Some will recall that my Friday post began:
On a previous thread, Steven Mosher asked:
“The greatest melt extent over the last 2 1/4 centuries occurred in 2007; however, this value is not statistically significantly different from the reconstructed melt extent during 20 other melt seasons, primarily during 1923–1961.â€
How high would 2010 have to be to be statistically different from the reconstructed melt?
The answer is: Let me reword your question so it can be answered. 🙂 I know this might sound like “reframing”, but unfortunately, sometimes questions need to be tweaked a little for me to figure out an answer. So, the question I’m going to try to answer is this:
Q1: How high would the reported ice melt index for 2010 have to be in order for us to reject the null hypothesis that the ice melt index for 2010 is less than or equal to the highest ice melt value that would have been recorded by a satellite prior to 1979? I think this is the testable question is the one most closely connected to the notion of “statistically different from the reconstructed melt”, but people could mean other things.
While mowing the lawn, I pondered what I said in the last paragraph, asking myself if, on further consideration I really thought the Q1 is the question most closely connected with ‘statistically different from the reconstructed melt”. I decided focusing on records might better match the notion of “is the 2007 melt unprecedented”. This is somewhat different form “statistically significantly different”, which often merely means: Assuming 2007 really does fall in the previous range, would we have seen a MI as high as seen in 2007 more than 97.5% of the time. (Here I’ve chosen a p=95% and I’m testing two sided. That’s what I generally do at the blog, and it’s pretty common.)
Based on that, I thought of two other questions that could be tested:
Of these I think Q3 may be the best question to translate into a test. For those wondering: Q3 is a sort of “intermediate” choice. What we will find is that if the reconstruction contains a large number of years (specifically more than 20), for a given observed melt index (e.g. the value in 2007), might find it falls outside the ±95% intervals under Q2 but not Q3 or Q1. If it’s a bit higher, it might fall outside Q2 and Q3, but still not be a record. If so we’d say it falls outside the ±95% confidence intervals for natural variability but it’s not unprecedented in the record. Finally, if an observation is high enough, it will be both outside the ±95% confidence intervals for natural variation and also a record.
I’ve already done Q1, but I’ve only explained “fail to reject”. I mentioned that it’s possible to show it’s probably not a record and I planned to show that 2007 is probably not a record tomorrow.
Because Q2 & Q3 occurred to me, and it turns out the answer to Q2 is different from the answer to Q1 I didn’t want to just leave this hanging in the air. I wanted to let people know that answer is different. It turns out Q2 is so trivial to do that as soon as I got done mowing the lawn, I opened up the R code used to answer Q1 and added the loop, sort and inspect required to find the answer to Q2 in 5 minutes. The answer is: 2007 falls outside the ±95% confidence intervals based on Q2. I’ll show how I estimated this later.
As I mentioned, I think Q3 is the “best” question to ask. I have not done Q3 yet as it requires some thought. (The difference between Q2 and Q3 is that the range of predictive variable temperature may be larger than the range observed. The fact that the temperatures exhibit lag-1 autocorrelation means I do need to account for that. It’s Mother’s day. I fixing dinner. I’m not going to do that now. But those wondering:
- If by “statistically different” we mean 2007 was a record: It probably wasn’t. the probability that it’s a record is quite low.
- If by “statistically different” we mean does it fall outside the ±95% confidence intervals of the “true” melt indices we would have observed if the satellite was operating during the years for which reconstructed values exist? The MI for 2007 falls outside that range.
- If by “statistically different” we mean: does it fall outside the ±95% confidence intervals for the “true” melt indices we would have observed if the satellite had been operating and we could “rerun” the earth over and over and over forever with the same forcings that existed during the period the reconstruction exists? I don’t know if the MI for 2007 falls inside or outside this range.
If people can suggest other precise statistical questions that might correspond to the concept of “statistically different from” the reconstruction period, let me know. As you can see the translation from an ill-posed question in English to a statistical tests can make a difference in saying whether something is “statistically different from”.
So:
- Happy Mother’s Day
- Suggest questions.
Update: I forgot to add Q4:Given the reconstruction, what’s the probability 2007 was a record. I haven’t shown that but the probability is p=12.6%. Some mild assumptions were made.
