Wind turbine wakes can extend over considerable distances and significantly diminish the power output of downstream turbines . When turbines are clustered into large arrays, the combined array wake (i.e., cluster wake) can propagate even farther downstream and reduce the power output of entire nearby wind farms . This phenomenon is particularly prevalent in offshore environments where the relatively low atmospheric turbulence , consistent winds along small wind direction sectors, and spatially dense installations of wind farms contribute to significant wake-induced energy losses. To this end, accurately quantifying energy losses as a result of the cluster wake effects is a crucial step toward securing efficient and transparent deployment of future wind farms.

Numerical models can be used to capture the physics of cluster wakes and calculate their impact on downstream turbine arrays. Traditionally, low-cost engineering wake models have been widely used in the wind energy industry to quantify wake losses. These simpler analytical models were originally derived for onshore wind farms, and they require site-specific tuning and calibration before they are used to calculate energy losses inside a single wind farm (i.e., internal wake effects). More recently, engineering wake models have been expanded and carefully tuned with the objective of accurately capturing cluster wakes offshore . Still, their inability to account for important physical mechanisms that modify wake evolution, like atmospheric stability and changes in surface roughness, makes them unfit for reliable wake assessments. Moreover, engineering wake models have historically been tuned in the North Sea and Baltic Sea e.g.,, where offshore wind development has been widespread. However, such model calibrations are not transferrable to regions with different dominant atmospheric stability conditions, like the US East Coast , and may require additional tuning and validation. As a result, engineering wake models may fall short in their ability to provide reliable solutions for a wide range of geographic locations, particularly when validation data are limited or nonexistent.

Mesoscale numerical weather prediction models, on the other hand, provide a computationally efficient alternative to represent cluster wakes over long distances in any region across the globe. Numerical weather prediction models can capture important atmospheric phenomena relevant to wake evolution, like atmospheric stability, and the effect of wind turbines in the flow using computationally inexpensive wind farm parameterizations (WFPs) . Furthermore, unlike typical engineering wake models, numerical weather prediction models are not tuned to a specific region and turbine size; therefore, these physics-based models may be scaled to better represent modern-sized wind turbines in a wide variety of regions. Due to their coarse spacing (Δx≈1–10 km), mesoscale models cannot resolve turbulence in the flow. Similarly, because the grid spacing is much larger than the rotor diameter of wind turbines (D≈200 m), mesoscale models cannot also resolve individual turbine wakes. Therefore, uncertainty persists regarding the precision of mesoscale models in accurately capturing the effects of internal and cluster wakes on the energy output of entire wind farms.

Validation of mesoscale simulations has primarily focused on their ability to capture the velocity deceleration downstream of wind farms. and compared long-term lidar measurements with mesoscale simulations of several wind farms in the German Bight. They report high agreement between the mesoscale model and the lidar observations for short- and long-range wake effects . Mesoscale model output has also been compared to aircraft wind measurements downstream of wind farm clusters, illustrating the ability of mesoscale simulations to capture the spatial extent of the wakes downstream of wind farms . Validating numerical simulations using observations over short periods is hindered by the ability to accurately capture the background meteorological conditions in the simulations. If the background flow is not well represented, then the validity of the mesoscale simulations cannot be evaluated . An alternative approach to model validation is to employ higher-fidelity numerical simulations to examine the skill of the mesoscale simulations in representing wake effects. Comparisons between mesoscale simulations and Reynolds-averaged Navier–Stokes (RANS) models and large-eddy simulations (LESs) support the fact that mesoscale models can capture the velocity downstream of the wind farms . also show that mesoscale simulations may not be suitable for representing the blockage effect upstream of wind farms and individual turbine wakes.

