How closely correlated are two weather stations? (warm, records, temperature)

[nei]

As in if one weather station is running above average, will a distant one in the same region also be above average? Started thinking about this from a post on tamino's blog:

A Tale of Two Cities « Open Mind

Compares Oxford and Paris, their trends match very well. (takes a few seconds to load)

Explains why for taking a global or national temperature average, long distances with poor weather station coverage might be ok, at least for finding the anamoly (you might get poor results for the absolute number due to poor station siting or a bad thermometer, but the fluctations should still be ok). If I have time, I might do a similar analysis for other places. For example how well can I guess the monthly average of NYC just from Amherst's numbers? Are there places where the correlation is low over shorter distances?

[nei]

Each point in the graph is a different year (July or January) with the Amherst departure from the mean on the x-axis and the New York City departure from the y-axis. You can see from the July graph that if it's warmer than usual in Amhest, it's very likely warmer than usual in NYC, but the relationship isn't tight. But the relationship is there, there's instance when Amherst is say, 2°F below normal and NYC is above normal. The July average for Amherst is 71.23°F and 76.35°F for New York City Central Park. The equation on the chart shows on average New York City varies by a little less than Amherst: if Amherst is 1°F warmer than usual, on average New York City will be only 0.77°F warmer.



The January relation shown below is much tighter. Interestingly for very cold months, the relationship breaks down. 2012 was 5.2°F above average in Amherst and 5.0°F above average in NYC. Both 1998 and 2002 had warmer Januarys (in both places). The chart would be more complete if I added other winter (or summer) months.

[Weatherfan2]

This all looks very complicated to me but I often compare my PWS numbers with a nearby met office official station, Leek Thorncliffe. About 10 miles away, and at 300m, slightly lower than me. My numbers, specially avg. max are very very close.

For example my daily highs for July vs Leek Thorncliffe (on the right), this difference is typical in any month.

My House - Met O Leek Thclf.
13.9 - 14.8
14.9 - 15.3
15.8 - 16.5
18.5 - 19.5
20.2 - 21.6
16.1 - 15.9
19.2 - 19.7
19 - 19.4
15.3 - 15.5
13.9 - 13.5
14.4 - 14.7
17.2 - 17
12.8 - 12.9
16.1 - 16.4
15.3 - 15.7
15.1 - 15.1
18.6 - 18.3
19.1 - 18.8
14.3 - 14.9
13.3 - 14.9
17.3 - 17.7
21.2 - 21.2
23.6 - 22.9
25 - 26.1
21.8 - 22.5
22.7 - 22.9
18.3 - 17.7
16.7 - 16.5
15.6 - 15.1
14.9 - 14.2
15.3 - 16

Avg: 17.3°C - Avg: 17.5°C

Now that's accurate for 10 miles distance.

Avg Max Differences for other months

Me - Leek

J: 6.0°C - 6.4°C
F: 5.4°C - 5.2°C
M: 11.5°C - 11.2°C
A: 8.7°C - 8.9°C
M: 15.1°C - 14.8°C
J: 15.0°C - 15.1°C

[ilovemycomputer90]

Is that forumula related to standard deviation? I should pull out my college stats textbook to refresh my memory on this stuff.

[owenc]

I don't know but my local weather station is on average 3c different to mines because it is on the coast. It always records higher mins and lower maxes in the summer.

[nei]

Originally Posted by ilovemycomputer90

Is that forumula related to standard deviation? I should pull out my college stats textbook to refresh my memory on this stuff.

Hmm. Maybe I didn't explain myself well. What did for the Amherst - NYC graphs is find the mean of both places (for either Jan or Jul) and then subtract each year from the mean to get the deviation from each year. So let's say in one year Amherst was 3°F above average and NYC 2°F above average. Then there would be a point for that year 3 units to the right (x-axis) of the graph center and 2 units up (y-axis). Each point on the graph is a different year.

The equation is the equation of the best fit line, the number times x is the slope of the black line on the graph.. The r^2 value is the square of the correlation coefficient, which describes how well the data fits the line. 1 is a perfect fit, 0 means there's no connection. The formula is connected to standard deviation but the same thing. This page gives an explanation:

R-squared

2nd half is the more important part.