I got into this investigation of Argo because I disbelieved their claimed error of 0.002°C for the annual average temperature of the top mile of the ocean. I discussed this in “Decimals of Precision“, where I showed that the error estimates were overly optimistic.
I wanted to know more about what the structure of the data looked like, which led to my posts Jason and the Argo Notes, Argo Notes Part Two, and Argo and the Ocean Temperature Maximum.
This is the next part of my slow wander through the Argo data. In How well can we derive Global Ocean Indicators from Argo data? (PDF, hereinafter SLT2011), K. von Schuckmann and P.-Y. Le Traon describe their method for analyzing the Argo data:
To evaluate GOIs [global oceanic indicators] from the irregularly distributed global Argo data, temperature and salinity profiles during the years 2005 to 2010 are uploaded spanning 10 to 1500m depth.
and
To estimate the GOIs from the irregularly distributed profiles, the global ocean is first divided into boxes of 5° latitude, 10° longitude and 3 month size. This provides a sufficient number of observations per box.
So I thought I’d take a look at some gridcell boxes. I’ve picked one which is typical, and shows some of the issues involved in determining a trend. Figure 1 shows the location of the temperature profiles for that gridbox, as well as showing the temperatures by latitude and day. The data in all cases is for the first three months of the year. The top row of Figure 1 shows all of the temperature for those three months (Jan-Feb-Mar) from all the years 2005-2011. The bottom row shows just the 2005 measurements. The following figures will show the other years.
Figure 1. Click on image for full size version. Gridcell is in the Atlantic, from 25°-30°N, and 30°-40°W. Left column shows the physical location of the samples within the gridbox. Colors in the left column are randomly assigned to different floats, one color per float. Right column shows the temperature by latitude. Small numbers above each sample show the day of the year that the sample was taken. Colors in the right column show the day the sample was taken, with red being day one of the year, shading through orange, yellow and green to end at blue at day 91. Top row shows all years. Bottom row shows 2005. Text in the right column gives the mean (average) of the temperature measurements, the standard deviation (StdDev), and the 95% confidence interval (95%CI) of the mean of the temperature data. The 95% CI is calculated as the standard error of the mean times 1.96.
Let’s consider the top row first. In the left column, we see the physical location of all samples that Argo floats took from 2005-2011. We have pretty good coverage of the area of the gridbox over that time. Note that the gridboxes are huge, half a million square kilometres for this particular one. So even with the 216 samples taken over the six-year period, that’s still only one sample per 2,500 square km.
Next, let’s consider the top right image. This shows how the temperatures vary by time and by latitude. As you would expect, the further north you go, the colder the ocean, with a swing of about three degrees from north to south.
In addition, you can see that the ocean is cooling from day 1 (start of January) to day 91 (end of March). The early records (red and orange) are on the right (warmer) side of the graph. The later records (green and blue) are concentrated in the left hand (cooler) side of the records.
This leads to a curious oddity. The spread (standard deviation) of the temperature records from any given float depends on the direction that the float is moving. If the float is moving south, it is moving into warmer waters, but the water generally is cooling, so the spread of temperatures is reduced. If the float is moving north, on the other hand, it is moving into cooler waters, and in addition the water is generally cooling, so the spread is increased. It is unclear what effect this will have on the results … but it won’t make them more accurate. You’d think that the directions of the floats might average out, but no such luck, south is more common than north in these months for this gridcell.
A second problem affecting the accuracy can be seen in the lower left graph of Figure 1. It seems that we have nine measurements … but they’re all located within one tiny part of the entire gridbox. This may or may not make a difference, depending on exactly where the measurements are located, and which direction the float is moving. We can see this in the upper row of Figure 2.
Figure 2. As in Figure 1, with the top row showing 2006, and the bottom row 2007.
