The Second Law, Radiative Transfer, and Global Warming

This post is part of a series, Nonsense and the Second Law of Thermodynamics. The previous post is entitled Spontaneous Change and Equilibrium.

Does global warming violate the second law of thermodynamics?  Such a claim may seem strange.  The idea that the vast majority of physical scientists would subscribe to an idea that somehow violates a fundamental law of thermodynamics on its face seems odd.  Yet, such a claim is often made by people calling the science behind global warming into question.

Carbon Dioxide Poll

A recently closed poll on this blog posed the following question.  "The bending mode of carbon dioxide is:" Respondents were to respond with the best answer.  Here were the choices:

• A Hoax
• Not Dipole Allowed
• Degenerate
• A Blackbody
• The reason the sky is blue
• Even though I understand Global Warming, I don't know
• I don't know

I should point out that the answer to the question can be found in a post on this blog. The results of the poll are shown here:

Reformatted Post on Beer's Law

I have had to reformat the post on Beer's Law.  The html editor at Blogspot seems to do strange things with <br> tags.

How To Convert To and From Wavenumbers

The question of how to convert from one set of units to another comes up from time-to-time, and I think it might be helpful to have a few short posts that simply address unit conversion.  This post addresses conversion to and from wavenumbers (cm^-1) (also called reciprocal centimeters, inverse centimeters or  Kaisers). A previous post What is Infrared Radiation (IR)? addresses the concepts behind this unit.  The unit is proportional to frequency, and can be considered a unit of frequency or of energy.

Radiative Transfer

If you are following this primer on infrared spectroscopy and global warming you already have some of the basics of radiative transfer.  The previous post in this series develops a simple multi-layer model of the carbon dioxide in the troposphere.  It leaves out many important features but shows conceptually how absorption and emission behave in layers of the troposphere.

The current post is intended to wrap up the topic and touch upon a few issues that were not discussed. It is possible to teach a year-long course in radiative transfer (or even multiple courses); so of course this post does not do the topic justice, but perhaps it provides some basic principles that give the reader a cursory understanding of the topic.

A Multi-Layer Model of Carbon Dioxide

I have put together a simple multi-layer model of  carbon dioxide in the troposphere.  It is based upon the same principles as the two-layer model and the three-layer model.  It accounts for the temperature and pressure profiles from the  previous post and it is part of a primer on infrared spectroscopy and global warming.  Just like those other models there are still caveats; this model is intended to be illustrative of concepts and therefore it is conceptually simple.

A Three-Layer Model

This post is part of a primer on infrared spectroscopy and global warming. The previous post introduces a two-layer model  and is a necessary prerequisite to understanding this post.  In this post I start with the following assumptions.  There is a source of infrared radiance that has emissivity of 1, i.e., it radiates as a perfect blackbody at a temperature of  288 K.  The radiance from that layer is I₀

There is a layer of air 1000 m thick with 380 ppm carbon dioxide at a temperature of 278 K.  There is another layer of air 1000 m thick with 380 ppm carbon dioxide at 268 K.  All layers are at a constant pressure of one atmosphere.

A Two-Layer Model

This post is part of a primer on infrared spectroscopy and global warming. The previous post discusses the issue of saturation in the 14-micron band of carbon dioxide in a single-layer model.   The post before that discusses Beer's Law, and is a necessary prerequisite to understanding this post.  This post starts to look beyond the single-layer model, by discussing a two-layer model, and beginning a discussion of radiative transfer.

A Note On Saturation of the Carbon Dioxide 15-micron Band

This post is part of a primer on infrared spectroscopy and global warming. The previous post discusses Beer's Law, and is a necessary prerequisite to understanding this post.  The previous post also introduced the idea of saturation of a single layer model.  This post looks more deeply at the single-layer model and the saturation of the 15-micron band of carbon dioxide.

