Back over a mile

I've whined a little here about my stress fracture; they're no fun. Past the problem itself, I was off enough, and had been at a low enough running base, that after getting the cast off I was basically starting over from scratch. Again.

This morning, I ran my first continuous mile. Yay! I'm doing run/walk for 30 minutes at the moment. With the progress, I've gone from 1 minute running : 1 minute walking to, now, averaging 6:30 to 1. I'm working on being positive about this, and not think too much about how fast I used to run, or how far. (50 km on trails is my longest (31 miles) Really don't need that thought in mind when I'm doing a tenth of that. Oops. Thought about it.)

The main thing is, aerobic activity is good for your health, improving or preserving physical and mental condition. It doesn't seem to matter much which aerobic activity you do* but quite important to do something. I like running, especially on trails, so that's my main aerobic activity. My wife prefers sculling, a coworker prefers tennis, another person likes hiking, someone else bikes, another swims, ... you get the idea. Doesn't matter much what it is, but important to find one you like.

*The exception here is that for prevention of osteoporosis, you need to be doing weight-bearing exercise. This includes walking, running, and weights, but not biking or swimming.

In terms of running, a lot of people tell me "I'm just not a runner. When I run a quarter mile, I get out of breath." There are problems with that. Most importantly is, almost everybody starts out by running too fast when they run. If you run a hard quarter mile (or block), you'll get out of breath regardless of how good your condition is. Most people run hard when the run at all. When you're getting started, you want to be running at a conversational effort level (makes it great for buddy-starting, more fun to talk with a friend). The next major problem is assuming that you have to start with some long distance. I started, after a 15 year layoff, with 50 yards/meters at a time of running. In time, I got to the 50 km trail race. Doesn't matter where you start. It does matter that you start.

Below is the current version of my progression table for going from being able to walk 30 minutes comfortably to running 30 minutes comfortably. Do check your health status with respect to running before starting, of course! It is also a good idea to look for running clubs near you. In the US, the RRCA is the national organization, which also has information on local clubs and more general notes about running. A good book for getting started is Alberto Salazar's Guide to Running. He's even more conservative than I am in some respects, as he allows a year for the progression. Most sources are less conservative than me, the RRCA included.


The run:walk column is the proportion of running to walking to do, in minutes:seconds. Stage 1 is to run 0:30 (30 seconds) and walk 7:00, then repeat this 4 times (giving a total of 30 minutes exercise, 2 minutes running).

The stages with a/b versions are fundamentally similar effort levels, but some people prefer the longer walk, or the shorter run. Try both and go with whichever version words best for you.

Stage 0: Walk 30 minutes straight, 4 or more times per week

For the following, do 3-4 times per week, with 36-48 hours between workouts.

stage  Run-walk   Repetitions  Running time
1          0:30-7:00    4                     2:00
2          0:30-5:30    5           2:30
3          0:30-4:30    6           3:00
4         0:30-4:00    7           3:30
5           1 - 5          5           5:00
6         1:30-4:30    5           7:30
7a         1 - 2        10           10
 b         2 - 4          5
8           2 - 3          6           12
9a        2:30-2:30    6           15
 b         1 - 1         15
10a       2 - 1         10          20
 b         4 - 2           5
11          4 - 1           6          24
12          5 - 1           5          25
13          9 - 1           3          27
14       14 - 1           2          28
15       30 minutes running

Note that some of these weeks have larger apparent jumps than others. The experience seems to work out, however, that they're about even in difficulty. I've based this in the early stages on Jim Fixx's Complete Book of Running, which is old but one of the few to address true beginning from the couch. The later stages are based on the RRCA's beginning runner programs. I've also made some adjustments based on feedback from runners over the years and my own experiences in re-beginning.

Irrespective of the apparent finely tuned mathematical precision of the list, the important parts are
* to run and walk at conversational effort level
* to get out consistently, 3-4 times per week
* to give yourself sufficient recovery time
As you do these things, you'll be able to run farther, faster, and more comfortably. The progression list is a guide, not a straightjacket.

This all leads to:
Stage I: 30 minutes running 3-4 times per week

This is a major milestone in your running. Once you're here, you can comfortably and confidently go out to area 5k races and have fun with running the whole distance (you can have fun with run/walk as well!). It is also a major plateau in running for health.
~

Recent Reading 1

Yesterday while the net was down at home, I did some real reading -- G. H. Hardy's A Mathematician's Apology. It's a good entry to how a serious creative mathematician looks at his subject, with some interesting general philosophy. I don't agree with everything he says; but he says it well, so I have some work to do to crystallize exactly how and why we disagree. Fun!

Not a recent reading as a classic that I've recently mentioned elsewhere. It's a very good book to read if you read ... pretty much anything. How to Lie With Statistics by Darrell Huff, illustrations by Irving Geis. The recent mention was prompted by someone who wanted to illustrate that there's no trend or not much -- by showing a graph where the vertical axis was far larger than the data range. This is a technique for lying straight out of the book. Once you've read it (it is old, 1954, so some current methods may not be mentioned, you should be able to recognize other methods of distortion.

Comment Policy

A start at a more explicit comment policy. Comments are welcome (themselves, and on this write up).

The main theme is that I want this to be an educational resource. Even though I sometimes take a broad view of what that means, please remember that this is the goal. To the end of being educational, it is best to provide a supporting argument and with a link or two to a more thorough source. See also my thoughts on link policy. I also am interested in discussion rather than debate. Part of that is that if a comment could be answered by 'read what the person actually wrote', I should simply reject it. (I haven't done this reliably, but will work on improving on that.)

Since my educational aims include jr. high students, the language also needs to be kept clean. This hasn't been much of an issue.

I do give an email address on my profile page, so if you think I've mistakenly rejected your note, you can drop me a line there and I can at least tell you what happened. Best to include the blog's name in your subject line as that account gets a ton of spam.

Questions to ask yourself in submitting a comment, or about a comment that doesn't get posted:

• Was the language clean (standard being what I think language-sensitive parents of jr. high class might think of you speaking to them)
• Was the comment substantive/educational? ('you're wrong' is not substantive, 'you're wrong because the moon is not made of green cheese' would be, if I'd said it was)
  
• If you're making a follow-up comment: Did you include new material, more detail, newer and better sources? (If your mention of the moon not being made of green cheese was insufficient to move me, provide a link to astro-cheeseological observations of the moon.)
• Are you responding to what was actually said?
  
• Are you on-topic?
• Is the comment in the same language as the original post?  [added 28 August 2010]
  

If the answers to any of these is no, there's a good chance the comment won't be posted. Also note that I'll be less lenient with posts that are from 'anonymous'. I do accept anonymous notes, respecting that sometimes people have reasons to not want a real name/address to show up. But, as inventing a name for yourself (as with my 'penguindreams') is quite easy, and gives readers a way to distinguish between different fundamentally anonymous commentators, I prefer that.

Comments? Additions? Deletions?

Evaluating a climate trend

After the second what is climate note and the second testing ideas note, how might one go about testing whether climate had changed, and, more specifically, whether a prediction of change were supported or not. At hand is the question of whether the IPCC projection (not forecast) of 0.2 C/decade for the first two decades of the century could be rejected by observations currently in hand. I concluded in the testing ideas post that the methods used there were not useful, as they hadn't compared like to like in making the tests, nor been working with climate variables.

Now that the second what is climate note is in hand, we can make a better sort of test. Still not rigorous, but better than the one I discussed. That is, let us take the 20 year average from 1981 to 2000 (IPCC was allowing 20 year averages, though preferred 30) and compare to the 7.6 year average from January 2001 to July 2008. The latter period is only 91 months, which is short for a climate definition, per our experience in the what is climate note. See again how wobbly the averages are for averages that are only that short.

I took the NCDC data again and computed the averages. (At least I hope so, I might have been off in my start periods, but probably only by a month or two.) For 1981-2000, the average was 0.277 C, with 0.155 standard error (if we also assume the terms are normally distributed, which is a question at this point). For 2001-present, the average was 0.540 with standard error 0.104. To compute the trend, we take the difference between those two averages (0.263) divided by the number of years between the midpoint -- 1990.5 and 2004.8, respectively. We wind up with 0.18 degrees/decade for our slope. Does that represent a significant difference from 0.2? Well, for starters, the 0.2 was a round figure from the IPCC -- their actual words were 'about 0.2'. 0.18 is 'about' 0.2. Eyeballing the spread of the different projections, a difference of 0.02 is within the envelope. Then, to be serious, we'd also have to allow for the errors of measurement that go in to computing the global averages.

The upshot is, to the extent that it's meaningful to test IPCC 4AR projection 13 years too early, observation of global average surface air temperature are pretty close to what's expected from this consideration. Allow for the fact that the sun's been quiet the since 2001 vs. warmer, and there's even better agreement.

One can definitely do a more rigorous test than this. And, for professional publication, would have to.

