A multi-modal probability distribution, such as the graphic below [from Schmittner 2011], cries out “MULTIPLE POPULATIONS”. Equilibrium Climate Sensitivity (expected temperature increase due to a doubling of CO2 levels, all else being equal) is distinctly different for Land and Ocean, with two peaks for Land (L1 and L2) and five peaks for Ocean (O1, O2, O3, O4, and O5).
When a probability distribution includes more than one population, the mean may, quite literally, have no MEANing! All bets are off.
Example of a Multi-Modal Distribution
According to the basic tenets of System Science (my PhD area) probability distributions that inadvertently mix multiple populations often lead to un-reliable conclusions. Here is an easy to understand example of how a multi-modal distribution leads to ridiculous results.
Say we graphed the heights of a group of infants and their mothers. We’d get a peak at, say 25″, representing the average height of the infants, and another at, say 65″, representing the mothers. The mean of that multi-modal distribution, 45″, would represent neither the mothers nor the infants – not a single baby nor mother would be 45″ tall!
If some “alien scientist” re-measured the heights of the cohort of children and their mothers over a decade, the mean would increase rapidly, perhaps from 45″ to 60″. If that “alien scientist” did not understand multi-modal distributions representing different populations, he or she might extrapolate and predict that, a decade hence, the mean would be 75″! Of course, actual measurements over a second decade, as the children reached their adult heights, would have a mean that would stabilize closer to 66″ (assuming about half the children were male). The “alien scientist’s” extrapolation would be as wrong as some IPCC predictions seem to be.
Implications of Multi-Modal CO2 Sensitivity
The [graph shown above], considering both land and ocean reconstructions, is multi-modal and displays a broad maximum with a double peak between 2 and 2.6 K [1 K = 1ºC], smaller local maxima around 2.8 K and 1.3 K and vanishing probabilities below 1 K and above 3.2 K. The distribution has its mean and median at 2.2 K and 2.3 K, respectively and its 66% and 90% cumulative probability intervals are 1.7–2.6 K, and 1.4–2.8 K, respectively. [my emphasis]
The caption for the graphic says:
Marginal posterior probability distributions for ECS2xC. Upper: estimated from land and ocean, land only, and ocean only temperature reconstructions using the standard assumptions (1 × dust, 0 × wind stress, 1 × sea level correction of ΔSSTSL = 0.32 K…). Lower: estimated under alternate assumptions about dust forcing, wind stress, and ΔSSTSL using land and ocean data.
So part of the cause of multi-modality is due to different sensitivity to dust, wind, and sea surface temperatures for the combined Ocean and Land data, and part due to differences between Ocean and Land. But, that is only part of the story. Please read on for how Geographic Zones seem to have different sensitivities.
Geographic Zones Have Different Sensitivities
Another Schmittner 2011 graphic, shown below, indicates how different the Arctic, North Temperate, Tropics, South Temperate, and Antarctic zones are. Indeed, there is a startling difference between the Arctic and Antarctic.
The thick black line represents the “climate reconstruction” (change in temperature in ºC) between current conditions and those of about 20,000 years ago during the Last Glacial Maximum. The LGM was the coldest period in the history of the Earth in the past 100,000 years. Note that the Tropics were about 2ºC cooler than they are now, the South Temperate zone was about 3ºC cooler, the North Temperate zone about 4ºC cooler, and the Antarctic about 8ºC cooler. However, according to the climate reconstruction, the Arctic was about 1ºC WARMER than it is today!
The estimated CO2 level during the LGM is 185 ppm, quite a bit below the estimated Pre-Industrial level of about 280 ppm, and about half that of the current measured level of about 390 ppm. Thus, IF CO2 DOUBLING CAUSED ALL of the temperature increase from the LGM to the present, the sensitivity for the geographic zones would range from +8ºC (Antarctic) to +4ºC (South Temperate) to +3ºC (North Temperate) to +2ºC (Tropics) to -1ºC (Arctic).
Of course, based on the Ice Core temperature records for several ice ages over the past 400,000 years, the warming 20,000 years after a Glacial Maximum tends to be significant (several degrees). Thus, while increases in CO2, all else being equal, do cause some increase in mean temperatures, it is clear from the Ice Core record, where temperature changes lead CO2 changes by from 800 to 1200 years, that something else causes the temperature to change and then the temperature change causes CO2 to change. Thus, it would be wrong, IMHO, to assign more than some small fraction of the warming since the LGM to CO2 increases.
