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Ocean temperatures – Is that warming statistically significant?

The oceans as measured by ARGO are warming, but that warming is not only far less than the models predicted, it is far less even than the instrument error.

The background of a crucial point

Everyone agrees: 90% of the energy in the Earth’s climate system is stored in the oceans. Rocks and sand don’t transmit the heat down, except at incredibly slow rates. The wil-o’-the-wisp-atmosphere hardly holds any energy. But water covers 70% of the surface, to an average depth of 3,700m, and it can store septillions of joules.

Climate models say the Earth’s energy balance is out of whack, and therefore 90% of the extra energy trapped by increasing greenhouse gases is stored in the ocean.  The oceans are warming (probably), but the extra energy found in the top 700m of the world’s oceans is not enough. The modelers argued the heat was hidden below, that from 700m-2,000m. Skeptics argue the missing energy was flung out to space. This is the big enchilada, and as far as measuring oceans goes, everything changed in 2003 when we finally got the ARGO system, and that’s why it’s worth a closer look now.

David points out that the errors might be seriously miscalculated. A single ARGO buoy (which measures ocean temperatures down to 2000m) has an uncertainty of about 0.1C. But using 3,000 buoys doesn’t make that uncertainty dramatically smaller when all that data is combined together. It would, if the 3,000 buoys were all measuring the same swimming pool. But each buoy measures a different piece of ocean, and the ocean does not have one global temperature. Or it would if all the world’s ocean localities warmed by the same increment due to global warming, in each time period. But that would be a very brave assumption, because different parts of the world’s oceans probably warm at different rates due to global warming. So the measurement uncertainty is closer to the instrument error of 0.1C than the 0.004C as claimed by fans of man-made global crisis, and since the oceans have only warmed by about 0.02C (if that) since we’ve been measuring it with ARGO, that tiny amount of warming might just be noise. Going back further, the pre-ARGO data is so bad that longer datasets have much larger uncertainties.

Overview of Measuring Ocean Temperatures

According to many neat diagonal graphs, the oceans are warming, it’s alarming, and we have to spend billions to stop it.  But is that warming enough, and how accurately can we measure it anyway?

For some inexplicable reason NOAA publish graphs of ocean heat content (OHC) but not ocean temperatures — the later are what the equipment measures, and what we relate to. So we need to convert OHC back to degrees C to find out the change in temperature.

Inspired by Willis Eschenbach, David Evans has done it with the ARGO data. (David doesn’t use non-ARGO data because he considers the XBT and buckets-off-boats stuff to be whimsical fantasy with error bars up where the unicorns fly, see below.) ARGO data only properly started in 2003, and any data at-depth before then was sparse. Compare it to the detail in our atmospheric measurements. We’ve been releasing weather-balloons twice a day from 800 sites around the Earth for five decades. To measure the global oceans we used 50 ships “of opportunity” (which happened to be in a shipping-lane) and XBT’s were fired down, not twice a day but once every few weeks. And vast tracts of the ocean hardly got measured, ever, especially the deepest parts. (XBT’s only get down to about 800m.)

ARGO data is good, but short. It’s fair to ask if such a short span is meaningful? Since thou shalt not create nor destroy energy — it is fair.  The imbalance caused by extra CO2 has run day in and day out for nearly 3000 days since ARGO began. That energy has to be somewhere.

Where are the error bars?

This is the standard diagonal scare-graph for ocean temperatures, but with added notes about which parts are reliable.

It looks like a convincingly big rise, but it’s not enough, and the error bars are huge. Even on the accurate ARGO buoys error margins are probably not a lot less than 0.1C. GRAPH UPDATED*

David Evans separated the layers of ocean so we can compare the rate of warming in the deeper layer, 700m – 2,000m, with that from the top layer, 0 – 700m. (Bear in mind, the “top” 700 m is not exactly shallow — it is the hull-crush depth of a military submarine.) David found that the rate of warming in the deeper layer is the same as the rate in the top 700m.

Over this short period, there is no acceleration evident in either layer.

If the instrument error is 0.1C, the error bars would be off the scale. [Jo says, “look”  the error bars are marked in white…] GRAPH UPDATED*

 You might almost think the slight appearance of warming matters, but let’s put it in perspective — it’s not remotely close to what the models predicted.



