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New Insights on the Physical Nature of the Atmospheric Greenhouse Effect Deduced from an Empirical Planetary Temperature Model
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Environment Pollution and Climate Change ate Change lim vironment P En ution and C oll Research Article Nikolov and Zeller, Environ Pollut Climate Change 2017, 1:2 OMICS International New Insights on the Physical Nature of the Atmospheric Greenhouse Effect Deduced from an Empirical Planetary Temperature Model Ned Nikolov* and Karl Zeller Ksubz LLC, 9401 Shoofly Lane, Wellington CO 80549, USA Abstract A recent study has revealed that the Earth’s natural atmospheric greenhouse effect is around 90 K or about 2 times stronger than assumed for the past 40 years. A thermal enhancement of such a magnitude cannot be explained with the observed amount of outgoing infrared long-wave radiation absorbed by the atmosphere (i. ≈ 158 W m-2), thus requiring a re-examination of the underlying Greenhouse theory. We present here a new investigation into the physical nature of the atmospheric thermal effect using a novel empirical approach toward predicting the Global Mean Annual near-surface equilibrium Temperature (GMAT) of rocky planets with diverse atmospheres. Our method utilizes Dimensional Analysis (DA) applied to a vetted set of observed data from six celestial bodies representing a broad range of physical environments in our Solar System, i. Venus, Earth, the Moon, Mars, Titan (a moon of Saturn), and Triton (a moon of Neptune). Twelve relationships (models) suggested by DA are explored via non-linear regression analyses that involve dimensionless products comprised of solar irradiance, greenhouse-gas partial pressure/density and total atmospheric pressure/density as forcing variables, and two temperature ratios as dependent variables. One non-linear regression model is found to statistically outperform the rest by a wide margin. Our analysis revealed that GMATs of rocky planets with tangible atmospheres and a negligible geothermal surface heating can accurately be predicted over a broad range of conditions using only two forcing variables: top-of-the-atmosphere solar irradiance and total surface atmospheric pressure. The hereto discovered interplanetary pressure-temperature relationship is shown to be statistically robust while describing a smooth physical continuum without climatic tipping points. This continuum fully explains the recently discovered 90 K thermal effect of Earth’s atmosphere. The new model displays characteristics of an emergent macro-level thermodynamic relationship heretofore unbeknown to science that has important theoretical implications. A key entailment from the model is that the atmospheric ‘greenhouse effect’ currently viewed as a radiative phenomenon is in fact an adiabatic (pressure-induced) thermal enhancement analogous to compression heating and independent of atmospheric composition. Consequently, the global down-welling long-wave flux presently assumed to drive Earth’s surface warming appears to be a product of the air temperature set by solar heating and atmospheric pressure. In other words, the so-called ‘greenhouse back radiation’ is globally a result of the atmospheric thermal effect rather than a cause for it. Our empirical model has also fundamental implications for the role of oceans, water vapour, and planetary albedo in global climate. Since produced by a rigorous attempt to describe planetary temperatures in the context of a cosmic continuum using an objective analysis of vetted observations from across the Solar System, these findings call for a paradigm shift in our understanding of the atmospheric ‘greenhouse effect’ as a fundamental property of climate. Keywords: Greenhouse effect; Emergent model; Planetary temperature; Atmospheric pressure; Greenhouse gas; Mars temperature Introduction In a recent study Volokin and ReLlez [1] demonstrated that the strength of Earth’s atmospheric Greenhouse Effect (GE) is about 90 K instead of 33 K as presently assumed by most researchers [2-7]. The new estimate corrected a long-standing mathematical error in the application of the Stefan–Boltzmann (SB) radiation law to a sphere pertaining to Hölder’s inequality between integrals. Since the current greenhouse theory strives to explain GE solely through a retention (trapping) of outgoing long-wavelength (LW) radiation by atmospheric gases [2,5,710], a thermal enhancement of 90 K creates a logical conundrum, since satellite observations constrain the global atmospheric LW absorption to 155–158 W m-2 [11-13]. Such a flux might only explain a surface warming up to 35 K. Hence, more than 60% of Earth’s 90 K atmospheric effect appears to remain inexplicable in the context of the current theory. Furthermore, satellite- and surface-based radiation measurements have shown [12-14] that the lower troposphere emits 42-44% more radiation towards the surface (i. 341-346 W m-2) than the net shortwave flux delivered to the Earth-atmosphere system by the Sun (i. 240 W m-2). In other words, the lower troposphere contains significantly more kinetic energy than expected from solar heating alone, a conclusion also supported by the new 90 K GE estimate. A similar but more extreme situation is observed on Venus as well, where the atmospheric downwelling LW radiation near the surface (>15,000 W m-2) exceeds the total absorbed solar flux (65–150 W m-2) by a factor of 100 or more [6]. The radiative greenhouse theory cannot explain this apparent paradox considering the fact that infrared-absorbing gases such as CO2, water Environ Pollut Climate Change, an open access journal vapor and methane only re-radiate available LW emissions and do not constitute significant heat storage or a net source of additional energy to the system. This raises a fundamental question about the origin of the observed energy surplus in the lower troposphere of terrestrial planets with respect to the solar input. The above inconsistencies between theory and observations prompted us to take a new look at the mechanisms controlling the atmospheric thermal effect. We began our study with the premise that processes controlling the Global Mean Annual near-surface Temperature (GMAT) of Earth are also responsible for creating the observed pattern of planetary temperatures across the Solar System. Thus, our working hypothesis was that a general physical model should exist, which accurately describes equilibrium GMATs of planets using a common set of drivers. If true, such a model would also reveal the forcing behind the atmospheric thermal effect. Instead of examining existing mechanistic models such as 3-D *Corresponding author: Ned Nikolov, Ksubz LLC, 9401 Shoofly Lane, Wellington CO 80549, USA, Tel: 970-980-3303, 970-206-0700; E-mail: ntconsulting@comcast Received November 11, 2016; Accepted February 06, 2017; Published February 13, 2017 Citation: Nikolov N, Zeller K (2017) New Insights on the Physical Nature of the Atmospheric Greenhouse Effect Deduced from an Empirical Planetary Temperature Model. Environ Pollut Climate Change 1: 112. Copyright: © 2017 Nikolov N, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Volume 1 • Issue 2 • 1000112 Citation: Nikolov N, Zeller K (2017) New Insights on the Physical Nature of the Atmospheric Greenhouse Effect Deduced from an Empirical Planetary Temperature Model. Environ Pollut Climate Change 1: 112. Page 2 of 22 GCMs, we decided to try an empirical approach not constrained by a particular physical theory. An important reason for this was the fact that current process-oriented climate models rely on numerous theoretical assumptions while utilizing planet-specific parameterizations of key processes such as vertical convection and cloud nucleation in order to simulate the surface thermal regime over a range of planetary environments [15]. These empirical parameterizations oftentimes depend on detailed