Unified Theory of Climate

Note: This was a poster, and adopted into a blog post by the author, Ned Nikolov, specifically for WUWT. My thanks to him for the extra effort in converting the poster to a more blog friendly format. – Anthony

Expanding the Concept of Atmospheric Greenhouse Effect Using Thermodynamic Principles: Implications for Predicting Future Climate Change

Ned Nikolov, Ph.D. & Karl Zeller, Ph.D.

USFS Rocky Mountain Research Station, Fort Collins CO, USA

Emails: ntconsulting@comcast.net kzeller@colostate.edu

Poster presented at the Open Science Conference of the World Climate Research Program,

24 October 2011, Denver CO, USA

http://www.wcrp-climate.org/conference2011/posters/C7/C7_Nikolov_M15A.pdf

Abstract

We present results from a new critical review of the atmospheric Greenhouse (GH) concept. Three main problems are identified with the current GH theory. It is demonstrated that thermodynamic principles based on the Gas Law need be invoked to fully explain the Natural Greenhouse Effect. We show via a novel analysis of planetary climates in the solar system that the physical nature of the so-called GH effect is a Pressure-induced Thermal Enhancement (PTE), which is independent of the atmospheric chemical composition. This finding leads to a new and very different paradigm of climate controls. Results from our research are combined with those from other studies to propose a new Unified Theory of Climate, which explains a number of phenomena that the current theory fails to explain. Implications of the new paradigm for predicting future climate trends are briefly discussed.

1. Introduction

Recent studies revealed that Global Climate Models (GCMs) have significantly overestimated the Planet’s warming since 1979 failing to predict the observed halt of global temperature rise over the past 13 years. (e.g. McKitrick et al. 2010). No consensus currently exists as to why the warming trend ceased in 1998 despite a continued increase in atmospheric CO₂ concentration. Moreover, the CO₂-temperature relationship shows large inconsistencies across time scales. In addition, GCM projections heavily depend on positive feedbacks, while satellite observations indicate that the climate system is likely governed by strong negative feedbacks (Lindzen & Choi 2009; Spencer & Braswell 2010). At the same time, there is a mounting political pressure for Cap-and-Trade legislation and a global carbon tax, while scientists and entrepreneurs propose geo-engineering solutions to cool the Planet that involve large-scale physical manipulation of the upper atmosphere. This unsettling situation calls for a thorough reexamination of the present climate-change paradigm; hence the reason for this study.

2.  The Greenhouse Effect: Reexamining the Basics

Figure 1. The Atmospheric Greenhouse Effect as taught at universities around the World (diagram from the website of the Penn State University Department of Meteorology).

According to the current theory, the Greenhouse Effect (GHE) is a radiative phenomenon caused by heat-trapping gases in the atmosphere such as CO₂ and water vapor that are assumed to reduce the rate of surface infrared cooling to Space by absorbing the outgoing long-wave (LW) emission and re-radiating part of it back, thus increasing the total energy flux toward the surface. This is thought to boost the Earth’s temperature by 18K – 33K compared to a gray body with no absorbent atmosphere such as the Moon; hence making our Planet habitable. Figure 1 illustrates this concept using a simple two-layer system known as the Idealized Greenhouse Model (IGM). In this popular example, S is the top-of-the atmosphere (TOA) solar irradiance (W m^-2), A is the Earth shortwave albedo, T_s is the surface temperature (K), T_e is the Earth’s effective emission temperature (K) often equated with the mean temperature of middle troposphere, ϵ is emissivity, and σ is the Stefan-Boltzmann (S-B) constant.

