Introduction to Climate Science

Introduction to Climate Science

Andreas Schmittner

Oregon State University

Corvallis, OR

Introduction to Climate Science by Andreas Schmittner is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License, except where otherwise noted.

Publication and ongoing maintenance of this textbook is possible due to grant support from Oregon State University Ecampus.

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Dedication

For Ella.

Contents

Preface

Acknowledgements

Content

1. Weather a) Weather and Climate b) The Climate System c) Processes Recorded Lectures References

2. Observations a) Atmosphere b) Cryosphere c) Ocean d) Biosphere and Carbon Cycle Videos References Links

3. Paleoclimate a) Methods b) The Last Two Millennia c) The Holocene d) The Ice Ages

4. Theory a) Electromagnetic Radiation b) The Greenhouse Effect c) Earth’s Energy Budget d) Radiative Forcings, Feedback Processes, and Climate Sensitivity Videos References

5. Carbon a) The Natural Carbon Cycle b) Anthropogenic Carbon c) Carbonate Chemistry and Ocean Acidification Videos References Additional Material

6. Processes a) Atmospheric Circulation b) The Hydrologic Cycle c) Ocean Circulation Videos References

7. Models a) Construction b) Evaluation c) Applications Videos References

8. Impacts a) Projections b) Ecosystems c) Long-Term Changes d) Regional Changes e) Extremes f) Impacts on Humans Videos References

9. Economics Economics and the climate change challenge: Understanding incentives and policies Videos References and links:

10. Ethics Do We Have a Moral Responsibility to Stop Global Temperature Rise?[footnote]Adapted from Moore and Nelson (2010, 2012)[/footnote]

11. Solutions a) Technology b) Politics c) Personal Actions d) Adaptation Videos References

Glossary

Creative Commons License

Recommended Citations

Versioning

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Preface

This book is an introduction to climate science for undergraduate students of both science and non-science majors and for everybody interested in the topic. It is quantitative and uses many graphs and numbers, but only a minimum amount of math is required.

Climate change is a controversial topic. You can find news and opinion articles about it on a daily basis. However, not all information is trustworthy and many articles are biased by political views and ideology (Oreskes and Conway, 2010). As a consequence of this misinformation the general public is confused and its views are quite different from those of climate scientists. Whereas almost all climate scientists think that the observed global warming over the past decades has mostly or exclusively been caused by humans (Cook et al., 2013), a view that is supported by major scientific organizations such as the National Academies of Sciences and the American Geophysical Union and my personal experiences from the scientific literature and conferences, only about half of all Americans think that way (Funk and Kennedy, 2016). I have written this book to contribute to a better informed public on this topic. My goal is to make the science accessible to everybody. For this reason the textbook is free and it includes up-to-date links to trustworthy science information.

Chapter 1 discusses differences between weather and climate and provides an introduction to the interacting components of Earth’s climate system. Chapters 2 and 3 summarize observations of current and past changes. Chapter 4 presents theoretical foundations and discusses relevant physical processes such as electromagnetic radiation, the greenhouse effect and Earth’s energy budget. Chapters 5 and 6 provide further details in how the climate system works by covering the carbon cycle and other processes such as atmospheric and oceanic circulations and the water cycle. Chapter 7 introduces climate models and chapter 8 summarizes projections of future climate change including possible impacts on natural and human systems. Economical and ethical aspects are discussed in chapters 9 and 10, followed by chapter 11, which covers possible solutions including adaptation to and mitigation of future climate change.

You will also learn some of the language climate scientists use. Highlighted words are explained in the glossary. Simply hover with the mouse over the word and an explanatory box will emerge. Exercises and questions appear in boxes such as the one below. After reading a chapter you should be able to answer the questions. Boxes are also used for some overarching concepts such as, oxygen isotopes (Chapter 3) or the budget equation (Chapter 4). Links to lecture videos are included before the references in each chapter.

Climate science has a rich history going back 200 years to French scientist Jean Baptiste Joseph Fourier. Here, we will not delve into this history, but for those interested there is a post and documentary (1.5 h) with more information. The documentary covers not only science history but also current scientists and other aspects of climate science.

Exercises Try it yourself and search the internet for “climate change news” or “global warming news” or similar key words and read a few (two longer or three shorter) articles or opinion pieces that sound interesting to you. You can also use an article in a paper journal or newspaper. Try to include different viewpoints and find arguments for and against human made climate change and whether or not we should do something about it. Summarize each piece in one or two paragraphs and provide the title and URL (if web source) or attach a copy (if paper source). Look for arguments that claim scientific facts or consensus and make a list of those. Be sure to include arguments both for and against human caused climate change. Indicate which arguments you think are trustworthy and why. What is your assessment of the articles? Have you learned something? Are there connections between the articles? What are the questions that remain? Beyond the above pieces, what are your personal questions about climate change? Please write in prose (except for the list of arguments) and keep your writing to 1-2 pages of text. Please bring your writing to class for discussion and be prepared to use the arguments in a mock debate. During the class discussion we split the students in two groups, one arguing for human caused climate change and that it is a bad thing, the other arguing against human caused climate change and that it is a good thing. Two students summarize the main points made by each group on the white board. The list of topics and questions of the students will be used throughout the class attempts will be made to get back and answer them based on what we’ll learn.

It can be difficult to distinguish between trustworthy information and misinformation. Here are some general tips that may help you to separate the wheat from the chaff. Trustworthy sources are the Intergovernmental Panel on Climate Change (IPCC), government agencies such as the National Oceanic and Atmospheric Administration (NOAA) and the National Aero and Space Administration (NASA), and scientific organizations such as the National Academies of Sciences, Engineering and Medicine, the American Geophysical Union (AGU), and the American Meteorological Society (AMS). The IPCC reviews the state of the science with regard to climate change every 6 years or so and summarizes the current understanding in assessment reports. The latest IPCC assessment reports (AR6) were published between 2021 and 2023. The IPCC consists of three working groups: WG1: The Physical Science Basis, WG2: Impacts, Adaptation, and Vulnerability, and WG3: Mitigation of Climate Change. Each working group publishes a detailed report. The three reports are summarized in a synthesis report. These reports are extensive (1,000+ pages) and a great source for scientists but not very accessible for the general public. However, the IPCC also summarizes its findings in its Summary for Policymakers, which are shorter and more accessible. I would recommend to read those. Climate scientists from around the world contribute to these reports. This textbook makes use of the IPCC reports findings and figures. Articles that refer to the peer-reviewed literature and that include links or references that can be traced to the original work are preferable to articles that don’t include references. Peer-review is an important part of modern scientific practice. As part of this process the editor of a journal selects independent reviewers that are experts in the field (peers), who then read and comment on a manuscript. These comments, which are often critical and point out weaknesses or inconsistencies, are relayed back to the authors who then can revise the manuscript taking the reviewers comments into account. Only after all reviewers agree to the publication is it that in most cases the article gets published (the editor decides). Sometimes multiple revisions are necessary until all reviewers are satisfied. Reviewers examine if the conclusions of the paper are supported by evidence presented. This process is a check that improves generally the quality of the papers and makes it more difficult to publish conclusions that are not supported by evidence. But, as all human endeavors, it is not perfect. Look at other articles on the same web page. If you see signs for conspiracy theories or claims that climate change is a hoax it is likely that you’re on a misleading webpage. Compare the claims with trustworthy sources. If there are major discrepancies you have a reason to be doubtful. Critically examine the arguments. Are they compelling? Do the authors cherry-pick data? Do they present only one side of the argument and neglect other evidence? Some articles are reviewed by scientists at ClimateFeedback.org. If in doubt ask a scientist. Feel free to write me or another climate scientist an email. The following are websites that, in my opinion, misrepresent and/or distort climate science: https://www.friendsofscience.org http://climatesciencenews.com https://www.climatedepot.com https://wattsupwiththat.com https://www.cato.org http://www.aei.org https://www.heartland.org http://principia-scientific.org

Videos

All lecture videos are available here.

Lectures

Lecture slides are available here.

References

Cook J., D. Nuccitelli, S. A. Green, M. Richardson, B. Winkler, R. Painting, R. Way, P. Jacobs and A. Skuce, 2013, Quantifying the consensus on anthropogenic global warming in the scientific literature, Environmental Research Letters, 8, doi:10.1088/1748-9326/8/2/024024.