Though the funny thing about having wider error bars is that even though the results look so different from the models, the predictions could still fall within the error bars! Why haven’t the modelers announced it? [Prediction from Jo: Trenberth channels Santer 2008, “reconciles model and ARGO data by revisiting error estimations!” Coming soon, with 17 authors and a major press release… Researchers investigate errors and find the missing energy!].

Dr David Evans discusses the ocean data

These notes about the graphs above and the following explanation of how he got the graphs and why he chooses to use ARGO over the other data sets are thanks to David.

Climate models predict the top 700m is warming at 0.07C per decade

The climate models predict that ocean heat content is increasing at about 0.7 × 10^22 Joules per year. (See Hansen et al, 2005:  where the increase in ocean heat content per square meter of surface, in the upper 750m, according to typical models, is around 6.0 Watt·year/m2 per year, which converts to 0.7 × 10^22 Joules per year for the entire ocean as explained at Bob Tisdale’s site. Converting to temperature, this corresponds to about 0.7 × 0.01C = 0.007 C per year.)

The deeper ocean

The deeper 700m – 2,000m layer has warmed at the same rate as the upper 0 – 700m layer in the deeper Argo period (measured from Q1 2005).

This contradicts a meme that the deeper oceans are warming faster. It is correct that the heat content of the deeper layer is rising faster, but when converted to temperature it turns out that both layers have warmed at the same rate. There is 1.85 2.18 times as much water in the deeper layer (700m – 2,000m) as the upper layer (0 – 700m).

The warming of the planet is allegedly because of a warmer atmosphere, due to more CO2. The extra warmth would therefore have to pass from the atmosphere through the 0 – 700m layer to reach the 700 – 2,000m layer of the ocean. Schemes whereby currents could somehow move the heat from the surface to below 700m without warming the first 700m on average have been proposed, and maybe some are plausible — but warmer water rises.

The upper layer 0 – 700m is much better measured by Argo than the deeper 700 – 2,000m layer, with both earlier and denser data. In any conflict between the 0 – 700m and 700 – 2,000m data, the former is far more likely to be correct.

Before Argo

In the era before Argo (2003), measurements of ocean temperature were made from ships by putting a thermometer in a bucket of water drawn up from the surface or in the inlet valves of the engines, or by diving darts (XBTs) that could dive down to 800m with a thermometer, transmitting the data back to the ship along thin wires. The uncertainties in the temperature measurements made by the XBTs falling through the ocean were huge, because the XBTs fell too quickly to come into thermal equilibrium with the water around them. Also, there is a very strong temperature gradient in the surface layer of the ocean to below the thermocline , so the depth attributed to each temperature data point is arrived at from an assumed rate of descent of the instrument. Any deviation from the assumed rate of descent will put the instrument (and temperature) at the wrong depth, making the calculated temperature still more uncertain.  Measurements from thermometers in buckets of water variously obtained are obviously hugely imprecise.

The geographic distribution of the sampling was sparse and very uneven, because the samples were taken along commercial shipping routes, somewhat irregularly. Most shipping lanes are in the northern hemisphere, but most of the world’s oceans are in the southern hemisphere — much of the southern ocean is hundreds or thousands of kilometers from where samples were taken. The oceans are really big, yet the presence of currents and layers at different temperatures means temperatures can be quite different in waters just a few hundred meters apart.

Obviously the errors are so huge compared to the expected/modeled increases (less than a tenth of a degree C per decade) that pre-Argo data is useless. One wonders at the morals of people using this data to convince people the world is warming.


Uncertainties in ARGO data are not as low as people claim

Errors are sometimes claimed for ARGO data of around 0.004C per data point, which is literally incredible. (The thermometers are that good? And the ocean is sampled often and closely enough… no, not even 3,000 floats/buoys is enough.) However the ARGO errors are much much smaller than the pre-ARGO measurements (maybe by two orders of magnitude, one for each temperature reading and one for the sparseness of sampling?).

For more information see: Bob Tisdale: Is Ocean Heat Content Data all it is stacked up to be, or Watts Up: Argo-notes-the-third | Where-in-the-world-is-argo | Krige-the-argo-probe-data-mr-spock | An-ocean-of-overconfidenceMore-ocean-sized-errors-in-levitus-et-al | Decimals-of-precision-trenberths-missing-heat | More-on-trenberths-missing-heat/#more-84228  (also says deep heating possible).

