A Note on the 50-50 Attribution Argument between Judith Curry and Gavin Schmidt

Yeah, db, a point that I, and Lindzen, and many others have tried to emphasize in discussion. You can actually take HADCRUT4 from the first half of the 20th century and the second half of the 20th century and put them side by side on similar scales but with the time scale hidden and ask which graph occurred with the help of anthropogenic CO_2? Not so easy to tell, unless you are aware of the individual features such as the terminating super-ENSO in the late 20th century. I sometimes think that the last round of tampering in the GISS anomaly was designed as much to erase this similarity and as much of the pause as possible without quite making it laughable compared to LTT. But that game is up — there will be no more adjustments of GISS or HADCRUT4 to further warm the present as they are now UAH/RSS constrained.
That hasn’t stopped them from trying to further cool the past, and now newcomers are appearing that re-krige and infill and homogenize areas that “haven’t shown enough warming” because they are less constrained by LTT; this further obfuscates if nothing else. HADCRUT4 — and earlier versions of HADCRUT even more — clearly give the lie to the assertion of “unprecedented” warming, though, in precisely this graph (which anybody can make, BTW, at least piecewise on woodfortrees).
However, even this graph omits the display of or discussion of two critical problems with assertions of warming or cooling or plain old knowledge of temperature.
The first and most glaring omission is the absence of any error bar or estimate on the data. This is insane! In what other field of human endeavor are so many data-derived graphs shown to so many people utterly devoid of error estimates? Note the obvious impact of error visible in the Jones curve. Does Jones, or anyone else, really think that the global average surface temperature anomaly was 10 times more volatile in the 1800’s, with the planet warming by 0.6C over as little as a year and then plunging down into 0.6C of cooling relative to some ill-defined mean in a year more? Because that’s what the error-bar free data shows.
Of course not! What the graph is showing is the impact of the sparseness of the record in the 19th century. With order of 10x as much variance, there is order of 100x less data contributing in the 19th century compared to the present. In the 19th century most of the Earth’s surface area was completely unsampled (I mean “most” literally — 70% of the surface that is ocean, the bulk of at least 3 or 4 continents were either terra incognita altogether, e.g. Antarctica, or barely penetrated by a thermometer — if you will excuse the image — and consider the Amazon, central Africa, much of Siberia and central Asia, Tibet, even much of the U.S.). The parts that were sampled were obviously quite volatile — one imagines that the bulk of what is producing these large variations were things like heat waves in Europe.
The variance quiets quite a lot when the colonial gold rush really gets underway in the 1880s and colonials carry thermometers with them to their newly annexed territories. The ocean remained a problem then, and remains a huge problem now with ARGO pitifully undersampling 70% of the Earth’s surface even today, and that in a highly biased fashion with buoys that float with thermohaline currents or are trapped in eddies (both unlikely to reflect their surrounding environment adequately) rather than be distributed according to a simple random number generator in Monte Carlo style (which would have a computable statistical error instead of an unknown bias). There is a surprising amount of variance for a global temperature anomaly today, but at least between the thermometric record and the LTT satellite record, we can think about resolving features of the presumably much less volatile actual anomaly from the statistical noise, by comparing the various “modelled” average temperatures. The error is almost certainly larger than the difference between, say, GISS and HADCRUT4 or Cowtan and Way, and at present these numbers are easily 0.2C or thereabouts apart much of the time.
HADCRUT4 acknowledges — IIRC — 0.15C of error in the present. I think this is an underestimate but let’s go with it, as the existence of the number we hope means that they actually computed it instead of pulled it out of their nether regions, as were the error estimates on graphs in the leaked early AR5 draft (figure 1.4?), which were obviously created by a graphical artist and not by anything like an algorithm. The scaling of the variance then suggests that the error estimate in the mid-1880s ought to be a whopping 1.5C — the eye suggests that a more modest 0.4 C error bar might encapsulate 60% of the data such as it is, but that is really the error for the sampled territories only and is a lower bound on the error estimate for global temperature. I’d suggest that 0.7C is a compromise — one can probably find proxies (with their own error and resolution problems) that that constrain the error to be less than 1 C. This statistical — not systematic — error would then systematically, but slowly, shrink from then to now. It wouldn’t really be linear — as I said, there is a relatively rapid diminishment in the late 19th century followed by a slower decrease into the late 20th, but it is likely fair to say that it is at least 0.3 to 0.4C for most of the record prior to the satellite era and ARGO, as only these have made it possible to push it down to ballpark of 0.2C.
