International Journal of Geosciences, 2010, 1, 99-101
doi:10.4236/ijg.2010.13013 Published Online November 2010 (
Copyright © 2010 SciRes. IJG
Recent Energy Balance of Earth
Robert S. Knox, David H. Douglass
Department of Physi cs a nd Ast r onomy, University of Rochester, Rochester, New York, USA
Received July 28, 2010; revised August 10, 2010; accepted August 30, 2010
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 –0.161
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.
Keywords: Energy Balance, Radiative Imbalance, Ocean Heat Content
1. Introduction
Recently Lyman et al. [1] 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 no t represen tative of the recen t
(2003-2008) warming/cooling rate because of a “flatten-
ing” that occurred around 2001-2002. Using only 2003-
2008 data, we find cooling, not warming. This result
does not support th e existence of a large freque ntly-cited
positive computed radiative imbalance (see, for example,
Trenberth and Fasullo [2]).
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 bathyther-
mograph (XBT) probes that have been shown to have
various biases and systematic errors (Wijffels et al. [3]).
The second is the more accurate and complete global
array of autonomous Argo floats [4], which were de-
ployed 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 [5]. We begin our
analysis with the more accurate Argo OHC data. There
are issues associated with a “short-time” segment of data,
which are addre ssed.
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 0.62 d(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 [6]. 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
Figure 1. Ocean heat content from Argo (left scale: blue,
original data; red, filtered) and ocean surface temperatures
(right scale, green). Conversion of the OHC slope to W/m2
is made by multiplying by 0.62, yielding –0.161 W/m2.
100 R. S. KNOX ET AL.
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 an-
nual 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 de-
viation, 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 co mputed, similarly fo r
July 2004 to Ju ne 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 [7], Loehle [8],
Douglass and Knox [9], and von Schuckmann et al.
[10]. 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
Table 1. Trends from analyses of Argo data. All studies
cover 2003 through 2008. “Implied FTOA” is given by FOHC
corrected by subtracting a geothermal flux contribution
0.09 W/m2 (Douglass and Knox [9]). Numbers in curly
brackets refer to the four methods described in the text.
Five Argo
OHC studies Depth range
(m) FOHC
(W/m2) Implied FTOA
This study (data
by Willis [6]) 0-700
–0.161 ± 0.04 {1},
–0.010 ± 0.24 {2},
–0.041 ± 0.20 {3},
–0.040 ± 0.15 {4}.
Average = –0.063
–0. 15
Loehle [8] 0-700 –0.22 ± 0.3 –0.31 ± 0.3
Pielke [7] 0-700 –0.076 ± 0.214 –0.163 ± 0.214
Douglass and
Knox [9] 0-700 –0.157 ± 0.99 –0.244 ± 0.99
Von Schuckmann
et al.[10] 0-2000 +0.77 ± 0.11 +0.68 ± 0.11
There are also XBT OHC data after 2001-2002. Even
though these data have the problems mentioned above
and do not have the quality of Argo data, they include
data after 2001-2002. W e have examined XBT OHC data
from the National Oceanographic Data Center (NOAA/
NODC) [11]. NODC give annual OHC data through
2009. For 2003 to 2009, one calculates FOHC = 0.009 ±
0.129 W/m2. Although this slope is not negative it is well
within the error bars produced above and far below the
Lyman et al. 1993-2008 value.
For comparison, we also show in Figure 1 the Hadley
Centre global ocean surface annual temperature anomaly
values, hadsst2gl, obtained from the Climate Research
Unit [12]. These data, which are the surface component
of the OHC database, show a decrease, in agreement
with most of the OHC tren ds for 2003-2008.
Thus, the relatively large positive “robust” trend found
by Lyman et al. for 1993-2008 is not the most recent
trend. These authors do acknowledge “flattening after
2003” and state “The causes of this flattening are un-
clear…”. They go on to say that “These uncertainties are
large enough that the interannual variations, such as the
2003-2008 flattening, are statistically meaningless.”
The uncertainties they mention refer to the XBT data,
not the Argo data. Our four estimates of the recent OHC
trend for 2003-2008 adequately consider interannual
variability and we find that the trend is negative. It is
possible that some unknown systematic error in the Argo
float system is causing the flattening. Such an error
would not explain the non-Argo NODC OHC result, nor
the surface cooling.
3. Discussion and Summary
As many autho rs have noted, knowing FOHC is importan t
because of its close relationship to FTOA, the net inward
radiative flux at the top of the atmosphere. Wetherald et
al. [13] and Hansen et al. [14] believe that this radiative
imbalance in Earth’s climate system is positive, amount-
ing recently [14] to approximately 0 .9 W/m2. Pielke [15]
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 [9]; 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 [14], have
been discussed by the present authors [9].
In steady state, FOHC should be zero and FTOA should
be nearly zero, having a small negative value to balance
Copyright © 2010 SciRes. IJG
Copyright © 2010 SciRes. IJG
the geothermal flux. 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
[16], based on a variety of time periods generally in the
1990s and 2000s, suggests that the deeper ocean contrib-
utes on the order of 0.09 W/m2. This is not sufficient to
explain the discrepancy.
Trenberth and Fasullo (TF) [2] 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
pro ble m is made much mor e s e vere i f 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 mod-
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 en-
4. Acknowledgements
The authors are indebted to Joshua Willis for the Argo
OHC data.
5. References
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per Ocean,” Nature, Vol. 465, May 2010, pp. 334-337.
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Science, Vol. 328, March 2010, pp. 316-317.
[3] S. E. Wijffels et al., “Changing Expendable Bathyther-
mograph Fall Rates and Their Impact on Estimates of
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21, 2008, pp. 5657-5672.
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[6] J. Willis (Private Communication, 20 February 2009. The
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[7] R. Pielke, “A Broader View of the Role of Humans in the
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[8] C. Loehle, “Cooling of the Global Ocean since 2003,”
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[10] K. von Schuckmann, F. Gaillard and P.-Y. Le Traon,
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[11] NOAA/NODC, 2010.
[12] CRU, 2010.
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[14] J. Hansen et al., “Earth’s Energy Imbalance: Confirma-
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[15] R. A. Pielke, “Heat Storage within the Earth System,”
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[16] S. G. Purkey and G. C. Johnson, “Antarctic Bottom Wa-
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