The last post certainly had lots of equations. We’ve seen that PCA seeks the directions in some multidimensional space of data which give the most variation of the data, i.e., along which most of the change is happening. If we can characterize almost all of the change with just a few directions in the multidimensional space, discarding the other dimensions, we’ll lose a lot of noise but almost no signal, and benefit from the simplifications of fewer dimensions. It’s a win-win situation.
A real-world example may clarify. There’s been some mention of the temperature history in Cedarville, CA, and the adjustments that are applied to that data. What’s happening in the Cedarville area? It was easy to find data for 5 stations in the region, all of which have enough to compute annual average anomaly from at least 1903 through at least 1998: Cedarville, Lakeview, Lovelock, Mt. Shasta, and Klamath.
These data look quite good from about 1935 onward; the different locations agree with each other strikingly well. But they show sizeable differences before 1935, including wild fluctuations from about the mid-1920s to mid-1930s. If we apply principal component analysis we find that because they all correlate strongly with each other, the 1st principal component is very nearly the average of all the locations (normalized data, times the square root of 5) and accounts for 64% of the variation of the data. It gives us the temperature history which the neighbors agree upon, which is almost certainly a pretty good picture of the overall temperature trend of the region, and that trend is increasing over the century:
There’s no sign in the 1st PC of the wild fluctuations seen in the mid-1920s to mid-1930s. But looking deeper, we find that of the 36% variation remaining after the 1st PC, half of it — 18% — is in the 2nd principal component (plotted here on the same scale as the 1st principal component):
Lo and behold, it shows a high value from the mid-1920s to mid-1930s, just at the time the data showed those wild fluctuations.
Looking at the eigenvector defining the 2nd principal component, we note the vector of values: [0.7314, 0.0537, -0.1813, -0.6526, 0.0588]. Note that by far the two largest components (in absolute value) are the first and fourth, corresponding to Cedarville and Mt. Shasta, and they’re of opposite sign. Hence the 2nd PC is pretty close to being proportional to the difference between Cedarville and Mt. Shasta. If we compare those two series to the 1st principal component, we see that during that 1920s-30s time period Cedarville is high and Mt. Shasta is low, while the others are in the middle near PC1:
The fact that PC2 accounts for half of the variation remaining after PC1, and that it singles out Cedarville and Mt. Shasta, indicates that both of these series are varying significantly from the “norm.” We can even take a look at the difference between Cedarville and a scaled version of PC1 to get an idea of how it deviates from norm:
Frankly the large difference between Cedarville and the 1st PC defined by its neighbors before 1935, compared to the small differences after 1935 (except for the odd year 1984), isn’t physically realistic. It’s not the real temperature history of Cedarville, but suggests instead that there’s an uncorrected error in the Cedarville data which introduces a spurious trend. Likewise, the large difference between Mt. Shasta and the 1st PC before 1935, compared to after, argues that Mt. Shasta data similarly have an uncorrected error before 1935.
One of the ways GISS applies homogeneity adjustments is to compute the difference between a series and the average of its neighbors (we’ve computed the difference from PC1, which is nearly the same thing), then fit a pair of straight lines which are connected at a “hinge point,” allowing the location of the hinge point to vary, in order to get the best fit. The difference between data and neighbors estimates the bias in a given location, and the pair of straight lines is designed to model that bias. The hinged-lines model was chosen to mimic urban heating in which there’s a spurious warming trend during early urbanization, followed by an even faster spurious warming trend during heavy urbanization. Then one can attempt to cancel out the spurious trend by applying a correction which negates it. In doing so, one makes the trend at a location match the trend of its region as defined by a large ensemble of data series.
The GISS adjustments turn out to be hinged lines (solid lines are the adjustments, dashed lines are the trend of the adjustment), and contrary to the graph legend the Cedarville adjustment is in red, the Mt. Shasta adjustment in blue:
For Cedarville this requires, from about 1930 onward, adding a warming trend to the data to cancel the false cooling trend. But before 1930 it requires adding a stronger (though briefer) cooling trend. The net effect on the century-long trend in Cedarville data is very small. For Mt. Shasta the opposite is true. From about 1930 to the present the correction adds a cooling trend to cancel a false warming trend, and before 1930 it adds a warming trend, with the net effect a significant century-long cooling correction to the Mt. Shasta data. The sum of the two corrections, gives early cooling until about 1930, followed by the two corrections cancelling each other out from 1930 to the present.
The “hinged lines” model may be a good one for approximating UHI. But it’s not a very good one for approximating the bias in Cedarville and Mt. Shasta data. I’d prefer simply to remove the erroneous early data from the analysis. Nonetheless, the correction generated by the hinged-line model does have a purpose: to cancel out the spurious trend introduced by the bias (in this case, the erroneous pre-1935 data).
Anthony Watts wonders about the adjustment to Cedarville data. What’s revealing is the commentary; the first comment gives the tone of the entire thread:
GISS has got to get rid of those warmer 1930s. So, cool them down and raise pre 1930s, then the whole series starts to look flat once smoothed and combined, and the hockey stick reappears like magic.
The thread makes interesting reading for those who like conspiracy theories, but apparently neither Anthony Watts nor any of his readers even considers the possibility that there might be a good reason for the adjustment, namely, a clearly established spurious cooling trend in Cedarsville after 1930 and a spurious warming trend before 1930, both of which are confirmed by comparison to neighboring stations.
Watts (and his readers) are definitely under the impression that GISS adjustments are adding false warming to all kinds of stations willy-nilly, leading to a false global-warming trend. They fail, of course, to mention nearby Mt. Shasta, with a spurious warming trend post-1930 and spurious cooling trend pre-1930, which has been adjusted in a manner opposite to Cedarville. They fail to mention that the two adjustments mostly cancel each other out, the net effect being slightly more cooling this century than without adjustments. The fail even to consider that in the global record, there’s a Mt. Shasta for every Cedarville, in fact one might guess that there are far more stations with a cooling adjustment than with a warming one, because the hinged-line adjustment was designed to mimic UHI which is predominantly false warming.
Some wants us to believe that GISS adjustments are designed to allow for false warming trends. The truth is, they are designed to protect us from false trends. The procedures are certainly not foolproof, nor are they final. Frankly the hinged-line adjustment doesn’t work very well for “outbursts” of erroneous data such as seen in Cedarville and Mt. Shasta. So I’ll paraphrase Churchill’s take on democracy, and say that the GISS procedure for handling global temperature data is the worst way possible — except for all the other ways it’s been done.
62 responses so far ↓
Gene // February 21, 2008 at 10:50 pm
“Watts (and his readers) are definitely under the impression that GISS adjustments are adding false warming to all kinds of stations willy-nilly, leading to a false global-warming trend. ”
Faith has to go both ways, if you want them to trust you don’t you have to trust their motives? If the process had a little documentation that could be found and followed easily working towards a common goal would be easier!
MarkR // February 21, 2008 at 11:40 pm
“They fail to mention that the two adjustments mostly cancel each other out…. The(y) fail even to consider that in the global record, there’s a Mt. Shasta for every Cedarville, in fact one might guess that there are far more stations with a cooling adjustment than with a warming one, designed to mimic UHI which is predominantly false warming.”
The old “two wrongs make a right law”, I guess?
[Response: Where did you get that? Errors exist. It's naive not to expect them to be both plus and minus. We can even quantify the likely random fluctuations.]
fredperkins // February 22, 2008 at 2:03 am
Does this bias removal process result in all average annual temperatures being adjusted? Does this mean the historical temperature record needs to be adjusted regularly to maintain the proper trend. It seems that this method results in each individual record being less accurate so that the long term average is more accurate.
dhogaza // February 22, 2008 at 5:54 am
And what, in principle, would be wrong with that?
