climate | Azimuth

Putting the Earth in a Box

19 June, 2011

guest post by Tim van Beek

Fried on Mercury

Is it possible to fly to Mercury in a spaceship without being fried?

If you think it should be possible to do a simple back-on-the-envelope calculation that answers this question, you’re right! And NASA has already done it:

This is interesting for astronauts—but it’s interesting for a first estimation of the climate of planets, too. In particular, for the Earth. In this post, I would like to talk about how this estimate is done and what it means for climate science.

The Simplest Possible Model

How do physicists model a farm? They say: “First, let’s assume that all cows are spherical with homogeneous milk distribution”. – Anonymous

Theoretical physicists have a knack for creating the simplest possible model for very complicated systems and still have some measure of success with it. This is no different when the system is the whole climate of the earth:

The back-on-the-envelope calculation mentioned above has a name; people call it a ‘zero-dimensional energy balance model‘.

Surprisingly, the story of energy balance models starts with a prominent figure in physics and one of the most important discoveries of 20th century physics: Max Planck and ‘black body radiation’.

Black Body Radiation

Matter emits electromagnetic radiation—at least the matter that we know best. Physicists have also postulated the existence of matter out in space that does not radiate at all, called ‘dark matter’, but that doesn’t need to concern us here.

Around 1900, the German physicist Max Planck set out to solve an important problem of thermodynamics: to calculate the amount of radiation emitted by matter based on first principles.

To solve the problem, Planck made a couple of simplifying assumptions about the kind of matter he would think of. These assumptions characterize what is known in physics as a perfect ‘black body’.

A black body is an object that perfectly absorbs and therefore also perfectly emits all electromagnetic radiation at all frequencies. Real bodies don’t have this property; instead, they absorb radiation at certain frequencies better than others, and some not at all. But there are materials that do come rather close to a black body. Usually one adds another assumption to the characterization of an ideal black body: namely, that the radiation is independent of the direction.

When the black body has a certain temperature $T$ , it will emit electromagnetic radiation, so it will send out a certain amount of energy per second for every square meter of surface area. We will call this the energy flux and denote this as $f$ . The SI unit for $f$ is $W/m^2$ : that is, watts per square meter. Here the watt is a unit of energy per time.

This electromagnetic radiation comes in different wavelengths. So, can ask how much energy flux our black body emits per change in wavelength. This depends on the wavelength. We will call this the monochromatic energy flux $f_{\lambda}$ . The SI unit for $f_{\lambda}$ is $W/(m^2 \; \mu m)$ , where $\mu m$ stands for micrometer: a millionth of a meter, which is a unit of wavelength. We call $f_\lambda$ the ‘monochromatic’ energy flux because it gives a number for any fixed wavelength $\lambda$ . When we integrate the monochromatic energy flux over all wavelengths, we get the energy flux $f$ .

For the ideal black body, it turned out to be possible for Max Planck to calculate the monochromatic energy flux $f_{\lambda}$ , but to his surprise, Planck had to introduce in addition the assumption that energy comes in quanta. This turned out to be the birth of quantum mechanics!

Understanding Thermodynamics: The Planck Distribution

His result is called the Planck distribution:

$\displaystyle{ f_{\lambda}(T) = \frac{c_1}{\lambda^5 (e^{c_2/\lambda T} - 1)} }$

Here I have written $c_1$ and $c_2$ for two constants. These can be calculated in terms of fundamental constants of physics. But for us this does not matter now. What matters is what the function looks like as a function of the wavelength $\lambda$ for the temperature of the Sun and the Earth.

As usual, Wikipedia has a great page about this:

• Black body radiation, Wikipedia.

The following picture shows the energy flux as a function of the wavelength, for different temperatures:

The Earth radiates roughly like the 300 kelvin curve and the Sun like the 5800 kelvin curve. You may notice that the maximum of the Sun’s radiation is at the wavelengths that are visible to human eyes.

Real surfaces are a little bit different than the ideal black body:

As we can see, the real surface emits less radiation than the ideal black body. This is not a coincidence: the black body is by definition the body that generates the highest energy flux at a fixed temperature.

A simple way to take this into account is to talk about a grey body, which is a body that has the same monochromatic energy flux as the black body, but reduced by a constant factor, the emissivity.

It is possible to integrate the black body radiation over all wavelengths, to get the relation between temperature $T$ and energy flux $f$ . The answer is surprisingly simple:

$f = \sigma \; T^4$

This is called the Stefan-Boltzmann law, and the constant $\sigma$ is called the Stefan-Boltzmann constant. Using this formula, we can assign to every energy flux $f$ a black body temperature $T$ , which is the temperature that an ideal black body would need to have to emit $f$ .

Energy Balance of Planets

A planet like Earth gets energy from the Sun and loses energy by radiating to space. Since the Earth sits in empty space, these two processes are the only relevant ones that describe the energy flow.

The radiation emitted by the Sun results at the distance of earth to an energy flux of about 1370 watts per square meter. We need to account for the fact, however, that the Earth receives energy from the Sun on one half of the globe only, on the area of a circle with the radius of the Earth, but radiates from the whole surface of the whole sphere. This means that the average outbound energy flux is actually $\frac{1}{4}$ of the inbound energy flux. (The question if there is some deeper reason for this simple relation was posed as a geometry puzzle here on Azimuth.)

So, now we are in a position to check if NASA got it right!

The Stefan-Boltzmann constant has a value of

$\sigma = 5.670 400 \times 10^{-8} \frac{W}{m^2 K^4}$

which results in a black body temperature of about 279 kelvin, which is about 6 °C:

$\frac{1370}{4} W m^{-2} \;\approx \; 5.67 \,\times \,10^{-8} \frac{W}{m^2 K^4} \, \times \, (279 K)^4$

That is not bad for a first approximation! The next step is to take into account the ‘albedo’ of the Earth. The albedo is the fraction of radiation that is instantly reflected without being absorbed. The albedo of a surface does depend on the material of the surface, and in particular on the wavelength of the radiation, of course. But in a first approximation for the average albedo of earth we can take:

$\mathrm{albedo}_{\mathrm{Earth}} = 0.3$

This means that 30% of the radiation is instantly reflected and only 70% contributes to heating earth. When we take this into account by multiplying the left side of the previous equation by 0.7, we get a black body temperature of 255 kelvin, which is -18 °C.

Note that the emissivity factor for grey bodies does not change the equation, because it works both ways: the absorption of the incoming radiation is reduced by the same factor as the emitted radiation.

The average temperature of earth is actually estimated to be some 33 kelvin higher, that is about +15 °C. This should not be a surprise: after all, 70% of the planet is covered by liquid water! This is an indication that the average temperature is most probably not below the freezing point of water.