observations that are not typically available for planetary bodies other than Earth. Hence, our goal was to develop a simple yet robust planetary temperature model of high predictive power that does not require case-specific parameter adjustments while successfully describing the observed range of planetary temperatures across the Solar System. Methods and Data In our model development we employed a ‘top-down’ empirical approach based on Dimensional Analysis (DA) of observed data from our Solar System. We chose DA as an analytic tool because of its ubiquitous past successes in solving complex problems of physics, engineering, mathematical biology, and biophysics [16-21]. To our knowledge DA has not previously been applied to constructing predictive models of macro-level properties such as the average global temperature of a planet; thus, the following overview of this technique is warranted. Dimensional analysis background DA is a method for extracting physically meaningful relationships from empirical data [22-24]. The goal of DA is to restructure a set of original variables deemed critical to describing a physical phenomenon into a smaller set of independent dimensionless products that may be combined into a dimensionally homogeneous model with predictive power. Dimensional homogeneity is a prerequisite for any robust physical relationship such as natural laws. DA distinguishes between measurement units and physical dimensions. For example, mass is a physical dimension that can be measured in gram, pound, metric ton etc.; time is another dimension measurable in seconds, hours, years, etc. While the physical dimension of a variable does not change, the units quantifying that variable may vary depending on the adopted measurement system. Many physical variables and constants can be described in terms of four fundamental dimensions, i. mass [M], length [L], time [T], and absolute temperature [Θ]. For example, an energy flux commonly measured in W m-2 has a physical dimension [M T-3] since 1 W m-2 = 1 J s-1 m-2 = 1 (kg m2 s-2) s-1 m-2 = kg s-3. Pressure may be reported in units of Pascal, bar, atm., PSI or Torr, but its physical dimension is always [M L-1 T-2] because 1 Pa = 1 N m-2 = 1 (kg m s-2) m-2 = 1 kg m-1 s-2. Thinking in terms of physical dimensions rather than measurement units fosters a deeper understanding of the underlying physical reality. For instance, a comparison between the physical dimensions of energy flux and pressure reveals that a flux is simply the product of pressure and the speed of moving particles [L T-1], i. [M T-3] = [M L-1 T-2] [L T-1]. Thus, a radiative flux FR (W m-2) can be expressed in terms of photon pressure Pph (Pa) and the speed of light c (m s-1) as FR = c Pph. Since c is constant within a medium, varying the intensity of electromagnetic radiation in a given medium effectively means altering the pressure of photons. Thus, the solar radiation reaching Earth’s upper atmosphere exerts a pressure (force) of sufficient magnitude to perturb the orbits of communication satellites over time [25,26]. Environ Pollut Climate Change, an open access journal The simplifying power of DA in model development stems from the Buckingham Pi Theorem [27], which states that a problem involving n dimensioned xi variables, i. f ( x1 , x2 ,… , xn ) = 0 can be reformulated into a simpler relationship of (n-m) dimensionless πi products derived from xi, i. ϕ(π1, π2, …. ,πn-m) = 0 where m is the number of fundamental dimensions comprising the original variables. This theorem determines the number of nondimensional πi variables to be found in a set of products, but it does not prescribe the number of sets that could be generated from the original variables defining a particular problem. In other words, there might be, and oftentimes is more than one set of (n-m) dimensionless products to analyze. DA provides an objective method for constructing the sets of πi variables employing simultaneous equations solved via either matrix inversion or substitution [22]. The second step of DA (after the construction of dimensionless products) is to search for a functional relationship between the πi variables of each set using regression analysis. DA does not disclose the best function capable of describing the empirical data. It is the investigator’s responsibility to identify a suitable regression model based on prior knowledge of the phenomenon and a general expertise in the subject area. DA only guarantees that the final model (whatever its functional form) will be dimensionally homogeneous, hence it may qualify as a physically meaningful relationship provided that it (a) is not based on a simple polynomial fit; (b) has a small standard error; (c) displays high predictive skill over a broad range of input data; and (d) is statistically robust. The regression coefficients of the final model will also be dimensionless, and may reveal true constants of Nature by virtue of being independent of the units utilized to measure the forcing variables. Selection of model variables A planet’s GMAT depends on many factors. In this study, we focused on drivers that are remotely measurable and/or theoretically estimable. Based on the current state of knowledge we identified seven physical variables of potential relevance to the global surface temperature: 1) topof-the-atmosphere (TOA) solar irradiance (S); 2) mean planetary surface temperature in the absence of atmospheric greenhouse effect, hereto called a reference temperature (Tr); 3) near-surface partial pressure of atmospheric greenhouse gases (Pgh); 4) near-surface mass density of atmospheric greenhouse gases (ρgh); 5) total surface atmospheric pressure (P); 6) total surface atmospheric density (ρ); and 7) minimum air pressure required for the existence of a liquid solvent at the surface, hereto called a reference pressure (Pr). Table 1 lists the above variables along with their SI units and physical dimensions. Note that, in order to simplify the derivation of dimensionless products, pressure and density are represented in Table 1 by the generic variables Px and ρx, respectively. As explained below, the regression analysis following the construction of πi variables explicitly distinguished between models involving partial pressure/density of greenhouse gases and those employing total atmospheric pressure/density at the surface. The planetary Bond albedo (αp) was omitted as a forcing variable in our DA despite its known effect on the surface energy budget, because it is already dimensionless and also partakes in the calculation of reference temperatures discussed below. Appendix A details the procedure employed to construct the πi variables. DA yielded two sets of πi products, each one consisting of two Volume 1 • Issue 2 • 1000112 Citation: Nikolov N, Zeller K (2017) New Insights on the Physical Nature of the Atmospheric Greenhouse Effect Deduced from an Empirical Planetary Temperature Model. Environ Pollut Climate Change 1: 112. Page 4 of 22 (1 − η ) S (1 − α ) + R + R 5 / 4 − ( R + R )5 / 4 e e c g C g + 1/ 4 (1 − ηe ) S (1 − αe )( εσ ) 2 Tna = 5 0η S (1 − α ) + R + R 5 / 4 − R + R 5 / 4 ( C g) e e c g 1/ 4 0ηe S (1 − αe )( εσ ) (4a) Regression analysis where αe is the effective shortwave albedo of the surface, ηe is the effective ground heat storage coefficient in a vacuum, Rc = σ 2 = 3 × 10-6 W m-2 is the CMBR [35], and Rg is the spatially averaged geothermal flux (W m-2) emanating from the subsurface. The heat storage term ηe is defined as a fraction of the absorbed shortwave flux conducted into the subsurface during daylight hour and subsequently released as heat at night. Since the effect of CMBR on Tna is negligible for S > 0 W m-2 [1] and the geothermal contribution to surface temperatures is insignificant for most planetary bodies, one can simplify Eq. (4a) by substituting Rc = Rg = 0 This produces: Tna = 2 S (1 − α e ) 5 εσ 0 (1 − ηe )0 + 0ηe 0 can only exists in a solid/vapor