29 April 2009

Hiatus time

I'll be away from the blog till about May 11th. Some articles might show up before then, but they'll be pre-programmed to appear. Comments and questions do get queued, so no worries there.

Fair number of good things going on. More news later. In the mean time, have a look at the good folks on my blog roll.

21 April 2009

Catching up on sea level

Bit of a place holder while I finish two other sea level things -- faq update, and comments on the Nature paper.

One important bit, which I was reminded of in email:
A good decade before the Noerdlinger and Brouwer paper, Phil Hays had mentioned to me that the ice shelves were a good 10 times the sea level effect of sea ice.

The sea level FAQ of mine I mentioned is quite old. What you see at the moment is the 1997 version, which is only minorly different from the 1991 version. I leave the 1997 available because as it's been cited in the professional literature, I do want that exact version available. Still, a fair amount has changed in the last 15 years. Not the main emphasis, which is largely time-independant. But many details are now in need of revision. Among them are: glaciers are more significant than my casual writing there suggested, Greenland is much less stable than indicated (recent discoveries), West Antarctica may be rather more stable.

Vernon: Maybe you could do some rewriting of your note(s)? I still can't figure out why you think my FAQ is misleading. My main point is that the sea level effect of sea ice is not zero, though it is a small number. Your conclusion is that the effect is not zero, though it's a small number. Note that the faq predates the Rothrock paper you mention. Also note that a) sea water's density dependance on temperature is somewhat different than fresh -- enough to matter for this situation b) global mean ocean water temperature is 3.5 C, not 20 (and at colder temperatures, the density depends less on temperature) c) you've assumed that all energy to melt the ice comes from the ocean, which is physically unlikely. As, to be sure, is it unlikely to be entirely from the atmosphere (which was effectively my take). The reason for my taking it all from the atmosphere was to isolate the haline effects of melting the ice from the thermal effects. Plus, the sea ice is usually in water colder than global average, i.e., very near freezing (by which time, the density dependance of sea water on temperature is very much smaller, about 16x if I remember right, than on salinity).

One feature of the sea level business is that once you try to attain accuracy, it gets very messy very quickly. c.f. Jay Alt's comment:

Even the 'simplest' calculations of sea level rise from earlier decades contain at least 10 components that influence the result. Tides, temps, winds, . . .

Here is a very nice resource from James Titus, who examined these issues in depth for EPA.

I've looked at the links and they're nice -- readable by nonprofessionals without losing the science.

The Nature paper http://www.nature.com/nature/journal/v458/n7240/full/nature07933.html is indeed interesting. It's also just far enough from my areas that it's difficult for me to be sure that something was missed, as opposed to being too obvious to mention in a professional setting. In short, though, it looks good and interesting, but may not mean quite what some of the press stories are suggesting. More to come.

13 April 2009

Ice and sea level

Melting sea ice or ice shelves can indeed change sea level. It turns out that I was probably the first person to compute by how much the sea ice can do so, and there's a story for tomorrow about why I wasn't the person to publish this in the scientific literature even though I had the answer more than a decade before the next person to look at the problem.

The first peer-reviewed investigation was published by Peter D. Noerdlinger and Kay R. Brower, in The Geophysical Journal International, 170, pp. 145-150, 2007 The melting of floating ice raises the ocean level. The DOI is 10.1111/j.1365-246X.2007.03472.x You can get the authors' copy at the linked title. They included a simple experimental demonstration as well, which I hadn't done. I also didn't think about the ice shelf contribution, which turns out to be 10 times larger than sea ice's. Oh well.

The wrong answer on this question is to say that a floating body displaces its own mass, so when it melts, the water level is unchanged. Now, as this is partly quoting Archimedes and he was an awfully bright guy, there's at least good company.

