This section gives a brief overview of the observational data sets. Additional information can be found in Sects. S1 and S2 in the Supplement and the metadata of the uploaded data sets (see “Code and data availability” section).

We evaluated the operational version of NOAA's HRRR model version 4, that has been operational since December 2020. The operational HRRR model is run hourly with an independent initial condition created by the HRRR Data Assimilation System (HRRRDAS) which leverages the Rapid Refresh model analyses twice daily as a background for data assimilation to constrain the synoptic scale evolution. The HRRR provides 18 h forecasts, but every 6 h, at 00:00, 06:00, 12:00, and 18:00 UTC, the forecast horizon is extended to 48 h. The HRRR assimilates a broad set of observations, including data from radiosondes, radars, aircraft, surface stations, buoys, and satellites. No measurements from the WFIP3 campaign that are used for the model evaluation in this study were assimilated. HRRR version 4 uses the Mellor-Yamada-Nakanishi-Niino eddy-diffusivity mass-flux (MYNN-EDMF) scheme for the planetary boundary and surface layer and subgrid-scale clouds, the Rapid Update Cycle land surface model (RUC LSM) for the land surface, the Rapid Radiative Transfer Model for general circulation models (RRTMG) for radiation, and the Thompson aerosol-aware scheme for cloud microphysics details in.

The first model level is just below 10 m, and vertical grid spacing increases from about 25 m near the surface to 300 m at 1.5 km with a total of 10 levels below 1.5 km. The horizontal grid spacing is 3 km, and we selected the grid point that is closest to the location of each site and over land for comparison to the observed profiles (Fig. d, f, h). In this study, we concatenated hourly model output for each forecast horizon starting at 0 (initialization time) out to 18. This resulted in a continuous time series for each forecast horizon that could be compared to the observations.

SST in the HRRR model comes from the Global Data Assimilation System (GDAS) operated by the NOAA National Centers for Environmental Prediction. We compared daily averaged HRRR SST to OSTIA SST at four locations (close to NANT, BLOC, RHOD, and Buoyz01) and found differences depending on location and season (Fig. ). When SST was cool (less than 15 °C), the HRRR SST and OSTIA SST agreed relatively well at all locations on the average (mean difference <1 °C). When SST exceeded 15 °C, which was approximately the case between June and November (Fig. S2), SST in the HRRR was frequently overestimated by several degrees at NANT, while it was slightly underestimated at RHOD and Buoyz01 on the average. found that the bias in SST between HRRR and OSTIA varied spatially in the New York Bight during summer sea-breeze events with a warm bias near the coasts and a cold bias further offshore possibly owing to coastal upwelling.

To detect LLJs in the observed and simulated hourly wind profiles, we used criteria based on maximum wind speed and wind speed decrease above the nose, which were first developed by and which has also been applied in previous studies on coastal LLJs in the area e.g.,. Other studies used a less restrictive method to detect LLJs in the area, e.g., who defined the LLJ as a wind speed maximum between 150 and 300 m. As pointed out by , there is no consensus regarding how LLJs should be defined and the choice of criteria a as well as the vertical window from which the LLJs are extracted impact the LLJ frequency and morphology. Hence care should be taken when making cross-study comparisons.

The observed and simulated temperature and wind profiles were linearly interpolated to an equidistant vertical grid with 10 m grid spacing. Profiles with less than 100 valid heights in the lowest 1500 m (corresponding to at least 1000 m in vertical coverage) were rejected. Then, the wind speed maximum in the lowest 1500 m was detected in each remaining hourly profile. This maximum had to occur in the lowest 700 m and exceed 8 ms-1. This speed threshold was 2 ms-1 lower than in and because we found that many profiles that clearly showed an LLJ structure and were hence of interest for model development would have been missed otherwise. Above the nose, wind speed had to decrease by at least 4 ms-1 to the next higher minimum or the 1500 m level, whatever is lower. We then classified the LLJ using five classes, based on the strength of the wind speed maximum at LLJ nose and above-nose wind speed decrease, following the pattern of and but with an additional class to account for weaker LLJs (Table ). Both thresholds need to be exceeded for an LLJ to fall into a certain class. For example, if LLJ nose wind speed is 17 ms-1 and above-nose wind speed decrease is 5 ms-1, the LLJ is classified as class 1, not class 3, because above-nose wind speed decrease does not exceed the threshold of 8 ms-1 for class 3. We tested the sensitivity of our results to the nose wind speed threshold by performing the same analysis using a 10 ms-1 threshold for nose wind speed, that is, only considering LLJs that fall into classes 1 through 4. While this reduced the number of LLJs in the data set, the model errors were largely the same when removing the weakest LLJ class.

