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Tracking the energy from global warming

Posted on 18 April 2010 by John Cook

The most striking feature of Climategate is how readily people assumed dark, sinister conspiracies from isolated email quotes without trying to understand the actual science being discussed. This is apparent in the "hide the decline" quote which many took (and continue to take) to mean a nefarious hiding of a decline in temperature. What it actually refered to was a decline in tree-ring growth that has been openly discussed in the peer-reviewed literature since 1995. Similarly, Trenberth's "travesty that we can't account for the lack of warming" was an issue openly discussed in the peer-reviewed literature (Trenberth 2009). The issue of Trenberth's missing heat is now further discussed in a new Science perspective by Trenberth and John Fasullo, "Tracking Earth's Energy".

The article examines the planet's energy imbalance. This can be measured by satellites which measure both the incoming sunlight and outgoing radiation. The absolute energy imbalance is too small to be measured directly. However, the satellite measurements are sufficiently stable from one year to the next so it's possible to track changes in the net radiation. What has been observed is an increasing energy imbalance.

Another way to calculate the energy imbalance is to add up all the heat accumulating in the various parts of our climate. This includes all the heat building in the oceans, warming of the land and atmosphere, melting of the Arctic sea ice, Greenland and Antarctic ice sheets and glaciers. There is fairly good agreement between the satellite imbalance and total heat content leading up to 2005. However after 2005, there is a discrepancy between the two metrics. A divergence problem, if you will.


Figure 1: Estimated rates of change of global energy. The curves are heavily smoothed. From 1992 to 2003, the decadal ocean heat content changes (blue), along with the contributions from melting glaciers, ice sheets, and sea ice and small contributions from land and atmosphere warming, suggest a total warming (red) for the planet of 0.6 ± 0.2 W/m2 (95% error bars). After 2000, observations from the top of the atmosphere ( 9) (black, referenced to the 2000 values) increasingly diverge from the observed total warming (red).

Figure 1 has many interesting features. The blue area shows the rate of ocean warming. Note that when it falls after 2005, this doesn't mean the ocean is cooling but that the rate of warming slows. The red line is the total amount of net energy change. This means that all the energy going into the melting of sea ice, ice sheets and glaciers plus the warming of land and atmosphere is the tiny gap between the blue area and the red line. However, the most interesting feature of this graph is the divergence after 2005. From this point, the satellite data (black line) continues to show a growing energy imbalance. But the ocean seems to be accumulating less heat.

Why the discrepancy? Some of the heat seems to be going into melting the ice sheets in Greenland and Antarctica which are losing ice mass at an accelerating rate. However, this doesn't add up to anywhere near the measured energy difference. There are two possibilities. Either the satellite observations are incorrect or the heat is penetrating into regions that are not adequately measured. The satellite observations also agree with model results that expect a growing energy imbalance as CO2 levels increase. These model results have had quantitative confirmation in independent satellite measurements of outgoing infrared spectrum (Harries 2001, Griggs 2004, Chen 2007).

This would indicate the missing heat is the more likely option. If so, where has the missing heat gone? Is the ocean sequestering heat deep below where the ARGO buoys measure water temperature? I had my own Dunning-Kruger moment after reading this paper. My theory was we already had observational proof that the heat must be sequestered in the deep ocean waters. While measurements of ocean heat going down to 700 metres have showed declining heat accumulation, von Schuckmann 2009 shows that measurements of ocean heat going down to 2000 metres find the oceans have been steadily accumulating heat at 0.77 W/m2 from 2003 to 2008.


Figure 2: Time series of global mean heat storage (0–2000 m), measured in 108 Joules per square metre.

I emailed Kevin Trenberth, asking if von Schuckmann's result was evidence that the missing heat was being sequestered in deeper waters. Trenberth replied promptly (the guy is a class act), informing me that von Schuckmann's energy imbalance of 0.77 W/m2 was for the ocean only and when you average it out over the whole globe, it gives a net energy imbalance of 0.54 W/m2. This is still insufficient to meet up with the satellite data and there are unresolved issues with how von Schuckmann handles the deep water heating.

In fact, after reading Roger Pielke's blow-by-blow with Trenberth, I have to credit Trenberth for his patience - I wonder how many bloggers contact him each day, saying "Hey Kevin, you heard of this paper?!" or "Hey Kevin, did it ever occur to you that the heat is in the deep ocean?!" Hopefully, Trenberth won't get bothered too much by nagging bloggers such as myself and he can get on with the important work of better tracking the flow of energy through our climate.

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Comments 101 to 129 out of 129:

