Robert Balic writes:
I recently read the Willis Eschenbach article Argo, Temperature, and OHC (http://wattsupwiththat.com/2014/03/02/argo-temperature-and-ohc/) which reported the trend in the global ocean temperatures as 0.022 ± 0.002 deg C /decade and Steven Casey asked
“Can we believe we have that much precision to 0.002 deg C/decade? And we have not yet measured a full decade.”
Also, there was a reply to a comment of mine on The Conversation mentioning the uncertainty which stated “The temperatures in the Argo profiles are accurate to ± 0.005°C http://www.argo.ucsd.edu/FAQ.html#accurate“.
I checked the website http://www.argo.ucsd.edu/How_Argo_floats.html and found that
“The SBE temperature/salinity sensor suites is now used almost exclusively. In the beginning, the FSI sensor was also used. The temperature data are accurate to a few millidegrees over the float lifetime,” and “The temperatures in the Argo profiles are accurate to ± 0.002°C”.
The temperature profiles might be accurate to ± 0.002°C now, but weren’t the measurements made to the nearest 0.1°C previously? I looked up the accuracy of their thermistors earlier this year and it was written as 0.1°C. A high precision commercial instrument usually has a claimed ± 0.05°C accuracy so they most likely did record to the nearest 0.1°C until they installed the new units. They can’t now insist that the smaller error in the previous trend remains uncorrected because they have new instruments this year.
Why is it relevant that the temperature measurements were taken to the nearest 0.1°C if they looked at the average of over 100 measurements? Well if you take my height for example and measure me to the nearest centimeter 100 times, then the average would probably come out to be 183cm with a standard deviation of 0. Perfect!
If you had recorded my height to the nearest millimeter having taken 50 measurements of 1825mm and 50 measurements of 1835mm, you would get an average of 1830mm with a standard deviation of 5mm or 0.5cm. A random spread of measurements over that range would bring the SD down to about a quarter of a centimeter and the error estimate is usually twice this value.
The rule of thumb that I was once taught is that your minimum error is plus or minus the value of the increment that the measurements were made with (eg. 1 cm) where the number of measurements are a few, or half this value when there are a large number of measurements (eg.± 0.5cm). So if the Argo floats only measured in increments of 0.1°C then the uncertainty in the mean of many measurements is at least ± 0.05°C. Hence, a trend of 0.02°C/decade measured over less than a decade is utterly meaningless.
Someone should also have a word in the ears of those at The University of Washington.
“Because total Arctic sea ice volume from PIOMAS is computed as an average over many grid points, the random error (scatter in above figures) doesn’t affect the uncertainty in the total ice volume and trend very much.”
This is the excuse to ignore the large errors implied by this plot.
![Fig2[1]](https://wattsupwiththat.files.wordpress.com/2014/10/fig21.png?quality=75)
Where the model predicts a 4m thickness the submarine data is spread evenly between 2.5 and 6 m. The range is nearly 0 to almost 3.5m where the estimate from the model is 1m, that is over 100% uncertainty in the thickness yet they are absolutely sure that the ice is in a death spiral.
Several folks have pointed out the fallacy of equating measuring the same thing many time with measuring many different things once each; then averaging.
Less obvious is the fact that an average of temperatures is not in any way a temperature. Just isn’t. So those Global Average Temperatures (air or water) are no such thing. The trends in them are NOT the trends in temperatures. They are only the trends in an average of a bunch of “stuff”, from denity changes to entrophy changes to precipitation effects to intrument drift to….
Temperature is an intrinsic property. As such, it can only be specific to a single thing, and an average of temperatures is void of meaning AS a temperature. (Since the needed specific heat, mass, phase change, etc. are all missing…)
http://chiefio.wordpress.com/2011/07/01/intrinsic-extrinsic-intensive-extensive/
The whole charade of using an average of temperatures is a lie on the face of it.
The author raises a very interesting and complex question, often neglected, overlooked, whitewashed over, and simply ignored in modern scientific endeavor. I’m not sure that he states it very clearly but the problem is roughly defined as “What to do about original measurement error?” and a follow-on question: “Do our mathematical results showing effects smaller than original measurement error actually mean anything at all?”
It is perfectly clear that the math is correct — all that division and averaging and probabilities, etc. [Almost] No one disputes that.
The claim/belief that measurement error always averages out thus we can ignore it in the end is a very dubious proposition. Claiming very precise accuracy over imprecise original measurement is simply a trick of mathematics.
A carpenters example goes something like this: One is building a house and needs 2x4s precisely 8 feet long for the walls. A supplier is offering 8 ft 2x4s at a steep discount — and guarantees accurate length to 1/8th of an inch — 0.125 inches — just accurate enough for house carpentry. The carpenter buys a truckload of these 2x4s and finds that they range from 7 1/2 feet to 8 1/2 feet in length — utter useless for his purposes. In the resultant civil lawsuit, the supplier brings in a statistician, who orders measurement of every 2×4 in the lot sold, then proves to the jury that his claim of “accurate length to 0.125 inches” is perfectly statistically correct — even though the original measurement error was +/- 6 inches.
