Sep 2, 2017 - Examination of the radiation budget at the surface of the Earth ... downwelling flux from the atmosphere and substituting this in the equation for the radiative ...... molecules that cannot acquire charge asymmetry by flexing or ...
September 2, 2017
Solution of the Greenhouse Effect equations shows no increase in Earth’s surface temperature from increase in carbon dioxide Trevor G. Underwood† †2425 Sunrise Key Blvd, Fort Lauderdale, FL 33304, USA Abstract Examination of the radiation budget at the surface of the Earth shows that there are five primary factors affecting the surface temperature; the amount of solar radiation absorbed by the atmosphere and by the surface respectively, the amount of heat emitted from the surface in the form of thermals and evaporation, and the proportion of infrared radiation emitted from the surface directly into space. The Greenhouse Effect equations are solved by calculating the downwelling flux from the atmosphere and substituting this in the equation for the radiative balance at Earth’s surface. If there were no leakage, the upwelling infrared radiation from the Earth’s surface would be equal to the incoming solar radiation absorbed by the atmosphere plus twice the solar radiation absorbed by the surface. At current levels of solar absorption, this would result in total upwelling radiation of approximately 398.6 W/m2, or a maximum surface temperature of 16.4°C. Allowing for leakage of infrared radiation through the atmospheric window, the resulting emission from the Earth’s surface due to the Greenhouse Effect is reduced to 372.5 or 388.6 W/m2, depending on the treatment of thermals, corresponding to surface temperature of 11.6 or 14.6°C. Absorption of infrared radiation by greenhouse gases is determined by the absorption bands for the respective gases and their concentrations. Examination of the absorption of the black body spectrum of terrestrial infrared radiation after passing through the atmosphere indicates that all emitted radiation that can be absorbed by greenhouse gases, primarily water vapor, with a small contribution from carbon dioxide and ozone, is already fully absorbed, and the leakage of around 5.5 percent corresponds to the part of the infrared red spectrum that is not absorbed by greenhouse gases. Emissions in the carbon dioxide absorption bands are most likely fully absorbed. In these circumstances, increased concentrations of greenhouse gases, and carbon dioxide in particular, will have no further effect. The surface temperature is probably at the thermodynamic limit for the current luminosity of the sun. Satellite based measurements since 1979 suggest that any recent increase in the surface temperature may be due to an increase in total solar irradiance, which we are still a decade or two from being able to confirm.
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Article This re-examination of the Greenhouse Effect followed two previous research projects that raised doubts about the claims of significant increases in the Earth’s surface temperature during the last 150 years, in particular by the US National Oceanic and Atmospheric Administration (NOAA) and the US National Aeronautics and Space Administration (NASA). The first was initiated by a conversation at a restaurant in Fort Lauderdale in December 2015 with a consulting engineer who had been involved in the 1973 construction of a sewage outfall pipeline off Hillsboro Inlet, Broward County, Florida. As this had involved cutting through the coral reef a geologist was brought in to survey the reef before the trench was refilled. The resulting report concluded that no Elkhorn coral (Acropora palmata) was found living on the reef at the time of the survey and that the part of the reef exposed by the ditch was a relict coral reef which had accumulated between 10 Kya (thousand years ago) and 6 Kya and was subsequently inactive despite being shallow enough in 1973 for vigorous coral growth (Lighty 1977). The report also noted the lack of any significant reef-framework accumulation since 6 Kya. This was attributed to cooler ocean temperatures during this period. A quick review of reports on the Nova National Coral Reef Institute (NCRI) website and other sources indicated that the staghorn coral and to a lesser extent the elkhorn coral had begun to recover off Broward County since 1973, presumably as the water temperature continued to rebound. This prompted an examination of paleo sea surface temperatures obtained from ocean drilling cores, based on analysis of oxygen isotopes in the calcite and Mg/Ca in particular species of foraminifera, at six locations spanning the North Atlantic, from the northeast Atlantic to the Dry Tortugas in the southwest, which were available on the NOAA website. This data was then combined with sea surface temperature (SST) data from 1870 to October 2015 from the UK Met Office Hadley SST data set for a grid square off the Broward reef, where the survey was conducted, and for the six other locations. Unfortunately, the available evidence was insufficient to indicate whether low sea surface temperatures at the Broward reef after 6 Kya were responsible for the lack of growth of the coral on the reef or subsequent warming for their recent recovery, but the results were surprising. Graphs of the time series from 1870 to 2015 showed a large latitudinal variation of average SST from 11°C in the northeast North Atlantic to 27°C in the Dry Tortugas, with corresponding seasonal ranges of between 5.0°C and 8.0°C, but little if any change in annual average sea surface temperatures at any of these locations, contrary to claims by NOAA and NASA (Underwood 2016). This led to the second research project; a detailed examination of the land air temperature (LAT), sea surface temperature (SST), and marine air temperature (MAT) data, and in particular to the adjustments to the data, on which recent global warming claims have been based. LAT are “homogenized” to try to remove the “heat island” effects of urbanization, and biases from 2
changes in instrumentation, station location (both in altitude and position), and observation times. SST are adjusted for generally cool biases arising from the use of semi-insulated wooden buckets, uninsulated canvas buckets and insulated rubber buckets to lift sea water onto the decks of ships, and for warm biases from the increasing use of engine room water intake (ERI) measurements in ship-based measurements prior to the more recent dominant use of buoy-based measurements. Night-time MAT are adjusted for a cool bias presumed to arise from the increasing deck height at which temperatures were measured, as ships increased in size. A critical look at the available adjusted and unadjusted in situ measures of the Earth’s surface temperature identified a divergence between land and marine surface temperatures, with land surface air temperatures showing a significant and increasing rate of warming of around 0.5°C between 1880 and 1981, and 0.7°C between 1982 and 2010, whilst marine air temperatures show little if any change between 1880 and 2010 (Underwood 2017). Other researchers are also beginning to question some of these adjustments and the consequent reliability of the adjusted in situ data on which claims of global warming rely (Kent et al 2017). As it is known that there has been a large increase in greenhouse gas concentrations in the atmosphere during this period, this raised questions about the Greenhouse Effect, and the presumed role of greenhouse gases, and in particular the recent increase in carbon dioxide, in the atmosphere in increasing the surface temperature of the Earth. This paper re-examines the theory behind the Greenhouse Effect and its application under present atmospheric conditions. Following a review of the literature, including the history of the greenhouse effect theory, it became apparent that a good starting point was Trenberth and Fasullo’s diagram of global energy flows shown below (Trenberth et al 2009; Trenberth and Fasullo 2012; Zhong & Haigh 2013).
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The global annual mean earth’s energy budget for 2000–2005 (W m-2). The broad arrows indicate the schematic flow of energy in proportion to their importance. Adapted from Trenberth et al (2009) (Fig. 1, Trenberth and Fasullo 2012).
