## Some Other Area Weighted Reconstrucions

Posted by Jeff Id on August 18, 2009

As we’re nearing completion of the improvements to Steig et al. Ryan has been working hard on getting the final details of the best reconstructions possble, Nic has found a couple dozen reference papers and I’m working on the relatively mundane verifications which as a side item include area weighted reconstrucions. In engineering, when you make a calculation and there is no text full of answers to go by, you need something as a backup, some kind of check to insure that you’re not using meters instead of feet or not missing some simple factor in the complexities of a powerful math calculations. R is wonderful in it’s open source nature, however it is hideously bad for verification of highly complex functions.

If you’re a programmer, imagine not being able to stop a complex calculation part way to see the contents of a variable. Imagine the debugging required to insure that things are working when you can’t see the status of the loop. R is a nightmare that way. Where R succeeds is in the same areas as MatLab, vector and array math are fast and easy. For example, you can have two enormous matrices and you can multiply them by typing A %*% B, there are libraries in C but there is also a lot of time. That’s very powerful when working with math, however MatLab still smokes R for its more standard debugging tools, yet MatLab is expensive and R is free. That makes it possible for nearly anyone to verify R code without additional costs or hurdles .

In Ryan’s work, he determined that the appropriate stations to use for the Antarctic were those inside the satellite AVHRR grid so no islands at all. To that end we’ve reduced the list of appropriate manned surface stations to 28 and appropriate ground stations with manned to a total of 63. There were no automatic weather stations (AWS) until after 1982 and much of their data is questionable due to snow burial, instrument failure, and other issues but their influence on the reconstruction is useful. This is similar to my previous area weighted reconstruction which used the closest available surface data to infill the satellite grid points. A Voroni diagram.

Where the again very clever methods of Steig, Mann and company can improve on an area weighted diagram is in the distribution of the information of each station according to measured covariance rather than by closest station. Still the results should be VERY similar.

Without presenting all the detail, Ryan has been successful at producing an Antarctic map using 28 PC’s of antarctic AVHRR data with NO overfitting. He used a method of regularized least squares which is more common than many of the techniques in climatology but better than that it is working. I’ll save the verification stats for later, after all the publishers need something to talk about.

The following was created by me using Ryan’s code and data.

This plot has some of the best verification statistics, one advantage is that it uses a regularized least squares method that takes 1/10th ish of the time of other algorithms to run. The question becomes, does this make any sense as a reasonable answer for the distribution of trends. People will remember tAV Verondi plots from before, however for verification the plot can only use the same stations as the satellite based reconstrucion. Previously there were different stations included so I’ve rewritten the code entirely about 3 times now and this is the most recent result.

For the plot below, the algorithm works by cycling through each of the satellite grid points and locating the #1 nearest temp station. If no data is available it looks to the next until it finds the closest available data. This insures that all points are infilled through the length of the 5509 series.

It’s amazing but you can really see the RTLS algorithm having basically no spatial information other than from PCA recreating nearly correctly located the trends of the Antarctic. Ryan’s post on it is here although this is an improved version.

Since the above Antarctic plot includes automatic weather stations which are known to be problematic, I reworked the calculations using only manned surface station data below.

It’s surprising to see so little effect on the final trend. The story isn’t finished however, there is another detial whcih isn’t terribly minor that we’ll cover tomorrow. I’m tired now so it will have to wait.

## Bob H said

Fascinating, and excellent work. Do we have any indication as sto why the peninsula is so hot compared to the rest of the continent. The Antarctic Oscillation had been mentioned as a candidate previously. Volcanic activity could also be possible. Any thoughts?

## Carl Gullans said

This might be offtopic a bit, but do you/Ryan O/others? have any idea when your antarctic reconstruction paper will be submitted to journals for review?

## timetochooseagain said

2-Ideally I would be a comment sent to Nature on Steig et al. but we are probably past the cutoff for that by now.

Plus the Journals will doubtless whine “but its all

Online, where’s the glory?!?!?” looks bad again.## Bernie said

Jeff:

I am coming back into this discussion so my aplogies if this point has already been addressed. The initial mapping is by using stations that in a certain sense are “teleconnected” rather than proximate. You then appear to integrate the satellite data based on proximity. Why not by its covariance? Or have I misunderstood what you are trying to do?

