The SST datasets used in this study are derived from varying underlying instrumentation and are available at varying spatial and temporal resolutions (Fig.  and Table ). Five SST datasets are downloaded from the Group for High Resolution Sea Surface Temperature Level-4 (GHRSST-L4) database, including the Canadian Meteorological Center (CMC) analysis product , the Office of Satellite and Product Operations (OSPO) analysis , the Multiscale Ultrahigh Resolution (MUR) dataset , the Naval Oceanographic Office (NAVO) dataset , and the Operational Sea Surface Temperature and Sea Ice Analysis (OSTIA) analysis . Additionally, an SST dataset from the Level-3 GOES-16 Advanced Baseline Imager (GOES-16) is downloaded from the GHRSST database  and gap filled using Data Interpolating Empirical Orthogonal Functions (DINEOF) .

Initial and boundary conditions for the model in this study are derived from the MERRA-2 reanalysis dataset . Within the MERRA-2 dataset, SST comes from the OSTIA dataset (Fig. a). Each auxiliary dataset overwrites skin temperature over water within the initial and boundary conditions for each simulation (Fig. b–g). On the outermost domain for the GOES-16 simulations (Fig. f), skin temperature is overwritten only over the area covered by domain 2 due to processing constraints. Because the spatial extent of domain 2 is large (600 km × 600 km) and encompasses the region of the ocean over which winds in this study are coming from, we expect this to have a negligible impact on the flow field over the region of interest. For every other setup, the satellite-derived SST products overwrite the skin temperature over water for the entirety of each domain.

Differences in the resolution of features between the various SST datasets are apparent (Fig. ). Most notably, the gradients in SST, which can be important forcing mechanisms for offshore LLJ formation , are better captured at finer scales in the GOES-16 and OSTIA datasets (Fig. f and e, respectively) than in the lower-granularity datasets such as NAVO and CMC (Fig. b and c, respectively). OSPO (Fig. d) and OSTIA (Fig. e) share the same granularity, yet the features within the OSTIA dataset contain much finer detail. The MUR dataset has the finest granularity (Fig. g), yet the resulting product appears much smoother than that of GOES-16 (twice the granularity) and even OSTIA (more than five-times the granularity). Note that while the native SST dataset within the MERRA-2 reanalysis product (Fig. a) is produced from the OSTIA dataset (Fig. e), the resolution of the MERRA-2 product is at the resolution of the MERRA-2 data at 0.62° latitude and 0.5° longitude. Based on the differences between these products, we expect to see differences in the simulated characteristics of the offshore LLJ, such as in jet-nose height, maximum wind speed, and low-level shear.

In 2019, two EOLOS FLS200 floating lidar buoys were deployed in the New York Bight by the New York State Energy Research and Development Authority (NYSERDA; OceanTech Services/DNV under contract to NYSERDA ). These buoys, named E05 and E06 (open and filled “X” in Fig. , respectively), contain vertically scanning lidars, ocean and wave sensors, and a small meteorological mast recording atmospheric variables such as temperature and pressure. Each lidar records data at 10 levels from 20 to 200 m above mean sea level at 20 m increments. The data are available at 10 min averaged output and are not corrected for wave or tidal variation. This correction has been shown to have a negligible effect in offshore floating lidar measurements when averaged at 10 min timescales . While both E05 and E06 capture the event of focus, only data from E06 are considered in this study, as explained in more detail in Sect. .

To analyze model performance over the full rotor-swept area, we consider an integrated parameter over the rotor layer: the rotor-equivalent wind speed (REWS). The calculation of REWS with veer used in this study is defined in Eq. (9) of : 1REWS=∑k=1NAijkAT|Uijk|cos⁡(θijk), where N is the number of layers within the total rotor-swept area, AT. Aijk is the area of the rotor at a given level, and Uijk is the average wind speed at this level. Veer is taken into consideration through θijk (the difference between the wind direction at hub height and the average wind direction in a given layer).