What is climate - 2

Since climate is a messy beast, there will probably be a number of these posts. If I ever put up one that strikes you as warranting publishing in the professional literature, let me know. I've done a few things already that others published years later, but I didn't think warranted my publishing. Conversely, if someone else has already presented the demonstrations I give, let me know who so I can give them their proper credit.

In the first what is climate note, I mentioned that climate has something to do with averaging and expectations, rather than precisely what you saw at any given instant. That's good, but it doesn't tell us a lot about how to average. Let us continue with 'global average surface temperature', as that's a popular variable to pick on. We may discover that other variables (rainfall, fraction of rainfall that's from intense storms, ...) need other techniques. But let's start somewhere.

One thing I observed over in the cherry-picking note was that we don't want our conclusions to depend sensitively on particular choices we make in our data (model, whatever) analysis. In the second testing ideas note, I mentioned that the WMO standard averaging period was 30 years, and the IPCC AR4 was using at times 20 years. But ... do those periods lead to one particular conclusion that we wouldn't get if we changed the averaging period? Conversely, maybe the 7 years used in the note I was criticizing there really are more than sufficient to look at climate change (my criticisms stand regardless, but maybe a proper test could be done).

Fluid dynamics (a course I neglected to mention earlier) gives us a nice way of looking at the problem. Over there, we use the 'continuum approximation'. While we know that air is made up of molecules, it isn't a useful way to look at the atmosphere. There are far (far!) too many molecules for us to work on each of them individually. What we do instead is work on a collection of molecules -- a large enough collection. How we define 'large enough' is to consider a variable of interest, say velocity. If we look into the atmosphere at a single molecule, we could see it heading due east at 1000 m/s. But the next could be heading due west at 1001 m/s. If we only took 1 molecule, we see a huge velocity eastward. If we take 2, we see a small westward velocity. What we have to do for the continuum approximation to work is take enough molecules that if we counted a few more, or a bit fewer, the resulting velocity would still be about the same. We don't want, on the other hand, to average up a very large fraction of the atmosphere. Then we'd be averaging out things that we care about, like hurricanes. So, on the 'too small' side, we see the averages jump around because there aren't enough data points. On the 'too large' side, we'd be averaging over processes that we want to study.

Here's a scatter plot of some climate numbers. I'll tell you later exactly where they came from, what the units are, and all that. But for now, let's just look at them with as few preconceptions as possible. One immediate feature we see is that they jump around a lot, a good 0.2 from one point to the next. The total range is from about -0.6 to +0.8, across the 1543 data points. If we're looking for climate in this set, we want to find the 'continuum' degree of averaging -- enough data points that the average holds steady.



What we observe is weather, what we expect is climate. Our given data point is a weather number. The appropriate average centered on that point is the climate, I'll say. So what I'll compute is the average of a given data point (say the 120th) plus all the data points from 5 before to 5 after that one. And repeat this for 1 before+after to 600 before+after. 600 before and after has us using 1201 data points out of our 1543, so we'll hope that we don't need to use so many. My first attempt is shown here:



The labels in the upper right are where in the data set I put the center. 120 starts averaging from data point 120 (early in the set) and 1200 is late in the set. They're separated by 120, which means that the averages start including overlapping data when the horizontal axis value is 60 or greater. Still, on this plot we can see that the jumping around that occurs near the start has pretty well settled out by the time we're using plus and minus 300. Now, since that's 40% of the data set (601 points), we're not very surprised. It's enough that to the extent that the curve for 1080 still looks to be rising with an increase in averaging we'd be willing to say that it's a climate change rather than insufficiently long averaging. The curve for 600 looks to have hit a stable value (near -0.1) very quickly, but most seem to be jumping around, including several crossings, in the first ... oh, 240.

So let's draw a new figure, this time only running out to 240 on the horizontal. Also, let's skip the curves for 1440, 1320, 1200, and 360 -- they're not crossing the others (crossing being an interesting feature), they're towards the finish and start of the data record (limiting our ability to extend the curves), they sit at the top and bottom of the figure, meaning that including them gives us less detail to look at the squiggles of the other curves, and they don't seem to do anything interesting that the other curves aren't. Here we go:


As we look here, we see that different averaging periods give us 'climate' values that vary by 0.1 to 0.2 (depending on which curve we look at). Now that 0.2 was the magnitude of the jitter we saw to start with, so we definitely don't want to do so little averaging that we're still in that range of variation. No point to doing the averaging in the first place, and maybe we'd have to say that there's no such thing as climate.

But if we look some more at the curves, we see that almost all of that variation is, as we'd hoped, near the start (short averaging periods). Between, say, 80 and 240 (end of the plot), the curves vary by only a couple hundredths, a good deal smaller than the 0.2 noise we started with. Hang on to this figure, we'll be coming back to it.

What the data are is the monthly global surface air temperature anomalies, in C, as computed by NCDC. The data start with point 0 being January 1880 and run through July 2008. The 120 data points apart translate to looking at points 10 years apart -- long enough that they shouldn't both be affected by El Nino, and shouldn't be stuck in opposite sides of a solar cycle (5-6 years could give us a problem). In averaging plus and minus 84 (months), we're spanning 14 years centered on the month of current interest.

A 7 year average (total) would be down at 42 (3.5 years either side) on the plot. As you see from the curves, particularly for 840, 960, 1080, once you're that short, your conclusions depend a lot on just what your averaging period is. With no averaging, 840 is about -0.2, 960 is about 0, and 1080 is about +0.2, enormous 'trend' of 0.2 per decade. But if we look out at 42 (3.5 years either side) we see 840 is still coldest, 960 is warmest, and 1080 is in the middle. An up and down with not quite as much down as up. Maybe you'd want to call that a warming trend, but now it's only about 0.025 degrees per decade. Go to 84 (7 years either side) and all three are practically on top of each other, no trend at all. Clearly, if we want to make any sort of stable conclusion about changes, we need more than a few data points. Also clearly, the values have some fuzz left -- the about 0.02 C that they change once we've gotten past about 14 year averaging (84 on the axis).

Back to our initial question about the 30 year (WMO) versus 20 year (IPCC with reluctance) versus 3.5 year averaging (taking a trend out of 7 years lets us only average 3.5 years and gives only 2 data points). The 3.5 years puts us down at 21 months (before and after) of averaging. That's clearly in the zone where conclusions depend strongly on just how long you make you averages, so is cherry-picking zone. The 20 years is 120 months before and after the month of interest. The curves have pretty much settled down at that point. The WMO 30 year period is out at 180 on the curves and things are generally even calmer there. Some of the curving which shows up (see the long version of this figure, above) suggests that 30 years might be too long an averaging period.

Project: I'm putting the data set, my C program, unix script, and my output on my personal website for any who are interested to pull down and see what they get. A different good test is to write it up yourself and see what you get instead. The figures I gave are all for looking at January. Do the conclusions hold the same for July? Other months? What happens if you first average the data year by year? Do I have an error in the program? Do you get the same type of results with other data sets (GISS, HadCRU)?

This is not a rigorous examination, just an exploratory start. Some things have been assumed that shouldn't be for a rigorous version. What are some? The importance of an exploration is not to give us a firm final conclusion, rather to start educating our intuition. When we turn to doing the rigorous analysis, we have some sanity checks at hand.

Discussion vs. Debate

How do you have a discussion when you disagree? Unless, no one should disagree be cause "its settled". was asked over at http://expeditionportal.com/forum/showthread.php?t=17837&page=6 by TheGillz. That's a point near and dear to my heart, and to what bothers me about much of the public ... words ... that are spoken regarding climate (actually most science, I just know this area better than most others).

It really isn't hard, just not the sort of thing we're used to seeing any more (in the US at least). We're used to seeing debates and listening to them on talk radio. It's also something of how cases are tried in court and we have many courtroom shows on TV. Namely, you set up two people and they have to defend some position (or attack the other guy's -- often they never present any positive information about their own). There are good reasons for doing it this way in law. But it isn't good for public understanding. I'll leave aside formal debate, but this captures what I think most of us have in mind regarding debate.

So what does discussion look like between two people who do disagree? No problem. My wife and I don't agree about everything, so we discuss the matters. Some things we'll probably never agree on, but we can understand why the other person thinks as they do even without agreeing with their conclusion. This is an important part of a discussion -- part of what you're after is to understand the other person's view and reasons. Time to be neutral and just listen. Just what do they think? Why do they think it? Sit back a little and let them speak for themselves; there'll be time for you to explain why their evidence is shoddy and their conclusions unsupported :-) But you can't have a civil discussion without understanding the other person.

Conversely, you have to think some about just why you have reached your own conclusion. Can't explain it without thinking about it yourself. This is related to the business that you generally understand things better yourself if you try to teach it to someone else. It is easier to hold a conclusion than to explain one, and far easier to hold it than to defend it. So the two of you explain your conclusions and how you got there. If it were debate, then you start the mutual attacking and never budging from your original point. That, I find boring.