If one includes the error estimate on the graphs, our certainty of any particular thermal history substantially diminishes. Maybe it warmed since the mid-1800’s. Maybe it has cooled. Maybe it warmed a lot more. Maybe the single 20 year period in the late 20th century when warming occurred has the steepest slope in the thermometric record, or — most importantly — maybe it does not! That’s the big statistical lie even in Jones relatively honest portrayal of the HADCRUT4 trends above. If one actually fit the data, with errors, and used e.g. a measure like Pearson’s to estimate the robustness of the linear trend, how likely it is that the slope is actually much larger or smaller than the simple regression fit, I promise that in the leftmost chord of the data we have almost no friggin’ idea what the linear temperature trend really was beyond “probably positive” (that is, maybe it is or something like that), that in the second chord we can probably say that it — again guestimating since I don’t have the data and cannot do a better analysis — , and that only the last push is known reasonably accurately at .
In other words, it could have warmed faster in either the mid-1800s or the early 1900s than it warmed in the late 1900s. It isn’t even improbable. It is even odds that one or the other of these warming trends was larger than the best fit slope, and 25% of the time they would both be larger, and larger by just a bit is enough to confound the assertion that the more strongly constrained third linear trend is the largest.
So much for “unprecedented warming” or the necessity for CO_2 forcing as an explanatory mechanism for warming at the rates in Jones’ figure above.
The second problem is that we are left with a profound paradox in all discussions of global average surface temperature. Even NASA GISS acknowledges that we have very little idea what it is. It is often given as 288 K, but this obscures the simple fact that no two models for computing it, working from the same or largely overlapping surface data, get numbers that are within half a degree of one another! Or even a degree. The most honest way to present the number might be K. Or K. It’s hard to say, and depends on who is doing the averaging and with what model for kriging, infilling, homogenizing, and dealing with error. It is also impossible to generate a proper estimate for the probable error including all sources, because what one can estimate is only the range of values produced by the models, which is (again) a strict lower bound in any honest error estimate. Since the models tend to share data sources they are hardly independent, and yet there is a spread of more than a degree in their average. Statistics 101 — the variance of sample means drawn from overlapping populations is too small because the number of independent and identically distributed samples is smaller than the number of samples that produced the variance.
To fix this is enormously difficult and requires some pretty serious statistical mojo. Indeed, it would probably be simplest to fix via Monte Carlo and just plain sampling — generate a simulated smooth temperature field with the “approximately correct” surface temperature moments, pull samples at the overlapping locations and feed them into the different models, determining both the distribution of the absolute error of the models (per model) given the data compared to the precisely known average temperature, as well how that variance compares to the multimodel variance with overlapping samples. This might then provide some sort of quantitative basis for determining the actual probable absolute global average surface temperature — note well not the anomaly — as well as a probable error estimate that has a quantitative basis (subject to various assumptions, but given time we could even investigate the effect of varying those assumptions).
In the meantime, we persist in the belief that we can measure and compute the anomaly in global average surface temperature almost an order of magnitude more precisely than we can compute the average surface temperature itself. In most systems, susceptibilities (effectively, the anomaly) are second moments and their error estimates are fourth moments of the underlying distribution — the variance of the variance, so to speak. We generally know the higher order cumulants of a distribution less accurately than we know the mean/first order. This isn’t always true, of course — sometimes what we measure is a deviation, not the absolute — but thermometers don’t measure deviations from an unknown or poorly known mean, they measure temperature, the absolute quantity in question. The argument is that if there is a systematic bias in the trend of each contributing thermometer (say, we have 100 thermometers at different places, all perfectly accurate, and if 40 of them show warming of 1 degree, 20 of them show no change, and 30 of them show cooling of 1 degree, then we can conclude that there has been a statistically significant systematic trend in the anomaly of (40 – 30 =10)/100 = 0.1 C even if, when we compute the actual statistical mean and standard error of the temperatures measured by those thermometers over whatever spatial region they are sampling, the error is 1C!