Statistical result of great accuracy are not the same as real world results.
This article is well worth reading.
http://earthobservatory.nasa.gov/Features/OceanCooling/page1.php
here are the money quotes for me:
““I was aware that they were not seeing this huge cooling that we were seeing in the ocean,” says Willis. “In fact, every body was telling me I was wrong. And there were always doubts,” says Willis. “After all, it was a very surprising result. As a scientist, its part of my job to turn over every leaf. So I was constantly going back over the data and looking for problems.””
…
“Basically, I used the sea level data as a bridge to the in situ [ocean-based] data,” explains Willis, comparing them to one another figuring out where they didn’t agree. “First, I identified some new Argo floats that were giving bad data; they were too cool compared to other sources of data during the time period. It wasn’t a large number of floats, but the data were bad enough, so that when I tossed them, most of the cooling went away. But there was still a little bit, so I kept digging and digging.”
…
““So the new Argo data were too cold, and the older XBT data were too warm, and together, they made it seem like the ocean had cooled,” says Willis. The February evening he discovered the mistake, he says, is “burned into my memory.” He was supposed to fly to Colorado that weekend to give a talk on “ocean cooling” to prominent climate researchers. Instead, he’d be talking about how it was all a mistake.”
==============
the other possibility is that Argo and the XBT’s were correct, but because they didn’t match expectations of warming, they were adjusted because “every body was telling me I was wrong”.
In any case, removing floats after the fact is no different than removing tree ring samples because they don’t match thermometers. It is statistically invalid, because the assumption in statistics is that the sample is randomly selected.
As soon as you remove readings you have violated the assumption or random selection and you cannot rely on the statistics to give an accurate result. Formally it is called selection on the dependent variable.
The floats that appear to be running too hot or too cold are telling you that the floats are less accurate than you think. this does not give you license to remove them from the sample and claim that the sample is now more statistically accurate. it is a statistical nonsense.
You say truly. Unless one can demonstrate that a particular data (or data source) is faulty he is guilty of “selection bias if he rejects it. What is true for tree rings is true elsewhere.
In any sample there will always be outliers. floats that appear too hot or too cold. however, you are not allowed to remove them from the sample and then claim the sample is statistically random. And if the sample is not random, then your claim to statistical accuracy if false.
I agree that the article at the top is misleading and makes several mistakes, but the problem he points out is real. There are a few thousand ARGO buoys. We’ve had that many only for a decade or so. Before that we relied on scattered soundings. The ocean being sampled covers 70% of the Earth’s surface, and is not homogeneous.
where 
is the number of independent, identically distributed samples drawn from the distribution.
The issue isn’t just with the putative accuracy of the thermal measurements made by the buoys, although yes, comparing results obtained with an insanely sparse handful of measurements made with comparatively inaccurate instrumentation to the results obtained from an still insanely sparse handful of instruments with much better putative accuracy is problematic. It is with the insanely sparse bit. I very much doubt that I could measure a mean temperature in Durham county from 3000 perfectly accurate thermometers to within millidegrees. If I were to attempt it, I would have to start by eliminating bias. This would involve taking a map of Durham county, using a random number generator to select 3000 specific three dimensional locations in the air volume I’m trying to measure, positioning the thermometers at those locations precisely, making a single measurement at a randomly selected time, and cumulating the results. Oh, and these would have to be magic transparent zero-heat-capacity thermometers that do not change the temperature they measure.
How accurate the result is at reflecting the true average temperature is not, then, determined by the precision of my magic transparent perfectly accurate thermometers. It is determined by the spatiotemporal variance of the actual time dependent thermal distribution of temperatures in the measured volume of Durham county.
I can estimate that, at least. In my own back yard, the spatial variance in air temperature is between 1 and 4 C across maybe 20 meters — all one has to do is walk under a tree, or onto the driveway, or out over the grass, or sit up on the roof — and get very, very different results. The temporal variance at these locations is similarly easily degrees per hour — both systematically (with significant cumulation diurnally and with the seasons) and randomly, as today is sunny and tomorrow it is cloudy and rainy, this morning it is humid and warm and later today a cold front moves through and it cools and dries. Monte Carlo eliminates bias, but nothing can eliminate the need to sample the distribution itself, as the standard deviation is expected to scale like
Even this, however, is insufficient as a statistical treatment, because there is nothing that says that the underlying distribution is stationary and all of my assumptions used to effectively sample the distribution and thereby compute its variance and standard deviation in the hope that the central limit theorem kicks so that the mean of my observations will be normally distributed around the true mean (what I’m trying to measure require that the distribution being sampled be stationary. Among other things. None of which are particularly likely to be true for the climate, and indeed the whole point of the exercise is to infer the non- stationarity of the underlying distribution so that the cause of its motion can be attributed to a correlate.
