Guest essay by Girma Orssengo, PhD
Orssengo at lycos dot com
What is the expected global warming if the atmospheric CO_{2} concentration doubles from 400 to 800 ppm? The answer to this question is essential for our understanding of the earth’s climate. Unfortunately, the estimates for the CO_{2} doubling global mean temperature (GMT) vary by a factor of three from 1.5 ^{o}C to 4.5 ^{o}C. Data analysis in the literature shows that this very large uncertainty is due to the multi-decadal oscillation (MDO) of the GMT, and when this oscillation is removed, we find a time-invariant CO_{2} doubling GMT of 1.4 ^{o}C.
The aim of this article is to determine the time-invariant CO_{2} doubling GMT using published results in the scientific literature for the GMT and the observed atmospheric CO_{2} for the Mauna Loa data (Tans and Keeling, 2017).
The CO_{2} doubling GMT T_{2x} is a parameter in a linear mathematical model that relates the logarithm of the annual atmospheric CO_{2} concentration ln(C) to the GMT T given by (Caldeira et al., 2003; Knutti and Hegerl, 2008; Wigley and Schlesinger, 1985)
where C_{o} is the atmospheric CO_{2} concentration corresponding to a reference GMT of T = 0. Note that since Eq. 1 could also be written as ln(C/C_{o}) = (ln(2)/T_{2x})T, when C/Co = 2, this equation gives T = T_{2x}. As a result, T_{2x} in Eq. 1 represents the CO_{2} doubling GMT.
To estimate the CO_{2} doubling GMT directly from observations, the reference atmospheric carbon dioxide C_{o} could be removed from Eq. 1 by differentiation of this equation with respect to year y, which gives
Solving for the CO_{2} doubling GMT T_{2x} in Eq. 2 gives
Using the mathematical model given by Eq. 3, if for a given middle year of a trend period, the GMT trend dT/dy and the relative atmospheric carbon dioxide trend (dC/dy)/C are known, the CO_{2} doubling GMT T_{2x} could be estimated directly form observations.
Under what condition could we determine the time-invariant CO_{2} doubling GMT from Eq. 3? We may answer this question by looking at the annual atmospheric CO_{2} data for Mauna Loa shown in Fig. 1, which suggests a monotonically increasing smoothed curve for the annual atmospheric CO_{2}. From Eq. 2 and Fig. 1, to obtain a constant CO_{2} doubling GMT T_{2x}, the GMT trend dT/dy must be proportional to the relative CO_{2} trend (dC/dy)/C at all times, which is only possible if the GMT T is also monotonically increasing like the annual atmospheric carbon dioxide C.
Fig. 1. Annual atmospheric CO_{2} for the Mauna Loa data (Tans, P. and Keeling, R., 2017) and an average atmospheric CO_{2} concentration of 343.32 ppm and a least squares average CO_{2 }trend of 1.46 ppm/year for the trend period middle year of 1983.
Several studies (Delsole et al., 2011; Knudsen et al., 2011; Latif and Keenlyside, 2011; Schlesinger and Ramankutty, 1994; Swanson et al., 2009; Wu et al., 2011) have reported that the annual GMT data has multi-decadal oscillation (MDO) having 55 to 70 year period. As a result, before the annual GMT could be used in Eq. 3, its MDO must be removed. Wu et al. (2011) have reported the secular GMT trend obtained after removing the MDO from the annual GMT data as given in Table 1, which approximately corresponds to the annual atmospheric CO_{2} data period shown in Fig. 1 and 2. Note that the annual atmospheric CO_{2} data for Mauna Loa starts from 1959.
From the results of Wu et al. (2011) for the secular GMT trend dT/dy for a given trend period middle year given in Table 1 and the observed relative atmospheric carbon dioxide trend (dC/dy)/C for the same trend period middle year, the CO_{2} doubling GMT could be calculated using the mathematical model given by T_{2x} = ln(2)(dT/dy)C/(dC/dy) (Eq. 3).
Table 1. Secular GMT trends obtained after removing the multi-decadal oscillation from the annual global mean temperature data (Wu et al. 2011).