The first thing that strikes anyone versed in the First Law of Thermodynamics is how does incoming solar energy at the top of the atmosphere (TOA) of 341 W/m2 (watts per square meter), or 262 W/m2 after allowing for 79 W/m2 solar radiation reflected back into space by the atmosphere, or 239 W/m2 (= 161 + 78) after further allowing for 23 W/m2 of solar radiation reflected back from the Earth’s surface back into space, generate upwelling surface infrared radiation of 396 W/m2 plus upwelling sensible heat (thermals) of 17 W/m2 plus upwelling latent heat (evaporation) of 80 W/m2? The answer to this conundrum lies in understanding the meaning of temperature and radiative fluxes, which are understood best in quantum mechanical terms. The temperature of a body is determined by the energy flux during a time period, i.e. the number and energy of the photons emitted from a surface during a particular time period. The global average temperature at the surface during a daily cycle is determined by the total emission of energy during this time period, not by the amount of energy itself, such as the daily solar energy absorbed by the Earth’s surface. This can include multiple emissions of the same energy represented in the form of photons if this energy is repetitively absorbed and re-emitted. The Greenhouse Effect arises because half of the solar energy absorbed by the Earth’s surface which is re-emitted and absorbed by the atmosphere is re-emitted by the atmosphere back to the Earth’s surface, where it is reabsorbed, then reemitted, in a continuing cycle. As a result of the repetitive absorptions and re-emissions, after 4
taking into account the absorption of solar energy by the atmosphere, other fluxes and terrestrial infrared radiation escaping directly into space, the global average radiative flux emitted by the Earth’s surface during a daily cycle is increased from the initial absorption of solar energy of 161 W/m2 to 396 W/m2, even though the total energy is conserved. This also explains how the atmosphere can emit 333 W/m2 downwards but only 217 W/m2 upward. The Earth’s surface behaves very similarly to a black body for infrared radiation so that the resulting temperature at the Earth’s surface can be calculated using the Stefan–Boltzmann law (Stefan 1879; Boltzmann 1884). This states that the total energy radiated per unit surface area of a black body across all wavelengths per unit time, E, is directly proportional to the fourth power of the black body's absolute temperature, T: E = σT4 where the constant of proportionality σ, is called the Stefan–Boltzmann constant. Max Planck derived this from quantum mechanics by showing that the flux distribution function for a blackbody is dependent only on wavelength and on the temperature T of the blackbody, known as Planck’s Law (Planck 1901): P(λ,T) = 2πhc2/λ5(ehc/kTλ – 1) where P(λ,T) is the amount of power per unit surface area in watts per square meters per unit solid angle per unit wavelength emitted at a wavelength λ meters by a black body at absolute temperature T °K (where 1 watt = 1 joule for 1 second = 1 joule-second); h = 6.63 x 10-34 joule-seconds is Planck's constant; c = 299,792,458 meters per second is the speed of light, and k = 1.38 x 10-23 joule per °K is Boltzmann's constant. Planck then integrating this function over the half-sphere and over all wavelengths to calculate the power emitted per unit area of the emitting body: E = σT4, where σ = 2π5 k4/15c2h3 = 5.670373 x 10-8 Wm-2 K-4 This infrared emission level of 396 W/m2 corresponds to the current average global surface temperature of 15.94 °C. T4 = E/σ = 396 x 108/5.67 = 69.84 x 108, so T = 289.09 °K = 289.09 – 273.15 = 15.94°C
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Radiation budget arithmetic Before proceeding further some the numbers in the Trenberth and Fasullo (2012) need to be made more precise and updated based on new information provided by Kopp and Lean (2011). The mean total solar irradiance (TSI) in January 2004 measured by the TIM instrument on the SORCE spacecraft was found to be around 1,361 W/m-2, about 5 W/m-2 lower than the 1,366 W/m-2 reported by PMOD, ACRIM and SARR at the same date. This difference was identified as due to uncorrected optical scatter in the earlier instruments. Alternative estimates reported by Wild et al (2013), as updated in Wild et al (2015), are also shown with a ‘*’. These do not include a value for upward infrared radiation escaping into space and consequently cannot be used to calculate the proportion of terrestrial infrared radiation absorbed by the atmosphere. Corrected (Kopp and Lean 2011). Flux of radiant solar energy at Earth’s surface = 1,365 W/m2 Average incoming solar radiation over globe = 1,365/4 = 341.3 W/m2 Area of circle exposed to radiation = πR2; surface area of a sphere = 4πR2 Downward solar radiation reflected back into space by clouds & atmosphere = 78.8 W/m2 (75*) Net downward solar radiation at atmosphere = 341.3 – 78.8 = 262.5 W/m2 (265*) Downward solar radiation absorbed by atmosphere = 78.2 W/m2 (80*) Downward solar radiation at Earth’s surface = 341.3 – 78.8 – 78.2 = 184.3 W/m2 (185*) Ocean = 190 Land = 203 Downward solar radiation reflected by Earth’s surface = 23.1 W/m2 (25*) Ocean = 12 Land = 53 Average reflectivity ratio at Earth’s surface = 23.1/184.3 = 12.5 % (13.5*) Downward solar radiation absorbed by Earth’s surface = 184.3 – 23.1 = 161.2 W/m2 (160*) Downward solar radiation absorbed by Earth’s surface and atmosphere = 78.2 + 161.2 = 239.4 W/m2 (240*) Downward solar radiation reflected back into space (1) by clouds & aerosols = 78.8 W/m2 (2) by Earth’s surface (snow, ice, deserts) = 23.1 W/m2 Average albedo (reflectance) of solar radiation = 101.9 W/m2 (100*) Average albedo of solar radiation = 101.9/ 341.3 = 29.8% (29.4*) 6
1,361 W/m2 340.3 W/m2 (340*)
261.5 W/m2
183.3 W/m2
12.6 % 160.2 W/m2 238.4 W/m2
30.0%
Downward infrared radiation from atmosphere = 333 W/m2 (342*) Ocean = 354 Land = 329 Computed as a residual. Considerable uncertainties exist. (Trenberth and Fasullo 2012.) Total radiation reaching Earth’s surface = 161.2 + 333 = 494.2 W/m2 (502*) 493.2 W/m2 ……………………….. Upward radiation reflected by Earth’s surface = 23.1 W/m2 (25*) Ocean = 12 Land = 53 Upward sensible heat flux (thermals) = 17 W/m2 (21*) Upward latent heat fluxes (evaporation) = 80 W/m2 (82*) Total sensible heat & latent heat fluxes = 17 + 80 = 97 W/m2 (103*) Upward infrared radiation emitted from Earth’s surface = 396 W/m2 (398*) Ocean = 402 Land = 394 Total heat from Earth’s surface = 97 + 396 = 493 W/m2 (501*) Upward infrared radiation escaping into space = 22 W/m2 Upward infrared radiation absorbed by atmosphere = 396 – 22 = 374 W/m2 Upward infrared radiation emitted by atmosphere = 187.4 + 30 = 217.4 W/m2 216.4 W/m2 Total outgoing infrared radiation = 217.4 + 22 = 239.4 W/m2 (239*) 238.4 W/m2 Net incoming solar radiation = 341.3 – 78.8 – 23.1 = 239.4 W/m2 (240*) 238.4 W/m2 Net outgoing heat flux absorbed by atmosphere = 17 + 80 + 396 – 333 = 160 W/m2 (159*) Net outgoing infrared radiation from Earth’s surface = 396 – 333 = 63 W/m2 (56*) Computed as a residual (Trenberth and Fasullo 2012). Energy imbalances: At Earth’s surface: Downward solar radiation absorbed by Earth’s surface = ES = 184.3 – 23.1 = 161.2 W/m2 Net outgoing heat flux from Earth’s surface absorbed by atmosphere = 17 + 80 + 396 – 333 = ETH + EEV + ET – ED = 160 W/m2 Net energy absorbed by Earth’s surface = 161.2 –160 = 1.2 W/m2 Radiative balance at Earth’s surface: ES = ETH + EEV + ET – ED where ES is the solar energy absorbed by the surface 7