2.1. Main Issues with the Current GHE Concept:

A) Magnitude of the Natural Greenhouse Effect. GHE is often quantified as a difference between the actual mean global surface temperature (T_s = 287.6K) and the planet’s average gray-body (no-atmosphere) temperature (T_gb), i.e. GHE = T_s – T_gb. In the current theory, T_gb is equated with the effective emission temperature (T_e) calculated straight from the S-B Law using Eq. (1):

where α_p is the planetary albedo of Earth (≈0.3). However, this is conceptually incorrect! Due to Hölder’s inequality between non-linear integrals (Kuptsov 2001), T_e is not physically compatible with a measurable true mean temperature of an airless planet. To be correct, T_gb must be computed via proper spherical integration of the planetary temperature field. This means calculating the temperature at every point on the Earth sphere first by taking the 4^th root from the S-B relationship and then averaging the resulting temperature field across the planet surface, i.e.

where α_gb is the Earth’s albedo without atmosphere (≈0.125), μ is the cosine of incident solar angle at any point, and c_s= 13.25e-5 is a small constant ensuring that T_gb = 2.72K (the temperature of deep Space) when S_o = 0. Equation (2) assumes a spatially constant albedo (α_gb), which is a reasonable approximation when trying to estimate an average planetary temperature.

Since in accordance with Hölder’s inequality T_gb ≪ T_e (T_gb =154.3K ), GHE becomes much larger than presently estimated.

According to Eq. (2), our atmosphere boosts Earth’s surface temperature not by 18K—33K as currently assumed, but by 133K! This raises the question: Can a handful of trace gases which amount to less than 0.5% of atmospheric mass trap enough radiant heat to cause such a huge thermal enhancement at the surface? Thermodynamics tells us that this not possible.

B) Role of Convection. The conceptual model in Fig. 1 can be mathematically described by the following simultaneous Equations (3),

where ν_a is the atmospheric fraction of the total shortwave radiation absorption. Figure 2 depicts the solution to Eq. (3) for temperatures over a range of atmospheric emissivities (ϵ) assuming S_o = 1366 W m^-2 and ν_a =0.326 (Trenberth et al. 2009). An increase in atmospheric emissivity does indeed cause a warming at the surface as stated by the current theory. However, Eq. (3) is physically incomplete, because it does not account for convection, which occurs simultaneously with radiative transfer. Adding a convective term to Eq. (3) (such as a sensible heat flux) yields the system:

where g_bH is the aerodynamic conductance to turbulent heat exchange. Equation (4) dramatically alters the solution to Eq. (3) by collapsing the difference between T_s, T_a and T_e and virtually erasing the GHE (Fig. 3). This is because convective cooling is many orders of magnitude more efficient that radiative cooling. These results do not change when using multi-layer models. In radiative transfer models, T_s increases with ϵ not as a result of heat trapping by greenhouse gases, but due to the lack of convective cooling, thus requiring a larger thermal gradient to export the necessary amount of heat. Modern GCMs do not solve simultaneously radiative transfer and convection. This decoupling of heat transports is the core reason for the projected surface warming by GCMs in response to rising atmospheric greenhouse-gas concentrations. Hence, the predicted CO₂-driven global temperature change is a model artifact!

Figure 2. Solution to the two-layer model in Eq. (3) for T_s and T_a as a function of atmospheric emissivity assuming a non-convective atmosphere. Also shown is the predicted down-welling LW flux(L_d). Note that L_d ≤ 239 W m^-2.

Figure 3. Solution to the two-layer model in Eq. (4) for T_s and T_a as a function of atmospheric emissivity assuming a convective atmosphere (g_bH = 0.075 m/s). Also shown is the predicted down-welling LW flux (L_d). Note that L_d ≤ 239 W m^-2.

Figure 4. According to observations, the Earth-Atmosphere System absorbs on average a net solar flux of 239 W m^-2, while the lower troposphere alone emits 343 W m^-2 thermal radiation toward the surface.

C) Extra Kinetic Energy in the Troposphere.