phase and not in a liquid form. The results of our analysis are not sensitive to the particular choice of a referencepressure value; hence, the selection of Pr is a matter of convention. ( ) (4b) Finding the best function to describe the observed variation of GMAT among celestial bodies requires that the πi variables generated by DA be subjected to regression analyses. As explained in Appendix A, twelve pairs of πi variables hereto called Models were investigated. In order to ease the curve fitting and simplify the visualization of results, we utilized natural logarithms of the constructed πi variables rather than their absolute values, i. we modeled the relationship ln (π1) = f (ln(π2)) instead of π1 = f(π2). In doing so we focused on monotonic functions of conservative shapes such as exponential, sigmoidal, hyperbolic, and logarithmic, for their fitting coefficients might be interpretable in physically meaningful terms. A key advantage of this type of functions (provided the existence of a good fit, of course) is that they also tend to yield reliable results outside the data range used to determine their coefficients. We specifically avoided non-monotonic functions such as polynomials because of their ability to accurately fit almost any dataset given a sufficiently large number of regression coefficients while at the same time showing poor predictive skills beyond the calibration data range. Due to their highly flexible shape, polynomials can easily fit random noise in a dataset, an outcome we particularly tried to avoid. where 0 = 0.7540. The complete formula (4a) must only be used if S ≤ 0 W m-2 and/or the magnitude of Rg is significantly greater than zero. For comparison, in the Solar System, the threshold S ≤ 0 W m-2 is encountered beyond 95 astronomical unis (AU) in the region of the inner Oort cloud. Volokin and ReLlez [1] verified Equations (4a) and The following four-parameter exponential-growth function was (4b) against Moon temperature data provided by the NASA Diviner found to best meet our criteria: Lunar Radiometer Experiment [29,36]. These authors also showed that y a exp ( b x ) + c exp ( d x ) (5) accounting for the subterranean heat storage (ηe) markedly improves = the physical realism and accuracy of the SAT model compared to the where x = ln (π2) and y = ln (π1) are the independent and dependent original formulation by Rubincam [34]. variable respectively while a, b, c and d are regression coefficients. This function has a rigid shape that can only describe specific exponential The conceptual difference between Equations (3) and (4b) is that Τe patterns found in our data. Equation (5) was fitted to each one of the represents the equilibrium temperature of a blackbody disk orthogonally 12 planetary data sets of logarithmic πi pairs suggested by DA using the illuminated by shortwave radiation with an intensity equal to the average standard method of least squares. The skills of the resulting regression solar flux absorbed by a sphere having a Bond albedo αp, while Τna is the models were evaluated via three statistical criteria: coefficient of area-weighted average temperature of a thermally heterogeneous airless determination (R2), adjusted R2, and standard error of the estimate (σest) sphere [1,37]. In other words, for spherical objects, Τe is an abstract [39,40]. All calculations were performed with SigmaPlotTM 13 graphing mathematical temperature, while Tna is the average kinetic temperature and analysis software. of an airless surface. Due to Hölder’s inequality between integrals, one always finds Τe >> Τna when using equivalent values of stellar irradiance and surface albedo in Equations (3) and (4b) [1]. To calculate the Tna temperatures for planetary bodies with tangible atmospheres, we assumed that the airless equivalents of such objects would be covered with a regolith of similar optical and thermo-physical properties as the Moon surface. This is based on the premise that, in the absence of a protective atmosphere, the open cosmic environment would erode and pulverize exposed surfaces of rocky planets over time in a similar manner [1]. Also, properties of the Moon surface are the best studied ones among all airless bodies in the Solar System. Hence, one could further simplify Eq. (4b) by combining the albedo, the heat storage fraction and the emissivity parameter into a single constant using applicable values for the Moon, i. αe = 0, ηe = 0 and ε = 0 [1,29]. This produces: Tna = 32 S 0 (4c) Equation (4c) was employed to estimate the ‘no-atmosphere’ reference temperatures of all planetary bodies participating in our analysis and discussed below. For a reference pressure, we used the gas-liquid-solid triple point of water, i. Pr = 611 Pa [38] defining a baric threshold, below which water Environ Pollut Climate Change, an open access journal Planetary data To ensure proper application of the DA methodology we compiled a dataset of diverse planetary environments in the Solar System using the best information available. Celestial bodies were selected for the analysis based on three criteria: (a) presence of a solid surface; (b) availability of reliable data on near-surface temperature, atmospheric composition, and total air pressure/density preferably from direct observations; and (c) representation of a broad range of physical environments defined in terms of TOA solar irradiance and atmospheric properties. This resulted in the selection of three planets: Venus, Earth, and Mars; and three natural satellites: Moon of Earth, Titan of Saturn, and Triton of Neptune. Each celestial body was described by nine parameters shown in Table 2 with data sources listed in Table 3. In an effort to minimize the effect of unforced (internal) climate variability on the derivation of our temperature model, we tried to assemble a dataset of means representing an observational period of 30 years, i. from 1981 to 2010. Thus, Voyager measurements of Titan from the early 1980s suggested an average surface temperature of 94 ± 0 K [41]. Subsequent observations by the Cassini mission between 2005 and 2010 indicated a mean global temperature of 93 ± 0 K for that moon [42,43]. Since Volume 1 • Issue 2 • 1000112 Citation: Nikolov N, Zeller K (2017) New Insights on the Physical Nature of the Atmospheric Greenhouse Effect Deduced from an Empirical Planetary Temperature Model. Environ Pollut Climate Change 1: 112. Page 5 of 22 Parameter Venus Earth Moon Mars Titan Triton Average distance to the Sun, rau (AU) 0 1 1 1 9 30 Average TOA solar irradiance, S (W m-2) 2,601 1,360 1,360 586 14 1 0 0 0 0 0 0 65 240 294 112 2 0 98,550 ± 6 2 × 10-10 ± 10-10 685 ± 14 146,700 ± 100 4 ± 1 65 ± 0 1 ± 0 2 × 10 ± 9 × 10-15 0 ± 3 × 10-4 5 ± 0 3 × 10-4 ± 9 × 10-5 96 CO2 3 N2 0 SO2 77 N2 20 O2 0 Ar 0 H2O 0 CO2 26 4He 26 20Ne 23 H2 20 40Ar 3 22Ne 95 CO2 2 N2 1 Ar 0 O2 0 CO 0 H2O 95 N2 4 CH4 99 N2 0 CO 0 CH4 Bond albedo, αp (decimal fraction) Average absorbed shortwave radiation, Sa = S(1-αp)/4 (W m-2) 9,300,000 ± 100,000 Global average surface atmospheric pressure, P (Pa) Global average surface atmospheric density, ρ (kg m-3) Chemical composition of the lower atmosphere (% of volume) Molar mass of the lower atmosphere, M (kg mol-1) GMAT, Ts (K) -15 0 0 0 0 0 0 737 ± 3 287 ± 0 197 ± 0 190 ± 0 93 ± 0 39 ± 1 Table 2: Planetary data set used in the Dimensional Analysis compiled from sources listed in Table 3. The estimation of Mars’ GMAT and the average surface atmospheric pressure are discussed in Appendix B. See text for details about the computational methods employed for some parameters. Planetary Body Information Sources Venus [32,44-48] Earth [12,13,32,49-55] Moon [1,29,32,48,56-59] Mars [32,48,60-63], Appendix B Titan [32,41-43,64-72] Triton [48,73-75] Table 3: Literature sources of the planetary data presented in Table 2. Saturn’s orbital period equals 29 Earth years, we averaged the above global temperature values to arrive at 93 ± 0 K as an estimate of Titan’s 