  1. Chris #100 I never said you should 'curve fit' only the last 7-8 years of 'noisy data' - why not curve fit your whole graph - since 1993; which is 17 years of noisy data?? Is that long enough to produce a valid result? The point is that sea level rise should be a lagging measure of OHC - the integral of the energy flux imbalances - so therefore if the sea level rise starts to flatten in the last 7 years - it confirms the 'lack of warming' trend discussed in Dr Trenberth's paper and other OHC analyses.
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  2. I have two possible solutions for the missing energy. The first could account for a substantial portion of the gap, the second... not so much. Based on the Global Net Energy Budget graph, the missing energy over 5 years is about 11 quadrillion kW-hrs. First: If all of this were absorbed into permafrost-bearing regions, it amounts to 490 kW-hr/m2. To absorb all of this energy difference requires melting 5.3 metric tons of ice per m2, or a depth of 17.6 meters of permafrost melted per square meter (30% ice content). While I have no idea if melting permafrost could realistically account for ALL of the missing energy (plausible depth melted, actual ice content/m3), it is plausible that more than several meters of permafrost have melted due to rising temperatures, thus accounting for a substantial fraction of the missing energy. A possible counterargument: Why would this energy sink suddenly show up over the last 5 years rather than gradually, tracking the ups and downs of temperature change? Well, global warming took a powder from the 1940s to early 70s, remaining essentially flat, and began rising after about 1974. That means, ASSUMING that permafrost region temperature paralleled global temperature in direction, permafrost would have been roughly stable from 194X through the late 1970s. It is only after temperature began rising that permafrost would have begun to melt. There would be a substantial lag in the initiation of permafrost melt, since the temperature change would have to propagate to the bottom-most layer of the permafrost, as much as 1000 meters deep, which would take years. Additionally the rate of energy transfer into the permafrost, and therefore melting rate at depth, would depend on the temperature difference, which initially was small, increasing as temperatures rose in the north polar regions, meaning the greatest melting rate is in the more recent years. Finally, given the imprecision inherent in calculating the values going into the above graph, it is plausible that the graph is not precisely correct and that the actual "energy gap" in reality extends back farther to earlier years. Second: It is documented that the mass of plant life is increasing in high latitude areas as trees and shrubs move northward. Also one could ask whether biomass is increasing globally due to fertilizing effect of CO2 in the atmosphere. Addition of biomass in permafrost regions-only would require 242 pounds of dry biomass added per square meter, clearly implausible, but nevertheless increased polar biomass could account for some small fraction of this energy gap (say, 5%?). World wide, the biomass increase to absorb all the energy gap would have to be 11 lbs dry/sq meter, which also seems unlikely, but again a global increase in biomass could account for a fraction of the energy gap. (I didn't say I was a climate scientist!)
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  3. Ken Lambert at 22:27 PM on 2 May, 2010 "why not curve fit your whole graph - since 1993; which is 17 years of noisy data" We've done that already Ken - see my post #76 and #100. Least squares fit of the satellite sea level record (the "whole graph") gives a value somewhere above 3 mm.yr-1; e.g. from analysis of the "whole graph": (a) Beckley, B. D. et al. (2007) determine that the sea level trend is 3.36 mm.yr-1 (b) Cazenave and Llovel (2010) determine that the trend is 3.4 mm.yr-1 (see links in my post #100) (c) The solid line in my post #76 is a least squares fit to the full satellite sea level record. The fit is 3.2 mm.yr-1 (d) likewise Trenberth (see Trenberth and Fasullo 2010, link in John Cook's top post):
    "Since 1992, sea level observations from satellite altimeters at millimeter accuracy have revealed an essentially linear global increase of ~3.2 mm per year, with an enhanced rate of rise during the 1997–1998 El Niño and a brief slowdown in the 2007– 2008 La Niña."
    There really isn't any evidence that the sea level rise "starts to flatten in the last 7 years". That's not to say that there might not be some reduction of heat uptake into the oceans. The data supports the conclusion that recently the mass component (land ice melt) has made a larger contribution to sea level rise [relative to the steric (thermal) component] compared to previous parts of the satellite record. This isn't unexpected considering that the last 7 years has coincided with the descending limb of the solar cycle which has been anomalously extended through cycle 23. However, considering that sea levels continue to rise at upwards of 3 mm.yr-1, it's difficult to draw major conclusions about ocean heat inupt from sea level change from the short period of the last few years, other than that the oceans must almost certainly be continuing to take up heat (because sea level rise can't be fully accounted for by the mass component). Perhaps one might suggest that sea levels should be rising a bit faster now than a decade ago; it wouldn't be surprising if this is observed during the next 5-6 years as the sun "swings" upwards through the rising limb of the solar cycle...
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  4. Chris #103 "There really isn't any evidence that the sea level rise "starts to flatten in the last 7 years". " Except for the evidence of your own eyes. Do a least squares for the last 7 years Chris and you get closer to 2mm than 3mm, which is where we started this discussion. If you assume that Dr Trenberth's figures are roughly correct for glaciers (approx 1mm) and major ice sheets (approx 1mm) then all the recent rise can be accounted by ice and none by thermal expansion. No thermal expansion means no increase in OHC, which is where this blog started viz. the missing heat.