The albedo depends a lot on the material: for example, it is almost 1 for fresh snow. This is one reason people wear sunglasses for winter sports, even though the winter sun is considerably dimmer than the summer sun in high latitudes.

Since a higher albedo results in a lower temperature for the Earth, you may wonder what happens when there is more snow and ice? This results in a lower absorption, which leads to less heat, which results in even more snow and ice. This is an example of positive feedback, which is a reaction that strengthens the process that caused the reaction. There is a theory that something like this happened to the Earth about 600 million years ago. The scenario is aptly called Snowball Earth. This theory is based on geological evidence that at that time there was a glaciation that reached the equator! And it works the other way around, too.

Since a higher temperature leads to a higher radiation and therefore to cooling, and a lower temperature leads to a lower radiation, according to the Planck distribution, there is always a negative feedback present in the climate system of the earth. This is dubbed the Planck feedback and has already been mentioned in week 302 of “This Weeks Finds” here on Azimuth.

Now, the only variable that a zero dimensional energy balance model calculates is the average temperature of earth. But does it even make sense to talk about the “average” temperature of the whole planet?

The Role of the Atmosphere and Rotation

It is always possible to “put a planet into a box”, calculate the inbound energy flux, and compute from this a black body temperature $T$ —given that the inbound energy per second is equal to the outgoing energy per second, which is the condition of thermodynamic equilibrium for this system. We will always be able to calculate this temperature $T$ , but of course there may be very strange things going on inside the box, that make it nonsense to talk about an average temperature. As far as we know, one side of the planet may be burning and the other side may be freezing, for example.

For planets with slow rotation and no atmosphere, this actually happens! This applies to Mercury and the moon of the Earth, for example. In the case of Earth itself, most of the heat energy is stored in the oceans and it spins rather fast. This means that it is not completely implausible to talk about a ‘mean surface air temperature’. But it could be interesting to take into account the different energy input at different latitudes! Models that do that are called ‘one-dimensional’ energy balance models. And we should of course take a closer look at the heat and mass transfer processes of the earth. But since this post is already rather long, I’ll skip that for now.

The Case of the Missing 33 Kelvins

The simple back-of-the-envelope calculation of the simplest possible climate model shows that there is a difference of roughly 33 kelvin between the black body temperature and the mean surface temperature on earth.

There is an explanation for this difference; I bet that you have already heard of it! But I’ll postpone that one for another post.

If you would like to learn more about climate models, you should check out this book:

• Kendal McGuffie and Ann Henderson-Sellers, A Climate Modelling Primer, 3rd edition, Wiley, New York, 2005.

Whenever I wrote “NASA” I was actually referring to this paper:

• Albert J. Juhasz, An analysis and procedure for determining space environmental sink temperatures with selected computational results, NASA/TM—2001-210063, 2001.

The pictures of black body radiation are taken from this book:

• Frank P. Incropera, David P. DeWitt, Theodore L. Bergman, Adrienne S. Lavine, Fundamentals of Heat and Mass Transfer, 6th edition, Wiley, New York, 2006.

Being Cool on Mercury

I want to paint it black. — The Rolling Stones

Last but not least: you can fly to Mercury without getting fried… but you have to paint your spaceship white in order to get a higher albedo.

Really? Well, it depends on the albedo of the whitest paint you can find: the one that reflects the Sun’s energy flux the most.

So, here’s a puzzle: what’s the whitest paint you can find? What’s its albedo? And how hot would a spaceship with this paint get, if it were in Mercury’s orbit?

89 Comments | climate | Permalink
Posted by John Baez

Your Model Is Verified, But Not Valid! Huh?

12 June, 2011

guest post by Tim van Beek

Among the prominent tools in climate science are complicated computer models. For more on those, try this blog:

• Steve Easterbrook, Serendipity, or What has Software Engineering got to do with Climate Change?

After reading Easterbrook’s blog post about “climate model validation”, and some discussions of this topic elsewhere, I noticed that there is some “computer terminology” floating around that disguises itself as plain English! This has led to some confusion, so I’d like to explain some of it here.

Technobabble: The Quest for Cooperation

Climate change may be the first problem in the history of humankind that has to be tackled on a global scale, by people all over the world working together. Of course, a prerequisite of working together is a mutual understanding and a mutual language. Unfortunately every single one of the many professions that scientists and engineers engage in have created their own dialect. And most experts are proud of it!

When I read about the confusion that “validation” versus “verification” of climate models has caused, I was reminded of the phrase “technobabble”, which screenwriters for the TV series Star Trek used whenever they had to write a dialog involving the engineers on the Starship Enterprise. Something like this:

“Captain, we have to send an inverse tachyon beam through the main deflector dish!”

“Ok, make it so!”

Fortunately, neither Captain Picard nor the audience had to understand what was really going on.

It’s a bit different in the real world, where not everyone may have the luxury of staying on the sidelines while the trustworthy crew members in the Enterprise’s engine room solve all the problems. We can start today by explaining some software engineering technobabble that came up in the context of climate models. But why would software engineers bother in the first place?

Short Review of Climate Models

Climate models come in a hierarchy of complexity. The simplest ones only try to simulate the energy balance of the planet earth. These are called energy balance models. They don’t take into account the spherical shape of the earth, for example.

At the opposite extreme, the most complex ones try to simulate the material and heat flow of the atmosphere and the oceans on a topographical model of the spinning earth. These are called general circulation models, or GCMs for short. GCMs have a lot of code, sometimes more than a million lines of code.

A line of code is basically one instruction for the computer to carry out, like:

add 1/2 and 1/6 and store the result in a variable called e

print e on the console

In order to understand what a computer program does, in theory, one has to memorize every single line of code and understand it. And most programs use a lot of other programs, so in theory one would have to understand those, too. This is of course not possible for a single person!

We hope that taking into account a lot of effects, which results in a lot of lines of code, makes the models more accurate. But it certainly means that they are complex enough to be interesting for software engineers.

In the case of software that is used to run an internet shop, a million lines of code isn’t much. But it is already too big for one single person to handle. Basically, this is where all the problems start, that software engineering seeks to solve.

When more than one person works on a software project things often get complicated.

(From the manual of CVS, the “Concurrent Versions System”.)

Software Design Circle

The job of software engineer is in some terms similar to the work of an architect. The differences are mainly due to the abstract nature of software. Everybody can see if a building is finished or if it isn’t, but that’s not possible with software. Nevertheless every software project does come to an end, and people have to decide whether or not the product, the software, is finished and does what it should. But since software is so abstract, people have come up with special ideas about how the software “production process” should work and how to tell if the software is correct. I would like to explain these a little bit further.

Stakeholders and Shifts in Stakeholder Analysis

There are many different people working in an office building with different interests: cleaning squads, janitors, plant security, and so on. When you design a new office building, you need to identify and take into account all the different interests of all these groups. Most software projects are similar, and the process just mentioned is usually called stakeholder analysis.