Discussion, on the other hand, is interesting. In discussion, you may both change your minds. You had some good reasons that lead to your conclusion, but so did your partner in discussion. (At least assume that to start with!) As you discuss, your partner may point out that one of your sources doesn't really support your conclusion (as, say, I have in looking at some sites). This doesn't make you a bad person, but it does mean that you need to find a stronger source to support that point -- or else modify your conclusion. Also doesn't mean that you have to abandon your eventual conclusion, just some portion of it, or maybe to place less confidence on it. Conversely, as you look at your partner's sources and reasons, they may well have encountered some information that you haven't -- and those different sources might lead you to a new position for yourself.

In a really good discussion, you both leave with different conclusions than you started with. In this vein, I've also had a discussion where a group of us started out in agreement in one direction (that a certain proposal was good) and as we discussed our reasons, wound up in agreement that the proposal was not good. People in general agreement can have discussions too, and wind up far from their original opinion.

Since the point of discussion is understanding, rather than 'winning', you can also relax a bit about ego. If you have a discussion and your new understanding has you change your mind, great! You understand more. If the person you're talking with changes their mind some because of the good information you provided, also great!

There are plenty of other places to go if what you want is debate. And plenty of others where you can see only one view, which is, to me, even less interesting than debate. Here, I'm looking for discussion, or at least helping folks do some learning.

Anyone else have a (brief) example of a good discussion they had?

Testing Ideas 2

Finally, in comments on my cherry-picking article, I was invited to take a look at http://rankexploits.com/musings/2008/ipcc-central-tendency-of-2ccentury-still-rejected The commentator didn't really say what I should be learning from the link or what relevance he thought the page had to cherry-picking. I discussed some basics about making good tests in part 1 on testing ideas. Please check out both prior posts as I'll assume you know their contents. It's a little work, I know, but in order to have intelligent disagreement, or agreement, we have to know what the other is saying.

The title of that article is "IPCC Central Tendency of 2C/century: Still rejected". Certainly catchy. But let's look at the substance: Does the IPCC say there's a central tendency (and if so, what is it that is supposed to have that central tendency) of 2C / century? An immediate red flag for me is that the site does not provide a reference to where the IPCC said any such thing. Being better about doing my homework, I went to the IPCC WG1 report itself and looked in the summary for policy makers and the chapter (10) which discussed the global climate projections. I invite you all to do so as well. In my look for 'central tendency', I found no such term in either section. In my reading, which has not been exhaustive, of the two sections, I still found nothing that could be construed as a 'central tendency'. The projections were projections, not forecasts, and were made for a number of different scenarios (assumptions about greenhouse gas emissions and other things). Some included ensemble means, but none of those were 2.0 C. One was 1.8, but calling that 2 is back to the problem of deciding whether I'm tall and letting me round to the nearest foot or meter. Not even out of the title and already there are problems.

In the lead paragraph, the author writes "... compared to the IPCC AR4’s projected central tendency of 2C/century for the first few decades of this century." Again, I don't find the IPCC saying that, and again, the author doesn't say where the claim comes from. The nearest match I find is in the Summary for Policy Makers, p. 12, where it says "For the next two decades, a warming of about 0.2 C per decade is projected for a range of SRES emission scenarios." The author mutated a term of precision, two decades, in to a vagary, the first few. Then the fuzzy term 'about 0.2 C per decade' got cast as a hard term of 2C/century. If nothing else, in reading this site, you're not reading a reliable reporter. Once I've reached that point, I generally stop reading a source. There was no need to misrepresent the original. Nothing was saved or simplified.

In terms of part 1, remember, I mentioned that you had to be careful to make a good test, including that it had to test the thing at hand. In that case, you had to be looking at my height and weight in order to decide whether I was 'tall and thin'. In this case, you have to compare (in some 'good' way) observations that bear on the thing actually predicted by the IPCC. When you read chapter 10, you'll discover several things. One is that the variable being projected is the global average surface air temperature. Another is that the models have interannual variability (they'd better -- nature does, as I mentioned in the cherry-picking and detecting climate change articles). And you'll see that 30 years is the normal period for averaging temperatures to make climate conclusions; but even so, the projections were being (gingerly, you'll notice if you know how scientists write) made about 20 year averages. One final thing buried in those 100 pages: The projections assume that there are no volcanoes and the sun's input remains fixed at the observed average value. We haven't had any major volcanic eruptions since Pinatubo, but the sun has been quiet since 2001 (below the average output).

So several things to go in to making a good test:

• We have to compare 20 year average vs. 20 year average (the variable being suggested as meaningful in the report, and 30 would be better).
• We have to look only at global mean surface air temperature.
• We have to adjust for the fact that the sun has been giving less energy than assumed in the projections.
• In making the test, we have to allow for the fact that the 0.2 C/decade itself has error bars (due to interannual variability and between-model variability)

The author does none of these things, and presents no reason why they are not necessary. Instead, she computes trend lines for January 2001 - present, not 20 year averages. She includes satellite observations of temperatures through the lower-mid troposphere (the UAH and RSS), rather than using only surface air temperatures. She ignores that the sun has been quiet. And she makes no allowance for the error bars on the IPCC projection.

Even if absolutely everything that was done in the statistics were right, which I'm not in a position to say much about, the test is not a good test so the result is at best meaningless. Chances are good that it's misleading (tests that aren't good are usually misleading).

The satellite temperatures show a cherry pick themselves. But first, why they shouldn't be used in this context in the first place. The thing is, they're not observing the variable that is being predicted. While it is connected, which might lead us to thinking that it's ok to use them, it still may not be. Back to the question of whether I'm tall. I think that the data you want is a measurement from the floor to the top of my head. It's true that leg length is related to height, at least in the sense that tall people generally have longer legs. So maybe you'd accept that instead. And say you took Michael Phelps' leg length too. If you looked at the two, you'd conclude that I'm taller than Phelps. (His legs are short for his height, mine are long for mine.) You'd be wrong, however; the data don't address well enough the question you're asking.

The cherry pick is that only 2 of the 4 satellite temperatures were taken, and it happens that the two are the two which show the least warming (you'd have to know about this, which is easy enough to find if you look but isn't universal knowledge). The author gives no reason for this selection. Further, even ignoring that, one of the two also is not a global data set. The RSS goes only 70 S to 82.5 N. There are good reasons for this, and, conversely, to not be confident about the UAH figures, but they get technical. It suffices here that only 2 of 4 data sources were picked, one of them isn't even global, and, worse, neither measures the variable of concern.

Even without knowing anything about statistical methods, we can see that the given site does not support its headline (and have some question about the headline as well). All that is needed is to check what the source (IPCC in this case) actually said, versus what was being tested. They're different things, so the test doesn't tell us about IPCC's projections.

We can't make the converse conclusion from this, that the IPCC projections are correct. We didn't test that idea, so no conclusion about it is possible here. We only checked whether the site was making a good test. It wasn't.

A non-digression to something related. While I've taken probability and statistics courses, they weren't very deep (I felt). I was thinking about taking more, and asked a coworker -- a statistician -- about doing so. We talked some about what I'd studied (and remembered, this was a good 15 years after I'd had the classes). She concluded that there was no real point for me to take the courses. More important, she said, was to understand the system I was working with. The appropriate statistical methods would suggest themselves, or at least I'd be able to hand a well-constructed question to a statistician. But without understanding the system, there was no point in applying statistics.

Project: Pull down the 5 data sources given at that site and compare the last 20 years (7/2008 to 8/1988) average global temperature against the previous 20 years, 8/1968 to 7/1988. Is the more recent average greater or not? Can't do that for the satellites as they don't go back that far. But try 8/1979 to 7/1994 versus 8/1995 to 7/2008. Only 15 years versus 14 years, so not very informative about climate, but it's all the data we have. Won't be a good test, but the best (perhaps misleading) that can be done given those data. (Try changing the periods too.)

johnathansawyer: as you invited me to look at the source, did the above affect your opinion about it? Why or why not? As usual, substantive reasons (either way).

[Update 28 August 2008] See my next two notes what is climate - 2? and evaluating climate trend for more on what appropriate averaging periods look like, and what happens if you compare the average of the last 7.6 years to the previous 20 years' average, respectively.

[Update 29 August 2008] rankexploits made a lengthy commentary on things related to this post, though misrepresenting even my first paragraph. Comments on that post are disabled (I get an error message in response to my comment attempt), my response is #5317 in http://rankexploits.com/musings/2008/ipcc-central-tendency-of-2ccentury-still-rejected

Folks who are getting heated about my 'advocacy', or defense of IPCC, or whatever. Take a minute. Read what exactly I said. Saying that a particular test was not good is far from saying that there can be no such test (I give an example of one that would be better myself!). Nor, as I said directly, does it mean that the projection is good. Let's see what happens when a good test (which mine isn't, just better) is made. Until one is presented, a poor test is still not useful.