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  5. Joe #103 Joe, please convert your kW-hrs to Joules x exponent 10, and we can talk the same language. Interesting proposition with the permafrost, except for the mechanism of channelling all the 'missing heat' there. I don't have a number for the surface area of permafrost on the globe, but is you use roughly 29% land and 71% ocean, and then look at the 29% land and partition the permafrost as say 20% of the land area then you get 6% of the globe surface as permafrost - I think nearly all in the northern hemisphere. Now think about the mechanism gathering Dr Trenberth's global 'Missing' heat residual of 30-100E20 (Av 65E20) Joules into that 6% of the global surface area in a particular part of the northern hemisphere - given the fact that the heat imbalance is global and not directed to any particular spots on the planet.
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  6. Ken Lambert at 11:55 AM on 3 May, 2010 O.K. fair enough Ken; we've pretty much come full circle and arrived back where we were a few days (and many posts!) ago. For a short period (largely 2006-2008) there was a brief reduction of sea level rise which has brought the trend down a tad when measured over a very short time period. However the sea level rise has now more or less caught up with the long term trend around 3-3.4 mm.yr-1. It is reported at the European Geoscience Union meeting this week that the recent ARGO ocean heat content meaurements are showing significant rises again (I've just heard this from a colleague; no doubt this will be discussed/published more widely in due course). Since glacial/polar ice melt is seemingly increasing (and as we have both pointed out on this thread, this seems to have contributed a larger proportion of sea level rise in the last 6-7 years than during the previous decade), and since measured upper ocean heat content may well be on the rise again, and the sun has grudgingly started its rise up the ascending limb of the solar cycle, it wouldn't be surprising if the rate of sea level rise made another acceleration. The point is that anomalies during very short time periods need to be interpreted with caution. It's possible that the apparent stutter in sea level rise/upper ocean heat content was due to some heat transfer to the deeper oceans which warm with a lesser contribution to thermal sea level rise than surface waters. Perhaps there was an anomalous period of atmospheric behaviour (clouds/aerosols). Perhaps some of the heat has just "disappeared".... We don't really know yet. That's actually the point of Trenberth's recent publications on this subject. My original post was to point out that Peter Berenyi's analysis (that the apparent energy budget "defecit" "bring(s) havoc to standard greenhouse theory" is unscientific. It really isn't helpful to unleash profound interpretations based on throwing numbers at very short time periods especially in the circumstance (Trenberth) that our measuring systems, though greatly improved during the last decade, aren't yet up to the task required for a full accounting of short term phenomena.
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  7. chris #106 The point is that the Sun is only doing 0.25W/sq.m from top to bottom of the 11 year cycle. You cannot argue that this accounts for the postulated 0.9W/sq.m imbalance in forcing. What the real Solar imbalance is underneath the 11 year cycle nobody knows. To know that - you need to know the pre-industrial equilibrium TSI - of which there is only proxy measurement. That assumes that the Earth was ever in equilibrium from Solar forcing which it probably never has been. The TIMS TSI is still 4.5W/sq.m lower than earlier satellite TSI readings - low accuracy but high precision. The average ocean depth is 3700m and we are covering the top 700-900m with Argo of unproven accuracy. The other approx 3000m is largely unknown and no real mechanism is known to get the heat down there in months to years time frames. Lots more accurate measurement is needed to find out what is really happening here.
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  8. KL #104
    Do a least squares for the last 7 years Chris and you get closer to 2mm than 3mm, which is where we started this discussion.
    Except that if you did this, you'd almost certainly find that the error term for the 7 year fit overlapped the error term for the 17 year fit indicating no statistically significant difference between the two slopes. Your continual use of this kind of invalid argument which ignores the statistical reality of the situation strongly suggests that your aim is to confirm your preconceptions, not actually come to a proper understanding of the field.
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  9. The issue is spreading misinformation in another thread: "Satellites have measured an energy imbalance at the top of the Earth's atmosphere". It's not allowed to challenge this proposition where it occurred, we were redirected here. Therefore let's reiterate the references given there. See e.g. Trenberth 2009: "There is a TOA imbalance of 6.4 W m-2 from CERES data and this is outside of the realm of current estimates of global imbalances that are expected from observed increases in carbon dioxide and other greenhouse gases in the atmosphere". Or Trenberh 2010: "The difference between the incoming and outgoing energy -- the planetary energy imbalance -- at the top of the atmosphere is too small to be measured directly from satellites". From this it is crystal clear that satellites in fact have not measured an energy imbalance at the top of Earth's atmosphere, which is inconsistent with the claim they have. So far so good. But we can certainly do better than that. There was an interesting presentation on the 12th CERES-II Science Team Meeting Wednesday, November 4, 2009, Marriott Hotel, Fort Collins, CO at 9:30 am by Paul Stackhouse et al.: FLASHFLUX Update. They merged three datasets.
    1. CERES Terra EBAF Edition 1A (3/2000 - 10/2005)
    2. CERES Terra ERBE-like ES4 Edition2_Rev1 (1/2003 - 8/2007)
    3. FLASHFlux Terra+Aqua (7/2006 - 9/2009)