In this study, we define the ensemble as the different SST setups for each domain (i.e., seven-member ensembles on each domain). We analyze the ensemble mean of individual variables and metrics (denoted by angle brackets), spread (Eq. , where N is the number of ensemble members), and ensemble mean error (EME; Eq. ) every 10 min. Note that the purpose of this ensemble is not to estimate the error, so we do not expect the values of these metrics to be similar. 2Spread=1N∑j=1N(memberj-Ens. Mean)23EME=(Obs.-Ens. Mean)2

The case study of interest in this work consists of an offshore LLJ that developed in the evening of 5 April 2020 off the coast of the Mid-Atlantic states, USA (data from the E06 buoy are shown in Fig. ). The dominant wind direction in this case was from the south, indicating the possibility of warm air advection as is commonly seen in the region . While there exist many techniques to detect low-level jets from wind profiles (see, for example, , and ), the observed low-level jet was detected using the technique described in . This algorithm detects a low-level jet based on meeting three criteria: (1) the maximum wind speed is not at the first or last lidar level; (2) the level of shear between the lowest lidar level and maximum wind speed is above 0.035 s⁻¹; and (3) the wind speed drop-off between the maximum wind speed and top lidar measurement is greater than 1.5 m s⁻¹, and the drop-off is more than 10 % of the maximum wind speed. The jet begins as 2 m air temperature begins to rise, and SST slowly decreases. The difference in 2 m air temperature and SST, ΔT, serves as a proxy for atmospheric stability, where, when positive, one can expect stable atmospheric conditions. As the air and sea surface temperatures diverge and ΔT grows larger, a strengthening in wind speeds occurs around 100 m and eventually leads to the formation of an LLJ. Over the 6 h period of interest beginning at 00Z on 6 April (08:00 PM local time on 5 April), the jet nose remains at ∼ 120 m at the E06 buoy location, with maximum wind speeds of around 16 m s⁻¹. The LLJ persisted for several hours before weakening as ΔT decreased towards zero with the passing of a cold front. This case was selected due to the clear and consistent LLJ signal and the apparent dependence on the air–sea temperature gradient.

For each simulation, the average modeled SST value at the E06 buoy may vary from domain to domain (Fig. ). This is more apparent when the higher-resolution SST datasets (GOES-16 and MUR) are employed. For the lower-resolution domains and Default SST dataset, SST may differ between domain 1 and domain 2, but values for domains 3–5 are very similar. Note that each dataset depicts colder SST values than what was observed.

Low-level jets have historically been detected via a vertical profile of wind speed, in which a maximum is reached at some height above the surface followed by a decrease in wind speed above that level. For the purposes of this study, we do not enforce requirements on the simulated low-level jets to meet certain thresholds for the amount of shear and drop-off in wind speeds above the jet nose in order to consider them “low-level jets”. Simply, for the simulations, the height of maximum wind speed is used to define the low-level jet height.

For wind energy purposes, shear – the difference in wind speed over a certain height, dU/dz – is often considered over the rotor-swept area. In this study, we will consider a rotor-swept area from 38 to 198 m (solid black lines in Fig. ). We define low-level shear as the bulk shear between the bottom of the rotor-swept area (38 m) and hub height (118 m; dashed line in Fig. ).

During the period of interest, maximum wind speeds are observed between 80 and 150 m (Fig. a). On the mesoscale domains (Fig. b and c), a maximum wind speed is reached around 200 m. (There is a decrease in wind speed above this height in the mesoscale domains, confirming that this is a low-level jet profile; not shown.) At low levels, the mesoscale simulations (Fig. b and c) often produce higher wind speeds than in observations (Fig. a). Here, low-level shear within the mesoscale simulations is too weak. The gray zone and microscale domains (Fig. d–f) recover the jet profile and bring the jet maxima down to levels near to but slightly higher than the observations, but these are slightly higher than in observations. The low-level wind speeds are much closer to observations but with a stronger jet maximum wind speed resulting in stronger shear than that observed. In each of the simulations, the LLJ peaks around 160 min before seen in the observations (see Fig.  for comparison). When shifting the observations in time to better match with simulated results (not shown), some metrics are slightly improved, but the overall message remains unchanged. The same can be said for changing the period of interest to several 3–5 h intervals between 01:00 and 06:00 UTC (not shown).

Comparing hub-height wind speeds for each SST setup (Fig. ) displays some subtle variability as SST is augmented between the datasets, but significant variation exists between domains within a setup. The differences between the mesoscale domains (shades of red) are greater than between the two LES domains (shades of blue), which follow each other closely. Domain 3 hub-height wind speeds fall in between that of domains 2 and 4 but more closely resemble the LES solutions. This pattern is also shown when analyzing the root mean square error (RMSE) and bias of hub-height wind speed (Fig. a and d). RMSE and bias between the mesoscale domains are similar, while the resulting RMSE and bias on domain 3 is quite different from that of the mesoscale domains. Then, on the microscale domains, there is not much of a change between the RMSE and bias for hub-height wind speed.