The effects I described above can be seen in the upper row, where the floats are in the northern half of the gridbox and moving generally southwards. There is a second effect visible, which is that one of the two floats (light blue circles) was only within the gridbox in the late (cooler) part of the period, with the first record being on day 62. As a result, the standard deviation of the measurements is small, and the temperature is anomalously low … which gives us a mean temperature of 20.8°C with a confidence interval of ± 0.36°C. In fact, the 95% confidence interval of the 2006 data does not overlap with the confidence interval of the mean of the entire 2005-2011 period (21.7° ± 0.12°C) … not a good sign at all
The 2007 data offers another problem … there weren’t any Argo floats at all in the gridcell for the entire three months. The authors say that in that case, they replace the year’s data with the “climatology”, which means the long-term average for the time period … but there’s a problem with that. The climatology covers the whole period, but there are more gaps in the first half of the record than in the latter half. As a result, if there is a trend in the data, this procedure is guaranteed to reduce that trend, by some unknown amount.
Figure 3 shows the next two years, 2008-2009.
Figure 3. As in Figure 1 and 2, for 2008 (top row) and 2009 (bottom row).
2008 averages out very close to the overall average … but that’s just the luck of the draw, as the floats were split between the north and south. 2009 wasn’t so lucky, with most of the records in the south, This leads to a warmer average, as well as a small 95%CI.
Finally, Figure 4 shows 2010 and 2011.
Figure 4. As in Figure 1 and 2, for 2010 (top row) and 2011 (bottom row).
In the final two years of the record, we are finally starting to get a more reasonable number of samples in the gridbox. However, there are still some interesting things going on. Look at the lower right graph. In the lower right of that graph there are two samples (day 71 and 81) from a float which didn’t move at all over that ten days (see bottom left graph, blue circles, with “81” on top of “71”). In that ten days, the temperature in that one single location dropped by almost half a degree …
DISCUSSION.
In this particular gridcell, the averages for each of the years 2005-2011 are 21.4°C, 20.8°C, no data, 21.7°C, 22°C, 21.9°C, and 21.7 °C. This gives a warming trend of 0.13°C/year, as shown in Figure 5.
Figure 5. Trend of the gridcell three-month temperatures
My question is, how accurate is this trend? Me, I’d say we can’t trust it as far as we can throw it. The problem is that the early years (2005, ’06, and ’07) way undersample the gridcell, but this is hidden because they take a number of samples in one or two small areas. As a result, the confidence intervals are way understated, and the averages do not represent a valid sampling in either time or space.
My conclusion is that we simply do not have the data to say a whole lot about this gridcell. In particular, despite the apparent statistical accuracy of a trend calculated from from these numbers, I don’t think we can even say whether the gridcell is warming or cooling.
Finally, the law of large numbers is generally understood to relate to repeated measurements of the same thing. But here, two measurements ten days apart are half a degree different, while two measurements at the same time in different areas of the gridcell are as much as three degrees apart … are we measuring the “same thing” here or not? And if not, if we are measuring different things, what effect does that have on the uncertainty? Finally, all of these error calculations assume what is called “stationarity”, that is to say that the mean of the data doesn’t change over a sufficiently long time period. However, there is no reason to believe this is true. What does this do to the uncertainties?
I don’t have any answers to these questions, and looking at the data seems to only bring up more questions and complications. However, I had said that I doubted we knew the temperature to anything like the precision claimed by the authors. Table 1 of the SLT2011 paper claims a precision for the annual average heat content of the top mile of the ocean of ± 0.21e+8 Joules. Given the volume involved (414e+8 cubic kilometres), this means they are claiming to measure the temperature of the top mile of the ocean to ± 0.002°C, two thousandths of a degree …
As cited above, I showed before that this was unlikely by noting that there are on the order of 3500 Argo floats. If the SLT2011 numbers are correct and the error from 3500 floats is ± 0.002°C, it means that 35 floats could measure the temperature of the top mile of the ocean to a tenth of that accuracy, or ± two hundredths of a degree. This is highly unlikely, the ocean is way too large to be measured to plus or minus two hundredths of a degree by 35 floats.
Finally, people have the idea that the ocean is well-mixed, and changes slowly and gradually from one temperature to another. Nothing could be further from the truth. The predominant feature of the ocean is eddies. These eddies have a curious property. They can travel, carrying the same water, for hundreds and hundreds of miles. Here’s an article on one eddy that they have studied. Their illustration is shown as Figure 6.
Figure 6. Illustration of an eddy transporting water for a long distance along the south coast of Australia.
Figure 7 shows another example of the eddying, non-uniform nature of the ocean. It is of the ocean off of the upper East Coast of the US, showing the Gulf Stream.
