pounds per calorie. Based on this we could say those 100 extra calories would result in an extra 6.7 pounds. We can assume the relationship between calories and weight is not linear therefore this result is not robust but it gives us a ball park estimate.

We could also use Michael’s approach and calculate the daily change in weight divided by the daily change in calories. If our subject Bob weighed and ate the same every day this obviously won’t work as we would be dividing zero by zero. It’s probably safe to say there will be variation though. Maybe Bob typically loses a bit of weight in the summer and gains some in the winter. If we have a long enough time-span that includes some ups and downs we should be able to determine the relationship right?

I’m not so sure. The amount of daily noise is huge. At a daily interval our weight changes for many reasons unrelated to calories – how much water we drink, the weight of the food we consumed, sickness, etc.

So let’s say we do the analysis and we get some very small number like 0.00067 pounds per calorie. Should we consider this a robust result? One thing we could do is look at our initial calculation that says on average, Bob maintains 0.067 pounds per calorie and while we assume the result will be different than that, we would not expect it to be two orders of magnitude different.

We also know a bit about metabolism. We know that Bob will continue to gain weight with his 100 calorie surplus until his basal metabolism reaches a new equilibrium. According to active.com this would be at 192 pounds. So is it reasonable to think Bob might gain 12 pounds? I would say yes. It’s only double our rough calculation of 6.7 pounds and that included parts of the body that don’t change weight – like bones and organs and such.

So lets apply this sanity check to Michael’s analysis on climate sensitivity. Michael claims climate sensitivity is about 0.015 K per w/m². The earth absorbs around 240 w/m² of radiation and has a temperature of 288 K. That’s 1.2K per w/m². Just like with the metabolism analogy we know the relationship isn’t linear so the next watt will most likely not produce exactly 1.2 degrees of extra temperature. But it does give us a ball park number to work with. If we do an analysis that results in a number that’s two orders of magnitude different, we ought to be extremely skeptical.

To summarize, I think Michael’s approach is interesting and innovative but it simply cannot be taken as meaningful or relevant with respect to climate sensitivity.