Trend period
length (year) |
Trend Period | Trend Period Middle Year | Secular GMT Trend
dT/dy (^{o}C/year) |
50 | 1958 to 2008 | 1983 | 0.0086 |
25 | 1983 to 2008 | 1995.5 | 0.0096 |
From Table 1, for the trend period middle year of 1983, the secular GMT trend dT/dy = 0.0086 ^{o}C/year. For the same trend period middle year of 1983, Fig. 1 shows an average atmospheric carbon dioxide concentration of C = 343.32 ppm and its average trend of dC/dy = 1.46 ppm/year. Substituting these values into Eq. 3 gives a CO_{2} doubling GMT of
This result means that if the atmospheric CO_{2} were doubled from, say, 400 to 800 ppm, the secular GMT would increase by 1.4 ^{o}C.
To verify whether this CO_{2} doubling GMT of 1.4 ^{o}C determined for the trend period middle year of 1983 is time-invariant, we calculate its value for a different trend period middle year. From Table 1, for the trend period middle year of 1995.5, the secular GMT trend dT/dy = 0.0096 ^{o}C/year. For the same trend period middle year of 1995.5, Fig. 2 shows an average atmospheric carbon dioxide concentration of C = 363 ppm and its average trend of dC/dy = 1.67 ppm/year. Substituting these values into Eq. 3 gives a CO_{2} doubling GMT of
The above results (Eq. 4 & 5) for two different time periods show that the time-invariant CO_{2} doubling GMT is 1.4 ^{o}C. This result is almost identical to the minimum possible CO_{2} doubling GMT of 1.5 ^{o}C reported in IPCC (2007): “The equilibrium climate sensitivity is a measure of the climate system response to sustained radiative forcing. It is not a projection but is defined as the global average surface warming following a doubling of carbon dioxide concentrations. It is likely to be in the range 2°C to 4.5°C with a best estimate of about 3°C, and is very unlikely to be less than 1.5°C.”
Regarding to the CO_{2} doubling GMT, in addition to its minimum possible value, IPCC (2007) had also reported: “It is likely to be in the range 2°C to 4.5°C with a best estimate of about 3°C”. How could we also determine these IPCC estimates using our mathematical model given by Eq. 3?
To determine IPCC’s CO_{2} doubling GMT estimates above using our empirical model, we use the GMT trends given in the same report (IPCC, 2007) : “Since IPCC’s first report in 1990, assessed projections have suggested global average temperature increases between about 0.15°C and 0.3°C per decade for 1990 to 2005. This can now be compared with observed values of about 0.2°C per decade, strengthening confidence in near-term projections.”
Note that these IPCC’s GMT trends of 0.02 and 0.03°C per year are much greater than the secular GMT trend of 0. 0096 ^{o}C per year reported by Wu et al (2011) given in Table 1.
The IPCC report quoted above suggests a central GMT trend of 0.02 ^{o}C/year. Replacing the secular GMT trend of dT/dy = 0.0096 ^{o}C/year in Eq. 5 from Wu et al. (2011) with IPCC’s central GMT trend of 0.02 ^{o}C/year gives
Remarkably, this calculated value for the central IPCC GMT trend is identical to the central CO_{2} doubling GMT of 3 ^{o}C reported in IPCC (2007).
Fig. 2. An average atmospheric CO_{2} concentration of 363.00 ppm and a least squares average CO_{2 }trend of 1.67 ppm/year for the trend period middle year of 1995.5 for the Mauna Loa data (Tans, P. and Keeling, R., 2017).
The IPCC report quoted above also suggests an upper GMT trend of 0.03 ^{o}C/year. Replacing IPCC’s central GMT trend of dT/dy = 0.02 ^{o}C/year in Eq. 6 with its upper GMT trend of 0.03 ^{o}C/year gives
Remarkably, again, this calculated value for the upper IPCC trend is identical to the upper CO_{2} doubling GMT of 4.5 ^{o}C reported by IPCC quoted above.
Regarding the history for the range of values for the CO_{2} doubling GMT, Kerr has reported an interesting story (Kerr, 2004): “On the first day of deliberations, Manabe told the committee that his model warmed 2°C when CO_{2} was doubled. The next day Hansen said his model had recently gotten 4°C for a doubling. According to Manabe, Charney chose 0.5°C as a not-unreasonable margin of error, subtracted it from Manabe’s number, and added it to Hansen’s. Thus was born the 1.5°C-to-4.5°C range of likely climate sensitivity that has appeared in every greenhouse assessment since, including the three by the Intergovernmental Panel on Climate Change (IPCC). More than one researcher at the workshop called Charney’s now-enshrined range and its attached best estimate of 3°C so much hand waving.”