    They used overlap periods to remove mean difference between datasets and anchored the entire time series to the absolute values of the EBAF. Their (improved) result is seen on slide 21. At the moment we are only interested in the lower panel, the net TOA radiation balance. Unfortunately it is only a picture one can't do much with, other than staring at it. Therefore it had to be re-digitized: Net_TOA_Imbalance_Stackhouse_2009.txt. As accuracy of satellite radiative imbalance measurements is very low, the baseline is of course arbitrary. It is simply aligned to EBAF and has nothing to do with the actual imbalance. However, since precision is a bit better, we can still use it to track changes of this imbalance over time. To anchor the baseline to reality we need another data source (not considered by Stackhouse et al.) Fortunately we have quarterly data for the heat content anomaly of the upper 700 m of oceans since 1955 at the NOAA NODC Global Ocean Heat Content page. OHC (Ocean heat Content) anomaly is perfect for intercalibration purposes, because it is a linear function of the temporal integral of radiative imbalance at TOA. That is, the average slope of OHC in a time interval is indicative of average imbalance over the same period. For intercalibration we need several full years, because Stackhouse et al. only provides deseasonalized data while Levitus et al. of NODC include seasonal signal. It is best to use data from the ARGO period, because prior to that OHC is poorly and sparsely measured by diverse systems while ARGO provides a homogeneous and dense dataset. Now, before about mid-2003 ARGO coverage was not yet global, so we have to settle to the 6 years between 4. quarter 2003 and 3. quarter 2009. In this period (taking into account the error bars provided by NODC) slope of the OHC anomaly curve (for the upper 700 m) is -1.8±9.6×1020 J/year, which translates to an imbalance of -11±60 mW/m2. That is, in this period the climate system was probably losing heat, not gaining it, but the gain, in any case was more than an order of magnitude smaller than Trenberth's 850 mW/m2: "The TOA energy imbalance can probably be most accurately determined from climate models and is estimated to be 0.85 ± 0.15 W m-2". Therefore heat accumulation for this period can be considered zero well within error bounds. It is fortunate, because only a fraction of the net heat content anomaly is realized in the upper 700 m of oceans, the rest comes from or goes to elsewhere (deep ocean, land, ice sheets), although at least two third remains in the upper ocean. Average of Stackhouse's net TOA imbalance for the 72 months between October 2003 and September 2009 is 202 mW/m2, that is, their baseline is probably too high. If 213 mW/m2 is subtracted from each of their values, it brings net TOA radiative imbalance in line with OHC data. Now, that we have the correct offset for TOA imbalance, we can calculate heat accumulation for the entire timespan covered by Stackhouse's data. It looks like this: As you can see the story the data tell is somewhat different from the standard one. Heat content of the climate system is not increasing, but decreasing. What is more, the radiative imbalance at TOA during the satellite era is about -0.26 W/m2, which is, according to Trenberth, inconsistent with the 0.85±0.15 W/m2 determined from climate models. Furthermore, if we suppose about 2/3 of heat content changes are realized in the upper 700 m of oceans, it turns out satellite radiative imbalance measurements at TOA are also inconsistent with pre-ARGO OHC measurements. It probably means before about mid-2003 OHC data are absolutely bogus and unusable for model testing and calibration.
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  10. Berényi Péter @109: 1)
    "As you can see the story the data tell is somewhat different from the standard one. Heat content of the climate system is not increasing, but decreasing."
    Stackhouse et al clearly indicate that there was a decrease in Out going Long Wave Radiation in 2008, and a decrease in Reflected Short Wave Radiation. With near constant incoming Short Wave Radiation, a reduction in outgoing radiation means there was an increase in energy stored in the ocean/atmosphere system. You have interpreted it as a decrease, which means you have the wrong sign for Heat Content anomaly as measured by satellites in your second and third graphs. That also means that the Heat Content Anomaly of the ocean/atmosphere system is increasing contrary to your claims. As the supposedly decreasing HCA is the basis of your entire analysis, your employing the wrong sign renders the analysis false. 2) On a side note, your rejection of Ocean Heat Content data prior to mid 2003 is without basis and constitutes the grossest sort of cherry picking. ARGO buoys where deployed as early as 1999. If there was a fundamental flaw in the Expendable Thermobathygraph (XBT) measurements, it would show in distinctly different trend in measured temperatures between XBT data and ARGO data. No such divergence in trends exists. Picking mid 2003 as the start of the ARGO era rather than 2002 when hundreds where already operational, or November 2007 when the target of 3000 operational buoys was first achieved has no basis other than to provide a high OHC as the start point of a cherry picking argument.
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  11. #110 Tom Curtis at 21:01 PM on 9 May, 2011 You have interpreted it as a decrease, which means you have the wrong sign for Heat Content anomaly as measured by satellites in your second and third graphs. That is not so. Please try to understand first what's being said and shown and subsequently provide your reflections. That sequence is much more convenient for all. The sign of satellite heat content anomaly is correct indeed, which, among other things, can be seen from the brief increase during 2008 and in the first half of 2009. If you still claim direct OHC measurements before mid-2003 are correct, you should inevitably say satellite radiative imbalance measurements at TOA prior to that date are in error. Is that your position? BTW, you may notice how ARGO coverage improved between April 2003 and April 2004, especially in the Southern Pacific. Here is current coverage:
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    Response:

    [DB] Tamino has much to say about this specific topic here.

  12. Daniel, you can of course delete any comment at will, but that does not change the fact Tamino does not even mention satellites in the post you have linked.
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    Response:

    [DB] Firstly: Your comment was deleted due to being in conflict with this portion of the Comments Policy

    Posting personal details of another user results in your account being banned from Skeptical Science.

    It is noted that Tamino does not regualarly make an appearance at SkS.  But since Tamino is his Internet nom de plume, honor that personal preference he has made.  Your repeated usage of his personal name is thus interpreted as being an invasion of privacy.  Please respect that in future comments.

    Secondly, Tamino's post was referenced as a prime example of the lengths that some go to take OHC data out of context.  A focus on recent expanded ARGO data without the context of historical data is also an example of that.

    OHC

    Lastly, if you feel that ARGO data is so suspect and unusable, then stand behind your position with the due diligence of publishing your analysis.  There exist a number of publishing entities that would do so.

  13. Berényi Péter @111: 1)
    "The FLASHFlux (Fast Longwave and Shortwave radiative Fluxes from CERES and MODIS) project derives daily averaged gridded top-of-atmosphere (TOA) and surface radiative fluxes within one week of observation. Production of CERES based TOA and surface fluxes is achieved by using the latest CERES calibration that is assumed constant in time and by making simplifying assumptions in the computation of time and space averaged quantities. Together these assumptions result in approximately a 1% increase in the uncertainty for FLASHFlux products over CERES. Analysis has clearly demonstrated that the global-annual mean outgoing longwave radiation shows a decrease of ~0.75 Wm-2, from 2007 to 2008, while the global-annual mean reflected shortwave radiation shows a decrease of 0.14 Wm-2 over that same period. Thus, the combined longwave and shortwave changes have resulted in an increase of ~0.89 Wm-2 in net radiation into the Earth climate system in 2008. A time series of TOA fluxes was constructed from CERES EBAF, CERES ERBE-like and FLASHFLUX. Relative to this multi-dataset average from 2001 to 2008, the 2008 global-annual mean anomalies are -0.54/-0.26/+0.80 Wm-2, respectively, for the longwave/shortwave/net radiation. These flux values, which were published in the NOAA 2008 State of the Climate Report, are within their corresponding 2-sigma interannual variabilities for this period. This paper extends these results through 2009, where the net flux is observed to recover. The TOA LW variability is also compared to AIRS OLR showing excellent agreement in the anomalies. The variability appears very well correlated to the to the 2007-2009 La Nina/El Nino cycles, which altered the global distribution of clouds, total column water vapor and temperature. Reassessments of these results are expected when newer Clouds and the Earth's Radiant Energy System (CERES) data are released."
    Stackhouse et al, 2010, my emphasis. I repeat, you have the sign wrong. An increase of "net radiation into the Earth Climate System" can only be interpreted as an increase in the energy stored in the Earth's climate system. 2) The only way the lack of coverage of the Southern Pacific can be significant is if it showed an opposite trend in temperatures to the rest of the worlds oceans, and of such magnitude as to cancel out the warming detected by pre April 2003 Argo buoys in the rest of the world's oceans: Nope. Sure looks like its warming to me. You have no basis to consider the number of Argo buoys pre April 2003 to be insufficient to get a reasonable sample. If you believe otherwise, show mathematically why 750 buoys, each making multiple samples is not a statistically significant sample. Alternatively, provide alternative evidence (from XBT buoys, for example) of the massive cooling trend in the South Pacific which is required for the operational Argo buoys to not have given a fair sample. You will, of course, be unable to provide either of these because the meme that Argo coverage was insufficient pre-2003 was made up by people wishing to cherry pick a high point in the data as their start point. Both I and Daniel Bailey have provided a link to an article which clearly explains this.
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    Response:

    [DB] Fixed graphic.  Tom, the GISS site uses a dynamic display; to ensure the graphic continues to be visible, post it to a static site and then link to it.  For example, I saved the image to my HD, uploaded it to SkS and then used the SkS URL to fix your html tag.  Clunky, but effective.

  14. #113 Tom Curtis at 01:52 AM on 10 May, 2011 I repeat, you have the sign wrong. Fine. You have repeated a false statement. It does not make it true. Now I will have to wait until you realize your misunderstanding, because it does not make much sense to proceed this way.
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  15. Tom @113, Re this comment made at #114: "Now I will have to wait until you realize your misunderstanding" This condescending attitude of BP's is not constructive or helpful. I had a quick look at the abstract for the FLASHFLUX link you provided @113 and they state that the net radiation in 2008 increased by 0.8 W m-2. Now in my line of work at least, that means that there is an increase in the energy available to the system.
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  16. Apart from the obvious error in the sign of the imbalance (unless Stackhouse et al. misinterpreted their own data), I can see no reason why the 0-700 m OHC should follow the radiation imbalance with no delay. The average ocean mixed layer depth is much smaller than this. The simple direct comparison is definitely misleading.
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  17. #115 Albatross at 02:42 AM on 10 May, 2011 I had a quick look at the abstract for the FLASHFLUX link you provided @113 and they state that the net radiation in 2008 increased by 0.8 W m-2. Now in my line of work at least, that means that there is an increase in the energy available to the system. Yes. And what do you see in the "Heat Content Anomaly of the Climate System" graph? First derivative of the blue line changes sign from negative to positive at the beginning of 2008. Just the way it should. Heat content is the temporal integral of radiative imbalance. If there is a step change in the latter one, local slope of the former one changes direction. Only there was more decrease in heat content between 2000 and 2008 (about -5×1022 J) than increase afterward (1.5×1022 J). It is pretty simple, really.
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  18. Berényi Péter @117:
    "Yes. And what do you see in the "Heat Content Anomaly of the Climate System" graph? First derivative of the blue line changes sign from negative to positive at the beginning of 2008. Just the way it should."
    And what do we see in this graph of the Net TOA anomaly? Why, a clear positive trend with a slight negative trend from 2008 to 2009. The reverse of the trends you show in your second and third graphs of post 109.
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  19. DB, thanks for the graphic fix.
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  20. Tom @118, I was just busy posting the same message (more or less) when SAFARI crashed on me. I have downloaded the data and the slope of the OLS line is positive. Hansen et al. (2011, in review) also have some interesting insights on the alleged "missing" heat.
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  21. #118 Tom Curtis at 07:30 AM on 10 May, 2011 And what do we see in this graph of the Net TOA anomaly? Why, a clear positive trend with a slight negative trend from 2008 to 2009. The reverse of the trends you show in your second and third graphs of post 109. Tom, you don't know what integral means, do you? Study it please and come back later.
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  22. Well, BP seems to believe that we are idiots or at the very least cannot grasp simple mathematical concepts. Hopefully he has more time and respect for Hansen, Sato, Kharecha and von Shuckmann (in review, 2011), but there are no guarantees on such maters with D-Ks. I have bolded some of the text: "The slowdown of ocean heat uptake, together with satellite radiation budget observations, led to a perception that Earth's energy budget is not closed (Trenberth, 2009; Trenberth and Fasullo, 2010), as summarized in Fig. 19A. However, our calculated energy imbalance is consistent with observations (Fig. 19b), implying that there is no missing energy in recent years. Note that, unlike Fig. 19b, real-world climate and planetary energy imbalance include unpredictable chaotic interannual and interdecadal variability. A climate model with realistic interannual variability (but muted El Nino variability) yields unforced interannual variability of global mean energy balance of 0.2-0.3 W/m2 (Fig. 1, Hansen et al., 2005)." And "An alternative potentially accurate approach to measure Earth's energy imbalance is via changes in the ocean heat content, as has been argued for decades (Hansen et al., 1997) and as is now feasible with Argo data (Roemmich and Gilson, 2009; Von Schuckmann and Le Traon, 2011). This approach also has sampling and instrument calibration problems, but it has a fundamental advantage: it is based on absolute measurements of ocean temperature. As a result, the accuracy improves as the record length increases, and it is the average energy imbalance over years and decades that is of greatest interest. The error estimated by von Schuckmann and Le Traon (2011) for ocean heat uptake in the upper 2000 m of the ocean, ± 0.1 W/m2 for the ocean area or ± 0.07 W/m2 for the planetary energy imbalance, does not include an estimate for any remaining systematic calibration errors that may exist. At least some such errors are likely to exist, so continuing efforts to test the data and improve calibrations are needed. The Argo program needs to be continued and expanded to achieve further improvement and minimization of error." Now who to trust on the science, BP or Hansen et al.? Easy, Hansen et al. of course.
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  23. And more from Hansen et al. (2011), again highlights are mine: "A verdict is provided by the ocean heat uptake found by von Schuckmann and Le Traon (2011), 0.42 W/m2 for 2005-2010, averaged over the planet. Adding the small terms for heat uptake in the deeper ocean, warming of the ground and atmosphere, and melting of ice, the net planetary energy imbalance exceeded +0.5 W/m2 during the solar minimum. This dominance of positive climate forcing during the solar minimum, and the consistency of the planet's energy imbalance with expectations based on estimated human-made climate forcing, together constitute a smoking gun, a fundamental verification that human-made climate forcing is the dominant forcing driving global climate change. Positive net forcing even during solar minimum assures that global warming will be continuing on decadal time scales."
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  24. #122 Albatross at 08:19 AM on 10 May, 2011 Now who to trust on the science, BP or Hansen et al.? Easy, Hansen et al. of course. Well, the last time I've checked no one was to be trusted on science. All you have to do is to understand what was being said and check the logic using your own mind. Admittedly, some effort and discipline is needed to stick to the subject at hand and not to talk about something else, but that's the price. Of course if you do not trust either CERES or ARGO data are presented faithfully, that's entirely another matter. And a serious accusation as well. But once the data are given as they are, the conclusion is inevitable. There is no missing heat, but there was some, in the past (it was not measured properly, that is).
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  25. Albatross - Thank you for the link and the information. It's great to see actual data and detailed analysis, rather than the subset analysis sometimes presented here as a skeptical argument. BP? Ken Lambert? I suggest you read the link Albatross provided to Hansen et al, in press 2011. I believe it to be a far more accurate and definitive description of the state of the climate than selecting the last 8 years starting with a high residual (i.e., 2003), or integrating poorly limited values over a century+ rather than looking at ongoing actual data.
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  26. Blimey, that paper is pretty extraordinary. There is a great deal in it to digest. I look forward to the publication.
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  27. The Schuckmann and La Traon paper referenced is also pretty pertinent though note that it is also in press.
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  28. KR and scaddenp, No worries. Yes, Hansen et al. (2011) is quite the paper, fantastic overview of the science. The von Shuckmann and La Traon paper is also impressive-- decimates Douglass and Knox's extremely poor effort.
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    Response:

    [DB] BTW, Tamino has a real nice post on 5-year trends; tangential to this discussion.

  29. Berényi Péter @121:
    "Tom, you don't know what integral means, do you? Study it please and come back later."
    I am no mathematician, at calculus tests the limits of my ability, but here goes ... The integral of a function is the area under the curve of that function. Given this, if a curve has a positive slope (ie, it increases in value with increasing x), then for equal segments on the x axis, the definite integral must increase with increasing x. Conversely, with a negative slope the definite integral must decrease with increasing x. As seen above, the graph of the deseasonalized net TOA anomaly has a positive trend from 2000 to 2008, and a negative trend from 2008 to 2009. Therefore the integral must increase on average over the period 2000 to 2008, and decrease from 2008 to 2009. You show the reverse. Of course, we don't need these mathematical meanderings to know that you have the sign wrong. All we need to notice is that you have mapped an increasing power coming in, to a decreasing energy received. According to you, receiving more Joules per second in 2008 than in 2000 in the climate system receiving fewer Joules per year in the year 2008 than it did in 2000.
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  30. #129 Tom Curtis at 23:42 PM on 10 May, 2011 if a curve has a positive slope (ie, it increases in value with increasing x), then for equal segments on the x axis, the definite integral must increase with increasing x. Conversely, with a negative slope the definite integral must decrease with increasing x. That's not so. The only thing that follows is if a curve has a positive slope, the definite integral is a convex function (for negative slope it is concave). Convex or concave functions can have either positive or negative slopes, or their slope may change sign (at most once).
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  31. Tom @ 129, If the function goes below zero then the area added is negative. The key to Berenyi's analysis then is the choice of his baseline to calibrate the TOA measurements and convert them into absolute values rather than anomalies. He explained it in @109, though the justification wasn't very rigorous.
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  32. The situation with satellite measurements of net TOA radiative imbalance is worse than we thought. I have already shown you ample evidence that the absolute magnitude of this imbalance is not measured at all by satellites alone in any reasonable sense. The only thing we can hope for is a relative measurement of net TOA radiative imbalance by satellites, that is, its changes over time independent of the (unknown) baseline. Indeed, using Net_TOA_Imbalance_Stackhouse_2009.txt derived from slide 21. Stackhouse 2009 and assuming a uniform error of ±0.41 W/m2 for their monthly averages (as indicated in the presentation), we get a positive trend of 113 ± 14 mW/m2/year for net TOA radiative imbalance between March 2000 and September 2009 (the entire timespan of their data). Therefore heat content accumulation in the climate system, being proportional to the temporal integral of net TOA radiation imbalance, should be accelerating in this nine and a half year long interval. That is, the acceleration term has a positive value of 0.182 ± 0.023 × 1022 J/year2. On the other hand all reconstructions show a marked deceleration of Upper Ocean Heat Content Anomaly accumulation for the same period. Specifically the NOAA NODC Global Ocean heat Content page shows the same. With the additional advantage of having digital data with proper error bars online, of course. Therefore it is possible to calculate the acceleration term for the accumulation of heat in the upper 700 m of oceans between 2nd quarter 2000 and 3rd quarter 2009. This value is −0.116 ± 0.038 × 1022 J/year2, it is negative, as expected. Heat content of the upper 700 m of oceans is only a fraction of heat content of the entire climate system, but it is a considerable fraction, close to 70%. That is, acceleration term of heat content accumulation calculated for the entire system should be even less, around −0.166 ± 0.054 × 1022 J/year2 Taking into account the error bars we have calculated for the acceleration term of heat content accumulation arrived at by two different methods (statellites for net TOA imbalance vs. in situ measurement of OHC), the results are absolutely inconsistent, separated by some (!). The inconsistency is indeed profound. And it shows up between two independent measurements of the same quantity, not between theory and measurement. It means the radiative imbalance at TOA is not measured at all, not even by satellites aided by OHC measurements. Something is surely wrong here, even if at this level on can't readily pinpoint the error. My best guess is the inferior quality of OHC data prior to mid-2003 (the ARGO era), which would imply a negative average radiative imbalance at TOA over the last decade, that is, net loss of heat by the climate system, not a gain, as it would be required by computational climate models. In other words, Trenberth's missing heat is not going into some mysterious current heat reservoir, but it can be found in the past (and was radiated out to space since then). But even if it is not so, the inconsistency shown above still begs for a resolution. If anyone knew a paper explicitly discusing the issue, a pointer is welcome.
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  33. BP: James Hansens recent analysis here shows that there is no missing heat. The slowing in heat increase in the ocean is due to a rebound effect from recent volcano eruptions and the recent solar minimum. The rebound effect is over and the solar cycle has started its upswing so we can expect record heat in the nexxt 5 years. It is obvious that since 2010 was a record setting hot year at the bottom of the solar minimum that the climate continues to heat up.
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  34. #133 michael sweet at 01:19 AM on 14 May, 2011 James Hansens recent analysis here shows that there is no missing heat. That's not a peer reviewed publication. On top of that, it does not discuss the problem at hand.
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  35. Hansen's publication has been submitted for peer review. You can wait for it to be published if you want, it usually takes six months to a year.
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  36. BP @133, "That's not a peer reviewed publication." Well, not yet :) Seriously, we'll see what it looks like after review, my understanding is that it is in review now, including by the public. So I'm sure Dr. Hansen would love to hear the errs of his ways from you BP. Talking of peer-review, Hansen et a. (2011) cite works that have undergone peer-review and that have been published, for example, von Schuckmann and Le Traon (2011).
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  37. e @131, if the graph of the function has a positive slope, then once it goes above zero it cannot go below zero (without changing slope) at a larger value of x. Therefore, while it may be below zero and have negative values for some x', for all x" > x' it will either be negative with a smaller absolute magnitude, or positive. And of course, -4 < -2 < 1. Hence I do not see how your point can refute my claim. Returning to his original calculation as shown in the second graph of 109, we see that it definitely shows total incoming energy in 2008 to be less than total incoming energy in 2000. The original data, however, shows that throughout 2008, the TOA radiative balance for 2008 was higher in Watts/meter squared than that for 2000. Therefore the Earth must have retained more energy in 2008 than in 2000 given the accuracy of the data. Despite this BP shows the reverse. Therefore he has made an error, and his ability to parrot the words "integrate", "convex function" and "concave function" cannot alter that. You cannot reduce the Joules received over the whole year by increasing the Joules received every second, but that is what BP would have us believe in his post @109. In his post 132 he suddenly changes tune without acknowledging the previous error and now wants to claim he has determined a rate of change (acceleration) in the satellite data from a linear trend. A constant rate of increase of the change between each year of 0.182 ± 0.023 × 1022 J/year^2 (not the years squared) does not result in a linear function, and so cannot be derived from a linear trend. I am not saying BP could not (or even has not) fit the data to and exponential function and hence derived an acceleration from the data. But he has certainly not shown us the fit, nor the correlation to the fit. Consequently he has not justified his claims about the "acceleration" of the satellite data; or even told us he has used a method that could justify it. To the extent that I can check BP's mathematics, it is garbage. It shows every indication of being stuck onto the analysis to convince the mathematically illiterate that he is making some profound analysis whereas he is really just spouting nonsense.