Funk C. and B. Kennedy, 2016, The Politics of Climate, Chapter 1: Public views on climate change and climate scientists, Pew Research Center.

Oreskes N. and E. Conway, 2010, Merchants of Doubt, Bloomsbury Press, New York, ISBN 978-1-59691-610-4.

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Acknowledgements

The cover picture of Earth was taken by the crew of the Apollo 17 on their journey to the moon on December 7, 1972 (from nasa.gov). I’m grateful to Laurie Houston, Susanne Capalbo, Kathleen Dean Moore, and Michael Paul Nelson for their contributions to the chapters on economics and ethics. I want to thank my wife Susanne for her support and patience on many evenings and weekends that I spent writing. I appreciate student’s comments, which have improved the book. I also want to thank Dianna Fisher, Gabe Higginbotham, and Devin Curtis from OSU’s open textbook project for their encouragement and technical help.

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1. Weather

a) Weather and Climate

Weather and climate are related but they differ in the time scales of changes and their predictability. They can be defined as follows.

Weather is the instantaneous state of the atmosphere around us. It consists of short-term variations over minutes to days of variables such as temperature, precipitation, humidity, air pressure, cloudiness, radiation, wind, and visibility. Due to the non-linear, chaotic nature of its governing equations, weather predictability is limited to days.

Climate is the statistics of weather over a longer period. It can be thought of as the average weather that varies slowly over periods of months, or longer. It does, however, also include other statistics such as probabilities or frequencies of extreme events. Climate is potentially predictable if the forcing is known because Earth’s average temperature is controlled by energy conservation. For climate, not only the state of the atmosphere is important but also that of the ocean, ice, land surface, and biosphere.

In short: ‘Climate is what you expect. Weather is what you get.’

b) The Climate System

Earth’s climate system consists of interacting components (Fig. 1). The atmosphere, which is the air and clouds above the surface, is about 10 km thick (more than two thirds of its mass is contained below that height). The ocean covers more than two thirds of Earth’s surface and has an average depth of roughly 4 km. Contrast those numbers with Earth’s radius which is approximately 6,400 km and you’ll find that Earth’s atmosphere and ocean are very thin layers compared to the size of the planet itself. In fact, they are about 1,000 times thinner. They are comparable perhaps to the outer layer of an onion or the water on a wet soccer ball. Yet all life is constrained to these thin layers. The major ocean basins are the Pacific, the Atlantic, the Indian, and the Southern Ocean. Ice and snow comprises the cryosphere, which includes sea ice, mountain glaciers and ice sheets on land. Sea ice is frozen sea water, up to several meters thick, floating on the ocean. Ice sheets on land, made out of compressed snow, can be several kilometers thick. The biosphere includes all living things on land and in the sea from the smallest microbes to trees and whales. The lithosphere, which is the solid Earth (upper crust and mantle), could also be considered an active part of Earth’s climate sytem because it responds to ice load14 and impacts atmospheric carbon dioxide (CO2) concentrations and climate on long timescales through the movements of the continents.

The components interact with each other by exchanging energy, water, momentum, and carbon thus creating a deliciously complex coupled system. Imagine water evaporating from the tropical ocean heated by the sun (Fig. 1). The air containing that water rises and cools. The water condenses into a cloud. The cloud is carried by winds over land where it rains. The rain sustains a forest. Trees are dark, having a low albedo. This influences the amount of sunlight absorbed by the Earth. Dark surfaces absorb more sunlight and get warmer compared to bright surfaces such as desert sand or snow. Air warmed by the surface rises and affects the wind.

c) Processes

Fig. 2 illustrates some of the important processes that contribute to the complex interactions within the climate system. Earth’s energy source is the sun. Both solar and terrestrial radiation are affected by gases, aerosols, and clouds in the atmosphere. Thus, the atmospheric composition affects the heating and cooling of the earth. Heating and cooling affect the temperature and circulation of the atmosphere and oceans. Circulations of the air and sea affect temperatures and precipitation over both ocean and land, which impact the biosphere and cryosphere. Atmosphere and oceans exchange heat, water (evaporation and precipitation), and momentum. Wind blowing over the ocean pushes the surface water ahead. Air temperatures and snow fall affect the growth and melting of glaciers and ice sheets. Water from melting ice flows through rivers into the ocean affecting its salinity, its density and movement. Variations in solar irradiance can cause global climate to change. Volcanoes can eject large amounts of aerosol into the atmosphere with climatic implications. Humans are influencing the climate system through emissions of greenhouse gases, aerosols, and land use changes.

The complexity makes studying the climate system challenging. Scientists from many disciplines contribute such as physicists, chemists, biologists, geologists, oceanographers, atmospheric scientists, paleoclimatologists, mathematicians, statisticians, and computer scientists. To me, the challenges and interdisciplinary nature of climate science are fascinating and fun. I learn something new about it every day.

Recorded Lectures

Weather and Climate

References

Le Treut, H., R. Somerville, U. Cubasch, Y. Ding, C. Mauritzen, A. Mokssit, T. Peterson and M. Prather, 2007: Historical Overview of Climate Change. In: Climate Change 2007: The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change [Solomon, S., D. Qin, M. Manning, Z. Chen, M. Marquis, K.B. Averyt, M. Tignor and H.L. Miller (eds.)]. Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA.

Questions What are the two main differences between weather and climate? How big is Earth? How thick is the atmosphere, how deep the ocean? What are the components of Earth’s climate system? List processes that cause interactions between the components: atmosphere-ocean, atmosphere-biosphere, atmosphere-cryosphere, ocean-biosphere, ocean-cryosphere. Name three processes (forcings) that can cause global climate to change.

Explore

Go to one of the following websites and explore temporal variations of surface temperature observations in a location of your interest. Plot today’s data, yesterday’s, last week’s, last month’s, last year’s, the last decade’s, as far back as you can and make some notes on what you observe. Note regular, predictable cycles such as the diurnal and annual cycle in contrast with irregular, unpredictable variations such as day-to-day and year-to-year fluctuations. What causes the regular cycles? Try to order the variations with respect to their amplitude (strength). Discuss with fellow students and instructor.

Hourly and daily data are available at: https://www.wunderground.com/history/. Enter a location of your interest. Click on the “Weekly”, “Monthly”, or “Custom” tabs to select different time periods. Unfortunately, when I tried it Jan. 30th, 2017 the “Custom” option didn’t allow one to plot more than one year of data. However, you may be able to identify diurnal (daily) cycles in temperature. Fig. 3 shows an example. Although some nights can be warmer than some days and sometimes days and nights have the same temperature, on average days are warmer than nights. Thus the average diurnal cycle is part of climate. It is forced by the diurnal cycle of solar irradiance. Does pressure have a diurnal cycle? Answer: no. What is the typical timescale of pressure variations? Often it is about a week or so. This timescale is associated with the transition of weather systems (high and low pressure systems) passing by.

Help on finding past weather data is available at https://www.weather.gov/help-past-weather. Following the instructions and clicking on Oregon brings up http://www.wrh.noaa.gov/pqr/.

Clicking on “local”, choosing the “Local Data/Records” tab, and clicking on “Daily Records for cities in Oregon” brings me to the website of the Western Regional Climate Center http://www.wrcc.dri.edu/summary/climsmor.html where I can choose a city. Now I choose “Corvallis Oregon State University” and scroll down on the left side menu to “Graph and Lister” under “Daily Data”. Now select the time period (I choose 20120101 to 20160101) and click on the “Daily Precipitation” button and then “Create Graph”.

Averaging many years of these weather data yields a climatology. At the WRCC website you can see plots of climatologies over 30 years by scrolling back up the left side menu and clicking on one of the “Daily Temp. Precip.” links. For Corvallis it shows average temperatures around 40°F (4°C) in winter and 65°F (18°C) in summer. It also shows a larger diurnal cycle in summer than in winter. What could be the reason for that? Answer: less cloud cover in summer. Clouds lead to cooler days and warmer nights, thus decreasing the diurnal cycle. As expected, precipitation is low in summer and high in winter. Curves are smooth in the climatology. In contrast to Fig. 4 the weather variations have been averaged out.

Now try a forecast of temperature for next August and next January. What is your guess? Answer: a good guess would be the climatology, i.e. 65°F for August and 40°F for January. Thus the average seasonal cycle is climate and it is predictable because it is forced by the seasonal cycle of solar irradiance. However, deviations from the climatology for a certain day next year are unpredictable weather.