Blogrolling

Some sites whose interests are close enough to mine that they are linking here. My apologies to the folks whose language I was guessing at if I guessed wrong. Please, someone who knows any of those languages, have a look and let me know the correct language. Also, if I'm missing places, please do send a comment.

atmoz.org/blog Climate and Weather Explained -- See especially the oblate spheroid edition of the simplest climate model
www.emretsson.net/ (Swedish)
scienceblogs.com/clock/ A Blog Around the Clock
tamino.wordpress.com/ Open Mind
koillinen.wordpress.com/ (Finnish?)
stigmikalsen.wordpress.com/(Norwegian?)
thingsbreak.wordpress.com/ The Way Things Break
bravenewclimate.com/
chriscolose.wordpress.com/ Climate Change
www.scruffydan.com/blog/
rationallythinkingoutloud.wordpress.com/
simondonner.blogspot.com/ Maribo
rabett.blogspot.com/ Rabett Run
scienceblogs.com/deltoid/ Deltoid

[Update 2 Sept 2008]: See also
http://initforthegold.blogspot.com/
http://jules-klimaat.blogspot.com/

Testing Ideas 1

I was invited (challenged, whatever) to take a look at a site that proposed to have disproved the 'IPCC prediction', over in comments to my cherry picking note. Here's part 1 of the look I promised in my comment reply over there. If you haven't already, please do read the cherry picking note. (Not only for my tiny little ego boost from having more page views, but because I'll be assuming here that you understand what all I mean by the term and examples of it for climate.)

Testing ideas is one of the central processes for science. Coming up with ideas is awfully easy. Supporting them takes work. Strengthening them so that they stand up to all good tests is extremely hard. But, they do have to be good tests. Same as it's harder to come up with supported ideas than just an idea, it's harder to come up with a good test than just a 'test'.

'Good test' does not mean 'comes up with the result I like'. Maybe it does, maybe it doesn't. You're usually much better off to not have specified before hand how you want the test to come out. A good test is one that is aware of the system it is studying, knowledgeable about the idea that it is testing, and has been devised carefully enough to confirm or deny the idea while also giving an idea of how firmly it is supporting or denying. Before launching in to the climate case, let's look at something very much simpler.

You might have the conjecture (even more tentative than a hypothesis), after having read my mention that I'm a distance runner, that I'm tall and thin. How would we test that? How can we make it a good test? You could just ask me. But that isn't a good test. You have no idea what I think is tall, nor do you have any idea what I think is thin. So if I say 'yes', you still don't really know anything. Poor test. You could try asking me my height and weight. But then you've made a poor test because you didn't establish what constituted tall or thin. If you're biased about the conclusion, it is far too easy to say after the fact that whatever figures I gave you do, or don't, constitute 'tall and thin'.

So you have to be precise about declaring what you're testing, what constitutes a pass and what constitutes a fail. You might arrive at something like 'taller than 80% of men your age means tall and lighter than 80% of men your height is thin'. Someone else might want those figures to be 90%, but, since you've specified how you arrived at your labels (and, of course, you will be sharing your data), they can examine for themselves whether they agree with your conclusion. You're still not out of the woods, however, because you don't know how I'm measuring my height and weight. Perhaps I'm wearing thick socks, shoes, and standing on my toes. Maybe I'm weighing myself fully clothed and carrying a backpack. You need to specify the conditions of the measurement as well. Further, you'll have to tell me how to report it. I could be 5'7" (170 cm) and round to the nearest foot/meter to tell you that I'm about 6' (2 meters) tall. That sort of ambiguity can completely ruin your test.

In any case, even for something as simple as deciding whether someone is 'tall and thin', you see that there can be quite a lot involved. One last thing, which winds up often being important in looking at people's conclusions. After going through the work of making a good test, you can only draw your conclusion about the thing you were testing. Suppose you decided that I was indeed tall and thin. That was your test, so that conclusion is reasonably good. What you cannot do, however, is conclude that because I am tall and thin, I'm a good distance runner. You never tested that, and haven't presented evidence that all tall and thin people are good distance runners. (They're not, nor is it true that all short and not-thin people are poor distance runners. Now you have to go back to the drawing board and decide what 'good distance runner' means and how to measure it.)

If something that simple involves so much work, something as complex as climate probably takes quite a bit more care. So, irrespective of much else, one thing to look for in reports about what is or isn't the case about climate is whether the author showed as much care in making their tests as I suggested for something as trivial as deciding whether someone was 'tall and thin'. In part 2, finally, I'll get to the examination I was invited to make.

Labelling instead of thinking

It's been interesting to see how rapidly some have labelled this blog and what labels are out there. Almost always, hence this note's title, labelling is done instead of thinking. Labels around the topic of climate include alarmist, believer, skeptic, denialist, and probably several others. Conspicuously absent is 'science-minded'. If you have to have a label for this blog, that'd be one to use. I like science and think it's a good way to answer scientific questions. Not all questions are scientific, but when they are, it's good.

So I'm puzzled that there's been reference to me being a 'believer'. What in, the source didn't say, and that's rather the problem with such labels. People using labels instead of reality often don't tell you what the label means. I do believe that science is a good way to answer scientific questions, but if that's all it takes to be a 'believer' then all scientific sources would have to be labelled so. Perhaps they are, which leaves me wondering what the utility of their classification is supposed to be. Help people avoid learning about the science?

Denialists, as I might use the term, used to be across the spectrum as to conclusions. That is, there were folks who insisted that sea level was going to rise and drown everyone (!) in the next few years (unless we all did what they wanted) and denied any and all evidence to the contrary. At the same time, there were folks who insisted that sea level couldn't possibly change except maybe to go down. And again, denied any and all evidence to the contrary. I don't see the former types much any more, but the latter have only gotten more vocal and seemingly numerous.

Skeptic ought to have been a good label for the science-minded. Instead, it's been appropriated by a very narrow viewpoint and, as usual for such swipings, one that is not skeptical at all. A true skeptic will sit down and look at all evidence regarding a point. They aren't foolish enough to think that there are only 2 sides. And they look even handedly at all evidence. They don't select only 1 'side' and make only that one defend their conclusion. They also use consistent standards of evidence. In my cherry-picking note, for instance, I mentioned some who (dishonestly) use trends from 1998 (or one or two other particular, even more recent, years) only to conclude that 'warming isn't happening'. If they were honest skeptics, they'd turn around and agree that warming is happening if 2009 were warmer than 1998 (or if, as already happened in one data set, 2005 were warmer). In practice, however, these fake 'skeptics' simply move on to some other point, never updating their conclusions in light of new information.

I'm also surprised to hear myself called 'alarmist'. Even less useful that 'believer', as folks throwing that label never do say what was alarming. Apparently they're scared to hear that there really is such a thing as the greenhouse effect. But I don't see that their being easily scared by reality should mean much to the rest of us. Again, the label has been taken by one particular group (the self-described 'skeptics', who also dishonestly took that label for themselves) to label only one viewpoint. Often, these same people turn around and make alarming statements themselves -- about how there'll be a worldwide depression if anything were done in response to climate change. That strikes me as much more alarming than a lab-tested statement about there being greenhouse gases.

In fairness, I do notice that I'm using a label myself -- 'unreliable'. On the other hand, I only use it after reading the source myself (and encouraging you to do so yourselves) and laying out exactly why I'm using it. It's a rather narrow usage, even more so since I'm only using it for sources which can be shown in error without knowing much science or math.

I'll encourage people writing here to not use the 'alarmist' 'denialist' and other such labels. If you think someone or some source (me included) is wrong about something, go ahead and say so and present the solid evidence (see my link policy) that supports your point. (Just saying you think they are, or I am, wrong is not enough and will likely be rejected regardless of who you think is wrong.)

Greenhouse Misnomer

It's a nuisance that greenhouses don't work by the greenhouse effect. Some seem to want to make it out to be some sort of catastrophe or indictment of science instead. But it is annoying nevertheless.

The greenhouse effect's existence was discovered by Fourier in 1827. Namely, the surface of the earth is too warm unless something else were going on -- as we found in our simplest climate model. Digressing a second, Fourier realized this even though it was more than 30 years before anyone knew that there were greenhouse gases. Tyndall published his experiments, that showed water vapor (H2O) and carbon dioxide (CO2) among others to be greenhouse gases in 1861. Conservation of energy is a very powerful law -- you can reach the conclusion even if you don't know how, exactly, it comes about.

In any case, the idea was that greenhouses let the sun's rays in and didn't let the air in the greenhouse radiate energy back out. The definition of 'greenhouse gas' became this -- that they were transparent to solar energy (completely or nearly so) but absorbed earthly radiation (in the infrared, rather than the visible and near-infrared of the sun).

Unfortunately for purists, greenhouses don't work that way even though 'greenhouse gases' do. The way greenhouses work is to physically trap air near the surface of the earth. The sun's rays heat the surface (by radiation) and the surface heats the air in the greenhouse (by conduction). Since the greenhouse is closed, the warm air can't rise very far and the greenhouse stays warm.

