My wife, Vickie, and I took part in 24 hour contests last weekend. Hers was the more formal -- a 24 hour short-story writing contest. They give a topic and the word length at noon one day, and the story is due by noon the next day. Neither of them really suited her; the length was only 850 words, which is quite short to write a good story in. But I believe she succeeded. And she discovered some more about her writing, and what she can do. So all to the good. We'll find out in a month or so what the judges thought.
My own contest was a bit more unusual, not least because there were no other contestants, no judge, and no rules. Still, it occurred to us that while Vickie was doing her 24 hours focused on writing, I could also do 24 hours focused on writing. But in my case, a science paper. Continuing with a paper I've already started and trying to finish it in 24 hours would not have been in keeping with the spirit of her contest, which was focused on novelty. I have a ton of ideas, though, lurking in the back of my mind at any given time, and several feet of them in cabinets if, for some reason, I don't like ones that are leaping to mind. So my challenge was to take one of them and give it a good hard run for 24 hours.
I didn't finish a paper, though I did get 2 good pages written. The writing was done in the first hour. (I'm a fast typist and have been thinking about this idea off and on for a few years.) Then in to the charge at data. Or, rather, the slow and careful sneaking up on data and hoping that it didn't bare its fangs and shred my idea in the first few seconds of contact.
After my 24 hours, the notion was still intact and, if anything, looking better. Didn't finish the paper, but no surprise there as actually there are quite a few papers to come from this idea. But I did make good progress on getting data and testing that the idea held up against some reasonably good counter-tests. More detail to come later, once I get a little farther. But things to be coming up here before then are the North Atlantic Oscillation, Arctic Oscillation, Pacific-North American, and Antarctic Oscillation (NAO, AO, PNA, and AAO, respectively).
29 September 2008
24 September 2008
Atmospheric Lapse Rates
The question place is serving its purposes, one of which is to bring up points that warrant some discussion in a fuller post. At hand is the atmospheric lapse rate, which Bart brought up by way of his question:
There are models, somewhere, that assume anything one could mention, so I suppose there are some which assume the lapse rate. As you correctly notice, though, lapse rates depend on conditions, and those conditions vary over the globe. A serious climate model couldn't assume the lapse rate. And, in truth, they don't. More in a moment, but something to look back at is my description of the 16 climate models
Let's start with the lapse rate itself. What it is, is the change in temperature with elevation. Through the troposphere, the lapse rate is a negative number (cooling with elevation). In the stratosphere, it turns to zero and then positive (warming with elevation). In the mesosphere, we go back to cooling with elevation. This is a strictly observational issue. You can find temperature profiles, say from the Standard Atmosphere (a specific thing; Project: take a web look for it and see what they look like; they've changed through time, by the way). And then find the temperature difference between two levels, and divide by the elevation difference. That'll give you the average lapse rate. You can also find, radiosonde soundings of temperature. (I'd start my search for this project at the National Climatic Data Center.) This will let you see how the lapse rates vary day to day at a location, and between locations.
On the theoretical side, we go back to Conservation of Energy. We start with a completely dry (meaning no water vapor) blob of air, in an insulating bag that prevents it from radiating, conducting, or convecting energy to or from the surroundings. Then we lift it through the atmosphere. As we do so we'll find that its temperature drops. This happens because our blob does work in expanding. The energy for that work comes from its own thermal energy store. We can compute exactly how much the air would cool under this circumstance. It is about 10 K per km near the surface of the earth. This is what we are referring to in talking about the Dry Adiabatic Lapse Rate. The 'adiabatic' refers to our insulating bag around the air blob.
The polar regions, particularly the Antarctic plateau, are not bad approximations to that situation. But most of the atmosphere has fairly significant amounts of water vapor. We start, now, with a slightly different bag. It still prevents heat to be added or lost to the bag from outside. But now there's a second energy source inside the bag. Water vapor can condense, and when it does, it will release energy. We take the approximation that all the heat energy goes to the gases in the bag, and that the newly-formed liquid water is immediately moved outside the bag.