30-year GMAT. Similarly, data gathered in the late 1970s by the Viking Landers on Mars were combined with more recent CuriosityRover surface measurements and 1999-2005 remote observations by the Mars Global Surveyor (MGS) spacecraft to derive representative estimates of GMAT and atmospheric surface pressure for the Red Planet. Some parameter values reported in the literature did not meet our criteria for global representativeness and/or physical plausibility and were recalculated using available observations as described below. The mean solar irradiances of all bodies were calculated as S = SE rau-2 where rau is the body’s average distance (semi-major axis) to the Sun (AU) and SE = 1,360 W m-2 is the Earth’s new lower irradiance at 1 AU according to recent satellite observations reported by Kopp and Lean [49]. Due to a design flaw in earlier spectrometers, the solar irradiance at Earth’s distance has been overestimated by ≈ 5 W m-2 prior to 2003 [49]. Consequently, our calculations yielded slightly lower irradiances for bodies such as Venus and Mars compared to previously published data. Our decision to recalculate S was based on the assumption that the orbital distances of planets are known with much greater accuracy than TOA solar irradiances. Hence, a correction made to Earth’s irradiance requires adjusting the ‘solar constants’ of all other planets as well. We found that quoted values for the mean global temperature and surface atmospheric pressure of Mars were either improbable or too uncertain to be useful for our analysis. Thus, studies published in the last 15 years report Mars’ GMAT being anywhere between 200 K and 240 K with the most frequently quoted values in the range 210–220 K [6,32,76-81]. However, in-situ measurements by Viking Lander 1 suggest that the average surface air temperature at a low-elevation site in the Martian subtropics does not exceed 207 K during the summerfall season (Appendix B). Therefore, the Red Planet’s GMAT must be lower than 207 K. The Viking records also indicate that average diurnal Environ Pollut Climate Change, an open access journal temperatures above 210 K can only occur on Mars during summertime. Hence, all such values must be significantly higher than the actual mean annual temperature at any Martian latitude. This is also supported by results from a 3-D global circulation model of the Red Planet obtained by Fenton et al. [82]. The surface atmospheric pressure on Mars varies appreciably with season and location. Its global average value has previously been reported between 600 Pa and 700 Pa [6,32,78,80,83,84], a range that was too broad for the target precision of our study. Hence our decision to calculate new annual global means of near-surface temperature and air pressure for Mars via a thorough analysis of available data from remote-sensing and in-situ observations. Appendix B details our computational procedure with the results presented in Table 2. It is noteworthy that our independent estimate of Mars’ GMAT (190 ± 0 K), while significantly lower than values quoted in recent years, is in perfect agreement with spherically integrated brightness temperatures of the Red Planet derived from remote microwave measurements in the late 1960s and early 1970s [85-87]. Moon’s GMAT was also not readily extractable from the published literature. Although lunar temperatures have been measured for more than 50 years both remotely and in situ [36] most studies focus on observed temperature extremes across the lunar surface [56] and rarely discuss the Moon’s average global temperature. Current GMAT estimates for the Moon cluster around two narrow ranges: 250–255 K and 269–271 K [32]. A careful examination of the published data reveals that the 250–255 K range is based on subterranean heat-flow measurements conducted at depths between 80 and 140 cm at the Apollo 15 and 17 landing sites located at 26oN; 3 and 20oN; 30, respectively [88]. Due to a strong temperature dependence of the lunar regolith thermal conductivity in the topmost 1-2 cm soil, the Moon’s average diurnal temperature increases steadily with depth. According to Apollo measurements, the mean daily temperature at 35 cm belowground is 40–45 K higher than that at the lunar surface [88]. The diurnal temperature fluctuations completely vanish below a depth of 80 cm. At 100 cm depth, the temperature of the lunar regolith ranged from 250 K to 252 K at the Apollo 15 site and between 254 K and 255 K at the Apollo 17 site [88]. Hence, reported Moon average temperatures in the range 250-255 K do not describe surface conditions. Moreover, since measured in the lunar subtropics, such temperatures do not likely even represent Moon’s global thermal environment at these depths. On the other hand, frequently quoted Moon global temperatures of ~270 K have actually been calculated from Eq. (3) and are not based on surface measurements. However, as demonstrated by Volokin and ReLlez [1], Volume 1 • Issue 2 • 1000112 Citation: Nikolov N, Zeller K (2017) New Insights on the Physical Nature of the Atmospheric Greenhouse Effect Deduced from an Empirical Planetary Temperature Model. Environ Pollut Climate Change 1: 112. Page 7 of 22 Figure 1: The relative atmospheric thermal enhancement (Ts/Tr) as a function of various dimensionless forcing variables generated by DA using data on solar irradiance, near-surface partial pressure/density of greenhouse gases, and total atmospheric pressure/density from Table 4. Panels a through f depict six regression models suggested by DA with the underlying celestial bodies plotted in the background for reference. Each pair of horizontal graphs represents different reference temperatures (Tr) defined as either Tr = Te (left) or Tr = Tna (right). which excludes Titan from the input dataset. This new curve had R2 = 1 and σest = 0. Although the two regression equations yield similar results over most of the relevant pressure range, we chose the one without Titan as final for Model 12 based on the assumption that Earth’s GMAT is likely known with a much greater accuracy than Titan’s mean annual temperature. Taking an antilogarithm of the final regression equation, which excludes Titan, yielded the following expression for Model 12: P Ts = exp 0 Tna Pr 0 1 P + 1 × 10−5 Pr (10a) Equation (10a) implies that GMATs of rocky planets can be calculated as a product of two quantities: the planet’s average surface temperature in the absence of an atmosphere (Tna, K) and a nondimensional factor (Ea ≥ 1) quantifying the relative thermal effect of the atmosphere, i. Ts = Tna Ea (10b ) (10b) where Τna is obtained from the SAT model (Eq. 4a) and Ea is a function of total pressure (P) given by: 0 1 P P The regression coefficients in Eq. (10a) are intentionally shown in exp 1×10−5 (11)(11) = Ea ( P ) exp 0 P Pr r full precision to allow an accurate calculation of RATE (i. the Ts/ Tna ratios) provided the strong non-linearity of the relationship and Note that, as P approaches 0 in Eq. (11), Ea approaches the physically to facilitate a successful replication of our results by other researchers. realistic limit of 1. Other physical aspects of this equation are Figure 4 depicts Eq. (10a) as a dependence of RATE on the average discussed below. surface air pressure. Superimposed on this graph are the six planetary bodies from Table 4 along with their uncertainty ranges. For bodies with tangible atmospheres (such as Venus, Earth, Environ Pollut Climate Change, an open access journal Volume 1 • Issue 2 • 1000112 Citation: Nikolov N, Zeller K (2017) New Insights on the Physical Nature of the Atmospheric Greenhouse Effect Deduced from an Empirical Planetary Temperature Model. Environ Pollut Climate Change 1: 112. Page 8 of 22 Figure 2: The same as in Figure 1 but for six additional regression models (panels a through f). Mars, Titan and Triton), one must calculate Tna using αe = 0 and ηe = 0, which assumes a Moon-like airless reference surface in accordance