Ok, those are two word pictures. Both are nice sets of words. But ... can we do an experiment that will show us which one is right? We can, and it was published in 1909. The experiment built two different greenhouses (small, but enough to test the idea). In one, the walls were the usual glass, which is transparent to sunlight but tends to absorb 'earthlight'. In the other, the walls were halite (rock salt) which is transparent to both sunlight and 'earthlight'. If the infrared properties of the walls matter, then the two greenhouses will reach different temperatures. If it is only important that there be a wall, the halite-walled greenhouse will get just as warm as the glass-walled. (Give or take a little for how well the two conduct heat.) The result was that the halite made just as effective a greenhouse as the glass. (Wouldn't work so well as a practical matter. Why? But just as effective for what was tested.)

So greenhouses don't work by the greenhouse effect. Planetary atmospheres, on the other hand, do. It's a nuisance that the words don't really apply thoroughly. But this is English. It's not like this is the first time there has been a definition that didn't make rigorous sense. We're talking in a language where flammable and inflammable mean the same thing after all.

Project: Build your own demonstration of the greenhouse effect versus greenhouses. See
http://www.wmconnolley.org.uk/sci/wood_rw.1909.html for the original experiment and a discussion of the significance.

Cherry Picking

Unfortunately I'm not talking about getting hold of a nice batch of fresh fruit. Instead, it's a particularly common dishonest tactic. It's also one that is flagrantly against the principles of doing science.

What it consists of is making a statement that is true only about a specific especially well-chosen circumstance, and then pretending that you've made a general statement about the system at hand. This is offensive to me as a scientist because in science we're trying to understand the system -- all of it. The cherry pickers abandon honesty for word games.

Suppose we're trying to understand the global mean surface air temperature. There are many other things we could try to understand, but this one is fairly often looked at. After we look a bit, we notice several things. One is that the temperature varies from year to year. As we look in to this further, we see that several things happen which affect the temperatures. This includes having a more active sun (warmer), having a recent major volcano erupt (cooler), having an El Nino (warmer) or La Nina (cooler). After doing our best to subtract out all those effects, we see that there is still some variation year to year. That's the 'free variability' (the scientist's way of saying 'stuff happens'). It turns out that there are also some contributions from anthropogenic aerosols (cooling), increased greenhouse gas levels (warming), and other human activity (depends).

As we try to make our honest understanding of this complex system (are there other things that affect global mean temperature? how much?) we also have to wonder about how much data we need to collect before we can tell the difference between that free variability and a trend caused by one source or another. Remember what happened when you tried my climate change detection experiment. Even with random numbers, you got runs of several consecutive 'years' of warming or cooling. Free variability does this to you. So if you're looking for trends or other systematic things, you need to look at a long enough period that the free variability can't lead you to a mistaken conclusion. Plus, of course, you have to make that allowance for all the things that you know happen and affect the variable (global mean temperature) you're interested in but are due to processes (solar variability, El Nino, volcanoes, ...) that you're not concerned about at the moment (greenhouse gas levels).

It can be very difficult to do this even when you're trying to do it all correctly. One of the first satellite sounding temperature analyses (Spencer and Christy, 1992 or 1993, if I remember rightly) showed a large cooling trend at the same time that all other data sets showed a warming. This was very puzzling. Not long after, however, Christy (same one) and McNider (1994 or so) showed that this was because the data record started near an anomalously warm period (strong El Nino in 1982-3) and ended near an anomalously cold period (after the eruption of Mount Pinatubo). It's anomalous because we're not (in looking for signs of whether human activity affects global mean temperature) concerned with El Nino and volcanoes. Once those two obvious anomalous events were taken out, the 'cooling' trend vanished. Science being a small world, I ran in to McNider not long after he'd published that paper and we talked about it among other things.

One thing you can look for, even with no particular knowledge, is whether the author (blogger, commenter, ...) is considering other factors that can be involved. Even easier, and the cherry-pick which prompts me here, is to see how they selected the time spans they used and the data sets that are used. In the satellite example above, for instance, it was straightforward -- the authors used all the satellite period they had data for. Fair enough.

Since 1998, though, there's been an industry that is careful to not use all the data they could. Indeed they're aggressive about ignoring data. You don't need to be a specialist to know that this doesn't square with honest understanding of a complex system. People who are seriously trying to understand climate are continually complaining about wanting more data. Throwing away good data is inconceivable to them. But in that industry, they're not concerned with honest understanding. They wish to arrive at a conclusion and if they pick the right starting year (1998) and data set (CRU rather than GISS, for instance), then they can get the answer (a cooling 'trend') that they want.

Now to get that, they have to choose only one or two years, both from recent history, as the time to start their 'analysis'. If they choose any of the 100+ years before 1998 that we have a surface temperature record for, their conclusion is gone. If they use GISS rather than CRU, their conclusion is gone.

Further, even choosing that one year as the start would not be enough to preserve their conclusion if they were honest enough to examine the other things we know affect the climate system -- that was a year with a strong El Nino (warming) and high solar activity (warming). Instead they ignore this (either dishonest or simply not doing their homework) and make various declarations against anthropogenic climate change.

With a couple questions, then, a legion of authors/sites can be pitched for being unreliable:
* Are they playing the 'global cooling since 1998' game?
* More generally, would their conclusions hold up if the start year were chosen differently?
* Are they assuming that only one thing affects global mean temperatures?

If the do the first or third, they're lying or not doing their homework. If they don't address the second, they're at least not doing their homework.

I've been aware of this particular cherry-pick for some years now, and the popularity of cherry-picking among anti-scientific groups even longer. So I'll let you do your own check of how many sites or sources within 15 minutes you can find that commit this error. Depending on your reading speed, you should make 5 easily, and 20 if you're a quicker reader and have a fast connection.

Types of Sea Ice

Earlier I talked some about types of ice in the climate system and types of ice ages. With the public discussion of what will happen to the Arctic ice pack this summer, it is time for some talk about the different types of sea ice and what their significance is. The main two involved are first year ice and multiyear ice. First year ice is in its first year of life. Multiyear ice has been around for more than 1 year. (We're really not very elaborate in our naming!)

Multiyear ice is generally thicker than first year. Part of this is because it has had an extra winter (or several) to freeze more ice on and grow this way. Part of it is because as the ice floes get shoved around by the winds and currents, they crash in to each other and can pile up. It also generally has a lower salt content than first year ice does. During the summer, the salt in ice makes the melting point lower there (same reason we put salt on roads in winter, at least if it's warm enough) and the saltier (brine) parts melt out of the ice floe, leaving behind nearly totally fresh water. Being fresh water or close to it also makes for mechanically stronger ice. It also makes the ice radiate differently than first year in the microwave, so it is possible to distinguish some between multiyear ice and first year ice from satellite sensors.

First year ice, then, is the (generally) thinner, mechanically weaker, saltier ice that formed some time during the most recent winter. All three of these properties make it easier to get rid of in the summer whether by atmospheric warming (straightforward melting), ocean warming (ditto), solar heating (easier to melt the saltier ice with the sun's rays), or by having a strong weather system hit the ice with high winds (breaking it up mechanically and helping it melt faster by exposing more surface area to the air and sea).

A different feature of thicker versus thinner ice is that thinner ice is harder to make weather-type predictions for/with. See, for example, The thermodynamic predictability of sea ice, Grumbine, Robert W., Journal of Glaciology, vol.40, Issue 135, pp.277-282, 1994.

There are many local names for various stages of growth in the first year ice. They include:
Grease ice -- small ice particles which give the ocean a 'greasy' appearance
Pancake ice -- ice floes maybe a meter or two across, more or less round like a pancake and with raised edges (collecting Grease ice)
Young ice -- let the pancakes grow and get thicker.

(The links will take you to places with good pictures and further explanation.)

A different sort is the 'fast ice'. This is ice which has frozen fast to the land. Otherwise it us much like the young and first year sea ice.

There are plenty more names and labels for sea ice types, and I'm not even starting in on the bestiary of names for iceberg types.

Women's Olympic Marathon

Watching the Women's Olympic Marathon last night was a particularly interesting experience for me. I like watching the distance races because I understand them better than sprints or other events like swimming. This time was the first that an Olympic Marathon was held on a course that I knew a fair part of. Earlier this summer I was in China, including Beijing, Tian'anmen Square, the Temple of Heaven, and Forbidden City, all of which figured in the course. I don't normally get to say 'I was there' in watching Olympics.

Understanding the race, and an injury, also changed part of my viewing this time. Paula Radcliffe was running the marathon with a recent (8 weeks ago) stress fracture to her femur. I got a stress fracture in my second metatarsal (base of second toe) at the end of April. Three months later, I was cleared by my podiatrist to start back running at 80%. 2 months after stress fracturing her femur -- the biggest, heaviest, hardest to fracture bone in the leg -- she was out running a marathon at Olympic speed, not one of my leisurely 5k jogs. I was watching in astonishment that she was still in the race and in the lead pack for most of it, while every time she landed on the bad leg and took off for her next step had to have been starting at painful and gotten worse for every one of the 12,000 or so steps she did it. If you start a marathon in perfect health and well-trained, you're still going to be hurting by the end if you race it. She took on all that ordinary pain plus the fact that she didn't start the race in perfect health or training.