Of course, if you take into account only the groups already mentioned, you’ll build an office building without any offices, because that would obviously be the simplest one to monitor and to keep working. Such an office building wouldn’t make much sense, of course! This is because we made a fatal mistake with our stakeholder analysis: we failed to take into account the most important stakeholders, the people who will actually use the offices. These are the key stakeholders of the office building project.

After all, the primary purpose of an office building is to provide offices. And in the end, if we have an office building without offices, we’ll notice that no one will pay us for our efforts.

Gathering Requirements

While it may be obvious what most people want from an office building, the situation is usually much more abstract, hence much more complicated, for software projects.

This is why software people carry out a requirement analysis, where they ask the stakeholders what they would like the software to do. A requirement for an office building might be, for example, “we need a railway station nearby, because most of the people who will work in the building don’t have cars.” A requirement for a software project might be, for example, “we need the system to send email notifications to our clients on a specific schedule”.

In an ideal world, the requirement analysis would result in a document —usually called something like a system specification—that contains both the requirements, and also descriptions of the test cases that are needed to test whether the finished system meets the requirements. For example:

“Employee A lives in an apartment 29 km away from the office building and does not have a car. She gets to work within 30 minutes by using public transportation.”

Verification versus Validation

When we have finished the office building (or the software system), we’ll have to do some acceptance testing, in order to convince our customer that she should pay us (or simply to use the system, if it is for free). When you buy a car, your “acceptance test” is driving away with it—if that does not work, you know that there is something wrong with your car! But for complicated software—or office buildings—we need to agree on what we do to test if the system is finished. That’s what we need the test cases for.

If we are lucky, the relevant test cases will already be described in the system specification, as noted above. But that is not the whole story.

Every scientific community that has its own identity invents its own new language, often borrowing words from everyday language and defining new, surprising, special meanings for them. Software engineers are no different. There are, for example, two very different aspects to testing a system:

• Did we do everything according to the system specification?

and:

• Now that the system is there, and our key stakeholders can see it for themselves, did we get the system specification right: is our product useful to them?

The first is called verification, the second validation. As you can see, software engineers took two almost synonymous words from everyday language and gave them quite different meanings!

For example, if you wrote in the specification for an online book seller:

“we calculate the book price by multiplying the ISBN number by pi”

and the final software system does just that, then the system is verified. But if the book seller would like to stay in business, I bet that he won’t say the system has been validated.

Stakeholders of Climate Models

So, for business applications, it’s not quite right to ask “is the software correct?” The really important question is: “is the software as useful for the key stakeholders as it should be?”

But in Mathematics Everything is Either True or False!

One may wonder if this “true versus useful” stuff above makes any sense when we think about a piece of software that calculates, for example, a known mathematical function like a “modified Bessel function of the first kind”. After all, it is defined precisely in mathematics what these functions look like.

If we are talking about creating a program that can evaluate these functions, there are a lot of technical choices that need to be specified. Here is a random example (if you don’t understand it, don’t worry, that is not necessary to get the point):

• Current computers know data types with a finite value range and finite precision only, so we need to agree on which such data type we want as a model of the real or complex numbers. For example, we might want to use the “double precision floating-point format”, which is an international standard.

Another aspect is, for example, “how long may the function take to return a value?” This is an example of a non-functional requirement (see Wikipedia). These requirements will play a role in the implementation too, of course.

However, apart from these technical choices, there is no ambiguity as to what the function should do, so there is no need to distinguish verification and validation. Thank god that mathematics is eternal! A Bessel function will always be the same, for all of eternity.

Unfortunately, this is no longer true when a computer program computes something that we would like to compare to the real world. Like, for example, a weather forecast. In this case the computer model will, like all models, include some aspects of the real world. Or rather, some specific implementations of a mathematical model of a part of the real world.

Verification will still be the same, if we understand it to be the stage where we test to see if the single pieces of the program compute what they are supposed to. The parts of the program that do things that can be defined in a mathematically precise way. But validation will be a whole different step if understood in the sense of “is the model useful?”

But Everybody Knows What Weather Is!

But still, does this apply to climate models at all? I mean, everybody knows what “climate” is, and “climate models” should simulate just that, right?

As it turns out, it is not so easy, because climate models serve very different purposes:

• Climate scientists want to test their understanding of basic climate processes, just as physicists calculate a lot of solutions to their favorite theories to gain a better understanding of what these theories can and do model.

• Climate models are also used to analyse observational data, to supplement such data and/or to correct them. Climate models have had success in detecting misconfiguration and biases in observational instruments.

• Finally, climate models are also used for global and/or local predictions of climate change.

The question “is my climate model right?” therefore translates to the question “is my climate model useful?” This question has to refer to a specific use of the model, or rather: to the viewpoint of the key stakeholders.

The Shift of Stakeholders

One problem of the discussions of the past seems to be due to a shift of the key stakeholders. For example: some climate models have been developed as a tool for climate scientists to play around with certain aspects of the climate. When the scientists published papers, including insights gained from these models, they usually did not publish anything about the implementation details. Mostly, they did not publish anything about the model at all.

This is nothing unusual. After all, a physicist or mathematician will routinely publish her results and conclusions—maybe with proofs. But she is not required to publish every single thought she had to think to produce her results.

But after the results of climate science became a topic in international politics, a change of the key stakeholders occurred: a lot of people outside the climate science community developed an interest in the models. This is a good thing. There is a legitimate need of researchers to limit participation in the review process, of course. But when the results of a scientific community become the basis of far-reaching political decisions, there is a legitimate public interest in the details of the ongoing research process, too. The problem in this case is that the requirements of the new key stakeholders, such as interested software engineers outside the climate research community, are quite different from the requirements of the former key stakeholders, climate scientists.

For example, if you write a program for your own eyes only, there is hardly any need to write a detailed documentation of it. If you write it for others to understand it, as rule of thumb, you’ll have to produce at least as much documentation as code.

Back to the Start: Farms, Fields and Forests

As an example of a rather prominent critic of climate models, let’s quote the physicist Freeman Dyson:

The models solve the equations of fluid dynamics and do a very good job of describing the fluid motions of the atmosphere and the oceans.

They do a very poor job of describing the clouds, the dust, the chemistry and the biology of fields, farms and forests. They are full of fudge factors so the models more or less agree with the observed data. But there is no reason to believe the same fudge factors would give the right behaviour in a world with different chemistry, for example in a world with increased CO₂.

Let’s assume that Dyson is talking here about GCMs, with all their parametrizations of unresolved processes (which he calls “fudge factors”). Then the first question that comes to my mind is “why would a climate model need to describe fields, farms and forests in more detail?”

I’m quite sure that the answer will depend on what aspects of the climate the model should represent, in what regions and over what timescale.

