Actually looking at some of the environmental information.
It seems as if there is a problem with poor fit of trend lines on periodic, or partially periodic functions.
I think some kind of a least-squares trend line is typically used. These calculations are based on the Slope() and Intercept() functions in OpenOffice.
To illustrate some of the problems, here are a couple of basic functions.
Plotting a trend line to a sine wave.
If I plotted for 0 to 1800 degrees (5 complete cycles), starting on a peak and ending on a valley, I got a really bad match (orange line)
I got a reasonably good match for the slope, but was off on the average/intercept if I plotted from 0 to 1620 (5 peaks, 4 valleys), or 180 to 1800 (4 peaks, 5 valleys).
The best match was plotting from peak to peak or valley to valley. (90 to 1530, or 270 to 1710).
Anyway, so choosing the end points is very important.
Then, I decided to try a sawtooth function (up slope, 10/8, down slope -10/2)
It turns out that it is very hard to get a good match for the trend line (which should have 0 slope, average of 5).
With the exception of starting on a peak and ending on a valley, the majority of the trend lines have a positive slope.
I suppose my problem is that if can't match a trend line to a simple geometric function... how can I trust matching it to natural systems.
Suggestions?