When it comes to trends, having trends be more accurate would seem to be an admirable goal.
steven mosher // February 22, 2008 at 6:18 am
Tamino the GISS adjustment works like this.
In the US 9 and parts of canada and mexco) the Unlit sites are used to adjust the
DIM and and the BRIGHT sites.
See H2001. IMhoff97 gives the explaination
of unlit/dim/bright.
Now, cedarville has 840 people, but a satilitte photo ( actually 231 passes)between 1994 and 1995 registered an illuminated pixel on more than 8% of the overpasses ( actually 8% of the cloudless overpasses). SO Cedarville is called DIM. That means it gets adjusted.
Here is the File decription of Cedarville
725830060 CEDARVILLE lat,lon (.1deg) 415 -1202 R2A cc=425 0
See that R2A? Here is what it means:
http://data.giss.nasa.gov/gistemp/station_data/station_list.txt
The P column is Population (R/S/U)
The N column is Nighlights (1/2/3)
The B column is from GHCN and is not used
by gisstemp
So R2 means Rural DIM.
Cedarville, population 840 or so, is Rural, But
It registered on the Satillite at greater than 8%,
SO, its DIM and will be adjusted.
Mount Shasta population 3600, is classified as BRIGHT by nighlights. here is what bright means according to Imhoff97 ( refernced by H2001) 89% of the time the pixel was lit ( for cloudless passes). For reference, CHICAGO is 89%.
That means SHASTA will also be adjusted.
So, Nightlights, (OLS) is used by Gisstemp to determine if sites should get adjusted. Nightlights categories sites in the US, Canada, and mexico as dark, dim or Bright. DARK sites
are used to adjust the dim sites and the bright sites.
DARK is supposed to capture the truely rural
Cedarville, population 840 is DIM.
Mount Shasta poplation 3600 is BRIGHT.
Brantford Canada population 77,000 is Dark.
here is the Giss record for Brantford
715270040 BRANTFORD CANADA lat,lon (.1deg) 431 -803 U1B cc=403 14
U1 means UrbanDARK.
The issue is not the adjustments. The issue is the correctness of the corrections.
Take a look at
717050000 MONCTON,N.B. lat,lon (.1deg) 461 -647 U1C cc=403 26
MONCTON is population 55,000. But Nighlights
says it is DARK. therefore it gets no adjustment.
You can check the GISS files on this.
Nighlights is used by GISSTEMP to identify “rural” sites in the US and adjacent canada and mexico. I think there are better satillite products to do the same thing. I dont think nighlights is the best proxy to determine
Urbanization. When a town of 3600 comes out bright, and a town of 77,000 ( today 90K) comes out dark, I think some improvement can be made.
Again, the change will be minor. We know it will be minor because we have a handful of records that track Giss fairly well.
fred // February 22, 2008 at 8:25 am
The adjustment isn’t legit because its purely statistical. You need some reason why temps did not behave that way in those years. What is the evidence? Maybe temps do and did vary from place to place as the record shows.
Also the other problem is, after you’ve adjusted the data, you have to carry through the uncertainty introduced into the data in all you subsequent stats, and I don’t know how you’d do that. So it screws up all your later stats as well, unless you are very careful and very sophisticated.
Nothing to do with whether its an up or down adjustment. This is just about how to handle observational data.
Bob North // February 22, 2008 at 4:48 pm
Tamino -
Thanks for this series on PCA. Although #2 was little heavy on the math for someone who hasn’t used that stuff much in 20+ years, Part 1 and this part were quite elucidating in terms of gaining a better understanding of just what it all means. Having a specific real world example, as you have done above with attempting to example why data from certain GISS stations that do not appear to require any adjustment, is helpful.
However, I am not sure I agree with the adjustment process or your conclusion that, based on the statistical analyses, the differences between the 1920s Cedarville data and the PC1 are not physically realistic. Doing a quick Google map lookup, I note that spread of the neighboring sites covers an area roughly the size of Pennsylvania. Also, there appear to be some variations in elevations, nearby topography, and physiographic provence (Cedarville appears to be just on the edge of the Basin and Range provence. Without better understanding the site specific factors that may account for the differences, automatically adjusting data from rural sites where UHI does not appear to be a factor just to better to match the trends of its neighbors seems like manufacturing data. Certainly, I do believe that findings such these should spur one to look for a reason why the data may be unrepresentative (e.g., station move, equipment change, poor recrding protocols, etc.) and if such a reason can be identified, then some sadjustment would be appropriate (probably just over the period of divergence [~1915- ~1935] rather than over the entire period of record. However, absent finding an explanation why the data is not representative, I am not sure that adjusting the data is the appropriate scientific approach. It seems to me that either 1) using the data as is; or 2) not using the suspect data at all would be the better approach. As noted by a commenter above, if the data is truly spurious one would expect errors in both directions (e.g., Cedarville and Mt. Shasta) so that in a large set of stations such “spurious” trends would more or less cancel out whether or not the data is adjusted. At minimum, a sensitivity analysis comparing the effects of using unadjusted vs. adjusted data would be appropriate.
In the grand scheme of things, this may not amount to more than a hill of beans, but it is these poorly explained or hidden adjustments that raise valid questions and concerns on the QA/QC of the entire data set.
Finally, while it seems that several commentors on Watts site just like to take pot shots (as do regulars on RC and here, btw), it seems to me that Watts’ main goal is just to make sure the data is really good, transparent, and defensible. Same with McIntyre. They definitely don’t deserve to lumped in with folks like Beck and his wacky historical CO2 trend analysis.
Regards,
Bob North
[Response: Areas bigger than Pennsylvania (which is a bit bigger than the area under study) show just the kind of spatial correlation that contradicts the Cedarville and Mt. Shasta data. You don't need PCA to see this. Compute, for each year, the average of all 5 stations. Also compute the variance of that estimate. Plot the variance as a function of time: the mid-1920s to mid-1930s data say, "We are not like the others."
That alone doesn't rule out a freak occurence of nature. But if you look at a lot more temperature data than just around Cedarville, and note the high degree of correlation that exists in areas even hundreds of miles apart, then you'll understand just how freak an occurence it would be. A *much* more likely explanation is that the pre-1935 data from Cedarville and Mt. Shasta are corrupted.
Personally I'd prefer to omit the suspect data, the hinged-lines model doesn't fit very well. But I'd prefer to keep as much of the data as can reasonably be accounted for. The high degree of spatial correlation of temperature trends is one of the best quality checks available.]
Lee // February 22, 2008 at 5:59 pm
Bob,
None of these adjustments are “poorly explained or hidden.” GISS procedures are described in their publications, and the code is available.
There is very good spatial coherence of temperature anomalies across large areas - even an area as large as “Pennsylvania.” This becomes more true as one looks at annual rather than daily temperature anomaly. You can see that coherence in annual anomalies in these records. If the deviation at Cedarville and Mt. Shasta is real and not an error in the records, something must have occurred that maintained that coherence - the positive and negative deviations from year to year still match the other adjacent stations - while adding or subtracting a constant offset. And then that offsetting change had to go away. And ti had to happen in this one small area, while leaving adjacent stations unaffected - at all. That seems… unlikely.
guthrie // February 22, 2008 at 6:32 pm
Bob- I have to disagree with you regarding Watts et al. Their approach has always been agressive, looking for ways of finding fault with the data and the adjustments. If they were really disinterestedly wanting defensible data, they would go and read up on what is done with it all, rather than attack the stations and their siting reading up on the relevant literature.