As the race neared the end, and had resolved to the race for second between Catherine Ndereba and Chunxiu Zhou, I had some sort-of inside information that let me pick the winner of the duel. That is, I've raced Ndereba before. At least for a very loose sense of the word 'raced'. I ran in the Beach to Beacon (Cape Elizabeth, ME) 10k in 2000. Ndereba raced there too, on her way to the Sydney Olympics. Aside from at the awards ceremony, of course, I never saw her. Her race was to win, my race was to run hard. We both succeeded, just that her success was to be close to 30 minutes and mine was around 45. Since then, though, I'd kept an ear out for her career. That included her later world record in the marathon, and the fact that among an extremely competitive group (elite marathoners are not casual folks!) she was considered extremely tough. So, come to the end of a marathon ... Chunxiu Zhou was a former 1500 m racer, which means plenty of speed. But the end of the marathon is much less about speed than sheer mental toughness. So my guess, which held up, was Ndereba.

Basic Sciences in Climatology

Last Friday I mentioned some math that you'd probably run in to when trying to study climate. You'll also encounter some of the basic sciences (as opposed to messy sciences like climate).

Extremely common as requirements are:
College Chemistry (year long sequence)
Physics (year long calculus-based sequence)
Thermodynamics (from one or another of Chemistry, Physics, or Engineering departments)
Plus, though I've never seen it required, it seems quite common for people to take it:
Astronomy. I think this is more a matter of personality than requirement.

Many people arrive in climate by way of physics, so they'll also have a year of modern physics, intermediate mechanics, intermediate electricity and magnetism, and some physics lab courses.

If they go to climate through geology, they'll have the above extremely common basic science courses, but then a batch of different messy science (geology) courses.

Climate Change Detection

You'll want some dice or a random number generator for our first efforts to think about climate change detection. Start with one six-sided die. We'll assume that it's a fair die -- that each face is just as likely as any other to turn up. If we toss it many times, the average of the numbers that shows up will be 3.5.

Weather and Climate
This is one of our distinctions between weather and climate. Weather is what we saw on any given throw and climate is that average. But 3.5 is not a number that you can get on any single throw. What's up with this? It turns out that this, too, is a reasonable thing for thinking about climate. If you look at some very small area, and only one parameter (say temperature), it's possible that you'll see the 'climatic norm' occur. But only for that small area and limited look. As soon as you look at a large scale, you find that although the weather (instantaneous state) can be generally close to climate, it is seldom close everywhere. See, for example, this sea surface temperature anomaly map(difference from climatology).

The 1 die model of climate doesn't work very well. On the map, we see that most of the area is near climatology, and that the farther away we are (hot or cold), the less area is present. A better model then is to use 5 dice (again 6 sided). In this case our 'climate' is a total of 17.5, which still doesn't happen as weather, although you can get close. The maximum is 30, and the minimum is 5. The maximum difference from climatology is 12.5. But most of the time we'll be close to climatology. Take 5 dice, throw them, add them up and record the result for a couple hundred throws. (If you're moderately quick with your addition, this takes only a few minutes; I've done it.)

Within your 200 totals, you'll find some runs of constantly increasing values, and about as many runs of constantly decreasing values. Some of the runs will be long, and some short. But the number of each is about the same whether it's increasing or decreasing. If you compute the average of the first 5 sums, then 10 sums, ... out to the whole 200, you'll see that the average wobbles around. It tends to be closer to 17.5 as time goes on (as you average more tosses) but only in a very jerky fashion.

Climate Change
Suppose I take one of your dice and tape a 6 over the side that should read 1. The average throw now totals 18.3333 (repeating), instead of 17.5. The minimum is now 6 instead of 5, but the maximum is unchanged. What will happen, though, is we'll see the high totals more often. Each of these is more or less a fair description of what we've seen in the climate of the last 120 years -- warmer minimum temperatures, higher averages, and not much change in maximum temperatures. (Not a perfect analog, but pretty good for only 5 dice.)

Repeat the exercise of tossing the dice and adding them up. How long do you have to do it before the average is obviously different from the first run? Remember that the first time the average jumped around for a while. You'll have to go on for longer than that this time.

How many throws do you need to make before you can tell that there are fewer low numbers? More high numbers?

In doing climate change detection professionally, these sorts of analyses are applied. Are there more extreme highs? Fewer extreme lows? Higher average? Just how many data points do we need to detect that in the statistics?

Final question: when did the climate change? When you have a long enough series of throws to detect it in the statistics reliably, or when you saw me tape over the 1 face with a 6?

People and Institutions

In an earlier post, I commented off-handedly that science is done by people, not institutions. Elsewhere in the blogosphere someone took exception to that. So it seems a point to expand a little.

The thing is, science is done by people, and scientists as people are rather heavy on individualism. Managers of scientists usually wind up making comments about 'herding cats'. Consequently, when you're talking about an institution that scientists are involved with, it's a near certainty that some of the people there disagree to some extent or other with what their colleagues published. Plus, as I mentioned in talking about peer review, merely getting published does not mean that you're right.

The scientists simply do not are not speak for their institutions unless you're told emphatically otherwise in some specific case. I do not speak for my employer, someone at NASA does not speak for NASA in writing a scientific paper, someone at NOAA does not speak for NOAA, someone at a University does not speak for the University, and so on.

There's a different aspect of that individualism. Even where the scientists are naturally inclined to be more conformist (which has struck me as rare), the rewards are set up for nonconformity. The surest way to prominence in science is to support an argument that what people previously believed to be true, isn't.

Between the two, by the time you can get scientists to agree overwhelmingly on something (the earth is round), it has ceased to be a scientific question. The shape of the earth question is now about things like whether the equatorial radius is 6378160 or 6378240 meters. (Maybe a narrower difference now; it's been a while since I looked.). There's agreement about round, but not about exactly how large, nor exactly how much squishing there is towards the poles.

Analyzing the simplest climate model

Before we try to solve the problem of why the temperature around us averages about 15 C (288 K) instead of the -18 C (255 K) we found in the simplest model, let's look some more at the model. It depends on 3 things -- the sun's energy input to the earth, the albedo of the earth, and the average distance between the earth and sun. How much does it depend on those things? By the end, we'll also have another site to ignore for its unreliability.

We know that the sun's output can vary by about 1 Watt per square meter during a solar cycle. So try computing the temperature with 1368 instead of 1367. Try again with 1366. How much difference does that make? I get about 0.05 K (0.09 F). That's a pretty small number. We'd be hard-pressed to get a thermometer to record it.

How about the albedo? I find about a 1 K change (0.9) for a 0.01 change in albedo. Such a change in albedo (or to increase it by this much) is plausible for the earth, though 0.10 would be a wild value, not expected by anybody I know of. Quick sanity check ... why is the albedo so much more important than solar term? Albedo multiplies the solar constant. The natural variation is 1 Watt per square meter. The 0.01 change in albedo means a 13.67 Watt per square meter change in energy entering the climate system, so we expect it to be much larger. (project: why is it 19 times more important rather than just 13.67?)

The mean distance from the earth to the sun does change -- on a long enough time scale. Changes in the earth's orbital eccentricity (how circular vs. how oval-shaped) can give changes in average distance of something like 0.001 AU. This translates to about 0.18 K (0.32 F) variations in earth's temperature to space. (These are Milankovitch variations in eccentricity, with the fastest time scale of change being 100,000 years; some are over 2 million years).

If we take those sizes of temperature change and divide by how fast they occur, we get a sense of which is most important for thinking about climate change on our time scale of interest. The sun's output changes along a solar cycle of about 11 years. The earth's albedo changes with the seasonal cycle, so 1 year. And the eccentricity is 100,000 years. Looking at degrees per year, we then have:

1. Albedo 1 degree per year
2. Solar cycle 0.005 degrees per year
3. Eccentricity 0.000002 degrees per year

So, if we're thinking about weather and climate over the next few years to centuries, the obvious candidate to be paying attention to is the albedo. Eccentricity changes too little and too slowly, and the solar cycle returns to its start before the century is up (net of zero change), and is much smaller than the albedo effect can be on a few year scale (albedo doesn't go in the same direction for a long time, but just how long and how much needs some thinking).

Variations in solar output and the earth's orbit are not part of the climate system itself, and the orbit can be predicted to very high accuracy for a very long time into the future. In terms of understanding the climate system, both the solar and orbit factors are good -- given these non-climate terms, we can compute a climate. If we know the albedo.