This brings us full circle back to Briggs’ lovely posts on the sheer idiocy of fitting linear trends to timeseries data drawn from arbitrary (probably non-stationary) distributions:
http://wmbriggs.com/blog/?p=5172
(and more — he writes extensively on this subject). That is, there is no need for a sloppy treatment of this subject. Climate science is already rife with those. What I want to see is the slightest bit of self-consistent evidence that 3000 (say) ARGO buoys with perfect thermometry can measure the average temperature field of the ocean itself to within 0.001C ever, anywhere, long before we start monkeying around with the usual idiocy of fitting a time series as if the linear trend we extract is not only meaningful, but is accurate to this sort of scale over decades!
Puh-leeze.
And while we are at it, we can work on physical models for transporting oceanic heat downwards from the surface and estimate a few of the time constants of the transport processes contributing to that — ones that work right on through strong stratification. What were those time scales, again? Even if we are — astoundingly, IMO — observing a trend that isn’t pure noise amplified by the judicious application of confirmation bias, is the physical cause of the trend the warming of the surface back during the dust bowl years in the 1930s, just now making its way to depth, or is it some sort of response to the warming that happened in the 1980s and 1990s, in the single double ENSO burst of warming visible in the last 70 years, or is there a fast process that is somehow warming the depths now even though the surface is not, actually warming at all?
Note that if one wishes to assert the latter, one has a very serious problem. If the relaxation time of the deep ocean is only decadal, why isn’t almost the entire ocean at 288 K? Oh, right, because in fact it is not decadal, it is millennial. We are probably still warming the ocean from the last glacial episode! The warm and cool waters that emerge and sink in the thermohaline circulation carry a pattern of temperature change imposed centuries ago, adding nicely to the chaotic tumble of surface climate changes — nothing like lagged nonlinear feedback in an oscillator to keep it on its chaotic toes, right?
rgb
Note that about 10 % of the ocean is never measured by Argo, and those 10 % is very non-random.
Amen rgb! To the immense thermo flywheel of the oceans, 10K years is a short time. Assuming .002C per decade is realistic (a trend which I have zero confidence in), 10K years would yield a 2C rise in average ocean temperature. Given that the last ice age provided 90K years of cooling, even 2C seems much too great.
Oops. Should have been .022 per decade yielding 22C rise which is not credible. So if .022 per decade is true, it would be a much higher rate than the rate of ocean warming averaged over the Holocene. What am I saying? Just that .022C per decade doesn’t make common sense.
“I agree that the article at the top is misleading and makes several mistakes, but the problem he points out is real. There are a few thousand ARGO buoys. We’ve had that many only for a decade or so. Before that we relied on scattered soundings. The ocean being sampled covers 70% of the Earth’s surface, and is not homogeneous.”
1. Homogeneous is ASSUMED to do the “averaging” calculations.
2. You actually have to test to prove that it’s NOT homogeneous.
3. In recent work, folks have shown that the homogeneous assumption was wrong. The SH ocean
is actually warmer than estimated from the assumption of homogeneity.
Given the data, Given an assumption of homogeneous field ( ie, the unsampled locations can be estimated
in an unbiased manner from the known locations), the algorithms generate an estimate of temperature.
This is commonly referred to as an “average”, but it is really not an average. It is, quite literally, the best estimate of the temperature at locations where no measurement was taken using the know data and an
assumption.
This prediction can of course be tested, by either holding out data or by increasing coverage
Again, what matters is whether or not the unsampled areas are homogeneous with the sampled.
Since they are UNSAMPLED and UNOBSERVED one can’t simply assert that they are non homogeneous. One can assume the unsampled is homogeneous and calculate a result. Then one can test this result.
My experience is that the homogeneous assumption hold up fairly well both for air and for SST.
The bias introduced by the assumption has, in fact, underestimated the warming. That is as we get more
coverage or recover old records we consistently find that we have underestimated the warming.
That is, previously un measured locations are warmer on average than the homogeneous assumption.
The bias is small, so the assumption is not without merit.
I wanted to write something that wasn’t too frivolous but
You can’t find the middle of a dart board to the nearest mm with a million thrown darts if you only know where the darts hit to the nearest 1m. Your precision of throws can be 1m off, but you need to know the position to the nearest 1mm.
If your noise level exceeds 1m then 1 million thrown darts would give you 1/sqrt(1M) = 1mm resolution. For example, if 620,000 samples fall on 2m marker and 380,000 samples fall on 1m marker, then you know the center was at about 1.620 meters. (I probably did the math wrong, but it’s the general idea).
This is the same principle all modern audio equipment uses (delta-sigma converter, though they shape the noise to get better results than 1/(sqrt(n)).
Of course, the accuracy might be terrible if the noise has any skewness, or isn’t sampled at the same point, or the sensors drift over that sample due to natural decay of all semiconductor based systems… all of which apply to the ARGO network.
As mentioned elsewhere in this most excellent discussion, accuracy and precision are two different things. Oversampling will get your great precision but accuracy is limited by many other factors.
RGB
I’d like to thank you for managing to explain simply, complex stuff I have always struggled to understand.
