Sensitivity of Offshore Wind Farm Wakes and Ocean Coupling to Vertical Resolution in the Stable Marine Boundary Layer

Abstract. Offshore wind farms in the Southern New England lease area frequently operate within a persistently stable marine at- mospheric boundary layer (MABL) during spring, when cold shelf waters beneath warm continental air suppress convective mixing and maintain a shallow planetary boundary layer height (PBLH) well below turbine hub height. Here we quantify the sensitivity of wind farm simulations to vertical resolution under these heavily stratified conditions. Our ensemble of WRF-Fitch mesoscale simulations of a large-scale offshore wind farm during a stratified period (2–8 May 2018) spans five vertical grid configurations, labeled by their first-layer thickness (∆z = 5–100 m), which place between 27 and 2 model levels within the 30–246 m rotor swept zone, and two ABL schemes (MYNN2 and YSU), coupled to a one-dimensional slab ocean to diagnose first-order air-sea interactions. The simulated mean PBLH of 92–118 m places 59–72 % of the rotor above the boundary-layer top, where strong stratification suppresses the turbulent redistribution of the wake and concentrates almost all of the shear across the disk below hub height. Hub-height wind speed and friction velocity are robustly represented for ∆z ≤ 50 m, departing by less than 1.2 % and 1 % respectively in MYNN2, but coarser grids (resembling operational system resolution) fail to resolve the sharp stable inversion: ∆z = 100 m overestimates PBLH by 87 % with MYNN2 and 22 % with YSU. Richardson extrapolation over the three finest grids shows most diagnostics to be effectively grid-converged at the reference resolution, but assigns PBLH a grid convergence index of about 13 %, reflecting its nature as a threshold diagnostic evaluated on model levels.

Crucially, the hub-height wake deficit and its downstream structure remain robust across vertical resolutions, so this 13 % PBLH error chiefly compromises PBLH-based diagnostics rather than the simulated wake and surface stresses. The time-mean wake deficit peaks at −3.2 m s⁻¹ at the cluster core and falls below 0.5 and 0.1 m s⁻¹ at 81 and 136 km downstream, driving a spatial PBLH dipole (a +90 m in-farm deepening and a −24 m downstream undershoot that recovers within 23 km), the former being consistent with recent observations on land. The ocean responds to the reduced wind stress (13.5 %) with a mixed-layer shoaling of 1.26 m (9.2 %) within the farm footprint, a sea-surface skin warming peaking at +0.32 °C, and an upward turbulent heat-flux anomaly of 2.23 W m⁻² (10.7 %) in the farm zone, reaching 3.18 W m⁻² some 47 km downwind of the stress minimum, consistent in sign and magnitude with fully coupled simulations of the same region. The air-sea fluxes and the mixed-layer response show no ordered dependence on resolution across the four finest grids, although the coarsest, operational-like resolution exaggerates every term.

These results establish that while the spatial structure of wake-induced atmospheric and oceanic perturbations is robust to vertical resolution once converged, the precise quantification of PBLH-dependent wake dynamics requires at least eight model levels within the rotor layer, corresponding here to ∆z ≤ 25 m. The ERA5 reanalysis that provides the boundary conditions for these simulations places eight levels within the same layer, so its vertical grid sits at the threshold identified here; regional forecast systems with coarser near-surface grids would not resolve it. Vertical refinement beyond this point is bounded by the horizontal discretization: at 1.5 km spacing the boundary-layer scheme remains a one-dimensional column closure, and further progress requires relaxing that assumption toward 3D turbulence resolved by Large Eddy Simulations rather than a still thinner grid aspect ratio.