Guest post by Willis Eschenbach
Inspired by this thread on the lack of data in the Arctic Ocean, I looked into how GISS creates data when there is no data.
GISS is the Goddard Institute for Space Studies, a part of NASA. The Director of GISS is Dr. James Hansen. Dr. Hansen is an impartial scientist who thinks people who don’t believe in his apocalyptic visions of the future should be put on trial for “high crimes against humanity”. GISS produces a surface temperature record called GISTEMP. Here is their record of the temperature anomaly for Dec-Jan-Feb 2010 :
Figure 1. GISS temperature anomalies DJF 2010. Grey areas are where there is no temperature data.
Now, what’s wrong with this picture?
The oddity about the picture is that we are given temperature data where none exists. We have very little temperature data for the Arctic Ocean, for example. Yet the GISS map shows radical heating in the Arctic Ocean. How do they do that?
The procedure is one that is laid out in a 1987 paper by Hansen and Lebedeff In that paper, they note that annual temperature changes are well correlated over a large distance, out to 1200 kilometres (~750 miles).
(“Correlation” is a mathematical measure of the similarity of two datasets. It’s value ranges from zero, meaning not similar at all, to plus or minus one, indicating totally similar. A negative value means they are similar, but when one goes up the other goes down.)
Based on Hansen and Lebedeff’s finding of a good correlation (+0.5 or greater) out to 1200 km from a given temperature station, GISS show us the presumed temperature trends within 1200 km of the coastline stations and 1200 km of the island stations. Areas outside of this are shown in gray. This 1200 km. radius allows them to show the “temperature trend” of the entire Arctic Ocean, as shown in Figure 1. This gets around the problem of the very poor coverage in the Arctic Ocean. Here is a small part of the problem, the coverage of the section of the Arctic Ocean north of 80° North:
Figure 2. Temperature stations around 80° north. Circles around the stations are 250 km (~ 150 miles) in diameter. Note that the circle at 80°N is about 1200 km in radius, the size out to which Hansen says we can extrapolate temperature trends.
Can we really assume that a single station could be representative of such a large area? Look at Fig.1, despite the lack of data, trends are given for all of the Arctic Ocean. Here is a bigger view, showing the entire Arctic Ocean.
Figure 3. Temperature stations around the Arctic Ocean. Circles around the stations are 250 km (~ 150 miles) in diameter. Note that the area north of 80°N (yellow circle) is about three times the land area of the state of Alaska.
What Drs. Hansen and Lebedeff didn’t notice in 1987, and no one seems to have noticed since then, is that there is a big problem with their finding about the correlation of widely separated stations. This is shown by the following graph:
Figure 4. Five pseudo temperature records. Note the differences in the shapes of the records, and the differences in the trends of the records.
Curiously, these pseudo temperature records, despite their obvious differences, are all very similar in one way — correlation. The correlation between each pseudo temperature record and every other pseudo temperature records is above 90%.
Figure 5. Correlation between the pseudo temperature datasets shown in Fig. 3
The inescapable conclusion from this is that high correlations between datasets do not mean that their trends are similar.
OK, I can hear you thinking, “Yea, right, for some imaginary short 20 year pseudo temperature datasets you can find some wild data that will have different trends. But what about real 50-year long temperature datasets like Hansen and Lebedeff used?”
Glad you asked … here are nineteen fifty-year long temperature datasets from Alaska. All of them have a correlation with Anchorage greater than 0.5 (max 0.94, min 0.51, avg 0.75). All are within about 500 miles of Anchorage. Figure 6 shows their trends:
Figure 6. Temperature trends of Alaskan stations. Photo is of Pioneer Park, Fairbanks.
As you can see, the trends range from about one degree in fifty years to nearly three degrees in fifty years. Despite this huge ~ 300% range in trends, all of them have a good correlation (greater than +0.5) with Anchorage. This clearly shows that good correlation between temperature datasets means nothing about their corresponding trends.
Finally, as far as I know, this extrapolation procedure is unique to James Hansen and GISTEMP. It is not used by the other creators of global or regional datasets, such as CRU, NCDC, or USHCN. As Kevin Trenberth stated in the CRU emails regarding the discrepancy between GISTEMP and the other datasets (emphasis mine):
My understanding is that the biggest source of this discrepancy [between global temperature datasets] is the way the Arctic is analyzed. We know that the sea ice was at record low values, 22% lower than the previous low in 2005. Some sea temperatures and air temperatures were as much as 7C above normal. But most places there is no conventional data. In NASA [GISTEMP] they extrapolate and build in the high temperatures in the Arctic. In the other records they do not. They use only the data available and the rest is missing.