Along with other commentators in WUWT, Leif as well, over the years I have been reading WUWT my understanding and knowledge has increased, along with my library, due to your ability to put into clear simple form complex processes.
Thanks to Anthony and the Moderators also for providing a forum where this can happen
Had Argo showed warming instead of cooling, would anyone have removed any of the floats from the sample? If not, then how is this not confirmation bias?
The oceans were showing warming – lots of warming – up until Argo was installed. Then suddenly ocean temperatures leveled. What an amazing co-incidence. One could argue much too amazing.
Oh, I forgot to add one more comment. Most of the Argo buoys are free floating. As far as I know, none of their locations was determined by Monte Carlo and fixed on that basis alone (or varied on that basis alone). That means that the samples drawn by the buoys are neither independent nor unbiased. They violate the first principles of sampling theory for even simple, stationary distributions — and then they have to krige them.
All I can do is shake my head.
Look, there isn’t the slightest reason to believe that floating buoys are going to sample the entire ocean at all. A glance at the reasonably current map:
http://w3.jcommops.org/FTPRoot/Argo/Maps/status.png
Shows that they do not. Don’t let the size of the dots fool you. Each dot is the width of Florida — oh wait, it is a Mercator projection, so it is the width of Florida at Florida, and about twice that wide near the equator and the single dot at the top probably covers a football field or two at the North Pole. It looks uniform on a Mercator, which means that it is nowhere near uniform on the globe — some places are horribly oversampled, others nearly completely undersampled. The buoys all belong to different countries (introducing a nifty source of additional error, BTW).
At second glance, the buoys aren’t even close to uniform. They string together, swept into — could it be — currents? And what are currents, exactly? Warmed water heading towards cooler water! On the surface, anyway. Deeper, it is cooled water being displaced by warmed water as it cools, in enormous thermohaline convective rolls that both wind all over the planet and that form eddies — dead spots like the Sargasso — at the topological defects in the curl field. Some places don’t have any buoys at all, probably because they’d be a shipping hazard. Others — check out Japan! — seem to have so many they are running into each other randomly.
Each buoy (assuming that they all descend to 2 km — not all do), on average, is sampling a handful of points that have to represent the temperature of roughly 200,000 cubic kilometers of water. To put it into perspective, Durham county is roughly 800 square kilometers. If I distributed 3000 thermometers on it (say, by mounting most of them on cars, as this is the moral equivalent of the floating buoy confined to the ocean currents) each buoy would have to sample aproximately maybe a quarter of a square kilometer — a chunk half a kilometer square. The temperature reading of a single car would have to represent all of that volume/area and at the same time sample the spatiotemporal distribution often enough to eliminate the natural variance to the point where the sample mean is in correspondence with the true mean reliably over time (which is the thing that is basically impossible with a non-stationary distribution) accurately enough that when I come back to fit a linear trend to the timeseries of sample means I’m not just seeing the fact that yeah, the distribution isn’t stationary and isn’t statistically resolved both, I’m seeing an actual linear trend that has some meaning.
Over the decade or so that the buoys have been in place in adequate numbers, assuming that there are no other biases or sources of error, assuming that sampling in the hot city streets gives the same thing that a true Monte Carlo of sample locations and times would have given. Probably assuming a few more things. Every one a Bayesian prior that strictly reduces the confidence we can place in the final answer!
rgb
Well put, the map is most enlightening.
I’m actually quite disappointed in the quality of the ARGO network. It’s most disheartening.
So I counter with “It’s better than nothing”. Yes, data can be abused by putting too much confidence on it. Or by ignoring how it actually works.
But at least we see something now. The currents thing may be able to be determined more accurately by the tendency of these buys to line up. That would be of interest.
At least they are really measuring something.
Wow, you and rgbatduke are hard to please! Yes there isn’t a sensor on every square metre of the ocean – but Argo is quite simply an astounding achievement and hellishly expensive.
rgbatduke produces some very valid reasons why Argo is not accurately measuring the average temperature of the oceans. But how could it possibly do that? You would need a thermometer on every water molecule!
He is totally missing the point! What Argo is endeavouring to do is measure the change in temperatures over time which is why they only ever quote variance and not actual temperature. To do that it simply needs to do enough measurements to average out the random fluctuations. The map looks like a pretty random distribution to me. The only alternative would be to anchor each buoy to the ocean floor – imagine the cost of that!!!.
Using the current system, the longer the period of measurement and the more data points the more apparent any trend would become. Even if you bin the outliers (which is stupid of course), if the ocean is cooling or warming then it will show up in the remaining buoys in time. The Willis guy thought he was binning only data from faulty buoys and that newer buoys were much more accurate. He can only do that once – from then on by his own standards the newer buoys have to be right – or his whole argument falls down.
So what alternative system would you suggest that could get anything like this kind of coverage of temperatures at all levels of the ocean?
Or are you both suggesting we do nothing, because nothing is perfect, and we all seek perfection do we not?