Limited validation has centered on mesoscale models' skill in capturing changes in wind turbine power caused by wakes. showed that mesoscale simulations are capable of representing wind turbine power variability across an onshore wind farm over a 4 d period. They showed that turbine power production tended to be overestimated by the model, likely due to a mismatch in the background atmospheric conditions. To reduce the uncertainty associated with capturing the atmospheric conditions of a particular date, employed long-term wind turbine power data and numerical simulations to examine long-range cluster wakes in the North Sea from a statistical perspective. found that mesoscale simulations generally represent the influence of cluster wakes on the front-row turbines; however, these models fail to capture cluster wake effects on the entire downstream wind farm, likely because they are not capable of representing internal wake dynamics. Using idealized mesoscale simulations and LES, also showed that the mesoscale simulations with grid spacing Δx≈1 km fail to capture changes in turbine power from internal wakes.

Despite limited validation for internal and external wake effects, mesoscale simulations are increasingly being used to estimate the wind resource and wake effect for large-scale wind deployment. and used a regional climate model to simulate future offshore wind energy production scenarios for the North Sea. They warn that densely spaced wind farm clusters may reduce the capacity factor of neighboring wind farms by about 20% in the North Sea . and conducted a similar analysis on the US East Coast. Using numerical simulations of 57 d, quantified the combined internal and cluster-wake-induced energy losses of hypothetical wind farm layouts, suggesting that mean energy losses could exceed 33%. In a similar vein, examined the combined cluster and internal wake effects from two mesoscale wind farm parameterizations on the US East Coast. In particular, indicated that the average combined wake losses can range from 11% to 37%, depending on the wind farm parameterization, and that internally waked turbines can sustain mean losses larger than 50%. employed a different framework to investigate the long-term effect of large-scale offshore wind deployment. Rather than simulating a subset of days, conducted numerical simulations of a complete annual cycle for the mid-Atlantic using multiple options for representing turbine-generated turbulence. They found that the combined effect of internal and cluster wakes can result in up to ≈38% reduction in power, with internal wakes accounting for the largest power losses . More recently, conducted numerical simulations across a “typical meteorological year” to examine wake-induced energy losses across the US East Coast, using wind farm layouts informed by up-to-date information to better approximate the installed density capacity of the individual lease areas. They highlight the need to revisit conventional wind-speed-deficit-based loss assessments to estimate energy losses from cluster wakes, especially in regions where hub-height winds are consistently above rated speed . A common denominator across numerical studies using mesoscale models is that in specific atmospheric conditions, wind farm wakes can persist in excess of 50km downstream of large clusters .

Here, we evaluate the ability of mesoscale simulations to capture the velocity deceleration downstream of wind farms and the effect of internal and cluster wakes on wind turbine power for a variety of realistic atmospheric conditions. Because large-scale deployment in the US is currently underway, we use LESs as a baseline to assess the mesoscale simulations. LESs can explicitly resolve turbulence in the flow and individual wind turbine wakes, thus offering a faithful representation of wake evolution. The article is structured as follows. A description of the numerical framework and the wind farms considered here is presented in Sect. . The atmospheric conditions covered in the study are described in Sect. . We evaluate the velocity in the wake of the wind farms for the mesoscale simulations and LES in Sect. , and we examine the ability of the mesoscale simulation to capture the effects on turbine power in Sect. . A discussion of our results and concluding remarks are provided in Sect. .

We perform mesoscale and large-eddy simulations of three offshore wind farms on the US East Coast using the Weather Research and Forecasting (WRF) model v4.2.2. The planned South Fork, Sunrise Wind, and Revolution Wind offshore wind farms are located off the coasts of Rhode Island and Massachusetts. South Fork and Revolution Wind are located about 10km downstream of Sunrise Wind along the predominant wind direction (southwesterly winds), providing an ideal setup to investigate cluster wake effects from closely spaced wind turbine arrays (Fig. ). All three wind farms are planned to use 11MW wind turbines, providing a combined nameplate capacity of 1.76GW. Here, we represent all wind turbines in the three wind farms using a scaled-down version of the International Energy Agency (IEA) 15MW reference wind turbine . To achieve a rated power of 11MW, the IEA 15MW reference wind turbine is scaled down by reducing its rotor diameter (D) to 206m. The turbine's hub height is also reduced to 133m.

