[Paper Review] Atmosphere and Greenhouse Gas Primer

W. A. van Wijngaarden, W. Happer|arXiv (Cornell University)|Mar 1, 2023

Atmospheric Ozone and Climate4 citations

TL;DR

This paper explains how greenhouse gases like CO₂ and H₂O create thermal resistance in Earth's atmosphere, leading to a convecting troposphere and a radiatively driven stratosphere. Using basic thermodynamics and radiation transfer, it shows that increased CO₂ raises surface temperature by enhancing atmospheric opacity, with model-satellite agreement confirming the accuracy of radiative transfer calculations despite complex spectral features.

ABSTRACT

We discuss how greenhouse gases affect radiation transfer in Earth's atmosphere. We explain how greenhouse gases like water vapor or carbon dioxide, differ from non-greenhouse gases like nitrogen or oxygen. Using simple thermodynamics and fluid mechanics, we show that a planet with sufficiently high concentrations of greenhouse gases must develop a convecting troposphere. The planet must also develop a non-convecting stratosphere above the tropopause. In the simplest approximation of an atmosphere that is transparent to sunlight and has frequency-independent opacity for thermal radiation, one can find simple formulas for the tropopause altitude, and for the altitude profiles of pressure and temperature. The troposphere is nearly isentropic and the stratosphere is nearly isothermal. Earth's real atmosphere is much more complicated but it does have a troposphere and a stratosphere. Between the surface and the tropopause the entropy per kilogram of real tropospheric air increases slowly with altitude. The entropy increases much more rapidly with altitude in the stratosphere. The stratosphere has a nearly isothermal lower part and a hotter upper part due to absorption of solar ultraviolet radiation by ozone. The thermal opacity of the real atmosphere has a complicated frequency dependence due to the hundreds of thousands of vibration-rotation transitions of its greenhouse molecules. Unlike the simple model where nearly all radiation to space originates at the tropopause altitude, radiation to space from Earth's real atmosphere originates from both the surface and all altitudes in the troposphere. A small additional amount of radiation originates in the stratosphere. When these complications are taken into account, model calculations of the thermal radiation spectrum at the top of the atmosphere can hardly be distinguished from satellite observations.

Motivation & Objective

• To explain the fundamental physical mechanisms by which greenhouse gases alter radiative transfer and atmospheric structure in Earth's atmosphere.
• To clarify the role of greenhouse gases in establishing a troposphere and stratosphere through convective and radiative processes.
• To demonstrate that model calculations of infrared emission spectra match satellite observations, validating the underlying physics despite atmospheric complexity.
• To assess the impact of increasing CO₂ on surface temperature, emphasizing the role of feedbacks and the lack of observational support for strong positive feedbacks.

Proposed method

• Uses basic thermodynamics and fluid mechanics to derive the conditions for a convecting troposphere and non-convecting stratosphere.
• Applies the Schwarzschild equation to model radiative transfer in the atmosphere with frequency-dependent opacity.
• Employs the concept of local thermodynamic equilibrium and the Boltzmann distribution to describe molecular energy states in the atmosphere.
• Compares model-predicted infrared emission spectra at the top of the atmosphere with actual satellite measurements from interferometers.
• Uses a simplified gray atmosphere model to derive analytical expressions for tropopause altitude, temperature, and pressure profiles.
• Analyzes the role of water vapor, clouds, and ozone in modifying radiative flux and albedo, particularly in the infrared window region.

Figure 1: The three vibrational modes of the CO 2 from Fermi’s classic paper on mode mixing [ 5 ] . For the most abundant isotopolgue, 16 O 12 C 16 O, the mode frequencies are: symmetric stretch (b) $\nu_{1}=1388$ cm -1 ; (c) bending $\nu_{2}=667$ cm -1 ; and (d) asymmetric stretch, $\nu_{3}=2349$ c

Experimental results

Research questions

• RQ1 How do greenhouse gases like CO₂ and H₂O differ from non-greenhouse gases like N₂ and O₂ in their radiative effects on the atmosphere?
• RQ2 What physical mechanisms lead to the formation of a troposphere and stratosphere in a planet with sufficient greenhouse gas concentrations?
• RQ3 To what extent does the real atmosphere's complex spectral opacity affect the altitude from which thermal radiation to space originates?
• RQ4 How well do simplified radiative transfer models reproduce observed satellite spectra of Earth's outgoing thermal radiation?
• RQ5 What is the quantitative impact of increasing CO₂ on surface temperature, and how do feedback mechanisms influence this effect?

Key findings

• The troposphere is nearly isentropic and the stratosphere is nearly isothermal in the simple gray atmosphere model, with the tropopause altitude determined by radiative and convective balance.
• In the real atmosphere, thermal radiation to space originates from multiple altitudes in the troposphere and a small contribution from the stratosphere, not just the tropopause as in the simple model.
• Model calculations of the infrared spectrum at the top of the atmosphere agree extremely well with satellite observations, even across diverse regions like the Sahara, Mediterranean, and Antarctica with varying water vapor.
• The surface temperature increase from CO₂ doubling is estimated at approximately 1 °C when all feedbacks are accounted for, with no observational support for large positive feedbacks.
• Clouds and albedo changes, such as from Arctic ice melt, have only regional impacts and do not significantly alter global energy balance.
• The atmosphere acts as a heat engine, with greenhouse gases serving as a thermal resistance that enables the vertical transport of energy and drives weather and climate dynamics.

Figure 2: To calculate greenhouse effects in detail, one must include the opacity of hundreds of thousands of individual line intensities, shown here as colored dots from the HITRAN data base. More details of how line intensities are used can be found in references [ 6 , 7 ] .