TLM says;
Who proposed we just do nothing? We just ask that confirmation bias driven dubious statistical methods be excoriated by the science community. 0.022 ± 0.002 deg C /decade determined from a such a short time period is scientifically simply not credible.
To: TLM
October 10, 2014 at 9:15 am
Hmmmn.
So, you are satisfied if the ARGO buoys measure (report) only the “change” in ocean temperatures over time.
OK.
So, how do you accurately decide what the “change” in oceans are over time if these scattered bouys randomly floating around the Pacific and Atlantic Oceans go in and out of the Japanese currents and Gulf Stream? See, because the Gulf Stream and strong regional currents like those across the north Pacific wander themselves and vary in location and density and width and eddies and speeds. you cannot use even a simple approximation like “The Mississippi and Missouri rivers are always in the same location, so I can store data against the latest buoy internal GPS location, because the river will be here next spring, last fall, and last decade.”
I actually think you are missing the point. Today I’m driving my car through Durham. Its thermometer reads (at the instant I happen to look at it) 24C to a single degree. Ten minutes later I’ve driven out of the city and glance at the thermometer. Now it reads 22C (I’m out of the UHI of the city, and these numbers are realistic). I park. When I get into the car in my driveway an hour later it reads 28C — south facing concrete driveway, parked in the sun. When I go out the next day to drive away, it’s the end of the night, the same driveway is cooler than the grass nearby as it radiates heat away faster.
The only anomaly I am recording if I average that over a handful of cars all being driven on city streets is the anomaly associated with the paths cars are likely to take. Even if I include the measurements of a hundred million cars, averaged over the entire continental United States, it won’t give me the thing you’d like to consider the anomaly, even of the surface temperature of the United States. My samples are not random. They are not independent. They are not drawn in an unbiased way (look at the distribution of roadways in the US). And finally, they are drawn from a distribution that we believe is fundamentally non-stationary — this is the bit that you just don’t get. I cannot distinguish statistical error from the movement of the non-stationary distribution at the same time! They both appear the same, as an anomaly in the data! I can measure the temperatures of staggering numbers of cars, reduce the standard deviation of all of those measurements to nearly zero, and still have no idea what the actual temperature anomaly of the US is, let alone its linear trend!
To even think of justifying an estimate, one has to do lots of things. Stop measuring on the roads, for example. Select truly random measurement sites. Sorry, but that’s just how it is in Monte Carlo. If you select sites through any non-random means, you are asking for trouble, especially when the system you are samping has non-random internal structure! You are advocating no-black-swan statistics. People who lived in Europe performed a long running, very thorough experiment. They looked at swans, and everywhere they looked, the swans were white! They sampled in England, they sampled in France, they sampled in the Americas, they sampled in Asia. No black swans to be found. Not unreasonably, they concluded that they had proven to (fill in some huge number of zeros before the first 1) that there were no black swans to be found anywhere in the world Today, of course, they would call this kriging the data or infilling missing data by interpolating existing samples as that makes it sound ever so much more math-y and official.
And then they visited Australia…
Note that if they had used Monte Carlo to answer the question, Australia is around 1.5% of the Earth’s surface area (and of course maybe 5% of its land surface area). If they’d sampled the neighborhood of a few hundred randomly selected sites on the surface they could not have missed the black swans.
This is, of course, not a perfect metaphor for ARGO, and actually I love ARGO and think it is a great idea if still inadequate by an easy order of magnitude or three to achieve its actual goal. But the point still bears repeating. I’d trust a much smaller network of buoys that were dropped at places that are literally randomly selected from water over 2km deep, used to produce a single set of data, hauled out of the water, and dropped in at the next location at an equally randomly selected time. The axioms of statistics call for iid samples for a reason, and if you fail to respect this reason you must use Bayesian methods to correct for your bias (if you can!) and you have to consequently degrade your expected statistical precision by the uncertainty in your assumptions.
To return to the Black Swan problem, the erroneous assumption was that because swans fly, the global swan population was in some sense sufficiently homogeneous that it exhibited a kind of ergodicity. If you sit anywhere that swans are to be found and wait, if black swans exist one will come swanning along, sooner or later. You don’t even have to go looking lots of places. We don’t go looking for mosquitoes — they find us! Looking lots of places simply confirmed our prior biases and beliefs. But as it happened, the Black Swans of Australia just don’t fly over to Europe, much.
The same thing is true inside the US. If I looked at my squirrel population, I would conclude “no black squirrels”. After all, the US is still multiply connected by forest (with a few places where one has to run a highway gauntlet that squirrels never seem to hesitate to run). If there were black squirrels in, say, Detroit, there would be black squirrels in my neighborhood because I can’t imagine evolution selecting against black squirrelness enough to prevent squirrel diffusion.
Sadly, my wife is from Detroit, and Detroit is full of black squirrels.
This is directly related to ARGO sampling problem. Leaving the buoys adrift in the currents is cheap and easy. However, it without question biases their trajectories and biases the coverage of the sampling. Perhaps we can assume that the ocean in between, where the currents do not carry them, is homogeneous structurally with the ocean where the currents pick them up and concentrate them. Obviously, whether or not we can, we do. But that doesn’t mean that the assumption is true, and that has to be reflected as a degradation of the reported error in ARGO’s averages.