A three-domain, one-way-nested setup is used to evaluate cluster and internal wake effects in the mesoscale simulation framework (Table ), following . The size and position of the mesoscale domains are shown in Fig. a. ERA5 reanalysis provides initial and boundary conditions to the outer mesoscale domain. Implicit Rayleigh damping in the top 6km of the domain prevents gravity wave reflection from the upper domain boundary . The three mesoscale domains employ a stretched vertical grid, where 15 of the 52 vertical levels are contained within the rotor layer of the 11MW turbine, per the recommendation of . Wind turbines are represented by a momentum sink and a source of turbulence kinetic energy via the Fitch WFP in the innermost domain only (i.e., domain M03 with Δx=1km) with a turbulence kinetic energy (TKE) generation factor of 1.0. Note that the correction for the blockage effect from was not used here.

We use a single domain to evaluate cluster and internal wake effects using LESs (Fig. b). Initial and boundary conditions for the LES are obtained via offline coupling from domain M03 of a precursor mesoscale simulation without wind turbines. A stretched vertical grid is used in the LES to resolve the small scales of turbulence near the surface. A uniform grid spacing of Δz=5m is used in the lowest 300m. The vertical grid spacing increases linearly to Δz=50m at z=700m to match the vertical grid spacing of the mesoscale simulation. Because the vertical grid spacing from the mesoscale boundary conditions is much coarser than in the LES near the surface, spurious gravity waves can develop and propagate throughout the domain. To mitigate spurious gravity wave activity, we include Rayleigh damping at the lateral domain boundaries (Appendix ). We also include implicit Rayleigh damping in the top 10km to prevent spurious reflections of gravity waves from the upper domain boundary. The 11MW wind turbines in the LES are represented using an actuator disk parameterization based on and , with modifications as described in Appendix .

The LES and mesoscale simulations employ similar physics parameterizations to ensure a direct comparison between both modeling frameworks. Water vapor, cloud water, rain, cloud ice, snow, and graupel processes are represented using the Thompson microphysics scheme . Longwave and shortwave radiation effects are included in the simulations via the Rapid Radiative Transfer Model for Global Climate Models RRTMG;. The Noah land surface model and Monin–Obukhov similarity theory are used to provide moisture, heat, and momentum fluxes at the bottom boundary of the domains. Unresolved convection in the outer mesoscale domain (i.e., domain M01) is modeled using the Kain–Fritsch scheme . Due to the grid spacing of the mesoscale simulations (Δx≥1 km), turbulence mixing must be parameterized. Here, we use the Mellor–Yamada–Nakanishi–Niino (MYNN) Level 2.5 boundary layer parameterization for all mesoscale domains. For the LES, we use the nonlinear backscatter and anisotropy model with turbulence kinetic energy (TKE)-based stress terms to represent subgrid-scale turbulence .

We investigate wake effects for a range of atmospheric conditions representative of the region under consideration. Winds on the US East Coast are predominantly from the southwest ; therefore, we search for dates when the wind direction at hub height is around ϕ=225°. To study internal wake effects, we also select cases when the wind direction creates an aligned wind farm arrangement (i.e., 205, 225, 240°). Based on these criteria, our analysis considers a narrow wind sector within [202.5, 247.5°]. Hub-height wind speeds below rated speed (11ms-1) are chosen so that the wake-induced velocity deficit translates entirely into power reduction. Finally, although we consider atmospheric stability conditions that range from weakly stable to weakly unstable, we focus our analysis on weakly stable conditions, as these can have a substantially higher impact on downstream wind turbines.