To investigate the capability of the model to correctly predict LLJ we computed the critical success index: 2CSI=HitsHits+Falsepositives+Misses.

CSI of 1 indicates a perfect forecast. CSI can be high for very frequent events even without real skill or low for rare events despite model skill. We also computed the frequency bias: 3FB=Hits+FalsepositivesHits+Misses.

FB of 1 indicates unbiased forecasts, values of less than 1 indicate an underestimation of frequency, and values larger than 1 indicate an overestimation.

We computed shear and static stability as the horizontal wind speed gradient and the virtual potential temperature gradient for the layer between 50 and 200 m. We chose 50 m as the lower boundary to at least partially mitigate the impact of the island and 200 m as the upper boundary because it was mostly below the LLJ nose. Virtual potential temperature θv profiles were computed using the dry-adiabatic lapse rate as 4θv(z)=Tv(z)+0.0098⋅z where Tv is the virtual temperature and z the height above ground.

As a measure of dynamic stability we computed the bulk Richardson number Ri e.g.,: 5Ri=gΔθv/Δzθv‾(ΔU/Δz)2, where g is gravitational acceleration, θv‾ is the layer-mean virtual potential temperature, Δθv/Δz is the virtual potential temperature gradient, and ΔU/Δz is the wind speed shear. Shear, static stability, and Ri were computed for the layer below the LLJ nose as well as for constant layers using the boundaries detailed above. Negative Ri indicate a statically unstable environment. Small positive Ri indicate that the conditions are dynamically unstable, and large positive Ri indicate that the conditions are dynamically stable. The value to mark the transition between dynamically stable and unstable conditions depends on various factors, such as layer depth, growing or decaying turbulence, and near-surface vs. internal layers, and a transitional range spanning values from 0.25 to larger than 1 have been reported e.g.,.

Monthly composites across the full diurnal range of observed horizontal wind speed (Fig. a) and potential temperature at NANT (Fig. a) show a strong seasonal cycle with generally higher wind speed during the colder months. A weak diurnal cycle in wind speed throughout the lowest 1.5 km was present on average with lower wind speeds during the day. Hardly any diurnal cycle in temperature was visible, except close to the surface, which likely represented the vertical extent of the internal boundary layer of the island at NANT. Above the internal island boundary layer, the marine boundary layer did not exhibit much of a diurnal cycle in temperature, which can likely be attributed to the damping impact of the water body on the marine boundary layer temporal evolution. Temperature stratification was statically stable on average with the strongest stability occurring in late spring and early summer (mean stability values are given in the upper right corner of each subplot in Fig. a). During these months, a low-level wind speed maximum in the lowest few hundred meters existed from late afternoon to early morning, indicating the occurrence of an LLJ (Fig. a). By visual comparison, the HRRR model did a very good job in capturing the seasonal and diurnal evolution of wind and temperature (Figs. b and b). Some differences are evident, especially during the warmer months, when low-level static stability and horizontal wind shear was too weak in the model on average, as indicated by numbers in the upper right corner of each subplot. For example, the observed average static stability in June was 0.0169 Km-1, while it was only 0.0082 Km-1 in the simulations, that is, it was underestimated by a factor of 2.

These errors in stability and shear were consistent with the composites of temperature and wind speed differences (Fig. ). During the warmer months, the HRRR model underestimated wind speed by more than 1 ms-1 on average in the lowest few hundred meters. During the colder months the underestimation of wind speed was less pronounced. The model overestimated temperature in roughly the lowest 200 m by up to a few degrees during the warmer months. This, in combination with an underestimation of temperature in the layers above, is consistent with the underestimation of low-level static stability (Fig. ). The underestimation of low-level wind speed was similar to that observed far offshore on a barge that was deployed for WFIP3 during a few months in summer 2024 . While wind speed errors at NANT did not show a distinct dependence on the time of the day, temperature overestimation below around 200 m was larger during the daytime hours during all months, especially during the summer. This diurnal variation in temperature difference indicates that there was an impact of the island topography at the site, with the HRRR model warming up too much during the midday hours over land in the lowest model layers. The general findings – a strong seasonal cycle and a weak diurnal cycle in observed horizontal wind speed and temperature and the frequent presence of an LLJ and statically stable stratification during the warmer months – also hold for the BLOC and RHOD sites (Sect. S4). The distinct low-level wind speed underestimation by the HRRR model was almost absent at RHOD (Fig. S8a) and weaker at BLOC where wind speed at the lowest height levels was even persistently overestimated (Fig. S5a). The overall overestimation of temperature close to the surface and an underestimation in the layers above by the HRRR model, especially during the warmer months, was also present at BLOC (Fig. S5b) and RHOD (Fig. S8b).