The question we need to test depends very much on what wider question we are trying to answer. Do we really doubt that Greenland is warmer? If so is the melt a particulalry useful way of confirming the temperature record. I think the answer is ‘no’ in both cases.
Consequently a more interesting question is the extent of the melt GIVEN the surface air temperature. In other words what is of more concern is whether the Greenland ice-sheet is, over time, gradually warming up because of successive warm-years and overall general change.
I think there is a difference between the degree of melting in a given year BECAUSE THAT PARTICULAR YEAR WAS WARM and the degree of melting because not only that year was warm but because of overal warming.
Re: Nyq Only (May 8 13:59),
I added the parenthetical with strikeouts, because I don’t think that’s quite what you meant. Yet, it fits with the point you are making.
That leaves me confused.
It seems to me that there will be a certain amount of melting in a given year, because of the warmth of that given year. Full stop. The icecap isn’t able to perceive whether a given year’s warmth is anomalous, or a random variation, or part of a long-term trend, anthropogenic or natural.
Apologies if I’m missing something obvious.
Nyq–
I’m not sure what your question is. Maybe you can clarify “other factors”?
Amac/Nyq–
I’m going to throw out a hypothetical to see if this helps Nyq clarify his concern. Suppose for some reason (possibly involving leprechauns), the temperatures in Greenland actually unwent a step change upward and then just stayed there. In this case, you might imagine that initially, summers would show lots of melting, but eventually the melt rate would decrease at matched temperatures. The reason for this would be because a lower fraction of Greenland’s surface was covered with ice and ice can only melt if it’s present.
What this argues is that one of the “other factors” is the amount of ice present. So, if the region merely warms by δT and stays there, we get a finite amount of melting.
This has some consequences for the possibility of bias in the FKM reconstruction. (Note however, that I’ve looked at the residuals to the reconstruction and there is no evidence of this bias was quantitatively meaningful to the actual fit in FKM. But hypothetically, it could lead to some bias if the only ‘proxy’ to reconstruction melt index is temperature.)
Luica (#75719),
Would not a bias require that the total ice surface area change significantly? The fractional area of Greenland not covered by ice does not look terribly different from what it was 70 years ago.
.
Another source of possible bias is a change in surface elevation due to melting (warmer at lower surface elevations, even if the coastal temperatures don’t change. But once again, there would appear to have to be quite a lot of loss in ice surface elevation to raise net surface temperature very much.
Yes. That’s why the bias is hypothetical. It doesn’t seem to be showing up for the period considered by FKM. I don’t know if this is the sort of thing Nyq is thinking of. But to figure out whether ‘other factors’ matter we need to know what other factors he’s suggesting might matter.
FKM considered NAO as a factor, but it didn’t make the cut for the final reconstruction.
Apologies I was rambling.
Presumably in a relatively warm winter the ice is warming and presumably, if there is an overall warming trend, a glacier or ice-cap is slowly warming also even if most of it is still below freezing. So, presumably the net effect of warming over years effects the amount of melt in a given year as well as the temperature in that particular spring/summer.
AMac: “The icecap isn’t able to perceive whether a given year’s warmth is anomalous, or a random variation, or part of a long-term trend, anthropogenic or natural.”
True but presumably the overall amount of heat in an ice-cap or glacier is something that changes over years. It isn’t going to reset each winter or summer. So presumably past years temperatures play a role. I assume that is taken into account.
Lucia: Maybe you can clarify “other factorsâ€? I don’t think I said “other factors” 🙂 – and I’m not sure what I’m asking either.I think what I’m trying to ask is overtime how much ‘hotter’ have the temperatures of greenlands ice got. If we stuck a thermometer some depth into the ice – how would that temeprature have changed over time. Given the mass of the underlying ice presumably that temperature fluctuates more slowly than the air-temperature around it. Apologies for the ramble – I’m just thinking out loud.
Re: Nyq Only (May 9 13:20),
Thanks for the clarification.
A comment I made on the earlier thread may inadvertently address part of your question. I was concerned that there was a time-dependence of the proxy (“autocorrelation”) that its error calculation did not take into account.
