Historical Note: Greenwich, England Mean Temperature, 35-yr Daily Averages 1815-1849

If +/- 1 °C is an “acceptable expected error” for a surface station, then isn’t the estimated global warming over the past century of 0.8 degrees within the margin of error?
No. Imagine measuring the heights of all of the students in a school with a meter stick. Let’s further imagine that you are a sloppy measurer and your measurements are only accurate within +/- 1 cm, but that your measurements are unbiased, that is, that you are as likely to err 1 cm (or less) up as 1 cm (or less) down. If the school has (say) 1000 students in it, the individual measurement errors will cancel in the mean, leaving you with a measurement-based error in the mean much smaller than 1 mm.
The problem with temperature measurements are those pesky systematic errors. You are extremely conscientious and always read to the nearest mm or 2. Your friend who is helping you take data is lazy and always rounds down to the nearest cm, never up, and he is only measuring the elementary school students so all low measurements are exaggerated low. Another friend is the opposite — they like to round up, their meter stick is old and has 3mm worn away from the bottom end, and they are measuring the basketball team (who all come out a full cm too tall, on average. Because of the power of averaging, rather than measure every student in all of the classes, people measure the height of just three students from some of the classes, and then extrapolate the measurements across (say) the interval from second grade to tenth grade where sadly, no one thought to measure at all.
The bulk of the error in the thermometric record is from precisely this sort of thing. For a stupendous stretch in it, we have almost no truly useful measurements for the 70% of the Earth’s surface covered by ocean (John Daly IIRC uncovered some truly horrendous sources of systematic error in the way oceangoing ships sampled sea surface temperatures — when they bothered to do it at all — along the principle shipping lanes, which constitute a tiny fraction of the whole ocean anyway). We have no useful coverage of whole continent-sized areas — Antarctica, central Australia, much of Africa, much of South America, and a good sized chunk of Asia were basically outside of the pale of instrumental civilization throughout the 19th and well into the 20th century, and when they did start to be sampled in the 20th century it was at a few well-defined urban locations that were both accessible and that had a relatively benign climate, not out in the wilds. “The wilds” are still horrendously undersampled and biased in their measurement even in the modern world by all means except satellite, which is one reason I “trust” UAH and RSS far more than I trust GISS or HADCRUT (quite aside from all of the ways the remote past data gets “adjusted” to presumably correct for all of these errors ON TOP of the substantial extrapolation errors introduced by using measurements in a few locations on the periphery of e.g. the Tibetan Plateau or the coast of Antarctica to infer temperatures for millions of square kilometers in a weighted average global surface temperature estimate.
This is one of the things Lief is struggling to correct in the sunspot record. Even though “the rules” for recording sunspot counts have been consistently enough stated, even though the instrumentation used was unchanged or little changed over very long stretches of time, individual recorders ended up “counting” spots slightly differently over decadal stretches (representing an entire career as an observer), plus noticeable changes as instrumentation quality discretely improved. These biases are (apparently) enough to completely alter the record, to create grand maxima where none really occurred, to exaggerate grand minima. Or are they? In the case of sunspots, it is comparatively easy to check as people recorded sketches at first and later photographs of the sun’s surface for at least a fair number of days of the record, so one can try to second guess their counts against a modern “standard” and use this plus statistical analysis to try to come up with a systematic correction per observer (to the extent that even an observer’s measurement bias is stationary in time — it probably isn’t).
I am a theoretical/computational physicist, and hence I get to deal with very systematic, typically unbiased error in e.g. Monte Carlo (where the biggest source of systematic bias are things like roundoff errors or biases in the random number generator used and hence managable although there are famous cases of either or both leading to complete garbage in long running computations). However, I work with friends who do experimental physics on e.g. the free electron laser or various accelerators or with ordinary lasers, and they have a hell of a time dealing with errors of all sorts in the analysis of their experimental data. Detectors often have a systematic bias, instrumentation in general has both systematic and random errors, human error creeps in everywhere, and nobody knows what all of the errors are in a complex measurement system and often there is literally no way to measure or infer the error from observation — it is what it is.
If all you’ve got is a meter stick with a worn end, all of your measurements will be a few millimeters long but you’ll never know it unless/until you have some “gold standard” meter stick you can measure to compare to. It’s great when you do — and of course in the case of actual meters we can define them with great precision — but with thermometers it isn’t so easy.
Both the Fahrenheit and Celsius thermometers are defined in terms of well-defined thermodynamic equilibrium points — a water/ice mixture, the boiling point of water, for example — with a fixed degree size in between and past both ends. However any actual thermometer’s accuracy depends on things like how precisely a hole can be drawn through glass, how precisely a bulb can be attached to the class with how precise an amount of e.g. mercury inside, how precisely the tube can be etched with a linear scale, how much the volume of the glass changes with temperature (noting that as the glass changes volume, so does the volume of the hole in the glass and hence the linear scale becomes nonlinear), and of course the fact that no material has a precisely linear thermal expansion coefficient so that in order to make a really precise mercury thermometer one has use nonlinear degree sizes. One even has a no-free-lunch element in their design — a very narrow hole makes comparatively large degree sizes (improving precision on the grid) but at the expense of increasing the nonlinear errors and increasing the engineering difficulty of building it in the first place. And at the end of the day, the thermometer is read for decades by a tall human who looks down on the instrument while reading it so that he always reads the meniscus of the mercury too high on the grid by 0.3C, to be replaced by a human who is shorter and reads the same instrument at eye level.