But what is albedo? It's the bouncing of energy from the sun back to space. Now what does that bouncing? Well, everything in the climate system -- clouds, gas molecules, ocean surface, trees, grass, desert, dirt, glaciers, snow cover, ice packs, ... The gas molecule term depends little on the climate, and, if I remember correctly, would bounce about 15% of the solar input even if the earth's surface were a perfect solar absorber (perfectly black). But it isn't; even the ocean, which is about the darkest part of the earth's surface, reflects at least 6% of the sun's energy (that reaches it), and that figure increases as the sun gets low in the sky.

If none of these things changed their albedo as the climate got colder or warmer, we'd only have an annoyance -- can't give a climate figure without looking at the system. But the extent of deserts, ice sheets, sea ice, ... does change depending on climate temperatures. That 'about 0.30' albedo is correct for recent times. It may not be correct in an ice age earth or an even warming than present earth. Consequently, while we can use this model to understand some points about the climate system, we can't use it to predict full climate responses. We're not surprised, since we're much warmer at the surface than the blackbody temperature. But this is an additional reason we're going to want a more complex model down the road.

On the other hand, it does help us understand the system -- we know now that albedo is very important, and how much it and solar input could be expected, on a simple basis, to affect climate.

We also, it turns out, have a tool for identifying unreliable sources. I was surprised to see this be the case, but Steve Milloy at junkscience(dot-com)/Greenhouse assumes that if there were no clouds, the earth's albedo would be zero. Even knowing nothing about the details of albedo, you know this has to be wrong. If the earth's albedo, aside from clouds, were zero, you couldn't see the earth except for the clouds. As this image reminds us, you can indeed see the earth from space. His writing where he makes the error says:
We should note that devoid of atmosphere Earth would actually be a less-cold -1 °C (272 K) because the first calculation strangely includes 31% reflection of solar radiation by clouds
He also seems to be calculating the solar constant rather than taking an observed value, and using odd values for the his calculation.

Project: what would be better values for each figure, and how would using them affect his results?

More from Icecap

Ah well. Still more errors from Icecap; I'll comment first about the ones aimed at me personally. The article opens

"Alarmist Blog Blocks Comments ala Real Climate
By Joseph D’Aleo, CCM, Fellow
Fashioning itself after Real Climate, Grumbine Science blog posted a blog on the recent Washington Examiner story I authored ..."

Alarmist? It would have been good if the author had pointed out what I said that was alarming.

Fashioning itself after Real Climate? Hardly. If I wanted that, I'd simply have joined up Real Climate. Check out Real Climate and see for yourself whether this is the same sort of site. (And if you think it is, please point out where, beyond an interest in science communication, you feel I'm copying.)

The name of the blog is also wrong. Grumbinescience is my sister's, for her jr. high science class. This is MoreGrumbineScience. (If my other sister starts one, I've told her she has to name it 'Even More Grumbine Science' or some such.)

I attempted to respond several times on the blog to the blogger and commenters questions or complaints but the moderator refused to post my responses so here they are.
I've received zero comment submissions from D'Aleo. I did get two from 'Anonymous' on that thread. One I published, the other I didn't. The one I didn't was not regarding icecap, rather my comment about it being a red flag of mine (regarding the guest article at Pielke's site) when an article calls for open debate where there is a no comment policy.

He comments in his (self-described) rant that: By the way we have been asked why we at Icecap don’t allow comments. I assure you if I were retired or we were getting huge contributions like Real Climate with their blank checks from Fenton Communications and I could devote full time to Icecap we would. It is a full-time job policing and monitoring and responding on an open blog. I have to make a living mainly from other consulting and forecasting jobs. What I get from Icecap is supplemental.

Dang! You mean I could get paid for this!? I'm getting zero dollars from anywhere, certainly not a 'supplemental' income. How about this Fenton bunch? Are they giving out checks of any size, much less blank? Can I get some? Well, if they are, it appears that it isn't to Real Climate -- a fact they mentioned more than 3 years ago.

More to the point, though, D'Aleo complains about being unable to get his comments posted here, while at the same time not allowing comments at his blog. He complains about being unable to allow comments while getting income for his blog, while I get paid nothing by anybody. He complains about being a one man show making it impossible to allow comments, while I am a one many show, and do allow comments.

It also strikes me that if someone wants to complain about not being able to get comments posted, he really should use his own name. An 'anonymous' had one post rejected, and an 'anonymous' had one get through despite being resource free. I'm more lenient with the posts that disagree with me than those which agree.

If his posts never reached me through blogger, I've also given, a few times, an email address for contacting me -- plutarchspam at aim dot com. I've received zero mail there.

But he did spell my name correctly and give a correct link here, so he wasn't wrong in every mention.


For the science, he ultimately says very little, I think. But, of course, check it out yourself:

He says the newspaper made him take away the UAH label from the MSU on the figure. It could have been in the text (and should, irrespective of the graph's label).

He never addresses my complaint about the misleading axis on CO2, instead saying that my complaint was about the smoothness of the curve.

On the ARGO observations of heat content he cites (after and NPR story and Pielke's blog -- neither being a scientific source):
Willis J. K., D. P. Chambers, R. S. Nerem (2008), Assessing the globally averaged sea level budget on seasonal to interannual timescales, J. Geophys. Res., 113, C06015, doi:10.1029/2007JC004517.

I'd searched on web (as scientists often have their papers listed, and even full content on their web site), Google scholar, Web of Science, and Meteorological and Geophysical Abstracts without turning up any newer Willis papers regarding ARGO than the 2007 correction. It turns out that this paper in its entirity is available (which surprised me as AGU is usually fairly restrictive) so I've put the link to the article and you can read it yourself. The abstract is:

Analysis of ocean temperature and salinity data from profiling floats along with satellite measurements of sea surface height and the time variable gravity field are used to investigate the causes of global mean sea level rise between mid-2003 and mid-2007. The observed interannual and seasonal fluctuations in sea level can be explained as the sum of a mass component and a steric (or density related) component to within the error bounds of each observing system. During most of 2005, seasonally adjusted sea level was approximately 5 mm higher than in 2004 owing primarily to a sudden increase in ocean mass in late 2004 and early 2005, with a negligible contribution from steric variability. Despite excellent agreement of seasonal and interannual sea level variability, the 4-year trends do not agree, suggesting that systematic long-period errors remain in one or more of these observing systems.

Now, remember that D'Aleo's original claim was that ARGO showed cooling. Does that abstract support his claim? It undermines it twice. The latter is obvious in the last sentence whether you're an oceanographer or not ...suggesting that systematic long-period errors remain in one or more of these observing systems. At least one of the systems -- satellite or ARGO -- has a systematic problem. It's therefore hard to say that ARGO shows, necessarily, either a warming or cooling since it could be the one that's got a systematic error.

That aside, though, there's the first undermining. You need to be enough of an oceanographer that steric refers to sea level change due to expansion or contraction of the water itself whether because of warming or cooling (respectively, thermosteric in the paper) or removal or addition of salt (ditto, halosteric). D'Aleo's claim is that ARGO shows a cooling -- that should show up as a drop in sea level (a negative steric contribution). In the abstract it only mentions that there was no contribution during 2 of the years -- no net steric change. No support for D'Aleo there either. In the paper itself, the text gives the steric component trend as -0.5 plus or minus 0.5 mm/year, as a net between the temperature and salinity contributions. The two are mentioned individually in the paper, but no error bar is given. Assuming they gave the 1 standard deviation bars, as usual, then there's about a 1 in 6 chance that the steric contribution is positive. And that's if we assume that the ARGO buoys are not the one (of the) source with a systematic problem.

This paper mentions a paper submitted by Willis in 2007 regarding ARGO and heat content. That's an important term, 'submitted'. If it had been published, it would be cited that way. If it had been accepted for publication (passed the peer review), it would have been described as 'in press'. At the time this paper was accepted, though (22 February 2008), the other had not been. It will be interesting to see what the other paper has to say. As I said before, I do hope they can work out the problems with the ARGO data for this purpose. (It's already very useful for other purposes.) But it's that other paper that D'Aleo needs, not this one.

As I'd suggested early on, you don't need to be a professional scientist to recognize many of the errors from some sources. Once you do, it's time to move elsewhere, I think. It's hard enough to understand the world when you're reading good sources (or at least, good enough that they're not making errors my sister's jr. high class could recognize).

Olympic Connection

I almost have a connection to the Olympics. While riding in a train, I started talking to the guy on the seat opposite. It turned out he (Simon Ayeko) was on his way to a track meet to try to qualify for the Ugandan Olympic team. He didn't make it, which I don't understand since he's run fast enough to meet the 'A' standard in his event -- the 3000 m steeple chase -- this year. They're sending nobody in that event. Also surprising since he only has the second best time from Uganda. Oh well. He's a young guy, so I hope he makes it to the 2012 games.