Lucia and Brandon pointed out that, for that issue, autocorrelation of the errors/residuals was the important point to consider, rather than autocorrelation of the melt itself. Lucia went on to post a graph that shows (if I am interpreting it correctly) that there isn’t much autocorrelation in the error/residual, if any.
That would seem to also address the issue you raise, that there could be multi-year “memory” by the icecap, in that its internal temperature will be colder after a string of cold years, than after a series of warm years. This in turn could influence summer melt.
If such memory is significant, ISTM that it would lead to autocorrelation effects, and that this should be detectable in the data. Assuming that there are enough strings of cold/warm years to contrast against variable periods.
Hopefully I’ve used big words like “autocorrelation” properly, and this comment is comprehensible 🙂
Nyq–
Sorry. I don’t know why I thought “other factors”. I think I just read you mention one, but I didn’t understand what you were trying to describe.
Now, it seems to me your argument is:
If it was cold before the melt season (e.g the winter before), the surface snow will be colder — as in possibly less than 0C. If it was or possibly cold the summer before, the deeper ice will be at a colder. So for the same summer temperature, we less melting if the immediate history was colder. You could then similarly propagate this back in time since possibly, the “deep ice” would still be cold if there was lots of ice at temperature slower than 0C around.
This is plausible, and is contrary to the factors I suggested. In this case, I’d also expect the total area covered in ice would be greater and so we might expect more melting.
Of course both things could happen, and then the situation is off setting.
The only way in which this is accounted for in the statistics is to see if the residuals to the fit are temporally auto-correlated. There’s no evidence they are. So, either both mechanisms are happening but off-setting or neither is sufficiently important to matter.
AMac (and Lucia): “Hopefully I’ve used big words like “autocorrelation†properly, and this comment is comprehensible”
Thanks. That does answer my question/thing/whateveritwas. I could see why we might expect autocorrelation of the data but then we’d be expecting that anyway. I hadn’t consider/noticed/grasped the point about autocorrelation of the residuals. I guess I’m still catching up…
The answer to the question is “no”. In fact, the question is a false premise to begin with. The icecaps have come and gone and are in fact an anomaly to the history of the earth. Therefore, it is painfully obvious that there is no melt record set. In order for a melt record to be set, one must compute total ice landmass of the icecaps throughout the historical record and find and instance where the past melt equaled 2007. Given that the ice caps have totally melted down before, the probability is more like 0.
My apologies for using the historical record. I fully understand that here that history is of no importance and the only things that count start in 1979.
Dr. Jay Cadbury, phd.
* My computation includes all years since 1840 and a few before that.
* On the larger issue of melt record for all time: the fact that a full computation always requires us to go back forever means that whether or not a record has been broken is rarely the best way to test statistical significance. If you have enough data, it becomes harder and harder to break records unless things really are changing.
* This is melt index, not the ice pack covering. When the ice is all melted, the amount of ice that melts during summer will be zero. I don’t know what melt index that corresponds to.
“Given that the ice caps have totally melted down before, the probability is more like 0. ”
Well aside from the issue of whether the whole-history-of-time-ever is a useful time frame your conclusion still doesn’t hold. That at times there have been no ice-caps doesn’t tell us anything about the extent of the melt in any given year. Consider a year when there is hardly any ice left – that year will not be a record year for melt simply because there isn’t much ice to melt that year.
There should be an eponymous internet law about blog commenters who append honorifics to their names.
Reunite Gondwanaland.
(Greenland’s discernible just before the 2-minute mark in this animation. No icecap back then–none!)
Zeke,
I think there should be punishment applied for those using dumb internet names like Vegtable Consumer and the like.
Andrew
AMac (Comment #75777)
May 10th, 2011 at 3:14 pm
“Reunite Gondwanaland.”
Another evil leftist plan for one world government! 🙂
Nyg Only,
My experience with people of the left is that this level of patience (continental movement) is nonexistent….. it is almost always now, Now, NOW! I think it is a psychological thing, because people of the left are certain they should control other people’s lives. Certitude that one is correct always fosters impatience. 😉
“My experience with people of the left is that this level of patience (continental movement) is nonexistent….. it is almost always now, Now, NOW! I think it is a psychological thing, because people of the left are certain they should control other people’s lives.”