160.2 W/m2
0.2 W/m2
ETH is the loss of energy from the surface through thermals EEV is the loss of energy from the surface through evaporation ET is the total infrared radiative flux emitted by the Earth’s surface ED is the total downwelling infrared flux from the atmosphere At atmosphere: Energy absorbed by atmosphere = EA + ETH + EEV + ET – EE – ED = 78.2 + 17 + 80 + 374 – 333 = 216.2 W/m2 [or energy absorbed by atmosphere = EA + ES – EE = 78.2 + 160.2 – 22 = 216.4 W/m2] Infrared radiation emitted by atmosphere into space = EOA = 187.4 + 30 = 217.4 W/m2 Net energy absorbed by atmosphere = 216.2 – 217.4 = – 1.2 W/m2
216.4 W/m2 – 0.2 W/m2
Radiative balance at atmosphere: EOA = EA + ETH + EEV + ET – EE – ED where EOA is the Infrared radiation emitted by atmosphere into space EA is the solar energy absorbed by the atmosphere At top of atmosphere (TOA): Incoming solar radiation = EI = 341.3 W/m2 Reflected solar radiation = ER = ERC + ERS = 78.8 + 23.1 = 101.9 W/m2 Incoming absorbed solar radiation = incoming solar radiation – reflected solar radiation = EI – ER = 341.3 – 101.9 = 239.4 W/m2 Total outgoing infrared radiation at TOA = EO = 239.4 W/m2 Net energy absorbed at TOA = 239.4 – 239.4 = 0.0 W/m2
340.3 W/m2
238.4 W/m2 238.4 W/m2 0.0 W/m2
Radiative balance at the top of the atmosphere: EO = EI + ER where EI is the incoming solar radiation at the top of the atmosphere ER is the total reflected incoming solar radiation ERC is the incoming solar radiation reflected by the clouds ERS is the incoming solar energy reflected by the Earth’s surface EO is the total outgoing infrared radiation It is interesting to note that Trenberth and Fasullo (2012) using uncorrected values concluded that “Both at the surface and TOA the imbalance is the same and … is estimated to be 0.9 W/m2” and attributed this to “Increasing concentrations of carbon dioxide and other greenhouse gases have led to a post-2000 imbalance at the TOA of 0.9 ± 0.5 W/m2 that produces ‘‘global warming’’ or, more correctly, an energy imbalance”. As can be seen above, these imbalances effectively disappeared once Kopp and Lean (2011)’s correction to the incoming solar radiation at the top of the atmosphere was applied. 8
Solution of the Greenhouse Effect equations The Greenhouse Effect equations can be solved for the total infrared flux emitted by the Earth’s surface, and consequently for the temperature at the surface, by calculating the downwelling flux from the atmosphere, ED, and substituting this in the equation for the radiative balance at Earth’s surface: ES = ETH + EEV + ET – ED. The total downwelling infrared flux from the atmosphere ED = Ra + Ra f/2 + Ra f2/4 + …… + Rafn/2n = Ra + Rar, or ED = (1 + r)Ra where Ra is the initial downward infrared flux from the atmosphere, f is the proportion of terrestrial infrared radiation absorbed by the atmosphere, and Ra = (ETH + EEV + EA + fES)/2 and r = f/2 + f2/4 + …… + fn/2n. This assumes that the heat resulting from thermals and evaporation is absorbed by the atmosphere and, as with the solar radiation and terrestrial infrared radiation absorbed by the atmosphere, changes the quantum state of the greenhouse gas molecules. On re-emission, half is radiated downward towards the Earth’s surface and half upward into the atmosphere. This is independent of the model assumed for the atmosphere, whether single or multi-layered, which is only required to calculate the temperature gradients in the atmosphere. r = f/2 + f2/4 + …… + fn/2n is a self-similar geometric series that can be summed by multiplying by the common ratio and subtracting: multiplying by f/2 gives rf/2 = f2/4 + …… + fn/2n, and subtracting r = f/2 + f2/4 + …… + fn/2n, gives r – rf/2 = f/2, or r = f/(2 – f). Recognizing that EE = (1 – f)ET, where EE is the total infrared radiation emitted from the Earth’s surface that escapes directly into space, EE = ET – f ET, so f ET = ET – EE, or f = (ET – EE)/ ET. Substituting values from the corrected Trenberth and Fasullo (2012) data in f = (ET – EE)/ ET, gives f = (ET – EE)/ ET = (396 – 22)/396 = 0.9444. With f = 0.9444, r = f/(2 – f) = 0.9444/1.0556 = 0.89, which is effectively reached after seven iterations: r = 0.9444/2 + 0.94442/4 + 0.94443/8 + 0.94444/16 + 0.94445/32 + …… + fn/2n, or r = 0.9444/2 + 0.89189/4 + 0.8423/8 + 0.79547/16 + 0.75124/32 + 0.70947/64 + 0.67003/128 +.. r = 0.4722 + 0.2230 + 0.1053 + 0.0497 + 0.0235 + 0.0111 + 0.0052 + …, so r = 0.89. Substituting r = f/(2 – f) in ED = (1 + r)Ra, gives ED = [1 + f/(2 – f)]Ra = [(2 – f + f)/(2 – f)]Ra, so ED = 2Ra/(2 – f), and substituting Ra = (ETH + EEV + EA + fES)/2 in ED = 2Ra/(2 – f), gives ED = (ETH + EEV + EA + fES)/(2 – f) 9
Substituting values from the corrected Trenberth and Fasullo (2012) data, gives ED = (17 + 80 + 78.2 + 0.9444 x 160.2)/(2 – 0.9444), or ED = (17 + 80 + 78.2 + 151.3)/1.0556, so ED = 326.5/1.0556 = 309.3 W/m2 (compared with Trenberth and Fasullo (2012)’s estimated residual of 333 W/m2 and Wild et al (2015)’s estimation of 342 W/m2). This equation shows that the size of the downwelling radiation, and consequently the infrared radiation from the surface, is highly dependent on the absorption of solar radiation by the atmosphere, and the existence of thermals and evaporation, in addition to the absorption of solar radiation by the Earth’s surface. Substituting ED = (ETH + EEV + EA + fES)/(2 – f) into the equation for the radiative balance at Earth’s surface: ES = ETH + EEV + ET – ED and expressing in terms of ET gives ET = ES – ETH – EEV + ED = ES – ETH – EEV + (ETH + EEV + EA + fES)/(2 – f), or ET(2 – f) = ES(2 – f) – ETH(2 – f) – EEV(2 – f) + ETH + EEV + EA + fES, or ET(2 – f) = ES(2 – f + f) – ETH(1 – f) – EEV(1 – f) + EA, which provides a solution of the Greenhouse Effect equations in terms of the surface temperature. At thermal equilibrium at the Earth’s surface, ET = [2ES – (1 – f)ETH – (1 – f)EEV + EA]/(2 – f) Substituting