An energetic look at the possible end of recent global warming
Generally, atmospheric physics articles such as the excellent van Wijngaarden and Happer primer [1] use the Stefan-Boltzmann law of thermal radiation by blackbodies to estimate what Earth’s temperature would be in the absence of an atmosphere containing ‘greenhouse gasses’ (GHG’s):
F=σT04 (Eqn. 1)
whereby F is the absorbed solar flux per unit area, σ is the Stefan Boltzmann constant (5.67×10−8 W m – 2 K 4), and T 0 the temperature of the blackbody.
Equation 1 predicts that an average Earth-incident solar flux of F = 340 W m-2 results in an Earth temperature of ~278 K (5 °C), which is significantly lower than its commonly-accepted mean value of ~287 K (14°C), the correspondent of a ~385 W m-2 solar flux.
The 45 W m-2 power density difference is usually attributed to Earth’s ‘greenhouse’ effect.
Atmospheric greenhouse gasses (GHG’s) – such as H2O and CO2 – are able to absorb certain frequencies of thermal radiation energy: they act as thermal resistors, delaying a planet’s thermal emission to space. Their presence in a planet’s atmosphere causes a troposphere to develop [1] . In the troposphere a large part of a planet’s absorbed heat energy is transported by atmospheric convection to the planet’s tropopause, where it can be effectively radiated to space.
Convection is a slower form of heat energy transport than radiation, so results in a delay of thermal energy emission to space and causes tropospheric temperatures to rise. A time-series cross-correlation (Fig.1) indicates the Earth’s Global Mean Surface Temperature (GMST) variations lag ~2-5 years behind solar flux (Total Solar Irradiance, TSI) variations.
Figure 1: Weak but statistically significant cross-correlation between GMST (Source: NASA [2] ) and TSI (Source: [10] ) for the 1880–1988 period.
Earth’s steady-state system Climate change and global warming are systemic changes from some (interpreted) steady- state. Most organizations (NOAA, NASA, IPCC, …) therefore present data as “anomalies”, differences from the steady-state average over a pre-defined period, usually 1951-1980.
Figure 2 presents the GMST and TSI “anomal
Figure 2 presents the GMST and TSI “anomaly” data sets used for this article. In addition, NASA/NOAA’s historical atmospheric CO2 data [5] are used.
If Earth’s incoming and outgoing radiation remain relatively constant then a steady-state system will develop, with only minor random or non-systemic GMST fluctuations. Large temperature changes on the order of 0.5 °C or more (Fig. 2) are therefore attributable to radiation variations, termed “Climate Forcings” by the IPCC [3]. Equation 1 predicts that
temperature variations on the order of ~0.5 °C are caused by forcings/power density variations on the order of ~2.7 W m-2.
Two main climate forcings were investigated by the IPCC [3]: “Natural” forcings, mainly the ~0.5-1.5 W m-2 cyclical variations in the “solar forcing” (TSI; Fig. 2), and Anthropogenic forcings, mainly the ~0.2 W m-2 per decade “Radiative Forcing due to CO2” (RFCO2) caused by the progressive increase in atmospheric CO2 content. Equation 1 suggests that fluctuations of ~1.5 W m-2can cause up to ~0.3 °C temperature fluctuations, while a ~0.2 W m -2 increase per decade can result in a ~0.04 °C decadal temperature increase.
Four main periods are apparent in the NASA GMST data (Fig. 2): An increase of 0.69°C between 1909-1944 A decrease of 0.38°C between 1944-1950 A period of relatively constant temperature between 1951-1980, commonly assumed to represent a “steady-state”
An increase of 0.58°C between 1981-2022 The 1965-1976 solar cycle (Fig. 3) sits squarely within the steady-state period, and demonstrates the steady-state interplay between the climate forcings and GMST. The period’s quadratic least squares GMST model (Q 65_76; black line in Fig. 3) will therefore be used as a reference model.
GMST did not systemically change over the cycle ( -0.11°C in 1965 versus -0.1°C in 1976) despite a slightly lower than average TSI over the period (-0.16 W m-2), which was possibly offset by the RFCO2 of ~0.2 W m-2. This latter number is estimated from the equation [4] : RFCO2 = 5.35 * ln(1 + ΔC/C 0) (Eqn. 2)whereby C0 is a reference concentration (in ppm) – here taken to be the 1965 value of 320.1ppm[5] and ΔC is the concentration change of 12.1 ppm[5] over the 1965-1976 solar cycle.