Figure 7. Oceanic temperature variation and eddies. Blue box is 5° latitude by 10° longitude. Temperature scale runs from blue (10°C, 50°F) to red (25°C, 77°F). SOURCE
The blue rectangle shows the size of the gridcell used in SLT2011. The red circles approximate the distribution within the gridbox of the measurements shown in the bottom row of Figure 1 for 2005. As you can see, this number and distribution of samples is way below the number and breadth of samples required to give us any kind of accuracy. Despite that, the strict statistical standard error of the mean would be very small, since there is little change in temperature in the immediate area. This gives an unwarranted and incorrect appearance of an accuracy of measurement that is simply not attainable by sampling a small area.
Why is this important? It is important because measuring the ocean temperature is part of determining the changes in the climate. My contention is that we still have far too little information to give us enough accuracy to say anything meaningful about “missing heat”.
Anyhow, that’s my latest wander through the Argo data. I find nothing to change my mind regarding what I see as greatly overstated precision for the temperature measurements.
My regards to everyone,
w.
Willis, Roger Tallbloke has a post up on Argo and, if I read it correctly, he says that screenshots of the current temps should be archived as the historic values are being altered downward to manufacture a warming trend. Or did I misunderstand his post?
Are the ARGO floats randomly distributed? If not, could their distribution be affected by temperature-related events, eg, winds, currents, upwellings, etc?
The Argo floats are free floating, which means they will tend to move away from areas of upwelling and stay at areas of ocean downwelling.
Outside polar regions, downwelling water is warmer than upwelling water,and this will cause an increasing warm bias over the life of a float.
There may be a similar effect with ocean eddies.
Even if Argo floats start out randomly distributed, they will become progressively less random relative to cool/warm areas of ocean.
‘My contention is that we still have far too little information to give us enough accuracy to say anything meaningful about “missing heat”.’
So all the M&Ms scattered about lead to the conclusion that we can’t say the missing heat is or is not in the oceans?
Here is a paper that describes how Argo floats have measured temperatures in upwelling/downwelling areas resulting from a Kelvin Wave. Although nothing about what bias may be introduced into ocean temp data.
http://w3.jcommops.org/FTProot/Argo/Doc/2007_mjo.pdf
Willis, IIRC, salinity has a non-trivial effect on thermal capacity and density. Can’t locate any numbers right now on thermal capacity vs salinity. Density increases for roughly 5% at 40 g/kg salt content.
The effect is obviously more pronounced in warmer waters where solubility is higher.
Willis: Take a look in the left hand column for a float and you can see which way the numbers are getting larger. They take samples about every ten days, so the numbers will be something like “4, 14, 24, 34, 45, 55 …”
Despite some overplotting of numbers, that is just possible if you match the dots on the left to the dots on the right that have the same latitude and day. Thanks.
I am still puzzled that the NH waters are cooling even as insolation (peak and duration) is increasing.
I am still puzzled that the NH waters are cooling even as insolation (peak and duration) is increasing.
The main driver of ocean heat loss is the temperature difference between the ocean surface and the atmosphere above the ocean.
In the NH winter the atmosphere is colder than the temperature than would result in temperature equilibrium with solar insolation heating the ocean, and as a result the oceans lose heat.
Alexander K says:
February 29, 2012 at 4:15 pm
Sorry, the good news is I’m banned by Roger Tallbloke because I said that N&Z’s claims violated conservation of energy. It’s good news because it saves me from the effort of trying to educate the ineducable.
w.
Septic Matthew says:
February 29, 2012 at 6:08 pm
That’s the lag in the system, which is large in ocean temps because of the heat capacity of the water.
w.
Excellent work Wllis. Thanks!
Willis – my take is the ARGO floats are diving to a density depth and not a specific depth below the sea surface. That means they are free to wander up and down as the weight of the water column above changes with density as they move about the grid as will an airplane on a cross-country flight. Is that the case, and given the unpredictable location of thermoclines in the ocean is there anything anyone is doing to fiddle the data to allow for thermocline crossings by these wandering floats?
