## What is the greenhouse effect? An accessible, scientific introduction. Part 1

2022 August 01
the greenhouse effect
1. Part 1: What is the greenhouse effect? An accessible, scientific introduction
2. Appendix A: What is the atmosphere?
3. Appendix B: Ozone
4. Part 2: Physics of light and temperature
5. Part 3: Temperature of the Earth without an atmosphere
6. Part 4: A model of the greenhouse effect
7. Part 5: Differences between model and reality

Click on images to zoom. An older version of this series is also available as a single pdf.

## Introduction

Growing up, I understood that it gets warmer in the summer because there was “excess” sunlight warming the Earth, and cooler in winter because there was “insufficient” sunlight1There is a subtlety here that I did not notice at the time: does it get warmer in summer because the excess sunlight causes more warming to happen each day than cooling happens in the night, or does it get warmer because the days get longer and therefore the equilibrium temperature of each day is higher than the previous? This is similar to asking on what time scale the Earth system returns to equilibrium – yearly, or daily. The (incomplete) answer is that the former effect is arguably dominant, as can be seen by observing that the hottest day of the year is usually about 1 to 2 months after summer solstice, and thus the days continue to get hotter even when they are getting shorter. More specifically, if we approximate the Earth’s temperature at a point as an exponential decay to equilibrium, subject to a sinusoidal forcing, then we find that the temperature is sinusoidal with a phase offset from the forcing such that the tangent of the phase offset equals the ratio of the decay timescale to the forcing period. Taking the phase offset to be 1.5 months of a 12 month year, the ratio is , so the time scale for the Earth to reach equilibrium is about 1 forcing period, i.e., 1 year.. However I was confused that these effects happened to cancel each other exactly: if there was any tendency for the summer warming to exceed the winter cooling on average, however slightly, then year after year the temperature would steadily increase unendingly. Why doesn’t this happen? Furthermore, I did not even think to wonder what “excess” or “insufficient” sunlight could even mean: surely any amount of sunlight would warm the Earth – by what process was the Earth cooling in winter?

Like many students in the US, the only time (until graduate school) I was taught about the Earth’s climate, climate change, or the greenhouse effect was in grade school. At that age, students are often not prepared to engage with such questions, much less have the necessary background in physics to answer them; and if we do not understand the processes by which the Earth warms and cools, then we will not understand how the greenhouse effect impacts those processes no matter how well, or poorly, it is taught.2As an example, here is a lesson plan designed by NASA in which students perform an experiment where greenhouse gases are “simulated” using plastic wrap – ironically how greenhouses work, but having nothing to do with the greenhouse effect. Here is an experiment for high schoolers in which students measure the temperature of bags with and without carbon dioxide (which is generated in situ by an exothermic chemical reaction). Neither of these plans contain any information related to the greenhouse effect. Many of these students have become adults who see the words “climate change” and “greenhouse effect” increasingly often in news media and policy discussion, without realizing that their grasp of these concepts is at best superficial.

The goal of this series is to better introduce the reader to the greenhouse effect by first covering the requisite topics in physics and then building off of it show how the greenhouse effect occurs as a consequence. Specifically, we investigate properties of energy, light, heat, and temperature, including the blackbody effect, that hot objects emit light, and is how the Earth cools off. Balancing the blackbody effect with sunlight and features of the Earth’s atmosphere leads inevitably to the greenhouse effect, that certain gases (called “greenhouse gases”) cause the Earth to be warmer.

Understanding the greenhouse effect is necessary to engage with public policy and the prospects for the climate of our future. Along the way to this goal, we will encounter a variety of other topics, such as geoengineering, the lifetime of different greenhouse gases in the atmosphere, the processes that govern the structure of the atmosphere, the temperature of black holes, and even color.

While this series is intended for a scientifically-curious reader, it does not presume any specific advanced scientific background, and the principles are introduced with digressions and examples to provide context and help connect them to real-world experience. Scientific terms are put in bold when their definition is given by the surrounding text, and in italics otherwise; that is, terms in italics are jargon that may have a different scientific meaning than their plain English meaning.

In part 1 we introduce and motivate the remaining parts. Readers who are satisfied with the summary may skip the rest of the series.

In part 2 we explain how energy enters and leaves the Earth, which happens in the form of light. We discuss light and the different types (that is, wavelengths) of light, and we introduce a graph called a spectrum which shows what types of light are in a beam. We then describe the blackbody effect, which states that all objects emit light, and relates the amount and type of light emitted by an object to the temperature of the object.