Jedwards // February 22, 2008 at 8:17 pm
Wait a minute, are you making the assumption that the large variation in PC2 therefore implies something is “wrong” with the data for Cedarville and Mt Shasta? From a scientific perspective, I would think that the large variation rather implies that there is something “interesting” about those two sites. Without a modicum of further research, one should not infer a priori that it is the data that is in error.
[Response: I quite agree, on principle. But a large body of experience with enough temperature data shows that temperature trends at locations this close together *just don't behave that way.* It's on the basis of much experience with temperature data, that the deviations for Cedarville and Mt. Shasta are not plausible.]
fred // February 22, 2008 at 8:33 pm
dhogaza asks: “And what, in principle, would be wrong with that? When it comes to trends, having trends be more accurate would seem to be an admirable goal.”
Yes indeed. If it could be done. It can’t, like this. You can average, and that will leave your station data alone and give you trends. You can do PCA leave your station data alone and get trends.
The one thing you cannot do is adjust your station data with no physical evidence to justify it, then put the results through statistics, and get accurate trends. At least, not any conventional statistics. You are going to have to do something, what I don’t know, and don’t even know if its possible, to carry through the uncertainty your adjustments introduced into the later stages.
How do you know the world was not just a bit irregular back in 1910? You have no way of knowing. It could be that the readings were just that way. How are you going to tell? Messing with your data with no physical explanation or justification is just guessing, its not science.
Isn’t it a bit funny that people who do not want to throw out any data from out of spec stations are perfectly ready to throw out readings from in spec stations? Its nuts. What we need is no adjustments to the readings, and only use readings from in spec stations.
This is so obvious its totally amazing anyone denies it.
Lee // February 22, 2008 at 9:17 pm
fred, would you please tell us how one goes about knowing whether a 1910 reading is from a station that is “in spec?”
Or why - given a backdrop where we know that undocumented changes in station condition can cause step changes in readings - why a station that co-varies quite nicely with neighboring stations, then undergoes a sudden large step change for 2 decades, then a sudden step change back down and thereafter in continuing agreement with neighboring stations, should be assumed to be ‘correct’ in the step change? Which is what you are arguing for, you know.
“This is so obvious its totally amazing anyone denies it.” Actually, fred, your assertion is so un-obvious its totally amazing anyone asserts it.
Lazar // February 22, 2008 at 10:03 pm
Fred writes;
Sorry, but discarding or adjusting anomalous data points, without physical understanding of the causes, is done all the time in physics and other research. The counter-argument to ‘you have no way of knowing the anomalous data is due to error’, is that you have no way of knowing that it is not. You try to balance the risk of false positives against the risk of false negatives. Ultimately, it’s a (difficult) value judgment left down to the experience and intuition of those involved.
steven mosher // February 22, 2008 at 10:26 pm
Let’s be clear on Mount Shasta. Mount Shasta has a population of 3,600. If mount shasta were in England, hansen would not adjust it.
If it were in China he would not adjust it. If were in Iran hre would not adjust it.
WHY? because Mount Shasta Has a population of Less than 10,000. It would be classified as RURAL. As such it would receive no adjustment.
But Mount SHASTA is in the United states. In the US, HANSEN2001 uses a different method for determining is a site gets adjusted. This method relies not on population but on a 1995 satillite photo: nighlights.
According to Nighlights, Mount SHASTA is bright. As such, it gets adjusted. A town of 3,600
( a really lovely place to visit if you get the chance) is called URBAN.
Lets look at another town. Brantford On. Population 77,000. Today it is more like 90K.
Since this town is close to the US H2001 uses nighlights to figure out what to do.
If Brantford were in England with a population of 77,000 it would be Urban. It would get adjusted. if it were in Turkey, it would be urban, it would be adjusted. BUT, because its close to the USA, nighlights is used as opposed to population. What does nighlights say? Well in 1995 the satillite didnt see enough light coming from this town of 77,000 so Nighlights said
that this town was DARK. Therefore, it gets no adjustment.
Cedarville. Sleepy cedarville. Town of about 800-900 people. In china GISS would call this town Rural. No adjustment. in England, it would be called Rural. no adjustment. In Peru a town this size would be called rural. ON any other continent, Cederville would be Rural, and it would NOT get adjusted. But Cedarville is in the US. In 1994- 1995 a satillite photo of the world
showed that on more than 8 % of the cloudless nights the Cedarville patch had lights on. That makes it a DIM site. That means it gets adjusted.
It’s a good thing to read the papers and look at the data sets.
The actual adjustments are the second question. The first question is this. Why is Mount Shasta adjusted? Why is Brantford not adjusted?
Lee // February 22, 2008 at 11:50 pm
Lazar says:
“Ultimately, it’s a (difficult) value judgment left down to the experience and intuition of those involved.”
You’re correct, Lazar.
But at least in part to try to avoid potential bias in application, Hansen et al establish criteria for those choices, define them in a algorithm, then run it identically on all stations. Inevitably this method isn’t perfect - and then the clueless critic find confusing individual instances and blast Hansen for making biased choices.
Hank Roberts // February 23, 2008 at 12:15 am
Fred, there’s a thread open for argumentation about the surface temperature record.
This is not it.
jl // February 23, 2008 at 12:36 am
725830060 CEDARVILLE lat,lon (.1deg) 415 -1202 R2A cc=425 0
725920030 MOUNT SHASTA lat,lon (.1deg) 413 -1223 R3B cc=425 13
both from http://data.giss.nasa.gov/gistemp/station_data/station_list.txt
Dano // February 23, 2008 at 12:39 am
We all anxiously await Mosher’s blockbuster paper, debunking whatever it is he’s debunking and, Galileo-like, sweeping aside hhhhhistory!
Surely the comments here are drafts, but are we supposed to be copy editing them, editing them for content, what?
Best,
D
Lazar // February 23, 2008 at 2:13 am
Hansen et. al [2001];
dhogaza // February 23, 2008 at 4:38 am
Just say “Mosher” and “CA” when you mean it, the meaning is much clearer.
fred // February 23, 2008 at 6:08 am
Hank R, perhaps you should address your admonitions to the other participants too?
The problem is the posting and the thread have veered off into the data, not the statistical method.
However, my statistical point remains valid. At least, it has not yet attracted a refuting comment. That is, you cannot legitimately do statistics on adjusted data without carrying through the introduced uncertainty downstream into your results. And I don’t know how to do this, and don’t see any signs GISS has done it.
As for the argument (Lazar) that you have no way of knowing the anomalous data is not in error. No, you have no more evidence one way or the other. So do not adjust it. I think I’ll adjust the dates of the battle of Gaugemala. Why not? I have no evidence either way, lets add a few years. Or subtract them maybe.
As to the point that you cannot check the circumstances of 1900 for in or out of spec. No, that is the problem in a nutshell. Its why the data has large error bars. You cannot now tell how good the observations were. Inconvenient but that’s how it is. Maybe the available data will not support the weight of inference it has come to be loaded with.
Notice, I am not attacking AGW. I just want data. There is data in the surface station record, its the readings. What we have after the adjustments is not data, its intuitions. I’m not interested in intuitions, and neither should anyone else be.
Have a look at the Burlington data by John Goetz on CA.
