Observations
Evening Transition Characterization
The near-surface region of the PBL undergoes a transition from convective to stable conditions at least 2 h before sunset (at 2051 LT) on 9 July 2011 (0151 UTC 10 July), with the stability parameter, z / L (where z is height and L is the Obukhov length) changing from negative to positive at 1830 LT (2330 UTC) (Fig. 3a). The value of the surface heat flux \(Q_{H}\) changes sign at the same time (Fig. 3b), while the latent heat flux decreases over time (Fig. 3b). The abrupt collapse of the absolute temporal TKE change (\(\left| {\hbox {d}{\bar{e}}/\hbox {d}t} \right| )\) at hub height (Fig. 3c), which signifies the onset of the transition (Nadeau et al. 2011), coincides with the stability change. The above evidence suggests a distinct evening transition before sunset, consistent with the observations of Grimsdell and Angevine (2002). The differences of z / L and heat fluxes between upwind and downwind sites are trivial, so the downwind stability observations are not presented here.
Wind Speed Deficits and Turbulence Generation
The stability, heat flux, and temporal TKE changes affect the wake behaviour in the evening, as illustrated in the upwind (Fig. 4a) and downwind (Fig. 4b) lidar wind profiles and the differences between them (Fig. 4c). When the PBL undergoes transition from an unstable to a stable state, the wake wind-speed deficit is less likely to extend above the height of the rotor top at 118.5 m (Fig. 4c). Before the transition, convective vertical mixing, initiated by surface heating, leads to relatively uniform upwind wind speeds across the daytime boundary layer (Fig. 4a). When the stable PBL begins to develop, stratification develops in the flow, with lower wind speeds near the surface and greater wind speeds aloft. Stable stratification is initiated at 1900 LT (0000 UTC 10 July), following the evening transition. As the stratification develops, the wind-speed deficit becomes less intermittent over time and is mostly confined to the rotor layer (Fig. 4c).
As with the wind-speed deficit, the turbulence enhancement caused by the wind turbines becomes steady during the evening transition, as evidenced by the upwind TI value (Fig. 5a), upwind \({\bar{e}}\) value (Fig. 5b), downwind TI value (Fig. 5c), downwind \({\bar{e}}\) value (Fig. 5d), TI difference (Fig. 5e), and \({\bar{e}}\) difference (Fig. 5f). From Eqs. 1 and 2, TI represents the variations in horizontal velocities, while the TKE \(({\bar{e}})\) also accounts for vertical velocity deviations. In the case study, both the upwind TI and \({\bar{e}}\) values decrease dramatically when the PBL becomes stable (Fig. 5a, b). After the transition, the downwind TI value is confined to the rotor layer (Fig. 5c), although the increase in the \({\bar{e}}\) value persists above the rotor layer (Fig. 5d). In the wake region, the TKE varies above the rotor layer before and after the evening transition (Fig. 5f), while TI values have no substantial differences above the rotor top (Fig. 5e). This contrast between TI and \({\bar{e}}\) values suggests that vertical velocity variations contribute most to the turbulence enhancement above the turbine rotor layer during the evening transition, consistent with previous wind-tunnel studies (Cal et al. 2010) and idealized LES results (Calaf et al. 2010), which emphasize the importance of the vertical flux stimulated by wakes.
Within the rotor layer, the altitude of the maximum in downwind turbulence enhancement evolves throughout the transition. The height of maximum downwind turbine-induced turbulence generation varies within the rotor layer before 2000 LT (0100 UTC 10 July) and stabilizes at 60 m afterwards (Fig. 5e). On the other hand, no distinct trends emerge regarding the changes in the height of the peak downwind TKE enhancement (Fig. 5f).
Although upwind turbulence intensity declines during the evening transition, the downwind turbulence enhancements within the rotor layer, due to the turbine, remain at the same order of magnitude throughout the evening transition. Our wake observations, recorded at a distance 3D downwind of turbines, differ from the conclusions of Magnusson and Smedman (1994), where the maximum values in turbulence enhancements diminish downwind more rapidly in unstable than in stable conditions. However, their observations, obtained at a distance 4.2D downwind, were only relevant to stable and unstable states and not to the transition period.
Wake Evolution with Heights and Wind Directions
Not surprisingly, wake features in the evening transition respond to subtle variations in the upwind wind profiles. The fluctuations of upwind variables decrease gradually during the transition, with the upwind hub-height wind speed oscillating around \(8\,\hbox {m } \hbox {s}^{-1}\) and fluctuating less frequently after 1900 LT (0000 UTC 10 July) (Fig. 6a). At the same time, the background TI and \({\bar{e}}\) values at hub height also begin to decline steadily (Fig. 6b, c). As the inflow becomes steady after the evening transition, the wake signatures in wind speed, TI and TKE are only observed below the rotor top. In contrast, before the evening transition, these wake signatures appear occasionally above the rotor top (Fig. 6d–f). All three wake parameters vary collectively below hub height after 2030 LT (0130 UTC 10 July). Overall, the maximum wake effects steadily become more distinct within the rotor layer as the evening progresses.