values from the corrected Trenberth and Fasullo (2012) data, ET = [(2 x 160.2 – (1 – 0.9444) x 17 – (1 – 0.9444) x 80 + 78.2)/(2 – 0.9444)], or ET = (320.4 – 0.95 – 4.45 + 78.2)/1.0556 = 393.2/1.0556 = 372.5 W/m2 (compared with Trenberth and Fasullo (2012)’s value of 396 W/m2 ). Under these assumptions and at this level of absorption, thermals and evaporation make only small contributions to the surface temperature, and the average global infrared radiation emitted by the Earth’s surface at radiative equilibrium is approximately equal to twice the absorption of incoming solar radiation by the surface plus the incoming solar radiation absorbed by the atmosphere. Substituting ET = 372.5 W/m2 in Planck’s formulation of the Stefan-Boltzmann Law, E = σT4, where σ = 2π5 k4/15c2h3 = 5.670373 x 10-8 Wm-2 K-4, or T4 = E/σ = 372.5 x 108/5.67 = 65.696649 x 108, and the surface temperature of the Earth, T = 284.70°K = 284.70 – 273.15 = 11.55°C (compared with 15.94°C based on Trenberth and Fasullo (2012)’s estimate for ET of 396 W/m2). It should be remembered that this is an estimate of the Greenhouse Effect, the effect of absorption of greenhouse gases in the atmosphere on the surface temperature, not a complete 10
estimate of the surface temperature. In the absence of an atmosphere, but allowing for an average reflection (albedo) from the Earth’s surface of 6.8% (= 23.1/341.3), the temperature of the surface of the Earth would be given by T4 = E/σ = 340.3 x (1 – 0.068) x 108/5.67 = 55.936507 x 108, so T = 273.48°K = 273.48 – 273.15 = 0.3°C. The existence of an atmosphere, through reflection and absorption of incoming solar radiation and absorption of upwelling terrestrial infrared radiation, followed by re-emission of infrared radiation, results in a net increase in the surface temperature of the Earth of around 8.5°C. Recognizing that the average global surface temperature is difficult to measure, and that this does not take account of other known influences, such as poleward transport of heat from the tropics, this appears to be reasonable first level approximation to the estimated value. Moreover, the treatment of thermals and evaporation in adding to the initial downwelling radiation probably requires some refinement (see below). If f = 1, ET = [2ES + fETH – (1 – f)EEV + EA]/(2 – f) becomes ET = 2ES + EA, independent of ETH and EEV. This states that with complete absorption by the atmosphere, and ignoring thermals, the infrared flux emitted by the Earth’s surface equals twice the solar radiation absorbed by the surface plus the solar radiation absorbed by the atmosphere. This formula can be derived more simply by recognizing that with f = 1, r = 1/2 + 1/22 + 1/23 + 1/24 + …..+ 1/2n = 1, showing that the cycle of emissions and re-radiations effectively doubles the downward flux from the atmosphere. Substituting values from the corrected Trenberth and Fasullo (2012) data in ET = 2ES + EA, ET = 2 x 160.2 + 78.2 = 398.6 W/m2, corresponding to a maximum surface temperature under these assumptions of 16.4°C. Substituting formulae for the fluxes in the Greenhouse Effect equation, ET = [2ES – (1 – f)ETH – (1 – f)EEV + EA]/(2 – f), σT4 = [2(1 – αp – αa)S0/4 – (1 – f)(ETH + EEV) + αaS0/4]/(2 – f), or σT4 = [(2 – 2αp – αa)S0/4 – (1 – f)(ETH + EEV)]/(2 – f) where αp is the proportion of incoming solar radiation reflected back into space by the clouds and Earth’s surface (the albedo), αa is the proportion of incoming solar radiation absorbed by the atmosphere, and S0 is the solar flux at the top of the atmosphere. From this it can be seen that the surface temperature is increased by a reduction in solar reflexivity or a reduction in solar atmospheric absorptivity as well as by an increase in the atmospheric infrared absorption coefficient; and, of course, is also increased by an increase in solar irradiance. 11
Alternative treatment of thermals If, alternatively, it is assumed that during the daily cycle the heat flux caused by thermals does not add to the radiation from the atmosphere because the photons are not absorbed by greenhouse gas molecules causing a change in the quantum state of the molecule and subsequent radiation, but instead this heat flux is reversed and returns to the surface where, on absorption by the Earth’s surface, it then adds to the terrestrial infrared radiation. Then the initial downward infrared flux from the atmosphere, Ra = ETH + (EEV + EA + fES)/2 and ED = (2ETH + EEV + EA + fES)/(2 – f). Substituting in ET = ES – ETH – EEV + ED, gives the solution to the Greenhouse Effect equations as ET = [2ES + fETH – (1 – f)EEV + EA]/(2 – f). Substituting values from the corrected Trenberth and Fasullo (2012) data, ED = (34 + 80 + 78.2 + 0.9444 x 160.2)/(2 – 0.9444), so ED = (34 + 80 + 78.2 + 151.3)/1.0556, and ED = 343.5/1.0556 = 325.4 W/m2 (compared with Trenberth and Fasullo (2012)’s estimated residual of 333 W/m2), and ET = [(2 x 160.2 + 0.9444 x 17 – (1 – 0.9444) x 80 + 78.2)/(2 – 0.9444)] ET = (320.4 + 16.05 – 4.45 + 78.2)/1.0556 = 410.2/1.0556 = 388.6 W/m2. This results in an average global surface temperature of 14.6°C, which is closer to 15.94°C based on Trenberth and Fasullo (2012)’s estimate for ET of 396 W/m2. If f = 1, ET = [2ES + fETH – (1 – f)EEV + EA]/(2 – f) becomes ET = 2ES + EA + ETH. Substituting values from the corrected Trenberth and Fasullo (2012) data, ET = 2 x 160.2 + 17 + 78.2 = 415.6 W/m2, corresponding to a surface temperature of 19.5°C (about 3°C higher than at present). Under this alternative assumption, thermals have a significant role in increasing the possible maximum average global surface temperature. Substituting formulae for the fluxes in the Greenhouse Effect equation, ET = [2ES + fETH – (1 – f)EEV + EA]/(2 – f), σT4 = [2(1 – αp – αa)S0/4 + fETH – (1 – f)EEV + αaS0/4]/(2 – f), or σT4 = [(2 – 2αp – αa)S0/4 + fETH – (1 – f)EEV]/(2 – f) where αp is the proportion of incoming solar radiation reflected back into space by the clouds and Earth’s surface (the albedo) and , αa is the proportion of incoming solar radiation absorbed by the atmosphere, S0 is the solar flux at the top of the atmosphere