Statistical propertiesof climate can be summarized in a frequency histogram. Let’s explore those with an example. Download from the WRCC website daily average temperature data from a certain day of year, e.g. May 1st. You can do this by clicking on the “Lister” link in the left menu. Next choose start and end days (e.g. 19851001 and 20160101) to create a list of 30 years of data. Enter “wrcc35” as the password. Let’s choose “Average Temperature” as the element to list. Now select a day of the year (e.g. May 1st) for both “Starting Date” and “Ending Date”, and click the “Get Listing” button. This gives the following list (or vector mathematically speaking) of N=30 temperatures T= (T1, T2, … , TN) = (52, 52, 44, 52, 52, 54, 48, 52, 50, 56, 59, 46, 64, 58, 55, 48, 54, 54, 63, 54, 51, 54, 42, 52, 52, 48, 48, 48, 66, 56). Here N = 1 corresponds to 1985, N = 2 to 1986 and so on. In order to construct the frequency histogram we first need to choose bin sizes. I propose to choose 6 bins: 40-44, 45-49, 50-54, 55-59, 60-64, and 65-70. Now simply count how many years fall into each bin. I get 2, 6, 14, 6, 2, 1. Using python I produced the following graph (Fig. 6).

Climate change can be expressed as a change in the mean, which would correspond simply to a shift of the whole histogram to warmer or colder temperatures. However, it can also change the shape of the histogram. For example by making the distribution wider or narrower. This would increase or decrease the occurrences of extreme events. And, of course, it can both change the mean and the width. Most of the time, including in this text, discussions of climate change consider only changes in the mean. But we should keep in mind that changes to the tails of the distribution may be equally important because it is those tails that can have large impacts (heat waves, cold spells, droughts, floods, etc).

Now let’s explore effects of spatial scales on climate variations. Go to https://www.ncdc.noaa.gov/cag and start with the U.S. tab selection. We want to compare the annual average temperature change in a city of your choice (e.g. Salem in Oregon), averaged over the larger region of a state, for the U.S. as a whole, and the globe (use “Globe” tab and plot “Land and Ocean”, “Land”, and “Ocean” separately). For “Timescale” select “Annual”. Check the “Display Trend” box. This will include a trend line on the graph. Compare the trends and year-to-year variations. Are the trends larger for the global ocean or for the global land?

Compare the year-to-year variations and trends in regionally and globally averaged temperatures (Figs. 7-12) to the local diurnal cycle, day-to-day weather fluctuations (Fig. 3), and to the seasonal cycle (Figs. 4-5). Even though the global temperature trends (~0.1°C/decade) are much smaller than diurnal, day-to-day or seasonal fluctuations, which can be 10°C or more, we will see in the remainder of this course that global temperature changes of a few degrees C will have important impacts on natural systems and human societies.

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2. Observations

Although Earth’s climate is currently changing rapidly relative to past changes, in most regions where we live changes are slow enough that we do not notice them directly during our daily lives. However, older people may have noticed changes during their lifetimes and in some regions changes are larger and more obvious than elsewhere. In this chapter we will discuss some observations from the past 100 years and data from regions that are particularly sensitive to climate change, where the most dramatic effects have occurred. This will not be a comprehensive documentation of existing observations. Additional observations will be discussed throughout the remainder of this book.

a) Atmosphere

Observations show that climate is changing on a global scale. Surface air temperature data, averaged over the whole Earth, indicate warming of about 1°C over the last ~100 years (Fig. 1). But that warming was neither steady nor smooth. From 1880 to about 1910 there was cooling, followed by warming until about 1940. After this slight cooling or approximately constant temperatures were observed until the 1970s, followed by a rapid warming until the present. Each year’s temperature is somewhat different from the next. Not all of these year-to-year changes are currently understood, but natural variations, which are not caused by humans, do play a role. For instance, strong El Niño years such as 1997-98 or 2015 show up as particularly warm years, whereas La Niña years such as 1999-2000 or 2011 show up as relatively cool. El Niño and La Niña, also known as ENSO (El Niño/Southern Oscillation), is climate variability in the tropical Pacific that impacts many other regions of the Earth.

Figure 1: Global average surface temperature change from 1880 to 2018. Anomalies from the 20th century average are shown. From the National Oceanographic and Atmospheric Administration’s (NOAA) web site

. There are a few other groups around the world who calculate global average surface temperatures, e.g. the National Aeronautics and Space Administration’s (NASA) Goddard Institute for Space Science (

), the Climate Research Unit (

) of the University of East Anglia, or the Berkeley Earth Surface Temperatures (

), and all come to very similar results. Errors due to unequal sampling have been

to be about 0.2°C during the early part of the record and decrease to 0.1°C during the more recent part. This is a key figure. The linear trend over the full period is 0.08°C/decade, that over the last 100 years is 0.10°C/decade and that over the last 50 years is 0.18°C/decade.

Explore Temperature Data Go to NOAA’s Climate at a Glance website to explore their global temperature data. Select “annual” to get the annual averages. Now list the 20 warmest years by clicking on the ANOMALY column in the table below until you have the warmest year listed on top. Which is the record warmest year? How many of the 20 warmest years have occurred since the year 2000? Click on the “Display Trend” button and enter different start and end dates. What is the trend over the last 50 (last 100) years? Interested in how temperature measurements from long ago have been recorded? Have a look at this fascinating interactive article.

The increase in atmospheric temperatures over the last 100 years has not been uniform everywhere. Fig. 2 shows that temperatures over land changed more than over the oceans and the Arctic warmed more than the tropics. These patterns are called land-sea contrast and polar amplification and are quite well understood and simulated in climate models as we will see later. The warming is indeed almost global. The only exception is the northern North Atlantic, which has been slightly cooling for reasons we will discuss later.

Analysis of thousands of temperature records into an estimate of global mean temperature change such as Fig. 1 is not trivial. Issues such as changes in station locations, instrumentation and data coverage have to be taken into account. The fact that five different groups analyzing the data using different methods come to the same conclusions suggests that the results are robust. The reliability of the data has been demonstrated and it has been shown that station locations (e.g. urban versus rural) don’t matter. See this blog for more discussion.

The global warming trend has made the probability of warm and extreme warm temperatures more likely and the probability of cold and extreme cold temperatures less likely. E.g. extremely warm (more than 3°C warmer than the 1951 to 1980 average) summer temperatures over Northern Hemisphere land areas had only a 0.1% chance of happening from 1951 to 1980, whereas during the decade from 2005 to 2015 the chance of those extreme warm temperatures to occur was 14.5%. Conversely, relatively cold summer temperatures (less than 0.5°C cooler than the 1951-1980 average) that happened about every third year from 1951 to 1980 only occurred 5% of the time during 2005 to 2015. See this article and this blog for additional information and graphs.

b) Cryosphere

One of the most sensitive regions to climate change is the Arctic. Sea ice cover there has decreased dramatically over the past 40 years particularly in late summer (Fig. 3). Arctic sea ice experiences a strong seasonal cycle. In late winter it covers about 15.4×106 km2 and decreases to about 6.4×106 km2 in late summer (Fig. 4). Therefore, the relative changes are larger in late summer, with a reduction of about 46 % or 2.9×106 km2 from 1980 to 2015. In winter the reduction was only about 9 % or 1.5×106 km2. The lost area of summer Arctic sea ice is more than 10 times the size of Oregon (255,000 km2) or four times the size of France (~650,000 km2).