To this end, we perform LESs and mesoscale simulations of five dates that match the desired wind speed, wind direction, and stability criteria. Table  summarizes the atmospheric conditions for each of the simulated cases. We characterize atmospheric stability at the surface and across the turbine rotor layer using data at the wind farms' locations using the finest-resolution mesoscale domain (M03) without turbines. Stability at the surface is defined here using the inverse of the Obukhov length normalized by height (Eq. ), where u* is the friction velocity, θs is the surface temperature, κ=0.4 is the von Kármán constant, g is the gravitational acceleration, Q˙s is the surface kinematic heat flux, and z=10m. Here, we define stable conditions as z/L>0 and unstable conditions as z/L≤0. Because atmospheric stability across the turbine rotor layer may differ from that at the surface , we also quantify stability across the turbine rotor layer using the bulk Richardson number (Eq. ), where the vertical gradients of potential temperature (θ) and wind speed (u,v) are estimated between the surface (z=10m) and the top of the turbine rotor layer (z=236m). Here, we define stable conditions as RiB>0 and unstable conditions as RiB≤0. 1z/L=zκgQ˙s-u*3θs2RiB=(g/θ‾)Δθ‾Δz(Δu‾)2+(Δv‾)2

The simulated cases cover a range of variability in wind speeds, wind directions, and temperature profiles throughout the lower portion of the boundary layer (Fig. ). 15 February 2017 is characterized by a near-constant wind speed across the rotor layer with a large (almost 35°) southerly shift in wind direction over time. Atmospheric stability at the surface and across the rotor layer is initially weakly unstable and evolves to be weakly stable. 27 July 2017 exhibits a shallow boundary layer with slow changes in wind speed and direction over time. Both the surface and the rotor layer stability transition from near-neutral conditions to weakly stable conditions. The boundary layer on 26 November 2019 remains weakly stable throughout the simulated times and shows a steady increase in wind speed as the wind shifts toward the west. On 1 November 2020, wind speed at turbine heights remains nearly constant over time, while the wind direction shifts toward the south. Atmospheric stability remains unstable at turbine heights and at the surface. Finally, 4 November 2020 exemplifies a transition from an unstable boundary layer to a near-neutral surface layer, while stability across the rotor layer becomes weakly stable. Wind speed varies slightly over time, while the wind shifts in direction toward more westerly flow.

Wind conditions throughout the five simulated cases enable analysis of internal and cluster wake effects for a variety of atmospheric stability conditions. To evaluate the representativeness of our simulations, we compare the simulated atmospheric conditions with long-term (20-year) data from the National Offshore Wind dataset NOW-23;. Hub-height wind speed for the selected cases is consistently below rated speed (Fig. a) so that the largest wake effects occur . The hub-height wind direction is ϕh=217°, on average, and includes the directions of alignment for the turbines in the wind farms (i.e., 205, 225, 240°) (Fig. b). Furthermore, the most common wind direction in the simulated cases is between 215 and 220°, matching the most frequent wind direction according to the climatology of the region. Surface layer and rotor layer stability is predominantly stable for the selected cases (Fig. ). Most of the simulated cases (75 %) exhibit stable conditions across the turbine rotor layer, whereas 25 % of cases exhibit unstable conditions at turbine heights (Fig. b). The long-term climatology also shows that a majority of cases are stable (79 %) rather than unstable (21 %) based on the Richardson number. Similarly, 68 % of the cases are stable and 32 % are unstable based on the surface stability criteria (Fig. a), which is comparable to the surface layer stability estimates from the climatology of the region (57 % stable and 43 % unstable). Note that these simulations are not designed to evaluate wake effects across atmospheric conditions that are fully representative of the climatology of this region; rather, the purpose is to capture typical conditions and examine how the mesoscale modeling framework performs.

The velocity fields at hub height (z=133m) are averaged in time to provide an adequate comparison between the LES and the mesoscale solution. The horizontal wind speed fields are averaged using 15 min time windows, corresponding to 15 time stamps from the LES and 3 time stamps for the mesoscale simulation. Figure  illustrates the time-averaged wind speed at hub height for the mesoscale simulation and LES on 4 November 2020 at 20:37 UTC.