No data available? No problem, just build in some high temperatures …
Conclusion?
Hansen and Lebedeff were correct that the annual temperature datasets of widely separated temperature stations tend to be well correlated. However, they were incorrect in thinking that this applies to the trends of the well correlated temperature datasets. Their trends may not be similar at all. As a result, extrapolating trends out to 1200 km from a given temperature station is an invalid procedure which does not have any mathematical foundation.
[Update 1] Fred N. pointed out below that GISS shows a polar view of the same data. Note the claimed coverage of the entirety of the Arctic Ocean. Thanks.
[Update 2] JAE pointed out below that Figure 1 did not show trends, but anomalies. boballab pointed me to the map of the actual trends. My thanks to both. Here’s the relevant map:
Willis Eschenbach (02:11:19) :
The correlation at 1200km was average of .5 for northern latitudes.
The spread was something like .2 to .8.
With GISS code up an running EMS could actual do a sensitivity on this parameter. Or god forbid you could actually make it a function of the demonstrated correlation for the region. Clearly for some regions you have good correlations at long distances and for others you have crappy figures.
And clearly if you are blindly mushing together an inland site with one on the coast ( which is more correlated with the changes in SST ) you will end up with mush. and if you blend over a region that changes from Ocean to Ice depending on the season you are also asking for trouble.
Hansen’s method is just a meat grinder approach.
“”” Willis Eschenbach (12:52:29) :
George E. Smith (10:51:53) : edit
Well a lot of babies are born in the spring time; which in the case of humans is nine months after the winter +/- a few months. It’s actually the same for other species; but who cares.
Where I live, the fall (autumn) comes nine months after the winter, and spring comes either three or fifteen months after the winter … where do you live? “””
Well Willis I live in California; where it was Spring last week and this week and for a while to come it will be Summer. You might have noticed I said +/- a few months; I was applying the obligatory climate science fudge factor. By that standard, my estimations are quite good.
George
Phil. (20:36:29) :
Keith G (18:32:14) :
“In that case where do you suppose the data for the DMI Arctic temperature linked to on this site come from? Willis shows 3 stations on the edge of the 80ºN parallel”
Re DMI: Three stations are likely to give fair results on such an icy plain with no topographic or cultural confounders but still this would give a maximum temperature on average I would think given that there may not have been a correction for latitude. Certainly DMI is more reliable than 1200km extrapolations from land, with icy and watery coasts. Also, although the ring of stations, which are all near the same latitude 70-80 might be expected to have significant correlations laterally but not in the N-S direction. For example, 1200km south of Longyearbyen, Svalbard is Reykjavik Iceland and even the Baltic Sea, Both significantly different in temperatures and in different weather regimes- on opposite sides of the jet stream for many months and the effects of the Gulf stream and return Arctic currents. Anyone know what adjustments are made with the data in terms of latitude?
“”” rbateman (10:21:39) :
The situation vis-a-vis the Arctic temp history is far worse than some have depicted, what with exrapolations to 1500 km.
The extrapolations, as bad as they are, are based on raw station data that commonly sports great gaps of multiple years/months.
It’s an Empire State Theory built on a mudflat with sinkholes.
Let me make it perfectly clear: The sub-Arctic land station data is bad enough as it is. “””
My understanding is that about 150 years ago the number of “weather stations” in the arctic >+60 deg N. was about 12. That number increased up to around 86 in the early-mid 20th century, and then declined to something about 72 today (approximately), and possibly due to the collapse of the Soviet Union.
Good luck on getting a believable temperature map from that.
I previously asked a question regarding Figure 4. In what meaningful sense is the steepest and most curvy purple Ps 5 deemed to have a better ‘correlation’ (0.97) to the almost flat-line red Ps 2, than does the in-between orange Ps 3 (0.91)?
What the numbers are saying is that the steep purple Ps 5 better represents the flat-line red Ps 2 than does the less steep orange Ps 3. In what sense is this so, if the statistical meaning for ‘correlation’ is to have any correlation to the usual definition?
Specifically, what I am asking, is what there is about Ps 5 that gives it a better technical ‘correlation’ to Ps 2.
Please realise that I am not rebutting; I am asking. I seriously doubt that I am the only one who wouldn’t understand this and without that understanding, Figure 4 is unhelpful.
Very interesting. Excellent detective work. You clearly must be thrown in jail.
This kind of ‘correlation’ has been used, on another level, to link virtually any and all effect or disaster to The Warming in the ongoing propaganda campaign so this is somehow not surprising…
Maybe there should be a new term for the ‘data’ that the IPCC gang uses to distinguish it from that which is credible?