In the Antarctic, sea ice experiences an even larger seasonal cycle but it has changed less over the last 40 years compared to the Arctic. Southern hemisphere sea ice has slightly increased. Note that year-to-year fluctuations are larger Antarctic than in the Arctic, whereas the long term trends in the Antarctic are much smaller than in the Arctic. This combination of larger short-term fluctuations and a smaller long-term trend makes Antarctic sea ice trends less statistically significant. A trend is statistically significant if it is larger than the uncertainties from short term fluctuations. Globally, Earth has lost about 2 million square kilometers of sea ice from 1980 to 2015, which is about 10% of the total. Compare that area to that of your favorite state or country. Explore Sea Ice Changes Go to the National Snow and Ice Data Center’s (NSIDC) website and click on a few years to see how Arctic sea ice cover has changed over the year. To get a time series for the current month go to their sea ice index site and click on the Monthly Sea Ice Extent Anomaly Graph in the lower right corner. By how much has the sea ice cover decreased since the 1980s? Estimate the decrease both in relative terms (percentage) and in absolute terms (million square kilometers). An animation is available here. Mountain glaciers are also sensitive to climate change. Fig. 5 shows an example from Muir Glacier, which has retreated dramatically since 1941. This is typical for most glaciers around the world. In fact, only a small number of glaciers show advances, whereas the vast majority of glaciers melt and retreat from the valleys up into higher elevations.
The World Glacier Monitoring Service (WGMS) has compiled information on hundreds of glaciers world-wide. Fig. 6 shows that since 1980 glaciers in all regions have been losing mass with an acceleration of loss in recent years. Watch this video of glacier changes in Iceland. Figure 6: Cumulative mass balance in meters water equivalent (w.e.) of mountain glaciers. From the World Glacier Monitoring Service. Explore Glacier and Ice Sheet Change Go to the Glacier Browser and select a glacier of your choice. What do you observe? Explore Greenland ice sheet change with this interactive chart, which shows the surface area experiencing melting. Click on a few years in the early part of the record (e.g. 1980s) and in the more recent part (e.g. 2010s). How has the melt area changed? Ice sheets are also melting. Observations from the Gravity Recovery and Climate Experiment (GRACE) satellites, which measure very precisely Earth’s gravity field and can detect changes in mass, show that since 2002 the Greenland ice sheet has lost about 4,000 Gt of mass, and the Antarctic ice sheet has lost about 2,500 Gt (Fig. 7). Here is a presentation about Greenland melting. Melting of the Greenland ice sheet contributes currently about 0.8 mm/yr to global sea level rise. Antarctica’s contribution is 0.4 mm/yr and mountain glaciers add about 0.6 mm/yr, for a total of 1.8 mm/yr sea level rise from melting of ice (IPCC 2019). Box 1: Rates of Change The rate of change of a variable X between two points in time t1 and t2 can be calculated as the difference (denoted by the greek letter delta Δ) of the value of the variable at time t2 minus the value of the variable at time t1 ΔX = X2 – X1 divided by the difference in time Δt = t2 – t1 (B1.1) Thus the units of the rate of change are the units of the variable divided by time. You can determine the rate of change from a timeseries graph such as Fig. 1 or Fig. 6 by selecting two points in time on the horizontal axis and reading the corresponding values of X1 and X2 from the vertical axis. Using Fig. 1 as an example our variable will be the temperature anomaly T. Choosing t1 = 1940 and t2 = 2010 we can read off T1 = 0ºC and T2 = 0.7ºC. Thus, ΔT = 0.7ºC, Δt = 70 years and the rate of change ΔT /Δt = 0.01ºC/yr = 0.1ºC/decade. Obviously, calculating the rate of change in this way the resulting value will depend on the two times picked. The rate of change of a whole set of data points can be calculated by assuming a linear relationship and minimizing the distance of all points from a straight line X = S×t + I, where S is the slope and I the intercept with the vertical axis. This is called linear regression. Simple formulae to calculate S and I can be found here. Linear regressions are commonly used to estimate rates of change. E.g. the straight lines in Fig. 4 in this chapter and Figs. 7-12 in chapter 1 have been calculated using the formulae for linear regression. Regression lines are also often referred to as trend lines. c) Ocean Subsurface temperature measurements in the oceans document warming over the last 60 years (Fig. 8). The ocean’s heat content has increased by about 30×1022 Joules during that time. The heat content of the ocean is its temperature T times the heat capacity of water cp = 4.2 J/(gK). Prior to 2005 subsurface temperature measurements were more limited in space and time because they were taken from ships by lowering CTD (conductivity, temperature, depth) instruments on a cable into the ocean. Since 2005 autonomous, free-drifting Argo floats measure temperature, salinity, pressure, and velocity of the upper 2 km of the water column. Currently there are about 4,000 floats out there, which provide much better spatial and temporal coverage than the previous ship-based measurements. The melting of mountain glaciers and ice sheets leads to increased runoff into the ocean, which contributes to sea level rise (Fig. 9). Sea level rise is also caused by warming sea water, which causes expansion and by increased runoff from pumping of groundwater out of aquifers. Estimates based on tide gauge records indicate that sea level has risen by about 20 cm from the 1870s to the year 2000 and another 6 cm since. The melting of mountain glaciers and ice sheets contributes about similarly to the current sea level rise, but if current trends continue it is likely that many mountain glaciers will completely disappear and the large ice sheets will contribute more and more to global sea level rise. Note that sea level rise is not spatially uniform. Explore Sea Level Changes Goto noaa.gov and explore local sea level changes from tide gauges. Where is sea level increasing? Where is it decreasing? Select a tide gauge. What is the time period covered? Here is a map of sea level measured from satellites. What time period is covered by the satellite data? Where is sea level increasing? Where is it decreasing? d) Biosphere and Carbon Cycle Plant and animal species have been observed to move poleward and upward in the mountains (Parmesan and Yohe (2003). This response is consistent with global warming and the tendency of organisms to stay in a temperature range to which they have adapted. Flowering dates of many plants have also shifted earlier in the spring such as for cherry blossoms. Carbon dioxide (CO2) has been measured in the atmosphere since 1958 at Mauna Loa Observatory in Hawaii (Fig. 10). At that time concentrations were just below 320 parts per million (ppm). Subsequently they increased to values of just over 400 ppm today. That is a 25 % increase. Overlaid on the long term trend is a seasonal cycle. Growth of the terrestrial biosphere in northern hemisphere spring leads to CO2 drawdown and decay of organic matter such as fallen leaves increases CO2 in the fall. As we will see later, CO2 is an important greenhouse gas, and its increase over the past decades is the main cause of the recent global warming. Figure 10: Atmospheric CO2 measured at Hawaii’s Mauna Loa Observatory. The measurements were pioneered by Charles Keeling from Scripps Institution of Oceanography in 1958. From noaa.gov. Explore Carbon Cycle Data Goto noaa.gov to explore CO2 data from other locations. Select a site and then “Carbon Cycle Gases” on the left and then “Timeseries”. Describe the observations. Questions Ask your parents or grandparents if they have noticed signs of climate changes during their lifetimes. My dad told me that as a boy he used to snow sled down the slopes of a hill in Germany where nowadays there is no more snow. By how much did global surface air temperatures increase during the last 100 years? How do we know? What was the average rate of change during that time? What was the rate of change for the last 50 years? Where was the warming larger over the oceans or over land, in the tropics or at high latitudes? How much did the upper 2 km ocean heat content change over the last 60 years? How do we know? What was the rate of change? What was the rate of change during the last 20 years? How much did the area covered by Arctic sea ice change during the last 35 years? How do we know? How have the Greenland and Antarctic Ice sheets changed during the last 15 years? How do we know? How much has global mean sea level risen since 1870? How do we know? Calculate the rate of change from 1870 to 2000. Calculate the rate of change from 2000 to the present. Has sea level rise accelerated? Check your answer with this paper. Videos Recorded Lecture: Observations Atmosphere Cryosphere Recorded Lecture: Observations Oceans Carbon References Parmesan, C., Yohe, G., 2003: A globally coherent fingerprint of climate change impacts across natural systems. Nature 421, 37–42, https://doi.org/10.1038/nature01286. Stocker, T.F., D. Qin, G.-K. Plattner, L.V. Alexander, S.K. Allen, N.L. Bindoff, F.-M. Bréon, J.A. Church, U. Cubasch, S. Emori, P. Forster, P. Friedlingstein, N. Gillett, J.M. Gregory, D.L. Hartmann, E. Jansen, B. Kirtman, R. Knutti, K. Krishna Kumar, P. Lemke, J. Marotzke, V. Masson-Delmotte, G.A. Meehl, I.I. Mokhov, S. Piao, V. Ramaswamy, D. Randall, M. Rhein, M. Rojas, C. Sabine, D. Shindell, L.D. Talley, D.G. Vaughan and S.