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The atmospheric window The spectrum of the Sun's solar radiation is close to that of a black body with a temperature of about 5,800°K. The Sun’s energy is made up of ultraviolet radiation (with wavelength, λ , between 10 and 400 nm, nanometers, or billionths of a meter); the visible spectrum (λ between 400 and 700 nm), which accounts for just under half of the Sun’s total energy, the infrared, primarily in the ‘near infrared’ (λ between 700 nm and 4 µm (micrometers – millionths of a meter), but also extending to the ‘far infrared”, up to 1mm (millimeter – thousandth of a meter). Solar radiation is not emitted in a smooth continuum. Superheated atoms in the Sun, particularly hydrogen and helium, absorb radiation in distinct wavelengths. The spectrum of terrestrial radiation is close to that of a black body with a temperature of about 285°K. Terrestrial radiation is primarily in the infrared spectrum (λ between 4 µm and 1mm). In order for an increase in carbon dioxide or other greenhouse gas concentration in the atmosphere to result in an increase in the surface temperature of the Earth, it must be able to increase the absorption of infrared radiation emitted from the surface. This would result in an increase in the absorption factor, f. However, as seen above f is currently around 0.9444. Absorption of infrared radiation by molecules of greenhouse gases, involves increasing the internal energy of the molecule by changing the quantum state of the molecules, which can only occur at particular wavelengths, known as absorption bands. The internal energy level is quantized in a series of electronic, vibrational, and rotational states, depending on the wavelength of the radiation. Electronic transitions correspond to ultraviolet radiation (λ < 0.4 mm); vibrational transitions correspond to the wavelength range of peak terrestrial radiation in the near infrared (λ = 0.7–20 mm); and rotational transitions require far infrared (λ >20 mm). Greenhouse gases absorb in the wavelength range 5-50 mm, where most terrestrial radiation is emitted, corresponding to vibrational and vibrational-rotational transitions. A selection rule from quantum mechanics is that vibrational transitions are allowed only if the change in vibrational state changes the dipole moment p of the molecule. Molecules that can acquire a charge asymmetry by stretching or flexing (CO2, H2O, N2O, O3, and hydrocarbons) are greenhouse gases; molecules that cannot acquire charge asymmetry by flexing or stretching (N 2, O2, and H2) are not greenhouse gases (Jacob 1999). These absorption bands can be extended by what is referred to as pressure broadening (Strong and Plass 1950; Kaplan 1952), but when all of the emitted infrared radiation within these absorption bands has been absorbed by greenhouse gas molecules in the atmosphere, no further absorption of the terrestrial radiation is possible. The radiation with wavelengths falling outside of the absorption bands passes through the atmosphere and escapes into space.
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(a) The normalized blackbody emission spectra for the Sun (T = 6,000°K) and Earth (T = 255°K) as a function of wavelength (top). (b) The fraction of radiation absorbed while passing from the ground to the top of the atmosphere as a function of wavelength. (c) The fraction of radiation absorbed from the tropopause (typically at a height of 11km) to the top of the atmosphere as a function of wavelength. The atmospheric molecules contributing the important absorption features at each frequency are also indicated. After Goody and Yung (1989). (Fig. 2.6, Yang 2016).
The efficiency of absorption of radiation by the atmosphere is shown in (b) above as a function of wavelength. Absorption of solar radiation in in the stratosphere is almost 100% efficient in the ultraviolet due to electronic transitions of oxygen (O2) and ozone (O3) and a significant amount of solar radiation is absorbed by water vapor (H2O) in the lower atmosphere. It is primarily the visible radiation that is absorbed at the Earth’s surface. In the infrared, absorption is again almost 100% efficient because of the greenhouse gases, but there is a window between 8 and 13 mm, near the peak of terrestrial emission, where the atmosphere is only a weak absorber except for a strong ozone feature at 9.6 mm. This atmospheric window allows direct escape of radiation from the surface of the Earth to space and is of importance in determining the temperature of the Earth's surface (Jacob 1999). Additional leakage could occur if the greenhouse gas concentration in the atmosphere were insufficient to absorb all of the infrared radiation in the absorption bands emitted by the Earth’s surface, but due to the extent of the atmosphere and its known unsaturated state, it is more likely 14
that the current leakage corresponds to radiation in the part of the infrared spectrum that does not fall in the greenhouse gas absorption and emission bands, referred to as the “infrared window”. As a consequence, even in the case where there is leakage of infrared radiation from the Earth’s surface directly into space, as long as the atmosphere is able to absorb all of the upwelling infrared radiation in the greenhouse gas absorption bands, neither the amount of this leakage nor the amount of the absorption will depend on concentration of greenhouse gases in the atmosphere. From the emission spectra (a) and absorption percentages (b) in the diagram above (Fig. 2.6, Yang 2016), where the 255°K blackbody curve represents the terrestrial radiation, it appears that at the current surface temperature and absorption factor of 0.9444 all of the radiation within the emission bands is fully absorbed, and that the remaining 5.56 percent of the infrared emission represents radiation with wavelengths within the atmospheric window. If this is true, there can be no further increase in f, and no increase in the surface temperature with an increase in carbon dioxide. Review of current explanations of the Greenhouse Effect As the conclusions from this analysis differ markedly from current dire warnings about the effect of an increase in carbon dioxide on the Earth’s surface temperature, a review of the available explanations of the role of the Greenhouse Effect seemed to be in order. In the apparent absence of a recently published peer reviewed paper in an academic journal, the explanations provided in two popular textbooks on atmospheric chemistry and physical climatology are reviewed (Jacob 1999; Hartmann 1994). Jacob (1999) uses a simple model to demonstrate the Greenhouse Effect in which the atmosphere is viewed as an isothermal layer placed some distance above the surface of the Earth, which is transparent to solar radiation, and absorbs a fraction f of terrestrial radiation because of the presence of greenhouse gases. In particular, this omits the absorption of solar radiation by the atmosphere (as well as thermals and evaporation) shown in the Trenberth and Fasullo (2012) diagram of global energy flows. In the diagram below, the temperature of the Earth's surface is T0°K and the temperature of the atmospheric layer is T1°K.
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Simple greenhouse model. Radiation fluxes per unit area of Earth's surface are shown (Fig. 7-12, Jacob 1999).