## Nic L said

On the topic that you mention of verifying R code, I have found what seems to be a nasty trap with the diag() function. When applied to a vector of length n this converts it to a n x n diagonal matrix with entries equal to the values constituting the vector, PROVIDED THAT n>1. If the vector is of length 1, with value Z, diag instead creates a trunc(Z) x trunc(Z) diagonal matrix whose entries are all 1.

This means, for instance, that the “diag(d[(rc+1):nd]” fragment in Steve M’s transliteration of TTLS RegEM would go wrong if rc(=regpar) were only one less than nd (the number of data series), and (more likely in practice) so would the “Xerr[j,kmisr[[j]] ]=dofC/dofS * t (sqrt(diag(S[[j]])))” line if there were only one missing value for that period. This behaviour of diag() would not necessarily cause an error or be at all obvious, but it would radically change the computations.

The lesson seems to be that if diag is applied to a vector whose length could possibly be only one, it is necessary to deal with that possibility separately, eg by:

if (length(x)==1) {y=as.matrix(x)} else {y=diag(x)}

## Ryan O said

Yah, Nic, it took me forever to figure out why the hell TTLS wouldn’t run with only one predictand. I think the latest script has that fixed.

## Ryan O said

#2 It is being written as we speak. My guess is ~1 month.

## Layman Lurker said

#7 What about a tip jar for publication costs. Is Lucia collecting for you?

## Carrick said

Could you break down the trend pre and post 1980?

What I have seen in other data sets (e.g., HADCRUT which gives 0.15 C/year < 1980 and -0.05C/year post 1980) is the pre-1980 data has a positive trend whereas the post 1980 is negative. This is of course backwards to the global trend if so.

## Ryan O said

0.090 +/- 0.109 for 1957-1980

-0.017 +/- 0.079 for 1980-2006

Both CIs are corrected for serial correlation of the residuals.

## Jeff Id said

I’m sorry for the lack of posting today. Apparently I’ve got the swine flu. At least it feels like that, and it seems terminal. However in god’s infinite sense of humor, I’ve also caught a fatal case of the bird flue and like a multivariate regression where the inputs have high correlation they seem to interact resulting in a slow torturous battle in my guts which may or may not be fatal.

If I live, I have a bunch of on and offline emails and comments to deal with so there will be some delay.

## tedthereviewer said

Congratulations! Our selection committee compiled an exclusive list of the Top 100 Climate Change Blogs, and yours was included! Check it out at http://thedailyreviewer.com/top/Climate-Change

You can claim your Top 100 Blogs Award Badge at http://thedailyreviewer.com/pages/badges

Cheers!

## Tim G said

Two things:

1) I hope you are planning on publishing a paper in a “peer reviewed” journal. I think that would be great.

2) I may be wrong on this: but I’d like to see a graph that gives an idea of what really happened to the climate in Antarctica. I /think/ that most of the warming/cooling shown on your maps is insignificant — no place is going to be /exactly/ the same temperature over 50 years. Better to clamp the red and blue to levels that are “significant” [I don’t know what that means] and paint the rest white. That would be a contrast to the cover of Nature. IOW, it looks like a small part of Antarctica has warmed and the rest has stayed (essentially) the same. That is a more instructive map (for the layperson, at least), if you ask me.

–t

## Jeff Id said

#4 Bernie,

Since I presented two calculation methods it’s difficult to be sure but I’ll go with the title of area weighted reconstructions. These are the simplest form of reconstructions we’ve done and are presented just to show the main reconstructions are in line with reality. This is a common method in engineering which I hope Dr. Steig reads at some time. It potentially would have prevented his continuously red Antarctic plot from happening in the first place. So I just looked for the closest thermometer for each region of the satellite grid.

In the case of the other reconstrucitons, Ryan employed covariance, correlation and in the plot above a regularized least squares fit to the spatial distribution PC’s of the satellite data. This method makes more sense than the others which I’ll hopefully show soon in a post I’m working on — along with several others.

There is another step to take regarding the area reconstructions first.

## Jeff Id said

#13 I think your idea of a plot would be interesting and should be easy to do.

It leads me to a point though which is often lost in climate science.

Is a significant trend real?