-P. Xie, 2013: Technical Summary. In: Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change [Stocker, T.F., D. Qin, G.-K. Plattner, M. Tignor, S.K. Allen, J. Boschung, A. Nauels, Y. Xia, V. Bex and P.M. Midgley (eds.)]. Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA. Available at ipcc.ch. Randall, M. Rhein, M. Rojas, C. Sabine, D. Shindell, L.D. Talley, D.G. Vaughan and S.-P. Xie, 2013: Technical Sum­mary. In: Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assess­ment Report of the Intergovernmental Panel on Climate Change [Stocker, T.F., D. Qin, G.-K. Plattner, M. Tignor, S.K. Allen, J. Boschung, A. Nauels, Y. Xia, V. Bex and P.M. Midgley (eds.)]. Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA. Available at ipcc.ch. IPCC, 2019: Summary for Policymakers. In: IPCC Special Report on the Ocean and Cryosphere in a Changing Climate [H.-O. Pörtner, D.C. Roberts, V. Masson-Delmotte, P. Zhai, M. Tignor, E. Poloczanska, K. Mintenbeck, M. Nicolai, A. Okem, J. Petzold, B. Rama, N. Weyer (eds.)]. Available at ipcc.ch. Links https://en.wikipedia.org/wiki/Instrumental_temperature_record https://www.skepticalscience.com/urban-heat-island-effect-basic.htm 3 3. Paleoclimate Measurements with modern instruments (the instrumental record) are available only for roughly the past century. This is insufficient to describe the full natural variability of the climate system, which makes attribution of observed changes difficult. We want to know if the changes observed in the recent past are unusual compared to pre-industrial climate variability. If they are it is more likely that they are anthropogenic, if not they could well be natural. Paleoclimate research is also important for a fundamental understanding of how the climate system works. Some paleoclimate changes, e.g. the ice age cycles, were much larger than those during the instrumental record. Thus, we can learn much from paleoclimate data about the impacts of large climate changes. a) Methods Paleoclimate research is able to extend the instrumental record back in time much further than the instrumental record and has delivered a fascinating history of past climate changes. Most paleoclimate evidence is indirect and based on proxies for climate variables. This evidence is less precise than measurements with modern instruments because of the additional uncertainty in the relation between the proxy and the climate variable. Examples for proxies are pollen (Fig. 1) found in lake sediments that can be used to reconstruct past vegetation cover, which in turn can be related to temperature and precipitation. Similarly, different species of planktic foraminifera prefer different temperatures. Some live in colder waters others prefer warmer waters. Their fossil shells accumulate in sediments, which can be retrieved with a coring device employed from a research vessel. Shells deeper in the sediment are older. If shells of cold-loving foraminfera are found at a site where currently warm-loving species live, it suggests that near surface temperatures in the past have been colder. Mathematical methods have been developed to quantify the temperature changes from the species composition. Other proxies are chemical such as the ratio of magnesium to calcium (Mg/Ca), which is related to temperature, or isotopes of oxygen or carbon in the calcium carbonate shells of foraminifera, which can be used to reconstruct temperature, salinity, ice volume and carbon cycling. Benthic foraminifera live on or in the ocean’s sediments and thus provide useful information on deep ocean properties. Here is an excellent interactive post about paleoclimate proxies. Figure 1: Electron microscope pictures of fossil foraminifera (top, two planktic foraminifera on top and one benthic foraminifera on the bottom) and pollen (bottom).
Proxies are found in different archivessuch as tree-rings, ice-cores, corals, ocean or lake sediment cores that cover different time periods at a range of temporal resolutions (Fig. 2). The resolutionof a record can be quantified as the time difference Δt= t2– t1between two adjacent samples t1and t2. The smaller Δtthe higher the resolution. Written historical accounts can be used to reconstruct past climatic conditions at very high temporal resolution – some ancient documents contain daily weather entries – back to about 1,000 years, but there are only a limited number of such records available. Tree-rings, corals and speleothems (cave deposits such as stalactites and stalagmites) provide reconstructions at annual to decadal resolution (Δt ~ years to decades) back many thousands of years. Ice cores have typically decadal to centennial resolution going back almost a million years for Antarctica and about 100,000 years for Greenland. Ocean sediment cores cover millions of years in the past but usually at low temporal resolution of centennial to millennial timescales (Δt ~ 100s to 1,000s of years). Several methods are used to date samples to construct chronologiesof paleoclimate records. Tree-rings are annual layers, which can be counted. Patterns of thin and thick rings can be matched from one tree to another, older one (Fig. 3). This way a large number of trees can be used to create a long layer-counted chronology. Layer counting can also be used in other archives with annual layers such as ice cores or lake sediments. Most ocean sediments don’t have annual layers because of bioturbation, which is the mixing of sediments by worms and other organisms that live in the sediment. When organic material is present radiocarbon dating can be used to determine the age of a sample. Radiocarbon (14C) decays exponentially with a half-life of 5,730 years. Thus, the lower the ratio of radiocarbon to regular carbon (14C/12C) in a sample, the older it is. This ratio can be measured precisely with a mass spectrometer. However, this method can only be used until about 40,000 years before the present because older material has unmeasurably small amounts of 14C. b) The Last Two Millennia Historical accounts such as pictures of the frozen Thames (Fig. 4) document a period of relatively cold conditions during the 16th to 19th centuries in Europe called the Little Ice Age. Conversely, relatively warm conditions during the 9th to 13th centuries, called the Medieval Warm Period, may have allowed Vikings to colonize Greenland and travel to North America. Figure 4: Left: Picture of the frozen Thames from 1683-84 by Thomas Wyke. Right: Ruins of Hvalsey Church from the Greenland settlements of the Norse.
Two recent reconstructions of global temperatures, however, indicate that the Medieval Warm Period was not a global phenomenon (Fig. 5). These reconstructions also suggest that there was a long term cooling trend during the past 2,000 years that culminated in the Little Ice Age, which was terminated by a relatively rapid warming during the 20th century. According to the PAGES 2k reconstruction global average temperature during the three decades from 1971 to 2000 was warmer than at any other 30-year period in the last 1,400 years. This suggests that the recent warming is unusual. The rate of change during the last ~100 years also seems to be unusually fast compared with the previous 2,000 years. The two independent reconstructions agree well in the cooling trend over the past 1,000 years, but the PAGES 2k reconstruction suggests slightly warmer conditions during the first millennium CE (Common Era). The Marcott et al. (2013) dataset is based mostly on lower resolution ocean sediment cores and is therefore smoothed compared to the higher resolution PAGES 2k dataset, which includes mostly land data such as pollen and tree rings. c) The Holocene Fig. 6 shows the full Holocene (the last 10,000 years) reconstruction of global average temperatures from Marcott et al. (2013). It suggests that the long term cooling trend of the last 2,000 years is part of a longer trend that extends back in time to the middle Holocene around 4,000 BC. The early Holocene from around 8,000 BC to 4,000 BC was relatively warm, similarly to recent decades. (This is debated in the scientific community; a recent paper suggest that it wasn’t warmer during the early Holocene and that biases in proxies related to seasonality are to blame. If this is true, the current warming will be unprecedented for more than 10,000 years, perhaps more than 100,000 years or longer.) The rate of temperature change appears to be much smaller compared with the last 100 years, but the relatively low resolution of the reconstruction leads to smoothing and does not allow a fair comparison with the instrumental record on 100 year timescales. Now let’s have a look at CO2. Is the observed increase in atmospheric CO2 during the last 60 years unusual compared to the pre-industrial Holocene? Ice cores can be used to answer this question. When snow accumulates on an ice sheet it compresses to firn and later to ice due to the pressure of the overlaying snow (Fig. 7). During this compaction process small bubbles of air are trapped within the ice. In the lab the air can be extracted from the ice, e.g. by mechanically crushing the ice, and its CO2 concentration, and other greenhouse gases, can be measured.	Figure 7: Ice cores have been drilled in different locations in Antarctica (top left) using drilling devices like the one depicted here (top center). Air gets trapped in the ice through compaction of snow and firn (top right). These air bubbles in the ice are visible by eye (bottom left) and in the microscope (bottom center). Sometimes dark ash layers are found in ice cores, which can help to date the ice (bottom right).	