Closest Station Antarctic Reconstruction

Update down below:

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In my last alternate reconstruction of Antarctic temperature I used the covariance of satellite information to weight surface stations. While the reconstruction is reasonable I found that it distributed the trends too far from the stations. This prompted me to think of a way to weight stations by area as best as I can. The algorithm I employed uses only surface station data laid on the 5509 grid cell locations of the Steig satellite reconstruction.

This new reconstruction was designed to provide as good a correlation vs distance as possible and the best possible area weighting of trend, it can’t make a good looking picture though but for the first time we can see the spatial limitations of the data. The idea was to manipulate the data as little as possible to make where the trend comes from as clear, simple and properly weighted as possible.

The algorithm I came up with works like this.

Calculate the distance from each of 42 surface stations to 5509 satellite points store them in a matrix 42 x 5509.

For each of 5509 points find the closest station and copy the data to that location. If there are missing values infill those from the next closest station looking farther and farther until all NA’s are infilled.

This is what the spatial distribution of trends looks like.

Figure 1

You can see how the trends are copied to the points of each polygon from each surface station. There’s quite a bit of noise in the graph but it seems that like temperatures are grouped reasonably well together.

The code looks for the above plot takes about 20 minutes to run.

#calc distance from surface stations to sat grid points
dist=array(0,dim=c(5509,42))

for(i in 1:42)
{
dist[,i]=circledist(lat1=Info$surface$lat[i],lon1=Info$surface$lon[i],lat2=sat_coord[,2],lon2=sat_coord[,1])
}

Circledist is Steve McIntyres’s great circle function with slight modifications.

circledist =function(lat1,lon1,lat2,lon2,R=6372.795)
{
pi180=pi/180;

y= abs(lon2 -lon1)
y[y>180]=360-y[y>180]
y[y<= -180]= 360+y[y<= -180]
delta= y *pi180

fromlat=lat1*pi180;
tolat=lat2*pi180;
tolong=lon2*pi180

theta= 2* asin( sqrt( sin( (tolat- fromlat)/2 )^2 + cos(tolat)*cos(fromlat)* (sin(delta/2))^2 ))
circledist=R*theta
circledist
}

Then I wrote a function to get the closest distance greater than a value ‘mindist’ I pass. The first call for the grid number ‘ ind’, mindist is set to zero and the closest station is returned. If the closest station has missing data, I infill what it does have and pass the distance from the closest station to mindist and get the second closest station returned. The process is repeated until all values are filled.

getnextclosestdistance = function(ind=0,mindist=0)
{
tdist=dist[ind,]

while(min(tdist)<=mindist)
{
mind=min(tdist)
if (mind<=mindist)
{
tdist=tdist[- (which(tdist == min(tdist), arr.ind = TRUE)[1])]
}
}
g= which(dist[ind,] == min(tdist), arr.ind = TRUE)[1]
g
}

This is the loop function that fills the array.

recon=array(NA,dim=c(600,5509))
recon=ts(recon,start=1957,deltat=1/12)

for (i in 1:5509)
{
lastdist=0
while(sum(is.na(recon[,i]))>0)
{
dd=getnextclosestdistance(i,mindist=lastdist)
lastdist=dist[i,dd]
mask = is.na(recon[,i])
recon[mask,i]=anomalies$surface[mask,dd]
print (paste(i,lastdist))
}
}

After that all that’s left is the plotting algorithms by RomanM SteveM and Jeff C which I’ve shown before.

The next graph is the trend calculated from all 5509 grid points.

Figure 2

The trend is again positive by 0.052 C/Decade, this time it is on the outer edge of the stated 95% confidence interval of Steig09 of 12 +/- 0.07C/Decade.

Like before I also looked at the trend from 1967 – 2007.

Figure 3

Figure 4

So from this reconstruction temperatures have dropped since 1967 at an average rate of 0.31 C/Decade. These results are similar to my previous reconstruction which looks like this.

The Antarctic, an engineers reconstruction.

Figure 5

Figure 6

And from 1967 – 2007

Figure 7

Figure 8

While I was initially happy with the engineers reconstruction, I found that station trends were not well localized by linear correlation weighting. (The correlation vs distance was not good) While peninsula station information stayed localized, the rest of the continent spread widely.

The trends shown match my last reconstruction reasonably well but in my opinion these are of superior quality.

Certainly the Antarctic temperatures have been flat or insignificantly cooling/warming in general for the last 40 years while 50 years ago there were lower temps recorded causing a very slight upslope in the 50 year trend. This is confirmed by the fact that sea ice has grown during the last 30 years among other observations.

The Steig 09 paper seems to be an artifact of the mathematics more than an actual trend. Amundsen Scott is the south pole data. The surface measurement is visually clean and has a downtrend for the full length of the data. This cooling is represented by the blue polygon in the center of the antarctic in this reconstruction.

TCO keeps asking me if I’ll post a trend higher than Steig. Every reconstruction I’ve done has reduced the trend from Steig 09. Every change no matter how small has resulted in a trend reduction from Steig 09, even the attempt to match Steig 09 has resulted in a slight trend reduction. I’ll say it now for the first time. In my opinion the paper is flawed and has an exaggerated warming trend due to bad mathematics. Temperature distributions on the continent are a result of artifacts in RegEM and not supported by the natural weather patterns as they were presented.

As an example which is pretty clear. Steig’s paper shows warming across the entire Antarctic. Here’s a plot of the ground data at the south pole.

Figure 9

A reconstruction cannot ignore a trend this strong. So TCO, it isn’t up to me. As Gavin likes to say, the data is the data. This data just cannot support Steig’s conclusions.

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Update, hat tip to David L. Hagen,

Here is an independently generated version of the Antarctic temp trends done in 2008 which looks amazingly similar to Fig 8.

This map of Antarctica shows the approximate boundaries of areas that have warmed or cooled over the past 35 years. The map is based on temperatures in a recently-constructed data set by NCAR scientist Andrew Monaghan and colleagues. The data combines observations from ground-based weather stations, which are few and far between, with analysis of ice cores used to reveal past temperatures. (Illustration by Steve Deyo, UCAR.)

Article here.

Climate Models Overheat Computer analyses of global climate have consistently overstated warming in Antarctica, concludes new research (5/10/2008)