Now when we lift the bag, things go a bit differently. Let's start with air at 70% relative humidity, a typical global mean value. As we lift the air, it first acts 'dry', so cools at the about 10 K per km rate. But after a while, we have cooled to the point of being at 100% relative humidity. When we start to lift any further, water starts condensing and releasing heat. The condensation only happens if we're still cooling, so it can't reverse that tendency. But it can greatly slow the rate of cooling. This gives us a Moist Lapse Rate. Note that I dropped 'adiabatic' from the description. Since material is leaving the bag, it isn't an adiabatic process any more. It is pseudoadiabatic (a term you'll see) -- almost adiabatic, as the loss of mass isn't large. But not entirely adiabatic.
As a typical ballpark value, we take 6.5 K per km as the moist lapse rate. But this obviously will depend a lot on how much water was in the bag to begin with, and the temperature. If we start with a very warm, saturated, bag of air, then the lapse rate can be even lower than the 6.5 K per km. If we start, though, with a cold blob of air, even if it is saturated, we are still close to 10 K per km lapse rate. The thing is as we get colder, there's less water vapor present, which gives less condensation, then less heating. Consequently even in the tropics, the lapse rate heads towards the dry adiabatic value as you get high above the surface.
Whether moist or dry, the lapse rate computed this way is an idealization. In the real atmosphere, radiation does move energy around, and blobs of air do mix with each other (even when rising). Still, it's derived from a strong scientific principle (conservation of energy), and it turns out to give us good ideas (in reasonable accord with observation) about what the atmosphere should look like in the vertical.
For the modelling, let's think back to the 16 models. First, many of them are never used, so we'll ignore the longitude-primarily models. That leaves us with the 0 dimensional model I've already given an example of, and there's not even the opportunity to impose or even make use of a lapse rate in that. The 4 dimensional model definitely doesn't assume a lapse rate -- doing so would force violations of conservation of energy. Radiative-convective models can't force the lapse rate for the same reason. For a discussion of such models, to which I'll be returning in another post about water vapor's greenhouse contribution, see Ramanathan and Coakley, 1978. As of that era, one did specify a critical lapse rate. This isn't the lapse rate that the model had to have, rather, it was a limit. If the limit were violated, something has to happen. That something is to conserve energy by mixing the layers that violated the limit. And Energy Balance Models, as I expected, don't even mention lapse rate. See North, 1975 for a discussion of energy balance models.
Either the models are too simple to know about lapse rates (0 dimensional, Energy Balance), or they compute the lapse rate (Radiative Convective, 4 dimensional). Either way, the lapse rate is not assumed before hand. It's an interesting after the fact diagnostic for the Radiative Convective or 4d models, or impossible to speak to.
One thing to do is find some better sources for you to read. I taught an introductory (freshman level) physical geology class with Lutgens and Tarbuck, and liked the text there. They have a text at that level for meteorology, but I haven't read it myself. It should be good, though. John M. Wallace and Peter V. Hobbs, Atmospheric Science: An Introductory Survey is an excellent book. In half the chapters, comfort with multivariate calculus is assumed. But the other half are descriptive/physical rather than quantitative/mathematical so should be approachable already. A second edition is now out, I used the first. Does anyone have suggestions for a good freshman level introduction to meteorology/climate?
2) I read elsewhere (I can only research what I read, I don't really have the ability to check much of this for myself) that models assume a constant lapse rate. Chris said the lapse rate is required for the greenhouse effect, but from everything I look at people only catgorize in "Dry" or "Moist" cases, but doesn't it vary everywhere over the globe?
There are models, somewhere, that assume anything one could mention, so I suppose there are some which assume the lapse rate. As you correctly notice, though, lapse rates depend on conditions, and those conditions vary over the globe. A serious climate model couldn't assume the lapse rate. And, in truth, they don't. More in a moment, but something to look back at is my description of the 16 climate models
Let's start with the lapse rate itself. What it is, is the change in temperature with elevation. Through the troposphere, the lapse rate is a negative number (cooling with elevation). In the stratosphere, it turns to zero and then positive (warming with elevation). In the mesosphere, we go back to cooling with elevation. This is a strictly observational issue. You can find temperature profiles, say from the Standard Atmosphere (a specific thing; Project: take a web look for it and see what they look like; they've changed through time, by the way). And then find the temperature difference between two levels, and divide by the elevation difference. That'll give you the average lapse rate. You can also find, radiosonde soundings of temperature. (I'd start my search for this project at the National Climatic Data Center.) This will let you see how the lapse rates vary day to day at a location, and between locations.