In Sect. , only forecast hour 12 of the HRRR was investigated. In Figs. and , bias and standard deviation of low-level wind speed and potential temperature dependence on forecast hour are shown per season. During the summer months (JJA), wind shear at NANT was too weak in all forecast hours (Fig. a), mostly caused by an underestimation of wind speed at 200 m by more than 0.5 ms-1 (Fig. c). During the other seasons, no systematic biases in wind shear were found on average at NANT. At BLOC, wind shear was consistently too weak during all seasons for all forecast hours (Fig. a). This was largely caused by wind speed that was too strong at 50 m (Fig. b). This overestimation of 50 m wind speed could be related to the misrepresentation of the island topography in the HRRR model. At RHOD, average wind shear errors were small for all seasons and all forecast hours. Horizontal wind speed in the model was lowest at initialization time at individual height levels (50 and 200 m) and accelerated during the first few forecast hours, resulting in a decrease in bias (e.g., at 200 m at NANT and BLOC) or the evolution of a positive bias (e.g., 50 m at BLOC) (Fig. b, c). While the bias was relatively constant after the first few forecast hours, standard deviation of wind speed at 50 and 200 m increased with forecast hour for all seasons and all sites (Fig. b, c), indicating that forecast variability errors grew faster than systematic mean errors, likely linked to the general degradation of model skill with forecast hour.

The bias in static stability, which was computed as the difference in simulated and observed virtual potential temperature gradient between 50 m and 200 m, showed that the model was not stable enough during all seasons and at all sites (Fig. a). Static stability was in particular too weak during spring (MAM) and summer (JJA). The errors in static stability can be linked to the errors at 50 and 200 m. At 50 m, temperature biases were mostly positive during all seasons. with the largest warm bias during MAM and JJA, and decreased in magnitude for longer forecast hours (Fig. b). At 200 m, the temperature bias was small and positive at initialization time and became negative for longer forecast hours (Fig. c). The combination of the sign of the errors at 50 and 200 m and their dependence on forecast hour, that is, the diminishing of a warm bias at 50 m and the growth of a cold bias at 200 m, resulted in stability errors that were nearly independent of forecast hour. The stability error was most pronounced at NANT, where SST was overestimated by more than 2 K on average during the summer months (JJA), which could contribute to the overestimation of 50 m temperature. This relationship will be investigated in more detail in Sect. . Similar to wind speed, the standard deviation at the two individual height levels (50 and 200 m) increased for longer forecast hours (Fig. b, c). In the following sections we will focus on forecast hour 12. Note that the general conclusions do not change for shorter or longer forecast hours, given the overall constant sign in errors for shear and stability.

In this section, we investigate the relationship between HRRR model errors in wind speed shear and static stability and wind direction. Wind direction was generally well forecasted, with a mean absolute deviation of less than 15° at NANT and BLOC and approximately 20° at RHOD (not shown). The histograms of wind direction on the y-axis in Fig. a–c reveal that westerly flow was dominant and flow from the southeasterly quadrant was least frequent. This distribution agrees with results based on buoy-lidar data or tower measurements .

Wind speed shear was both overestimated and underestimated at NANT depending on wind direction (Fig. a). The strongest underestimation occurred for southwesterly flow, mostly caused by an underestimation of 200 m wind speed (not shown). Other wind directions showed either a slight overestimation of shear (northwesterly flow) or no systematic errors (northeasterly flow). Static stability was predominantly too weak in the HRRR model. The largest stability error occurred for southwesterly flow (wind direction roughly between 180 and 260°). As shown in Sect. , the too-weak static stability was caused by a too-cold temperature at 200 m and a too-warm temperature at 50 m at this forecast hour.

