Zero Point Three times the Forcing

Guest Post by Willis Eschenbach

Now that my blood pressure has returned to normal after responding to Dr. Trenberth, I returned to thinking about my earlier somewhat unsatisfying attempt to make a very simple emulation of the GISS Model E (herinafter GISSE) climate model. I described that attempt here, please see that post for the sources of the datasets used in this exercise.

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.

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). Figure 1 shows that result:

Figure 1. GISSE climate model hindcast temperatures, compared with temperatures hindcast using the formula ∆T = 0.3 ∆Q, where T is temperature and Q is the same forcings used by the GISSE model, with the volcanic forcing reduced by 60%.

What are the implications of this curious finding?

First, a necessary detour into black boxes. For the purpose of this exercise, I have treated the GISS-E model as a black box, for which I know only the inputs (forcings) and outputs (hindcast temperatures). It’s like a detective game, trying to emulate what’s happening inside the GISSE black box without being able to see inside.

The resulting emulation can’t tell us what actually is happening inside the black box. For example, the black box may take the input, divide it by four, and then multiply the result by eight and output that number.

Looking at this from the outside of the black box, what we see is that if we input the number 2, the black box outputs the number 4. We input 3 and get 6, we input 5 and we get 10, and so on. So we conclude that the black box multiplies the input by 2.

Of course, the black box is not actually multiplying the input by 2. It is dividing by 4 and multiplying by 8. But from outside the black box that doesn’t matter. It is effectively multiplying the input by 2. We cannot use the emulation to say what is actually happening inside the black box. But we can say that the black box is functionally equivalent to a black box that multiplies by two. The functional equivalence means that we can replace one black box with the other because they give the same result. It also allows us to discover and state what the first black box is effectively doing. Not what it is actually doing, but what it is effectively doing. I will return to this idea of functional equivalence shortly.

METHODS

Let me describe what I have done to get to the conclusions in Figure 1. First, I did a multiple linear regression using all the forcings, to see if the GISSE temperature hindcast could be expressed as a linear combination of the forcing inputs. It can, with an r^2 of 0.95. That’s a good fit.

However, that result is almost certainly subject to “overfitting”, because there are ten individual forcings that make up the total. With so many forcings, you end up with lots of parameters, so you can match most anything. This means that the good fit doesn’t mean a lot.

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, and we have the result shown in Figure 1. Temperature change is 30% of the change in the adjusted forcing. Simple as that. It’s a really, really short methods section because what the GISSE model is effectively doing is really, really simple.

DISCUSSION

Now, what are (and aren’t) the implications available within this interesting finding? What does it mean that regarding temperature, to within an accuracy of five hundredths of a degree (0.05°C RMS error) the GISSE model black box is functionally equivalent to a black box that simply multiplies the adjusted forcing times 0.3?

My first implication would have to be that the almost unbelievable complexity of the Model E, with thousands of gridcells and dozens of atmospheric and oceanic levels simulated, and ice and land and lakes and everything else, all of that complexity masks a correspondingly almost unbelievable simplicity. The modellers really weren’t kidding when they said everything else averages out and all that’s left is radiation and temperature. I don’t think the climate works that way … but their model certainly does.

The second implication is an odd one, and quite important. Consider the fact that their temperature change hindcast (in degrees) is simply 0.3 times the forcing change (in watts per meter squared). But that is also a statement of the climate sensitivity, 0.3 degrees per W/m2. Converting this to degrees of warming for a doubling of CO2 gives us (0.3°C per W/m2) times (3.7 W/m2 per doubling of CO2), which yields a climate sensitivity of 1.1°C for a doubling of CO2. This is far below the canonical value given by the GISSE modelers, which is about 0.8°C per W/m2 or about 3°C per doubling.

The third implication is that there appears to be surprisingly little lag in their system. I can improve the fit of the above model slightly by adding a lag term based on the change in forcing with time d(Q)/dt. But that only improves the r^2 to 0.95, mainly by clipping the peaks of the volcanic excursions (temperature drops in e.g. 1885, 1964). A more complex lag expression could probably improve that, but with the initial expression having an r^2 of 0.92, that only leaves 0.08 of room for improvement, and some of that is surely random noise.

The fourth implication is that the model slavishly follows the radiative forcings. The model results are a 5-run average, so it is not clear how far an individual model run might stray from the fold. But since the five runs’ temperatures average out so close to 0.3 times the forcings, no individual one of them can be very far from the forcings.

Anyhow, that’s what I get out of the exercise. Further inferences, questions, objections, influences and expansions welcomed, politeness roolz, and please, no speculation about motives. Motives don’t matter.

w.