In a different way, I do have a connection to the Olympics. My wife and I went to Greece for our honeymoon. While there, we visited Delphi. One part of the site at Delphi was the stadium in which the Pythian Games were held. The games at Olympus were not the only ones. So I ran full out for the 1 stade (178 meters) race, starting from where the racers would have 2500 years ago. Didn't succeed in getting some high school students who were posing at the start to join in a race. But I ran my best, while thinking of the competitors representing their cities those centuries ago.

International Science

This weekend we'll be celebrating the new citizenships of two of my coworkers. This is one of the things we mean when we talk about science being international. Science isn't some vapor that floats around the world, rather it is people sharing ideas all over world. And working together in many parts of the world. Some like their new locations enough to take citizenship there. So this weekend we'll be welcoming two coworkers to their new citizenship with some food, drink, and conversation. Perhaps rather a lot of conversation; you may have noticed that I'm a bit chatty. I'm not terribly unusual in this among my group, or scientists generally.

There's an important -- to having confidence in scientific results -- flip side represented by the distribution of scientists. If all scientists are wealthy northwest European men (which was nearly the case in the 1800s), then it wouldn't be too surprising for a particular idea to strike the fancy of them all for the same cultural reasons rather than being good science. Today, though, with scientists spread across every continent, from different ends of the economic spectrum (my going to college required the limit in loans, work study, summer jobs, etc., plus academic scholarships, not family wealth; while some good scientists still come from financial backgrounds like those 1800s folks), both men and women (not as many women in my area as I'd like, but my postdoctoral adviser was one and there are more now than 30 years ago), different races, religions, ethnic groups, political preferences, ... it's very hard for an idea to be shared across those different groups unless there's something to it. (Ok, yes, scientists are very prone to believing that science is interesting and a good way to study scientific problems. But that's not a scientific conclusion, it's an assumption.)

Linking

It seems my notions about links are wildly unusual (and thanks Jules for adding them Wednesday). My idea is that since we're discussing science here, if you disagree with some point I make, or have a point to add yourself, then it is a good idea to include a link or full reference to a good source. One of the things about doing science is that you don't take people's reporting as gospel. Scientists are people, and people make mistakes. So it's a good idea to make it easy for people to check out the full original source. When you've described something well, they can be thankful for your much better description. Or maybe they can learn more about the topic. Wins all around.

Maybe there's something about how the blog world works that makes this a bad idea. If so, let me know how and why. In the mean time, please make it easy for people to follow up the science you bring up.

Math in Climatology

I'm doing my best to keep the math to a minimum here, because one can indeed understand a lot of the fundamentals without it, also because I know many people suffer from math anxiety. Then a large contribution from the fact that I know if I start down the road towards using math, I'll use a lot of it.

Now, on the math anxiety side, I highly recommend Sheila Tobias' Overcoming Math Anxiety. Unlike your probable expectations, she is not some outsider who never had the problem herself. She had a big case of it, but decided that physics was interesting and she'd bite the bullet and try to learn the math needed. She did, along the way dealing with a number of anxieties and false impressions about mathematics. One of the major problems shared by many people is the notion that only certain 'special' people can do mathematics. If you're talking the seriously hard core stuff that wins Fields Medals, that's probably true. If you're thinking about the level that I'm using here, the answer is ... nonsense. Anybody without a serious learning disability can learn this, regardless of age, gender, race, religion, part of world you live in, etc.

Here's a sampling of courses or material that one would almost certainly encounter on the way to being able to study climatology professionally:

Algebra I
Algebra II
Trigonometry
Differential Calculus
Integral Calculus
Calculus of Several Variables
Probability and/or Statistics
Ordinary Differential Equations

That's just warming up. You'd also likely encounter several of:
Linear Algebra
Partial Differential Equations (probably multiple courses)
Complex Analysis
Numerical methods (probably multiple courses)
Statistics (in a multi-term sequence)


... and probably several more that aren't leaping to my mind right now.

Building the Simplest Climate Model

Where did the simplest model come from? Nice that I showed a model that gives realistic answers, but even better to know how it works!

The model is built on one of the great conservation laws of science -- conservation of energy. If you track all the ways that energy enters your 'system', and all the ways that it leaves, you can know quite a lot about it even without knowing very much about what's going on inside. That word 'system' may not mean what you're thinking. What I mean here is that we draw an imaginary box around, in this case, the earth, and see what passes through the box.

We have, in general, three ways to get energy through the box. We can carry some material from one side to the other (advection or convection). But the earth doesn't gain or lose material from space, so can't gain or lose energy this way. Another way is to conduct heat across the boundary. A frying pan does this in making the handle hot even though the flame is a good distance away. But with a vacuum on the other side of our box, there's nothing to conduct to. The third way is as radiation. Everything emits some radiation. The hotter is is the more it emits. A traditional thermos tries to minimize all three -- the inside is glass, a poor conductor, the glass is almost totally surrounded by a vacuum to cut down conduction even further, it is sealed, to prevent convection, and the inner wall of the thermos is reflective, to prevent the wall from gaining or losing heat by radiation to your drink.

In looking at what can cross the boundary of the earth system we have only two things -- radiation from the sun, and radiation from the earth. We all know that many things can happen inside the box: storms, building and melting ice sheets, forest growth and decay, and so on. But they're all inside. For our simplest model of the temperature of the earth we don't need to know about those, just income versus outgo. (Well, more to it than this, but hang on for now.)

The sun's radiation all comes in to the box, passing through a disk whose area is pi*r^2, where r is the radius of the earth and pi is the usual 3.14159... Same as the sun and moon look like disks to us, we look like a disk to the sun. Some of that solar energy gets bounced right back out. The fraction of the incoming solar energy that gets bounced out is called the albedo. For the earth, it is about 0.30 averaged over the whole planet, through the whole year. Particular surfaces can be much higher (snow can be 0.8) or much lower (oceans can be 0.06). But since we're only concerned with what passes through the box, we don't need to worry about those details yet.

The earth also emits radiation, as does everything that's not at absolute zero. For an ideal black body, that emission is proportional to s*T^4. This is the Stefan-Boltzmann law, and s is the Stefan Boltzmann constant, equal to 5.67e-8 Watts per square meter per K^4. Every square meter of the earth radiates like this. Since the earth is (very nearly) a sphere, the total area is 4 * pi * r^2. Again, r is the radius of the earth.





Conservation laws are written in terms of a balance of income and outgo. If the earth is in energy balance, then the following equation is exact. If it isn't, we'll have to look at how far out we are.
Income = pi * r^2 * S

Outgo =
pi * r^2 * S * a (albedo reflecting energy immediately away from the earth)
+ 4 * pi * r^2 * s * T^4

For the conservation law being Income = Outgo, we get
pi * r^2 * S = pi * r^2 * S * a + 4 * pi * r^2 * s * T^4

We notice two things rapidly. First, pi * r^2 is in every term. We can divide the equation by that and simplify. Second, the solar term is on both sides. We can subtract the albedo term from both sides to get all the solar-related terms on one side, and the earth on the other. So now we have:

S*(1-a) = 4*s*T^4

If we solve for T, we're back to the equation I gave in the original note

It's remarkable that the size of the earth doesn't show up here. Actually, it does -- that 4 is the remaining part. It's 4 because the entire area of the (spherical) earth emits energy to space, while the sun only contributes energy through a circular disk, and the area of the sphere is 4 times larger than the area of that disk.

This leads to a point that I see commonly missed. When solar observers talk about how much the solar output changes, they're referring to the S -- seen by the disk of the earth. During a solar cycle, it varies by about 1 Watt per square meter. In looking at climate, though, we think in terms of the spherical earth we're standing on, rather than the disk in space a satellite is using. When climate people talk about Watts per square meter, we're talking about 4 times as many square meters as solar observers. To make the two comparable, climatologists often divide the equation by 4, meaning that when a solar observer says 1 Watt per square meter, climate folks will treat it as 0.25. Not because we don't think the sun's important, but because the 0.25 gives a description that we can compare to earthly climate processes we observe all over the sphere.

On Monday, there'll be a third post in this set -- analyzing this model. In the mean time, a project for the more mathematically skilled out there: How is this model affected by using a proper oblate spheroid for the earth? Is it? And, for everyone, try out the spreadsheet version and see how it behaves as you change the parameters.

Ah, I should note that the S above isn't exactly the S in the original. Here it's the solar constant divided by mean earth-sun distance (in AU), while I left the two separate in the original. As tamino showed, the two are awfully close to each other since the mean earth-sun distance (over a year) doesn't change much even as the orbit varies on tens of thousand year time scales.

A different and more important matter if you're not used to this is that the temperatures will come out in Kelvin -- the scientific absolute temperature scale. Celsius is used, but when we are concerned about energy, it's best to use Kelvin (K). Fahrenheit is probably never used in doing science (even if someone did, it never gets published that way). Kelvin is Celsius plus 273, so water freezes at about 273 K, boils at about 373 K. (Or Celsius is Kelvin minus 273.) The earth's black body temperature is about 255 K, or -18 C.