On the theoretical side, we go back to Conservation of Energy. We start with a completely dry (meaning no water vapor) blob of air, in an insulating bag that prevents it from radiating, conducting, or convecting energy to or from the surroundings. Then we lift it through the atmosphere. As we do so we'll find that its temperature drops. This happens because our blob does work in expanding. The energy for that work comes from its own thermal energy store. We can compute exactly how much the air would cool under this circumstance. It is about 10 K per km near the surface of the earth. This is what we are referring to in talking about the Dry Adiabatic Lapse Rate. The 'adiabatic' refers to our insulating bag around the air blob.
The polar regions, particularly the Antarctic plateau, are not bad approximations to that situation. But most of the atmosphere has fairly significant amounts of water vapor. We start, now, with a slightly different bag. It still prevents heat to be added or lost to the bag from outside. But now there's a second energy source inside the bag. Water vapor can condense, and when it does, it will release energy. We take the approximation that all the heat energy goes to the gases in the bag, and that the newly-formed liquid water is immediately moved outside the bag.
Now when we lift the bag, things go a bit differently. Let's start with air at 70% relative humidity, a typical global mean value. As we lift the air, it first acts 'dry', so cools at the about 10 K per km rate. But after a while, we have cooled to the point of being at 100% relative humidity. When we start to lift any further, water starts condensing and releasing heat. The condensation only happens if we're still cooling, so it can't reverse that tendency. But it can greatly slow the rate of cooling. This gives us a Moist Lapse Rate. Note that I dropped 'adiabatic' from the description. Since material is leaving the bag, it isn't an adiabatic process any more. It is pseudoadiabatic (a term you'll see) -- almost adiabatic, as the loss of mass isn't large. But not entirely adiabatic.
As a typical ballpark value, we take 6.5 K per km as the moist lapse rate. But this obviously will depend a lot on how much water was in the bag to begin with, and the temperature. If we start with a very warm, saturated, bag of air, then the lapse rate can be even lower than the 6.5 K per km. If we start, though, with a cold blob of air, even if it is saturated, we are still close to 10 K per km lapse rate. The thing is as we get colder, there's less water vapor present, which gives less condensation, then less heating. Consequently even in the tropics, the lapse rate heads towards the dry adiabatic value as you get high above the surface.
Whether moist or dry, the lapse rate computed this way is an idealization. In the real atmosphere, radiation does move energy around, and blobs of air do mix with each other (even when rising). Still, it's derived from a strong scientific principle (conservation of energy), and it turns out to give us good ideas (in reasonable accord with observation) about what the atmosphere should look like in the vertical.
For the modelling, let's think back to the 16 models. First, many of them are never used, so we'll ignore the longitude-primarily models. That leaves us with the 0 dimensional model I've already given an example of, and there's not even the opportunity to impose or even make use of a lapse rate in that. The 4 dimensional model definitely doesn't assume a lapse rate -- doing so would force violations of conservation of energy. Radiative-convective models can't force the lapse rate for the same reason. For a discussion of such models, to which I'll be returning in another post about water vapor's greenhouse contribution, see Ramanathan and Coakley, 1978. As of that era, one did specify a critical lapse rate. This isn't the lapse rate that the model had to have, rather, it was a limit. If the limit were violated, something has to happen. That something is to conserve energy by mixing the layers that violated the limit. And Energy Balance Models, as I expected, don't even mention lapse rate. See North, 1975 for a discussion of energy balance models.
Either the models are too simple to know about lapse rates (0 dimensional, Energy Balance), or they compute the lapse rate (Radiative Convective, 4 dimensional). Either way, the lapse rate is not assumed before hand. It's an interesting after the fact diagnostic for the Radiative Convective or 4d models, or impossible to speak to.
One thing to do is find some better sources for you to read. I taught an introductory (freshman level) physical geology class with Lutgens and Tarbuck, and liked the text there. They have a text at that level for meteorology, but I haven't read it myself. It should be good, though. John M. Wallace and Peter V. Hobbs, Atmospheric Science: An Introductory Survey is an excellent book. In half the chapters, comfort with multivariate calculus is assumed. But the other half are descriptive/physical rather than quantitative/mathematical so should be approachable already. A second edition is now out, I used the first. Does anyone have suggestions for a good freshman level introduction to meteorology/climate?