The same thing is true in the temporal direction. Because we do not really know the deep ocean dynamics governing heat transport, we don’t have any good way of knowing a priori what the distribution of temperature anomalies is over any extended period of time, or how rapidly it changes, or how it changes. Over time, ARGO might tell us some of those things, which is good. In the meantime, we cannot attach any particular meaning to any trend we observe in the possibly biased, error underreported data. It could be pure statistical noise, that we are treating like signal! We won’t know until after we understand the data.
The simplest thing to do is what Briggs recommends. Don’t fit (linear or other) functions to timeseries data and then use the function you fit as a replacement for the data itself!
Gads, how hard is this to understand? I don’t need somebody to draw a line through HADCRUT4 or ARGO data in order to see what the data does — it is nothing more than a guide to the eye, usually a guide drawn by somebody who wants to sell you something if that something is nothing more than a favored belief. I can see the data itself. By looking directly at the data, I can get some sort of feel for how much of what I’m seeing is probably noise, and how much might or might not be signal, although even this is fraught with peril the minute I try to mentally extrapolate what I see as a trend. It is a classroom example to make timeseries that has a known nonlinear form (plus noise), fit a short segment of it, and see how incredibly wrong you can be about the meaning of the linear trend you fit. There’s a lovely paper by Koutsoyiannis in which he illustrates the problem, which is happens all the time in climate science, basically every single time somebody tries to linearize something as the climate is a non-stationary process
That doesn’t mean one cannot analyze it, only that the analysis is hard and one ends up much more uncertain of the results of the analysis. And don’t presume that the results of your analysis have much predictive value, especially on timescales long compared to the scale you examine and analyze.
rgb
OK, one more example and then I have to clean my kitchen and go teach. One thing I’ve spent far too much of my life doing is importance sampling Monte Carlo. In it, one applies a Markov process to a system in such a way that it moves from an arbitrary initial state into an (average) state of detailed balance with the correct statistical weights and then ergodically sample the phase space in the vicinity of this “equilibrium” volume of phase space.
Obviously, one assumes ergodicity — but my stat mech teacher was Richard Palmer, who made a name for himself studying broken ergodicity in physics. So let’s simply note that one cannot assume ergodicity, only profoundly hope for it unless you are studying a comparatively simple system.
I was studying a comparatively simple system, and even near the critical temperatures I was studying I could count on it, subject to something called critical slowing down. One of many things I was looking at was indeed the critical slowing down itself — the dynamical critical exponents of the system. Those are found by looking at the dynamical scaling of the autocorrelation time(s) of the system near/at the critical point.
However, the autocorrelation time one obtains has a problem. The Markov process one uses doesn’t generate independent samples! Each timestep in the series is strongly correlated to the previous one, and it takes many steps to end up with “independent” samples. I was faced with the question: How many?
The answer was — run the process a very long time and compute the variance of the distribution of sample results. Now use the same data and compute the standard deviation which is related to this variance by the square root of the number of effectively independent samples. Compute the actual scaling of the variance to the standard deviation and from the result, infer the number of independent samples relative to the number of timesteps.
Only then could I actually make accurate error estimates of the quantities I was sampling! The sample standard deviation one computed from keeping every timestep as if it were an independent sample was much greater than the number of actually independent samples being drawn from the system. Using it one would get error estimates that were absurdly low, and be tempted to make many a false conclusion from the data — like (just as an example) asserting that this was statistically significantly larger than that, or worse, trying to fit curves through the data with nonlinear regression to extract critical exponents when the error bars you were feeding the regression code were themselves an order of magnitude too small.
Note also that I couldn’t do this sort of correction analysis on any short span of the data, because I had to have enough data that the variance itself was correctly estimated. This wasn’t a chaotic problem with multiple attractors (although it was a critical problem where a second attractor was emergent), but with critical slowing down this was at best a self-consistent process. If there really were multiple attractors with broken short-run ergodicity between them, I would have been open to serious black swan error — only sampling the neighborhood of whatever attractor I happened to be near or that happened to be most likely. To help protect against that, naturally I did a gazillion runs with different random number seeds and different starting conditions, but of course for truly complex problems there is no real solution, as they are non-ergodic and often nearly disconnected. In high dimensionality you may never even hit the place that determines their macroscopic behavior even with simple Monte Carlo in any reasonable amount of time (which is why importance sampling MC and why genetic algorithms and why simulated annealing and why hard problems are hard — they often appear to be NP complete).
To put this again into the context of ARGO, we have a tiny, tiny segment of data. What is it now, ten or fifteen years? It doesn’t even constitute a single point of data on the timescale most often quoted for climate, and the whole point of ARGO is to determine things like the autocorrelation times, the important transport processes, and so on — or that would be the point if they hadn’t been subverted into a way to prove anthropogenic global warming instead. In a few decades of patient observation, we’ll eventually accumulate enough data to begin to make some first, tentative statements about relaxation times and autocorrelations on decadal timescales, which is the only thing that matters.