And that certainly depends on the answer to the question “what will we use our model for?” Dyson seems to assume that the answer to this question is obvious, but I don’t think that this is true. So, maybe we should start with “stakeholder analysis” first.

32 Comments | climate, software | Permalink
Posted by John Baez

How Sea Level Rise Will Affect New York

9 June, 2011

Let’s try answering this question on Quora:

How will global warming, and particularly sea level rises, affect New York City?

I doubt sea level rise will be the first way we’ll get badly hurt by global warming. I think it’ll be crop losses caused by floods, droughts and heat waves, and property damage caused by storms. But the question focuses on sea level rise, so perhaps we should think about that… along with any other ways that New York City is particularly susceptible to the effects of global warming.

Suppose you know a lot about New York, but you need an estimate of sea level rise to get started. In the Azimuth Project page on sea level rise, you’ll see a lot of discussion of this subject. Naturally, it’s complicated. But say you just want some numbers. Okay: very roughly, by the end of the century we can expect a sea level of at least 0.6 meters, not counting any melting from Greenland and Antarctica and at most 2 meters, including Greenland and Antarctica. That’s roughly between 2 and 6 feet.

On the other hand, there’s at least one report saying sea levels may rise in the Northeast US at twice the average global rate. What’s the latest word on that?

Now, here’s a website that claims to show what various amounts of sea level rise would do to different areas:

• Firetree.net, Flood maps, including New York City.

Details on how these maps were made are here. One problem is that they focus too much on really big sea level rises: the smallest rise shown is 1 meter, then 2 meters… and it goes up to 60 meters!

Anyway, here’s part of New York City now:

Here it is after a 1-meter (3-foot) sea level rise:

(Click to enlarge any of these.) And here’s 2 meters, or 6 feet:

It’s a bit hard to spot the effects in Manhattan. They’re much more noticeable in the low-lying areas between Jersey City and Secaucus. What are those: parks, industrial areas, or suburbs? I’ve heard New Yorkers crack jokes about the ‘swamps of Jersey’…

But of course, a lot of the city is underground. What will happen to subways and other infrastructure, like sewage systems? And what about water supplies? On coastlines, saltwater can infiltrate into surface waters and aquifers. Where does freshwater meet saltwater near New York City? How will the effect of floods and storms change?

And of course, there are other parts of New York City these little maps don’t show: for those, go here. But watch out: at first you’ll see the effect of a 7-meter sea level rise… you’ll need to change the settings to see the effects of a more realistic rise.

If you live in a place that will be flooded, let me know!

Luckily, we don’t have to figure everything out ourselves: the state of New York has a task force devoted to this. And as task forces do, they’ve written a report:

• New York Department of Environmental Conservation, Sea Level Rise Task Force, Final Report.

New York City also has an ambitious environmental plan:

• New York City, PlaNYC 2030.

Finally, let me quote part of this:

• Jim O’Grady, Sea level rise could turn New York into Venice, experts warn, WNYC News, 9 February 2011.

Because it looks ahead 200 years, this article paints a more dire picture than my remarks above:

David Bragdon, Director of the Mayor’s Office of Long-Term Planning & Sustainability, is charged with preparing for the dangers of climate change. He said the city is taking precautions like raising the pumps at a wastewater treatment plant in the Rockaways and building the Willets Point development in Queens on six feet of landfill. The goal is to manage the risk from 100-year storms—one of the most severe. The mayor’s report says by the end of this century, 100-year storms could start arriving every 15 to 35 years.

Klaus Jacob, a Columbia University research scientist who specializes in disaster risk management, said that estimate may be too conservative. “What is now the impact of a 100-year storm will be, by the end of this century, roughly a 10-year storm,” he warned.

Back on the waterfront, oceanographer Malcolm Bowman offered what he said is a suitably outsized solution to this existential threat: storm surge barriers.

They would rise from the waters at Throgs Neck, where Long Island Sound and the East River meet, and at the opening to the lower harbor between the Rockaways and Sandy Hook, New Jersey. Like the barriers on the Thames River that protect London, they would stay open most of the time to let ships pass but close to protect the city during hurricanes and severe storms.

The structures at their highest points would be 30 feet above the harbor surface. Preliminary engineering studies put the cost at around $11 billion.

Jacob suggested a different but equally drastic approach. He said sea level rise may force New Yorkers to pull back from vulnerable neighborhoods. “We will have to densify the high-lying areas and use the low-lying areas as parks and buffer zones,” he said.

In this scenario, New York in 200 years looks like Venice. Concentrations of greenhouse gases in the atmosphere have melted ice sheets in Greenland and Antarctica and raised our local sea level by six to eight feet. Inundating storms at certain times of year swell the harbor until it spills into the streets. Dozens of skyscrapers in Lower Manhattan have been sealed at the base and entrances added to higher floors. The streets of the financial district have become canals.

“You may have to build bridges or get Venice gondolas or your little speed boats ferrying yourself up to those buildings,” Jacob said.

David Bragdon is not comfortable with such scenarios. He’d rather talk about the concrete steps he’s taking now, like updating the city’s flood evacuation plan to show more neighborhoods at risk. That would help the people living in them be better prepared to evacuate.

He said it’s too soon to contemplate the “extreme” step of moving “two, three, four hundred thousand people out of areas they’ve occupied for generations,” and disinvesting “literally billions of dollars of infrastructure in those areas.” On the other hand: “Another extreme would be to hide our heads in the sand and say, ‘Nothing’s going to happen.’”

Bragdon said he doesn’t think New Yorkers of the future will have to retreat very far from shore, if at all, but he’s not sure. And he would neither commit to storm surge barriers nor eliminate them as an option. He said what’s needed is more study—and that he’ll have further details in April, when the city updates PlaNYC.

Jacob warned that in preparing for disaster, no matter how far off, there’s a gulf between study and action. “There’s a good intent,” he said of New York’s climate change planning to date. “But, you know, mother nature doesn’t care about intent. Mother nature wants to see resiliency. And that is questionable, whether we have that.”

29 Comments | climate, questions, risks | Permalink
Posted by John Baez

Earth System Research for Global Sustainability

4 June, 2011

Some good news!

The International Mathematical Union or IMU is mainly famous for running the International Congress of Mathematicians every four years. But they do other things, too. The new vice-president of the IMU is Christiane Rousseau. Rousseau was already spearheading the Mathematics of Planet Earth 2013 project. Now she’s trying to get the IMU involved in a ten-year research initiative on sustainability.

As you can see from this editorial, she treats climate change and sustainability with the seriousness they deserve. Let’s hope more mathematicians join in!

I would like to get involved somehow, but I’m not exactly sure how.