21 September 2008
Excess Precision
Excessive precision is one of the first methods mentioned in How to Lie With Statistics. It's one that my wife (a nonscientist) had discovered herself. It's very common, which makes it a handy warning signal when reading suspect sources.
In joke form, it goes like this:
Psychology students were training rats to run mazes. In the final report, they noted "33.3333% of the rats learned to run the maze. 33.3333% of the rats failed to learn. And the third rat escaped."
If you didn't at least wince, here's why you should have. In reporting scientific numbers, one of the things you need to do is represent how good the numbers are. In order to talk about 33.3333% of the rats, you'd have to have a population of a million rats or more. 33.3333% is saying that the figure is not 33.3334% or 33.3332%. You only should be showing as much precision as you have data for. Even though your calculator will happily give you 6-12 digits, you should be representing how accurate your number is. In the case of the rat problem, if 1 more rat had been run, one of those 33% figures would change to 25 or 50. The changes of +17% or -8% are so large that they should not even have reported at the 1% level of precision. What the students should have done was just list the numbers, rather than percentages, of rats all along.
As a reader, a useful test is to look for how large the population is versus how many digits they report in percentages. Every digit in the percentage requires 10 times as large a population. Need 10 for the first digit (again, the psych. students shouldn't have reported percents), 100 for the second, and so on. A related question is 'how much would the percentages change with one more success/failure?' This is what I looked at with running the extra rat.
Related is to consider how precise the numbers involved were at the start. When I looked at that bogus petition, for instance, I reported 0.3 and 0.8%. Now the number of signers was given in 4 or 5 digits. That would permit quite a few more than the 1 I reported. The reason for only 1 is that I was dividing the number of signers by the size of the populations (2,000,000 and 800,000) -- and the population numbers looked like they'd been rounded heavily, down to only 1 digit of precision. When working with numbers of different precisions, the final answer can only have as many digits precision as the worst number in the entire chain.
An example, and maybe the single most commonly repeated one from climate, is this page, which gives (variously, but table 3 is the piece de resistance) the fraction of the greenhouse effect due to water vapor as 95.000% That's a lot of digits!
Let's take a look at the sources he gives, and then think a little about the situation to see whether 5 digits precision is reasonable. Well, the sources he has valid links for (1 of the 9 is broken, and one source doesn't have a link; I'll follow that up at lunch at work in a bit) certainly don't show much precision. Or being scientific, for that matter (news opinion pieces and the like). My favorite is the 21st century science and technology (a LaRouche publication), whose cover articles include "LaRouche on the Pagan Worship of Newton". The figures given are 96-99% (LaRouche mag), 'over 90%', 'about 95%', and the like. Not a single one gives a high precision 95.000%, or a high precision for any other figure. This should have been a red flag to the author, and certainly is to us readers. Whatever can be said about the fraction of greenhouse effect due to water vapor, it obviously can't be said with much precision. Not if you're being honest about it. (We'll come back in a later post to what can be said about water vapor, and it turns out that even the lowest of the figures is too high if you look at the science.)
Now for a bit of thinking on water vapor. The colder the atmosphere is, the less water vapor there can be before it starts to condense. (It's wrong to call it the atmosphere 'holding' the water vapor, but more in another post.) It also turns out to vary quite a lot depending on temperature. In wintertime here (0 C, 32 F being a typical temperature), the pressure of water vapor varies from about, say, 2 to 6 mb. In summer, it's more like 10 to 30. (30 million?! It gets very soggy here, though not as much as Tampa.) On a day that it's 30 mb here, it can be 10 mb a couple hundred km/miles to the west. Water vapor varies strongly through both time and space. As a plausibility test, then, it makes no sense for there to be 5 digits precision to the contribution of something that varies by over a factor of 10 in the course of a year, and even more than that from place to place on the planet.
In joke form, it goes like this:
Psychology students were training rats to run mazes. In the final report, they noted "33.3333% of the rats learned to run the maze. 33.3333% of the rats failed to learn. And the third rat escaped."