The reason it fails (and, by the way, it isn't clear that Archimedes didn't know about this) is that what is melting when we melt sea ice or ice shelves is not the same stuff as what it is floating in -- sea water. Sea water is salty, about 3.5% salt. Sea ice is fairly fresh, about 0.5% salt. And ice shelves are completely fresh. If we were melting ice shelf in to fresh water, the level would indeed not change. You can test this with a glass of water and some ice cubes. To find just what happens when you melt frozen stuff that's floating in a liquid, you have to do the math. I've got it in my Sea Level Change FAQ. The result is, sea level rises slightly. I found a few millimeters (about 4) for sea ice. Noerdlinger and Brower found a few centimeters (also about 4) for ice shelves. It isn't much, but it isn't exactly zero.

A way to think about what happens, minus most of the math, is to envision a block of ice floating in the ocean. The density of ice is lower than ocean water -- about 917 kg per cubic meter for ice, versus 1028 kg per cubic meter for ocean water. The difference is why '90'% of an ice berg is below the surface. Conversely, 10% is above the surface. It's actually (1028-917)/1028 above the surface, 10.8%. Now melt the fresh ice, but don't let it spread out or mix with the ocean. That gives us a material with density near 1000 kg per cubic meter. That blob, for the same reason that the ice was floating in the first place, sits (1028 - 1000)/1028 of itself above the water level -- 2.7%. That bit sticking above water level means that melting such ice does contribute to sea level change. If the density of the stuff you melt is different than the stuff it is floating in, you can indeed have a rise (or fall, if the melt is denser than what it floats in) in fluid level.

This example is also why I, in particular, and scientists more generally, want you to 'show me the math'. The thing is, when I first wrote the sea level FAQ, I made the same error as everybody else was making. It was an early commentator (Rick Chappell) who told me I was wrong (he didn't have the math, but did have the above principle) that prompted me to work out the math in detail. I was doing show just to show him in detail that he was wrong. In fact, at the end of my calculation, I'd shown myself that I was wrong. So updated the FAQ and my thanks to Rick. Merely asserting principles would not have changed anybody's mind. The problem being that, although a principle might be true (if I jump, the earth moves the other way), the effect might be too tiny to worry about. It's only when we do the math, get quantitative, that we can decide whether something is too tiny or not.

A slightly different example, prompted by this point going back to ancient Greece. There is an Aristotelean (or at least his time) principle that "Nature abhors a vacuum." Now, for many purposes in daily life, this is not a bad principle. If you try making a vacuum, you'll need to do things to shield it against nature trying to fill it back up. On the other hand, it was also an argument that there were no such things as atoms. The argument being, if there were atoms (discrete bits of matter) then there would be gaps between the atoms. But those gaps would be vaccum -- and 'nature abhors vacuum'. Now that we know that there are indeed atoms, the principle applies, but it is directed to how nature responds, and in which cases.

12 April 2009

Semi-open thread 1

This is the first semi-open thread for the blog, as opposed to the many question place threads. Please first read on commenting before putting up your comment. Given other comments I've been receiving lately, I'll also suggest reading:

Cherry Picking
Why you need 20-30 years to decide climate trends

Questions are, of course, welcome here as well!

On commenting

I really prefer to simply hit publish when a comment comes in to my box for moderation. Some recent comments have been making this difficult. At best, this means delays before your comment appears. At worst, it means, as happened to Gary and Greyshark, that the comment doesn't appear at all. So I'll remind about some of the notions which might be peculiar to this blog.

One thing to remember is, I'm aiming at science education. There are zillions of blogs for political wrangling. If that's your aim, visit one of them. Some of the blogs on my roll are more aimed to that end of the spectrum. A minus caused by that goal of mine is that your bare comment is often not furthering my goal of science education.

The corresponding plus is, I permit and indeed encourage links to scientific sources to support your points. So, Greyshark, when you say that there's not enough fossil fuel available to drive atmospheric CO2 levels to 560 ppm, it's time to provide a citation to a scientific source that supports your claim. This even more so since the science I've read says we could easily reach 4x preindustrial CO2 levels based on known reserves of coal and oil.

A second side of things to remember is that comments should be on topic. If your comment is about a cooling trend you perceive (Greyshark) the place for it is to a post where I talk about climate trends. For example, why you need 20-30 years to decide a climate trend. I don't close comments on the posts, so they're always available. I also provide a link for people to get a feed of the comments, not just my original posts, and I encourage its use. My commentators often make substantial contributions, so I hope readers do check the comments too. Sometimes the substantial contribution is to explain how I made a mistake. That's very welcome.

