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Open Mind: Combining Stations

February 8th, 2010

On a non-climate note, I congratulate the New Orleans Saints for their victory in Super Bowl XLIV. It was a well-deserved victory for the underdogs, and is a source of pride for a city which still shows massive scars from the ravages of Hurricane Katrina.

We’ve already looked at a way to combine data from different locations to obtain a grid-wide average of station anomalies. In that post, I computed anomalies for each location then combined the anomalies. It’s also possible to combine raw temperature data, then compute anomalies for the grid averages. I also combined station records in a simple way, by starting with a “reference station” then adding one new location at a time, computing an offset to align it with existing data and then incorporating it into the average. But I’ve noted that this is not the “optimal” way, that optimally (in a least-squares sense) one would compute the offsets which give the minimum sum of squared differences between all stations.

Read the rest of the post at the source…
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This comment was posted on Tamino's ironically named blog on February 13, 2010:

ReplyDelete=======

You don’t seem to get a lot of technical observations from your regular commenters in a thread such as this so I thought I might offer some comments about the method you are using to estimate the “offsets” for each station.

I don’t know if you are aware of it, but the “optimal” method appears to be a disguised two factor weighted analysis of variance. One factor is the stations (whose coefficients are the “offsets”) and the second is time (in this case months) treated as a numeric variable. This is not immediately obvious from the form in which you formulated the sum of squares that you are minimizing, but some fairly simple algebra can re-express that SS in a way which is more obviously consistent with an anova. The weights for a given temperature measurement are proportional to the number of stations which have available data for that month. I would have run some comparisons for your example in R, but your aversion to posting data and code makes that more difficult. However, I wrote a simple R program for calculating the offsets as well as some scripts for the anova and ran them on randomly generated data with identical results for both methods.

The side benefit of this is that the estimated monthly grid values are calculated simultaneously with the offsets rather than as (possibly sub-optimal averages) of the offset adjusted temperature series. Variability estimates can also be computed more easily as well.

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One might expect that a technical comment about a technical post might actually not be inconvenient, but then, you never know...

I have some discussion on this at my blog here:

http://statpad.wordpress.com/2010/02/13/rejected-again-open-mind-isn’t/

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