Ice cores from Greenland are not suitable for CO2reconstructions because they are contaminated by impurities (e.g. dust) that can lead to CO2production in the ice. However, Antarctic ice is so pure that it provides excellent records of past atmospheric CO2concentrations. Different ice cores have been drilled in Antarctica (Fig. 7). The measurements from the youngest ice and firn match up very well with the direct measurements of modern air from Mauna Loa (Fig. 8). Also, the measurements from different ice cores agree with each other (different colored symbols in Fig. 8). This indicates that Antarctic ice cores faithfully record past atmospheric CO2concentrations. The results show that atmospheric CO2concentrations have been relatively constant between about 260 and 280 ppm during the Holocene (the last 10,000 years). It was only during the last 200 years that CO2concentrations started to increase. Thus, we have answered the question posed above and conclude that the CO2increase during the last 200 years is very unusual and has not happened before during the last 10,000 years. We also know that burning of fossil fuels has increased dramatically after the industrial revolution (1760-1840). In the carbon cycle chapter below, more evidence will be presented that demonstrates that the subsequently observed CO2increase was indeed due to human activities such as the burning of fossil fuels. Other greenhouse gases have also been measured in air extracted from ice cores. Methane (CH4) and nitrous oxide (N2O) show a very similar behavior to CO2, such that their concentrations were relatively constant throughout the Holocene around 700 ppb and 260 ppb, respectively, and increased dramatically during the last 200 years to values around 1,700 and 310 ppb, respectively (IPCC, 2007). d) The Ice Ages Fig. 6 already hints at a cold period before the Holocene. Indeed we now know that for a long time Earth had been in an ice age, or glacial state, before the current warm period of the Holocene begun. But it was only in the 19th century that scientists realized that Earth has experienced ice ages on a global scale. This discovery was made by Louis Agassiz, a Swiss geologist, who hypothesized that not only Alpine glaciers were advanced but also large ice sheets moved south from northern Europe and America leaving glacial landforms behind (Fig. 9). For a fascinating and more detailed account of this discovery the reader is referred to Imbrie and Imbrie (1979). Figure 9: Glacial Landforms. Top: Polished bedrock with striations indicate a glacier was moving over it. The glacier incorporates rocks into its base and by pushing them over the underlying bedrock creates grooves. This example is from Mount Rainier National Park. Bottom left: Moraines (this example is from Svalbard) are glacial deposits formed at the side (lateral moraines) or end (terminal moraines) of a moving glacier. Bottom right: Erratic boulders like this one from Scotland, many miles from a possible bedrock source, have been attributed by Louis Agassiz to the action of ice-age glaciers.
During the height of the last ice age, the Last Glacial Maximum (LGM) roughly 20,000 years ago, large additional ice sheets covered parts of North America and northern Europe (Fig. 10). The Laurentide Ice Sheet was more than 3 km thick and covered all of what is now Canada and part of the northern United States reaching as far south as New York City, Chicago, and Seattle. The Eurasian (or Fennoscandian) Ice Sheet covered all of Scandinavia, much of the British isles, the Baltic Sea, and surrounding land areas from northeastern Germany to northwestern Russia. Mountain glaciers also descended further down valleys and often into the low lands. Because so much more water was locked up as ice on land, sea level was 120 m lower during the LGM than it is today. Imagine your favorite beach of today. There was no water there at the LGM. Explore with NOAA’s interactive bathymetry viewer how much further it would have been to the water during the LGM at your favorite beach. The LGM is a well-studied time period in paleoclimate research, and we have a wealth of data available. Ice cores show lower concentrations of atmospheric greenhouse gases such as CO2 (180 ppm vs 280 ppm during the late pre-anthropogenic Holocene; Fig. 11) and methane. Vegetation reconstructions show that forests were replaced by tundra and grasslands over large parts of the mid- to high latitudes (Prentice et al., 2011). We also know from ice and ocean sediment cores that the air was dustier. Temperature proxies show colder temperatures almost everywhere (Fig. 10). However, temperature changes were not the same everywhere. Temperature changes over large parts of the tropical and subtropical oceans were rather small. Globally-averaged sea surface temperatures have been estimated to be only 2°C cooler than the present (MARGO, 2009). Land areas in the tropics experienced moderate cooling of about 3°C (Bartlein et al., 2011). The largest cooling of more than 8°C occurred over land at mid-to-high latitudes and over Antarctica (Fig. 11). Globally averaged surface air temperature has been estimated to be 4°C colder during the LGM (Annan and Hargreaves, 2013). More recent, yet unpublished studies suggest 5°C indicating some uncertainty in these estimates. These authors also suggest that on average the cooling over land was 3 times larger than over the oceans. The land-sea contrast and polar amplification are similar to what we’ve seen in observed warming over the past century (Fig. 2 in Chapter 2). This suggests that those are robust properties of the climate system. Box 1: Oxygen Isotopes Isotopes are variations of the same element with a different number of neutrons, which leads to a different mass (Fig. B1). Since different isotopes of the same element have the same number of electrons (yellow circles in Fig. B1) they react chemically identically or very similar. Water molecules (H2O) with 18O are (20 – 18)/18 = 11% heavier than those with 16O. The mass of a molecule affects how likely it will participate in a phase change such as evaporation or condensation. Water molecules at a certain temperature in the water phase have a distribution of kinetic energy Here is an analogy. Imagine a number of black and white soccer balls are lined up at the center line of a soccer field. The black balls are slightly heavier than the white balls. Now a player will shoot the balls, one after another, alternatively black and white, towards the goal. When he/she is done you count the balls that made it across the goal line. Will there be more black or white balls? Yes, indeed, more white balls, because they are lighter and they fly farther due to larger velocities put in by the player who exerts about the same amount of energy for each shot. In this analogy the white balls are the light isotopes. Isotopes are usually expressed as delta values such as Figure B2: Typical δ18O values (in permil). Surface ocean water has δ18O values of around zero. Due to fractionation during evaporation less heavy isotopes make it into the air, which leads to negative delta values of around -10 ‰. Condensation prefers the heavy isotopes for reasons analogous to evaporation. In this example the first precipitation thus has a δ18O value of about -2 ‰, the remaining water vapor will be further depleted in 18O relative to 16O thus that its δ18O value is approximately -20 ‰. Any subsequent precipitation event further depletes 18O. This process is known as Rayleigh distillation and leads to very low δ18O values of less than -30 ‰ for snow falling onto ice sheets. Thus, ice has very negative δ18O of between -30 and -55 ‰. Deep ocean values today are about +3 to +4 ‰. During the LGM, as more water was locked up in ice sheets, the remaining ocean water became heavier in δ18O by about 2 ‰. We know this because foraminifera build their calcium carbonate (CaCO3) shells using the surrounding sea water. Thus they incorporate the oxygen isotopic composition of the water into their shells which are preserved in the sediments and can be measured in the lab. We conclude that paleoclimate data from the LGM show that Earth was dramatically different from today, with large ice sheets, low sea level, and different vegetation. These changes happened even though the global average temperatures changed only by 4-5°C. This is comparable to changes projected for some future scenarios. Geologic evidence such as that shown in Fig. 9 is abundant only for the last major glaciation because each glacial advance erases evidence from previous glaciations. However, because of our friends, the foraminifera, we know many details of previous glaciations. How can that be? Foraminifera live in the ocean. Well, as explained in the box, the δ18O of sea water records the amount of ice volume and thus sea level. Since foraminifera record the δ18O of sea water in their shells, we can amazingly reconstruct past ice volume from tiny shells found in mud on the ocean floor. Fig. 11 shows that there were about 9 glacial-interglacial cycles during the past 800,000 years. Most of the time sea level was lower than today, during some of the glacial maxima by more than 120 m. Ice core records show that glacial periods were always associated with low atmospheric CO2 concentrations and low temperatures in Antarctica. CO2 concentrations varied between about 180 ppm during glacial maxima and 280 ppm during interglacials. The correlation between these completely independent datasets, one from Antarctic ice cores, the other from deep sea foraminifera, is astounding. It demonstrates that climate and the carbon cycle are tightly interlinked. High CO2 concentrations are always associated with warm temperatures, high sea level, and low ice volume. This indicates the importance of atmospheric CO2 concentrations for climate but it also suggests that climate impacts the carbon cycle and causes changes in CO2. Closer inspection of leads and lags shows that during the last deglaciation CO2 and Antarctic temperature lead global temperature, which suggests that CO2 is an important forcing mechanism for the