I'll encourage newcomers to take a look at Debate vs. Discussion. I'm looking for discussion here. If you want debate, again, many other places to go. Discussion, I grant, is more work. Among other things, it means you need to support your opinion, not just hold it. (Again, cites are welcome, so you can provide that support for us all to learn from.) On the other hand, and the great plus, is, it means you and I and other commentators and readers can learn something new and come away with different ideas than we started.

A related feature of this blog is the periodic 'question place' post, which is open for questions. While I will see it wherever you post, I do realize a recent post is easier to work with. I think this time, I'll start a semi-open thread. Semi because it won't be open to absolutely everything. You do need to be somewhere near a topic I do discuss in the blog, or would. And it does need to be more aimed at education (maybe of me, which is always welcome) than mere argument (not welcome) and follow the usual comment guidelines.

11 April 2009

Lazyness and research

A commentator mentioned his lazyness in asking a question over in a comment thread. Didn't occur to me just now to mention this aspect; I merely made what answer I could.

The thing is, one of the important parts of doing science is to find out what is already known. For the topic at hand there, details of Antarctic ice shelf structure and responses. People have been tramping around the Antarctic ice shelves, taking cores, doing seismic study, last few decades have included satellite remote sensing, etc.. So you'd think that most questions that could be asked simply would already have answers. Proper scientific thing to do is find out if it's already been answered. In this case, it looks like maybe it hasn't. Or hasn't been much.

So, excitement! There's something researchable out there that hasn't been beaten to death! Now, if you're not in a position to do the research yourself, it can be frustrating. But what I do in that case is become an informed spectator. I now know a topic that something very interesting to me will have some papers coming out. I don't know when, but I know it's going to happen. When it does, I can be all over it. It's a bit like watching a movie then. You may think you know how it's going to come out, good defeats evil, the girl gets the guy, whatever. But even if you're right, you can enjoy a lot about how you get from the start of the show to the final triumph.

I've also made use of the asking questions approach. Don't call it lazyness. I had an interesting idea far enough from my main work that I wasn't confident it was new. Seemed to be, but ... not sure. I could have racked my brains some and spent a lot of time tracking down the literature, and still not been confident since this particular problem goes back over 100 years. Instead, I asked a friend who does know that area and has published in it. Turns out my notion is indeed novel, and it probably explains a lot more than I thought it did. ... which is actually what I should be working on now (it isn't something related to my day job) instead of blogging. oops. More about this one when I get the paper submitted and get the response. (Journals don't like it if you publish the ideas elsewhere before the journal gets it out.)

10 April 2009

Another one bites the dust

Another ice shelf bites the dust, to little surprise in the polar community. In this case, it's the Wordie ice shelf, and you can see a photo and a short write up at:

The reason I'm not surprised, and anybody who has been reading the science is not surprised, is that we knew years ago that warming was going to lead to the breakup of ice shelves. See, for example:

Rapid disintegration of the Wordie Ice Shelf in response to atmospheric warming, by C. S. M. Doake & D. G. Vaughan
. That was 1991. You do have to remember that glaciologists are used to things that move at glacial speeds.

The breakup was more specifically tied to atmospheric warming in a more recent (1996) paper by D. G. Vaughan & C. S. M. Doake Recent atmospheric warming and retreat of ice shelves on the Antarctic Peninsula. The authors cite the earliest suggestions of problems for Antarctic ice shelves in a warming world as Mercer's 1978 paper
West Antarctic ice sheet and CO2 greenhouse effect: a threat of disaster. Rather drastic title. But it serves to both establish that the collapse of these ice shelves due to CO2-induced climate change is an old issue, and to provide yet another example of a scientist in the 1970s who was not expecting 'another ice age' any time soon.

The scientific question left on ice shelf collapses on the Antarctic peninsula is not whether, but which one is going to go next, and how soon. For the ice shelves farther to the pole -- which are the big ones and of the greatest concern (the reason for the 'threat of disaster' in Mercer's title) for the future, we still have several scientific questions about whether, and what happens how fast if they do go.