The incoming solar radiation absorbed per unit area of the Earth's surface is assumed to be FS(1 – A)/4, where FS is solar radiation flux and A is the proportion of solar radiation reflected back to space by clouds, snow, ice, etc, known as the planetary albedo. The emission flux from the Earth is assumed to be that of a blackbody at temperature TE°K, so applying the Stefan-Boltzmann blackbody radiation law, the terrestrial radiation flux emitted by the Earth’s surface is σT04, of which fσT04 is absorbed by the atmospheric layer and fσT04 escapes directly into space (Jacob 1999). The resulting energy balance equation for the Earth’s surface, given as FS(1 – A)/4 = (1 – f)σT04 + fσT14 is more problematic, as is the energy balance equation for the atmospheric layer given as fσT04 = 2fσT14. Neither of these equations represents the radiative flux balance at thermal equilibrium, even though substitution for fσT14 produces the reduced form of the Greenhouse Effect equation, FS(1 – A)/4 = (1 – f/2)σT04. Ignoring thermals and evaporation, ETH = 0 and EEV = 0, and σT4 = [2(1 – αp – αa)S0/4 – (1 – f)(ETH + EEV) + αaS0/4]/(2 – f), or (1 – αp – αa)S0/4 – (1 – f)(ETH + EEV)/2 + αaS0/8 = (1 – f/2)σT4 reduces to (1 – αp – αa)S0/4 + αaS0/8 = (1 – f/2)σT4. Ignoring solar absorption by the atmosphere, αa = 0, and (1 – αp)S0/4 = (1 – f/2)σT4. The term, FS(1 – A)/4, on the left of the energy balance equation for the Earth’s surface, FS(1 – A)/4 = (1 – f)σT04 + fσT14, represents the solar energy absorbed by the surface; (1 – f)σT04 , the first term on the right represents the proportion of terrestrial radiation lost to space; and the second term, fσT14, is intended to represent the downwelling emission from the atmosphere. However, the black body radiative flux emitted upward and downward from the atmosphere at temperature T1 is σT14, not fσT14. Jacob (1999) then assumes the energy balance equation for the atmospheric layer as fσT04 = 2fσT14, where fσT04 represents the proportion of the radiation flux from the surface absorbed by the atmospheric layer, and fσT14 represents the radiation flux emitted upward and downward from the atmosphere. As the same error is repeated, the two
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errors cancel each other out when fσT14 is substituted in FS(1 – A)/4 = (1 – f)σT04 + fσT14, resulting in FS(1 – A)/4 = (1 – f)σT04 + fσT04/2 = (1 – f/2)σT04, or σT04 = FS(1 – A)/4(1 – f/2). Substituting values from the corrected Trenberth and Fasullo (2012) data in T04 = FS(1 – A)/4(1 – f/2)σ gives T04 = (340.3 – 78.8 – 23.1) x 108/5.67 x (1 – 0.9444/2) = 238.4 x 108/5.67 x 0.5278, or T04 = 451.7 x 108/5.67 = 79.6649, or T = 298.76°K = 298.76 – 273.15 = 25.61°C, which is not surprising when the solar radiation absorbed by the surface is increased from 160.2 W/m2 to 238.4 W/m2. By setting A = 0.28 and reducing f from 0.9444 to f = 0.77, Jacob (1999) was able to produce a surface temperature closer to the estimated average global surface temperature, T04 = FS(1 – A)/4(1 – f/2)σ = 340.3 x (1 – 0.28) x 108/5.67 x (1 – 0.77/2) = 245.0 x 108/5.67 x 0.615, or T04 = 398.4 x 108/5.67 = 70.2646, or T = 289.52°K = 289.52 – 273.15 = 16.4°C. Jacob (1999) notes that the observed global mean surface temperature is T 0 = 288°K, corresponding to f = 0.77 … “We can thus reproduce the observed surface temperature by assuming that the atmospheric layer absorbs 77% of terrestrial radiation. This result is not inconsistent with the data in Figure 7-11; better comparison would require a wavelengthdependent calculation. … Increasing concentrations of greenhouse gases increase the absorption efficiency f of the atmosphere, and we see from equation (7.16) that an increase in the surface temperature T0 will result”1. 1. Professor Jacob’s course notes for Atmospheric Chemistry at the Department of Earth and Planetary Sciences at Harvard University for Spring 2017 show that this explanation remains unchanged after two decades (Jacob. 2017).
Hartmann (1994) uses an even more simplified model by assuming, in addition, that the atmospheric layer absorbs all of the energy emitted by the surface below it, i.e. that f = 1. The surface energy balance using Jacob (1999)’s terminology is expressed as S0(1 – A)/4 + σT14 = σT04 and the energy balance at the top of the atmosphere, stated as S0(1 – A)/4 = σT14, is used to solve for T0, resulting in σT04 = 2S0(1 – A)/4 or 2σT14 = σT04. 2σT14 = σT04 gives T04/ T14 = 2, so T0/ T1 = 21/4 = 1.19, showing that the absorption of terrestrial infrared radiation by the atmosphere doubles the radiative flux at the surface and increases the surface temperature by a factor of 21/4 or 1.19. Hartmann (1994) notes that “The surface temperature is increased because the atmosphere does not inhibit the flow of solar energy to the surface, but augments the solar heating of the surface with its own downward emission of longwave radiation, which in this case is equal to the solar heating. The atmospheric greenhouse effect warms the surface because the atmosphere is relatively transparent to solar radiation and yet absorbs and emits terrestrial radiation very effectively.” 17
These two models are stated in terms of radiative fluxes at thermal equilibrium expressed in terms of the corresponding black body surface temperatures, which is elegant but prevents inclusion of other fluxes such as thermals and evaporation and absorption of solar radiation by the atmosphere. Jacob (1999) notes that this simple model can be improved upon by viewing the atmosphere as a vertically continuous absorbing medium, rather than a single discrete layer, and applying the energy balance equation to elemental slabs of atmosphere, with f varying with height, though this "gray atmosphere" model is more useful in explaining the change in temperature with altitude rather than calculating the change in surface temperature with an increase in greenhouse gases. Jacob (1999) also referred to radiative models, which are used to resolve the wavelength distribution of radiation; and radiative-convective models, used to take account of the buoyant transport of heat as a term in the energy balance equations, which would help refine the treatment of thermals. In recent decades, the main reliance for assessing climate response to increases in greenhouse gases has been on general circulation models (GCMs), which attempt to resolve the horizontal heterogeneity of the surface and its atmosphere by solving globally the 3-dimensional equations for conservation of energy, mass, and momentum. However, there is still considerable doubt about the extent to which currently available GCMs can usefully contribute to the analysis of the impact of an increase in carbon dioxide on the surface temperature of the Earth. Other explanations for global warming; increase in solar irradiance The analysis described in this paper suggests that at current levels of greenhouse gases in the atmosphere, a further increase in carbon dioxide or other greenhouse gases is unlikely to contribute to an increase in surface temperatures. However, this is based on current radiative fluxes and may not have been true during the whole of the last 150 years, during which greenhouse gas concentrations nearly doubled. As noted in the introduction, there are also questions about the reliability of the published historical record of in situ global surface temperatures, but if there is evidence of recent increases in surface temperatures, an alternative explanation may be required. The most likely is an increase in solar irradiance. The amount of radiation arriving from the Sun is not constant. It varies from the average value of the total solar irradiance (TSI) —1,361 W/m2—on a daily basis. Variations in TSI are due to a balance between decreases caused by sunspots and increases caused by bright areas called faculae which surround sunspots. Although solar energy reaching the Earth decreases when the portion of the Sun’s surface that faces the Earth happens to be rife with spots and faculae, the total energy averaged over a full 30-day solar rotation actually increases. Therefore the TSI is larger during the portion of the 11 year cycle when there are more sunspots, even though the individual spots themselves cause a decrease in TSI when facing Earth. The number of sunspots on the Sun’s surface is roughly proportional to total solar irradiance. Historical sunspot records suggest that no sunspots existed on the Sun’s surface during the time period from 1650 to 1715 18
