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Frank Pennycook
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Rob, sure, "time by itself does not increase heat in the Arctic", I can't disagree with that! What I meant was that since we know there is a secular trend it might pay to work it in for predictive purposes. However, I see the value of not *assuming* it. In fact it is implicitly included in that June extent and the other variables are themselves subject to the trend and the results of warming. Indeed, the correlations are very good, with the physical variables alone. By the way, I think NASA might have worked out their own similar method, this was published last week: Petty et al, Skillful spring forecasts of September Arctic sea ice extent using passive microwave sea ice observations, Earth's Future, 27 February 2017
Toggle Commented Mar 6, 2017 on PIOMAS February 2017 at Arctic Sea Ice
Hi Rob, yes awk -- an old friend! I don't have much call for it now, mostly, but I'm an everyday user of vim and grep. Any of those langs - R, C, python (plus others) would do, the thing is to get used to one and stick with it. If you use C (and/or ++) that's going to be fine. I love working in C, but I do find python easier to get up and running for a one-off "quick and dirty" investigation. Thanks for the data. I will have a go. Just give me a few days to get around to it. I may report in this thread if it's still going, or on the forum. From eyeballing the numbers it is striking how considerably higher the correlations are in June from May and April, as if the season's outcome is more or less set by then. And also, since "year" is such a strong factor, should it not be included in the analysis? To reflect, as you say, the long-term trend.
Toggle Commented Mar 5, 2017 on PIOMAS February 2017 at Arctic Sea Ice
Hi Rob, maybe I should unlurk more! Thanks. It's probably worth the initial effort getting set up for multiple regression, as it would then be so much easier to add more variables or repeat the analysis to include data from recent years. Your program for linear regression - what's it written in? In most languages there's going to be a stats library. I'm mostly using python at the moment. Here's some info about statistical methods in it (incl MLR): If you have the data handy, or could point me to it, I'll have a look at it if that would help. Incidentally, how does the correlation come out for the individual factors?
Toggle Commented Mar 4, 2017 on PIOMAS February 2017 at Arctic Sea Ice
Your outline of a philosophy of science strikes me as impoverished. There are times when an experiment to isolate a single cause is critical, and fundamental laws can be unified thereby. Equally there are times when science examines more complex networks of causation. But we are not talking here about a search for Newton's Laws. We are examining a single system, that inevitably is influenced by multiple factors, all within the framework of basic physics and chemistry of course. I do not accept your criterion for deciding if I am engaging in a serious debate. Perhaps you are a "serious investigator". Why then have you refrained from testing the correlation you describe? I have already explained why I do not think such a single factor correlation, or the lack of it, would be instructive. Your "method" is not correct, and I have explained my reasons for saying so.
Toggle Commented Mar 3, 2017 on PIOMAS February 2017 at Arctic Sea Ice
(1) Continuous functions of time: the sea ice extent is a value which exists at any time. You could measure it at 12:00 and 12:01. It cannot be very different at 12:01 from what it was at 12:00. This differs from a plot of points to which one might try to fit a line. (2) Fifth guesses. I indulged in rhetoric here. You described your idea of a correlation between Land Snow Cover and melt rate as "the first guess". But it is not. It is a step backwards from the information gained by considering the influence of several factors simultaneously. (3) "What would be the value of me testing for the correlation?" I don't know, it's your suggestion.
Toggle Commented Mar 3, 2017 on PIOMAS February 2017 at Arctic Sea Ice
Trying to best fit a seasonal cycle with a straight line is not the way to separate signal from noise. If you wish to eliminate daily variability take a range such as averaging +/- 5 days of each endpoint. But there is no need for that. Because the function of sea ice extent or area with time is a continuous one. Not a scatter plot. Best fit lines should be used when it is reasonable to hypothesize that the underlying relationship might be linear. Not otherwise. Am I wrong? If you wish to test whether the Land Snow Cover on (or around) 1 June has an effect on September extent, yes, it is reasonable to check for a correlation. Have you done so? But, importantly, that is not "the first guess". The first to fifth or sixth guesses have already been made and we have in front of us the useful analyses of Bill Fothergill and Rob Dekker to build on. Yet you have done little except pour scorn on them and their work. I have not seen a single calculation from you beyond links to interactive plotters such as woodfortrees.