The gray zone and LES domains generally improve the simulation of hub-height wind speeds for much of the period of interest (Fig. ). Towards 05:00 UTC, these wind speeds increase to well above what was observed. The mesoscale domains are deficient in hub-height winds for the majority of the period but increase to around what was observed at 05:00 UTC. During this ramp-up in wind speeds, domain 1 wind speeds often increase well beyond those observed, while domain 2 wind speeds remain much closer to the lidar wind speeds. Overall, the bias on the mesoscale domains remains positive, while on domain 3 and the microscale domains the bias is negative (Fig. d). For many setups, we see improvement in hub-height wind speed predictions in the gray zone, with a jump in performance occurring on domain 3.

The prediction of low-level shear generally improves when moving from the mesoscale domains to LES with, again, a large jump in performance on domain 3 (Figs.  and b and e). The mesoscale domains underpredict the low-level shear, while LES domain predictions come closer to the observed shear but are too large. The gray-zone results are closest to observations in all SST setups. For the performance on the LES domains, this is mostly due to wind speeds being too low at the bottom of the rotor layer (Fig. ). For the mesoscale domains, wind speeds at the bottom of the rotor layer are faster than observed, while wind speeds at hub height are too slow. Domain 3 benefits from slightly faster wind speeds than LES at lower levels but similar wind speeds at hub height, which produces more accurate predictions of low-level shear. Again, the variability across the mesoscale domains is greater than between the microscale domains.

Model performance considering REWS (Eq. ) improves in each setup from domain 1 to domain 2 (Fig. c and f). The largest change in performance, as with the other variables, occurs on domain 3, in which RMSE increases and bias becomes more negative, with the worst performance occurring on domain 5 in each setup. This is due to the overprediction of wind speeds at and above hub height within the microscale domains and domain 3.

Note that the wind speeds modeled are in the rated portion of most wind turbines. For reference, if we were in the cubic portion of the power curve, the overprediction of wind speeds by this amount would result in overpredictions of energy production during this period by between 3 % and 16 % for the mesoscale domains and between 15 % and 27 % for domain 3 and the LES domains (assuming wind speeds that are below the rated wind speed and above the cut-in speed, a performance coefficient of 0.4, and an average air density of 1.225 kg m³).

Simulated low-level jets are highly dependent on surface forcing characteristics. If the surface forcing is inaccurate, then the resulting low-level jet can be expected to be inaccurate. Comparing simulated 2 m temperature against observations, we see that for every setup the RMSE decreases from the mesoscale domains to domain 3, while bias is also reduced to be closer to zero (Fig. a and d). Once on the microscale domains, RMSE increases and bias becomes more positive – close to what was seen on domain 1. RMSE and bias of SST improve in most setups between domain 1 and domain 3 but then remain relatively constant on the microscale domains (Fig. b and e).

Analyzing 2 m temperature and SST alone do not depict the true surface forcing conditions. For that, we analyze ΔT, as discussed in Sect. . Although the biases in both 2 m temperature and SST are positive, the differences between the two are larger than what is observed (Fig. f), producing a negative overall bias for each setup on nearly all domains. RMSE is largest on domain 3 for each setup and then reduces on the microscale domains (Fig. c).

In order to quantify model sensitivity to SST across scales, it is helpful to consider results from all SST setups together as opposed to on a setup-by-setup basis. Recall that “setups” refers to the set of simulations run with varied SST datasets. Ensemble results are generated on each domain by averaging data from all setups.

The vertical profile of the ensemble mean wind speed is drastically different between the mesoscale domains and the LES domains over time (Fig. a–c). On average, the LES domains slightly underpredict wind speed at low levels and overpredict the jet height and jet maximum wind speed (Fig. d). Meanwhile, the mesoscale domains produce lower amounts of vertical shear and overpredictions of jet-nose height. Further, the range in values over all SST setups on the LES domains is often much larger than that on the mesoscale domains (Fig. a–c). This produces a larger time-averaged spread (denoted by an over-bar) throughout the lowest 200 m in the LES domains when SST is varied (Fig. e). Notably, domain 3 has a similar spread to domains 4 and 5 at upper levels but produces spread between the mesoscale simulations and the remaining LES simulations below the jet nose. Increasing the model resolution from domain 1 to domain 2 results in an increase in the spread of wind speed throughout the majority of the profile.