AD, creating a minimum in solar energy output, the Maunder Minimum, which may have been partly responsible for the Little Ice Age in Europe. Subsequently there has been a slow increase in the overall sunspots and solar energy throughout each subsequent 11-year cycle, which may be responsible for as much as half of the 0.6°C of global warming over the last 110 years (Weiss 1999; Weier and Cahalan 2003; IPCC 2001). Prior to 1979, scientists did not have accurate data on the total amount of energy from the Sun that reaches the Earth’s outermost atmosphere. Variable absorption of sunlight by clouds and aerosols prevented researchers from accurately measuring solar radiation before it strikes the Earth’s atmosphere. However, since the launch of the Nimbus-7 satellite in 1978, NASA scientists have been able to detect sunlight without interference from the atmosphere. There has subsequently been a succession of satellites measuring total solar irradiance from the top of the Earth’s atmosphere, but by 2014, after contact with ACRIM3 was lost in December 2013, there were only two remaining projects with more than one solar cycle of TSI data; the Solar and Heliospheric Observatory (SOHO) spacecraft and the Solar Radiation and Climate Experiment (SORCE) satellite. Most of the data that has been collected is for TSI. Relatively little has been gathered on the spectral changes in the sun, nor do we have complete measurements of the energy variation for the distinct wavelengths of incoming solar radiation (Weier and Cahalan 2003). The Solar and Heliospheric Observatory (SOHO) spacecraft, which was built by a European industrial consortium as a joint project of the European Space Agency (ESA) and NASA began operations in May 1996. It flies in a halo orbit between 206,000 km and 668,000 km above the Earth’s surface, where the balance of the Sun’s gravity and the Earth’s gravity is equal to the centripetal force needed for it to have the same orbital period around the Sun as the Earth. Originally planned as a two year mission, it has been extended multiple times, most recently through the end of 2018. It carries 12 instruments developed by 12 international consortia, including the Variability of Solar Irradiance and Gravity Oscillations (VIRGO) instrument for measuring total solar irradiance. This has provided the longest continuous record of satellite based TSI data spanning more than 21 years, or close to two solar cycles (ESA website). In an attempt to reduce the uncertainty of solar energy measurements, NASA launched the Solar Radiation and Climate Experiment (SORCE) satellite in January, 2003. The satellite flies at a much lower altitude of 640 km, at the top of the Earth’s atmosphere, in a 40-degree-inclination orbit around the Earth. On board SORCE are four instruments that measure variations in solar radiation much more accurately and observe some of the spectral properties of solar radiation for the first time. All instruments take readings of the Sun during each of the satellite’s 15 daily orbits. The Total Irradiance Monitor (TIM) is used to measure the TSI by recording the sum of the energy from nearly all the Sun’s wavelengths. The improved accuracy of the SORCE TIM of around 0.035 % is expected to detect a change in TSI of 0.08 % per century (equivalent to the 19
estimated global warming) in about 35 years. The Spectral Irradiance Monitor (SIM) measures the upper portion of the ultraviolet spectrum (λ = 200 – 400 nm), the full visible range, and the near infrared up to λ = 2,000 nm. The Solar Stellar Irradiance Comparison Experiment (SOLSTICE) measures the full ultraviolet beginning at λ = 100 nm, and includes the lower half of the ultraviolet region of SIM (λ = 200 – 300 nm) (LASP 2017 (1)). Three previous composite satellite based irradiance records, PMOD, ACRIM and SARR showed different secular trends for the total solar irradiance (TSI) between 1978 and 2004 because of different cross-calibrations and drift adjustments applied to individual radiometric (Fröhlich and Lean 2004; Willson and Mordvinov 2003; Dewitte et al 2005; Lean et al 2005).
Shown in the upper three panels are different composite records of total solar irradiance during the era of space-based monitoring. For quantitative comparison, the slopes of the time series are computed from 7538 daily values between November 1978 and June 2004 (Fig.4, Lean et al 2005). 20
PMOD showed a decadal trend in total solar irradiance (TSI) between November 1978 and June 2004 of – 0.023 W/m2; ACRIM showed a decadal increase of 0.219 W/m2 ; and SARR a decadal increase of 0.251 W/m2 (Lean et al 2005).
VIRGO TSI (original scale) is compared to ACRIM and TIM. The ACRIM values are on the scale of ACRIM3 (version 1311). (Fig. 3.8, pmodwrc 2016).
The difference between the minima showed an increase of 0.2812 W/m2for VIRGO; 0.4701 W/m-2 for ACRIM; and 0.2650 W/m2 for ACRIM + TIM over the 11.6 year solar cycle 23 beginning in May 1996 and ending in January 2008; or 0.24 W/m2 per decade for VIRGO, 0.40 W/m2 per decade for ACRIM, and 0.23 W/m2 per decade for ACRIM + TIM (pmodwrc 2016). These decadal increases in TSI from ACRIM, SARR, VIRGO and ACRIM + TIM are sufficient to explain the whole of the increase in surface temperature estimated from in situ data during the last 100 years. They compare with the six published model-based estimates of forcing examined in Schwartz (2012) that showed forcing by incremental greenhouse gases and aerosols over the twentieth century ranging between 0.11 and 0.21 W/m2 per decade. Unfortunately, the SORC TIM instrument started experiencing a failing battery in November 2012, and was moved into power-cycling mode, which resulted in much larger thermal fluctuations and an absence of dark measurements during eclipse, affecting data quality and introducing time-dependent uncertainties. This resulted in all SORC instruments ceasing operations at the end of July, 2013. From March 2014, TIM was operated in daylight-only 21
operations mode with reduced TSI data production; then after further battery degradation was switched to brown-out mode in December 2014, with even less measurements and greater measurement uncertainties (LASP 2017(1)). Since the SORCE TIM was put into orbit in 2003, an improved TIM instrument was developed for the Glory mission, scheduled for no earlier than October 2009. This was a more sophisticated version of this class of radiometers, known as solar bolometers that had been flown on ten previous missions, starting with Nimbus-7 in 1978, and related in concept to the earliest groundbased solar bolometer, which was invented by Samuel Pierpoint Langley in 1878. This latest version was estimated to be three times more accurate than the SORCE TIM, sufficient to detect a change in TSI of 0.08 % per century (equivalent to the estimated global warming) in about 10 years. Unfortunately, this instrument, together with the Aerosol Polarimetry Sensor (APS), designed to measure the effects of aerosols on the Earth’s climate, and NASA’s Glory low Earth orbit (LEO) scientific research satellite, was lost in the Southern Pacific Ocean on March 4, 2011, when the Taurus XL rocket’s nose cone failed to disengage, making it too heavy to achieve orbit (NASA 2017). Another instrument, the Total and Spectral Solar Irradiance Sensor (TSIS), first selected in 1998, combining the SORCE Total Irradiance Monitor (TIM) and Spectral Irradiance Monitor (SIM), is scheduled to be delivered to the International Space Station on a Space X Falcon 9 rocket and Dragon capsule in November 2017, and be operational by February 2018, in order to maintain continuity of the record of TSI and SSI. This lacks the accuracy of the lost TIM instrument sets back the time before the decadal change in TSI can be determined by another 20 years (LASP 2017(2)). Conclusion Solution of the Greenhouse Effect equations based on a more realistic atmospheric model that includes absorption of solar radiation by the atmosphere, thermals and evaporation, and an examination of the fraction of terrestrial infrared radiation absorbed whilst passing through the atmosphere, suggests that the contribution of greenhouse gases to the surface temperature is close to its upper limit. Any further contribution would depend on an increase in the infrared absorption factor of the atmosphere from its current level of around 0.9444, which seems unlikely. As this appears to correspond to total absorption of all black body infrared emission from the Earth’s surface at wavelengths at which there are greenhouse gas absorption bands, including for water vapor, it seems likely that we are close to the thermodynamic limit of greenhouse warming for the current luminosity of the sun, and that any further increase in carbon dioxide concentration in the atmosphere will have little or no effect on the surface temperature of the Earth. Questions about the reliability of in situ measurements of surface temperatures also raise questions about current estimates of global warming. Moreover, recent evidence from 22
satellite measurements of solar irradiance, indicate that any recent warming could be due to increasing solar irradiance, but, after losing a critical instrument when NASA’s Glory satellite failed to achieve orbit in 2011, it will now be another 20 years before we have enough data to be sure. If this proves to be correct, we may need to consider increasing carbon or other aerosols in the atmosphere to constrain further increases in the surface temperature.