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  38. Tom@137, I have to respectfully disagree with your specific criticism of BP's math (having the sign wrong) though note I'm not agreeing with BP's analysis in general. By way of example, here is a graph of y = x - 10. Note that the function is negative until x=10, and represents a constant positive linear trend: And here is the integral of that function: Note that the value of the integral is negative with increasing absolute magnitude until x=10, after which the absolute magnitude decreases though the actual value remains negative. Also note the similarity in shape to BP's graph, with x=10 being roughly equivalent to 2008. Again, the key to his analysis was how he baselined the anomaly data. As an example if I take my sample function above, and move the baseline down by 10 (y = x), then we see a very different story when we take the integral: >"...definitely shows total incoming energy in 2008 to be less than total incoming energy in 2000." By taking the integral, BP is basically showing the "running total" of energy in the system from t=2000 to the point in question. So his graph is showing that total energy in the system mostly decreasing from 2000 to 2008, and then mostly increasing in 2008 and onwards. Overall his graph shows that energy lost from 2000-2008 was greater than energy gained in 2008 and onwards. This does not contradict the fact that the net anomaly was higher in 2008 than it was 2000.
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  39. #138 e at 05:49 AM on 14 May, 2011 Tom@137, I have to respectfully disagree with your specific criticism of BP's math (having the sign wrong) Thanks, perhaps I could not explain it as clearly as you did. though note I'm not agreeing with BP's analysis in general. I see. But you should be a bit more specific than that. It is too easy not to agree with something "in general". It is harder (and more helpful) to explicate exactly how your analysis differs from mine, i.e. which steps do you see as problematic. #136 Albatross at 01:59 AM on 14 May, 2011 Seriously, we'll see what it looks like after review, my understanding is that it is in review now, including by the public. So I'm sure Dr. Hansen would love to hear the errs of his ways from you BP. I hope so. Anyway, if it is in fact an open peer review process, I can only support it. Let's start with something Dr. Hansen has to say about satellite measurements of radiative energy imbalance at TOA (Top of Atmosphere). "The precision achieved by the most advanced generation of radiation budget satellites is indicated by the planetary energy imbalance measured by the ongoing CERES (Clouds and the Earth's Radiant Energy System) instrument (Loeb et al., 2009), which finds a measured 5-year-mean imbalance of 6.5 W/m2 (Loeb et al., 2009). Because this result is implausible, instrumentation calibration factors were introduced to reduce the imbalance to the imbalance suggested by climate models, 0.85 W/m2 (Loeb et al., 2009). The problems being addressed with this tuning probably involve the high variability and changes of the angular distribution functions for outgoing radiation and the very limited sampling of the radiation field that is possible from an orbiting satellite, as well as, perhaps, detector calibration. There can be no credible expectation that this tuning/calibration procedure can reduce the error by two orders of magnitude as required to measure changes of Earth's energy balance to an accuracy of 0.1 W/m2." This brings us back to #109 where I have started to analyse the truth-value to be assigned to the proposition "Satellites have measured an energy imbalance at the top of the Earth's atmosphere" found in another thread at this site, and concluded it was false. As you can see, Dr. Hansen agrees with this evaluation, therefore if nothing else, but on his sheer authority one could put a red flag to all occurrences of this misleading proposition at this site (also repeated in e.g. The Big Picture). We could leave it at that. However, this time I am also tasked with a reflection on Dr. Hansen's essay. The first thing to note is that Dr. Hansen in his elaboration on satellite measurements of radiative inbalance at TOA hopelessly mixes up accuracy and precision. While it is true, that accuracy of satellite measurements is insufficient to determine a radiative imbalance, their precision is much better, that is, they are suitable to determine relative changes in this quantity. And the inconvenient fact is they show an overall upward trend during the last decade or so. On the other hand OHC data show the opposite, a downward trend in energy accumulation rate. The claimed error bars for both kind of measurement are such, that these results are inconsistent with each other (error bars do not overlap, by a wide margin). Dr. Hansen takes the easy escape route when he dismisses satellite data altogether based on their low accuracy. However, in a review article like this it is not the proper thing to do. If his opinion is such that even long term stability and precision of satellite net radiative imbalance measurements at TOA is insufficient to determine a meaningful trend over time, either because of intercalibration problems between different measurement systems (like EBAF, ES4 or FLASHFlux), detector calibration issues or high variability and changes of the angular distribution functions for outgoing radiation that make error bars wide enough to prevent such an application, then he has to say so explicitly. It is a perfectly legitimate stance, but in a review paper it should be supported by some evidence, that is, he should dig up the literature for peer reviewed publications arriving at a conclusion that from satellite data alone we can't even determine the sign of the imbalance trend for the last decade. Unfortunately he fails to do so and dismisses the whole issue based on a single study (Loeb 2009) which deals with something else, namely the inferior absolute accuracy of satellite data. That's surely not the way to go. If he did such an investigation, it could prove not even a weaker version of the proposition above like "Satellites have helped infer an energy imbalance at the top of the Earth's atmosphere" would stand. In that case we would be left with OHC measurements alone indeed, as Dr. Hansen claims, and there would be no independent measurement at all to check our OHC time series against in any way. I do not believe it is the case, but he may try to take such a track. On the other hand, if he can't substantiate the impossibility of deriving an imbalance trend from satellite data, he has no choice but fully expose the inconsistency between the two lines of independent evidence. A trend line surely can't go both up and down at the same time. This latter proposition is at the kernel of Trenberth's travesty. Intercalibration between OHC and satellite radiative imbalance measurements at TOA can't be done for the full period within error bounds, simply because upward and downward trends can never be aligned by adding a constant to one of them. Dr. Trenberth chooses to use the early part of CERES and OHC data for intercalibration (between 2000 and 2005) so he has a tremendous amount of recent "missing heat" in the system, possibly sequestered into an as-yet-unknown and somewhat mysterious heat reservoir. If we do not follow him in this respect and use the late part of data for intercalibration (between 2003 & 2009 or 2005 & 2010 perhaps), we get a different picture. There is no recent "missing heat" at all, but there used to be some missing (that is, unmeasured) heat in the system before the ARGO era. It would mean the long term (decadal) rate of heat accumulation in the system is much smaller than shown by unadjusted OHC data and certainly smaller than the 0.85 ± 0.15 W/m2 indicated by computational climate models. It is entirely possible that the question is still open, that is, the science is not settled in this respect, but it is impossible to pretend there is no question at all. And precisely that's what Dr. Hansen is trying to do. It goes against one of the main purposes of review papers, that is, to uncover open areas for future investigation.
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  40. BP: Where did you come up with the idea that Hansens' paper is a review paper? The paper gives new data on "missing heat", concluding that there is no missing heat, and he gives a new estimate of the aerosol effect which he claims is substantially higher than the IPCC estimates. Your claim that it is a review paper is just tosh so that you can criticize the paper. Stay on topic.
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  41. #140 michael sweet at 00:40 AM on 16 May, 2011 Where did you come up with the idea that Hansens' paper is a review paper? He does not have any original research supporting the idea of dismissing satellite net TOA radiation balance measurements altogether, not even looking at changes in the rate of heat accumulation. At least in that respect it is a review paper, or not even that, because he does not have any reference supporting the low precision of satellite data in addition to their well known low accuracy. If satellite data are disregarded, there is of course no any "missing heat". Heat can only be "missing" relative to something, in itself heat is just heat without any further qualification. He pretends the "missing heat" problem is a supposed discrepancy between computational climate model projections and OHC measurements, that is, between theory and measurement. It is not. The thing is we have two independent measurements of the same quantity, rate of change for radiative imbalance, and they are inconsistent with each other. We can't even begin to compare theory to measurement until the measurement problem itself is settled.
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