Observations show that the lower troposphere emits 44% more radiation toward the surface than the total solar flux absorbed by the entire Earth-Atmosphere System (Pavlakis et al. 2003) (Fig. 4). Radiative transfer alone cannot explain this effect (e.g. Figs. 2 & 3) given the negligible heat storage capacity of air, no matter how detailed the model is. Thus, empirical evidence indicates that the lower atmosphere contains more kinetic energy than provided by the Sun. Understanding the origin of this extra energy is a key to the GHE.

3. The Atmospheric Thermal Enhancement

Previous studies have noted that the term Greenhouse Effect is a misnomer when applied to the atmosphere, since real greenhouses retain heat through an entirely different mechanism compared to the free atmosphere, i.e. by physically trapping air mass and restricting convective heat exchange. Hence, we propose a new term instead, Near-surface Atmospheric Thermal Enhancement (ATE) defined as a non-dimensional ratio (N_TE) of the planet actual mean surface air temperature (T_s, K) to the average temperature of a Standard Planetary Gray Body (SPGB) with no atmosphere (T_gb, K) receiving the same solar irradiance, i.e. N_TE = T_s /T_gb. This new definition emphasizes the essence of GHE, which is the temperature boost at the surface due to the presence of an atmosphere. We employ Eq. (2) to estimate T_gb assuming an albedo α_gb = 0.12 and a surface emissivity ϵ = 0.955 for the SPGB based on data for Moon, Mercury, and the Earth surface. Using S_o = 1362 W m^-2 (Kopp & Lean 2011) in Eq. (2) yields T_gb = 154.3K and N_TE = 287.6/154.3 = 1.863 for Earth. This prompts the question: What mechanism enables our atmosphere to boost the planet surface temperature some 86% above that of a SPGB? To answer it we turn on to the classical Thermodynamics.

3.1. Climate Implications of the Ideal Gas Law

The average thermodynamic state of a planet’s atmosphere can be accurately described by the Ideal Gas Law (IGL):

PV = nRT (5)

where P is pressure (Pa), V is the gas volume (m³), n is the gas amount (mole), R = 8.314 J K^-1 mol^-1is the universal gas constant, and T is the gas temperature (K). Equation (5) has three features that are chiefly important to our discussion: a) the product P×V defines the internal kinetic energy of a gas (measured in Jules) that produces its temperature; b) the linear relationship in Eq. (5) guarantees that a mean global temperature can be accurately estimated from planetary averages of surface pressure and air volume (or density). This is in stark contrast to the non-linear relationship between temperature and radiant fluxes (Eq. 1) governed by Hölder’s inequality of integrals; c) on a planetary scale, pressure in the lower troposphere is effectively independent of other variables in Eq. (5) and is only a function of gravity (g), total atmospheric mass (M_at), and the planet surface area (A_s), i.e. P_s = g M_at/A_s. Hence, the near-surface atmospheric dynamics can safely be assumed to be governed (over non-geological time scales) by nearly isobaric processes on average, i.e. operating under constant pressure. This isobaric nature of tropospheric thermodynamics implies that the average atmospheric volume varies in a fixed proportion to changes in the mean surface air temperature following the Charles/Gay-Lussac Law, i.e. T_s/V = const. This can be written in terms of the average air density ρ (kg m^-3) as

ρT_s = const. = P_s M / R (6)

where P_s is the mean surface air pressure (Pa) and M is the molecular mass of air (kg mol^-1). Eq. (6) reveals an important characteristic of the average thermodynamic process at the surface, namely that a variation of global pressure due to either increase or decrease of total atmospheric mass will alter both temperature and atmospheric density. What is presently unknown is the differential effect of a global pressure change on each variable. We offer a solution to this in & 3.3. Equations (5) and (6) imply that pressure directly controls the kinetic energy and temperature of the atmosphere. Under equal solar insolation, a higher surface pressure (due to a larger atmospheric mass) would produce a warmer troposphere, while a lower pressure would result in a cooler troposphere. At the limit, a zero pressure (due to the complete absence of an atmosphere) would yield the planet’s gray-body temperature.

