Four out of five ARGO data studies now show Ocean Heat Content declining
Readers may recall that Dr. Kevin Trenberth said this in one of the Climategate emails:
“The fact is that we can’t account for the lack of warming at the moment and it is a travesty that we can’t.”
Recent energy balance of Earth
R. S. Knox and D. H. Douglass
Department of Physics and Astronomy, University of Rochester, Rochester, NY
A recently published estimate of Earth’s global warming trend is 0.63 ± 0.28 W/m2, as calculated from ocean heat content anomaly data spanning 1993–2008. This value is not representative of the recent (2003–2008) warming/cooling rate because of a “flattening” that occurred around 2001–2002. Using only 2003–2008 data from Argo floats, we find
by four different algorithms that the recent trend ranges from –0.010 to –0.160 W/m2 with a typical error bar of ±0.2 W/m2. These results fail to support the existence of a frequently-cited large positive computed radiative imbalance.
Recently Lyman et al.  have estimated a robust global warming trend of 0.63 ± 0.28 W/m2 for Earth during 1993–2008, calculated from ocean heat content anomaly
(OHC) data. This value is not representative of the recent (2003–2008) warming/cooling rate because of a “flattening” that occurred around 2001–2002. Using only 2003-2008 data, we find cooling, not warming.
This result does not support the existence of a large frequently- cited positive computed radiative imbalance (see, for example, Trenberth and Fasullo ).
A sufficiently accurate data set available for the time period subsequent to 2001–2002 now exists. There are two different observational systems for determining OHC. The first and older is based upon expendable bathythermograph (XBT) probes that have been shown to have various biases and systematic errors (Wijffels et al. ). The second is the more accurate and complete global array of autonomous Argo floats , which were deployed as of the early 2000s. These floats are free from the biases and errors of the XBT probes although they have had other systematic errors . We begin our analysis with the more accurate Argo OHC data. There are issues associated with a “short-time”
segment of data, which are addressed.
2. Data and Analysis
In what follows, we make reference to FOHC, defined as the rate of change of OHC divided by Earth’s area. It has units of energy flux and is therefore convenient when discussing heating of the whole climate system. In W/m2, FOHC is given by 0.62d(OHC)/dt when the rate of change of OHC is presented in units of 1022 J/yr.
Figure 1 shows OHC data from July 2003 through June 2008 (blue data points, left scale) as obtained from Willis . These data appear to show a negative trend (slope) but there is an obvious annual variation that must be “removed.” We estimated the trend in four different ways, all of which reduce the annual effect. Method 1. The data were put through a 12-month symmetric box filter (Figure 1, red curve). Note that the length of the time segment is four years. The slope through these data, including standard error, is –0.260 ± 0.064 × 1022 J/yr, or FOHC = –0.161 ± 0.040 W/m2.
Method 2. The difference between the OHC value for July 2007 and July 2003 is divided by 4, giving one annual slope estimate. Next, the difference between
August 2007 and August 2003 is calculated. This is done ten more times, the last difference being June 2008 minus June 2004. The average slope of these twelve values, including standard deviation, is –0.0166 ± 0.4122 × 1022 J/year, or FOHC = –0.0103 ± 0.2445 W/m2. Method 2’s advantage is that the difference of four years is free
from short-term correlations.
Method 3. Slopes of all January values were computed and this was repeated for each of the other months. The average of the twelve estimates, including standard deviation, is –0.066 ± 0.320 × 1022 J/year, or FOHC = –0.041 ± 0.198 W/m2.
Method 4. The average of OHC for the 12 months from July 2003 to June 2004 was computed, similarly for July 2004 to June 2005, etc. For the five values the slope found, including standard error, is –0.0654 ± 0.240 × 1022 J/yr, or FOHC = –0.0405 ± 0.1488 W/m2.
These results are listed in Table 1.
There have been four other recent estimates of slopes from the Argo OHC data, by Pielke , Loehle , Douglass and Knox , and von Schuckmann et al. . Each of these studies of Argo OHC data with the exception of von Schuckmann’s, which differs in the ocean depth covered (0–2000 m), show a negative trend with an uncertainty of several 0.1 W/m2. Why the von Schuckmann case is an “outlier” is worthy of further study.
3. Discussion and Summary
As many authors have noted, knowing FOHC is important because of its close relationship to FTOA, the net inward radiative flux at the top of the atmosphere. Wetherald et al.  and Hansen et al.  believe that this radiative imbalance in Earth’s climate system is positive, amounting recently  to approximately 0.9 W/m2. Pielke  has pointed out that at least 90% of the variable heat content of Earth resides in the upper ocean.
Thus, to a good approximation, FOHC may be employed to infer the magnitude of FTOA, and the positive radiation imbalance should be directly reflected in FOHC (when
adjusted for geothermal flux ; see Table 1 caption). The principal approximations involved in using this equality, which include the neglect of heat transfers to land masses and those associated with the melting and freezing of ice, estimated to be of the order of 0.04 W/m2 , have been discussed by the present authors .
In steady state, the state of radiative balance, both quantities FTOA and FOHC should be zero. If FTOA > FOHC, “missing energy” is being produced if no sink other than the ocean can be identified. We note that one recent deep-ocean analysis , based on a variety
of time periods generally in the 1990s and 2000s, suggests that the deeper ocean contributes on the order of 0.09 W/m2. This is not sufficient to explain the discrepancy.
Trenberth and Fasullo (TF)  believe that missing energy has been accumulating at a considerable rate since 2005. According to their rough graph, as of 2010 the missing energy production rate is about 1.0 W/m2, which represents the difference between FTOA ~ 1.4 and FOHC ~ 0.4 W/m2. It is clear that the TF missing-energy problem is made much more severe if FOHC is negative or even zero. In our opinion, the missing energy problem is probably caused by a serious overestimate by TF of FTOA, which, they state, is most accurately determined by modeling.
In summary, we find that estimates of the recent (2003–2008) OHC rates of change are preponderantly negative. This does not support the existence of either a large positive radiative imbalance or a “missing energy.”
Read the full paper available here at the authors University of Rcohester website:
For those wondering how ARGO works unattended, this image shows how:
Simple Mission Operation: The float descends to cruising depth, drifts for several days, ascends while taking salinity and temperature profiles, and then transmits data to satellites. More here
h/t to Russ Steele