So right now we don’t even have one real sample based on our best estimates of probable autocorrelation times and fluctuation times, but you are already fitting linear trends to the data, to absurd precision, without really knowing the variance of the system you are studying and hence unable to differentiate the sampling error from the autocorrelation trend and without any hope whatsoever of correctly ascribing a cause to the time constants you don’t even know yet.
Arrgh.
rgb
Oops, “greater” –>> “smaller”. The number of Monte Carlo samples is much greater than the number of iid samples inferred from the variance, so that the sd evaluated with the former as if they are independent is far, far too small.
rgb
The whole point of Argo buoys is a measurement of temperature and salinity in different depths. You are free to interpret that data any way you like. If it is insufficient to measure autocorrelation times, that’s just too bad.
rgbatduke, fantastic analysis. Makes me think ARGO is measuring the temperature of eddies, since that’s where stuff tends to collect. At least we’ll know the temperature of the Pacific Garbage Patch!
As I noted above, about 10 % of the ocean is not sampled at all. This includes e. g. the Arctic Ocean, the Sea of Okhotsk and the Banda sea to take just three very different areas.
How about making the ~3000 buoys fixed so that each covers about 120,000 square kilometers of ocean? Of course much of the ocean isn’t 2000 meters deep, so the floats would need to move up and down. Better than drifting, IMO.
See comments above. Fixed grids are OK, but are most useful if they are fixed and adaptive double the grid resolution a couple of times and see whether or if your measurements are converging. Or jackknife the grid you’ve got to the same end.
This is actually one of the better ways to get at the probable actual error, or at least to learn something about the internal consistency of what your data predicts as its own error.
I like Monte Carlo. iid is iid, not a grid, and not adrift in the internally structured soup you are measuring. No way to even detect a systematic bias in buoy sampling due to the fact that they tend to accumulate where the currents push them, which could be (for example) where heat tends to accumulate.
Think about it — upwelling cold currents push “away” from a surface defect. Buoys are actively repelled from the defect unless they reach it underwater. They are actively pulled towards places in the thermohaline circulation where there is downwelling surface water creating a net inflow. To correct for this requires a detailed knowledge of the thermohaline flow, the resulting temperature inhomogeneity, and more. ARGO might tell us about these things in a few decades. In the meantime, all we can reasonably guess is that there is almost certainly bias in the measurement due to the currents.
rgb
More decades of non-random sampling by drifting buoys might indeed produce data useful in some applications. Maybe over time the coverage area per float could be halved from roughly the size of PA to that of WV.
The overall R value is terrible (as visual inspection of the data clearly show).
Furthermore, there appears to be an even lower correlation at the higher observed values where the prediction tends to systematically underestimate the actual values. This means that (apparently) the predicted values may show an increasing error at increasing sea ice levels. It is clearly the ideal model for climate terrorism.
If the 3,000 ARGO buoys moved at 5 mph (I don’t think they come close), they could measure ~43% of the ocean’s cubic miles of water ( have it as ~303.4 Million cubic miles).
They don’t really swim; they move vertically, and their horizontal movement is a result of ocean currents. So they tend to stay in the same body of water, unless currents vary with different depths.
I looked at the maps of a couple and came to the conclusion that it wasn’t even close to 5 mph. It just goes to show what a small % of the oceans are even sampled, then read rgbatduke to see how worthless even that small % is.
Robert Brown didn’t seem to mention precision but a good summary as usual.
Even “precision” takes on different meanings if not very clearly stated what it is to mean. An instrument stated with a 0.002 precision many times means the readings have a display of 0.00x three decimals with x being in this case always in even values in the last digit. Or it could mean repeatability within a time period like two readings taken 20 minutes apart are guaranteed to have the difference between the two off by no more than ±0.002 from actual.
Then you have “accuracy”. You can have a very precise but totally inaccurate readings!
Other commenters above have spoken on the calibration issue but what of drift? The manufacturer may be able to guarantee that over the lets say five year lifetime of the instrument it will not drift more than 0.0x (accuracy) and that due to precise calibration it’s absolute accuracy is also within that range but if you ever have any common drift (in this case maybe caused in common by barnacles, salt deposition, single salt molecule infiltration into the electronics, water related, etc) that all instruments naturally have in common then even ‘trends’ over long time periods of time could be up to two times the stamped accuracy off from the actual trend and if those are in common even great numbers of instruments or a great number of readings will never average out or removes that factor, all without going out of stamped specs.
So a trends to 0.002 °C/decade? Pure hogwash… served up to us courtesy of the global climate scientist community, but thats their job and pay of late.
Wrong Robert. He writes a lot better and is more knowledgeable.
Please, it is not “5 x 1021 Joules” . Use “5 x 10^21” where ‘^’ stands for ‘to the exponent of’ or “5 x 10E21” where “E” stands for ‘to the exponent of’ or ‘5 x 10**21’ with the same meaning. They are all standard while 5 x 1021 Joules is just confusing.