warming (Shakun et al., 2012). But we also know that climate affects the carbon cycle. For example, CO2 is more soluble in colder water, which causes the ice age ocean to take up additional carbon from the atmosphere. Another likely reason for the lower glacial CO2 concentrations in the atmosphere is iron fertilization. The colder glacial atmosphere was also dustier. Dust contains iron and thus iron delivery to currently iron limited regions such as the Southern Ocean was increased during the ice age. This intensified phytoplankton growth and the biological pump, which describes processes of sinking and sequestering of carbon in the deep ocean. Our recent research indicates that about half (~45 ppm) of the glacial-interglacial CO2 variations can be explained by temperature and another 25-35 ppm by iron fertilization (Khatiwala et al., 2019). However, this topic is not settled and subject to ongoing research. More about how climate can affect CO2 will be discussed in the carbon cycle chapter. For now let’s just conclude that climate and the carbon cycle are tightly linked. But what causes glacial-interglacial cycles? They are caused by changes in Earth’s orbit around the sun, which affects the seasonal distribution of incoming solar radiation. This theory was proposed in 1938 by Serbian astronomer Milutin Milankovich, who calculated effects of variations in Earth’s orbital parameters on solar radiation and linked those to past ice ages. Earth’s orbit can be described by three parameters (Fig. 12). The eccentricity E is the deviation from a perfectly circular orbit. Earth’s orbit is a slight ellipse although it is close to circular. E varies on ~100,000 year cycles between zero and 0.06. The tilt T, or obliquity, describes the angle between Earth’s axis of rotation and the ecliptic, which is the plane of Earth’s orbit around the sun. It is currently T = 23.5° but it varies between 24.5° and 22.5° on a 40,000 year cycle. Precession P is the wobble of Earth’s axis, like the wobble of a top. Currently we’re closest to the sun in January, which corresponds to the axis tilted towards the left in Fig. 12. P varies on a 23,000 year cycle and is strongly modulated by eccentricity. These variations are caused by gravitational forces from the other planets, particularly Jupiter and Saturn.	Figure 12: Milankovitch Cycles. Top: Earth’s orbit around the sun is determined by eccentricity (E), tilt (T) or obliquity, and precession (P). Bottom: Variation of Earth’s orbital parameters through time. Negative numbers towards the left show the past and positive numbers show the future.
The idea, proposed by the Irish intellectual Joseph John Murphy and promoted by Milankovitch, Wladimir Köppen and Alfred Wegener, is that summer insolation in the northern hemisphere controls the waxing and waning of the ice sheets (Berger, 2021). When summer insolation is high, all snow from the previous winter will melt away. When summer insolation is low, some snow survives and during the next winter more snow accumulates. In this way, an ice sheet can grow. The northern hemisphere is important because that is where the major land masses are, where additional ice sheets can grow. The Antarctic ice sheet did not fundamentally change during the ice ages, although it grew somewhat bigger during the ice ages and shrunk a bit during interglacials and the Patagonian ice sheet was much smaller than those in the north. The orbital forcing theory was essentially confirmed by spectral analysis of deep sea δ18O data, which shows all the predicted periodicities (Hays et al., 1976). However, exactly when and why ice ages start and end remain active topics of research. While the orbital forcing theory explains the cyclicity and timing of glacial-interglacial cycles it does not explain their amplitudes (how much global average temperatures have changed). Simulations with global climate models show that the amplitude of glacial-interglacial temperature changes can only be reproduced if CO2 changes are accounted for (e.g. Shakun et al., 2012). This leads us to conclude that CO2 changes are an important (feedback) factor in determining glacial-interglacial temperature changes although the ultimate cause of the ice age cycles are Earth’s orbital cycles. Questions What are paleoclimate proxies? What is a paleoclimate archive? Which paleoclimate record has higher resolution: record A, which has data every 100 years, or record B, which as data every 1,000 years? What is a chronology? Name two methods that are used to date paleoclimate samples? How much colder was global average surface air temperatures during the LGM? How much colder was global average sea surface temperatures during the LGM? How much lower was global sea level during the LGM? How much lower was atmospheric CO2 during the LGM compared to the pre-industrial late Holocene? What is the Milankovich theory? How do we know the extent of glaciation during the last ice age? How do we know sea level and ice volume during previous glaciations? Videos Lecture: Last 2,000 Years, Holocene Lecture: Ice Ages Isotopes Lecture: Milankovitch YouTube: How Ancient Ice Proves Climate Change Is Real from It’s Okay To Be Smart References Annan, J. D., and J. C. Hargreaves (2013), A new global reconstruction of temperature changes at the Last Glacial Maximum, Clim Past, 9 (1), 367-376, doi:10.5194/cp-9-367-2013. Bartlein, P., et al. (2011), Pollen-based continental climate reconstructions at 6 and 21 ka: a global synthesis, Clim Dynam, 37, 775-802, doi:10.1007/s00382-010-0904-1. Berger, A. (2021) Milankovitch, the father of paleoclimate modeling, Clim. Past, 17, 1727–1733, https://doi.org/10.5194/cp-17-1727-2021. Hays, J. D., J. Imbrie, and N. J. Shackleton (1976), Variations in Earths Orbit – Pacemaker of Ice Ages, Science, 194 (4270), 1121-1132, doi:10.1126/science.194.4270.1121. IPCC (2007) Summary for Policymakers. In: Climate Change 2007: The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change [S. Solomon, D. Qin, M. Manning, Z. Chen, M. Marquis, K. B. Averyt, M. Tignor, H. L. Miller, (eds.)]. Cambridge University Press, Cambridge, United Kingdom, New York, NY, USA. Imbrie, J., and K. P. Imbrie (1979) Ice ages: solving the mystery, Harvard University Press, Cambridge Massachusetts and London, England, 224 pp, ISBN 9780674440753. Jouzel, J., et al. 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Theory We have seen how global climate has changed and we’ve learned that some of these changes have been related to forcings and feedbacks such as atmospheric CO2 concentrations and the seasonal distribution of solar irradiance. Now we want to proceed to understand quantitatively why climate is changing. To do this we will consider Earth’s energy budget, review what electromagnetic radiation is, how it interacts with matter, how it passes through the atmosphere, and how this creates the greenhouse effect. But first, we will briefly discuss the general budget equation because it is widely used by scientists and it will be used at different occasions throughout this book. Box 1: Budget Equation Scientists like to keep track of things: energy, water, carbon, anything really because it allows them to exploit conservation laws. In physics, for example, we have the law of energy conservation. It is the first law of thermodynamics and states that energy cannot be destroyed or created; it can only change between different forms or flow from one object to another. Similarly, the total amounts of water and carbon on earth are conserved although they may change forms or flow from one component to another one. To start, we need a well-defined quantity of interest. Let’s call that quantity X. It could be energy, water, carbon, or something else that obeys a conservation law. It can be restricted to a specific part or component of the climate system, e.g. water in the cryosphere. Mathematically a budget equation can be written as (B1.1) where the differentials ∂ denote an infinitesimally small change, t is time, I is the input, and O is the output. The left-hand-side of this equation is the rate-of-change of X. In practice the differentials can be replaced by finite differences (Δ) such that we get (B1.2) Finite differences can be easily calculated: ΔX = X2 – X1 and Δt = t2 – t1. Here X1 corresponds to the quantity X at time t1 and X2 correspond to the quantity X at time t2. Note that the inputs and outputs have units of the quantity X divided by time. They are often called fluxes. Different boxes can be connected such that the output of one box becomes the input of another box. A budget is in balance if the quantity X does not change in time. In this case ΔX = 0 and the input equals the output: (B1.3) Let’s do a little example. Assume a student gets a monthly stipend of $1,000 and $400 from his/her parents. Those are the inputs to the student’s bank account in units of dollars per month I = $1,000/month + $400/month = $1,400/month. The outputs would be the student’s monthly expenses. Let’s say he/she pays $400 for tuition, $420 for rent, $390 for food, and $100 for books (not for this one though) such that O = $400/month + $420/month + $390/month + $100/month = $1,310/month. The rate-of-change of his/her bank account is ΔX/Δt = I – O = $1,400/month – $1,310/month = $90/month. The student saves $90 per month. Equation B1.2 can be used to predict the quantity X at time t2 (B1.4) from its value X1 at time t1 if the inputs and outputs are known. In climate modeling this method, called forward modeling, is used to predict quantities into the future one time step Δt at a time. In our example, if the student starts at time t1, let’s say in January, with X1= $330 in his/her bank account then we can predict that in February he/she will have X2 = $330 + ($1,400/month – $1,310/month)×(1 month) = $330 + $90 = $420. Note that