Editorial

I had the privilege of being elected Vice-president of the IMU at the last General Assembly, and it is now five months that I am following the activities of the IMU. The subjects discussed at the Executive Committee are quite diverse, from the establishment of the permanent office to the ranking and pricing of journals, to mathematics in developing countries and the future ICM, and the members of the
Executive Committee tend to specialize on one or two dossiers. Although I am a pure mathematician myself, I am becoming more and more interested in the science of sustainability, so let me talk to you of this.

IMU is one of the international unions inside the International Council of Science (ICSU). At the Executive we regularly receive messages from ICSU asking for input from its members. While it is not new that scientists are involved in the study of climate change and sustainability issues, a new feeling of emergency has developed. The warning signs are becoming more numerous that urgent action is needed if we want to save the planet from a disastrous future, since we may not be far from a point of no return: climate change with more extreme weather events, rising of the sea level with the melting of glaciers, shortage of food and water in the near future because of the increase of the world population and the climate change, loss of biodiversity, new epidemics or invasive species, etc. This explains why ICSU is starting a new 10-year research initiative: EARTH SYSTEM RESEARCH FOR GLOBAL SUSTAINABILITY, and a Steering Committee for this initiative is presently nominated. The goals of the Initiative are to:

1. Deliver at global and regional scales the knowledge that societies need to effectively respond to global change while meeting economic and social goals;

2. Coordinate and focus international scientific research to address the Grand Challenges and Belmont Challenge;

3. Engage a new generation of researchers in the social, economic, natural, health, and engineering sciences in global sustainability research.

In the same spirit, ICSU is preparing a strong scientific presence at the next United Nations Conference on Sustainable Development (Rio+20) that will take place on June 4-6, 2012 in Rio de Janeiro. For this, ICSU is organizing a number of preparatory regional and global meetings. It is clear that mathematical sciences have an essential role in the interdisciplinary research that needs to take place in order to achieve significant impact. The other scientific disciplines concerned are numerous from physics, to biology, to economics, etc.

Let me quote Graciela Chichilnisky, the author of the carbon market of the UN Kyoto Protocol: “It is the physicists that study the climate change, but it is the economists who advise the politicians that take the decisions.” Considering the importance of the contribution of mathematical sciences in sustainability issues, IMU has asked to participate actively in these preparatory meetings and be represented at Rio+20. This should be an occasion to build partnerships with the other scientific unions inside ICSU. More and more mathematicians and research institutes around the world become interested in sustainable development as is acknowledged by the large participation in Mathematics of Planet Earth 2013 which was recently endorsed by IMU. But the world needs more than a one year initiative. The science of sustainability is full of challenging problems which are very interesting mathematically. Many of these problems require new mathematical techniques. We could hope that these initiatives will allow training a new generation of researchers in mathematical sciences who will be able to work in interdisciplinary teams to address these issues.

Christiane Rousseau
Vice-President of Executive Committee of IMU

2 Comments | climate, conferences, mathematics, sustainability | Permalink
Posted by John Baez

The Stockholm Memorandum

1 June, 2011

In May this year, the 3rd Nobel Laureate Symposium produced a document called The Stockholm Memorandum signed by 17 Nobel laureates, presumably from among these participants. It’s a clear call to action, so I’ll reproduce it all here.

I. Mind-shift for a Great Transformation

The Earth system is complex. There are many aspects that we do not yet understand. Nevertheless, we are the first generation with the insight of the new global risks facing humanity.

We face the evidence that our progress as the dominant species has come at a very high price. Unsustainable patterns of production, consumption, and population growth are challenging the resilience of the planet to support human activity. At the same time, inequalities between and within societies remain high, leaving behind billions with unmet basic human needs and disproportionate vulnerability to global environmental change.

This situation concerns us deeply. As members of the 3rd Nobel Laureate Symposium we call upon all leaders of the 21st century to exercise a collective responsibility of planetary stewardship. This means laying the foundation for a sustainable and equitable global civilization in which the entire Earth community is secure and prosperous.

Science indicates that we are transgressing planetary boundaries that have kept civilization safe for the past 10,000 years. Evidence is growing that human pressures are starting to overwhelm the Earth’s buffering capacity.

Humans are now the most significant driver of global change, propelling the planet into a new geological epoch, the Anthropocene. We can no longer exclude the possibility that our collective actions will trigger tipping points, risking abrupt and irreversible consequences for human communities and ecological systems.

We cannot continue on our current path. The time for procrastination is over. We cannot afford the luxury of denial. We must respond rationally, equipped with scientific evidence.

Our predicament can only be redressed by reconnecting human development and global sustainability, moving away from the false dichotomy that places them in opposition.

In an interconnected and constrained world, in which we have a symbiotic relationship with the planet, environmental sustainability is a precondition for poverty eradication, economic development, and social justice.

Our call is for fundamental transformation and innovation in all spheres and at all scales in order to stop and reverse global environmental change and move toward fair and lasting prosperity for present and future generations.

II. Priorities for Coherent Global Action

We recommend a dual track approach:

a) emergency solutions now, that begin to stop and reverse negative environmental trends and redress inequalities in the inadequate institutional frameworks within which we operate, and

b) long term structural solutions that gradually change values, institutions and policy frameworks. We need to support our ability to innovate, adapt, and learn.

1. Reaching a more equitable world

Unequal distribution of the benefits of economic development are at the root of poverty. Despite efforts to address poverty, more than a third of the world’s population still live on less than $2 per day. This needs our immediate attention. Environment and development must go hand in hand. We need to:

• Achieve the Millennium Development Goals, in the spirit of the Millennium Declaration, recognising that global sustainability is a precondition of success.

• Adopt a global contract between industrialized and developing countries to scale up investment in approaches that integrate poverty reduction, climate stabilization, and ecosystem stewardship.

2. Managing the climate – energy challenge

We urge governments to agree on global emission reductions guided by science and embedded in ethics and justice. At the same time, the energy needs of the three billion people who lack access to reliable sources of energy need to be fulfilled. Global efforts need to:

• Keep global warming below 2°C, implying a peak in global CO₂ emissions no later than 2015 and recognise that even a warming of 2°C carries a very high risk of serious impacts and the need for major adaptation efforts.

• Put a sufficiently high price on carbon and deliver the G-20 commitment to phase out fossil fuel subsidies, using these funds to contribute to the several hundred billion US dollars per year needed to scale up investments in renewable energy.

3. Creating an efficiency revolution

We must transform the way we use energy and materials. In practice this means massive efforts to enhance energy efficiency and resource productivity, avoiding unintended secondary consequences. The “throw away concept” must give way to systematic efforts to develop circular material flows. We must:

• Introduce strict resource efficiency standards to enable a decoupling of economic growth from resource use.

• Develop new business models, based on radically improved energy and material efficiency.