Mann-made? Hansenized?
Oh well. No worries. The Caitlin Expedition will soon return from their historic quest for the truth and then we’ll all know what’s up with that.
Anu (21:36:11)
Thanks for the good luck wishes, Anu. I got some time so I took a look at the paper on NOAA satellite data you cite above. Here’s the problem. They are looking at sea surface temperature, and GISS is looking at surface air temperature. Usually, they are quite similar … but not always. Here’s how NOAA adjust SST for ice coverage:
So in locations where there is more than 90% ice, the SST is quite reasonably set to the freezing temperature of sea water, -1.8°C. That’s fine.
But above the ice, the freezing polar winds can be twenty, thirty, forty degrees below zero … and the SST doesn’t reflect that reality, which is the one we are trying to get at. So the satellites don’t help us in the slightest where there is ice.
w.
Sean McHugh (15:13:38)
Sorry for missing your question above, Sean.
Mathematical correlation is defined as:
where x and y are the individual datapoints, and x and y with the overbar are the average of all x and the average of all y.
What this does is measures how much the variations of x from the average of x are like the corresponding y variations.
Note that this does not include any information about the trend. For example, two straight lines like Ps 1 and Ps 2 have a correlation of 1.0, despite their wide differences in trend.
So in response to your question about how a dataset with a high trend can have a higher correlation to dataset X than a dataset with a low trend, the answer is that trend is not a part of the mathematical calculation of correlation.
Now, this makes sense how?
Well, suppose every time x goes up by one, y goes up by three, and every time x goes down by one, y goes down by three. Because of this, the correlation will be 1.0, because every twitch in x has an exactly corresponding (but larger) twitch in y … but the trends will be very different.
And this is exactly the problem that I am highlighting, which is that correlation means nothing about trends, so we can’t use it to extrapolate temperature trends out 1200 km, or any number of kilometres for that matter.
Hope this helps, but if not, ask more questions. The only foolish questions are the ones you don’t ask.
Steve Goddard (21:55:56) : edit
DMI has very accurate measurements north of 80N, and has for many decades.
http://ocean.dmi.dk/arctic/meant80n.uk.php
Steve, despite an extensive search, I can’t find a list of the stations that they use for their graphs. Do you have one?
Thanks,
w.
It helped tremendously. Thank you for putting so much effort into assisting. I did check out the maths before asking, but even though I could understand the equation, it didn’t give me a conceptual handle. This is the statement that really did the trick:
That completely explains to me the twist in Figure 4. I will now read the whole thing again. Thanks again.
Willis,
We are cosntantly reminded how good an insulator ice is. So it is no wonder that satellite measurments of atmospheric data above the ice give little information on SSTs as you point out.
Certainly for areas of the arctic where sea ice coverage is more or less total, that would seem to be a given.
Willis Eschenbach (16:16:58) :
If I have read you right, extrapolating from Station X1 on land out 600 km to the Polar region will impose a trend, but it won’t give you the actual temperature there. If there is no Station X2 on the Ice Cap, one really doesn’t know that the trends actually correlate, and neither does one have an anomaly.
What you do have is a WAG.
Why not infill using the satellite data?
We’d get a warm trend in the Arctic greater than any other large-scale region on the planet.
North Pole trend – 0.45/dec.
UAH data
Their figure roughly corroborates Hansen’s – even though satellite coverage is also poor for the region. I request a post on why we shouldn’t trust Spencer and Christy.
Anu (22:01:02) :
Ah, another carefully crafted comment moderated away.
……………………………………………………………………………………………………..
It was only your line of comment on cigarette smoke that was snipped. Anyone could see that. You comments related to this thread are still there. Even though you do not agree with the writer of this thread you were not deleted for it.
This would not be the case at RealClimate. Comments that are not in agreement with the writers there are customarily deleted even though they are on topic.
Anu (22:01:02) :
Ah, another carefully crafted comment moderated away.
………………………………………………………………………………………………………
Anu,
I am sure someone in your position does have to carefully craft what they say. That’s all I’ll say about that.
Re: Willis Eschenbach (Mar 26 12:50),
Of course for a locality the average, and the changes over the average have a meaning from cultivation to what to wear to tourism.
In my example thermometer 1 will give an average T1 because the heat source passed close to it more often than for thermometer 2 with average T2. Then the anomaly of thermo1, say falls because the moving heat source is far away from the average distance it had when the average was taken, while the anomaly of thermo2 goes up because the moving heat source came closer than when the average was taken.
