collaborators: Dr. Brian Fiedler, Dr. Melissa Bukovsky, Dr. Manda Adams, David Sherman (funding for David Sherman provided by EPRI)
Suppose a giant windfarm is constructed to supply 20% of the electricity in
the USA, consistent with the plans of DOE.
Here is a simulation with WRF, nested within NNRP data.
62 years of warm seasons were simulated, both with and without a giant wind farm.
The grid spacing was 30 km, with the MYJ boundary layer
and the KF cumulus precipitation (which produced the bulk of the precipitation). The
parameterized wind farm ranged from the Texas panhandle to northern Nebraska, covering
182,700 square kilometers with 1.25 turbines per square kilometer, for a total of 228,375 wind
turbines. The parameterization was developed by Adams and Keith (2009). It
includes both elevated wind drag at the height of the rotor and the generation of TKE. The
parameterized wind turbines are based on a Bonus 2.0MW turbine with a 60 m hub height and a
76 m rotor diameter resulting in an installed capacity of .457 TW.
Summary plot of precipitation climatology
For some readers, this plot may be all that is needed:
1948
Now some more details. We first look at one warm season, 1948.
Wind speed at second level (approximately 130 m) WITHOUT WINDFARM:
... WITH WINDFARM:
Wind speed WITH minus WITHOUT: What effect might the wind farm
have on the precipitation?
Note below the 24 precipitation difference over 1948-07-16.
The wind farm has shifted a storm track northward in Nebraska,
and caused a storm to appear over Indiana-Ohio, that otherwise did not exist.
Below is the entire 1948 warm season precipitation difference.
The above storm tracks that occurred on the day 1948-07-16
contribute substantially to the seasonal difference along the storm track.
A small wind farm can also have a big influence on downstream weather and precipitation.
See the small wind farm covering 60 x 60 km in the Texas panhandle. The average power production for the small wind farm was 1.5 GW.
Same as above, but a tiny wind farm covering 30 x 30 km in the Texas panhandle. The average power production for the tiny wind farm was 0.46 GW.
The WRF integrations are being run on a dual-core I5 desktop Linux box. The "with" and "without" integrations are being run out of separate directories. Perhaps a programming error, such as a difference in a configuration file is causing the difference? Let's set the wind farm size to be zero in the "with" directory. Happily, there is no difference
between with and without for that case:
62 warm seasons
What happens if we collect simulated precipitation forecasts for 62 years of warm seasons (May thru August)?
Does the modeled wind farm effect the modeled precipitation climate?
The plot below summarizes the 62 year precipitation difference, ("with"-"without")/"without":
At every model grid point, the seasonal total precipitation provides a data value in two time series of
62 data values: a time-series with the wind farm and a time series without the wind farm.
A single time series is formed from the difference. A single-sample t-test is then performed on the
difference, to check the confidence that the mean value is different from 0. Here is plot of the
t-values, where t-value=sqrt(62) * mean/std :
An analysis of the above three plot does not show any
compelling evidence that the presence of individual points with high t-values is
due to anything but the limited sampling of 62 years. So we look deeper, and
average rainfall over areas of interest (a low-pass filter). The effectiveness of the averaging
is shown here on bogus data.
Next we calculate a time-series of the area-averaged precipitation within the three indicated boxes, and
one isolated point. Those four time series are shown below. Here is the time series data.
The t-values on the area-average can be much greater than the area-average of the t-values.
For the time-series of the area-average precipitation in the red box,
we find a t-value of 4.71, which is much larger
than the average t-value .555 for the time-series of individual grid points within the red box.
The student's t-test gives with t=4.71 and 61 degrees of freedom gives a one-sided p=.000008
The fraction of the total area within the red box is f=0.11. Thus f/p=13,750 . So
that facts give a confidence of 0.99993 that the 1.0% precipitation enhancement is not due to chance.
Confidence interval analysis gives 90% confidence that the true mean is between 0.6% and 1.3% enhancement.
A resampling with replacement analysis of 10,000 resamples of
the above data gives 90.0 % confidence that the true mean is between 1.49 mm and 3.09 mm, or exactly as with the assumption of a normal distribution: 0.6% and 1.3% enhancement.
Normalized histogram and gaussian for above difference time series:
Autocorrelation of the above difference time series, compared with a bogus random series:
Next is a time series of an individual point with high t-value,
within the southern most small magenta speck in the state of Arkansas.
Being an individual grid point,
the fraction of area is small, and the student's t-test yields f/p<1.
In the Gulf of Mexico,
there is a paired region of enhanced and diminished precipitation.
The time-series for a region within the white box shows that the difference is dominated by the wind farm
suppressing two monstrous precipitation events in that locale.
The time-series is decidedly non-Gaussian and the student's t-test does not formally apply.
Nevertheless, we are left with little confidence, formal or otherwise, that this study with 62 warms seasons
is revealing the pattern in the Gulf of Mexico consistent with an infinite number of warm season experiments.
Similarly, in the area within the magenta box north-east of the wind farm,
in South Dakota and Minnesota, we do not find confidence
that the observed diminution of rain is for reasons other than chance.
Why no drought? The average rainfall in the entire domain is increased, though the f/p value is not nearly as impressive as the red box.
Boxes with drought will be harder to find.
Some more 62-year climatology
Rainfall plots for the 62 years
Left: total warm season precip in a year. Right: average warm season precip to that year.
