Precipitation reduction during Hurricane Harvey with simulated offshore wind farms

The model domain is set up to cover the coast of Texas and Louisiana, as shown in figure 1. The horizontal resolution is Δx = Δy = 10.667 km. The initial and boundary condition data are taken from the North American Mesoscale Forecast System with a resolution of 12 km. The model is integrated for four days from 0000 UTC August 25, 2017 to 0000 UTC August 29, 2017 with a 6 hour spin-up. The 1.5-order, 2.5 level MYNN PBL scheme (Nakanishi and Niino 2009) is selected since the wind farm parameterization is dependent on this scheme and it is widely used in the literature (Fitch et al 2013, Volker et al 2015, Eriksson et al 2015). The Kain–Fritsch convective parameterization scheme (Kain and Fritsch 1992, Kain 2004) is used to predict the convective component of precipitation and the land-surface model is Noah (Ek et al 2003). The details of the simulation setup are presented in table 1.

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The wind farms are modeled using the Fitch wind farm parameterization (Fitch et al 2012), which models the wind farms as a momentum sink and an added turbulent kinetic energy (TKE) source. The magnitude of the drag force on the atmosphere induced by one wind turbine can be expressed as:

$$\begin{equation} F = \frac{1}{2}C_T (V)\rho V^2 A, \end{equation} \tag{ 1 }$$

where V is the horizontal wind speed over the disk, C_T is the thrust coefficient, ρ is the air density, and A is the disk area swept by the turbine rotor. The rate of loss of kinetic energy in the wind $\frac{{\partial KE}}{{\partial t}}$ is therefore:

$$\begin{equation} \frac{\partial KE}{\partial t} = \frac{1}{2} C_T (V)\rho V^3 A. \end{equation} \tag{ 2 }$$

The extracted kinetic energy in the wind goes into the electric power (via a power coefficient) and additional turbulent kinetic energy (via a TKE coefficient). The energy losses induced by heat via friction and mechanical losses are ignored. Note that the wind turbines in the Fitch parameterization correctly extract kinetic energy in a manner that depends on the thrust coefficient, which is a function of wind speed (C_T (V)). As such, no energy is extracted at wind speeds below the cut-in or above the cut-out wind speeds, as real turbines do. If the wind at a grid cell reaches or surpasses the cut-out wind speed during a hurricane simulation, then the turbines are effectively shut down at that grid cell.

The other approach employed to parameterize the wind farms is to increase surface roughness, which was first introduced by Keith et al (2004). Although the surface roughness parameterization is overly-simplified, as wind turbines extract energy not near the surface, but rather around the rotor disk, it is computationally efficient and therefore has been used extensively in large-scale simulations of wind farms (Kirk-Davidoff and Keith 2008, Barrie and Kirk-Davidoff 2010, Wang and Prinn 2010, Miller et al 2011). In this study, the surface roughness parameterization is used to model a supplemental case for sensitivity purposes, aimed at demonstrating that the conclusions derived from our study are robust and do not depend on the exact implementation of the wind farm parameterization.

A control case with no wind farms, denoted as CTRL, is run first. The CTRL case is set up to ensure the accuracy of the simulations and highlight the precipitation differences induced by the turbines under the same model configurations. Five additional cases with different layouts are run next (details in table 2). For all cases, turbines are installed in waters up to 200 m in depth, due to the technical difficulty and high construction costs in deeper water areas. The wind turbine model is the 7.5-MW Enercon 126 with a diameter D = 126 m and cut-in and cut-out wind speeds of 3 and 34 m s⁻¹ respectively. To study the best wind farm location, three basic cases (LWF, MWF, SWF for large, medium, and small wind farm), shown in figure 2, are modeled that cover differently sized offshore areas, but with the same inter-turbine spacing. Two additional cases cover the same areas as MWF, but with tight (MWF-TS) and wide (MWF-WS) inter-turbine spacings. For all the wind farm cases except SWF, all the turbines were placed along the coast, ranging from the coastline to 100 km offshore (including the bay areas). The SWF case is similar to the MWF case, but only the turbines within the commercial lease zone from the Bureau of Ocean Environment and Management (BOEM) are modeled, in order to avoid the non-construction areas and achieve a more realistic configuration. A supplemental case (MWF-Z0) is modeled with the same setup as MWF but with an increased surface roughness z₀ = 0.5 m over the turbine areas. The surface roughness value was determined via a series of tests, as described later in section 3.2.