Some folks are making comments which mix up sea ice and ice shelves. Please don't do that! See my note about ice types for the simple differences between the sorts of ice.

It's also been mentioned that the breakup of ice shelves can't change sea level. This isn't actually true. I'll take up the details in two notes to come. First, why it isn't true (you can get ahead by reading the Sea Level Change FAQ -- same process that means sea ice can change sea level applies to ice shelf ice). Second, why it is someone else published it first, even though I had the answer 10 years earlier. A bit of how science is done, and reminder that scientists are fallible.

09 April 2009

20 who deny CO2 is correlated with temperature

Over in my Does CO2 correlate with temperature? post, some of the commentators are claiming that nobody says CO2 is not correlated with temperature. This is odd, since I name a source there which does so. But, in the spirit of my 20 links game, here are 20 (more) who say so.

First, a word about doing science, and weeding sources. One thing about doing science is that you're supposed to read the source you're commenting on. As some commentators demonstrated, they didn't read my article before making their comment. That would have been the easiest way to discover a source which did as claimed. More work, but still easy, is to do a search and see if the comment is out there. Now, as you know from reading my 20 links game earlier, I think pretty much any statement you'd care to name is being asserted somewhere on the web, and probably in at least 20 different locations. If you've been looking at the web for a while, you've seen some pretty strange statements being made seriously.

Where the commentators agree with me is that it's absurd to claim that there's no correlation between temperature and CO2. Consequently, any source which does claim so is unreliable and you'd be better off moving on. (Oddly, they don't seem to agree with this part.)

So, here are 20 sources (well, 21) which assert no correlation between temperature and CO2, and are referring to recent (last 150 years) climate:
  1. Joseph D'Aleo on Jennifer Marohasy's blog
  2. Powerpoint presentation, see slide 47
  3. Ken Gregory
  4. Christopher Horner, Lawyer
  5. Lee C. Gerhard, Center for Science and Public Policy
  6. Warwick Hughes, repeat of preceding
  7. Article by Dennis Avery, quoting Timothy Patterson
  8. Article by Timothy Patterson, published in Financial Post, copied to this site
  9. An englishman's castle, blog
  10. Noel Sheppard, at Newsbusters
  11. Glen Meakam, Pittsburgh Tribune Review 25 January 2009 (cached version)
  12. Joseph D'Aleo, on his own site
  13. Jim Manzi, taking Steve Milloy to task for claiming no correlation
  14. Capitalism Magazine, quoting Timothy Ball
  15. Martin Durkin, the producer of the documentary The Great Global Warming Swindle
  16. Geoaffair
  17. Jules has been engaging in discussion and documenting Hans Labohm's denial of any correlation between CO2 and Temperature (Labohm goes farther than any others I've seen, and denies it for all time scales from tenths of years to millions of years)
  18. Christopher Monckton at Science and Public Policy
  19. Paul Drallos, PhD (Physics)
  20. user 'bravo22c' at the Telegraph, UK
  21. Alan Caruba in the Canada Free Press

Took 90 minutes since I didn't accept blog comments -- all these are original articles, sources that get quoted elsewhere. I also didn't take many copies of the same sources, which, again, would have shortened the search. Also no videos. But I threw in a bonus cite. Some cherry pick their periods ('last 10 years', '1945-1970' or the like), some leave it at 'recent', without saying what 'recent' means.

As I discussed before, you need 20-30 years to be talking about a climate trend. So the sources which use only 10 or so are being doubly misleading.

06 April 2009

Running in Thunderstorms, longer

Last summer I posted a short note about running in thunderstorms (don't), but just a quickie. A little more length in case someone is thinking that I'm just chicken and a Real Runner would go out anyhow. As I mentioned last time, I've run in snow, rain, sleet, well below freezing temperatures, high heat and humidity, and so on. It is only the thunderstorms that stop me.