If you didn't at least wince, here's why you should have. In reporting scientific numbers, one of the things you need to do is represent how good the numbers are. In order to talk about 33.3333% of the rats, you'd have to have a population of a million rats or more. 33.3333% is saying that the figure is not 33.3334% or 33.3332%. You only should be showing as much precision as you have data for. Even though your calculator will happily give you 6-12 digits, you should be representing how accurate your number is. In the case of the rat problem, if 1 more rat had been run, one of those 33% figures would change to 25 or 50. The changes of +17% or -8% are so large that they should not even have reported at the 1% level of precision. What the students should have done was just list the numbers, rather than percentages, of rats all along.
As a reader, a useful test is to look for how large the population is versus how many digits they report in percentages. Every digit in the percentage requires 10 times as large a population. Need 10 for the first digit (again, the psych. students shouldn't have reported percents), 100 for the second, and so on. A related question is 'how much would the percentages change with one more success/failure?' This is what I looked at with running the extra rat.
Related is to consider how precise the numbers involved were at the start. When I looked at that bogus petition, for instance, I reported 0.3 and 0.8%. Now the number of signers was given in 4 or 5 digits. That would permit quite a few more than the 1 I reported. The reason for only 1 is that I was dividing the number of signers by the size of the populations (2,000,000 and 800,000) -- and the population numbers looked like they'd been rounded heavily, down to only 1 digit of precision. When working with numbers of different precisions, the final answer can only have as many digits precision as the worst number in the entire chain.
An example, and maybe the single most commonly repeated one from climate, is this page, which gives (variously, but table 3 is the piece de resistance) the fraction of the greenhouse effect due to water vapor as 95.000% That's a lot of digits!
Let's take a look at the sources he gives, and then think a little about the situation to see whether 5 digits precision is reasonable. Well, the sources he has valid links for (1 of the 9 is broken, and one source doesn't have a link; I'll follow that up at lunch at work in a bit) certainly don't show much precision. Or being scientific, for that matter (news opinion pieces and the like). My favorite is the 21st century science and technology (a LaRouche publication), whose cover articles include "LaRouche on the Pagan Worship of Newton". The figures given are 96-99% (LaRouche mag), 'over 90%', 'about 95%', and the like. Not a single one gives a high precision 95.000%, or a high precision for any other figure. This should have been a red flag to the author, and certainly is to us readers. Whatever can be said about the fraction of greenhouse effect due to water vapor, it obviously can't be said with much precision. Not if you're being honest about it. (We'll come back in a later post to what can be said about water vapor, and it turns out that even the lowest of the figures is too high if you look at the science.)
Now for a bit of thinking on water vapor. The colder the atmosphere is, the less water vapor there can be before it starts to condense. (It's wrong to call it the atmosphere 'holding' the water vapor, but more in another post.) It also turns out to vary quite a lot depending on temperature. In wintertime here (0 C, 32 F being a typical temperature), the pressure of water vapor varies from about, say, 2 to 6 mb. In summer, it's more like 10 to 30. (30 million?! It gets very soggy here, though not as much as Tampa.) On a day that it's 30 mb here, it can be 10 mb a couple hundred km/miles to the west. Water vapor varies strongly through both time and space. As a plausibility test, then, it makes no sense for there to be 5 digits precision to the contribution of something that varies by over a factor of 10 in the course of a year, and even more than that from place to place on the planet.
18 September 2008
1970s Mythology
One of the more popular myths repeated by those who don't want to deal with the science on climate is that 'in the 70s they were calling for an imminent ice age' and such like nonsense, where 'they' is supposedly the scientists in climate. This has long been known to be false to anyone who paid attention to the scientific publications from the time, or even to William Connolley's efforts in documenting what was actually in the literature over the last several years. Now, William and two other authors (he's actually the second author on the paper) have put that documentation into high profile peer-reviewed literature -- the Bulletin of the American Meteorological Society. For the briefer version, see William's comments over at Stoat and web links therein. That page also includes a link to the full paper in .pdf format.
16 September 2008
Sea Ice Packs
I've already mentioned types of sea ice, but that's only a bare scratch on the surface of the subject of sea ice. Another bit of vocabulary before diving in to today's sea ice: a chunk of sea ice is called a 'floe'. Not a flow, nor a sheet, a floe. Ice sheet is something quite different.