There is warming. Obviously. This stuff is not telling us any more about it after the adjustments than before.
fred // February 23, 2008 at 12:40 pm
Tamino, you probably know the answer to this immediately. What is the implication of doing PCA on data which has been in effect adjusted beforehand to reduce noise?
Like in the present case, we take a data series and adjust it in some way rightly or wrongly. We then do PCA on it. Should we not really be doing PCA on the unadjusted series, and then use PCA to get the signal separated out from the low significance noise? I don’t understand how you quantify the validity of a PCA done on anything but the original data.
Well, I understand if you found systematic bias in an instrument of course - it reads off 6 inches. But that is not what we are doing here, we are adjusting some years on what seems to be the ground that they are noise and not signal.
Isn’t this like the notorious traps in doing correlations with smoothed series?
RomanM // February 23, 2008 at 3:58 pm
What a pile of nonsense:
“…suggests instead that there’s an uncorrected error in the Cedarville”.
“…the large difference between Mt. Shasta and the 1st PC before 1935, compared to after, argues that
Mt. Shasta data similarly have an uncorrected error before 1935″.
You look at 5 stations and find that not one, but two of them differ from the others during the same time period and you want us to believe that BOTH of these records must be wrong! What happened? Did someone hang the thermometers at these two locations upside down for several years? Ignore the fact that local weather patterns need not be stationary - we have several years of mis-readings here. Give me a break!
The justification for this? Let’s look at Pennsylvania: “Areas bigger than Pennsylvania (which is a bit bigger than the area under study) show just the kind of spatial correlation that contradicts the Cedarville and Mt. Shasta data”. Let’s ignore the differences in location and geography. It doesn’t matter. Let’s assume that all these stations everywhere are like peas in a pod - let’s treat them that way. You don’t need to look at the details. We’re just looking for a trend…
You don’t need “freak occurrences” to produce differences in local weather. Rather than applying ad hoc adjustments for trend, how about looking to see if there might not be other reasons - changes in rainfall patterns or cloud patterns or any of many other variables which have an effect on temperature to decide that this data is wrong? But hey, that’s climate science…
Unfortunately, these induced “trends” which come from the adjustments made (so what is the REAL trend at that location?) have some unintended negative results. One effect is that proper error bounds cannot be calculated and are seriously underestimated due to this process. The much more serious problem is that the temperature record becomes contaminated and basically unusable for any serious analysis trying to examine the effect of other climate variables on both local and global temperatures. Since these variables were completely ignored when the adjustments were made on other reasons, the effect of these variables will at best be clouded and at worst completely erased. What will remain is the induced trend that has been artificially entrenched into the record. No scientist should be using the adjusted temperatures for any serious studies. Quality control should be limited to just that and not include any arbitrary adjustments based on spurious assumptions.
On a technical note, perhaps you can explain to me what differences in the interpretation of the results one might expect when applying principal component theory to a set of non-stationary time series as opposed to a collection of independent normal multivariate observations.
[Response: Do you think this is the first temperature data I've looked at? Do ya think I have no idea how nearby station records behave and how they correlate with/diverge from each other? I didn't just "look at 5 stations" and decide that two of them are wrong because they don't match very well. I've looked at a LOT more than that, and I recognize anomalous behavior when I see it. And I've explained exactly that in responses to previous comments.
But -- right on cue -- along you come, the pompous ass who does NOT know how temperature records really behave, clearly has NOT studied them, has no knowledge of the degree or consistency of spatial coherence, and just plain doesn't know his ass from a hole in the ground, but sure feels qualified to pontificate to the rest of us how we should interpret data. The most astounding thing about the entire global warming "debate" is how folks like you combine such zeal with such astounding ignorance.]
Lazar // February 23, 2008 at 4:46 pm
Fred writes;
That is a choice which assumes the anomalous data is not in error, i.e. risk of a false negative. If you decide the data is in error, you risk a false positive. “Not adjusting” is a decision, it is not an easy nor consequence free way out of the situation.
The battle of Gaugemala is not an anomalous point relative to other data, particularly a trend line.
Hank Roberts // February 23, 2008 at 4:59 pm
Tamino, here’s another published (paywall) paper that might be interesting as an example sometime:
http://www.springerlink.com/content/3662578943475334/
“to investigate the effect of different cigarette-lighting devices on the chemical composition of the mainstream smoke from the first cigarette puff. Lighting devices examined were a Borgwaldt electric lighter, a propane/butane gas lighter, a match, a candle, and the burning zone of another cigarette. To eliminate the effects of the different masses of tobacco burnt by use of the different lighting methods a normalisation procedure was performed which enabled investigation of changes in the chemical patterns of the resulting smoke. … The chemical patterns generated by the different lighting devices could, however, be separated by principal-component analyses.”
Phil. // February 23, 2008 at 6:31 pm
Fred why do you assume that the data Tamino is working with has been adjusted? He doesn’t say so in the original post.
Timothy Chase // February 23, 2008 at 9:07 pm
In criticisms of classifying stations by satellite-measured brightness as urban, periurban or rural, I see references to the populations of towns and cities according to census counts. However, according to the passage quoted by Lazar…
… the questions which concern Hansen are: “How stale is the census data? What is the spatial resolution?”, and most importantly, “What is the population density where the station is located?”
Population density rather than population — where the station is actually located. It seems reasonable to expect a station on the outskirts of Chicago in area of low population density will experience a far smaller Urban Heat Island effect than a station located in the center of some small but more densely-populated town. References to head-counts per city hall are irrelevant at best.
Timothy Chase // February 23, 2008 at 11:15 pm
fred wrote:
Actually you do.
Please see Tamino’s inline:
Temperatures vary over short distances, but yearly temperature anomalies are highly correlated over great distances. The “anomolous data” as you call it (which is anomolous because the trends given at those stations deviate so much for a period decades ago from what was happening to their neighbors, while the stations are well-correlated with their neighbors in recent decades) is itself evidence that the data is in error. And there is more evidence in favor of this interpretation — in the temperature records of the other, neighboring sites.
As Tamino points out in the main article, the hinge-procedure employed by GISS is mathematically defined, adds cooling and warming to trends — rather than just warming as certain groups would have you believe — and has a negligible effect century-long trend in local temperature anomaly, and a far smaller effect upon the trend in in average temperature anomaly. So feel free to calculate the trend in average temperature anomaly over a suitably large area, with or without the hinge-point procedure — and you will get virtually the same results.
Bob North // February 24, 2008 at 5:06 am
Tim - If you get virtually the same results, then why do it except in cases where potential UHI is a significant issue?
Lazar - You seem to indicate that deciding whether to adjust apparently anomalous data is a choice. From my background (geology/enviornmental science), anomalous data should not be adjusted unless there is a sound basis to do so. In other words, the null hypothesis is that the data is correct and the burden of proof is on those that advocate adjustment. More on this later as I have been plugging through some site data as suggested by Tamino in his response to my original post. Personally, for UHI issues, I believe it would be better to not use potentially UHI contaminated data than to make adjustments that may or may not reflect reality. BTW, for at least a good portion of the eastern US and the Artic, using rural site data that has not been homogenized still shows a pretty darn strong warming trend since about 1975-1980, but what seems to be getting suppressed is the warm temperatures in the 20s-40s.
Bob North
fred // February 24, 2008 at 7:18 am
I don’t understand. If you get virtually the same results, it shows the process is not worth doing. This is very strange statistics. We amend our data before processing and we defend doing it on the grounds that it is legitimate and necessary to do so. And also that it makes no difference? So why do it?