with our pre-analysis premise. For bodies with tenuous atmospheres (such as Mercury, the Moon, Calisto and Europa), Tna should be calculated from Eq. (4a) (or Eq. 4b respectively if S > 0 W m-2 and/or Rg ≈ 0 W m-2) using the body’s observed values of Bond albedo αe and ground heat storage fraction ηe. In the context of this model, a tangible atmosphere is defined as one that has significantly modified the optical and thermo-physical properties of a planet’s surface compared to an airless environment and/or noticeably impacted the overall planetary albedo by enabling the formation of clouds and haze. A tenuous atmosphere, on the other hand, is one that has not had a measurable influence on the surface albedo and regolith thermo-physical properties and is completely transparent to shortwave radiation. The need for such delineation of atmospheric masses when calculating Tna arises from the fact that Eq. (10a) accurately describes RATEs of planetary bodies with tangible atmospheres over a wide range of conditions without explicitly accounting for the observed large differences in albedos (i. from 0 to 0) while assuming constant values of αe and ηe for the airless equivalent of these bodies. One possible explanation for this counterintuitive empirical result is that atmospheric pressure alters the planetary albedo and heat storage properties of the Environ Pollut Climate Change, an open access journal surface in a way that transforms these parameters from independent controllers of the global temperature in airless bodies to intrinsic byproducts of the climate system itself in worlds with appreciable atmospheres. In other words, once atmospheric pressure rises above a certain level, the effects of albedo and ground heat storage on GMAT become implicitly accounted for by Eq. (11). Although this hypothesis requires a further investigation beyond the scope of the present study, one finds an initial support for it in the observation that, according to data in Table 2, GMATs of bodies with tangible atmospheres do not show a physically meaningful relationship with the amounts of absorbed shortwave radiation determined by albedos. Our discovery for the need to utilize different albedos and heat storage coefficients between airless worlds and worlds with tangible atmospheres is not unique as a methodological approach. In many areas of science and engineering, it is sometime necessary to use disparate model parameterizations to successfully describe different aspects of the same phenomenon. An example is the distinction made in fluid mechanics between laminar and turbulent flow, where the non-dimensional Reynold’s number is employed to separate the two regimes that are subjected to different mathematical treatments. Volume 1 • Issue 2 • 1000112 Citation: Nikolov N, Zeller K (2017) New Insights on the Physical Nature of the Atmospheric Greenhouse Effect Deduced from an Empirical Planetary Temperature Model. Environ Pollut Climate Change 1: 112. Page 10 of 22 K). Equation (10b) produces 95 K for Titan at Saturn’s semi-major axis (9 AU) corresponding to a solar irradiance S = 14 W m-2. This estimate is virtually identical to the 95 K average surface temperature reported for that moon by the NASA JPL Voyager Mission website [94]. The Voyager spacecraft 1 and 2 reached Saturn and its moons in November 1980 and August 1981, respectively, when the gas giant was at a distance between 9 AU and 9 AU from the Sun corresponding approximately to Saturn’s semi-major axis [95]. Figure 4: The relative atmospheric thermal enhancement (Ts/Tna ratio) as a function of the average surface air pressure according to Eq. (10a) derived from data representing a broad range of planetary environments in the solar system. Saturn’s moon Titan has been excluded from the regression analysis leading to Eq. (10a). Error bars of some bodies are not clearly visible due to their small size relative to the scale of the axes. See Table 2 for the actual error estimates. Data acquired by Voyager 1 suggested an average surface temperature of 94 ± 0 K for Titan, while Voyager 2 indicated a temperature close to 95 K [41]. Measurements obtained between 2005 and 2010 by the Cassini-Huygens mission revealed Ts ≈ 93 ± 0 K [42,43]. Using Saturn’s perihelion (9 AU) and aphelion (10 AU) one can compute Titan’s TOA solar irradiance at the closest and furthest approach to the Sun, i. 16 W m-2 and 13 W m-2, respectively. Inserting these values into Eq. (10b) produces the expected upper and lower limit of Titan’s mean global surface temperature according to our model, i. 92 K ≤ Ts ≤ 98 K. Notably this range encompasses all current observation-based estimates of Titan’s GMAT. Since both Voyager and Cassini mission covered shorter periods than a single Titan season (Saturn’s orbital period is 29 Earth years), the available measurements may not well represent that moon’s annual thermal cycle. In addition, due to a thermal inertia, Titan’s average surface temperature likely lags variations in the TOA solar irradiance caused by Saturn’s orbital eccentricity. Thus, the observed 1 K discrepancy between our independent model prediction and Titan’s current best-known GMAT seems to be within the range of plausible global temperature fluctuations on that moon. Hence, further observations are needed to more precisely constrain Titan’s long-term GMAT. Measurements conducted by the Voyager spacecraft in 1989 indicated a global mean temperature of 38 ± 1 K and an average atmospheric pressure of 1 Pa at the surface of Triton [73]. Even though Eq. (10a) is based on slightly different data for Triton (i. Ts = 39 ±1 K and P = 4 Pa) obtained by more recent stellar occultation measurements [73], employing the Voyager-reported pressure in Eq. (10b) produces Ts = 38 K for Triton’s GMAT, a value well within the uncertainty of the 1989 temperature measurements. Figure 5: Absolute differences between modeled average global temperatures by Eq. (10b) and observed GMATs (Table 2) for the studied celestial bodies. Saturn’s moon Titan represents an independent data point, since it was excluded from the regression analysis leading to Eq. (10a). (ηe), the average geothermal flux reaching the surface (Rg), and the total surface atmospheric pressure (P). For planets with tangible atmospheres (P > 10-2 Pa) and a negligible geothermal heating of the surface (Rg ≈ 0), the equilibrium GMAT becomes only a function of two factors: S and P, i. Τs = 32 S0α(P). The final model (Eq. 10b) can also be cast in terms of Ts as a function of a planet’s distance to the Sun (rau, AU) by replacing S in Equations (4a), (4b) or (4c) with 1360 rau-2. Environmental scope and numerical accuracy of the new model Figure 5 portrays the residuals between modeled and observed absolute planetary temperatures. For celestial bodies participating in the regression analysis (i. Venus, Earth, Moon, Mars and Triton), the maximum model error does not exceed 0 K and is well within the uncertainty of observations. The error for Titan, an independent data point, is 1 K or 1% of that moon’s current best-known GMAT (93 Environ Pollut Climate Change, an open access journal The above comparisons indicate that Eq. (10b) rather accurately describes the observed variation of the mean surface temperature across a wide range of planetary environments in terms of solar irradiance (from 1 W m-2 to 2,602 W m-2), total atmospheric pressure (from near vacuum to 9,300 kPa) and greenhouse-gas concentrations (from 0% to over 96% per volume). While true that Eq. (10a) is based on data from only 6 celestial objects, one should keep in mind that these constitute virtually all bodies in the Solar System meeting our criteria for availability and quality of measured data. Although function (5) has 4 free parameters estimated from just 5-6 data points, there are no signs of model overfitting in this case because (a) Eq. (5) represents a monotonic function of a rigid shape that can only describe