# Expected deviation and uncertainty for a number of environmental measurements

I have a couple of measurements for an environmental variable on different locations (7 measurement stations) as time series with averages for every year.

For the single locations I have calculated the deviations of single years from the long term average. The annual deviations are not normally distributed as there are trends in the data. I cannot describe these trends as I have not enough knowledge about the influences. Further more the data for the single locations show different trends because of local influences. Also the absolute hight of the measurement value is different for the single locations (by more than 10% in the long term average).

To get an idea on how the locations compare to each other I calculated the relative root mean square deviation of the single years from the long term average and the 5th and the 95th percentile of the relative deviations to get an symmetric coverage interval for the uncertainty at the 90% level.

My results look as follows:

location  RMSD[%] P5[%] P95[%]

1         3.8      -5.6   -1.3
2         3.1      -5.1    5.2
3         5.1      -0.6    8.6
4         3.3      -6.2    3.6
5         3.8      -6.7    1.8
6         2.8       0.2    4.0
7         3.7      -6.1    3.9


I want to get an estimate of the expected deviation of a single year from the long term average and the uncertainty of the deviation for an arbitrary location in the region the measurements are taken from.

What would be a statistically valid way to do this? I am thinking about using the average over all measurement locations I have, but as the locations are a lot different from another, I am not sure if this is ok.

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