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To ensure the accuracy of the simulations, with and without wind farms, the results of the CTRL case (without wind farms) are compared with the observations, including hurricane track, minimum sea level pressure, maximum wind speed, and precipitation. The precipitation data are provided by the Harris County Flood Warning System (2017), and other observations data are from the National Hurricane Center (NHC) accessed from The Weather Company (2017).

The simulated track of Hurricane Harvey agrees well with the observation data prior to August 29, 2017 and is slightly off afterwards (figure 1). Considering that the rainiest days for the metro-Houston area were before August 29, only the results of the first four days will be analyzed in this study. The time series of simulated maximum 10 m wind speed and minimum sea level pressure during the four days prior to August 29 show a good level of accuracy when compared against observations from NHC data, especially considering that no observations were assimilated into the simulation (figure 3). The modeled minimum sea level pressure (figure 3(b)) generally follows the trend of the observations, except for an underestimate at the time when the hurricane was strongest. However, the timing of the lowest minimum coincides almost perfectly with the observations.

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In order to validate the precipitation predictions, simulated values were extracted at a grid point located downtown Houston from the model domain. Data from 15 gauges from Harris County Flood Warning System (2017) located within the downtown grid point were averaged to make the simulation results and observation data comparable. The simulation results generally underestimated precipitation (figure 3(c)), but most of the time the results are within the error bars. The timings of the two peaks between August 27 and 29 are both close to the observed. The discrepancy between the model results and the observations is possibly due to the lack of vortex initialization and data assimilation, which have been proven to improve the accuracy of the cyclone track and intensity (Kurihara et al 1995, Wang 1998, Cavallo et al 2013, Zhang et al 2009, Zhang et al 2011, Hamill et al 2011) but cannot be used for sensitivity runs as those conducted in this study. Although the magnitude of the prediction is slightly off from the observations, the general trend of the results matches. Thus, the CTRL results can be used as a reference state to further evaluate the impacts of the wind farms.

The wind farm parameterization correctly extracts kinetic energy at the wind farm locations, as shown by the horizontal distribution of wind speed at hub height at 0900 UTC on August 25, 2017 (figure 4). For the same farm, the wind speed reductions depend on the density of turbines. For example, higher wind speed reductions (and therefore higher energy generation) are achieved in the MWF-TS than in the MWF or MWF-WS cases, due to the higher number of turbines (59 312 vs. 33 363 and 22 242, respectively).

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From figure 3(c), the largest precipitation amounts occurred during the last three days (August 26 to 29) and therefore this time period is selected for further analysis. Looking at 72 hour accumulated precipitation patterns (figure 5), both areas with increased precipitation and areas with reduced precipitation are found due to the presence of the wind farms, but not in a random manner. Rather, increased precipitation is found mostly offshore, upstream of or within the wind farms, while reduced precipitation is found onshore or close to the coastline, downstream of the wind farms. Considering the damage caused by precipitation and flooding in the metro-Houston area, this coherent pattern of reduced precipitation onshore suggests that huge potential benefits, in terms of avoided damage and lives saved, could be harnessed by installing large offshore wind farms in the Gulf.

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Compared with the MWF case (figure 5(c)), the LWF case (figure 5(b)) produces very similar changes in precipitation patterns, especially along the coast near Houston, even though the latter covers a much larger area and has more than twice the number of wind turbines. The physical mechanisms behind this finding will be explained in the next paragraph, but for the moment it can be concluded that an array of wind farms as large as that in the LWF case is not necessary since it produces little improvement in the benefits with much higher costs than the MWF case. This is the reason that the sensitivity tests to inter-turbine spacings in section 3.2 will be based on the MWF case.

To better quantify the changes in precipitation, a sector covering south Houston (−95.7° W to −95.2° W and 29.5° N to 29.8° N) is selected for further analysis. The simulated precipitation amount is averaged over this sector. The reduction in the 72 hour accumulated precipitation (see table 3) is approximately 15% for both the MWF and LWF case. For the SWF case, the reduction is only about 10%, which suggests that the wind farms placed in the Galveston Bay areas, missing in SWF, could be of great importance for the city of Houston.