In climate science they like to say the current reduction in temperature is not significant and Tamino even impled the cooling trend didn’t exist in one of his headposts. However this is a misnomer (not saying you Tim, I’m just putting thoughts down). The point of the significance of a trend is a bit of a circular argument. First it must be assumed that any signal other than the linear trend is random, then the random noise is modeled and repeated, trends are then measured in the random noise and anything within the outer 5% each way are considered significant.

What happened though is that from our assumptions we’ve determined that anything outside the linear trend is random and insignificant. By simply assuming some curvature to the trend, the limits change. So when Tim’s question about what really happened to the climate in Antarctica is asked, the answer is in the graphs above.

The level of significance only compares it to the typical instrument and climate variance on a 50 year climate trend.

Another way to put it is the variations in the short term signal are often real, measured, actual variances. What significance implies is that these variances are continuous ongoing effects which have nothing to do with the trend. However, the pre-ordained assumption in the math is actually that these variances have nothing to do with trend.

So then you need to ask,– How realistic or even more correctly how useful is the assumption of linear trend?

## Layman Lurker said

#14

Jeff, if AGW is real, then wouldn’t the signal reflect the monotonic (almost linear) increase in CO2? Climate response to CO2 would then be noise or oscilation.

## Jeff Id said

Layman,

I suppose that’s true but what we’ve done then is assumed a priori that the non-linear short term forcings are not significant to the signal. My point isn’t that the linear assumption is stupid or incorrect but rather to demonstrate the circular nature of the logic.

What we measure is real minus instrument error. Significance only refers to the significance of the linear fit to a temperature signal.

I don’t know if it’s making any sense but significance of a linear trend does not define reality. It defines how likely that the trend you’re seeing is created by short term variation in the non-linear portion of the signal. It is also easy to mess with.

## Layman Lurker said

#17

I don’t disagree with you at all. IMO it is very difficult to untangle a linear CO2 signal from observed temperatures without re-jigging the decadal scale physics of the climate models. Then you have the “catch-22” situation that Mark T alluded to – increasing the uncertainty of the linear trend.

This scenario begs for alternative explanations of temperature observations as much (or more) as re-constructing the AGW model.

## Tim G said

Like I said above, I really don’t know what “significant” means. I’m not a stats person. But maybe there is a common method. Standard deviation? Any area that has heated (or cooled) more than one standard deviation of the entire continent? I don’t know. Just a thought.

The Steig cover on Nature had the whole continent red (IIRC). But if the warming was just noise, the graph is much more misleading than it is informative. I know some people think that might be on purpose. I’m not really a conspiracy theorist. I’m just someone who wants to know what is really going on.

Thanks,

tim

## Sera said

Slightly OT, but the latest from the NAS about data archiving, releasing code and integrity (?)

http://books.nap.edu/openbook.php?record_id=12615&page=R1

## PaulM said

Tim G

” it looks like a small part of Antarctica has warmed and the rest has stayed (essentially) the same. ”

This is exactly correct. The peninsula has warmed a lot, the rest of Antarctica not significantly. The silly thing is, we have known this for years.

Just look at the plot of the raw data from the temperature stations.

Go to Gistemp at

http://data.giss.nasa.gov/gistemp/station_data/

and click on Antarctica, then look at non-peninsula stations like Halley and Amundsen Scott – no warming, then look at peninsula stations like Faraday and Base Esperanz – strong warming

So Ryan’s plot is no surprise, its exactly what you’d expect.

It’s the Steig plot that it is a surprise, and wrong.

There is a really good summary at

http://www.coolantarctica.com/Antarctica fact file/science/global_warming.htm

(by someone who is clearly an AGW believer). He says:

“The Antarctic Peninsula is particularly sensitive to small rises in the annual average temperature, this has increased about 2.5°C in the region in the last 50 years, this is 2 or 3 times faster than the average in the rest of the world. This makes it an excellent study area.”

“The temperature of the rest of Antarctica – the other 96% – shows no current indications of rising.”

“There is no unusual significant loss of ice of any kind from the larger 96% of Antarctica that is not the Peninsula.”

I hope that Ryan and Jeff will make this obvious point in their paper.

I also hope they will release a draft version of the paper very soon!

## Antarctic Trends, Graphics and Discussion « the Air Vent said

[…] editing and the original version contained some area weighted reconstructions similar to those presented here and below. It was later removed from the SI after the first two reviews required us to completely […]