The reasoning of the folks who have argued that it's ok to run in thunderstorms is that 'well, very few people are hit by lightning, so I'll take that tiny risk'. They're banking on arithmetic like this: 300 people per year are hit by lightning in the US, and there are 300 million people in the US, so their 'odds' are 1 in a million of being hit. Unfortunately, this is numerology rather than sound statistics.

The problem with that approach is, almost none of those 300 million are in a place where they could be hit by lightning. Most people, most of the time, are indoors or inside a car -- places you should go to avoid getting hit by lightning. So, with no effort or attention, most people could not be hit even if there were a thunderstorm in the area.

Once there is a thunderstorm in the area, almost everybody heads for safety -- and everybody should. Go inside your house (and stay away from the pipes); if you are away from homes, go to your car; if that's too far or you didn't drive, head for low ground; if you're in Flatlandia (which is where I grew up) head away from anything tall -- away from trees, telephone poles, and especially away from metal towers. These steps are easy and almost everybody takes them.

The right statistical question is "Of the people who are in a position where they could be hit, what fraction do get hit." This figure is more like 1 in 3000, rather than 1 in 1,000,000. Almost everybody does, intentionally or accidentally, take suitable precautions. Be one of them.

Since most of us who run, do so for our health, I'll point out that being hit by lightning is not good for your health. A high fraction of people hit, are killed. Of those who do not die, a high fraction have permanent health problems.

Beyond the fact that it's bad for your health and easy to take appropriate precautions, is the fact that shifting your schedule a little will let you get your run in easily. You need to give a thunderstorm about a 30 minute clearance, wait for 30 minutes after the last thunder you hear. But, an individual thunderstorm is not a long-lived event. 90 minutes is long. Moving your run 2 hours only means go out at 7 instead of 5, or vice versa. If it's very important to get the run in, then moving it a couple of hours is easy enough, and enormously safer. If you're looking at a line of thunderstorms, or a supercell, it's a longer window and you may well have to miss the run. On the other hand, such systems also produce tornadoes and large hail and have severe winds such that it'd be hard to do a workout anyhow.

For more information about thunderstorm and lightning safety:
Red Cross on Thunderstorm and lightning preparedness
NWS Lightning Safety
NWS home page -- with current watch and warning areas

Added: from Hank Roberts' September 21, 2010 comment:

04 April 2009

New blogs on roll

In several cases, I'm surprised that they're not already on the blogroll, my apologies folks.

Newly-added are:
Bad Astronomy (Phil Plait)
Old man in a cave (Fergus Brown)
Hot Topic -- Global Warming and the Future of New Zealand
Die Klimakrise (in German / auf Deutsch)
Rust Never Sleeps
Stoat (William Connolley)

Farther afield, I'll mention
Greg Laden's Blog

Plus, it'd be a help if someone could explain how to set up Digg links easily, and preferably, automatically. According to sitemeter, a fair number of folks are finding this blog by that route. I'd as soon make it easier. Similarly reddit. Explanations of technorati also welcome.

03 April 2009

How much detail is there really?

I'm thinking about sea surface temperature (SST) these days, but the approach here is one that can be applied to many situations, even ones outside weather and climate. A common, important, and not always easy, questions is -- just how much detail do you need? The more detail, the more expensive it is to make a good product, whether that's an analysis of sea surface temperature, a climate model, or a surface in a video game. Of course, what I'd like is the sea surface temperature every few meters over the entire globe. If that's more than necessary at some time, I could average it down. But ... it would take an awful lot of storage to save temperatures every few meters (my back yard, my neighbor's, my front yard, ...) over the whole globe.

Let's start by looking at an actual high resolution global product, though not every few meters! The SST analysis at http://polar.ncep.noaa.gov/sst/ gives a value every 1/12th of a degree in latitude and longitude, one about every 9 km (6 miles). It has about 9 million values. Let's also suppose that this is fine enough resolution that everything important is represented.