4. Ensuring affordable food for all

Current food production systems are often unsustainable, inefficient and wasteful, and increasingly threatened by dwindling oil and phosphorus resources, financial speculation, and climate impacts. This is already causing widespread hunger and malnutrition today. We can no longer afford the massive loss of biodiversity and reduction in carbon sinks when ecosystems are converted into cropland. We need to:

• Foster a new agricultural revolution where more food is produced in a sustainable way on current agricultural land and within safe boundaries of water resources.

• Fund appropriate sustainable agricultural technology to deliver significant yield increases on small farms in developing countries.

5. Moving beyond green growth

There are compelling reasons to rethink the conventional model of economic development. Tinkering with the economic system that generated the global crises is not enough. Markets and entrepreneurship will be prime drivers of decision making and economic change, but must be complemented by policy frameworks that promote a new industrial metabolism and resource use. We should:

• Take account of natural capital, ecosystem services and social aspects of progress in all economic decisions and poverty reduction strategies. This requires the development of new welfare indicators that address the shortcomings of GDP as an indicator of growth.

• Reset economic incentives so that innovation is driven by wider societal interests and reaches the large proportion of the global population that is currently not benefitting from these innovations.

6. Reducing human pressures

Consumerism, inefficient resource use and inappropriate technologies are the primary drivers of humanity’s growing impact on the planet. However, population growth also needs attention. We must:

• Raise public awareness about the impacts of unsustainable consumption and shift away from the prevailing culture of consumerism to sustainability.

• Greatly increase access to reproductive health services, education and credit, aiming at empowering women all over the world. Such measures are important in their own right but will also reduce birth rates.

7. Strengthening earth system governance

The multilateral system must be reformed to cope with the defining challenges of our time, namely transforming humanity’s relationship with the planet and rebuilding trust between people and nations. Global governance must be strengthened to respect planetary boundaries and to support regional, national and local approaches. We should:

• Develop and strengthen institutions that can integrate the climate, biodiversity and development agendas.

• Explore new institutions that help to address the legitimate interests of future generations.

8. Enacting a new contract between science and society

Filling gaps in our knowledge and deepening our understanding is necessary to find solutions to the challenges of the Anthropocene, and calls for major investments in science. A dialogue with decision-makers and the general public is also an important part of a new contract between science and society. We need to:

• Launch a major initiative on the earth system research for global sustainability, at a scale similar to those devoted to areas such as space, defence and health, to tap all sources of ingenuity across disciplines and across the globe.

• Scale up our education efforts to increase scientific literacy especially among the young.

We are the first generation facing the evidence of global change. It therefore falls upon us to change our relationship with the planet, in order to tip the scales towards a sustainable world for future generations.

12 Comments | climate, economics, energy | Permalink
Posted by John Baez

The One Best Thing Everyone Could Do to Slow Climate Change

27 May, 2011

There’s a website called Quora where people can ask and answer questions of all sorts. Lots of people use it, so Curtis Faith suggested that we—that is, everyone here reading this blog—try answering some of the questions there. That sounded like a nice idea, so now there’s a ‘topic’ on Quora called Azimuth Project. The questions we tackle will be listed there, so people can easily find them.

To get the ball rolling, Curtis posted this question:

What is the one best thing everyone could do to slow down climate change?

If you’re like me, the first thing you’ll want to do is question the question. Are we really looking for the one best thing everyone could do? Everyone in the world, including the billion poorest people?

In that case, many answers that leap to mind are no good. We can’t say “take fewer airplane trips” because most of those people don’t take airplane trips to begin with. We can’t say “drive less” because most of those people don’t have cars. And so on. It’s no fair! We need an easier question!

Well… let’s not try to second-guess the question. It’s actually fun to take it seriously and try to answer it. It’ll force us to think about the world as a whole, instead of the sins of our rich neighbors.

Here are 50 tips for how to fight global warming from Global Warming Facts. Could any of these be the right answer? How many of these are things that everyone on this Earth can do?