well certain exponential pattern as evident from Figures 1 and 2 and the statistical scores in Table 5; (b) a simple scatter plot of ln (P/Pr) vs. ln(Ts/ Tna) visibly reveals the presence of an exponential relationship free of data noise; and (c) no polynomial can fit the data points in Figure 2f as accurately as Eq. (5) while also producing a physically meaningful response curve similar to known pressure-temperature relationships in other systems. These facts indicate that Eq. (5) is not too complicated to cause an over-fitting but just right for describing the data at hand. The fact that only one of the investigated twelve non-linear regressions yielded a tight relationship suggests that Model 12 describes Volume 1 • Issue 2 • 1000112 Citation: Nikolov N, Zeller K (2017) New Insights on the Physical Nature of the Atmospheric Greenhouse Effect Deduced from an Empirical Planetary Temperature Model. Environ Pollut Climate Change 1: 112. Page 11 of 22 a macro-level thermodynamic property of planetary atmospheres heretofore unbeknown to science. A function of such predictive power spanning the entire breadth of the Solar System cannot be just a result of chance. Indeed, complex natural systems consisting of myriad interacting agents have been known to sometime exhibit emergent responses at higher levels of hierarchical organization that are amenable to accurate modeling using top-down statistical approaches [96]. Equation (10a) also displays several other characteristics discussed below that lend further support to the above notion. Model robustness Model robustness defines the degree to which a statistical relationship would hold when recalculated using a different dataset. To test the robustness of Eq. (10a) we performed an alternative regression analysis, which excluded Earth and Titan from the input data and only utilized logarithmic pairs of Ts/Tna and P/Pr for Venus, the Moon, Mars and Triton from Table 4. The goal was to evaluate how well the resulting new regression equation would predict the observed mean surface temperatures of Earth and Titan. Since these two bodies occupy a highly non-linear region in Model 12 (Figure 2f), eliminating them from the regression analysis would leave a key portion of the curve poorly defined. As in all previous cases, function (5) was fitted to the incomplete dataset (omitting Earth and Titan), which yielded the following expression: 0 3 P P Ts = exp 0 + 5 ×10−15 Tna P P r r (12a) Substituting the reference temperature Tna in Eq. (12a) with its equivalent from Eq. (4c) and solving for Ts produces Ts 0 3 P P exp 5 × 10−15 32 S 0 exp 0 P P r r (12b) (12b ) It is evident that the regression coefficients in the first exponent term of Eq. (12a) are nearly identical to those in Eq. (10a). This term dominates the Ts-P relationship over the pressure range 0-400 kPa accounting for more than 97% of the predicted temperature magnitudes. The regression coefficients of the second exponent differ somewhat between the two formulas causing a divergence of calculated RATE values over the pressure interval 400–9,100 kPa. The models converge again between 9,000 kPa and 9,300 kPa. Figure 6 illustrates the similarity of responses between Equations (10a) and (12a) over the pressure range 0–300 kPa with Earth and Titan plotted in the foreground for reference. Equation (12b) reproduces the observed global surface temperature of Earth with an error of 0% (-1 K) and that of Titan with an error of 1% (+0 K). For Titan, the error of the new Eq. (12b) is even slightly smaller than that of the original model (Eq. 10b). The ability of Model 12 to predict Earth’s GMAT with an accuracy of 99% using a relationship inferred from disparate environments such as those found on Venus, Moon, Mars and Triton indicates that (a) this model is statistically robust, and (b) Earth’s temperature is a part of a cosmic thermodynamic continuum well described by Eq. (10b). The apparent smoothness of this continuum for bodies with tangible atmospheres (illustrated in Figure 4) suggests that planetary climates are wellbuffered and have no ‘tipping points’ in reality, i. states enabling rapid and irreversible changes in the global equilibrium temperature as a result of destabilizing positive feedbacks assumed to operate within climate systems. This robustness test also serves as a cross-validation suggesting that the new model has a universal nature and it is not a product of overfitting. Environ Pollut Climate Change, an open access journal Figure 6: Demonstration of the robustness of Model 12. The solid black curve depicts Eq. (10a) based on data from 5 celestial bodies (i. Venus, Earth, Moon, Mars and Triton). The dashed grey curve portrays Eq. (12a) derived from data of only 4 bodies (i. Venus, Moon, Mars and Triton) while excluding Earth and Titan from the regression analysis. The alternative Eq. (12b) predicts the observed GMATs of Earth and Titan with accuracy greater than 99% indicating that Model 12 is statistically robust. The above characteristics of Eq. (10a) including dimensional homogeneity, high predictive accuracy, broad environmental scope of 12a ) (validity and statistical robustness indicate that it represents an emergent macro-physical model of theoretical significance deserving further investigation. This conclusive result is also supported by the physical meaningfulness of the response curve described by Eq. (10a). Discussion Given the high statistical scores of the new model discussed above, it is important to address its physical significance, potential limitations, and broad implications for the current climate theory. Similarity of the new model to Poisson’s formula and the SB radiation law The functional response of Eq. (10a) portrayed in Figure 4 closely resembles the shape of the dry adiabatic temperature curve in Figure 7a described by the Poisson formula and derived from the First Law of Thermodynamics and the Ideal Gas Law [4], i. T p = To po R/cp (13) (13) Here, To and po are reference values for temperature and pressure typically measured at the surface, while T and p are corresponding scalars in the free atmosphere, and cp is the molar heat capacity of air (J mol-1 K-1). For the Earth’s atmosphere, R/cp = 0. Equation (13) essentially describes the direct effect of pressure p on the gas temperature (T) in the absence of any heat exchange with the surrounding environment. Equation (10a) is structurally similar to Eq. (13) in a sense that both expressions relate a temperature ratio to a pressure ratio, or more precisely, a relative thermal enhancement to a ratio of physical forces. However, while the Poisson formula typically produces 0 ≤ T/To ≤ 1, Eq. (10a) always yields Ts/Tna ≥ 1. The key difference between the two models stems from the fact that Eq. (13) describes vertical temperature changes in a free and dry atmosphere induced by a gravity-controlled pressure gradient, while Eq. (10a) predicts the equilibrium response of a planet’s global surface air temperature to variations in total atmospheric Volume 1 • Issue 2 • 1000112 Citation: Nikolov N, Zeller K (2017) New Insights on the Physical Nature of the Atmospheric Greenhouse Effect Deduced from an Empirical Planetary Temperature Model. Environ Pollut Climate Change 1: 112. Page 13 of 22 not the result of an increased atmospheric pressure. Recent analyses of observed dimming and brightening periods worldwide [97-99] suggest that the warming over the past 130 years might have been caused by a decrease in global cloud cover and a subsequent increased absorption of solar radiation by the surface. Similarly, the mega shift of Earth’s climate from a ‘hothouse’ to an ‘icehouse’ evident in the sedimentary archives over the past 51 My cannot be explained by Eq. (10b) unless caused by a large loss of atmospheric mass and a corresponding significant drop in surface air pressure since the early Eocene. Pleistocene fluctuations of global temperature in the order of 3–8 