The thermal effect of pressure is vividly demonstrated on a cosmic scale by the process of star formation, where gravity-induced rise of gas pressure boosts the temperature of an interstellar cloud to the threshold of nuclear fusion. At a planetary level, the effect is manifest in Chinook winds, where adiabatically heated downslope airflow raises the local temperature by 20C-30C in a matter of hours. This leads to a logical question: Could air pressure be responsible for the observed thermal enhancement at the Earth surface presently known as a ‘Natural Greenhouse Effect’? To answer this we must analyze the relationship between N_TEfactor and key atmospheric variables including pressure over a wide range of planetary climates. Fortunately, our solar system offers a suitable spectrum of celestial bodies for such analysis.

3.2. Interplanetary Data Set

We based our selection of celestial bodies for the ATE analysis on three criteria: 1) presence of a solid planetary surface with at least traces of atmosphere; 2) availability of reliable data on surface temperature, total pressure, atmospheric composition etc. preferably from direct measurements; and 3) representation of a wide range of atmospheric masses and compositions. This approach resulted in choosing of four planets – Mercury, Venus, Earth, and Mars, and four natural satellites – Moon of Earth, Europa of Jupiter, Titan of Saturn, and Triton of Neptune. Each celestial body was described by 14 parameters listed in Table 1.

For planets with tangible atmospheres, i.e. Venus, Earth and Mars, the temperatures calculated from IGL agreed rather well with observations. Note that, for extremely low pressures such as on Mercury and Moon, the Gas Law produces T_s ≈ 0.0. The SPGB temperatures for each celestial body were estimated from Eq. (2) using published data on solar irradiance and assuming α_gb = 0.12 and ϵ = 0.955. For Mars, global means of surface temperature and air pressure were calculated from remote sensing data retrieved via the method of radio occultation by the Radio Science Team (RST) at Stanford University using observations by the Mars Global Surveyor (MGS) spacecraft from 1999 to 2005. Since the MGS RST analysis has a wide spatial coverage, the new means represent current average conditions on the Red Planet much more accurately than older data based on Viking’s spot observations from 1970s.

Table 1. Planetary data used to analyze the physical nature of the Atmospheric Near-Surface Thermal Enhancement (N_TE). Information was gathered from multiple sources using cross-referencing. The bottom three rows of data were estimated in this study using equations discussed in the text.

3.3. Physical Nature of ATE / GHE

Our analysis of interplanetary data in Table 1 found no meaningful relationships between ATE (N_TE) and variables such as total absorbed solar radiation by planets or the amount of greenhouse gases in their atmospheres. However, we discovered that N_TE was strongly related to total surface pressure through a nearly perfect regression fit via the following nonlinear function:

where P_s is in Pa. Figure 5 displays Eq. (7) graphically. The tight relationship signals a causal effect of pressure on N_TE, which is theoretically supported by the IGL (see & 3.1). Also, the P_s–N_TE curve in Fig. 5 strikingly resembles the response of the temperature/potential temp. (T/θ) ratio to altitudinal changes of pressure described by the well-known Poisson formula derived from IGL (Fig. 6). Such a similarity in responses suggests that both N_TE and θ embody the effect of pressure-controlled adiabatic heating on air, even though the two mechanisms are not identical. This leads to a fundamental conclusion that the ‘Natural Greenhouse Effect’ is in fact a Pressure-induced Thermal Enhancement (PTE) in nature.

