Nature hates straight lines

Guest Post by Willis Eschenbach

Yeah, I know Nature doesn’t have human emotions, give me a break. I’m aware it is unscientific and dare I call it atavistic and perhaps even socially unseemly to say Nature “hates” straight lines, but hey, it’s a headline, cut me some poetic slack.

My point is, everyone is aware that nature doesn’t deal in straight lines. Natural things move in fits and starts along complex paths, not straight from point to point. Phenomena have thresholds and edges, not slow linear changes at the perimeter. Tree branches and coastlines are jagged and bent. Things move in arcs and circles, relationships are complex and cyclical. Very little in nature is linear, particularly in complex systems.

Forcing is generally taken to mean downward radiation measured at the TOA (top of atmosphere). The IPCC says that when TOA forcing changes, the surface temperature changes linearly with that TOA forcing change. If there is twice the forcing change (twice the change in solar radiation, for example), the IPCC says we’ll see twice the temperature change. The proportionality constant (not a variable but a constant) that the IPCC says linearly relates temperature and TOA forcing is called the “climate sensitivity”.

Figure 1. Photo of impending change in climate sensitivity.

Today I stumbled across the IPCC justification of this linearity assumption. This is the basis of their claim of the existence of a constant called “climate sensitivity”. I quote it below.

I’ve removed the references and broken it into paragraphs it for easy reading. The references are in the original cited above. I reproduce all of the text on the web page. This is their entire justification for the linearity assumption. Having solved linearity in a few sentences, they then proceed to other matters. Here is their entire scientific justification for the assumption of linearity between forcing and temperature change (emphasis mine):

Linearity of the Forcing-Response Relationship

Reporting findings from several studies, the TAR [IPCC Third Assessment Report] concluded that responses to individual RFs [Radiative Forcings] could be linearly added to gauge the global mean response, but not necessarily the regional response.

Since then, studies with several equilibrium and/or transient integrations of several different GCMs [Global Climate Models] have found no evidence of any nonlinearity for changes in greenhouse gases and sulphate aerosol. Two of these studies also examined realistic changes in many other forcing agents without finding evidence of a nonlinear response.

In all four studies, even the regional changes typically added linearly. However, Meehl et al observed that neither precipitation changes nor all regional temperature changes were linearly additive. This linear relationship also breaks down for global mean temperatures when aerosol-cloud interactions beyond the cloud albedo RF are included in GCMs. Studies that include these effects modify clouds in their models, producing an additional radiative imbalance.

Rotstayn and Penner (2001) found that if these aerosol-cloud effects are accounted for as additional forcing terms, the inference of linearity can be restored. Studies also find nonlinearities for large negative RFs, where static stability changes in the upper troposphere affect the climate feedback (e.g., Hansen et al., 2005).

For the magnitude and range of realistic RFs discussed in this chapter, and excluding cloud-aerosol interaction effects, there is high confidence in a linear relationship between global mean RF [radiative forcing] and global mean surface temperature response.

Now, what strikes you as odd about that explanation of the scientific basis for their claim of linearity?

Before I discuss the oddity of that IPCC explanation, a short recap regarding climate sensitivity. I have held elsewhere that climate sensitivity changes with temperature. I will repeat the example I used to show how climate sensitivity goes down as temperature rises. This can be seen clearly in the tropics.

In the morning the tropical ocean and land is cool, and the skies are clear. As a result, the surface warms rapidly with increasing solar radiation. Climate sensitivity (which is the amount of temperature change for a given change in forcing) is high. High sensitivity, in other words, means that small changes in solar forcing make large changes in surface temperature.

By late morning, the surface has warmed significantly. As a result of the rising temperature, cumulus clouds start to form. They block some of the sun. After that, despite increasing solar forcing, the surface does not warm as fast as before. In other words, climate sensitivity is lower.

In the afternoon, with continued surface warming, thunderstorms start to form. These bring cool air and cool rain from aloft, and move warm air from the surface aloft. They cool the surface in those and a number of other ways. Since thunderstorms are generated in response to rising temperatures, further temperature increases are quickly countered by increasing numbers of thunderstorms. This brings climate sensitivity near to zero.

Finally, thunderstorms have a unique ability. They can drive the surface temperature underneath them below the temperature at which the thunderstorm formed. In this case, we have local areas of negative climate sensitivity – the solar forcing can be increasing while the surface is cooling.