The hypothesis put forward here is that changes in precipitation—increases offshore and decreases onshore—are associated with changes in horizontal wind divergence and in vertical wind speed caused by the wind farms. To verify this hypothesis, the difference between these two terms in the LWF case minus the CTRL case at landfall are shown in figure 6. To the northeast of the hurricane center, the wind is blowing from the sea towards the land. In these areas, the horizontal wind divergence difference (LWF minus CTRL in figure 6(a) is negative upstream of the wind farms, as the wind slows down because of the presence of the wind farms, and is positive downstream of the wind farms, as the wind speed recovers past the wind farms. Correspondingly, the vertical wind speed difference (figure 6(b)) is positive upstream of the wind farms, meaning that upward motion is enhanced and therefore precipitation is increased, and negative downstream of the wind farms, meaning that upward motion is suppressed and therefore precipitation is reduced. To the south of the hurricane center, the wind is coming from the shore, so changes in the horizontal wind divergence and vertical wind speed are opposite to those to the northeast of the hurricane center. However, over the entire 3 day period, no substantial changes in precipitation were found in these areas.

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To assess the sensitivity to inter-turbine spacing and parameterization formulation, the focus of this section will be on the 24 hour accumulated precipitation from 26 to 27 August 2017, during which the winds were strongest and the effects of the wind farms on precipitation were more pronounced (figure 5(c) vs. figure 7 (a)). From the 24 hour accumulated precipitation difference between the wind farm cases with various inter-turbine spacings and the MWF case with no wind turbines (figure 7), obvious precipitation reductions onshore can be noticed. The compact case (figure 7(b)), with more turbines than the MWF case (figure 7(a)), exhibits a stronger reduction in precipitation inland and a stronger increase in precipitation offshore and over larger areas. Vice versa, in the wide-spacing case MWF-WS (figure 7(c)), the precipitation changes are qualitatively the same, but smaller in magnitude and areal extent.

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In addition to the wind farm cases modeled with the Fitch wind farm parameterization, case MWF-Z0 was run with a different treatment of the effect of the wind farms, namely, an increase in the value of surface roughness z₀ only over the wind farm area. Although overly simplified, as wind farms are elevated, not surface-based, drag elements (Fitch et al 2013, Jacobson and Archer 2012), increasing surface roughness is a treatment of wind farms used in many studies in the past (Keith et al 2004, Kirk Davidoff and Keith 2008, Barrie and Kirk Davidoff 2010, Wang and Prinn 2010, Miller et al 2011). There is not a well-established method to determine by how much surface roughness should be increased to better represent the effect of wind farms. In the literature, a series of values ranging from 0.12 m to 3.4 m values have been proposed (Calaf et al 2010, Wang and Prinn 2010, Jacobson and Archer 2012, Fitch et al 2013). Here we tested several values between 0.2 m and 0.8 m and compared the resulting wind speed profiles averaged over the wind farm area to identify which gave a distribution of wind speed around hub height that was closest to that of the MWF case. The selected value of surface roughness is 0.5 m and the case is named MWF-Z0.

Results from MWF-Z0 confirm that precipitation is reduced inland and increased offshore, with a spatial pattern overall similar to that of the previous cases (figure 7(d)), although closest to the results from the case with tight inter-turbine spacing (MWF-TS in figure 7(b)) in terms of magnitude. This suggests that using an increased value of surface roughness may exaggerate the effects on precipitation overall, although the spatial distribution of the precipitation change was such that the Houston area was less affected with MWF-Z0 and SWF than with the other cases. At the same time, the comparison against the MWF-Z0 results was useful because it confirmed that offshore wind farms can impact the precipitation distribution during a hurricane such as Harvey regardless of the details of the wind farm parameterization used. Note that the idea of treating offshore wind farms as increased surface roughness is consistent with treating them as an 'extension' of the land into the ocean. Previous studies (Ogino et al 2016, Ogino et al 2017) have found precipitation maxima along the coast during tropical storms, where convergence occurs due to the slowing down of the winds, consistent with the precipitation enhancement found here upstream of the offshore wind farms.

To highlight the sensitivity of the precipitation to different layouts and parameterizations, table 3 shows a summary of the precipitation reduction of all the cases in the sector covering south Houston, described previously in section 3.1. The LWF and MWF simulations achieve almost the same benefit (∼15%), despite the fact that the LWF simulation includes more than twice the number of turbine of MWF. Increasing the number of turbines in the same area as MWF causes a larger reduction in precipitation (MWF-TS: 21.17%) and, vice versa, decreasing the number of turbines causes a smaller reduction (MWF-WS: 12.08%). Although the MWF-Z0 case shows a stronger precipitation reduction than MWF inland (figure 7), the percentage of precipitation reduction in the Houston area is lower than that of MWF (10.41% vs. 15.29%). The SWF case has the lowest precipitation reduction in all the cases (9.54%), which is possibly due to the absence of turbines in the Galveston Bay.