So true – if I had been just a little more patient I’d have finished my mind-control ray* by now instead of wasting time trying to control all your minds with subliminal steganographic messages hidden in the distribution of vowels in the Harry Potter novels.:)
[*And those who claim my mind control ray is just an old TV and a lava-lamp better watch out once I get it working.]
“That at times there have been no ice-caps doesn’t tell us anything about the extent of the melt in any given year. ”
You could say that about “average” temperature as well. Because of data resolution you can’t tell what happens in the past in an individual year either (and to think you know down to tenths of degree (or not) is even more arrogant). The good “doctor’s” point is a good one. We have because of earth scientists all over the world sea level high stands data to look at. And they show us at the top of the last interglacial period (top of the Milankovitch Cycle) 125,000 years ago, sea level was 20 ft higher then it is today. C02 concentrations were lower too. And we are in/at /going through the peak of this current interglacial and no where near that. There are places you can see how much and how fast sea level rose in the recent past in the geologic record. Like from the blue holes expeditions which I have pointed to many times here in the conversations. All were ignored. Sometimes they said; climate changed in a amount of time equal to a human life span in those data.
So the planet’s NOT even close to the NATURAL variability /warm conditions it can have. And you all are still arguing about millimeters and tenths of a degree…
“my mind-control ray*”
Nyq,
Evidently, someone had already developed a working one and used it on you . 😉
Andrew
Andrew_KY “Evidently, someone had already developed a working one and used it on you”
Nah – they control my mind using fluoride in water 🙂 and with the liberallamestreammeedia…
“Nah – they control my mind …with the liberallamestreammeedia…”
Yeah, you guys make it that easy. 😉
Andrew
You continually talk about changes over much longer periods of time than we are experiencing now, and resolutely ignore the effect that a few degrees of change can have on biological systems. The Milankovich cycles produce mass extinctions. Saying that we havent’ had it that bad yet, is not much comfort, and the current warming hasn’t even finished. It is going to go on for a few more centuries yet, at a rate wich is much faster than the Milankovich cycles produce.
bugs, I generally agree with your comments, however, prior to the instrumentation period, our knowledge of the amplitude of higher frequency variability is pretty limited (most proxies are bandwidth limited).
You’re right though that lisa is inappropriately comparing amplitudes for periods of millennia and even millions to the much shorter periods associated with recent warming…
Carrick (Comment #75854) May 12th, 2011 at 4:59 pm
No I am not. Did you miss the part AGAIN when I mentioned there is evidence that climate changed fast …on a human life span timescale and referenced the Blue Holes research??? (and there are others) This is about the fourth of fifth time these FACTS have been ignored on this blog.
And bugs, I am not saying “we haven’t had it that bad yet’ either. I am pointing out that this very short “warm period” may not be unusual given that we can’t see individual years or such small time frames for the recent past. Temperature on a global scale could go up and down 1 degree or more all time. Or are you guys still trying to get rid of the MWP? And certainly the “climate” doesn’t live up to those scary “projections” you worship associated with CO2 so far. So listen to me.
Bottom line: None of you have any evidence or know if this is unusual climate/temperature the earth is experiencing at all. I’d say it has changed 0, Zip nada and in fact I’d say the climate in my part of the world has gotten COLDER. You are all still just guessing about the future as well!
“The Milankovich cycles produce mass extinctions. ”
Forgot to point this out as well. That is a false statement. There is no evidence for this notion at all.
liza,
Dont worry. Global Warming fossils like Carrick and bugs can agree with each ’till the cows come home for all the difference it makes.
Andrew
Andrew_Ky, seriously …they just make stuff up! The knowledge we have from geologic record (that researchers put themselves in danger and even risk their lives to collect sometimes!) says quite the contrary to what they think, feel and imagine and they have the gall to brush it away. The arrogance is stunning!
lisa, as to blue hole and other research, if people stick to paraphrasing without attribution, I generally don’t pay it much heed. Which is my prerogative.
/suggest “look in a mirror”
Being a Warmer means you can know the global climate without ever having to stop looking at your computer screen. Just find another Warmer or two to confirm whatever belief you like best. Alarmist? Covered. Luke-Warmer? Just as good. We got Squiggly Lines to fit your need. Zero-effort science. Virtual confirmation. We got it all.
Andrew