As expected (Fig. 1), the TSI anomalies peak (in 1969) 2-3 years before the least-squares model peaks (1971-1972). The model’s temperature variations are small, on the order of 0.12°C, and are therefore consistent with the 0.13 °C temperature variations predicted by Eqn. 1 for the 1965-1969 (relatively low) TSI range of 0.65 W m
The 1977-1985 solar cycle still occurs within the steady-state period, while the 1986-1996 solar cycle documents its end (Fig. 4). The GMST did not systemically change over the 1977-1985 cycle: the cycle’s least squares quadratic GMST (LSQG) model roughly ends (1985:
0.11°C) at the same temperature that it begins (1977: 0.06°C). The slightly higher end temperature can likely be attributed to the shorter cycle duration (8 years). The cycle’s LSQG model is a scaled version of its Q65_76 counterpart, with a maximum (1981-1982) roughly 2-3 years after the TSI maximum (1979). The cycle’s mean TSI (0.04W m-2) and its range (0.7W m-2) are both significantly higher than the 1965-1976 cycle, which helps explain why both its mean GMST and variability are higher. TSI variability is significantly larger than the RFCO2 increase of ~0.19 W m-2 caused by the 12 ppm CO2 increase [5]over the period.
In contrast, the 1986-1996 cycle shows evidence that a significant new forcing started around 1995, causing Earth’s GMST to depart from its steady-state. The cycle’s LSQG model is not a scaled version of its Q65_76 counterpart: its maximum occurs roughly six years (1995) after the TSI maximum (1989). This relatively abrupt end to the steady-state in 1995 is also reflected in the Arctic and lower and mid-troposphere temperature time series (Fig. 5).
As neither TSI and RFCO2 show any significant or sudden increases around 1995, the only explanation for the end of the steady-state is that a significant new forcing started around then. Two independent studies – one [8] based on earthquake data, one [9] based on geomagnetic data – independently arrived at the conclusion that geothermal forcing – a change in the Earth’s internal heat emitted at surface – is the missing forcing (Fig. 6).
The 1995-2019 period of global warming
Figure 7 demonstrates that a linear least squares model fits the 1995-2018 GMST data well. GMST variability around the line (of up to 0.2°C) is attributable to TSI variations and randomness.
A back-of-the envelop calculation demonstrates that geothermal forcing is mainly responsible for the systemic 1995-2016 GMST increase. GMST increased by 0.57 °C over the 1995-2016 period, the equivalent (Eqn. 1) of a 3.0 W m-2 increase in total climate forcing.
The RFCO2 of 0.6 W m-2 caused by the atmospheric CO2 concentration increase of 42.8 ppm over the period is therefore insufficient: an additional forcing of at least 2.4W m-2 must have occurred.
Figure 8 documents the 1955-2019 increase in ocean power density versus a 1981-2010 baseline. This ocean heat should be seen as a natural – yet unmodeled by IPCC – forcing: the increase in the ocean’s power density effects an increase of ocean heat radiated to the troposphere, causing tropospheric temperatures to rise.
Assuming a 1 Wm-2 (Fig. 8) power density increase occurred in the Atlantic and Arctic oceans over the 1995-2019 period (aconservative model), and that the increase occurred linearly (0.04 W m -2 per year), the cumulative ocean heat forcing (0.04Wm-2in 1995, 0.08Wm-2 in 1996, etc.) over the period is 13 W m-2. As the two oceans cover roughly 20 percent of the Earth’s surface, this number must be multiplied by 0.2: globally this “ocean heat forcing” was therefore on the order of 2.6 Wm-2, which exceeds the 2.4 W m-2requirement calculated above.
The total natural and anthropogenic forcing of 3.2 W m-2 over the 1995-2019 period is therefore more than sufficient to cause a 0.57 °C increase. Note that only 20 percent of the increase – or roughly 0.1°C– was caused by the changes in atmospheric CO2.