N_TE should not be confused with an actual energy, however, since it only defines the relative (fractional) increase of a planet’s surface temperature above that of a SPGB. Pressure by itself is not a source of energy! Instead, it enhances (amplifies) the energy supplied by an external source such as the Sun through density-dependent rates of molecular collision. This relative enhancement only manifests as an actual energy in the presence of external heating. Thus, Earth and Titan have similar N_TE values, yet their absolute surface temperatures are very different due to vastly dissimilar solar insolation. While pressure (P) controls the magnitude of the enhancement factor, solar heating determines the average atmospheric volume (V), and the product P×V defines the total kinetic energy and temperature of the atmosphere. Therefore, for particular solar insolation, the N_TE factor gives rise to extra kinetic energy in the lower atmosphere beyond the amount supplied by the Sun. This additional energy is responsible for keeping the Earth surface 133K warmer than it would be in the absence of atmosphere, and is the source for the observed 44% extra down-welling LW flux in the lower troposphere (see &2.1 C). Hence, the atmosphere does not act as a ‘blanket’ reducing the surface infrared cooling to space as maintained by the current GH theory, but is in and of itself a source of extra energy through pressure. This makes the GH effect a thermodynamic phenomenon, not a radiative one as presently assumed!

Equation (7) allows us to derive a simple yet robust formula for predicting a planet’s mean surface temperature as a function of only two variables – TOA solar irradiance and mean atmospheric surface pressure, i.e.

Figure 5. Atmospheric near-surface Thermal Enhancement (N_TE) as a function of mean total surface pressure (P_s) for 8 celestial bodies listed in Table 1. See Eq. (7) for the exact mathematical formula.

Figure 6. Temperature/potential temperature ratio as a function of atmospheric pressure according to the Poisson formula based on the Gas Law (P_o = 100 kPa.). Note the striking similarity in shape with the curve in Fig. 5.

where N_TE(P_s) is defined by Eq. (7). Equation (8) almost completely explains the variation of T_s among analyzed celestial bodies, thus providing a needed function to parse the effect of a global pressure change on the dependent variables ρ and T_sin Eq. (6). Together Equations (6) and (8) imply that the chemical composition of an atmosphere affects average air density through the molecular mass of air, but has no impact on the mean surface temperature.

4. Implications of the new ATE Concept

The implications of the above findings are numerous and paradigm-altering. These are but a few examples:

Figure 7. Dynamics of global temperature and 12-month forward shifted cloud cover types from satellite observations. Cloud changes precede temperature variations by 6 to 24 months and appear to have been controlling the latter during the past 30 years (Nikolov & Zeller, manuscript).

A) Global surface temperature is independent of the down-welling LW flux known as greenhouse or back radiation, because both quantities derive from the same pool of atmospheric kinetic energy maintained by solar heating and air pressure. Variations in the downward LW flux (caused by an increase of tropospheric emissivity, for example) are completely counterbalanced (offset) by changes in the rate of surface convective cooling, for this is how the system conserves its internal energy.

B) Modifying chemical composition of the atmosphere cannot alter the system’s total kinetic energy, hence the size of ATE (GHE). This is supported by IGL and the fact that planets of vastly different atmospheric composition follow the same P_s–N_TE relationship in Fig. 5. The lack of impact by the atmospheric composition on surface temperature is explained via the compensating effect of convective cooling on back-radiation discussed above.

C) Equation (8) suggests that the planet’s albedo is largely a product of climate rather than a driver of it. This is because the bulk of the albedo is a function of the kinetic energy supplied by the Sun and the atmospheric pressure. However, independent small changes in albedo are possible and do occur owning to 1%-3% secular variations in cloud cover, which are most likely driven by solar magnetic activity. These cloud-cover changes cause ±0.7C semi-periodic fluctuations in global temperature on a decadal to centennial time scale as indicated by recent satellite observations (see Fig. 7) and climate reconstructions for the past 10,000 years.

Figure 8. Dynamics of global surface temperature during the Cenozoic Era reconstructed from ¹⁸O proxies in marine sediments (Hansen et al. 2008).

Figure 9. Dynamics of mean surface atmospheric pressure during the Cenozoic Era reconstructed from the temperature record in Fig. 8 by inverting Eq. (8).

