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GFDL AGCM: Wind Farm Experiments

All experiments were performed with GFDL AGCM version AM2p10, with prescribed SST. This is a B-grid model with resolution 2.5 degrees longitude by 2 degrees latitude, 18 layers in vertical.

wfarms1.nonclimo.10m
This experiment was performed with non-climatological (interannually-varying) sea surface temperature (SST), from 1982 to 1998. The map of the wind farms used in this case is shown on the figure to the right (click to get a bigger picture). The total area covered by wind farms in this case is about 0.3%
To parameterize the influence of the wind farms, the surface roughness for momentum over wind farm sites was set to 10m; the ratio of momentum roughness to heat/tracer roughness was kept constant (about 7.3)
Here are some seasonal and annual-mean results of the run: wfarms1.nonclimo.10m.pdf, wfarms1.nonclimo.10m-zonal.pdf. The plots show the difference between the numerical experiment and the control run, averaged over 16 years (1983-1998, the first year of the run was thrown away from analysis as a spin-up year). The area where the difference is statistically significant with 95% level of confidence is hatched. The numbers above each plot indicate the percentage of grid points where the difference is statistically significant.
The total kinetic energy dissipation on the surface in this case increased by 4.26e12 W compared with control run.
wfarms1.nonclimo.03m
Same as above, except windfarm roughness for momentum was set to 3 m.
The results are here: wfarms1.nonclimo.03m.pdf, wfarms1.nonclimo.03m-zonal.pdf. Kinetic energy dissipation increase is 1.46e12 W.
wfarms2.climo
In this experiment the map of the wind farms was different (see figure to the right), and the surface roughness for momentum was set to 5 m over wind farms. The total area of wind farms in this map is close to 1% of the total area of Earth.
In addition, climatological (that is, not varying from year to year) SST was used.
The simulation ran for 21 years, and again first year was thrown away from the analysis as a spin-up year.
The results are here: wfarms2.climo.pdf, wfarms2.climo-zonal.pdf. The differences and significance numbers are calculated relative to the similar control run (that is, the run with climatological SST). The total kinetic energy dissipation on the surface in this case increased by 4.87e12 W compared to control run.
wfarms2.nonclimo
Same as experiment wfarms2.climo above, except interannually-varying SST was used instead of climatological.
The results are here: wfarms2.nonclimo.pdf, wfarms2.nonclimo-zonal.pdf. The total kinetic energy dissipation on the surface in this case increased by 4.8e12 W compared to control run.
wfarms2.climo.drag
Same as experiment wfarms2.climo above, except parameterization of wind farms was different.
Instead of specifying equivalent surface roughness, an attempt was made to represent drag produced by wind farms directly. Each turbine was assumed to be a 100-m diameter circle with its hub at 100 m above the surface, taking 0.4 of kinetic energy of resolved flow away from it. The turbines work only if wind is stronger than 1 m/s. The spacial density of wind farms was assumed to be one wind turbine per square kilometer, with turbines always facing the wind.
The results are here: wfarms2.climo.drag.pdf, wfarms2.climo.drag-zonal.pdf. The total kinetic energy dissipation on wind farms in this case is 3.7e12 W, which means about 0.63 W/m2 over surface of wind farms on average. The maximum of resolved kinetic energy dissipation is close to 2 W/m2, which, given spacial density of one turbine per square kilometer, corresponds to 2MW generated by a turbine.
wfarms9.climo.drag

This experiment uses yet larger wind farm coverage map, shown in the picture to the right, and almost the same parameterization as the wfarms2.climo.drag experiment above. The only difference is that the spacial density of wind mill was set higher, 1 per 36e4 m2 (1 turbine per 600 m). The density was increased to tune up the dissipated energy to be approximately 20 TW. The wind farms cover about 3% of Earth surface. The results are here: wfarms9.climo.drag.pdf, wfarms9.climo.drag-zonal.pdf. Here are some plots of the geopotential hight response: wfarms9.climo.drag.dyn.pdf.
The simulation ran for 21 years, and again first year was thrown away from the analysis as a spin-up year.
Total kinetic energy dissipation in this experiment is 18.1e12 W, max annual mean value is about 2.4 W/m2, while average is about 0.94 W/m2.
wfarms9.climo.rough
The same wind farm map as in previous experiment (wfarms9.climo.drag) with the parameterisation of the wind farms through the increase of surface roughness, similar to the experiments wfarms1.nonclimo.10m and wfarms1.nonclimo.03m. However, in this case the wind farm surface roughness was not prescribed directly: rather, it was calculated based on prescribed increase of neutral drag coefficient, as decsribed in David Keith's notes of April 6, 2003. In this run the increase of dimensionless drag coefficients for both heat and momentum was prescribed to be 0.03.The results are here: wfarms9.climo.rough.pdf, wfarms9.climo.rough-zonal.pdf. Here are some plots of the geopotential hight response: wfarms9.climo.rough.dyn.pdf.
The simulation ran for 21 years, and again first year was thrown away from the analysis as a spin-up year.
Total kinetic energy dissipation on wind farms in this experiment, calculated using David Keith's EWIND technique, is 12.8e12 W. In EWIND-type calculations, boundary layer physics runs twice, first with unperturbed roughness and then with increased roughness, and the difference in dissipation is assumed to be disipation due to wind farms. Note that the same wind and stability is used in both cases. Interestingly enough, the total energy dissipation on the surface in this run actually decreased realtive to control run, although not significantly (less than 1% of unperturbed value). The explanation is perharps that the perturbations of the momentum roughness length is modest compared to the previous experiments and therefore changes in dissipation are dominated by natural variability. You can see change in momentum roughness length here, and heat roughness length here.
comparison of 2 members of an ensemble run

This is actually not a result of wind farm simulation, but comparison between two members of the ensemble (that is, the simulations performed with the same model and the same boundary conditions, starting with different initial conditions). This is presented here to illustrate to what degree simulations can different just because of "natural variability" of the model. The results are here: AM2p11.ARC.01-02.pdf.
Note that this simulations were performed with interannually-varying SST, therefore one can hardly expect many statistically significant differences in near-surface values over ocean (just because much of variability is prescribed, not random). The choice of ensemble members for comparison was random.