The crux of the matter is the claim that ARGO errors are reduced because there are so many samples. This would be true if ARGO buoys were independent observations of the same quantity, that is, independent samples drawn on the same population. But each ARGO buoy independently measures a different part of the ocean — they are not all  independently recording (changes in) “the global ocean temperature”. Thus 3,000 ARGO buoys do not give 3,000 independent estimates of the ocean heat content at a particular time; each observation gives a single estimate of the temperature at a particular location and depth. It is therefore erroneous to suggest that the estimate of the global average ocean temperature is given by the instrument accuracy divided by the square root of the number of observations (as you would if the observations were of the same quantity):

(0.1C)/(3000^⅟2) = 0.1C/55 ~ 0.002C.

The error of each estimate of global average temperature of an ocean layer remains closer to that of the instruments, or about 0.1C. There is some correlation between changes in temperature due to global warming in different parts of the ocean, so there might be some reduction below 0.1C, but how much and how has it been measured? Thus the alleged trends may have no statistical significance! (h/t Bill Kininmonth)

Data sources

Ocean Heat Content, Various measurement methods, 0 – 700m

Columns: Quarter, heat content of oceans to 700m in units of 10^22 Joules. The Argo system started in mid-2003 (though there were some ARGO floats in the 1990’s), so the Argo data starts at 2003-6 (the prior data is bucket and XBT data). It is seasonally corrected data (ugh), but that seems to be all there is available.

Ocean Heat Content, Various measurement methods, 0 – 2,000m

Columns: Quarter, heat content of oceans to 2,000m in units of 10^22 Joules. Starting Q1 2005, two years after 0 – 700m data. The records are sparser than the 0 – 700m data, so more uncertain. Again, seasonally corrected.

Conversion factors

Approximate conversions between changes in ocean heat content (OHC) and temperature, for the world’s oceans:

There are a couple of ways to estimate the volume of the oceans and hence the temperature. Ideally one would download data on the depth of the oceans, work out the weight of water in each horizontal layer of interest (water is nearly incompressible so volume is proportional to weight), and note that it takes 4 megajoules to warm a tonne of water by 1°C. More lazily:

  1. See NOAA’s PDF, table T1 (on page 14): heat content change for the 0 – 700m layer of the world’s ocean of 15.913 * 10^22 Joules corresponds to a change in mean temperature of 0.168 deg C, so an increase of 10^22 Joules in 0-700m of the world’s oceans corresponds to a temperature rise of 0.168/15.913 = 0.0106 deg C.
  2. Alternatively, use Willis Eschenbach’s calculations based on ocean areas and depths (whew, he did the calculation for us).  Reading ΔH and ΔT from his graphs for 1955 to current, for 0 -100m, 100m-700m, and 700m – 2000m, and noting that mass = ΔH/(4× 10^6 * ΔT),  gives the figures above.


Hansen et al  (2005) Earth’s energy imbalance: Confirmation and implications. Science, 308, 1431-1435, page 1432 (PDF)

Santer, B. D., et al [2008], Consistency of modeled and observed temperature trends in the tropical troposphere. International Journal of Climatology, 28: 1703–1722. doi: 10.1002/joc.1756 [Abstract] [PDF]  [abstract]


Other related posts


UPDATE: Several commenters are pointing out just how much ocean volume each ARGO buoy is measuring.

Mike Jowsey

May 19, 2013 at 12:34 pm

On average there is one Argo buoy per 320km x 320km, or 102,400 square kilometres. Average depth as above in article, 3.6km, therefore on average each Argo buoy is sitting somewhere in 368,640 cubic kilometres of water.

As Willis notes in this article, Feb 2012:

• The sampling of the oceans is by no means as uniform as I had expected. Part of the ocean is undersampled, sometimes badly so, compared to other areas. Half of the global ocean has been sampled less than 20 times per 10,000 sq. km, and 14% has never been sampled by Argo floats at all.


*UPDATED: The ARGO Graph now has another 6 months of data thanks to Nice One for noticing NODC had more up to date numbers. The update adds an uptick at the end, but makes little difference to the trend or the conclusion.  As to the start date, ARGO began in the 1990’s, but it was not fully operational to 700m until mid 2003. The buoy data to 2000m was not fully operational until 2005. If someone can find predictions to 2000m  David can compare models to observations for that depth.

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