We compare the time-averaged velocity from the LES and mesoscale simulation at two different locations to examine the ability of the mesoscale model to represent cluster wakes. We consider the velocity field immediately upstream of South Fork and Revolution Wind to investigate the combined wake of all turbines in Sunrise Wind (transect 1 in Fig. ). We sample the velocity field approximately 2Δxmeso (Δxmeso=1km) south of the leading turbines in South Fork and Revolution Wind to avoid mesoscale winds at turbine-containing grid points, which is equivalent to approximately 5.2km, or 25.2 rotor diameters (25.2D), north of Sunrise Wind. We also consider the velocity field downstream of the three wind farms to investigate the combined wake of all turbines in the domain (transect 2 in Fig. ). Transect 2 is approximately perpendicular to the mean wind direction for the simulated cases and is about 7.4km (36D) downstream of Revolution Wind. The location of Transect 2 is selected to capture the full spatial extent of the wake under the wind directions analyzed here.

The transects of the time-averaged velocity field from the LES are averaged spatially to provide a more direct comparison with the mesoscale wind fields. A 1km moving average is applied to the LES velocity transects to filter out flow features smaller than the grid spacing of the mesoscale domain. Spatial averaging effectively removes small-scale features of the flow that cannot be captured by the mesoscale grid while retaining the signal from individual turbine wakes that sometimes persist far downstream.

Differences in the wake between the LES and mesoscale simulation are evaluated using the root-mean-square error (RMSE). The RMSE between the LES and mesoscale simulation for each 15 min time window t is calculated following Eq. (), where U‾LES(t,x) is the time- and space-averaged velocity transect of the LES, U‾meso(t,x) is the time-averaged transect of the mesoscale simulation, xi is the distance along each transect T defined in Fig. , and N is the number of grid points along each transect. Note that the velocity transect for the mesoscale simulation is interpolated to match the spatial resolution of the LES. We also calculate the RMSE of the normalized velocity difference between the LES and mesoscale simulation (RMSE^) to account for larger differences at faster wind speeds (Eq. ). 3RMSE(t)=∑xi∈TU‾meso(t,xi)-U‾LES(t,xi)2N4RMSE^(t)=∑xi∈TU‾meso(t,xi)-U‾LES(t,xi)2U‾LES2(t,xi)N

To compare the power production of the turbines in the LES and mesoscale simulation, we apply a 10 min moving average to the power data in the LES to remove fluctuations in power production caused by turbulence in the flow. Furthermore, we normalize the time-averaged power production of each turbine in the domain. The normalized power production of the ith turbine in the domain (P^i) is defined as the ratio between the time-averaged power (P‾i) and the mean power of the front-row turbines in Sunrise Wind 〈P‾j(t)〉j∈FR for southwesterly flow (illustrated as black circles in Fig. ). In this way, we evaluate the ability of the mesoscale model to capture changes in power production relative to freestream conditions for a variety of wind speeds. 5P^i(t)=P‾i(t)〈P‾j(t)〉j∈FR

We compare the normalized power between the LES and the mesoscale simulation for turbines that are subject to internal wakes and turbines that only experience wakes from an upstream cluster. A turbine is considered to be subject to internal wakes when it has an immediate upstream neighbor under southwesterly flow (ϕh≈225°). Because the turbines in each wind farm are separated by 1.852km (9D), any turbine with an upstream neighbor within 3km (14.5D) will be subject to internal wakes (red circles in Fig. ). Because some turbines in South Fork and Revolution Wind will experience a combination of internal and external wakes, we only consider turbines in Sunrise Wind for the internal wake analysis. To examine cluster wakes, we consider the turbines in South Fork and Revolution Wind that are only expected to be impacted by the wake from Sunrise Wind (blue circles in Fig. ).