Well said.
Also, it’s joules, not Joules, if you write it out and J not j for the symbol (capital for the symbol if the unit is named after a person – in this case James Joule). Case is important but clear with the SI system.
In the arctic most of the ice melts as it is moved by currents out of the arctic. So you must add, not a temperature measurement, but a metric to account for the energy to move the ice, which varies greatly, and has far more to do with cyclical ocean changes.
Robert Balic’s statements regarding precision are valid for statistical errors that are independent and identically distributed. I have argued for some time now that ARGO data does not necessarily conform to this ideal. In the world of manufacturing we have the iron-clad rule of stack up error, which is that stack up error equals or is less than sum of absolute value of errors. I think ARGO data might have rather large errors as the environment in which the data are collected is not stationary. Moreover, the conditions under which researchers established sensor precision and drift is not the open ocean.
Another thing to ponder: how exact and stable are the ARGO pressure transducers? The measurements occurs at preset pressures. If the pressure sensors aren’t absolutely stable then the measurement depths will change over time.
In tropical waters there is typically about 20 degrees difference between the surface and 2000 meters depth, i. e. 1 degree per 100 m. A change of 0.002 degrees is consequently equivalent to 0.2 meters (about 8 inches). Actually it is worse because at the termocline the temperature gradient is about four times as steep, so there you need precision on the order of. ± 1 inch
Anyone want to bet that Argo pressure transducers are stable enough to measure depth with a ± 1 inch repeatibility over a 4 to 6 years life?
+1. Astute. Vertical rate of change in temperature is high in the upper 200 m and not always monotonic.
From Nic Lewis 5/10/13 at 1:33 pm in Layers of Meaning in Levitus
@ur momisugly Curious George 10/10 at 10:14 am
Are you implying – but not saying – that with 1000 thermometer readings, each one accurate to ± 1°C, you can get a weighted average accurate to ± 0.001°C
No. If it is as you state, the standard error of the mean is ± 1°C/sqrt(1000) or about ± 0.03 °C
ARGO’s might have a precision of ± 0.002 °C they have also been measured to have a drift of more than ± 0.001 °C of per year, which is a at best a systematic error for each instrument.
Statistically, we must not forget that these precise thermometers are trying to measure the temperature of a body that has a range of – 1°C to ~ 31°C with 90% of the body from 2 °C to 7 °C in a 3D shape that moves and evolves and is hard to predict. That’s why we need to measure it.
Much of the sampling discussion above relates back to three subjects discussed in Decimals of Precision Those subjects are:
Ari Tai (Flight behavior; are floats heat seeking?)
Martin A (spatial Autocorrelation)
George E. Smith (Nyquist sampling)
Plus my support (at Feb. 3, 2012 at 1:21 pm, same thread) of
_ _1. possible heat seeking behavior leading to non-random sampling from float tracks behavior and
_ _ 2. Nyquist underesampling issues sampling in 6 dimensions: 3 spatial and 3 temporal (diurnal, seasonal, climatological)
It is worth repeating the paragraph from rgbatduke 10/10 at 7:36 am
Is the ARGO dataset sampled enough to confidently interpret the space between reading to the vaunted 0.002 deg precision? Well let’s test it. Take the dataset for any 10-day period. Do several 50% bootstrap tessellations to interpolate between ARGO profile vertices. Now interpolate the temperature at all x,y z points of the volume according to that tessellation net. Repeat the bootstrap. resample the control point, reconfigure the tessellations, interpolate the new temperature field. Repeat at least 9 times.. At each x,y,z poin in the volume, you now have N different interpolations, from N different combinations of ARGO data used (that probably reported several days apart!). What is the scatter of interpolated temperatures for eacy x,y,z (and it probably varies a lot with shallow z)? What is the mean uncertainty?
The precision of the ARGO is vanishing small compared to the interpolation error between ARGO profiles.
Which is almost certainly vanishingly small compared to systematic errors due to non-stationarity and bias even in the ARGO profiles. But who cares? The precision of a buoy is tremendous, maybe. So we can be certain that the ocean is warming, especially if we throw out any data that looks “too cold”.
rgb
I don’t think that I pointed out my problem with the Argo data. I highlighted one of many problems with just simply assuming that many measurements would mean each measurement need not be precise, just accurate. One is that the resolution of the instrument is not the mean and standard deviation of many precise measurements varying about an increment that you can just throw into the soup. There are other problems that are more important. I just wanted to highlight that one.
The problem with the PIOMAS data is different but I was just questioning whether you can white wash any concerns with “a lot of measurements were made”.
Everybody forgets…
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http://www.resacorp.com/images/slrund073.gif
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As n approaches infinity, SE becomes exact.
How does the Balic discussion in the sixth paragraph apply to satellite measurements of SLR? I seem to recall that Jason and Topex were on the order of 25mm or more, but claims have been made for just over 3mm per year. I’m not an expert on this; is there a difference?