idealized demonstration

Idealized data demonstration for Windfarm Precip Project

produced by: Dr. Brian Fiedler

We take the control case and make a bogus difference field with the difference rainfall consisting of white noise (thus with zero true mean for an infinite sample) plus a signal of 1/50 the amplitude of the noise. The signal is the product of a sinuoid in the vertical and horizontal. The signal has fixed spatial stucture, but random variation in time, with standard deviation equal to the mean which is non-zero (2 mm, in fact).

Here is the mean rainfall difference over 62 years. Note the slight enhancement (blue) in the NE and SW and the slight diminishment in the SE and NW:

Here is the t-test of the 62 sample time-series that was used to make the previous plot:

Here is the time series comparison in the center of the red box. No confidence that the true mean is not 0:

Here is the time series comparison for the average rainfall within the red box. The sample mean is 1.154: Note the t-value "tval" and fraction of domain covered by red box "f" and the two-tailed p-value "2p":

Same as above, zoomed in. We can calculate 90% confidence the true-mean will be between 0.405 and 1.904:

Unlike the windfarm project, we know exactly what the climate signal is in this bogus data:

Zoom of above. Note the signal has a mean of 1.516, which is in the middle of the 90% confidence interval predicted for it when it was embedded in noise.

If the windfarm does effect the climate of rainfall, we expect the size of areas impacted to be comparable to the area of the wind farm, rather than isolated grid points. If that will be the case, the statistical method of averaging rainfall over an area is justifiable to find the climate signal. There is nothing new or amazing about this demonstration. The method employs a low-pass filter.

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False alaram

Let's check that our method doesn't find a signal where there isn't any.

Let's check the magentabox, which straddles the positive and negative signal.

Here is the time series comparison in the center of the magenta box. No confidence that the true mean is not 0:

Here is the time series comparison for the average rainfall within the magenta box. The sample mean is -0.174: Note the t-value "tval" and fraction of domain covered by magenta box "f" and the two-tailed p-value "2p":

Same as above, zoomed in. We can calculate 90% confidence the true-mean will be between -0.923 and .574:

Unlike the windfarm project, we know exactly what the climate signal is in this bogus data:

Zoom of above. Note the signal has a mean of 0., which is in the middle of the 90% confidence interval predicted for it when it was embedded in noise.