The mesoscale simulation shows more skill in capturing the effect of short-range cluster wakes than that of internal wakes within a wind farm (Fig. ). Although the mesoscale simulation can accurately capture the velocity deceleration from the entire Sunrise Wind cluster (Sect. ), the normalized power production of the front-row turbines in Revolution Wind and South Fork is not necessarily well represented (Fig. a). The slope of the regression line of the LES and mesoscale simulation data is only 0.55, and the regression coefficient is R2=0.5 for cluster-waked turbines. Nevertheless, the median normalized power across all wind direction sectors is P^=0.893 and P^=0.895 for the LES and mesoscale simulation, respectively. This behavior shows that, although the mesoscale simulation is not capable of capturing the mean variability in turbine power, it may be capable of representing the average cluster wake effect on downstream turbines when considering a broad range of wind direction sectors, albeit perhaps due to compensating errors. The mesoscale simulation struggles even more in capturing the mean variability in turbine power inside the wind farms (Fig. b). Both the slope of the regression line and the regression coefficient are smaller for internal wakes than for cluster wake effects. The mesoscale simulations generally underestimate internal wake effects within the wind farms compared to the LES for the same wind directions. The median normalized power of internally waked turbines is P^=0.87 in the LES, whereas it is P^=0.84 in the mesoscale simulations.

To provide additional insight into the strengths and limitations of mesoscale simulations, we now segregate the normalized power production based on the time-averaged wind direction at the location of each turbine. The mean distance (dinter) between the last-row turbines in Sunrise Wind and the southernmost turbines in South Fork and Revolution Wind (Fig. ) varies with wind direction. The effective spacings between the trailing turbines in Sunrise Wind and the leading turbines in the downstream wind farms are, on average, 9.5km (46D), 10.9km (53D), 12.4km (60D), 14.8km (72D), and 21.2km (103D) for the wind direction sectors 200°≤ϕ<210°, 210°≤ϕ<220°, 220°≤ϕ<230°, 230°≤ϕ<240°, and 240°≤ϕ<250°, respectively. The average spacing of turbines inside the wind farms (dintra) also varies with wind direction (Fig. ). Turbines are closest to their upstream neighbor (dintra=2.7km≈13D) when the wind direction is within 220°≤ϕ<230°. The effective turbine spacing increases to dintra=4.1km≈20D for wind direction sectors 200°≤ϕ<210° and 240°≤ϕ<250°. The farthest effective spacing occurs for 210°≤ϕ<220° and 230°≤ϕ<240°, with dintra=6.7km≈33D.

This article presents a comprehensive case study highlighting the strengths and limitations of mesoscale simulations in capturing wake effects from wind turbine clusters and their impact on the power production of nearby turbine arrays. To this end, we provide a direct comparison of the data generated by mesoscale and LES modeling frameworks for three planned offshore wind farms on the US East Coast. The analysis considers realistic atmospheric conditions, including atmospheric stability for the most common wind directions and wind speeds in this region. To investigate the ability of mesoscale simulations to capture cluster wakes, we compare the velocity field from the mesoscale simulation and LES in the wake of a single wind turbine cluster and multiple wind turbine clusters. Because mesoscale simulations are increasingly being used to quantify wake effects in large wind farms, we also evaluate the variability in mean turbine power production in the mesoscale simulations and compare it with the LES results.

Mesoscale simulations are able to capture the velocity downstream of both a single wind turbine cluster and multiple offshore wind turbine clusters. The RMSE between the mesoscale simulation and LES is approximately 5%, on average, downstream of a single wind farm and multiple wind farms. Moreover, the mesoscale simulation accurately captures stability-driven variations in wind farm wake behavior – for instance, narrower, faster-recovering wakes during unstable conditions and broader, longer-lasting wakes during stable conditions. Our findings concur with validation studies using field measurements and higher-fidelity models , which found that mesoscale simulations adequately represent the velocity in the wake of wind turbine arrays. However, our results offer added value through a direct comparison between mesoscale simulation and LES frameworks under realistic atmospheric conditions.