There is no analogy between changing scales in thermometers and using local average temperatures as a base on which to measure temperature differences. The average of each thermometer will be different depending on the energy sources affecting it. When one starts looking at the differences over these variable averages, in different locations with different energy source variations, one is diluting the proxy process to an undecipherable level.
It is the scientific meaning I am after, whether anomalies are proxies for global heating and cooling. You are talking in the post of the way the anomaly averaging is done, I am talking that already from the logical basis, anomalies are very bad proxies of heating and cooling of the globe, by construction.
If there were only one energy source, e.g. radiation from the sun that the static energy budget models use, anomalies would reflect temperature variations which would reflect ground temperature variations. Fortuitously, there are oceans and an air atmosphere that generates large movements of energy over the globe that distort and may reverse what anomalies are measured with respect to the ground temperatures.
The recent winter is a good example because the motion of the air currents has brought cold to the south of the arctic and brought warmth to the arctic, but the storm systems distributed and negated( precipitation) the cold while the north kept a large part of the warmth so the total anomalies average out unreal as far as heat content and human perception goes. We feel heat and cold, not anomalies.
Re: Willis Eschenbach (Mar 26 15:53),
So in locations where there is more than 90% ice, the SST is quite reasonably set to the freezing temperature of sea water, -1.8°C. That’s fine.
But above the ice, the freezing polar winds can be twenty, thirty, forty degrees below zero … and the SST doesn’t reflect that reality, which is the one we are trying to get at. So the satellites don’t help us in the slightest where there is ice.
This harks back to another bone of mine, that it is surface ground temperatures that are important for a radiation budget using black body formulae.
SST is the reality as far as energy balance goes. Air surface temperatures at 2 meters used for the radiation budget in this case would give tens of watts off the true radiation budget of the solid.
barry (18:39:00)
Ummm … no. Here’s a look at the difference in GISS (ground stations) and UAH (satellite) trends, from here:
Don’t like the UAH satellite analysis? You prefer RSS? Here’s that:
As you can see, the biggest difference is in the far north, where GISS shows much greater warming than either UAH or RSS … in other words, the region that we are discussing.
And you “request a post on why we shouldn’t trust Spencer and Christy.”? Here’s how it works. I post on what I find interesting, I don’t have enough time to post or research everything I’d like to, and so I depend on AGW supporters covering what they want to see covered. Go for it, let us know what you find.
Willis, I’m not disputing there’s a difference. I said that UAH show a large warming trend over the Arctic – larger than any other region on Earth, just as GISS do. And I said that in response to the question upthread, which I quoted, not to your article.
I am also aware that:
1) The UAH record and record-keepers are held in some esteem here, while surface records and their producers are routinely maligned. The UAH record is seen as a reference point with which to check the validity of surface records.
2) Temp-recording satellites are not able to cover the poles adequately.
The GISS record is here rebutted because of insufficient coverage and assumptions re correlation and trends. With these things in mind, and while I was answering the question upthread, I added my request to make a small point.
As many people contribute articles here, my request was not addressed to you specifically. The point behind my request is that skepticism is not equally applied.
While there has been talk of it in comments sections, I may have missed the WUWT article in the past where Spencer and Christy have been taken to task for producing polar temp records – anomalies and trends – when there is so little satellite coverage for the poles. If I am mistaken, I would appreciate a pointer (from anyone).
anna v (22:48:11) : edit
Anna, in general I agree. The problem is, we don’t have data on the ground temperatures and we do on the surface air temperatures.
As I mentioned before, in practice I don’t think this is too much of a problem. The ground runs hotter than the surface during the day, and colder during the night, so the averages won’t be too far apart. Or at least that’s what my experience says … hmmm … data … data …
Data on this is very hard to find, so I turn to my bible, Geiger’s exhaustive tome, “Climate Near The Ground”. It shows a graph of tautochrones of temperature both above and below the ground in Nebraska on the 24th of August 1953 (back in the days when climate scientists actually measured things) for a 36 hour period. This is good, because summer would be when we would expect the difference in temperature between the ground and air to be the greatest due to fast ground heating in the hot summer sun. Digitizing it … scan it, straighten it, overlay some lines, get the temperatures for each hour … … OK, thanks for waiting, I get an average ground temperature over 24 hours (using hourly temperatures) of 26.8°, and an average air temperature at 1.5 metres above the ground of 28.9°. So the ground in the summer is a couple degrees warmer than the air at the elevation above ground at which it is measured. In the winter it will be less. Of course, over the ocean the difference will be smaller than on land (in many temperature averages the air temperature is taken as being equal to the sea temperature). And most of the planet is ocean.