This sensitivity of the height of the maximum downwind wind-speed deficit to atmospheric stability has yet to be examined in the literature. Aitken et al. (2014a) summarized the discrepancy on the altitudes of peak wind-speed deficit among previous investigations, although the role of atmospheric stability was not discussed, since stability was not always quantified in the historical observational studies. Using LES, Bhaganagar and Debnath (2015) characterized wind-speed deficit in two stable scenarios with different surface cooling rates. They concluded that in strongly stable atmospheric conditions, the maximum downwind deficit was found below hub height, while in weakly stable atmospheric conditions, the maximum downwind deficit developed above hub height. The contrast of wakes in different atmospheric stabilities was, nonetheless, not discussed. Abkar and Porté-Agel (2015) hypothesized that the maximum wind-speed deficit occurred at hub height regardless of atmospheric stability, though we have found different results in this case study: the height of maximum wind-speed deficit changes over time as the atmosphere evolves from unstable to stable stratification.
In addition to the change in altitude of the maximum wake wind-speed deficit, the wake also becomes more sensitive to upwind wind direction during the evening transition, likely due to the smaller effect of ambient turbulence on the wake. Upwind wind direction influences the wake parameters across the rotor layer. Additionally, veering, or clockwise turning with height in the wind profile, commences during the evening transition; this veering affects the wake. Before the evening transition, southerly inflow ranges from directions \(176^{\circ }\) to \(200^{\circ }\) and produces the strongest normalized downwind wind-speed deficit centred at \(185^{\circ }\) (Fig. 7a), while the downwind turbulence enhancement is relatively weak in magnitude and thus indistinct (Fig. 7c, e). After the evening transition, both the inflow and the wake start to veer with height. The wind-speed deficit is greatest around \(185^{\circ }\), especially below hub height (Fig. 7b). In the same way, the normalized TI and \({\bar{e}}\) differences demonstrate intensifying wake effects, mainly at and below hub height (Fig. 7d, f). In general, the turbulence enhancements veer with height, and have the greatest values around \(185^{\circ }\). Note that Fig. 7 only illustrates data up to 100 m a.g.l., since the downwind lidar may well sample partial wakes beyond that height. Overall, the wakes veer and become more distinct during the evening transition of 9 July.
Observation-Simulation Comparison
We first evaluate the skill of the WRF model in simulating the evolution of the upwind profiles of wind speed, wind direction, and TKE. Although the maximum absolute error of wind speed at hub height before, during and after the evening transition is \(1.5\,\hbox {m } \hbox {s}^{-1}\), the model captures the temporal trend of the wind-speed profile (Fig. 8a). Even as the error of the wind-direction profile grows over time, the simulation error in the 80-m wind direction is less than \(10^{\circ }\) throughout the evening transition (Fig. 8b). Moreover, the simulated TKE profile and its decline in magnitude during the transition generally agree with the observations (Fig. 8c), with a hub-height maximum error in \({\bar{e}}\) of \(0.18\,\hbox {m}^{2}\,\hbox {s}^{-2}\). Note that the observed TKE is the lidar-measured, 2-min averaged TKE. The WRF-calculated TKE is a mesoscale representation of atmospheric turbulence over the entire grid cell, and as such is not directly comparable to the observations, but is shown for reference in Figs. 8c, 9c.
Likewise, the comparison between modelled and observed time series further supports the claim that the WRF model is capable of simulating the upwind condition. The mean absolute errors between the simulated and observed time series of hub-height wind speed, hub-height wind direction, hub-height TKE (\({\bar{e}}\)) and surface heat flux \(Q_{H}\) on 9 July are small, being \(1.1\,\hbox {m } \hbox {s}^{-1}\), \(7.7^{\circ }\), \(0.17\,\hbox {m}^{2}\,\hbox {s}^{-2}\) and \(21\,\hbox {W } \hbox {m}^{-2}\), respectively (Fig. 9). On the other hand, the timing of the simulated atmospheric stability change is within 1 h of the actual change: \(Q_{H}\) changed sign at 1755 LT (2255 UTC) in the WRF model, 35 min earlier than that observed. However, the simulated hub-height TKE experiences abrupt decay at the same time as that observed, 1900 LT (0000 UTC 10 July) (Fig. 9c). Overall, the WRF model produces satisfactory background flows for this 9 July case study.