D) Large climatic shifts evident in the paleo-record such as the 16C directional cooling of the Globe during the past 51 million years (Fig. 8) can now be explained via changes in atmospheric mass and surface pressure caused by geologic variations in Earth’s tectonic activity. Thus, we hypothesize that the observed mega-cooling of Earth since the early Eocene was due to a 53% net loss of atmosphere to Space brought about by a reduction in mantle degasing as a result of a slowdown in continental drifts and ocean floor spreading. Figure 9 depicts reconstructed dynamics of the mean surface pressure for the past 65.5M years based on Eq. (8) and the temperature record in Fig. 8.

5. Unified Theory of Climate

The above findings can help rectify physical inconsistencies in the current GH concept and assist in the development of a Unified Theory of Climate (UTC) based on a deeper and more robust understanding of various climate forcings and the time scales of their operation. Figure 10 outlines a hierarchy of climate forcings as part of a proposed UTC that is consistent with results from our research as well as other studies published over the past 15 years. A proposed key new driver of climate is the variation of total atmospheric mass and surface pressure over geological time scales (i.e. tens of thousands to hundreds of millions of years). According to our new theory, the climate change over the past 100-300 years is due to variations of global cloud albedo that are not related to GHE/ATE. This is principally different from the present GH concept, which attempts to explain climate changes over a broad range of time scales (i.e. from decades to tens of millions of years) with the same forcing attributed to variations in atmospheric CO₂ and other heat-absorbing trace gases (e.g. Lacis et al. 2010).

Earth’s climate is currently in one of the warmest periods of the Holocene (past 10K years). It is unlikely that the Planet will become any warmer over the next 100 years, because the cloud cover appears to have reached a minimum for the present levels of solar irradiance and atmospheric pressure, and the solar magnetic activity began declining, which may lead to more clouds and a higher planetary albedo. At this point, only a sizable increase of the total atmospheric mass can bring about a significant and sustained warming. However, human-induced gaseous emissions are extremely unlikely to produce such a mass increase.

Figure 10. Global climate forcings and their time scales of operation according to the hereto proposed Unified Theory of Climate (UTC). Arrows indicate process interactions.

6. References

Kopp, G. and J. L. Lean (2011). A new, lower value of total solar irradiance: Evidence and climate significance, Geophys. Res. Lett., 38, L01706, doi:10.1029/2010GL045777.

Kuptsov, L. P. (2001) Hölder inequality, in Hazewinkel, Michiel, Encyclopedia of Mathematics, Springer, ISBN 978-1556080104.

Lacis, A. A., G. A. Schmidt, D. Rind, and R. A. Ruedy (2010). Atmospheric CO₂: Principal control knob governing earth’s temperature. Science 330:356-359.

Lindzen, R. S. and Y.-S. Choi (2009). On the determination of climate feedbacks from ERBE data. Geophys. Res. Lett., 36, L16705, doi:10.1029/2009GL039628.

McKitrick, R. R. et al. (2010). Panel and Multivariate Methods for Tests of Trend Equivalence in Climate Data Series. Atmospheric Science Letters, Vol. 11, Issue 4, pages 270–277.

Nikolov, N and K. F. Zeller (manuscript). Observational evidence for the role of planetary cloud-cover dynamics as the dominant forcing of global temperature changes since 1982.

Pavlakis, K. G., D. Hatzidimitriou, C. Matsoukas, E. Drakakis, N. Hatzianastassiou, and I. Vardavas (2003). Ten-year global distribution of down-welling long-wave radiation. Atmos. Chem. Phys. Discuss., 3, 5099-5137.

Spencer, R. W. and W. D. Braswell (2010). On the diagnosis of radiative feedback in the presence of unknown radiative forcing, J. Geophys. Res., 115, D16109, doi:10.1029/2009JD013371

Trenberth, K.E., J.T. Fasullo, and J. Kiehl (2009). Earth’s global energy budget. BAMS, March:311-323

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UPDATE: This thread is closed – see the newest one “A matter of some Gravity” where the discussion continues.