According to CA, whose workings I have not personally checked “we do have 3 ‘adjusted’ versions from 3 different sets of experts, which have a range of 3 deg C in their estimates of summer temperature in Dawson, Yukon” The charts show roughly this.
My question is, if you are doing trend/PCA analysis with adjusted data with this level of uncertainty, how do you carry the uncertainty through the processing?
P. Lewis // February 24, 2008 at 11:23 am
Fred wrote a lot of things, amongst which was
and
Raw data usage for climate change study is not ordinarily encouraged, e.g. instrument bias and error, incorrect noting of data measurements, subsequent digitisation errors, missing data, location/timing changes, equipment changes, operator changes, autocorrelation, …. Raw data are homogenised to remove such breaks, outliers, biases, etc. It’s a long-practised custom, long before climate change became an issue with a dwindling band of ….
Health warnings come with homogenised data series about how the data were adjusted, and the professional or educated amateur analyser of these data knows that they have to make themselves aware of what impacts these homogenisation adjustments are likely to have on their analyses.
Good places to start on reviewing homogeneity procedures and issues are the following:
Peterson TC et al. 1998. Homogeneity adjustments of in situ atmospheric climate data: a review. Int. J. Climatol. 18: 1493–1517.
Jones PD et al. 1986. Northern hemisphere surface air temperature variations: 1851–1984. J. Clim. Appl. Meteorol. 25: 161–179.
Both the above are only available on payment I think, i.e. I haven’t checked to see whether there are any preprints, etc. available on the web.
Then there’s
Karl TR, Williams Jr CN. 1987. An approach to adjusting climatological time series for discontinuous inhomogeneities. J. Clim. Appl. Meteorol. 26: 1744–1763.
which contains a lot of useful info concerning a definition of a homogeneous data series and on some of the methods adopted (in this paper).
And Xiaolan Wang’s powerpoint presentation is … mind blowing.
And this powerpoint presentation from Enric Aguilar on (amongst other things) a temperature series for Quebec City is illustrative of why raw temperature series data analysis is not necessarily a good idea for drawing conclusions on.
The professionals who carry out the work of data series homogenisation (whose methods have changed over the years as new homogenisation techniques have emerged) know their stuff. And peer reviewers, who should and do know about these things, review authors’ methods of data handling to ensure that they are sound, or ensure that the authors can defend their choice.
If you use raw data, then you, too, will likely have to homogenise that data (within and across different data series) before you can use it to draw any useful conclusions/comparisons from it from anything other than a local area (in fact, probably just the station’s data you’re examining — and even then your conclusions may be in error), as opposed to regional to hemispherical to global scales.
Lee // February 24, 2008 at 5:06 pm
One more time - we do have very good reason to suspet that data is “wrong.” The spatial correlation of annual anomaly data is very high, across large distances. We have a lot of observational data that shows that temperature anomalies simply do not depart like that at single stations when compared to neighboring stations. Tamino’s analysis detects that departure in the original temperature series, in PC2, and apparently in the variance as well, and behaving in a way that we simply do not see modern observed stations behave without some physical ‘error.’.
Why on earth anyone would argue to leave that data in the analysis uncorrected is beyond me.
Hank Roberts // February 24, 2008 at 6:30 pm
You’ll find websites aplenty citing those; I found a lot of pages quoting a few free market thinktanks attacking these studies and the very idea that global temperature can be studied.
None were by statisticians, nor got published in science journals. Eschew bogosity.
You’ll find some additional science.
ftp://podaac.jpl.nasa.gov/pub/sea_surface_temperature/buoy/gostaplus/binary/document/papers/2_jofc/2_jofc.htm
Journal of Climate, Vol. 7, No. 11, November 1994
Hemispheric Surface Air Temperature Variations: A Reanalysis and an Update to 1993; P.D. Jones
Lazar // February 24, 2008 at 6:47 pm
Bob North;
Yes.
… wherein physics, as far as my experience goes, outliers are adjusted probably more summarily as regards the following…
The statement “the null hypothesis is that the [anomalous] data is correct” is an assumption — i.e. a choice. There are good logical arguments both for and against in the general case. I’m agnostic, and therefore leave such decisions to the judgment of those involved (which I trust). In the specific case, Lee, Timothy Chase, and P. Lewis have provided reasons for adjustment. Now, each individual can weigh up those arguments and decide whether the adjustments are justified. Which bring me I suppose to my ultimate point, there is no reasonably objective ‘right’ or ‘wrong’ here, but anyone who disagrees with the GISSTEMP treatment may attempt to quantify an error, or to create their own analysis. Simply objecting that GISSTEMP adjusts outliers is fine, but frankly, I don’t see the logic in doing so. Similarly, regarding Steven Mosher’s criticisms regarding classification of stations…
if there’s an error, quantify it, or do an analysis that better suits tastes. (I agree with P. Lewis here.)
Lazar // February 24, 2008 at 7:27 pm
Fred writes;
Fred, processed data is still data, it’s not ‘intuitions’. For example; I once had to decide on a low pass circuit that would filter an audio signal subsequently passed to FFT analysis. The level of filtration, and therefore the circuit design, was my choice, and it was necessarily subjective. Nevertheless the output strongly resembled the input, and in fact was more useful having undergone filtration.
You “just want data”. Well, you have it, but what do you do with it?
Practically every experiment involves many design decisions that are somewhat arbitrary/subjective, and that are guided by intuition resulting from experience. These decisions will effect results. Often they may involve ‘unscientic’ considerations like time and cost. If you disagree with these decisions, you are free to quantify errors, or to design your own experiment. Experiments are not manufactured accoring to rules. Rules are generalizations, and often very poor substitutes for subjective decision making. This points in my view a serious flaw to the ‘auditing’ approach to science, which has been the cause so far of many misunderstandings.
S2 // February 24, 2008 at 11:27 pm
I’m currently looking at (on a very amateur level) the impact of changes in insolation on global temperatures.
Milankovitch, obviously.
But when it comes to solar variations, it isn’t so easy.
I’m particularly interested in the “Bond” cycle - which (if it exists at all) is very weak, but seems to generate a strong response in the climate (at least according to Singer and Avery).
I’m guessing here - but I think I’d need to do a Fourier analysis first to determine if there really is a 1,500 year cycle, make sure I know about all other cycles that could affect global temperature, and then do a PCA.
It’s probably already been done by someone else, and I’m not yet convinced that I could do it anyway - any feedback would be appreciated.
nanny_govt_sucks // February 25, 2008 at 5:16 am
But isn’t this the “noise” that PCA is supposed to remove?
fred // February 25, 2008 at 7:10 am
“Why on earth anyone would argue to leave that data in the analysis uncorrected is beyond me.”
Simple reason: experts seem not to agree on what a correction would look like. Take Dawson. You have adjustments by different bodies that apparently differ by 3 degrees C for the early 1900s. That’s what the CA graph of the different adjustments appears to show.
If you do not know how to correct, leave alone.
I’m following up the various links to adjustment, starting with the ppt one, which I confess to finding very obscure. However, it did not seem to get to what looks to me like the crucial issue.
You change the data by 3 degrees for reasons that may or may not be valid, and which experts differ on. How do you then take account of whatever uncertainty you’ve introduced in the later stages of processing?
As nanny says above, ‘isn’t this the “noise” that PCA is supposed to remove?’
I do not get it.