When we get a bunch of floes together, we start to have an ice pack. Three terms come up for describing a region of the ice pack (or maybe the entirety): concentration, area, and extent. Ice pack area makes the most intuitive sense -- add up the area of all ice floes, and that's the area of the ice pack. Concentration and extent are a little more removed. For concentration, draw a curve around some region you're interested in. Then divide the area of sea ice by the total area of the region bounded by your curve. Two common 'curves' used in the science are the footprint of a satellite sensor, and the area of a grid cell. The latter is what you'll see presented on any of the graphics at the sea ice sites I link to. For extent, you then take your grid and for every cell that has more than some concentration (which you'll specify), you add up the area of the entire grid cell. Extent will always be greater than area.
The usual concentration cutoff, and the one to assume if it isn't specified, is 15%. Below this, the ice is not reliably detected by the most commonly-used sensors, and it is a greatly smaller practical problem for ships. Not that ships appreciate bashing in to ice floes, but that at this concentration or lower, it can be manageable to move around them (and get out of the ice pack you were surprised by!).
The most common type of sensor to use for detecting sea ice from space uses passive microwaves. The ice (it turns out) emits microwave energy much more effectively than the ocean around it. This gives it a higher brightness temperature. Between that and some other details, we can get back an estimate of the concentration of sea ice that the satellite was looking at. A word, though, as we're coming out of summer: the method relies on the difference between ice and water. If you have ponds of water sitting on the ice floes, which can happen on thick ice such as the Arctic can have, then your concentration (area) estimate will be biased low. The extent is probably still not too bad. The reason is, by the time you're falling below 15% cover, the thick floes will have been storm-tossed enough that the ponds will have been emptied, or that it's late enough in the season that the melt pond melted its way through the ice floe and there really isn't any ice under the apparent water any more.
In looking at the NSIDC and Cryosphere Today pages on the Arctic melt, one thing to keep in mind is that one uses extent and the other uses area. Their numbers aren't directly comparable. They also differ in how they compute their estimates, in that one uses a longer averaging period than the other. The longer period gives you more confidence about the value (weather over the ice, or ocean, can give you false readings, but it moves pretty fast compared to the ice cover), but will miss some of the details in time.
More to come ... (bwahaha) But, in the mean time, questions you have about sea ice are welcome here.
When we get a bunch of floes together, we start to have an ice pack. Three terms come up for describing a region of the ice pack (or maybe the entirety): concentration, area, and extent. Ice pack area makes the most intuitive sense -- add up the area of all ice floes, and that's the area of the ice pack. Concentration and extent are a little more removed. For concentration, draw a curve around some region you're interested in. Then divide the area of sea ice by the total area of the region bounded by your curve. Two common 'curves' used in the science are the footprint of a satellite sensor, and the area of a grid cell. The latter is what you'll see presented on any of the graphics at the sea ice sites I link to. For extent, you then take your grid and for every cell that has more than some concentration (which you'll specify), you add up the area of the entire grid cell. Extent will always be greater than area.
The usual concentration cutoff, and the one to assume if it isn't specified, is 15%. Below this, the ice is not reliably detected by the most commonly-used sensors, and it is a greatly smaller practical problem for ships. Not that ships appreciate bashing in to ice floes, but that at this concentration or lower, it can be manageable to move around them (and get out of the ice pack you were surprised by!).
The most common type of sensor to use for detecting sea ice from space uses passive microwaves. The ice (it turns out) emits microwave energy much more effectively than the ocean around it. This gives it a higher brightness temperature. Between that and some other details, we can get back an estimate of the concentration of sea ice that the satellite was looking at. A word, though, as we're coming out of summer: the method relies on the difference between ice and water. If you have ponds of water sitting on the ice floes, which can happen on thick ice such as the Arctic can have, then your concentration (area) estimate will be biased low. The extent is probably still not too bad. The reason is, by the time you're falling below 15% cover, the thick floes will have been storm-tossed enough that the ponds will have been emptied, or that it's late enough in the season that the melt pond melted its way through the ice floe and there really isn't any ice under the apparent water any more.
In looking at the NSIDC and Cryosphere Today pages on the Arctic melt, one thing to keep in mind is that one uses extent and the other uses area. Their numbers aren't directly comparable. They also differ in how they compute their estimates, in that one uses a longer averaging period than the other. The longer period gives you more confidence about the value (weather over the ice, or ocean, can give you false readings, but it moves pretty fast compared to the ice cover), but will miss some of the details in time.
More to come ... (bwahaha) But, in the mean time, questions you have about sea ice are welcome here.
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