Also note that increases in atmospheric CO2 very likely did not cause the increase in ocean heat. The geographical heat distribution alone (Fig. 8) indicates the heating was the result of a local, not global, process. A 0.2 W m-2 decadal increase in RFCO2 is insufficient to cause the observed GMST increase of the atmosphere, let alone the upper 2000 m+ of the much higher
heat capacity oceans. In contrast, geothermal energy due to submarine volcanoes and higher ocean floor heat flux must travel through the entire ocean column before being shed to atmosphere at the ocean surface.
Studies [8,9] have successfully correlated the Arctic and Atlantic heat increases to higher geothermal heat fluxes at the Arctic and Atlantic ocean ridge spreading plate boundaries.
Has Earth entered a period of global cooling?
Unfortunately (spoiler alert) the answer is: too soon to tell, wait a few more years. Fig. 6 suggests the post-2016 (predicted) reduction in geothermal forcing may be reflected in the 2021 (0.85 °C ) and 2022 (0.9 °C) GMST anomalies that are down from a 2020 high of 1.02 °C.
The post-2016 reduction in geothermal forcing (Fig. 6) corresponds well to the post-2016 reduction in Arctic temperatures (Fig. 5), indicating that ocean heating at the source (Atlantic and Arctic ocean sea floor) may already be declining, although the 1995-2016 geothermal energy bump took at least 3 more years its way through the tropopause.
A comparison with the 1943-1950 period of GMST decrease (Fig. 9) demonstrates what to look for in the coming years. The 1944-1950 drop in GMST is almost certainly due to a reduction of geothermal forcing: both solar forcing and RFCO2 were increasing during a period when GMST was dropping.
In contrast, geothermal forcing (Fig. 6, right) decreased sharply after World War II. The 1944-1946 drop in GMST during a period of increased solar forcing and RFCO2 is therefore analogous (so far) to the 2020-2022 drop, though at present it is still too early to tell whether the drop is due to a reduction in geothermal forcing – as is suggested by Fig. 6 – or due to random variations. The coming years will tell.
References:
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Tom
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I guess I missed the start of GW.
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Tom Anderson
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The above is the usual impressive but vacuous flow of simulation on simulation springing from repudiated experiment and never confirmed assumptions – the usual stuff of the CAGWH alarmism. The so-called “hypothesis” – wrote physicists Gerlich and Tscheuschner supported by Kramm and Dlugi – is really fact-free conjecture. And the idea that carbon dioxide threatens warming inverts observed reality.
CO2’s leading radiating peak of 15 microns wavelength is at 193K or minus 80 degrees Celsius (-80°C and-112°F). Also it doesn’t cause anything. Currently, atmospheric concentrations of CO2 do not precede but follow changed temperature by months, according to seven studies, including one intended to disprove it. The lag is 800 years in the Antarctic fossil ice core. Causes precede and do not follow effects.
Satellite imaging shows CO2 radiating incoming solar energy and outgoing terrestrial heat away to space, thereby cooling. A half-dozen recent studies show it has that cooling property on Mars and (surprise!) Venus. A 1971 NASA report advised against CO2 from burning fuels to stave off a threatened ice age because its aerosols (smoke) screen out and reflect back solar energy, making them, in the study’s words, “coolants.” They still are! Where can we line up to get paid to lie about this?
I recommend, incidentally, reading the two “Related” articles above relating to Stefan-Boltzman. Known facts well presented and explained!
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VOWG
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The globe has been doing what the globe has done for millions of years, nothing. Climate and weather will do as it has done millions of years, vary and change. Get used to it, get over it, and adapt, those are the only choices.
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Alan
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It odd that the moon receives the same amount of energy from the sun and its temperature reaches 106C. We would be burnt to a crisp without the atmosphere.
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Herb Rose
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Hi Alan,
It is the continuous evaporation of water from the surface that regulates the weather. A gallon of rain represents 2,250,000 calories of heat absorbed from the surface and released into space.
Herb
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Tom Anderson
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Good point. The oceans absorb 93.4% of solar energy compared to about 2.2% in the atmosphere. Their heat capacity is about 1,000 times greater the atmosphere’s. They release enormous amounts of energy in the El Niño Southern Oscillations of the Pacific Ocean and the Norrth Atlantic Oscillation. Indications are increasingly that at least some oscillations are solar-induced. Koutrsoyannis and Feistel and Hellmuth suggest that “the climate of the Earth is ultimately determined by the temperatures of the oceans.”
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