I also do not understand how it can be that data from all the stations however out of spec must be used, because we must not throw away data, but readings from the same stations must be changed, because they are inconsistent with data from others. This also makes no sense, despite 40 pages of dense mathematical formulae. I suspect even after several hundred it will make even less sense, because its wrong. Its not math, its logic.
fred // February 25, 2008 at 7:23 am
Sorry to post twice. Just looked again at CA where M now posts about adjustments in Latin America. The adjustments since about 1950 have the effect of making the stations cited cooler in the fifties by single numbers of degrees, in one case 4 degrees. First, I simply can’t imagine how you can now tell that a station under recorded by 4 degrees in 1950. But second, I still can’t believe that having made adjustments of that magnitude you can treat the resulting series statistically as if it were on the same level as unadjusted data derived from a trustworthy and calibrated instrument. Its not that you have found a systematic upreading constant over the years. Its that you have done a statistical adjustment by a declining amount each year, until you reach today, when the instruments apparently become correct. What is going on?
I am sure to be abused for being a so called denialist, but this makes no sense.
Bob North // February 25, 2008 at 1:28 pm
Hank -
Thank you for posting the various references on homogeneization. The Aquilar powerpoint and Karl paper are very useful. The Chen PP will take some time to digest to say the least. ONe thing I take away for the first two docs is that the purpose of the homogenization is to adjust for discontinuities due to station moves, intrument calibration, misreporting, etc., which I do not disagree with. In fact, Aquilar stressed the importance of good metadata for each station, which seems to be what Watt et al are trying to develop. It seems that maybe more time should be spent in reviewing and qualifying a small set of the “best” sites (probably wouldn’t need more than 150 or so for the US) that have good metadata and minimal adjustments for use in global climate evaluations.
Bob North
steven mosher // February 25, 2008 at 2:15 pm
Lazar,
Since I just figured out the data structure and the code this week, it’s abit early to be asking for results. However, in the ROW Giss uses Popuation to adjust the record. Rural does not get adjusted, semi urban and urban do. In the US, nighlights are used to determine the adjustment, dark means rural. So, the question is why? H2001 doesnt provide a clear reason.
Especially since we have nightlights for the whole world. as for the accuracy, IMhoff97 is a good place to start.
For comparison Gallo98 comapred various methods POPulation, OLS, LULC and combinations of these. read that.
steven mosher // February 25, 2008 at 2:27 pm
Dano,
I have no intention of writing a paper. I’m just curious and I enjoy reading and figuring things out. it’s fun. Like a puzzle. I’ll give you an example. In H2001 Hansen writes that the early part of the Lake Spaulding record was elimated because of abnormal cooling. Sure enough when you read the code you see that BEFORE any processing was done, the eraly parts of this record are removed. I asked for more explaination, how was ‘abnormal’ defined?
People said read the paper. H2001 doesnt explain. So, I looked at the raw data. Sure enough, something weird was going on. but what? Now H2001 wasnt mistaken in removng it, just incomplete in its explaination.
take a look, later I’ll explain what I think was going on
Hank Roberts // February 25, 2008 at 6:21 pm
Bob — we both want to thank
P. Lewis // February 24, 2008
for those references! I just added an update from a brief and not thorough web search, shortly after P. Lewis posted them.
fred // February 25, 2008 at 9:47 pm
Hank and Bob
I’ve now worked through all of the public refs - Chen will take another few passes.
The Quebec ones are a model of how to do it right. The papers show, and they say, you have to have accurate and detailed metadata to do adjusting.
Now, if this exists and was used on Texas and Peru, and Dawson, lets have a look at it. If not, we are not adjusting, but altering.
Which is what I increasingly suspect is going on.
Hank Roberts // February 26, 2008 at 1:54 am
http://ams.confex.com/ams/88Annual/techprogram/session_20830.htm
19th Conference on Probability and Statistics, Session 6
Statistical Climatology
P. Lewis // February 26, 2008 at 2:26 am
N_g_s, time-series inhomogeneity can be analysed by any statistical test which compares the statistical parameters of two data samples. And you may/will have to use more than one stats test to achieve homogeneous data.
FrancisT // February 28, 2008 at 12:43 pm
This is excellent stuff. After reading all 3 PCA posts I find my understanding of PCA vastly improved, many thanks.
I note that I’m still wary of the GISS hinges because it seems to me that what you are doing is losing the independence of the variables and fixing something to a straight line (or couple of lines) that should not be so fixed.
It seems to me it might be better to do some kind of outlier removal. I.e. in this example presumably removing the 1920s/1930s values of Cedarville & Mt Shasta. One could perhaps look at the Olympic (figure skating?) rule where they discard the highest and lowest judges scores and keep the rest. Or perhaps just removing points that are > X standard deviations (say 2) from the mean result for that year or better > X std devs from the mean excluding those points. I’m sure I’m missing something here but in capacity management and queueing theory we tend to harshly remove outliers because in the majority of the cases outliers are indicative of either a one off event or a data gathering failure. And discard entire data groups (hours or days for networks or servers, years in climate analysis) where the variance is too great compared to other data groups. E.g. if in 1928 the variance between stations was 3 times greater than the average for other years during the century we’d simply remove the 1928 data entirely.
[Response: Thanks for the compliments.
I agree that the two-legged linear adjustment is not a good model for many stations (including these). It seems like a sensible model of UHI, although I don't consider that established beyond doubt. NASA does remove data that are more than a certain amount different from expectation based on that station's data alone, but only if there's no corroborating evidence of extreme behavior from neighboring stations. And if I recall correctly, it has to be 5 standard deviations departure, which is a rather strict requirement. The motivation seems to be to avoid deletion unless there's overwhelming evidence it's genuinely bogus; setting such strict standards for data removal is not uncommon.
So I'll say that the GISS adjustment is the worst possible choice -- except for all the other ways it's being done.]
Christopher // February 29, 2008 at 5:09 am
I’ve enjoyed the series on PCA as well. Could you perhaps explain how you combined the first 3 PCs to get a proxy? I have the ice data and have been trying to recreate your plots in R and Matlab so it really sinks in. In any event I’m stumped on creating the proxy. I think part of my confusion is scale. The PCs are effectively scaled by sqrt(n) but in your proxy vs observed plot that appears to no longer be the case. Also what temp. record did you use? Thanks again.
Nylo // February 29, 2008 at 9:35 am
Tamino, you claim that this adjustment is the worst except for all the other ways it’s being done. But this doesn’t mean that it cannot be made better, nor does it mean that it should stay and the scientific community shouldn’t look for better ways to do the adjustments.
I think the main issue with CA and the other denialists is that, even if you are just following the rules you created when you add a further heating trend to a urban station, and even if the rules sound logical in an abstract, theorical way, you seem to fail to explain why the human influence in a urban site could cause the place to cool down instead of warm up. It’s against all intuition because cities don’t get smaller, not even if they lose population. This lack of an explanation is what makes the adjustments look weird. We all hear about the heat islands that cities become, but no one has heard of an explanation for the contrary.
As long as an explanation is not provided for an increased cooling trend in a city, you will only be changing the trend because of the trend itself, which sounds bad. It doesn’t mean that you have to explain every city that cools down. Just to give a couple of examples for human influences that can cool down a city.
I have a suggestion as to how the adjusting procedure could be made better. This idea is: do not adjust an urban trend when the average of the surrounding rural sites show a different trend, but only when ALL of the surrounding rural sites show a difference in the same direction. If an urban site shows more cooling/warming than ALL of the surrounding rural stations, then adjust. If it only shows more cooling than some ot them and the average, don’t. The idea is that if you can find one rural and, allegedly, non-UHI-contaminated site that supports the trend of the city, you shouldn’t consider that the trend of the city is because of its UHI.