So like I say, in practice this is not a large difference, so we will not be far wrong using the air temperature as a proxy for the ground temperature.
I can’t recommend Geiger’s book enough, get a copy if this subject fascinates you the way it does me. Not cheap, I got my copy at a college used book store, but worth every penny.
Geiger is fantastic.
I am just a simple professional civil engineer, so please bear with me. If I would go to a relative “flat” area, such as say Kansas, or Florida, I could, by these “climate scientists'” methodology, take a measurement of elevation at points miles away from each other, and then, design a highway between those points and set my grade lines according to these far away points of elevations (benchmarks), do my earthwork calcs and be quite accurate. What balderdash! I have done earthwork calculations by way of the average horizontal area of cross sections method, as well as by the average end area of cross-sections method, and the average contour area method yields far more accurate results. These “interpolated” values are nothing other than worthless. And, worthless, however better it is than other available methods is still of no real value. A guess is still a guess, no matter the “scientific terminology” in which it is expressed.
I wouldn’t be setting horizontal grade lines on such scant data, and expect an earthwork quantity balance (equal amounts of cut and fill) and neither should we be accepting these “interpolated” values as having any value, no matter that they are “the best” we can manage. Worthless data gets no better no matter how well it is massaged.
The point I am trying to make is that the temperature measuring stations were not placed with determining an “average temperature” of any specific land mass area in mind, but for other purposes. As it is, it would be the same as if I, as a highway designer, used random points of elevation to determine how my horizontal grade lines should be set to obtain a balance of earthwork quantities. Not at all a viable concept.
This attempted use of existing temperature measuring stations (particularly since so many are poorly sited, as Anthony has demonstrated) is a “balls up” venture such as I have ever seen. No good can come of it, and the research money could be spent at far greater value to we, the taxpayers.
What I do not understand: why has no one dropped a couple of weather station onto the ice cap? Sure, it might not live more than a few months, but the cost would be trivial compared to the value of the data.
Re: Willis Eschenbach (Mar 27 00:11),
… OK, thanks for waiting, I get an average ground temperature over 24 hours (using hourly temperatures) of 26.8°, and an average air temperature at 1.5 metres above the ground of 28.9°. So the ground in the summer is a couple degrees warmer than the air at the elevation above ground at which it is measured. In the winter it will be less.
Well, your numbers must be reversed.
If I take the black body formula for 26.8C I get 458 watts/m^2 radiated away
28.9C 471″
This is an error of 11 watts in the radiation budget
If I take your numbers of ice being 0C and air -40C
for 0C 372watts/m^2 radiated away
for -40C 162 ”
an error over 200 watts.
As these tables show , http://isccp.giss.nasa.gov/products/browsesurf1.html
if you choose skin surface temperature in the menu,
and ascii in the output for down loading data, there are differences of more than two degrees on most of the globe:
One line from the top of the table (must be either arctic or antarctic):
Air:
243.912, 244.836, 245.338, 243.642, 243.293, 241.826, 242.496, 245.537
skin surface:
224.47 0, 226 .452, 227.834, 225.682, 222.531, 222.986, 227.104, 235.266
and one line from somewhere in the middle, where the differences are smaller than 1 degree:
air
301.578, 301.622, 301.588, 301.574, 301.555, 301.582, 301.605, 301.548
skin surface
302.377, 302.388, 302.356, 302.386, 302.501, 302.495, 302.499, 302.361
In this case, the watts radiated if air temperature is assumed, for example
301.6 is 469Watts/m^2
the corresponding skin value is 302.4 and 474.1Watts/m^2
I am trying to illustrate that talking of radiation budgets with values of 1 and 2 and 4 watts/m^2 is futile when one is not using the correct temperatures in the study.
Richard Telford
Richard, years ago, I wrote a lot of code for modelling coal seams and mineral deposits (mainly coal seams, though) from borehole logs. The process was started by creating a polygon of influence around all the boreholes simultaneously, with due allowance for known faults etc and then triangulating the polygons. By definition they are all convex so that is a trivial process that can be done in k * log(n) time. I think the problem here is not susceptible to that process because of the very large distances across the “empty” polar region compared with the relatively small distances between the actual stations. An exploration company would, I think, do “infill drilling” above 80N in such a situation.
Pending getting the station data and performing some reasonableness checks against the empty region, I think the best that could be done would start with some kind of trend analysis – crudely, it must tend to get colder to closer one approaches the pole.
What do you think?