K during the last 2 My revealed by multiple proxies [100] are also not predictable by Eq. (10b) if due to factors other than changes in total atmospheric pressure and/ or TOA solar irradiance. The current prevailing view mostly based on theoretical considerations and results from climate models is that the Pleistocene glacial-interglacial cycles have been caused by a combination of three forcing agents: Milankovitch orbital variations, changes in atmospheric concentrations of greenhouse gases, and a hypothesized positive icealbedo feedback [101,102]. However, recent studies have shown that orbital forcing and the ice-albedo feedback cannot explain key features of the glacial-interglacial oscillations such as the observed magnitudes of global temperature changes, the skewness of temperature response (i. slow glaciations followed by rapid meltdowns), and the midPleistocene transition from a 41 Ky to 100 Ky cycle length [103-105]. The only significant forcing remaining in the present paleo-climatological toolbox to explicate the Pleistocene cycles are variations in greenhousegas concentrations. Hence, it is difficult to explain, from a standpoint of the current climate theory, the high accuracy of Eq. (11) describing the relative thermal effect of diverse planetary atmospheres without any consideration of greenhouse gases. If presumed forcing agents such as greenhouse-gas concentrations and the planetary albedo were indeed responsible for the observed past temperature dynamics on Earth, why did these agents not show up as predictors of contemporary planetary temperatures in our analysis as well? Could it be because these agents have not really been driving Earth’s climate on geological time scales? We address the potential role of greenhouse gases in more details below. Since the relationship portrayed in Figure 4 is undoubtedly real, our model results point toward the need to reexamine some fundamental climate processes thought to be well understood for decades. For example, we are currently testing a hypothesis that Pleistocene glacial cycles might have been caused by variations in Earth’s total atmospheric mass and surface air pressure. Preliminary results based on the ability of an extended version of our planetary model (simulating meridional temperature gradients) to predict the observed polar amplification during the Last Glacial Maximum indicate that such a hypothesis is not unreasonable. However, conclusive findings from this research will be discussed elsewhere. According to the present understanding, Earth’s atmospheric pressure has remained nearly invariant during the Cenozoic era (last 65 My). However, this notion is primarily based on theoretical analyses [106], since there are currently no known geo-chemical proxies permitting a reliable reconstruction of past pressure changes in a manner similar to that provided by various temperature proxies such as isotopic oxygen 18, alkenones and TEX86 in sediments, and Ar-N isotope ratios and deuterium concentrations in ice. The lack of independent pressure proxies makes the assumption of a constant atmospheric mass throughout the Cenozoic a priori and thus questionable. Although this topic is beyond the scope of our present study, allowing for the possibility that atmospheric pressure on Earth might have varied Environ Pollut Climate Change, an open access journal significantly over the past 65 My could open exciting new research venues in Earth sciences in general and paleoclimatology in particular. Role of greenhouse gasses from a perspective of the new model Our analysis revealed a poor relationship between GMAT and the amount of greenhouse gases in planetary atmospheres across a broad range of environments in the Solar System (Figures 1-3 and Table 5). This is a surprising result from the standpoint of the current Greenhouse theory, which assumes that an atmosphere warms the surface of a planet (or moon) via trapping of radiant heat by certain gases controlling the atmospheric infrared optical depth [4,9,10]. The atmospheric opacity to LW radiation depends on air density and gas absorptivity, which in turn are functions of total pressure, temperature, and greenhouse-gas concentrations [9]. Pressure also controls the broadening of infrared absorption lines in individual gases. Therefore, the higher the pressure, the larger the infrared optical depth of an atmosphere, and the stronger the expected greenhouse effect would be. According to the current climate theory, pressure only indirectly affects global surface temperature through the atmospheric infrared opacity and its presumed constraint on the planet’s LW emission to Space [9,107]. There are four plausible explanations for the apparent lack of a close relationship between GMAT and atmospheric greenhouse gasses in our results: 1) The amounts of greenhouse gases considered in our analysis only refer to near-surface atmospheric compositions and do not describe the infrared optical depth of the entire atmospheric column; 2) The analysis lumped all greenhouse gases together and did not take into account differences in the infrared spectral absorptivity of individual gasses; 3) The effect of atmospheric pressure on broadening the infrared gas absorption lines might be stronger in reality than simulated by current radiative-transfer models, so that total pressure overrides the effect of a varying atmospheric composition across a wide range of planetary environments; and 4) Pressure as a force per unit area directly impacts the internal kinetic energy and temperature of a system in accordance with thermodynamic principles inferred from the Gas Law; hence, air pressure might be the actual physical causative factor controlling a planet’s surface temperature rather than the atmospheric infrared optical depth, which merely correlates with temperature due to its co-dependence on pressure. Based on evidence discussed earlier, we argue that option #4 is the most likely reason for the poor predictive skill of greenhouse gases with respect to planetary GMATs revealed in our study (Figures 1-3). By definition, the infrared optical depth of an atmosphere is a dimensionless quantity that carries no units of force or energy [3,4,9]. Therefore, it is difficult to fathom from a fundamental physics standpoint of view, how this non-dimensional parameter could increase the kinetic energy (and temperature) of the lower troposphere in the presence of free convection provided that the latter dominates the heat transport in gaseous systems. Pressure, on the other hand, has a dimension of force per unit area and as such is intimately related to the internal kinetic energy of an atmosphere E (J) defined as the product of gas pressure (P, Pa) and gas volume (V, m3), i. E (J) = PV. Hence, the direct effect of pressure on a system’s internal energy and temperature follows straight from fundamental parameter definitions in classical thermodynamics. Generally speaking, kinetic energy cannot exist without a pressure force. Even electromagnetic radiation has pressure. In climate models, the effect of infrared optical depth on surface temperature is simulated by mathematically decoupling radiative transfer from convective heat exchange. Specifically, the LW Volume 1 • Issue 2 • 1000112 Citation: Nikolov N, Zeller K (2017) New Insights on the Physical Nature of the Atmospheric Greenhouse Effect Deduced from an Empirical Planetary Temperature Model. Environ Pollut Climate Change 1: 112. Page 14 of 22 radiative transfer is calculated in these models without simultaneous consideration of sensible- and latent heat fluxes in the solution matrix. Radiative transfer modules compute the so-called heating rates (K/ day) strictly as a function of atmospheric infrared opacity, which under constant-pressure conditions solely depends on greenhousegas concentrations. These heating rates are subsequently added to the thermodynamic portion of climate models and distributed