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International Journal of Geosciences, 2010, 1, 99-101 doi:10.4236/ijg.2010.13013 Published Online November 2010 (http://www.SciRP.org/journal/ijg) 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 E-mail: rsk@pas.rochester.edu Received July 28, 2010; revised August 10, 2010; accepted August 30, 2010 Abstract 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 study. 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 (W/m2) 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 R. S. KNOX ET AL. Copyright © 2010 SciRes. IJG 101 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- eling. 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- ergy.” 4. Acknowledgements The authors are indebted to Joshua Willis for the Argo OHC data. 5. References [1] J. M. Lyman et al., “Robust Warming of the Global Up- per Ocean,” Nature, Vol. 465, May 2010, pp. 334-337. [2] K. Trenberth and J. Fasullo, “Tracking Earth’s Energy,” 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 Thermosteric Sea Level Rise,” Journal of Climate, Vol. 21, 2008, pp. 5657-5672. [4] J. Willis, D. Chambers and R. Nerem, “Assessing the Globally Averaged Sea Level Budget on Seasonal to In- terannual Timescales,” Journal of Geophysical Research A, Vol. 113, 2008, p. C06015. [5] J. K. Willis, J. M. Lyman, G. C. Johnson and J. Gilson, “Correction to ‘Recent Cooling of the Upper Ocean’,” Geophysical Research Letters, Vol. 34, July 2007, p. L16601. [6] J. Willis (Private Communication, 20 February 2009. The last 5 months are preliminary.) [7] R. Pielke, “A Broader View of the Role of Humans in the Climate System,” Physics Today, Vol. 61, No. 11, 2008, pp. 54-55. [8] C. Loehle, “Cooling of the Global Ocean since 2003,” Energy and Environment, Vol. 20, No. 1-2, January 2009, pp. 101-104. [9] D. H. Douglass and R. S. Knox, “Ocean Heat Content and Earth’s Radiation Imbalance,” Physics Letters A, Vol. 373, No. 36, August 2009, pp. 3296-3300. [10] K. von Schuckmann, F. Gaillard and P.-Y. Le Traon, “Global Hydrographic Variability Patterns during 2003- 2008,” Journal of Geophysical Research C, Vol. 114, 2009, pp. 1-17. [11] NOAA/NODC, 2010. ftp://ftp.nodc.noaa.gov/pub/data. nodc/woa/DATA_ANALYSIS/3M_HEAT_CONTENT/ DATA/basin/yearly/h22-w0-700m.dat [12] CRU, 2010. http://www.cru.uea.ac.uk/cru/data/tempera- ture/hadsst2gl.txt [13] R. T. Wetherald, R. J. Stouffer and K. W. Dixen, “Com- mitted Warming and Its Implications for Climate Change,” Geophysical Research Letters, Vol. 28, No. 8, 2001, pp. 1535- 1538. [14] J. Hansen et al., “Earth’s Energy Imbalance: Confirma- tion and Implications,” Science, Vol. 308, No. 5727, June 2005, pp. 1431- 1435. [15] R. A. Pielke, “Heat Storage within the Earth System,” Bulletin of the American Meteorological Society, Vol. 84, No. 3, 2003, pp. 331-335. [16] S. G. Purkey and G. C. Johnson, “Antarctic Bottom Wa- ter Warming between the 1990s and the 2000s: Contribu- tion to Global Heat and Sea Level Rise Budgets,” Journal of Climate, in Press, 2010, doi: 10.1175/2010JCLI3682.1, Preliminary Version on Line. |