The colored lines in the above graphic correspond to modeled temperatures based on different assumed CO2 sensitivities, ranging from 0.3ºC to +8.4ºC. The darker blue line, corresponding to a sensitivity of 2.3ºC, is the best match for the thick black climate reconstruction line.
IPCC CO2 Sensitivities are Mono-Modal and have “Fat Tails”
So, how do the IPCC AR4 Figure 9.20 graphs of Equilibrium Climate Sensitivity compare to the Schmittner 2011 results? Not too well, as the graphic below indicates!
First of all, notice that NONE of the individual IPCC graphs are multi-modal! Yet, taken as a group, there are several distinct peaks, indicating that each of the researchers characterized only one of a number of multi-modal peaks, and were inadvertently (or purposely?) blind to the other populations. Thus, the IPCC curves, taken as a group, seem to support Schmittner’s results of multi-modality.
For example, compare the green curve (Andronova 01) to the red curve (Forest 06). They hardly overlap, indicating that they have sampled different populations.
There is another, less obvious problem with the IPCC curves. Notice that they each have a relatively “normal” tail on the left and what is called a “Fat Tail” on the right. What does that mean? Well, a “normal curve” has a single peak, representing both the mode and the mean, and two “normal” tails that approach zero at about +/- 3ơ (Greek letter sigma, representing standard deviation). A mono-modal curve may skew to the left or right a bit, which would put the mode (peak) to the left or right of the mean.
The problem with the IPCC curves is that, in addition to the skew, the right-hand tail extends quite far to the right, out to 10ºC and beyond, before approaching zero. According to Schmittner 2011:
…High sensitivity models (ECS2xC > 6.3 K) show a runaway effect resulting in a completely ice-covered planet. Once snow and ice cover reach a critical latitude, the positive ice-albedo feedback is larger than the negative feedback due to reduced longwave radiation (Planck feedback), triggering an irreversible transition … During the LGM Earth was covered by more ice and snow than it is today, but continental ice sheets did not extend equatorward of ~40°N/S, and the tropics and subtropics were ice free except at high altitudes. Our model thus suggests that large climate sensitivities (ECS2xC > 6 K) cannot be reconciled with paleoclimatic and geologic evidence, and hence should be assigned near-zero probability….[my emphasis]
Based on the above argument, I have annotated the IPCC figure to “X-out” the Fat Tails beyond 6°C. I did that because any sensitivity greater than 6°C would retrodict a “total snowball Earth” at the LGM which contradicts clear evidence that the ice sheets did not extend equatorward beyond the middle of the USA or corresponding latitudes in Europe, Asia, South America, or Africa. Indeed, if Schmittner is correct, the tails of the IPCC graphs that extend beyond 5°C (or perhaps even 4°C) should approach zero probability.
Schmittner 2011 contradicts the IPCC climate sensitivity estimates and thus brings into question all IPCC temperature predictions due to human-caused CO2 increases.
It is clear from the several, widely-spaced peaks in the IPCC AR4 Figure 9.20 curves that Equilibrium Climate Sensitivity is indeed multi-modal. Yet, ALL the individual curves are mono-modal. Thus, the IPCC figure is, on its face, self-contradictory.
If Schmittner 2011 is correct that sensitivity beyond about 6°C is impossible based on the fact that Tropical and Sub-Tropical zones were not ice-covered during the LGM, the Fat Tails of all the IPCC Equilibrium Climate Sensitivity curves are wrong. That calls into question each and every one of those curves.
The multi-modal nature of CO2 sensitivity indicates that the effects of CO2 levels are quite different between geographic zones as well as between Ocean and Land. Thus, the very concept of a whole-Earth Equilibrium Climate Sensitivity based on a doubling of CO2 levels may be misplaced.
Finally, if CO2 is as strong a driver of surface temperatures as the IPCC would have us believe, how in the world can anyone explain the apparent fact that, given a doubling of CO2 levels, the modern Arctic is about 1°C COLDER than the LGM Arctic?
BOTTOM LINE: The Climate System is multi-faceted and extraordinarily complex. Even the most competent Climate Scientists, with the best and purest of intentions are rather like the blind men trying to characterize and understand the elephant. (One happens upon the elephant’s leg and proclaims “the elephant is like a tree”. Another happens to grab the tail and says with equal certainty “the elephant is like a snake”. The third bumps into the side of the elephant and confidently shouts “No, the elephant is like a wall!”) Each in his or her way is correct, but none can really understand all the aspects nor characterize or predict the behavior of the actual Climate System. And, sadly, not all Climate Scientists are competent, and some have impure intentions.