The worst resolution is to use 1 number for the entire globe, the average for all ocean points. To measure how bad this is, I'm going to compute the root mean square error. (Those who know what this is can skip to the next paragraph.) It is often abbreviated rmse. To find it, we go through every ocean point in the grid and find the difference between the value there and the average. Then we multiply this difference by itself (square it -- this avoids the marksmen statistician story*). Then add up these squares for every ocean point. This is a big and not interesting number. One thing that would be more interesting is the average value of the squared error -- the mean square error. So we divide by the number of points that were involved. This also tells us the error variance. Since we think more in terms of temperature and temperature changes than squares of temperature changes, we take the square root of the mean square error -- get the rmse. This is a figure which represents a typical magnitude of how far off we expect to be. We could be either warmer or colder by this much, but this is the magnitude.

* Two statisticians went to a shooting range and each fired at the target. The first missed by 1 meter to the left (-1 meter). The second missed by 1 meter to the right (+1 meter). They then congratulated each other on their fine marksmanship because on average they had hit the bullseye. Their average error was indeed zero. But their rms error was 1 meter.

When I compute the RMSE for using global mean temperature instead of the full resolution grid, I find 12 C. That's ... enormous. The difference between water at 20 C (68 F) and 32 C (90 F) is pretty large! So, clearly, we can't be satisfied with an RMSE of 12 C. But now we have a method for looking at the resolution we need, and a notion of how bad you can get.

Then I made my program average over smaller boxes than the whole globe, say 90 degrees on a side -- London to Chicago, equator to pole -- and found the RMSE comparing those box averages to the original temperatures in the full resolution grid. No surprise that boxes that large were pretty bad. But ... once I got down to boxes 2 degrees on a side (which is something like 200 km, or 120 miles), the RMSE was down to 0.5 degrees.

This is still definitely not zero, but it isn't bad. When a typical satellite used for the job -- such as the AVHRR instrument on NOAA-18 -- is used to make an observation, it has an RMSE (compared to a buoy's thermometer at about the same location at about the same time) of about 0.5 degrees. In other words, with boxes 2 degrees on a side, the average represents what is happening in sea surface temperature about as well as getting a single observation from satellite. We've also managed to reduce our RMS error by about 95% as compared to using only a single number. On the other hand, even though we've captured 95% of what's going on, we only need to use 16,200 numbers -- instead of the 9,331,200 we started with. 95% of the information of the full grid, with only 0.2% as much data.

We've caught 90% of what is happening (reduced the rmse by 90%) when the boxes are 6 degrees on a side (600 km, 360 miles). And it's 99% once we're down to boxes only 0.5 degrees (50 km, 30 miles) on a side (which means only about 3% as many data points are needed to represent the full data set to 99% accuracy).

Now, let's translate this back to some situations we might care about. In trying to construct climatologies of sea surface temperature, we run in to the problem that as we go back in time, there are fewer and fewer data points. On the other hand, if we have 1 observation in each box 6 degrees on a side, we've managed to capture 90% of what is happening in the sea surface temperature. In other words, a much sparser data set than we might imagine could indeed represent an awful lot of what is happening in the ocean. A global grid at 6 degrees resolution has only 1800 points, so we need only 1800 observations to fill it in our simple-minded way.

At 2 degrees resolution, we've captured 95% of what happens in sea surface temperature (at least to this quick little glance -- I only looked at 1 day, as analyzed by 1 center, etc.) So, if we had a good global ocean model at 2 degree resolution, we'd actually be pretty far along in being able to predict sea surface temperatures (model climate, etc.) well. In practice, there are processes that happen in smaller areas than the 2 degree box which can change the whole box's average and we, therefore, want finer resolution than 2 degrees. More about that in a different post.

In thinking about observing systems, if we only 'need' 1 observation every 200 km or so, and we have satellites that can take an observation every 4 km (like the one above) we're all done, right? Unfortunately, no. The problem is, that satellite looks for clouds. If there are clouds -- and cloudy areas can easily stretch for 1000 km -- the satellite can't see the sea surface to tell us what the temperature is down there. So we need other data sources -- ships, buoys, other sorts of satellite (ones that can see through clouds) to fill in even just the 200 km (2 degrees latitude-longitude) boxes each day. Plus we need to observe the detail in the oceans that are involved in those other processes I mentioned. It isn't just for models that they're important -- fishing also cares.

