MKing: How is anyone supposed to determine statistical significance of a trend if you haven't figured out the natural variation the trend is hiding within? You see, if you claim a mean trend of +0.3C or something (the signal), it becomes a bit unbelievable if the uncertainty around the mean from which the trend is drawn is +/- 5C (the noise).

We must be homing in on why we are at cross-purposes, because I still don't get what you are worried about.

I'm not worried about anything. Are you not familiar with exploratory data analysis, or forensic statistics?

I trying to establish A) the size and shape of natural variability in temperature data at a single station, B) the size and shape of the uncertainty around the mean that this natural variability leads to, C) the correlation between the movement of those means at multiple stations across a wide area, and D) assuming C) is true, the distance at which C) holds true.

Think of it like a semi-variogram, I am trying to find the kernel and sill for temperature.

I realize that this is all probably Climate 101 stuff to the climate guys, but amazingly I haven't been able to find such basic analysis, only the conclusions and results of heaps of correlations between huge blocks of area.

Sure the T(annual mean) data has a lot of noise in it, and T(daily mean) would have a lot more, but so what?

Calculate the uncertainty around the mean with, and without correlation, and the range of uncertainty changes. That matters when you are trying to find a signal of +0.3C and your confidence interval is +/- 5C. Or worse.

As long as the trend type chosen (linear, sum of differences or sum of square of differences) is sensible for the dataset being studied,

and the number of data points in the data set is sufficiently large, which it is,

I don't see how those evil climate scientists could be putting a spin on the trend.

The establishment of statistical significance comes before claims of validity.

I can enter what I want at the NOAA website, but it doesn't have a "Download" button or an "add to cart" button, so I am still without the data.

NOAA has a WONDERFUL way of collecting the data. After you find what you are interested in (I can provide the station ID for Aberdeen ID if you need it) you do add it to the cart, and then you go to the cart, choose what you might be interested in (I just collect temperature data) and provide an email address. They then email you a link when the product has been assembled into a CSV file, and provide you a link in the email. You then download your data.

Collected a 100MB download the other day to begin assembling a profile for Idaho using stations that have long consistent strings. Using 25+ stations, I now have distributions for every day for the past century for Idaho..can't figure out how to show 36,000+ distributions in one shot though. It's about 1 million data points, might have some software issues whenI try and do the entire Pac NW.