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References Boltzmann, L. 1884. Ableitung des Stefan'schen Gesetzes, betreffend die Abhängigkeit der Wärmestrahlung von der Temperatur aus der electromagnetischen Lichttheorie" [Derivation of Stefan's little law concerning the dependence of thermal radiation on the temperature of the electro-magnetic theory of light], Annalen der Physik und Chemie, 258 (6), 291–294. Dewitte et al. 2005. Measurement and uncertainty of the long-term total solar irradiance trend. Sol. Phys., 224, 209–216, 2004, doi: 10.1007/s11207-005-5698-7. ESA. 2017. SOHO Fact Sheet, European Space Agency website. Fröhlich and Lean. 2004. Solar radiative output and its variability: evidence and mechanisms. Astron. Astrophys. Rev., 12 (4), 273–320, 2004, doi: 10.1007/s00159-004-0024-1 Goody and Yung. 1989. Atmospheric Radiation: Theoretical Basis, Oxford University Press. Hartmann. 1994. Global Physical Climatology, Academic Press. IPCC. 2001. Summary for Policymakers, A Report of Working Group I of the Intergovernmental Panel on Climate Change, Geneva, Switzerland, 2-13. Jacob, D. J. 1999. Introduction to Atmospheric Chemistry, Princeton University Press. Jacob, D. J. 2017. Course notes for Atmospheric Chemistry, Department of Earth and Planetary Sciences, Harvard University website. Kaplan, L. D. 1952. On the pressure dependence of radiative heat transfer in the atmosphere. J. Met., 9, 1, 1-12. Kent et al. 2017. A call for new approaches to quantifying biases in observations of sea-surface temperatures, Amer. Met. Soc. doi: 10.1175/BAMS-D-15-00251.1. Kopp and Lean. 2011. A new lower value of total solar irradiance: evidence and climate significance, Geophys. Res. Lett., 38, L01706. LASP. 2017 (1). SORCE Spacecraft, Laboratory for Atmospheric and Space Physics, University of Colorado website. LASP. 2017 (2). TSIS Mission Introduction, Laboratory for Atmospheric and Space Physics, University of Colorado website. Lean et al. 2005. SORCE contributions to new understanding of global change and solar variability. Sol. Phys., 230, 27– 53. Lighty, R. G. 1977. Relict shelf-edge Holocene coral reef: southeast coast of Florida. Third International Coral Reef Symposium, May 1977. NASA. 2017. Glory Mission Science, NASA website. Planck, M. (1901). Über das Gesetz der Energieverteilung im Normalspektrum [On the Law of Distribution of Energy in the Normal Spectrum]. Annalen der Physik, 4 (3), 553–563, translated by Koji Ando, K, Kyoto University. pmodwrc. 2016. VIRGO investigation for solar radiance variability and helio-seismology on ESA/NASA SOHO Mission, World Radiation Cente, Physikalisch-Meteorologisches Observatorium Davos website. 24
Schwartz, S. E. 2012. Determination of Earth’s Transient and Equilibrium Climate Sensitivities from Observations Over the Twentieth Century: Strong Dependence on Assumed Forcing. Surv. Geophys., doi:10.1007/s10712-012-9180-4. Stefan, J. 1879. Über die Beziehung zwischen der Wärmestrahlung und der Temperatur" [On the relationship between heat radiation and temperature] (PDF), Sitzungsberichte der mathematisch-naturwissenschaftlichen Classe der kaiserlichen Akademie der Wissenschaften, Vienna, 79, 391–428. Strong and Plass. 1950. The effect of pressure broadening of spectral lines on atmospheric temperature. Astrophys. J., 112, 365-379. Trenberth et al. 2009. Earth’s global energy budget. Bull. Am. Meteorological Soc., doi:10.1175/2008BAMS2634.1. Trenberth and Fasullo. 2012. Tracking Earth’s Energy: From El Nino to Global Warming. Surv. Geophys., 33:413-426. Underwood, T. G. 2016. Sea Surface Temperatures in the North Atlantic, unpublished. Underwood, T. G. 2017. Examination of adjustments to land air temperature, sea surface temperature, and marine air temperature data. Unpublished. Weier and Cahalan. 2003. Solar Radiation and Climate Experiment (SORCE), SORCE website, NASA. Weiss, N.O. 1999. Solar Activity and Climatic Change. UK National Astronomy Meeting, Guernsey, Royal Astronomical Society website. Wild et al. 2013. The global energy balance from a surface perspective, Clim. Dyn., 40, 3107– 3134. Wild et al. 2015. The energy balance over land and oceans: an assessment based on direct observations and CMIP5 climate models, Clim. Dyn., 44, 3393–3429. Willson and Mordvinov. 2003. Secular total solar irradiance trend during solar cycles 21–23. Geophys. Res. Lett., 30 (5), 1199–1202, 2003, doi: 10.1029/2002GL016038. Yang, Z-L. 2016. Course notes for Physical Climatology, Department of Geological Sciences, University of Texas website. Zhong & Haigh. 2013. The greenhouse effect and carbon dioxide. Bull. of Royal Meteorological Soc., 68, 100-105.
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