02 April 2009


I'm actually referring to an important mathematical and physical concept, rather than the comments you give (which I also value).

Feedback is an extremely common process. Perhaps the most common case that people know is feedback involved public address systems. You have a microphone to pick up sound, which goes to an amplifier, and then out a speaker. If you put the microphone too near the speaker, then the microphone picks up some minor sound (say the sound of someone putting papers on the stand near the microphone), it goes through the amplifier and the louder sound comes out the speaker. The microphone now picks up that sound, it gets amplified even more and comes out the speaker again. Repeat through a number of cycles and the speaker is now as loud as it can be. This is a runaway feedback. Not all feedback is runaway.

A feedback can also be limited. Consider the atmosphere in this case. It has a temperature, carbon dioxide level, and water vapor level. Both carbon dioxide and water vapor are greenhouse gases, so if there is more of them, the temperature goes up. Suppose we put enough carbon dioxide into the atmosphere that its greenhouse effect (alone) raised temperature by 1 degree. If the atmosphere is warmer, we expect it to have more water vapor. That extra water vapor, let's say, produces another 0.5 degrees of warming. But, since temperature has gone up again, there's still more warming -- another half of this, for 0.25 degrees. This feeds back through increasing the water vapor to make another 0.125 degrees warming. Keep cycling through this feedback and it turns out to add another 1 degree of warming (1 = 0.5 + 0.25 + 0.125 + ...) after you've gone through an infinite number of steps. It's pretty close after a limited number of steps (99.9% of the way there after 10 cycles). We can look at these feedbacks in terms of how much of a response (multiplier) there is to a 1 degree kick to the system. I made up the number 0.5 here (every step is 0.5 times the previous). That's actually about the right size, in addition to being simple to work with. If the response multiplier is, say, 0.75 instead, then instead of getting back a total warming of 2 degrees, we would get back 4 degrees. The formula is
total = 1 / (1 - x)
where x is this multiplier, and the multiplier has to be less than 1.

Feedbacks can also produce cycles. A common illustration of this is predators and prey -- sharks and fish, or foxes and hares. Suppose one year, there are more fish than usual. The sharks, then, have a lot to eat and give birth and raise more sharks than usual. But, now that there are more sharks, they eat up even more fish than usual. That decreases the number of fish below the usual level. With fewer than normal fish, the sharks start dying off. That eventually gives us fewer than normal sharks, so the fish population recovers. And so on. The two populations could keep cycling (if the balances are right), or one could crash (depends on whether the extra sharks eat up too many fish, or whether the time of few fish lasts too long for any sharks to survive).

In the climate system, there are definitely some amplifying feedbacks and some cycling feedbacks. There don't appear to be any runaway feedbacks. That's not terribly reassuring, however, because life can get quite unpleasant even if temperatures don't run off to boiling the oceans.

01 April 2009

Miscellaneous recent things

Been doing interesting (to me, at least) things at work and home, which has translated to not doing much by way of the blog. Some of those activities will translate to blog entries one of these days. For now, some odds and ends of thoughts.

I've just finished Dante's Inferno (the Ciardi translation). I'm more than a little puzzled about how this is supposed to be great literature. Any ideas?

A little farther back, I finally read my copy of Copernicus' On the Revolution of the Heavenly Spheres -- his 1543 book that contributed so much to the intellectual revolutions of the next couple centuries. It was interesting on a number of counts, and I'll be blogging about some of them. Shortly after that, I read Jack Repchack's Copernicus' Secret, which gives an interesting biography of Copernicus and context he was working in.

I've had an interrupted return to my running this year, calf complaints off and on. But Sunday I did make my first run of 30 minutes with no walking. Good news, as the 30 is a major fitness point and means I can go to a local 5k and finish it ok. Not fast, but ok.

Day job:
I'm officially moving in to working on sea surface temperature. That's been under way for a while, but recently took up some new bits. So expect some entries about what sea surface temperature is (turns out there are multiple answers), how it's measured, and the like.

Ok, I know that on April 1 I am supposed to write some kind of a joke or spoof. But I'm just not feeling creative today. At least not that sort of creative.