It is very difficult to repair these measurement problems a century after the fact. As I said, my experimentalist friends have a difficult time either repairing or accounting for them all now, with the most modern of electronic instrumentation — how can one detect a problem with one’s measurement apparatus, after all? Many problems only arise transiently and are entirely absent when calibrating the instrumentation but appear only during actual measurement. Notably when the research professor does the calibrating using 20 years of experience and the greatest of care, but Joe the graduate student who likes to smoke reefer during his lunch break does the boring, repetitive measurements over two years of his life, infilling a bit of data missed because he zones out using from the day before with what he imagines to be “random” noise so nobody will ever know (humans, BTW, make terrible random number generators).
Records like the one above are indeed useful, because at least it represents a record that is minimally contaminated by this sort of thing. The instrumentation was good, I’m guessing it was periodically checked and recalibrated, observations were made very systematically with respect to location and time, careful records were kept, and averages consistently evaluated. It is difficult for me to tell from the chart exactly how the “daily average” temperature was computed — there are enormously different ways, depending on how the temperature was sampled — but with luck the method used was carefully described in the text.
Much has been made of resolution error on this list. It is very difficult to compare data with different spatiotemporal resolution. Casual electronic weather stations costing around a few hundred dollars and located in people’s back yards, that use wireless to update a computer with instantaneous temperature, wind speed and direction, humidity, barometric pressure, and cumulative rainfall, are now commonplace and their processed data can be readily accessed on the internet via e.g. the Weather Underground. Any of these stations is probably more precise than anything ever used back in the 19th or almost all of the 20th century even by professionals, and they are no more likely to be badly sited than any of the professional sites from Anthony’s direct observations. Their temporal resolution is astounding — one can actually create a credible true average temperature reading on a daily basis, if one can agree on what to call “a day” (is it midnight to midnight? noon to noon? 6 am to 6 am?) in the specific sense of summing (say) 1440 minute-grid measurements and dividing by 1440. It is rather certain that a record averaged in this way can in no way be compared to the “average” displayed in the chart in the top article, which is far more likely to average the max/min per day for the daily number, or perhaps (if they were willing to pay warm bodies to watch the thermometer all day and all night) hourly measurements. There is no way in hell they recorded temperatures minute by minute, though, as they’d fill paper books with the longhand-written data and they’d have needed multiple observers capable of doing a completely mind-numbing task perfectly for decades for 1440 measurements a day just to avoid huge gaps when somebody has to go to the bathroom.
And really, there is little to stop modern weather stations from returning data a time granularity of 1 second, or even less. I’m guessing that the latch time on the analog to digital converters, plus the time needed for some electronic processing and the transmission of the actual packet, are the rate limiting factors and those could probably run at a granularity of 0.01 seconds or thereabouts, maybe even faster.
The weather underground personal weather stations provide a stupendous resource for those seeking to understand things like the UHI. For one thing, they actually sample a (not really random, but “randomer”) field of locations with a spatial resolution of less than 10 km in many locations (e.g. around Durham where I live). For example:
http://www.wunderground.com/wundermap/?lat=35.979&lon=-78.966&zoom=13
I live almost exactly halfway between station 51 and the 1717 tag, right up against Duke Forest (the shaded green). Urban Durham is on the right side of the map, and the left side is dominated by rural/suburban neighborhoods mixed in with farmland and forest. Station 51 is terribly sited (I’ve written about it before) and consistently reads 1-2 degrees too hot (I’m guessing it is sitting right above their driveway or air conditioning unit on the southwest side of the house). I use unit 50, located in a field next to Duke Forest at Durham Academy about a mile from my house. It reads very close to what I read in my back yard without a PWS. All of the stations shown are substantially corrupted by UHI, and are located at different heights in the hilly piedmont. I’ve watched temperatures vary (drop) by as much as 3 C just driving from the physics building inside Duke proper (heavily paved and covered with buildings and up on a hill of sorts) down hill, around a corner into Duke Forest, down hill further to a creek, up a hill, and then down a hill into my neighborhood to my house — a total distance of maybe 3 km. They vary by 1-2 C from the front (SW facing, exposed on a hill that amplifies the solar heating of yard and especially driveway) of my house to the back (NE, with tall cypresses maintaining both shade and blocking the wind).
It would be utterly fascinating to actually do a systematic study and put a dense grid of PWS units on a roughly 1 km grid with microlocation determined by a monte carlo process (to avoid biasing the location to always be someplace easy for humans to get to). I’ll bet that the area around Durham has an entire thermal profile as one goes up hills and down hills into microclimates that differ by 1-5 C in their mean temperature, systematically warming as one goes into Durham from the surrounding countryside on top of any geographical factors. UHI isn’t a simple correction — in fact, trying to correct for it in the absence of this sort of systematic study is probably impossible.
To conclude, while plus or minus one degree accuracy in measurements doesn’t mean that averages will be that inaccurate, even instrumentation capable of much greater precision can still be even more inaccurate, and can be inaccurate in systematic ways that do not cancel in the mean. One cannot fairly compare data taken at different spatiotemporal resolution — low frequency measurements erase fluctuations that may or may not be themselves biased or that may or may not bias high frequency measurements relative to the low frequency measurements. One cannot easily “correct” the past temperature record or compare it to the present. And one day, I will talk about the dubious nature of treating the “anomaly” as if it were something that is known more precisely than the raw number across instrumentation and decades of time.
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