Toggle Commented Mar 3, 2017 on PIOMAS February 2017 at Arctic Sea Ice
Zebra, I'm happy to hear what you've got to say, so long as Neven is content. However, I commented as part of a group discussion. I'm not committing myself to a one on one. If I don't reply for some time it's likely I'm away or perhaps haven't got anything to contribute at that moment. But I'm here now. Go for it.
Toggle Commented Mar 3, 2017 on PIOMAS February 2017 at Arctic Sea Ice
In my opinion Rob's description of the procedure he followed is mostly self-explanatory. In a nutshell, he picks three measurements in June and seeks a linear combination of these as a predictor of September sea ice (extent or area). The choice of the variables is based on physical intuition and he has an initial guess at the coefficients as a test. This guess already shows a relationship with the historical data, so he goes on to improve the fit. He varies the coefficients in order to maximise the resulting correlation coefficient (between observed and predicted sea ice in September). Exactly what tool or iterative approach he used for the optimization I'm not sure -- I'm guessing if you asked Rob (nicely) he'd tell you. But the theory is clear. The outcome then is a linear formula that predicts September sea ice from values known in June, which is based on physical reasoning, and which has excellent fit with known observations. I would make a suggestion, though. If I were doing it I would skip the step of making the line (alpha+beta*F). I'll show you why. Call the measurements in June M1 M2 M3 and the coefficients p1, p2 and p3. Then the so-called melt factor F = p1.M1 + p2.M2 + p3.M3 And the prediction for September, S = alpha + beta * F. But then S = alpha + beta.p1.M1 + beta.p2.M2 + beta.p3.M3 I would view beta.p1 as a single coefficient, the weighting for Snow Cover or whichever measurement M1 represents. Call it a1. Call alpha a0 (because I can't do a Greek font here!). Now S = a0 + a1.M1 + a2.M2 + a3.M3 From my point of view I find it clearer to see it this way. We would find the best fit coefficients using "least squares", that is, minimizing the sum of the squares of the residuals. This is multivariate linear regression, and would be a more standard approach. I believe, but am not certain, that Rob's method should come to the same answer anyway. It's possible we would require some assumptions about some distributions being well-behaved (normal or so on). I would have to crunch some equations to check that. Oh, and Rob, useful work, very interesting. I've been following this blog for a couple of years but hadn't come across this item of yours before.
Toggle Commented Mar 3, 2017 on PIOMAS February 2017 at Arctic Sea Ice
I can't take it any more. I mainly lurk here, because arctic ice is not my field, and I benefit from others' expertise. I have an understanding of the science, but I am not a scientist. I am a mathematician. Zebra, please. Your so-called "correct method" is deeply misguided in so many ways it is hard to know where to begin. The issue is the relationship between June conditions and September conditions. You narrowed this down to the question of whether June land snow cover is correlated to September sea ice. This is not very relevant to Rob's multi-factor analysis. There could be very well be zero or low correlation, or even anti-correlation, for one factor, yet a reliable and quantifiable relationship based on the multiple factors. Then to address this you propose to fit a straight line to a non-linear variable, sea ice extent, which is seasonally cyclical. However, as you remark, over the range concerned (Jun-Sep) the curve does look fairly straight. OK. But to the extent that it is straight, you don't need to fit it, because its slope can be determined from the end datapoints. And to the extent that it is not straight, your method will give the wrong answer because a "best fit" line has no meaning for this dataset. Rob pointed this out further up the thread. It seems clear to me that if you want to investigate the relationship between September data and June conditions you use the values at one end (as dependent variables) and the values at the other (as independent variables). You stress that you concentrate on the "rate" of sea ice loss. But over the fixed period concerned the daily rate is only the amount of ice lost divided by a number of days, which is always the same number of days. So this is division by a constant, and will make no difference to any correlations observed. So you propose an outrageously convoluted method to inaccurately calculate a correlation that will not in any way shed light on the work which Rob did. And you tell him he is confused about maths and physics. Incidentally, you repeatedly carp at others for supposedly using spreadsheets. What's the problem here? Statistics can be correctly computed using all sorts of tools. It doesn't matter if I use R, a python library, pencil and paper or Napier's bones. If the correct procedure is followed the answer should be the same.