Infrared Spectra of Molecules of Interest

This post is part of a primer on infrared spectroscopy and global warming. The previous post concludes a three-post series that looks at molecules and radiation and discusses how molecules give rise to infrared spectra.  This post discusses the infrared spectra of some molecules of interest.

 Figure Source

Molecules and Radiation III: Vibration, Dipoles, and Ro-Vibrational Spectra

This post is part of a primer on infrared spectroscopy and global warming. The previous post looked at the vibrational modes of several molecules including HCl and several molecules of atmospheric interest. This post discusses how these modes relate to infrared absorption and uses HCl as an example.

Molecules and Radiation II: Molecular Vibration, Rotation, and Translation

This post is part of a primer on infrared spectroscopy and global warming. The previous post  starts the process of looking at the interaction between infrared radiation and molecules and discusses the degrees of freedom of molecules and the Born-Oppenheimer approximation.  The result of the previous post is that for the purposes of IR spectroscopy, one can focus on the motion of the atomic nuclei and separate them from the electronic degrees of freedom of a molecule.

Figure Source

There are 3N nuclear degrees of freedom for a molecule that has N nuclei.  For the HCl molecule that means there are 6 degrees of freedom.

Molecules and Radiation I: Molecular Structure

This post is part of a primer on infrared spectroscopy and global warming. The previous post  starts the process of looking at the interaction between infrared radiation and matter and discusses black-bodies and relationship between temperature and infrared radiation.  This post goes further and looks at how gas phase molecules interact with infrared radiation.

I

For a molecule to absorb radiation, several conditions must hold.  First, energy must be conserved: if the molecule absorbs energy from a photon, the molecule must be able to store that energy in some manner. 

Infrared Radiation, Black-bodies, and Temperature

This post is part of a primer on infrared spectroscopy and global warming. The previous post discusses the nature of  infrared radiation. This post starts the process of looking at the interaction between infrared radiation and matter and discusses black-bodies and the relationship between temperature and infrared radiation.

 

Figure source.

What is Infrared Radiation (IR)?

This post is part of a primer on infrared spectroscopy and global warming. The  main post gives an overview of the topic and provides links to each of  the sections. This post examines what infrared radiation (IR) is, a necessary first step to understanding the importance of IR in discussions about global warming.

Figure source

IR is a type of electromagnetic radiation; so the starting place is to understand electromagnetic radiation.

The Beer-Lambert Law

Introduction 


This post is part of a primer on infrared spectroscopy and global warming. The previous post  looks at the features of the spectra of molecules of interest molecules and radiation and discusses how molecules give rise to infrared spectra.  This post looks at the question of how much radiation is absorbed by gas phase molecules in a laboratory setting and examines some of the differences between the laboratory gas cell and the earth's atmosphere.

A Primer on Infrared Spectroscopy and Global Warming

Introduction

This post and the posts linked to it through section headers together form a primer on infrared spectroscopy and how it relates to global warming.  The purpose of the primer is not be to convince skeptics that global warming is real, but rather to explain some of the terms and issues being discussed in climate science.  My goal is not to write a super technical explanation of infrared spectroscopy.  That's been done so many times that it is hardly worth doing again.

Rather, my intent is to write something that clearly describes infrared spectroscopy and relates it to global warming that tries to explain some fairly technical concepts in reasonably plain language.  As such there is an inevitable loss of fidelity about some of the fine points of infrared spectroscopy.  Anyone interested in such detail can follow some of the sources that I will provide.  At some point one has to compromise between accessibility and technical accuracy.  I hope that the choices made in this primer are helpful to some people trying to understand this topic.  This post is an outline of the topics addressed in the linked entries.

What is Infrared Radiation (IR)?

Figure source

This first post starts with the basics.  It discusses the electromagnetic spectrum and where infrared radiation fits into it.  It discusses waves and their measures.  It introduces the idea of electric dipole radiation.  It discusses the units of radiation wavelength, frequency. It ends by discussing photons and energy quantization.