In part 3 we introduce the concept of an equilibrium of a system, which could be a typical or average state for the system to be in; it is frequently much easier to find the equilibria of a system than to describe the exact behavior of a system as it changes over time. We discuss equilibria in the context of temperature and calculate the equilibrium temperature for the Earth in the absence of the atmosphere.

In part 4 we present a simplified model of the Earth and its atmosphere. We calculate the equilibrium temperature of the model Earth, and see what exactly changes as we change the amount of greenhouse gas. The finding that the temperature goes up as greenhouse gas is added is the greenhouse effect.

In part 5 we explore the differences between the simple model and the real-world climate of the Earth.

In appendix A we give an overview of what the atmosphere is, starting from questions like why it is thicker on the bottom and whether it has a top.

In appendix B we discuss the ozone layer and ozone hole. While they have no bearing on the greenhouse effect, they are a frequent point of confusion with the greenhouse effect. The worldwide effort to control the ozone hole by regulating CFCs is also the only notable example of a global agreement to address a global environmental problem, and thus makes a useful point of comparison to the future regulation of carbon dioxide emissions.

## Summary

The Earth is warmed by visible light it receives from the Sun, and is cooled by emitting infrared light (which is invisible) to space. Greenhouse gases in the atmosphere are those that absorb infrared light, but not visible light. Some of the infrared light emitted by the Earth is absorbed by the greenhouse gases and then re-emitted, some of which hits the Earth.

The Earth’s temperature is in balance when the total energy it receives equals the total energy it emits. As infrared light is returned to the Earth by greenhouse gases, the energy the Earth receives is increased, so it must emit more energy to maintain balance. The Earth emits more light when it is warmer. In this way adding greenhouse gases to the atmosphere causes the Earth to become warmer.

A very short and easy to read introduction to climate change is What We Know About Climate Change by Kerry Emanuel. The book is about as long as this series and is targeted to a non-scientific audience. In addition to reviewing the material covered here (without any equations), the book discusses what climate change is, how we know it is happening, what the effects of climate change are, and what can be done about climate change.

Sustainable Energy – Without the Hot Air by David MacKay is an excellent, readable introduction to energy in modern society, and is also targeted to non-scientists. The book discusses the major uses of energy and the major available sources of energy, and invites the reader to consider how to balance these against each other in a future without fossil fuels. The reader is empowered with the information necessary to come up with their own energy plan, and in doing so is forced to confront with the difficulty of finding an agreeable plan where energy production satisfies energy demand.

## Temperature units

For more information, see my four-part series on temperature, beginning with What is negative temperature?

In this series we use a mixture of three different scales for describing temperature: degrees Celsius (formerly called “centigrade”), which is the international standard temperature for day-to-day use; degrees Fahrenheit, which is standard in the United States for day-to-day use; and Kelvin, which is typically used within physics and other sciences when discussing temperatures far from room temperature or for theoretical physics. The reason for the difficulty converting between this different scales is that Celsius and Fahrenheit do not have zero temperature at zero degrees, but rather at -273.15 C and -459.67 F, respectively. Indeed, both of those scales were invented and popularized long before the scientific community reached a consensus that there was such a thing as zero temperature (called absolute zero to avoid confusion with other temperatures like 0 C or 0 F) or how cold it was compared to known temperatures.

To rectify these shortcomings, Lord Kelvin invented a temperature scale with zero temperature at zero degrees and was the first to reliably calculate the difference between that temperature and known temperatures, building off of contemporary work in thermodynamics by him and other scientists. This Kelvin scale was scaled so that the difference between two temperatures is the same number of degrees as in the Celsius scale, so as a result one can convert from Celsius to Kelvin by simply adding 273.15 degrees, which has the effect of shifting the zero to the correct place. To convert between Fahrenheit and the other two scales requires both shifting and multiplying by a constant.

Celsius and Fahrenheit continue to be more useful than Kelvin for describing temperatures near room temperature (for which Kelvin can be unwieldy), but are very inconvenient in the context of thermodynamics. Climate science in general, and this series in particular, is mostly concerned with physical processes that take place near room temperature, but explains these processes with thermodynamics, and so uses both Celsius and Kelvin according to what is convenient in each context. (American meteorology continues to primarily use Fahrenheit for historical reasons.)