Thought y’all might enjoy this … it shows the data split out by day of the year, latitude, temperature, and year. You can see the problem with the meaning and value of any presumed trend …
w.
dp says:
February 29, 2012 at 10:25 pm
Interesting quesion, dp. Inherently, the Argo float measures pressure at each profile level. This then has to be converted to depth, taking into account temperature and salinity. I’m using data which has been converted and then interpolated onto standard depth intervals … none of which is too relevant since in this analysis I’m just looking at the surface.
You are correct that their “parking level” is set by pressure and not depth. However, from what I’ve looked at the variations in depth for a given pressure given the common variation in temperature and salinity is not that great.
Also, their parking depth is generally down at 1000 hPa, which is about 1,000 metres down. There’s not too much in the way of thermoclines down that deep, the main thermocline (between the “mixed layer” and the deep ocean), is way shallower than that.
All the best,
w.
Further inquiry considers the linear model …
Call: lm(formula = OceanTemp ~ Lat + Day) Residuals: Min 1Q Median 3Q Max -1.37268 -0.32732 0.00971 0.33637 1.35744 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 33.097190 0.602039 54.98 <2e-16 *** Lat -0.390053 0.021958 -17.76 <2e-16 *** Day -0.015264 0.001215 -12.56 <2e-16 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 0.4839 on 213 degrees of freedom Multiple R-squared: 0.6999, Adjusted R-squared: 0.6971 F-statistic: 248.4 on 2 and 213 DF, p-value: < 2.2e-16Translation. The second line says that the linear model (lm) is that the Argo measured surface temperature (OceanTemp) is a function (shown in R as “~”) of both the latitude (Lat) and the day of the year (Day). Both of these are shown to be highly significant factors. In the section headed “Coefficients”, they both have “p-values” ≈ zero (shown as “Pr(>|t|)” above), and by the “significance codes” of three stars. The R-squared value (how much of the variation the model explains) is about 0.7.
Next, I looked at the same thing, but I added the year of the observation as another variable. This allows me to see if there is a year-over-year trend. Here are those values …
Call: lm(formula = OceanTemp ~ Lat + Day + Year) Residuals: Min 1Q Median 3Q Max -1.375763 -0.325941 0.009697 0.334971 1.361894 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 33.075825 0.642312 51.495 <2e-16 *** Lat -0.389551 0.022608 -17.231 <2e-16 *** Day -0.015239 0.001243 -12.257 <2e-16 *** Year 0.001078 0.011102 0.097 0.923 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 0.485 on 212 degrees of freedom Multiple R-squared: 0.6999, Adjusted R-squared: 0.6957 F-statistic: 164.8 on 3 and 212 DF, p-value: < 2.2e-16Adding the year does not improve the model in the slightest. The “p-value” of the Year variable is 0.92, meaning far from significant. So there is no statistically significant trend in the data.
Anyhow, that’s my interpretation of those results, your mileage may vary, your comments solicited.
w.
Oh, yeah, here’s the residuals of the linear model … that’s what’s left over after you subtract what your model predicts.
The colors are by float, and correspond to the floats colors in the top left graph in Figure 1.
Note that 2012 only has the first part of the data for JanFebMar.
w.
Willis,
I too, appreciate your efforts.
re the argo’s, argo placement might be more useful by being anchored, maybe with the concrete foundations of defunct wind turbines, cut to size.
argo mark 3 or whatever could, for example, be strategically placed to monitor currents, volcanic activity, ‘open’ ocean, and items of interest.
I’m betting that if the argo enterprise doesn’t become redundant, future floats will be designed for particular placement, such as in shallow water.
regards,
William (Bill) Martin
Thanks Willis.
William Martin says:
re the argo’s, argo placement might be more useful by being anchored
The solution to non-random horizontal drift is to make them powered. This will allow them to be relocated using some randomizing algorithm or even keep them at a single location.
I’m rather surprised this wasn’t build into the Argo floats in the first place.