EME, averaged in time, is reduced near the surface as resolution increases from domain 1 through to domain 3 but then begins to increase again from domain 4 to domain 5 (Fig. f). Above the observed jet nose, EME on the LES domains increases rapidly. This increase in error is mostly attributed to an overprediction of maximum wind speed with an overprediction of jet height. The mesoscale domains do not represent the shear and jet height well but produce lower error by not overshooting wind speed and overpredicting jet height.

Changes in SST also generate a larger spread on the gray zone and LES domains for low-level shear and hub-height wind speed (Fig. a and c, respectively). Additionally, EME for these variables is also reduced as compared to the mesoscale domains for much of the period of interest on the gray zone and LES domains (Fig. b and d, respectively).

When considering the wind speed over the rotor-swept area, spread on all domains is very similar (Fig. e). EME of REWS is lowest on domain 2 and highest on the LES domains (Fig. f). While agreement between the observations and simulations is decent below 100 m, the mesoscale domains do not overpredict the wind speeds as much as the LES domains do above the jet height (Fig. d), which reduces error in REWS.

Analyzing the time series of the ensemble mean of bias in low-level shear (Fig. a), the mesoscale domains underpredict low-level shear, while LES domains overpredict. The gray-zone domain minimizes bias due to producing slightly faster near-surface wind speeds than the LES domains. In order to determine if increased stability is the cause of this disparity, the temperature difference between 2 m temperature and SST, ΔT, is calculated (Fig. b). While ΔT is not a perfect metric for stability, it is possible to compare the model against observations using this metric to glean some insight into the near-surface stability. The bias for ΔT on each domain is similar until late in the period of interest. ΔT bias is predominantly near zero or negative, indicating stronger stable conditions in the simulations. This is confirmed by examining surface sensible heat flux (SHFX; Fig. c) where the values are negative throughout the period. It is interesting to note that the mesoscale domains produce larger negative values of SHFX than the LES domains, which indicates more stable conditions. This is reinforced when checking the potential temperature profiles in which the lapse rate near the surface for the mesoscale domains is stronger than that of the LES domains (not shown). In more stable conditions, one might expect shear to be stronger at low levels ; this is not the case in these simulations. For the majority of the period of interest, domain 1 produces a larger negative value of SHFX than domain 5 until around 05:30 UTC when the SHFX values become similar. Inspecting low-level shear bias, the differences between domain 1 and domain 5 remain fairly constant throughout the period of interest. When the sudden increase in SHFX on domain 1 occurs (bringing the value close to that of domain 5), the difference in low-level shear bias is actually increased even though SHFX values become similar. This suggests that the separation in performance of low-level shear bias appears to be more closely related to whether the domain is a mesoscale or microscale domain rather than the actual value of SHFX. It is possible that the PBL scheme on the mesoscale domains is over-mixing. It is also possible that the drag forcing over water on the LES domain is misrepresented, resulting in shear being too strong at low levels. This is discussed in more detail in Sect. .

Running an ensemble of LES is computationally expensive. To save computational resources and maximize model performance, it is logical to perform various simulations varying components of the model (e.g., parameterizations, initial and boundary conditions) on the mesoscale in order to find the best model setup. This best setup can then be used to drive the LES run, which would be assumed to produce the best possible LES result from the available mesoscale setups. We recognize that the definition of “best” performer is subjective and likely to change based on the phenomena of interest as well as the metrics in which one is interested. Unless there is a single metric to be optimized, the comparison of simulation results requires consideration of several variables and weighting the performance based on the interests of the study at hand. That said, when assuming that the best mesoscale result will produce the best microscale result, we are assuming that each LES simulation will perform similarly as the parent mesoscale simulation that drives it. This in turn assumes that the spread between the mesoscale runs and LES runs will be similar; the same goes for ensemble mean error. It has been shown that ensemble error and spread change among domains from the mesoscale to microscale; thus, we investigate whether we can safely assume that the best-performing setup on the mesoscale will lead to the best-performing microscale simulation.

Considering RMSE and bias with respect to observations for each setup on the mesoscale and microscale domains over the period of interest for a variety of variables, model performance can be assessed to determine the top mesoscale performers. The variables considered important in the context of wind energy here are (1) low-level shear, (2) hub-height wind speed, and (3) REWS. Considering REWS, the CMC and GOES-16 datasets are among the top performers on the mesoscale domains, particularly domain 2, while OSPO is among the worst performers for REWS in error and bias (Fig. c and f). On the other hand, the OSTIA dataset is one of the worst performers on the mesoscale domains for each of these metrics, with the exception of REWS bias. Thus, the following top performers for the mesoscale with respect to wind profile characteristics are identified as GOES-16, CMC, and OSPO. The worst-performing ensemble member is OSTIA (see Table ).