This isn’t impossible, of course. We can certainly imagine systems where we could reliably measure the anomaly accurately but the mean inaccurately, the simplest one being that all of the thermometers themselves were perfectly accurate, but that a demented child scribed the scales on the side so that the supposed “zero” of the all of the thermometers was randomly distributed on some wide range. Each thermometer would then precisely record deltas/displacements, but the origin of their coordinates would be a random variable. But is that a reasonable assumption for the thermometric record? It seems equally plausible (for example) that the glass bore of (say) a mercury thermometer and the actual volume of the mercury in the thermometer are random variables, but that the person who zero’d the thermometer scale was an obsessive compulsive. In that case the absolute measurement of the thermometer might be very accurate, at least when it was made at temperatures close to the reference temperature used to set the scale, but the anomaly might have a bias that might, or might not, be randomly distributed.
This problem has hardly gone away now. Anthony has actually tested supposed accurate electronic thermometers in personal weather station kits obtained (for example) from China and found that they experience substantial absolute error and time dependent drift. Now and in the past, even a thermometer that was precisely made, and carefully zero’d and scaled with respect to multiple reference temperatures so that it worked perfectly the first day it was hung up in a weather station could easily experience a systematic, and biased, drift over a decade or five of usage. Spring thermometers gradually anneal and become less springy. Liquid thermometers outgas and deform. We assume that things remain the same over long times because we can’t see them moving, but they don’t.
Throw in biases recorded in weather station metadata, throw in all of the occult, slow biases not recoverable from any sort of metadata — a tree line that slowly grows over time, the UHI effect as a station that was initially rural finds itself in the middle of a prosperous concrete jungle, throw in unrecorded and variable idiosyncracies of the humans who performed the measurements as they changed over the decades, and you have substantial variance not only in the absolute temperatures any given thermometer might measure, but in the trend, in the anomaly. And some of those biases might well be slow, systematic, unrecorded and virtually impossible to retroactively correct for.
Again, we could probably learn quite a bit from simulations of the models used to compute the anomalies, by simply generating an (ensemble of) simulated smooth temperatures on the surface of a sphere with a given, known time variation that has or doesn’t have any given trend. Sample it, and add noise to the samples, both white unbiased noise and trended noise that might (for example) model the UHI on urban stations, or delta correlated shifts that might occur when station personnel changes, or trended noise that might represent various distributions of slow non-UHI environmental shifts — conversion of surrounding countryside from forest to pasture, the building of impoundments that transform small rivers into vast lakes (this has happened, for example, in the immediate vicinity of RDU airport, the source of our “official” temperature — Falls Lake and Lake Jordan are between them tens of thousands of acres and flank the airport, adding yet another confounding factor between comparing temperatures before the early 80’s to temperatures afterwards at this site). Where is that accounted for in the site metadata?
Who even knows what sort of effect turning a mix of forest and human occupied farmland into 60 or 70 thousand acres’ worth reservoirs might have on the surrounding temperatures and “climate”, at the same time that the weather station itself went from being a tiny regional airport to being a hub for a large commercial carrier, at the same time the surrounding farmland turned into one giant suburban and urban mega-community? We don’t know, of course — and not even BEST can account for or correct for this — but we might, perhaps, simulate some range of the possibilities and see what they do not to the anomaly itself — per model, it is what it is — but to the best estimate for the uncertainty in the anomaly when any give model ignores a source of potential systematic bias. As (apparently) HADCRUT4 does when they do not correct for UHI at all, however eager they are to cool the past or warm the present in other ways.
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This kind of graph not only shows no relation to CO2 (human or “natural”) it also shows that the main driver(s) must be something cyclic. Yet it was only very recently that the PDO and AMO were identified and we don’t appear to fully understand either.