To further understand the reason for the stability error, we more closely investigated the relationship between the errors in static stability and SST (Fig. c). These errors were weakly negatively correlated (R=-0.3), meaning that static stability in the HRRR model was getting increasingly too weak with growing SST error. This was mostly linked to an overestimation of temperature at the bottom of the layer used for the static stability computation, that is at 50 m, where the SST and temperature errors were weakly correlated (R=0.3). This indicates that many of the cases with too-weak static stability in the model were linked to an overestimation of SST and consequently warm biased low-level temperature, suggesting that the specification of the lower boundary conditions are likely a contributing factor to the near-surface model errors. The relationship between stability errors, SST errors, and southwesterly flow indicates that those could be linked to coastal cold water upwelling that may occur under persistent southwesterly flow as shown by e.g. for the New York Bight.

The largest errors in low-level wind speed and static stability occurred for southwesterly flow (Fig. a, b). These errors became even more visible when selecting only the samples when an LLJ was observed (Fig. d, e). The histogram of wind direction on the y-axis shows that southwesterly LLJs were most common, followed by northeasterly LLJs. This is in agreement with previous studies on LLJs in the area e.g.,. Most of the southwesterly LLJs were associated with an underestimation of wind speed shear (Fig. d) and static stability that was too weak (Fig. e). Northeasterly LLJs showed similar but weaker error. Consistent with the findings for all times, static stability was particularly too weak when SST was overestimated (Fig. f). While wind shear errors at BLOC (Fig. S9a, d) were similar to those at NANT, that is, the largest underestimation occurred for southwesterly flow, they were mostly caused by an overestimation of 50 m wind speed and not by an underestimation of 200 m wind speed, which could be related to the misrepresentation of the island topography as discussed before. At RHOD no systematic large shear errors were visible (Fig. S10a, d). Static stability errors were similar at BLOC (Fig. S9b, d) and RHOD (Fig. S10b,d), with the static stability being mostly too weak in the HRRR. Like at NANT, the stability error at BLOC was weakly negatively correlated with the SST error (R=-0.1) (Fig. S9c, f). The lack of any correlation at RHOD (R=0.0) (Fig. S10c, f) may indicate that conditions at this site are too strongly impacted by land to be ideally suited to evaluate errors in the lower part of the marine boundary layer in the HRRR model. SST errors in the HRRR varied spatially (Fig. ). While the SST was much too warm during the warmer months near NANT it was very well captured at the buoy location further south. Since SST has an impact on low-level static stability, stability errors in the HRRR model may thus be different in other parts of the investigation area.

In the previous section, we showed that LLJs were often associated with relatively large systematic model errors (Fig. ). This motivates a more detailed investigation of the observed LLJs and the ability of the model to predict them. The contingency table for observed and simulated LLJs is shown in Table , and statistics for LLJ characteristics are shown in Fig. .

LLJs were detected in 18 %–21 % of the observed profiles and in 14 %–16 % of the simulated profiles using only valid profiles with sufficient data availability (numbers in the legend of Fig. a). The percentage at RHOD was similar to NANT and BLOC despite the much lower number of valid profiles. About 35 %–40 % of all the observed LLJs in the area were classified as the weakest class 0, with a nose wind speed exceeding 8 ms-1 and shear above nose exceeding 4 ms-1. Class 1 and 2 LLJs occurred with similar frequency (each about 25 %–30 %). This distribution is fairly consistent at the three sites and captured well by the HRRR model. The monthly averaged LLJ nose height ranged between around 250 m in June to more than 400 m in the colder months, with the model overestimating LLJ nose height by 50 to 100 m on average (Fig. b). LLJ occurrence shows a clear seasonal cycle with more frequent occurrence during the warmer months from April to early summer (Fig. c), which was well captured by the HRRR model. In June, between 30 % and 40 % of all valid profiles had an LLJ shape independent of the site. LLJ frequency showed a secondary peak in September, especially at NANT, which was also present in the model, although underestimated. LLJs in September were predominantly associated with northeasterly flow (not shown) and likely linked to frontal passages. This distinguishes them from the LLJs that occur in late spring and early summer, which are predominantly from the southwest and likely driven by the land-sea temperature difference between the warm land and still cool ocean surface. Observed and simulated LLJ frequency ramped up in the afternoon and peaked during the first half of the night (Fig. d). The seasonal and diurnal cycle is in agreement with other studies on LLJs in this region e.g., and can be explained by the diurnal heating and cooling of the land (Sect. ). The diurnal cycle was most pronounced at RHOD at the coast with LLJs occurring less than 5 % of the time around midday. At NANT the diurnal cycle was weaker, with LLJ frequency not falling below 15 % in the observations. The HRRR model underestimated LLJ frequency at NANT pretty consistently by 5 %–10 % for all hours of the day.