Replace a regular incandescent light bulb with a compact fluorescent light bulb (cfl)
CFLs use 60% less energy than a regular bulb. This simple switch will save about 300 pounds of carbon dioxide a year.
We recommend you purchase your CFL bulbs at 1000bulbs.com, they have great deals on both screw-in and plug-in light bulbs.
Install a programmable thermostat
Programmable thermostats will automatically lower the heat or air conditioning at night and raise them again in the morning. They can save you $100 a year on your energy bill.
Move your thermostat down 2° in winter and up 2° in summer
Almost half of the energy we use in our homes goes to heating and cooling. You could save about 2,000 pounds of carbon dioxide a year with this simple adjustment.
Clean or replace filters on your furnace and air conditioner
Cleaning a dirty air filter can save 350 pounds of carbon dioxide a year.
Choose energy efficient appliances when making new purchases
Look for the Energy Star label on new appliances to choose the most energy efficient products
available.
Do not leave appliances on standby
Use the “on/off” function on the machine itself. A TV set that’s switched on for 3 hours a day (the average time Europeans spend watching TV) and in standby mode during the remaining 21 hours uses about 40% of its energy in standby mode.
Wrap your water heater in an insulation blanket
You’ll save 1,000 pounds of carbon dioxide a year with this simple action. You can save another 550 pounds per year by setting the thermostat no higher than 50°C.
Move your fridge and freezer
Placing them next to the cooker or boiler consumes much more energy than if they were standing on their own. For example, if you put them in a hot cellar room where the room temperature is 30-35ºC, energy use is almost double and causes an extra 160 kg of CO₂ emissions for fridges per year and 320 kg for freezers.
Defrost old fridges and freezers regularly
Even better is to replace them with newer models, which all have automatic defrost cycles and are generally up to two times more energy-efficient than their predecessors.
Don’t let heat escape from your house over a long period
When airing your house, open the windows for only a few minutes. If you leave a small opening all day long, the energy needed to keep it warm inside during six cold months (10ºC or less outside temperature) would result in almost 1 ton of CO₂ emissions.
Replace your old single-glazed windows with double-glazing
This requires a bit of upfront investment, but will halve the energy lost through windows and pay off in the long term. If you go for the best the market has to offer (wooden-framed double-glazed units with low-emission glass and filled with argon gas), you can even save more than 70% of the energy lost.
Get a home energy audit
Many utilities offer free home energy audits to find where your home is poorly insulated or energy inefficient. You can save up to 30% off your energy bill and 1,000 pounds of carbon dioxide a year. Energy Star can help you find an energy specialist.
Cover your pots while cooking
Doing so can save a lot of the energy needed for preparing the dish. Even better are pressure cookers and steamers: they can save around 70%!
Use the washing machine or dishwasher only when they are full
If you need to use it when it is half full, then use the half-load or economy setting. There is also no need to set the temperatures high. Nowadays detergents are so efficient that they get your clothes and dishes clean at low temperatures.
Take a shower instead of a bath
A shower takes up to four times less energy than a bath. To maximize the energy saving, avoid power showers and use low-flow showerheads, which are cheap and provide the same comfort.
Use less hot water
It takes a lot of energy to heat water. You can use less hot water by installing a low flow showerhead (350 pounds of carbon dioxide saved per year) and washing your clothes in cold or warm water (500 pounds saved per year) instead of hot.
Use a clothesline instead of a dryer whenever possible
You can save 700 pounds of carbon dioxide when you air dry your clothes for 6 months out of the year.
Insulate and weatherize your home
Properly insulating your walls and ceilings can save 25% of your home heating bill and 2,000 pounds of carbon dioxide a year. Caulking and weather-stripping can save another 1,700 pounds per year. Energy Efficient has more information on how to better insulate your home.
Be sure you’re recycling at home
You can save 2,400 pounds of carbon dioxide a year by recycling half of the waste your household generates.
Recycle your organic waste
Around 3% of the greenhouse gas emissions through the methane is released by decomposing bio-degradable waste. By recycling organic waste or composting it if you have a garden, you can help eliminate this problem! Just make sure that you compost it properly, so it decomposes with sufficient oxygen, otherwise your compost will cause methane emissions and smell foul.
Buy intelligently
One bottle of 1.5l requires less energy and produces less waste than three bottles of 0.5l. As well, buy recycled paper products: it takes less 70 to 90% less energy to make recycled paper and it prevents the loss of forests worldwide.
Choose products that come with little packaging and buy refills when you can
You will also cut down on waste production and energy use… another help against global warming.
Reuse your shopping bag
When shopping, it saves energy and waste to use a reusable bag instead of accepting a disposable one in each shop. Waste not only discharges CO2 and methane into the atmosphere, it can also pollute the air, groundwater and soil.
Reduce waste
Most products we buy cause greenhouse gas emissions in one or another way, e.g. during production and distribution. By taking your lunch in a reusable lunch box instead of a disposable one, you save the energy needed to produce new lunch boxes.
Plant a tree
A single tree will absorb one ton of carbon dioxide over its lifetime. Shade provided by trees can also reduce your air conditioning bill by 10 to 15%. The Arbor Day Foundation has information on planting and provides trees you can plant with membership.
Switch to green power
In many areas, you can switch to energy generated by clean, renewable sources such as wind and solar. In some of these, you can even get refunds by government if you choose to switch to a clean energy producer, and you can also earn money by selling the energy you produce and don’t use for yourself.
Buy locally grown and produced foods
The average meal in the United States travels 1,200 miles from the farm to your plate. Buying locally will save fuel and keep money in your community.
Buy fresh foods instead of frozen
Frozen food uses 10 times more energy to produce.
Seek out and support local farmers markets
They reduce the amount of energy required to grow and transport the food to you by one fifth. Seek farmer’s markets in your area, and go for them.
Buy organic foods as much as possible
Organic soils capture and store carbon dioxide at much higher levels than soils from conventional farms. If we grew all of our corn and soybeans organically, we’d remove 580 billion pounds of carbon dioxide from the atmosphere!
Eat less meat
Methane is the second most significant greenhouse gas and cows are one of the greatest methane emitters. Their grassy diet and multiple stomachs cause them to produce methane, which they exhale with every breath.
Reduce the number of miles you drive by walking, biking, carpooling or taking mass transit wherever possible
Avoiding just 10 miles of driving every week would eliminate about 500 pounds of carbon dioxide emissions a year! Look for transit options in your area.
Start a carpool with your coworkers or classmates
Sharing a ride with someone just 2 days a week will reduce your carbon dioxide emissions by 1,590 pounds a year. eRideShare.com runs a free service connecting North American commuters and travelers.
Don’t leave an empty roof rack on your car
This can increase fuel consumption and CO₂ emissions by up to 10% due to wind resistance and the extra weight – removing it is a better idea.
Keep your car tuned up
Regular maintenance helps improve fuel efficiency and reduces emissions. When just 1% of car owners properly maintain their cars, nearly a billion pounds of carbon dioxide are kept out of the atmosphere.
Drive carefully and do not waste fuel
You can reduce CO₂ emissions by readjusting your driving style. Choose proper gears, do not abuse the gas pedal, use the engine brake instead of the pedal brake when possible and turn off your engine when your vehicle is motionless for more than one minute. By readjusting your driving style you can save money on both fuel and car maintenance.
Check your tires weekly to make sure they’re properly inflated
Proper tire inflation can improve gas mileage by more than 3%. Since every gallon of gasoline saved keeps 20 pounds of carbon dioxide out of the atmosphere, every increase in fuel efficiency makes a difference!
When it is time for a new car, choose a more fuel efficient vehicle
You can save 3,000 pounds of carbon dioxide every year if your new car gets only 3 miles per gallon more than your current one. You can get up to 60 miles per gallon with a hybrid! You can find information on fuel efficiency on FuelEconomy and on GreenCars websites.
Try car sharing
Need a car but don’t want to buy one? Community car sharing organizations provide access to a car and your membership fee covers gas, maintenance and insurance. Many companies – such as Flexcar – offer low emission or hybrid cars too! Also, see ZipCar.
Try telecommuting from home
Telecommuting can help you drastically reduce the number of miles you drive every week. For more information, check out the Telework Coalition.
Fly less
Air travel produces large amounts of emissions so reducing how much you fly by even one or two trips a year can reduce your emissions significantly. You can also offset your air travel carbon emissions by investing in renewable energy projects.
Encourage your school or business to reduce emissions
You can extend your positive influence on global warming well beyond your home by actively encouraging other to take action.
Join the virtual march
The Stop Global Warming Virtual March is a non-political effort to bring people concerned about global warming together in one place. Add your voice to the hundreds of
thousands of other people urging action on this issue.
Encourage the switch to renewable energy
Successfully combating global warming requires a national transition to renewable energy sources such as solar, wind and biomass. These technologies are ready to be deployed more widely but there are regulatory barriers impeding them. U.S. citizens, take action to break down those barriers with Vote Solar.
Protect and conserve forest worldwide
Forests play a critical role in global warming: they store carbon. When forests are burned or cut down, their stored carbon is release into the atmosphere – deforestation now accounts for about 20% of carbon dioxide emissions each year. Conservation International has more information on saving forests from global warming.
Consider the impact of your investments
If you invest your money, you should consider the impact that your investments and savings will have on global warming. Check out SocialInvest and Ceres to can learn more about how to ensure your money is being invested in companies, products and projects that address issues related to climate change.
Make your city cool
Cities and states around the country have taken action to stop global warming by passing innovative transportation and energy saving legislation. If you’re in the U.S., join the cool cities list.
Tell Congress to act
The McCain Lieberman Climate Stewardship and Innovation Act would set a firm limit on carbon dioxide emissions and then use free market incentives to lower costs, promote efficiency and spur innovation. Tell your representative to support it.
Make sure your voice is heard!
Americans must have a stronger commitment from their government in order to stop global warming and implement solutions and such a commitment won’t come without a dramatic increase in citizen lobbying for new laws with teeth. Get the facts about U.S. politicians and candidates at Project Vote Smart and The League of Conservation Voters. Make sure your voice is heard by voting!
Share this list!
Spread this list worldwide and help people doing their part: the more people you will manage to enlighten, the greater YOUR help to save the planet will be (but please take action on first person too)! If you like, you are free to republish, adapt or translate the list and post it in your blog, website or forum as long as you give us credit with a link to the original source.