Willis,
Nice to see that you have begun an analysis of the sources of variance in the ARGO data. In your earlier ‘decimals of precision’ post, I had made the comment that there are other sources of variability besides the instrument precision. At the time I offered some possible sources of variability, several of which you have included in the current posting. My brainstorm suggestions were:
*Time window (month or season)
*Ocean subdivided into Ocean region (eg N S E W or Gulf Stream – sub sections don’t necessarily need to be the same size and shape)
*Latitude (to account for such things as Gulf Stream cooling as it moves from Bahama to Iceland)
*Ocean ‘phase’ (such as AMO, PDO, El Nino, etc)
*Thermocline (percentage of an Argo profile above vs below the thermocline)
In this post you show estimates of 95% confidence interval significantly larger than the 0.002°C from SLT2011 because they include other sources of variance. Although you minimized my suggestion at the time, it is gratifying to see a first slice at quantifying some of those other sources of variance.
cheers,
Dave
In this post you show estimates of 95% confidence interval significantly larger than the 0.002°C from SLT2011 because — your estimated values — include other sources of variance.
which is what I meant, although ‘they’ in my earlier posting was not succinct.
I’ve suggested the use of kriging, but just about anything would be better than this method.
Their method also suffers from the foolishness of being divided into months, which also introduces spurious values into the outcome … but none of this ever seems to sink in to the climate folks, who generally deal with objections by saying they’ve “moved on” ™ since whatever it is you are pointing out is wrong, and they now have some newer and stranger method that they are flogging.
Precisely — kriging, perhaps with Gaussians, would be a reasonable thing to try, although I’d want to try several things and not just one. In all cases the real problem isn’t the dense zones where “anything” works — it is the sparse places where a single sample can have a disproportionate effect on a large volume. If you give neighboring samples too great a “range”, the real data gets overwhelmed by data from somewhere else, and in a non-uniform equatorially peaked distribution, that will always lead to net warming (compared to the correct answer, the true average) because there are simply more buoys in more area near the warmer equator than there are near the poles. If you give it too little range, your model has big holes.
We’ve seen this problem in spades recently in the infamous Antarctica paper, where a large number of densely packed thermal sensors in the one part of Antarctica that unambiguously warmed actually raised the assigned temperature of sensors thousands of miles away on the other side of the continent. Doing this right isn’t rocket science, but it does require a modicum of mathematical and statistical competence, ideally applied without (confirmation) bias that causes you to always pick corrections that seem to make everything just a bit warmer.
It sounds like they have equal problems with time, especially given that the buoys move, and move in bodies of water that are not well-mixed. And I don’t doubt that they have problems with depth. Building an accurate three dimensional thermal map of the ocean is a daunting project, the first step of which is to study the data, study it some more, maybe spend some time with the data, live with the data, and only then think about how to take the data and begin to transform it into a map, using some real mathematics.
Sadly, I think you’ve very definitely proven one thing. You are dead right — their error estimate is truly absurd. But then, I was convinced of that before I even read you very first article on the subject. Given the volume of the ocean and the number of buoys and the observed thermal granularity visible in TOA IR pictures of the ocean (which clearly reveals currents of water with very different SSTs forming a paisley mosaic at many scales) one would require very nearly photographic resolution in sampling buoys to get the kind of accuracy they claim.
In fact, that’s a very simple test right there. One can infer the SSTs from satellite data. One can also infer it from the buoy data. One can compare. I vote for satellites as being the gold standard, but either way if they aren’t in agreement within 0.002C — truly, an absurd assertion as I”m not certain how I would measure the water in my bathtub’s average temperature to that precision assuming that I had a thermometer accurate to (say) 0.00001C — then sorry, major fail.
rgb
Thought y’all might enjoy this … it shows the data split out by day of the year, latitude, temperature, and year. You can see the problem with the meaning and value of any presumed trend …
Hi Willis,
I’m having trouble understanding the box data. Shouldn’t it be toroidally symmetric on day of year? I’m having a hard time visualizing why polar temperatures jump up on Jan 1 if the data does, as it appears to, stretch between corners. Also, does this include NH and SH data? Finally, I assume that the latitude range is equator-to-pole (or as close to pole as one can get) but I would have expected it to get a lot sparser for the polar data. A LOT sparser, given that Antarctica sort of occupies the south polar region and the Arctic ocean is really rather small.
Or maybe my question is just, what exactly are the ranges of the axes and what are the data points?
rgb
Dr. Brown,
I agree, the climate research space is full of poor spatial analysis. Just as the base stat work needed a professional review, the spatial underpinnings need a good look.
I have learned at school that when experimenting and measuring one should change as little as possible. Why did they not position the floats at fixed anchored positions?
Thanks WIllis, your tenacity is amazing.