Think of big cities. There is a big probability that there are allegedly rural sites that, in reality, are very small towns which are rapidly increasing population, but this process means a lot of UHI heating, a heating that the big city wouldn’t suffer to that extent because population increases in already big cities are less important to the trend. To rule them out and not create a false warming trend in the city, you would only need ONE rural site with a similar trend to that of the city. So it is a far more conservative aproach, but in my opinion it is strongly convenient.
Thanks
Nylo // February 29, 2008 at 9:56 am
I have also another suggestion. Because experience tells that climate doesn’t change in steps, either for cooling or warming, when you see a station that has an average temperature and trend for decades, then there is a step, and then the average suffers a significant step upwards or downwards without a clear change in the trend after it, the step is most probably caused by a change in the immediate environment of the station, or the station changing its place, and the step shouldn’t be taken into account when dealing with the trend of the overall region.
So what to do? Consider that station as 2 separate stations, one whose data finishes before the step, and another whose data begins after the step. The direction of the step is not important. The step itself should be avoided. If it is an upwards step, it will introduce false warming in the trend, and viceversa for a false cooling trend.
Thanks.
Hank Roberts // February 29, 2008 at 4:15 pm
Nylo writes above:
> explain why the human influence in
> a urban site could cause the place to
> cool down instead of warm up. It’s
> against all intuition
Nylo, do you know how to disprove your intuitions? You can test them.
Take phrases you wrote. Paste them into Google Scholar.
Just one, merely for example:
> Aerosols also decreased
> precipitation, surface solar, and
> near-surface temperatures. …
http://www.agu.org/pubs/crossref/2007/2007JD008922.shtml
Muse on this:
“Strange! If we read over the works of the ancients we are tempted to class them all among the intuitionalists. And yet nature is always the same; it is hardly probable that it has begun in this century to create minds devoted to logic. If we could put ourselves into the flow of ideas which reigned in their time, we should recognize that many of the old geometers were in tendency analysts. Euclid, for example, erected a scientific structure wherein his contemporaries could find no fault. In this vast construction, of which each piece however is due to intuition, we may still to-day, without much effort, recognize the work of a logician.
It is not minds that have changed, it is ideas; the intuitional minds have remained the same; but their readers have required of them greater concessions.
What is the cause of this evolution? It is not hard to find. Intuition can not give us rigour, nor even certainty ….
————-
Intuition and Logic in Mathematics
by Henri Poincaré, 1905.
http://www-groups.dcs.st-and.ac.uk/~history/Extras/Poincare_Intuition.html
Nylo // February 29, 2008 at 6:19 pm
I think it is no point of discussion that cities are “heat islands”. I have nowhere heard of them being “cool islands” nor do I know of any example: cities are always warmer than their immediate surrounding rural areas. Even cities with large parks and lots of trees like Madrid have a strong hot microclimate. If I am wrong about this, please tell me.
If I am not, then again I see no reason for showing a cooling trend because of human activity. It’s the broad presence of humans and human activities that makes them a heat island. In order for it to cool, you would need it to become “less of a city”, by losing population or industry or both.
I can believe that the paper you make reference to showed a city (Los Angeles) with what could be a cooling trend because of human activities, aerosols, etc. But that was the thing within the model, not in real life. Is Los Angeles cooling in real world? If you can find a city in the real world which is somewhat colder than its immediate surroundings (say, comparing the temperatures in the middle of the city with those 3km from the city boundaries), then I can believe that there can be some cooling induced by humans. But that is still to be found, am I wrong? What is the average temperature of Los Angeles compared to nearby rural places? And I mean nearby, not 100km far. If Los Angeles is hotter, I strongly doubt that it is getting colder because of the human activities. It’s the human activities that make it hot!
Don’t give me a computer model. Find me a city with an average temperature 0.5 degrees colder than a rural site 3km from the city boundaries, and I will start to believe that humans can create a cooling effect.
Again I repeat, that the problem is that a good explanation for the humans creating a cooling trend, with the corresponding example must be given for it to be accepted. Otherwise it is more likely that the surrounding areas are the ones warming because of not being entirely rural. That was the case with Peru. An urban station was forced into warming because of its rural surroundings… which happened to be not rural at all. What is the most logical explanation? The others were warming because of growing faster in population.
The adjustments policy has been correctly applied, but the policy needs some changes because it doesn’t protect you against wrong-classification cases like this. A different approach could avoid this kind of mistakes, and denialists would not be feeding on it.
BTW, I’m not one of them. I believe that there has been some warming going on, although I’m not so sure about the expected future trends or its origins or consecuences. But the warming itself is so far clear for me. So I’m not saying that the correct procedure would show more cooling or more heating… probably little difference. It would just be more correct and less prone to criticism.
MrPete // March 6, 2008 at 2:20 am
Just browsing this thread for the first time.
Tamino, first, I too want to thank you for taking the time to clearly explain so much about PCA. I know that’s a ton of work!
Second, I believe you when you say you’ve examined a lot of temp records. But your interpretation of the Cedarville / Shasta situation suggests to me you have little field experience with temperature, particularly in the not-flat-like-the east West.
I’ve discussed this elsewhere here. In the West, a huge variety of ecosystem factors work together to modify the climate over amazingly short distances.
My first, second, third and fourth guess about the “anomalies” among neighboring rural stations in would hardly be that there’s an error in need of correction. To begin with, I’d look at air flow, precipitation and humidity patterns (natural heating/cooling), geology (what are the major nearby rock formations?), water features, etc etc.
I’m constantly surprised how often people assume patterns in nature that they’ve personally experienced will apply everywhere else.
Now, permit me to connect that some clarifying questions about the PCA exposition. My questions are similar to TCO’s… with perhaps more direct practical application.
You said: “some climate factors (volcanic eruptions, el Nino) are not, strictly speaking, noise — they’re governed by firm physical laws — but they’re either chaotic or simply too complex for our present understanding to predict. So, they are often (and quite validly) *treated* as noise.”
As far as I can tell, PCA is a way of more or less “redistributing” the data to identify components that are mathematically model-able highly correlated “factors” with largest, 2nd largest, etc variation (i.e. “signal”) — no matter what they might mean.
In addition, it tends to redistribute random “factors” to be spread evenly among all components with the effect that such factors will not impact the overall situation.
Doing ok so far?
Now comes the fun part, which I believe you plan to cover in your next installment. So perhaps you can consider these pre-lecture questions :)
If in reality we have four climate signals:
a) Something with high repeatability and variability
b) Something with high repeatability and less variability
c) Something that’s relatively chaotic in the time scale of measurement
d) Something that fits neither a, b or c
Then will it not be true that (a) will be PC1, (b) will be PC2, and c and d will not really be noticed?
Of even more interest, will it not be true that we have no reason to assume that a, b, c and d are actually represented in our data or analysis?
For example, suppose we’re looking for a temp proxy. Yet suppose signal a is related to humidity, b is related to wind speed, c is related to peak wind gusts, and d is related to daily deer migration patterns. All plausible… and we could very easily not find temperature anywhere, even though that’s what we believe we’re seeking.
Bottom line: seems to me the tough part about PCA, even done completely correctly, is finding a way to validate that we’re looking at what we think we’re looking at. Spurious correlation seems a huge challenge.
Same with my suspicion that there may be nothing at all wrong with the Cedarville and Mt Shasta measurements. They may just look erroneous to someone who has insufficient experience with western microclimates.
dhogaza // March 6, 2008 at 5:29 am
I challenge the assumption that the west, on the whole, which is dominated by the basin and range province, is “flatter” than the east.