throughout the atmosphere. In this manner, the surface warming becomes a function of an increasing atmospheric infrared opacity. This approach to modeling of radiative-convective energy transport rests on the principle of superposition, which is only applicable to linear systems, where the overall solution can be obtained as a sum of the solutions to individual system components. However, the integral heat transport within a free atmosphere is inherently nonlinear with respect to temperature. This is because, in the energy balance equation, radiant heat transfer is contingent upon power gradients of absolute temperatures, while convective cooling/heating depends on linear temperature differences in the case of sensible heat flux and on simple vapor pressure gradients in the case of latent heat flux [4]. The latent heat transport is in turn a function of a solvent’s saturation vapor pressure, which increases exponentially with temperature [3]. Thus, the superposition principle cannot be employed in energy budget calculations. The artificial decoupling between radiative and convective heat-transfer processes adopted in climate models leads to mathematically and physically incorrect solutions with respect to surface temperature. The LW radiative transfer in a real climate system is intimately intertwined with turbulent convection/advection as both transport mechanisms occur simultaneously. Since convection (and especially the moist one) is orders of magnitude more efficient in transferring energy than LW radiation [3,4], and because heat preferentially travels along the path of least resistance, a properly coupled radiative-convective algorithm of energy exchange will produce quantitatively and qualitatively different temperature solutions in response to a changing atmospheric composition than the ones obtained by current climate models. Specifically, a correctly coupled convective-radiative system will render the surface temperature insensitive to variations in the atmospheric infrared optical depth, a result indirectly supported by our analysis as well. This topic requires further investigation beyond the scope of the present study. is fundamentally different from the hypothesized ‘trapping’ of LW radiation by atmospheric trace gases first proposed in the 19th century and presently forming the core of the Greenhouse climate theory. However, a radiant-heat trapping by freely convective gases has never been demonstrated experimentally. We should point out that the hereto deduced adiabatic (pressure-controlled) nature of the atmospheric thermal effect rests on an objective analysis of vetted planetary observations from across the Solar System and is backed by proven thermodynamic principles, while the ‘trapping’ of LW radiation by an unconstrained atmosphere surmised by Fourier, Tyndall and Arrhenius in the 1800s was based on a theoretical conjecture. The latter has later been coded into algorithms that describe the surface temperature as a function of atmospheric infrared optical depth (instead of pressure) by artificially decoupling radiative transfer from convective heat exchange. Note also that the Ideal Gas Law (PV = nRT) forming the basis of atmospheric physics is indifferent to the gas chemical composition. The direct effect of atmospheric pressure on the global surface temperature has received virtually no attention in climate science thus far. However, the results from our empirical data analysis suggest that it deserves a serious consideration in the future. Atmospheric back radiation and surface temperature: Since (according to Eq. 10b) the equilibrium GMAT of a planet is mainly determined by the TOA solar irradiance and surface atmospheric pressure, the down-welling LW radiation appears to be globally a product of the air temperature rather than a driver of the surface warming. In other words, on a planetary scale, the so-called back radiation is a consequence of the atmospheric thermal effect rather than a cause for it. This explains the broad variation in the size of the observed downwelling LW flux among celestial bodies irrespective of the amount of absorbed solar radiation. Therefore, a change in this thermal flux brought about by a shift in atmospheric LW emissivity cannot be expected to impact the global surface temperature. Any variation in the global infrared back radiation caused by a change in atmospheric composition would be compensated for by a corresponding shift in the intensity of the vertical convective heat transport. Such a balance between changes in atmospheric infrared heating and the upward convective cooling at the surface is required by the First Law of Thermodynamics. However, current climate models do not simulate this compensatory effect of sensible and latent heat fluxes due to an improper decoupling between radiative transfer and turbulent convection in the computation of total energy exchange. Theoretical implications relationship of the new interplanetary The hereto discovered pressure-temperature relationship quantified by Eq. (10a) and depicted in Figure 4 has broad theoretical implications that can be summarized as follows: Physical nature of the atmospheric ‘greenhouse effect’: According to Eq. (10b), the heating mechanism of planetary atmospheres is analogous to a gravity-controlled adiabatic compression acting upon the entire surface. This means that the atmosphere does not function as an insulator reducing the rate of planet’s infrared cooling to space as presently assumed [9,10], but instead adiabatically boosts the kinetic energy of the lower troposphere beyond the level of solar input through gas compression. Hence, the physical nature of the atmospheric ‘greenhouse effect’ is a pressure-induced thermal enhancement (PTE) independent of atmospheric composition. This mechanism Environ Pollut Climate Change, an open access journal Effect of pressure on temperature: Atmospheric pressure provides in and of itself only a relative thermal enhancement (RATE) to the surface quantified by Eq. (11). The absolute thermal effect of an atmosphere depends on both pressure and the TOA solar irradiance. For example, at a total air pressure of 98 kPa, Earth’s RATE is 1, which keeps our planet 90 K warmer in its present orbit than it would be in the absence of an atmosphere. Hence, our model fully explains the new ~90 K estimate of Earth’s atmospheric thermal effect derived by Volokin and ReLlez [1] using a different line of reasoning. If one moves Earth to the orbit of Titan (located at ~9 AU from the Sun) without changing the overall pressure, our planet’s RATE will remain the same, but the absolute thermal effect of the atmosphere would drop to about 29 K due to a vastly reduced solar flux. In other words, the absolute effect of pressure on a system’s temperature depends on the background energy level of the environment. This implies that the absolute temperature of a gas may not follow variations of pressure if the gas energy absorption changes in opposite direction to that of pressure. For instance, the temperature of Earth’s stratosphere increases with altitude above the tropopause despite a falling air pressure, because the absorption of UV radiation by ozone steeply increases with height, thus offsetting the effect of a dropping pressure. If the UV absorption were constant throughout the stratosphere, the air temperature would decrease with altitude. Volume 1 • Issue 2 • 1000112 Citation: Nikolov N, Zeller K (2017) New Insights on the Physical Nature of the Atmospheric Greenhouse Effect Deduced from an Empirical Planetary Temperature Model. Environ Pollut Climate Change 1: 112. Page 16 of 22 where S(1-α)ηe is the absorbed solar flux (W m-2) stored as heat into the subsurface. The geothermal heat flux on Europa is poorly known. However, based
New Insights on the Physical Nature of the Atmospheric Greenhouse Effect Deduced from an Empirical Planetary Temperature Model
University: University of Idaho