There are a lot of great ideas here, but if we look for those that everyone can do, there aren’t many.

What’s the most important item that was left off this list?

I’ll give my answer to Curtis’ question after I’ve heard some of yours. It’s a tough question but I have an idea. And no, it’s not “join the Azimuth Project”.

143 Comments | azimuth, climate, questions | Permalink
Posted by John Baez

The Melting of Greenland and West Antarctica

19 May, 2011

Ice is melting at an accelerating pace in Greenland and the Antarctic. You may know all about this. But maybe like me you’re still just catching up on the basics. If so, here’s a quick intro.

If all the ice in Antarctica melted, it would raise the sea by 61 meters! Such mammoth sea level changes do happen:

But it seems they take millennia. In the shorter term, meaning the next century or two, people tend to focus their concern on the West Antarctic Ice Sheet, or WAIS:

If the entire WAIS melted, it would make sea levels rise 4.8 meters. Another region of concern is Greenland: if all the ice there melted, it would cause a global sea level rise of 7.2 meters. This would inundate many of the world’s coastal cities.

Luckily, it seems no reputable glaciologists think the WAIS or Greenland will completely melt in the coming century. But amount of melting of these ice sheets has been a big challenge to predict.

The last International Panel on Climate Change report, back in 2007, took a pretty conservative stance, and assumed these ice sheets would melt at a slow and more or less constant rate until 2100. Their conclusion was that about 75% of sea level rise would be caused by the oceans expanding as they warmed. The melting of small glaciers, ice caps and Greenland would account for most of the rest. The Antarctic, they believed, would actually provide a small net reduction in sea levels, with increases in snowfall more than enough to outweigh the effects of melting. They predicted an overall sea level rise of between 0.18 and 0.59 meters, with most of the uncertainty arising from different assumptions about what the world economy will do.

However, almost as soon as the 4th IPCC report was released, evidence started accumulating that the melting of Greenland and the West Antarctic Ice Sheet were speeding up. For example:

This graph, taken from Skeptical Science, shows Isabella Velicogna’s estimates of the mass of the Greenland ice sheet. Unfiltered data are blue crosses. Data filtered to eliminate seasonal variations are shown as red crosses. The best fit by a quadratic function is shown in green. The data came from the Gravity Recovery and Climate Experiment—or GRACE, for short. This remarkable project uses a pair of satellites to accurately measure small variations from place to place in the Earth’s gravitational field. When ice sheets melt, GRACE can detect it.

The big news, of course, was that the melting is speeding up. Here’s the same sort of graph for Antarctica, again created by Velicogna:

• I. Velicogna, Increasing rates of ice mass loss from the Greenland and Antarctic ice sheets revealed by GRACE, Geophysical Research Letters, 36 (2009), L19503.

More recently, Eric Rignot et al compared GRACE data to another way of keeping track of these ice sheets:

• Eric Rignot, Acceleration of the contribution of the Greenland and Antarctic ice sheets to sea level rise, Geophysical Research Letters 38, L05503.

Satellites and radio echo soundings measure ice leaving these sheets, while regional atmospheric climate model data can be used to estimate the amount of snow being added. The difference should be the overall loss of ice.

These graphs show Rignot’s results:

Graph a is Greenland, graph b is Antarctica and graph c is the total of both. These graphs show not the amount of ice, but the rate at which the amount of ice is changing, in gigatonnes per year. So, a line sloping down would mean that the ice loss is accelerating at a constant rate.

By fitting a line to satellite and atmospheric data, Rignot’s team found that over the last 18 years, Greenland has been losing an average of 22 gigatonnes more ice each year. Antarctica has been losing an average of 14.5 gigatonnes more each year.

But also note the black versus the red on the top two graphs! The GRACE data is in red. The other approach is in black. They match fairly well, though of course not perfectly.

The upshot? Rignot says:

That ice sheets will dominate future sea level rise is not surprising—they hold a lot more ice mass than mountain glaciers. What is surprising is this increased contribution by the ice sheets is already happening. If present trends continue, sea level is likely to be significantly higher than levels projected by the United Nations Intergovernmental Panel on Climate Change in 2007.

But how much sea level rise, exactly? Opinions still vary. A recent National Academy of Sciences report said at least 0.6 meters by 2100. But this still doesn’t include any melting of Greenland or the Antarctic!

This paper tries to take Greenland and the Antarctic into account:

• S. Jevrejeva, J. C. Moore and A. Grinsted, How will sea level respond to changes in natural and anthropogenic forcings by 2100?, Geophysical Research Letters 37 (2010), L07703.

The authors say their estimates are in line with past sea level responses to temperature change, and they suggest that estimates based on ice and ocean thermal responses alone may be misleading. With six different IPCC scenarios they estimate a sea level rise of 0.6–1.6 meters by 2100, and are confident the rise will be between 0.59 and 1.8 meters.

This paper suggests an upper bound on sea level rise 2 meters per century (if you max out everything) and a more realistic upper bound of 1 meter/century for this century (it could accelerate later):

• W. T. Pfeffer, J. T. Harper and S. O’Neel, Kinematic constraints on glacier contributions to 21st-century sea-level rise, Science 321 (2008), 1340-1343.

So, except for James Hansen, it sounds like most people would agree on an upper bound of about 2 meters of sea level rise by 2100. This is considerably more than the 4th IPCC report: remember, that gave an upper bound of about 0.6 meters.

I guess one moral is: stay tuned for further developments.

Everything you just read here, and more, was put together by the Azimuth Project team:

• Sea level rise, Azimuth Library.

I thank everyone who contributed, especially Staffan Liljgeren and Frederik de Roo.

25 Comments | climate | Permalink
Posted by John Baez

	Outside in - Involve… on Planets in the Fourth Dim…
	John Baez on Relative Entropy in Biological…
	WebHubTelescope on Regime Shift?
	WebHubTelescope (@WH… on Regime Shift?
	WebHubTelescope (@WH… on Regime Shift?
	John Baez on Crooks’ Fluctuation Theo…
	Blake Stacey on Crooks’ Fluctuation Theo…
	Thoughts on “R… on Regime Shift?
	John Baez on Regime Shift?
	John Baez on Crooks’ Fluctuation Theo…