To select a single best-performing mesoscale setup, one might also consider how well the low-level forcing variables are captured in each setup. The low-level forcing variables considered here are (1) 2 m temperature, (2) SST, and (3) ΔT. RMSE and bias of 2 m temperature at the E06 buoy location are best for the GOES-16 setup on the mesoscale domains, while CMC and OSPO are in the mid-to-lower tier of performers (Fig. a and d). For SST, CMC performs reasonably well, while GOES-16 and OSPO are among the worst performers on the mesoscale domains (Fig. b and e). The main driver for the surface forcing, however, is the difference between 2 m temperature and SST, ΔT. The GOES-16 setup results in some of the highest error and largest bias (Fig. c and f), leading to the assumption that perhaps the mesoscale domains in this case were getting the right answer for the wrong reasons. Meanwhile, OSTIA, the worst-performing ensemble member for the mesoscale domain, captures ΔT reasonably well with relatively low RMSE and the smallest bias. Of the three selected best mesoscale performers, CMC produces the best results for ΔT on the mesoscale and could reasonably be chosen as the setup to drive the LES runs.

Ranking the performance is highly dependent on the specific feature being studied. For this study, we consider performance of the dynamic variables above (low-level shear, hub-height wind speed, and REWS) and forcing conditions (2 m temperature, SST, and ΔT) to rank the mesoscale setup performance. Considering these variables and weighting them equally, we rank the mesoscale SST dataset performance from best to worst as follows: CMC, OSPO, GOES-16, Default SST, NAVO, MUR, OSTIA (Table ).

On the mesoscale domains (domain 1 and domain 2), the lowest RMSE and smallest bias in low-level shear are from the OSPO, GOES-16, and CMC SST datasets (Fig. b and e). The same three datasets produce the lowest RMSE for hub-height wind speed for domain 2, with only the NAVO dataset performing better on domain 1 (Fig. a). Hub-height wind speed is underpredicted on the mesoscale, resulting in positive biases for all SST setups (Fig. d).

When the simulation grid spacing enters the gray zone with an LES turbulence closure scheme, the results for the wind field (Fig. ) and near-surface forcing (Fig. ) change drastically (with the exception of SST, in which little variation is found across all domains). Biases for low-level wind shear and hub-height wind speed jump from positive to negative due to decreases in wind speed near the surface and higher wind speeds at the jet nose. The RMSE of low-level shear reaches local minimum in all SST setups due to the near-surface wind speed being slightly faster than the LES domains while maintaining a similar wind speed at hub height (Fig. d). Similarly, 2 m temperature RMSE reaches a local minimum on domain 3, while bias is nearest to zero for all SST setups (Fig. a and d).

Considering now the LES domains, the temperature forcing field's performance recover from the step change in domain 3 to remain more or less static between the mesoscale and microscale (Fig. ). There are some adjustments in the ranked performance in these fields but no large shifts from worst on mesoscale to best on microscale. From this, we might expect that performance in the important variables identified above would also not change dramatically.

For the wind profile characteristic variables, the best performers in low-level shear on the LES domains are the default SST setup and the OSTIA setup (Fig. b and e). Recall that the OSTIA setup was the worst performer on the mesoscale. OSTIA also improves to be among the middle-to-top performers for hub-height wind speed and REWS (Fig. a, c, d, and f). GOES-16 and CMC performed at opposite ends of the spectrum for ΔT, yet produce similarly good results on both the mesoscale and microscale. Ranking the setups for microscale performance results in CMC, GOES-16, OSTIA, MUR, Default SST, NAVO, OSPO (Table ). Note that two of the top three performers on the mesoscale are the top two of the microscale performance ranking. However, OSPO moves from the second-best overall performer on the mesoscale to the worst performer on the microscale. Likewise, the worst mesoscale performer improves to the third-best performer on the microscale domain.

OSPO was one of the better performers for low-level shear and hub-height wind speed on the mesoscale. Depending on the metric that is of most interest to a study, it could have been selected as the best-performing mesoscale study. However, the OSPO setup is the worst performer for these metrics on the microscale (Fig. a, b, d, and e). This is significant due to the fact that the SST and 2 m temperature (and resulting ΔT) performance for OSPO remains fairly constant from mesoscale to microscale – a finding that would suggest that relative performance would also not change. The fact that a large swing in performance is found suggests that there are other significant factors in determining model performance across scales.