in this case the time step Δt = 1 month. a) Electromagnetic Radiation Earth’s energy budget is determined by energy input from the sun (solar radiation) and energy loss to space by thermal or terrestrial radiation, which is emitted from Earth itself. Solar radiation has shorter wavelengths than terrestrial radiation because the sun is hotter than Earth. To understand this let’s consider the electromagnetic radiation spectrum (Fig. 1). Electromagnetic radiation are waves of electric and magnetic fields that can travel through vacuum and matter (e.g. air) at the speed of light (c). It is one way that energy can be transferred from one place to another. The wavelength of electromagnetic radiation (λ), which is the distance from one peak to the next, varies by more than 16 orders of magnitude. Visible light, which has wavelengths from about 400 nm (nanometers, 1 nm = 10-9 m = one millionth of a millimeter) to about 700 nm, occupies only a small part of the entire spectrum of electromagnetic radiation. The frequency (ν) times the wavelength equals the speed of light c = νλ. Albert Einstein showed in 1905 that electromagnetic radiation has particle properties. In modern quantum physics the light particle is called a photon. Each photon has a discrete amount of energy E = hv = hc/λthat corresponds to its wavelength, where h = 6.63×10-34 Js is Planck’s constant. The shorter the wavelength the higher the energy. High energy photons at ultraviolet, X-ray, and gamma ray wavelengths can be harmful to biological organisms because they can destroy organic molecules such as DNA. Interaction of electromagnetic radiation with matter depends on the wavelength of the radiation. Molecules have different discrete energy states and they can transition from one state to another one by absorbing or emitting a photon at a wavelength that corresponds to that energy difference (Fig. 2). Absorption (capture) of a photon leads to a transition from a lower to a higher energy state. Note that once absorbed the photon is gone and its energy has been added to the molecule. Emission (release) of a photon leads to a transition from a higher to a lower state (reversing the direction of the arrows in the top panel of Fig. 2). Note that the emitted photon can have a different wavelength that the absorbed photon. If, e.g., a UV photon was absorbed and has caused the energy of the molecule to increase from the ground electronic state to the second excited state, the molecule can emit two visible photons, first one that leads to a transition from the second to the first excited electronic state, and then another that leads to a transition to the ground state. In physics, a blackbody is an idealized object that can absorb and emit radiation at all frequencies. A blackbody emits radiation according to Planck’s law (Fig. 3). In classical physics experiments, a closed box covered on the inside with graphite is used to study its properties. It has only a small hole as an opening to measure the radiation that comes out of the box. Although a blackbody is an idealization many objects behave like a blackbody. Even fresh snow. Or the sun. Integration of the Planck curve overall frequencies results in the Stefan-Boltzmann law (1) which states that the total energy flux F in units of watts per square meter (Wm-2) emitted from an object is proportional to the absolute temperature of the object T in units of Kelvin (K) to the power four. The Stefan Boltzmann constant is σ = 5.67×10-8 Wm-2K-4 and ε is the emissivity (0 ε 1), a material-specific constant that allows for deviations from the ideal blackbody behavior (for which ε = 1). For ε = 1, F represents the area under the Planck curve. The emissivity for ice is 0.97, that for water is 0.96, and that for snow it is between 0.8 and 0.9. Thus, water and ice are almost perfect blackbodies, whereas for snow the approximation is less perfect but still good. Highly reflective materials such as polished silver (ε = 0.02) and aluminum foil (ε = 0.03) have low emissivities. Equation (1) states that any object at a temperature larger than absolute zero emits energy. The energy emitted increases rapidly with temperature. E.g. a doubling of temperature will cause its radiative energy output to increase by a factor of 24 = 16. Box 2: Earth’s Energy Balance Model 1 (Bare Rock) One or more interactive elements has been excluded from this version of the text. You can view them online here: https://open.oregonstate.education/climatechange/?p=104#video-104-1 Figure B2.1: Illustration of the ‘Bare Rock’ Energy Balance Model. Yellow arrows indicate solar radiation. The red arrow represents terrestrial radiation. We can now attempt to construct a simple model of the Earth’s energy budget in balance. The energy input is the absorbed solar radiation (ASR). The energy output is the emitted terrestrial radiation (ETR). Thus, equation B1.3 becomes (B2.1) The absorbed solar radiation can be calculated from the total solar irradiance (TSI = 1,370 Wm-2), which is the flux of solar radiation through a plane perpendicular to the sun’s rays. (TSI is also sometimes called the solar constant although it is not constant but varies slightly as we’ll see below.) Since Earth is a rotating sphere the amount of radiation received per area is S = TSI/4 = 342 Wm-2 because the area of a sphere is 4 times the area of a disc with the same radius. Part of the incident solar radiation is reflected to space by bright surfaces such as clouds or snow. This part is called albedo (a) or reflectivity. Earth’s average albedo is about a = 0.3. This means that one third of the incident solar radiation is reflected to space and does not contribute to heating the climate system. Therefore ASR = (1 – a) S = 240 Wm-2. Assuming Earth is a perfect blackbody ETR = σT4. With this equation B2.1 becomes (B2.2) and we can solve for T = ((1 – a) S / σ)1/4. Inserting the above values for a, S, and σ gives T = 255 K or T = -18°C, suggesting Earth would completely freeze over as illustrated by ice sheets moving from the pole to the equator in the above animation. This is of course not what is going on in the real world and Earth’s actual average surface temperature, which is about 15°C, is much warmer. What’s wrong with this model? It is bare rock without an atmosphere! The model works well for planets without or with a very thin atmosphere like Mars, but it fails for planets that have thick atmospheres with gases that absorb infrared radiation such as Venus or Earth. The concept of Earth’s energy balance goes back 200 years to French scientist Jean-Baptiste Fourier, as explained in this (1.5 h) documentary (discussion of Fourier’s contributions start at 9:52). Temperature is the macroscopic expression of the molecular motions in a substance. In any substance such as the ideal gas depicted in Fig. 4 molecules are constantly in motion. They bump into each other and thus exchange energy. A single molecule is sometimes slow and at other times fast, but it is their average velocity that determines the temperature of a gas. More precisely, the temperature of an ideal gas T ~ E is proportional to the average kinetic energy The lower panel in Fig. (3) shows blackbody curves for temperatures representative of the sun and Earth. Due to Earth’s lower temperature the peak in the radiation occurs at longer wavelengths around 10 μm in the infrared part of the spectrum. The sun’s radiation peaks around 0.5 μm in the visible part of the spectrum, but it also emits radiation at ultra-violet and near infrared wavelengths. Sunlight at the top-of-the-atmosphere is almost perfectly described by a blackbody curve (Fig. 5). Some solar radiation is absorbed by gases in the atmosphere but most is transmitted. b) The Greenhouse Effect Absorption by water vapor in the infrared and by ozone (O3) in the ultraviolet and scattering of light remove 25-30% of solar radiation before it hits the surface (Fig. 6). For Earth’s radiation, on the other hand, total absorption is with 70-85% much larger. The most important absorbers in the infrared are water vapor and CO2 whereas oxygen/ozone, methane, and nitrous oxide absorb smaller amounts. Gases that absorb infrared radiation are called greenhouse gases. There is only a relatively narrow window around 10 μm through which Earth’s atmosphere allows radiation to pass without much absorption. Thus, Earth’s atmosphere is mostly transparent to solar radiation, whereas it is mostly opaque to terrestrial radiation. Why is it that only certain gases in the atmosphere absorb infrared radiation? After all there is much more nitrogen (N2) and oxygen (O2) gas in the atmosphere than water vapor and CO2 (Fig. 7). However, nitrogen and oxygen gas both consist of two atoms of the same element. Therefore, they do not have an electric dipole moment, which is critical for the interaction with electromagnetic radiation. Gas molecules that consist of different elements like water or CO2, on the other hand, do have dipole moments and can interact with electromagnetic radiation. Since CO2 is a linear and symmetric molecule it does not have a permanent dipole moment. However, during certain vibrational modes (Fig. 7) it attains a dipole moment and can absorb and emit infrared radiation. Detailed spectroscopic measurements of absorption coefficients show thousands of individual peaks in the spectra for water vapor and CO2 caused by the interaction of vibrational with rotational modes and broadening of lines by collisions (e.g. Pierrehumbert, 2011). These data are used by detailed, line-by-line radiative transfer models to simulate atmospheric transmission, absorption, and emission of radiation at individual wavelengths. Figure 7:
Composition of the dry atmosphere. Water vapor, which is not included in the image, varies widely but on average makes up about 1 % of the troposphere.