As you can see, in the real world the temperature cannot be calculated as some mythical constant “climate sensitivity” times the forcing change. Sensitivity goes down as temperature goes up in the tropics, the area where the majority of solar energy enters our climate system.

So the IPCC claim of linearity, of the imagined slavish response of surface temperature to a given change in TOA forcing, goes against our daily experience.

Let me now return to the question I posed earlier. I asked above what struck you as odd about the IPCC explanation of their claim of linearity regarding forcing and temperature. It’s not the fact that they think it is linear and I disagree. That is not noteworthy.

Here’s what made me stand back and genuflect in awe of their claims. Perhaps I missed it, but I didn’t see a single word about real world observations in that entire (and most important) justification for one of their core positions.

I didn’t see anyone referenced who said something like ‘We measured solar radiation and downwelling longwave radiation and temperature at this location, and guess what? Temperatures changed linearly with the changes in radiation.’ I didn’t see anything at all like that, you know, actual scientific observations that support linearity.

Instead, their claim seems to rest on the studies showing that scientists looked at four different climate models, and in each and every one of the models the temperature change was linearly related to forcing changes. And in addition, another model found the same thing, so the issue is settled to a “high confidence” …

I gotta confess, that wasn’t the first time I’ve walked away from the IPCC Report shaking my head, but that one deserves some kind of prize or award for sheer audacity of their logic. Not a prize for the fact that they think the relationship is linear when Nature nature hates straight lines, that’s understandable, it’s the IPCC after all.

It is the logic of their argument that left me stammering.

Of course the model results are linear. The models are linear. They don’t contain non-linear mechanisms. And of course, if you look at the results of linear models, you will conclude with “high confidence” that there is a linear relationship between forcing and temperature. They looked into five of them, and case closed.

I mean, you really gotta admire these guys. They are so far into their models that they actually are using the linearity of the model results to justify the assumption of linearity embodied in those same models … breathtaking.

I mean, I approve of people pulling themselves up by their own bootstraps, but that was too twisted for me. The circularity of their logic made my neck ache. I kept looking over my shoulder to see if the other end of their syllogism was circling behind to strike me again. That’s why I genuflected in awe. I was overcome by the sheer beauty of using a circular argument to claim that Nature moves in straight lines … those guys are artists.

Meanwhile, back in the real world, almost no such linear relationships exist. Nature constantly runs at the edge of turbulence, with no linearity in sight. As my example above shows, the climate sensitivity changes with the temperature.

And even that change in tropical climate sensitivity with temperature is not linear. It has two distinct thresholds. One is at the temperature where the cumulus start to form. The other is at the slightly higher temperature where the thunderstorms start to form. At each of these thresholds there is an abrupt change in the climate sensitivity. It is nowhere near linear.

Like other natural flow systems, the climate is constantly restructuring to run “as fast as it can.” In other words, it runs at the edge of turbulence, “up against the stops” for any given combination of conditions. In the case of the tropics, the “stops” that prevents overheating is the rapid proliferation of thunderstorms. These form rapidly in response to only a slight temperature rise above the temperature threshold where the first thunderstorm forms. Above that threshold, most of any increase in the incoming energy is being evaporated and used to pump massive amounts of warm air through protected tubes to the upper troposphere, cooling the surface. Above the thunderstorm threshold temperature, little additional radiation energy goes into warming the surface. It goes into evaporation and vertical movement. This means that the climate sensitivity is near zero.

Now it is tempting to argue that the IPCC linearity claim is true because it only applies to a global average temperature. The IPCC only formally say that there is “a linear relationship between global mean RF [radiative forcing] and global mean surface temperature response.” So it might be argued that the relationship is linear for the global average situation.

But the average of non-linear data is almost always non-linear. Since daily forcing and temperature vary non-linearly, there is no reason to think that real-world global averages vary linearly. The real-world global average is an average of days during which climate sensitivity varies with temperature. And the average of such temperature-sensitive records is perforce temperature sensitive itself. No way around it.

The IPCC argument, that temperature is linearly related to forcing, is at the heart of their claims and their models. I have shown elsewhere that in other complex systems, such an assumed linearity of forcing and response does not exist.

Given the centrality of the claim to their results and to the very models themselves, I think that something more than ‘we found linearity in every model we examined” is necessary to substantiate this most important claim of linearity. And given the general lack of linearity in complex natural systems, I would say that their claim of linearity is an extraordinary claim that requires extraordinary evidence.

At a minimum, I think we can say with “high confidence” that it is a claim that requires something more weighty than ‘the models told me so’ ...