Toggle Commented Mar 3, 2017 on PIOMAS February 2017 at Arctic Sea Ice
Hi, a long-time lurker here. I agree with those interested in a zoomed-out view of the PIOMAS 365-day average, so I've plotted a few years. Please bear with me if it doesn't display correctly, I'm not sure about the system for posting images.
Toggle Commented Dec 8, 2016 on PIOMAS December 2016 at Arctic Sea Ice
2.75 My fairly uninformed guess. I can see why some have gone high, based on the variability and the chance of a rebound as has happened after previous lows. But I'm swayed by the thought of all the thin and first year ice, and by the volume trend, to think the reduction in extent is likely to accelerate even more from here.
There was also this one: Hopefully global warming will cause sea levels to rise, and with a bit of luck, all those foaming liberals that want us to live in powerless hovels eating insects will drown. Might go some way to solving the population problem. I like that. Concise and to the point.
Re - 520 ppm. I agree with Artful Dodger's points about seasonal trend and increasing rate. I'd go further, there's every reason to expect 520ppm CO2 by 2050 or even sooner. The rate of increase is increasing pretty steadily, I've done a projection based on a quadratic fit with an acceleration of 0.0235 ppm/yr/yr. This gives the best fit for the period 1980 - 2012. On this basis, we reach 520 by 2050. But the future course of CO2 levels is very dependent on what populous developing countries like India and Brazil do - if they follow China to European levels of output then the rise will be quicker. And that's not to mention any natural feedbacks or other GHGs either.
I've been wondering too why there isn't more "buzz" or maybe "shock and alarm" would be more appropriate! I think it is because the chain of causation is too long, for most people. The press has to communicate to a public which really requires a glaring fact. When you can get on a ship, in spring, and look out across the undisturbed waters of the Arctic Ocean, then we'll be able to comprehend, "Oh, the ice is gone". Too late. Until then it is graphs and statistics, a language that to a great many people is terrifying mumbo-jumbo, which is what the FUD tactics of the deniers exploit.
Hi, I'm a new poster to here. Great blog and hugely informative discussion, thanks to all of you. I'm interested that iceman mentioned above the idea of analysing the downtrends: Maybe comparing the time-shift in downtrends will yield some insight. Following the big drop in ice thickness in 2007, the downslope in volume anomaly has been earlier and/or steeper than before. .. because that's just what I've been doing. My aim was to see what eventual minimum to expect from the PIOMAS volume measure this year. Since day 238 is the last available datapoint for us at the moment, I looked at how previous years had compared, calculating the ratio of PIOMAS minimum to day 238 value, and also comparing the minimum against a 5-day mean ending on day 238 in case of one-off anomalous values. From 1979 to 2007 (inclusive) the eventual minimum, whenever it occurs, averages 95% of the mean of days 234 to 238. The variation is small (std. dev. of 0.016) in these years. After that, for the last four years, the ratio plunges and gets more erratic, averaging 89% which is significantly outside the range of variation seen in 1979-2007. The impact, applied to this year, would be to predict a minimum for PIOMAS in the range 3.1-3.5 km^3. A prediction based on the behaviour of earlier years would overlap the top of this range, e.g. 3.4-3.6 As to the timing, I checked the date of the minimum over the whole series. Because there is sometimes some double-dipping and because the timing of the minimum could be sensitive to a single outlier I used a ten-day running mean. I found that the date of the minimum appears not to trend and almost always occurs between days 255 and 270. I'm somewhat surprised by the timing result, but thought the abrupt change in the behaviour of the last few days of the downward slope was interesting in the light of discussions on this site about the clear changes in the shape of the melt curve since 2007. What minimum value does anyone here think we'll see for PIOMAS volume this season?
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Sep 4, 2012