In this article, we showed that Charney’s range are not “so much hand waving” because they could be determined using the mathematical model T_{2x} = ln(2)(dT/dy)C/(dC/dy) (Eq. 3), the observed relative atmospheric CO_{2 }trend (dC/dy)/C (Fig. 2), and IPCC’s GMT trends dT/dy.
In conclusion, we found a time-invariant CO_{2} doubling GMT of 1.4 ^{o}C (Eq. 4 & 5). We also showed that the higher CO_{2} doubling GMT values reported in IPCC (2007) are for secular GMT trends of 0.2 and 0.3 ^{o}C/decade that are inconsistent with the observed secular GMT trend of about 0.1 ^{o}C/decade (Delsole et al., 2011; Wu et al., 2011). Note that as the annual GMT has been reported to have a multi-decadal oscillation (MDO) of about 55 to 70 years for the last 8000 years (Knudsen et al., 2011), a linear trend of at least a 70-year period should be used to remove the contribution of the MDO to determine the secular GMT trend, which gives about 0.1 ^{o}C/decade for the latest 70-year period from 1946 to 2016.
From about 1960 to 1990 with a trough in the mid-1970s, the MDO was in its cool phase, and it has been in its warm phase since 1990 that is expected to continue until about 2020. In the early-2020s, the cool phase of the MDO is expected to start with its trough in mid-2030s. The empirical evidence for this drop in global mean surface temperature would be the recovery of arctic sea ice and cooling of the Northern Hemisphere for the period from about 2020 to 2050.
When we start to see a steady increase in arctic sea ice in the 2020s that continues until the 2050s, what would happen to the “Theory of Man Made Global Warming”?
References
Caldeira, K., Jain, A.K., Hoffert, M.I., 2003. Climate Sensitivity Uncertainty and the Need for Energy Without CO2 Emission. Science 299, 2052–2054. https://doi.org/10.1126/science.1078938
Delsole, T., Tippett, M.K., Shukla, J., 2011. A significant component of unforced multidecadal variability in the recent acceleration of global warming. Journal of Climate 24, 909–926. https://doi.org/10.1175/2010JCLI3659.1
IPCC, 2007. Climate Change 2007: The Physical Science Basis, Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change. Cambridge University Press.
Kerr, R.A., 2004. Three degrees of consensus: climate researchers are finally homing in on just how bad greenhouse warming could get–and it seems increasingly unlikely that we will escape with a mild warming. Science 305, 932–935.
Knudsen, M.F., Seidenkrantz, M.-S., Jacobsen, B.H., Kuijpers, A., 2011. Tracking the Atlantic Multidecadal Oscillation through the last 8,000 years. Nature Communications 2, 178. https://doi.org/10.1038/ncomms1186
Knutti, R., Hegerl, G.C., 2008. The equilibrium sensitivity of the Earth’s temperature to radiation changes. Nature Geosci 1, 735–743.
Latif, M., Keenlyside, N.S., 2011. A perspective on decadal climate variability and predictability. Deep-Sea Research Part II: Topical Studies in Oceanography 58, 1880–1894. https://doi.org/10.1016/j.dsr2.2010.10.066
Schlesinger, M.E., Ramankutty, N., 1994. An oscillation in the global climate system of period 65–70 years. Nature 367, 723–726. https://doi.org/10.1038/367723a0
Swanson, K.L., Sugihara, G., Tsonis, A. a, 2009. Long-term natural variability and 20th century climate change. Proceedings of the National Academy of Sciences of the United States of America 106, 16120–16123. https://doi.org/10.1073/pnas.0908699106
Tans, P., Keeling, R., 2017. Trends in Carbon Dioxide [WWW Document]. URL https://www.esrl.noaa.gov/gmd/ccgg/trends/
Wigley, T.M.L., Schlesinger, M.E., 1985. Analytical solution for the effect of increasing CO2 on global mean temperature. Nature 315, 649–652. https://doi.org/10.1038/315649a0
Wu, Z., Huang, N.E., Wallace, J.M., Smoliak, B.V., Chen, X., 2011. On the time-varying trend in global-mean surface temperature. Climate Dynamics 37, 759–773. https://doi.org/10.1007/s00382-011-1128-8
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January 28, 2018 at 01:31PM