Willis Eschenbach has a new post on WUWT. It’s actually a follow-up to this one, which we’ll look at in detail. In it he claims that the temperature result from the GISS modelE is just 0.3 times the forcing, i.e., it’s simply a linear function of the input forcing. That one is a follow-up to this one, in which he discovers that the model output is not simply a linear function of the input forcing. Yet in its follow-up he finds that it is! Problem is, the “forcing” he uses to get this result is a fake.



Eschenbach seems to think that if a model responds roughly linearly to climate forcing, something must be wrong. I expect the opposite. The changes in forcing due to natural and man-made influences are small compared to the total forcing, and the changes in temperature are small compared to the absolute temperature (on the Kelvin scale). Based on fundamental energy balance for the globe as a whole, I’d be quite surprised if we were far enough outside the “linear regime” that the response — both for a good model and for the real climate system — was not linear.

But I would not expect the real climate system to show simple linear response to forcing. I would expect the physics to be well-approximated by linear response, with a zero-dimensional energy-balance model as a first approximation. But that doesn’t mean linear response to the forcing.

You can get the GISS modelE results here. I changed the “mean period” to 1 in order to avoid smoothing, and the “output” to “Formatted page w/ download links” to get a link to actual data, then I took 1-year averages of the model output to get annual values. The forcing data is here, but it’s not what Eschenbach used. He tried, but the fit wasn’t very good. Here’s a simple linear fit of forcing to GISS modelE output:

Compare that to Eschenbach’s result:

The difficulty is that the forcing from volcanic eruptions, which doesn’t persist for very long, doesn’t have as strong an impact as the other forcings which evolve on a much longer time scale. To prevent the volcanic excursions from straying too far from the temperature, the linear fit suppresses the forcing coefficient. But then the slower forcing is also suppressed, so it fails adequately to model the long-term temperature change. It’s almost as though we need the model to respond on two different time scales, including both a “fast response” and a “slow response.” But wait — if the model does that, it might be following some actual physics.

In the first post, Eschenbach added a linear time trend in addition to linear response to forcing, which allowed his theory to track the long-term temperature change. But such a trend is purely an ad hoc addition, there’s no physical (or mathematical) justification. Then he accused GISS of “excessive use of forcing” and of essentially fabricating forcing data to make their model go. They didn’t — but Eschenbach does.

In the follow-up he tried multiple regression against all the separate forcings that GISS uses. This led him to conclude:



After some reflection and investigation, I realized that the GISSE model treats all of the forcings equally … except volcanoes. For whatever reason, the GISSE climate model only gives the volcanic forcings about 40% of the weight of the rest of the forcings.



This is based on his multiple regression, as he says:



I looked further, and I saw that the total forcing versus temperature match was excellent except for one forcing — the volcanoes. Experimentation showed that the GISSE climate model is underweighting the volcanic forcings by about 60% from the original value, while the rest of the forcings are given full value. Then I used the total GISS forcing with the appropriately reduced volcanic contribution …



He further adds:



So I took the total forcings, and reduced the volcanic forcing by 60%. Then it was easy, because nothing further was required. It turns out that the GISSE model temperature hindcast is that the temperature change in degrees C will be 30% of the adjusted forcing change in watts per square metre (W/m2).



Let me translate: the actual forcing didn’t fit his preconception, so he changed it to a fake forcing.

What he doesn’t do is make the connection: that the short-lived volcanic impulses have reduced impact, not because the GISS modelE treats them differently from all the others, but because they are short-lived and there’s more than one time scale for the model’s climate system response. There is for the real climate system, too — a potent argument for the fundamental soundness of the GISS modelE.

I also took the GISS forcing data, translated it into a fake forcing by reducing the volcanic component to 40% of its actual value, and fit the modelE temperature data to that:

Compare to Eschenbach’s:

It’s a better fit — not because Eschenbach is right about the GISS modelE treatment of volcanic forcing, but because reducing the volcanic component emulates the reduced impact of short-lived forcing components, i.e., the “fast response” part of the climate system.

In his latest post, he uses a model suggested in a comment by Paul_K to his previous post. It’s actually just a discretized version of the solution to the zero-dimensional 1-box energy balance model used in Schwartz 2007. This model is that the temperature is influenced by time-dependent forcing via

,

where is the climate sensitivity and is a “time constant” for the climate system as a whole. Instead of creating fake forcing by keeping only 40% of the volcanic forcing, Paul_K creates a different fake forcing by keeping only 72.4% of the volcanic forcing, then fitting the “exponentially smoothed” forcing to the GISS modelE data. By exponentially smoothing the forcing with a given time constant, you effectively solve the 1-box energy balance model — but the forcing data used are still a fake. I can do that too:

Compare to Paul_K’s:

Bottom line: if you put in enough parameters, and fake the data because otherwise your model isn’t very good, you can get an excellent fit to the GISS modelE output. But it’s nothing but curve-fitting; the work of Willis Eschenbach and Paul_K is an outstanding example of mathturbation.

There’s no justification for them to fake the forcing, physical or mathematical. There’s no investigation of “effective forcing” to see how different forcings might actually have a different impact (in part because of feedbacks). That’s an effort which has been pioneered by James Hansen and colleagues. To contribute meaningfully, you’d have to do some actual science other than make an ad hoc change to the forcing data so you can impugn the results of somebody’s climate model.

What kind of physical theory — even rudimentary — might make just as good a fit? There are two major flaws with Schwarz’s model. One is that his method of diagnosing the time constant is flawed. Seriously flawed — even if his model were correct his method would give the wrong result. The other major flaw is that the real climate system has more than one “time constant.”

Maybe we could do better with a 2-box energy balance model. This has two time constants, and , one of which represents the “fast response” of the part of the climate system with less heat capacity, the other the “slow response” from the more sluggish part with more heat capacity. I too can get an outstandingly good fit to the modelE temperature, using a 2-box model with time constants about 2 and 45 years:

This fit uses the total net forcing, unmodified. It’s not based on changing the data, it’s based on physics. What a concept.

In my opinion, the fact that the GISS modelE output is so close to that of a 2-box energy balance model is a powerful argument for its correctness. The GISS model is built on the laws of physics, applied to detailed interactions over the entire globe, which enables it to simulate a helluva lot more than just global average temperature — like the geographical distribution of temperature changes, patterns of precipitation, wind, clouds, snow and ice. But global average temperature should be well approximated by fundamental considerations of energy balance, albeit with more than one time constant. If the GISS model did not fit the 2-box (or 3-box or more) energy balance model, then I’d be surprised.

We can even fit the 2-box model to actual (not model output) temperature data, and get a real-world estimate of climate sensitivity as well:

Doing so indicates sensitivity of 0.64 deg.C/(W/m^2), or 2.4 deg.C per doubling of CO2. What a surprise.