Yes, the extremes (death valley, the rockies) are much greater, but in the great basin, and the columbia plateau, the landscape is dominated by long, flat empty stretches.
Drive south from denio junction nv to winnemucca, and you’ll go 100 miles with one left turn and just two small sections of noticable elevation change (noticable primarily because of the flatness separating them).
East from Wendover, UT to SLC? A hundred miles of flat.
Including, for instance, the bonneville salt flats.
The whole point of attacking the problem statistically is that you can get a valid result even if there are individual adjustments that are wrong.
And the whole reason for doing so is that we know that ALL measurements are wrong.
Perhaps the algorithm being used exaggerates the adjustment for some sites. It also undoubtably minimizes the ideal adjustment for others.
Statistically, that’s not really the issue.
Nor is the issue “is the GISS reconstruction correct”.
The issue is “does the GISS reconstruction lie within its calculated error bounds”.
If so (and nothing with this cherry-picking, emphasis on individual stations, etc effort will change that unless you can prove the METHODOLOGY itself is incorrect overall, not just for particular stations), then the only real possible improvement is the narrowing of the error bounds.
Which is not what you and your like want, of course. You don’t want to narrow the uncertainty around the already established surface station record.
You imagine, somehow, that you’re going to dump it to the trash and well … what do you hope to prove?
That by trashing the surface temp record you’re going to prove that the satellite record is bogus, too?
dhogaza // March 6, 2008 at 5:30 am
Sorry, meant the assumption that the west is less flat than the east, oops :)
Ian // March 6, 2008 at 2:16 pm
MrPete,
Let me take a crack at interpreting your questions – my apologies if I’m misreading you.
First, I don’t think anyone would disagree that local climate can vary widely over small areas, and for a host of reasons. That’s why climate analysis involves anomalies, not raw temperatures. For example (again my apologies if I’m belaboring the obvious), I live at the bottom of a hill by a stream. Compared to me, my neighbors at the top of the hill have shifted growing seasons and different daily temperatures. What’s important for climate, however, is not the moment-to-moment difference in measurements at the top and bottom of the hill. Instead, we’d want to calculate an anomaly measure, such as the changes over many years at the bottom of the hill, and compare it to any changes in the same period at the top of the hill. Hence the local variation in climate (that is, top to bottom of the hill) drops out.
Now, in the data above, it certainly could be that there was a “real” shift in local climates in the 1920s and 30s with a physical cause, which then reverted to its previous state. But since it would be a *very* unusual and large change to produce the anomaly data above, and since we have no independent information about such local climate changes, we go with the base rates and adjust based on other stations.
Second, for your other questions: I may misunderstand your thinking here, but PCA is looking for variables that “clump together” – that is, for variables that tend to be correlated with one another and not with other variables. So, as with simple correlation, it’s possible that random noise could appear in any given data set in a way that you misinterpret as a “signal.” Also, what you call high “repeatability” (here I confess I’m not sure what you have in mind) wouldn’t necessarily come through as the first PC.
Technically, you’re right that we may not find a temperature “signal” among measures of humidity, wind, and deer, but we may wrongly think we have. As with correlation, the output of the analysis *by itself* is generally not persuasive. Our interpretation of the output would have to be consistent with other findings, be predicted by theory, etc.
Lee // March 6, 2008 at 5:25 pm
I grew up in Redding, in what locals sometimes call Superior California, because it is north of Northern California.
Redding is on the extreme northern end of the central valley, and transitions into the cascade mountains at its northern and western edge. It is fricking hot in summer - sometimes the hottest town in California.
An hour drive east of Redding, up into the northern extensions of the Sierra, is the town of Burney, nestled into a valley that gets cold drainage winds from the surrounding mountains. Burney is sometimes the coldest place in California.
In fact, I remember days in summer when Burney overnight low temp was the coldest in California, and that afternoon, Redding daily high was the hottest. An hour drive apart, dramatically different microclimates.
And yet - when Redding is hotter than normal, Burney is very, very likely to be hotter than normal. When Redding is colder than normal, Burney is very, very likely to be colder than normal. Not always, no, but as a rule, yes - and for annual anomalies, this gets averaged across 365 days.
Even more, I often used to drive up to Susanville, on the other side of a mountain range, and on the edge of the high sagebrush desert basin and range climate. If Redding was really hot when we left, Susanville was almost certain to be really hot (for Susanville climate) when we got there.
Temperature ANOMALIES have very high spatial coherence, especially when averaged across a year, even when absolute temps do not, and even in the highly varied microclimates of the west.
J // March 6, 2008 at 6:54 pm
MrPete writes:
I believe you when you say you’ve examined a lot of temp records. But your interpretation of the Cedarville / Shasta situation suggests to me you have little field experience with temperature, particularly in the not-flat-like-the east West.
I’ve discussed this elsewhere here. In the West, a huge variety of ecosystem factors work together to modify the climate over amazingly short distances. [...]
I’m constantly surprised how often people assume patterns in nature that they’ve personally experienced will apply everywhere else.
As others have said, your intuition is actually wrong on this point. Yes, the temperature may vary dramatically over short distances, particularly in mountainous regions.
But the temperature anomaly really doesn’t vary that much.
Here’s a demonstration that you might appreciate, since it involves a mountainous region in the western US.
I downloaded the USHCN/Filnet monthly mean temp data for Telluride, CO and Las Animas, CO. Telluride is a small, high-elevation town in the Rocky Mountains (weather station is at 8672 feet). Las Animas is a similar-sized town on the Great Plains (elev. 3890 feet).
Both towns have data from 1936-2006. Over that period, as you’d expect, the temperatures are quite different (Telluride’s mean is 37 F, Las Animas’s is 53 F).
But when you calculate the temperature anomaly, they’re quite similar. Both show no trend at all from 1936-1974, then rapid warming from 1975-2006 (Telluride = 0.9F/decade, Las Animas = 0.7F/decade).
MrPete is hardly the first person to come through here and express surprise at the idea that temperature anomalies are correlated over large distances, even when there are big differences in altitude, ecosystem, physiographic province … Maybe Tamino/HB would like to do a post sometime that would show a comparison like this?
J // March 6, 2008 at 7:06 pm
Oops. I just realized that’s the second time in two days that I’ve suggested Tamino do something … and now from catching up on the other threads I see that for some reason there’s been a sudden flood of suggestions for ideas for posts. Most of them, of course, are better than mine.
So I apologize, and I’m going to try to wait a month or two before writing anything along the lines of “Hey, Tamino, why don’t you …”
Thanks for the blog, which continues to be wonderful.
frost // March 14, 2008 at 1:14 pm
Are there any simple programs that will do PCA? I would guess that R would be able to do that but I’m hoping for something that is more beginner friendly. This is for a non-climate related problem.
Thanks.
P. Lewis // March 14, 2008 at 2:10 pm
You could try Scilab (which I’m currently trying to come to terms with; it’s the free equivalent of Matlab), but I’d hazard it’s learning curve is as great as R.
A Google search threw up statistiXL, XLSTAT and XLMiner (the latter is just a 30-day free trial), which are addins for Excel.
But there are others about. Google’s your friend.
frost // March 16, 2008 at 2:52 am
I did do a Google search but ease of use is hard to gauge from web blurbs. All packages are powerful but easy to use. So, I was hoping for personal testimony on a magic bullet.
Thanks for your response, tho.
Leave a Comment