Simulations with the WFP Scheme
Downwind Meteorological Impacts
Via the WFP scheme, virtual wind turbines are introduced in the 9 July WRF model simulation to characterize the evolution of wake effects during the evening transition. Wind-speed deficit, calculated by subtracting the horizontal wind speed of the “control” run with no virtual wind turbines from that of the “WFP” run with virtual turbines, is the primary method to quantify wind-farm wakes. The modelled wind-speed deficits produced by the 100-turbine wind farm intensify at hub height over time, and extend further downwind after the evening transition at 1830 LT (2330 UTC) (Fig. 10a–d). The wind-speed deficits reach a maximum value within a distance of 5 km downwind from the northern edge of the virtual wind farm, and the wind-speed deficits erode for distances further downwind. As the simulated wind direction shifts from south-westerly to southerly throughout the transition, the location of the wake wind-speed deficits changes accordingly. Additionally, the hub-height wind speed of the control run varies between 8 and \(11\,\hbox {m } \hbox {s}^{-1}\) during the 2 h before and after the evening transition (Fig. 9a). The wind-farm drag reduces the downwind wind speed by more than \(1.2\,\hbox {m } \hbox {s}^{-1}\) throughout the transition; this wind-farm wake represents more than 10% of the inflow wind speed at the end of the transition (Fig. 10d).
The simulated wind-speed deficit within the rotor layer also becomes greater during the evening transition. Throughout the evening transition, the wind-speed deficit is greater below hub height than above (Fig. 11). At the top of the rotor disk, the wind-speed reduction is minimal before the evening transition, but doubles after the transition (Fig. 11d, h). At all altitudes across the rotor disk, the wind-speed deficits stretch further downwind after the transition than before the transition.
Although the absolute changes in hub-height TKE difference decrease over time (Fig. 10e–h), the virtual wind turbines increase the relative downwind TKE difference during the evening transition. Since the background TKE diminishes as the evening progresses (Fig. 9c), the TKE enhancement produced by the wind farm decreases in absolute terms but increases in relative terms. One hour before the evening transition, the turbines generate a maximum downwind TKE enhancement of more than \(0.18\,\hbox {m}^{2}\,\hbox {s}^{-2}\) (Fig. 10f), which is about 20% of the average ambient TKE value of the hour in the control run (Fig. 9c). By the end of the transition, the downwind TKE enhancement is more than 50% of its base value (Fig. 10h): the downwind TKE increases by 50% due to the existence of the wind farm.
Furthermore, the downwind TKE differences across the rotor layer display irregular variations, in contrast to the wind-speed deficits. In general, the downwind TKE enhancement increases with height within the rotor layer throughout the evening transition (Fig. 12). Particularly below hub height, the TKE enhancement induced by the virtual wind farm diminishes after the transition (Fig. 12e, f). On the other hand, above hub height, the differences in TKE enhancement before and after the transition are more subtle (Fig. 12c, d, g, h). Furthermore, in terms of horizontal extent, the downwind wind-speed deficit at hub height persists for a distance of more than 15 km downwind after the evening transition (Fig. 10c, d), but the TKE enhancement dissipates after a distance of 10 km downwind (Fig. 10g, h).
Besides, wind turbines also interrupt the evening reduction of the surface heat flux \(Q_{H}\) downwind, as well as the emergence of the near-surface stable layer. At the beginning of the evening transition, the virtual wind farm increases \(Q_{H}\) by less than 2 W m\(^{-2}\) consistently (Fig. 10i), which is less than 10% of the control value (Fig. 9d). As the evening progresses, the wind farm enhances and expands the downwind flux increase by more than 6 W m\(^{-2}\) at the end of the transition (Fig. 10l), which is about 20% of the ambient value (Fig. 9d). In contrast, \(Q_{H}\) in a typical environment should decrease and become negative in the evening. Therefore, the positive downwind heat-flux difference during the evening transition suggests the modelled wind turbines impede downwind surface cooling and hence the development of the nocturnal stable boundary layer.
Power Production Evolution
In the “WFP” simulations, turbine-power production can be calculated from the wind speed at hub height in a simulation cell. The power ratio (Fig. 13) represents the ratio between the WFP-simulated power production and the calculated power production derived from the wind speeds of the same turbine-containing grid cells in the “control” run, based on the turbine power curve. As expected, waked grid cells produce less power. Because the wind direction shifts from south-south-westerly to southerly, the grid cells on the south-western half of the wind farm consistently yield higher power per turbine than those in the north-eastern half, which are usually waked. Note that the WFP scheme assumes that the virtual wind turbines are always oriented perpendicular to the flow (Fitch et al. 2012), and the power production of each grid cell is proportional to the number of turbines contained therein.
Because of the strengthening wakes during the 4-h evening transition, the 1-h averaged power ratio gradually decreases to 68%, from 82% (Fig. 13). The reduction in the power ratio during the first 2 h can be explained by the larger decline in the average wind speed of the WFP run compared to that of the control run (Fig. 14). Meanwhile, the mean power ratio continues to decrease even when the wind speeds increase after 1900 LT (0000 UTC 10 July) (Fig. 14), indicating a growing discrepancy between the potential and the WFP-simulated power productions throughout the evening transition. The continuous reduction in power ratio (Figs. 13, 14) illustrates that the maturing wakes undermine the power production of downwind turbines.