Central Australian warming

I've been arguing again, at Climate Etc. Blogger Euan Mearns has a guest post in which he claims to demonstrate that stations within 1000km of Alice Springs show no warming.

I'll post about it here, because it illustrates the averaging fallacies I've been writing about regarding Steven Goddard and colleagues (also here). And also because "Alice Springs" is one of those words naysayers sometimes throw at you as if no further explanation is required (like Reykjavik). People who do that generally don't know what they are talking about, but I'm curious, since I've been there.

There are actually two issues - the familiar time series of averages of a varying set of stations, and anomalies not using a common time base. I'll discuss both.

The stations are obtained from the GISS site. If you bring up Alice Springs, it will indicate other stations within a radius of 1000 km. My list was 29, after removing repetitions. I've given here a list of the stations, together with the calculated trends (°C/century) and the long term normals. For all calculations I have used annual averages, discarding years with fewer than nine months data. The annual data (unadjusted GHCN V3 monthly from here) that I used is in CSV form here.

The Goddard Fallacy

So Euan's post shows a time series of whetever reported in each year:



And, sure enough, not much trend. But he also showed (in comments) the number of stations reporting



Now what his average is really mainly showing is whether that highly variable set has, from year to year, hotter or colder locations. To show that, as usual I plot the same averaging process applied to just the station normals. This has no weather aspect:



You see the red curve. That incorporates much of the signal that the fallacious black curve includes.

The effect is not as severe as Goddard's, because the stations are more homogeneous. The range of normal variation is less. It can be reduced, of course, by subtracting the mean. That is the green "anomaly" plot that I've shown. It is more regular, but still not much trend. That brings up the anomaly fallacy.

The anomaly fallacy

This is the fault of comparing anomalies using varying base intervals. I've described it in some detail here. If the stations have widely different periods of data, then the normals themselves incorporate some of the trend. And subtraction removes it.

This is a well-known problem, addressed by methods like "common anomaly method" (Jones), "reference stations method" (GISS), "first difference method" (NOAA). I mention these just to say that it is a real problem that major efforts have been made to overcome.

As a quick and mostly OK fix, I recommend using regression fits for a common year, as described here. But the more complete method is a combined regression as used in TempLS (details here)
Update - to be more specific, as in the link it is best to do this in conjunction with some scheme for preferring data local to a region. There I used weighting. But to stick closest to the convention of using a fixed interval like 1961-90, my process would be:
1. If there is enough data in that interval (say 80%) use the regression mean over the interval
2. If not, then extend the interval to the minimum extent necessary to get 30 (or 24) years of data.

The anomaly fix

So I've done a combined regression average:



It's clearly warming since about 1940. And by about a degree.

Other evidence of warming

The station trends over their observed periods are almost all positive. So they are over a fixed period. Here, from the active trend map is a snap of trends in Australia since 1967:



Plots of the station data are somewhat obscured by noise. From Climate Etc:



It is rising. But a modest degree of smoothing - a 9 point triangular filter, gives:



The uptrend is now unmistakeable.