Although the mesoscale simulations can represent the velocity in the wake of wind farms, they are a poor predictor of wake effects in the special circumstance when individual wakes persist over long distances and impact downstream turbines. Because individual turbine wakes typically influence only nearby downstream turbines within a wind farm, the mesoscale simulation highly underestimates changes in turbine power caused by internal wakes, especially when turbines become aligned with the predominant wind direction, as discussed in . Our findings agree with idealized simulations from , who showed that mesoscale simulations with grid spacing Δx≈1km underestimate internal wake effects. It is possible that mesoscale simulations with finer grid spacing (Δx⪅1km) can capture internal wake effects ; however, the assumptions made in boundary layer parameterizations do not hold with such grid spacing , requiring parameterizations that can represent horizontal gradients of mean quantities . Individual turbine wakes can also persist over long distances within the broader wind farm wake. Under these conditions, mesoscale simulations underestimate short-range cluster wake effects, as turbine power variations are driven more by localized velocity deficits from individual wakes than by the broader-scale flow deceleration of the full wind farm wake. Because mesoscale simulations do not resolve individual turbine wakes, they are better suited to capture short-range cluster and internal wake effects under unstable conditions, where wakes recover more rapidly, than under stable conditions, where wakes persist over longer distances. In addition, the discretization of turbine positions in the mesoscale grid introduces offsets from their physical locations that modify the effective directions of alignment and turbine spacing, contributing additional uncertainty to internal wake estimates. Mesoscale simulations are also more appropriate for representing long-range cluster wake effects, where individual wakes merge into the broader wind farm wake .

Although mesoscale simulations consistently underestimate changes in wind turbine power from internal and cluster wakes, they can still provide an accurate estimate of the combined power losses over some wind direction sectors. For the wind direction sectors considered here, the mesoscale simulations overestimate the combined cluster and internal wake impact for ϕ∈[210°,220°) and underestimate losses for ϕ∈[220°,230°). However, the mesoscale simulations accurately predict the combined internal and cluster wake losses across other wind direction sectors, even if the variability in turbine power caused by internal wakes is not well represented. Depending on the wind rose and the wind farm layout, it is possible for the internal wake under- and overestimations across wind direction sectors to balance out. For instance, if the wind direction sectors where wake losses are underestimated and overestimated are equally weighted and if the level of underestimation and overestimation is also comparable between both, then the mesoscale simulation may be an accurate predictor of the combined cluster and internal wake effect. However, it is likely that inaccuracies in the mesoscale simulation estimates will also change with the grid spacing, as larger grid spacing will change how neighboring turbines are wrongfully waked in the coarse grid.

A direct comparison of mesoscale simulations and LES of three offshore wind farms on the US East Coast highlights some of the limitations and strengths of mesoscale simulations in capturing wake effects. Although we show that the mesoscale simulations can accurately represent wind farm wake behavior, we find that they struggle to capture changes in energy output, especially from internal wake effects. This counterintuitive finding stems from the grid spacing and numerical discretization of the mesoscale framework, which limit the ability of mesoscale simulations to resolve internal wake dynamics . Future work should directly quantify the contribution of turbine position errors in the mesoscale grid to the uncertainty in internal wake estimates, for example, by comparing simulations with physical and discretized turbine positions under otherwise identical conditions. The inability of mesoscale simulations to capture internal wake effects, which are typically larger than cluster wake effects, underscores the limitations of using such models to estimate wind farm energy output, especially for highly skewed wind roses. Although the findings from this study are derived from offshore simulations, the limitations from the mesoscale model also extend to onshore conditions because they are intrinsic to the model and not to the flow characteristics that distinguish onshore from offshore conditions. A limitation of our study is its representativeness across wind farm layouts and different mesoscale modeling frameworks. Different wind farm layouts will likely produce differences in the internal wake effects captured by the mesoscale simulation. Moreover, the choice of the mesoscale grid spacing , boundary layer parameterization , and wind farm parameterization options will also modify wake effects in the mesoscale model. Future studies should evaluate whether mesoscale simulations can represent the evolution of cluster wakes over longer distances (>50km). In addition, a combination of mesoscale simulations and LES may be employed in future studies to consider the combined effect of long-range cluster wakes on downstream wind farms.