The capability of the model to correctly detect LLJs is investigated by means of CSI and FB (Sect. ). The HRRR model underestimated LLJ frequency, indicated by FB values less than 1 (Fig. e). The underestimation is larger at NANT than at BLOC and RHOD during the warmer months, with FB less than 0.75. This is consistent with the observed and simulated LLJ frequency in Fig. c. FB at NANT did not show a clear diurnal cycle (Fig. f), which means that the model did not systematically fail to predict LLJ profiles at a certain time of the day. At BLOC and RHOD, the model captured LLJ frequency best in the morning hours with FB values generally exceeding 0.80. CSI mostly ranged between 0.25 and 0.60, with the largest values in spring and early summer. In June, up to 60 % of the LLJ profiles were correctly predicted by the model at all sites.

For a more detailed evaluation of HRRR model errors, we stratified the data for LLJ hits, misses, false positives, and correct rejections. Errors in LLJ nose height and shear and stability below and above the nose are shown for LLJ hits in Fig. . The model overestimates nose height by approximately 75 m at NANT, 40 m at BLOC, and 33 m at RHOD on mean average. Wind speed at nose height, wind shear below nose height, and wind shear above nose height are underestimated at all sites. The wind speed underestimation ranged between -0.5 ms-1 at BLOC and -0.8 ms-1 at NANT on average. The overestimation in nose height and underestimation of wind speed contribute to the underestimation in wind shear below nose height. The overestimation in nose height and underestimation in wind speed might be related to the relatively coarse vertical resolution with only 10 model levels below 1500 m. However, found very little sensitivity of errors during LLJs to increasing the vertical or horizontal grid spacing. Below the nose, static stability is too weak at all sites on average, in particular at NANT. Above-nose static stability is also too weak at NANT on average, while it is too stable at RHOD.

The analysis of shear and stability errors is extended to LLJ misses, false positives, and correct rejections by looking at fixed heights (Fig. ). Shear in the 50–200 m layer, which is usually below the observed and simulated LLJ nose height, was underestimated at all three sites for LLJ hits (Fig. a). The too-weak shear at NANT was caused by too-weak wind speed at 200 m, while at BLOC and RHOD an overestimation of the 50 m wind was mainly responsible. Static stability below 200 m was too weak, especially at NANT, which can be largely attributed to a warm bias at 50 m and a slightly cold bias at 200 m on average. Although wind speed was too weak during LLJ misses, the underestimation of shear was similar in magnitude to the LLJ hits (Fig. b). Not surprisingly, wind speed was overestimated during LLJ false positives, reducing the errors in shear (Fig. c). Static stability errors were negative at all sites for LLJ hits, misses, and false positives. This indicates that errors in the thermodynamic conditions were likely not the main reason for the HRRR to miss or falsely predict an LLJ. Many of the misses and false positives might be due to a misclassification when the minimum peak wind speed either in the model (misses) or in the observations (false positives) failed to meet the LLJ criteria. Wind speed and shear errors during correct rejections were smaller than during hits, which indicates the absence of large systematic wind speed errors outside of LLJ cases (Fig. d).

To evaluate how well the HRRR model captures the dynamic stability during LLJ hits, we compute the relationship between horizontal wind speed shear and static stability below LLJ nose from the observations and simulations (Fig. a–c). Most of the observed and simulated LLJ profiles occurred under stably stratified conditions and were associated with positive low-level wind shear. In agreement with Fig. , the shear in the model during LLJ hits was too low. The model completely missed the high shear present in the observations. This resulted from the underestimation of wind speed at nose height, the overestimation of nose height (Fig. ), and the overestimation of wind speed at 50 m (Fig. a). The frequency of profiles with weak static stability (<0.015 Km-1) was overestimated, and the frequency of profiles with larger static stability (>0.015 Km-1) was underestimated (Fig. a). Although the too weak shear partly compensated for the too weak static stability, the HRRR model still largely failed to produce low Ri (<0.5) conditions in the layer below the LLJ nose, especially at NANT and BLOC, which can be seen when comparing the frequency distributions of the observed and simulated Ri with the theoretical black lines in Fig. . This means that the model was too dynamically stable. In particular low Ri values that are associated with high shear values rarely occurred in the model. The observed Ri values at all sites are higher than what has been observed for continental LLJs, which is likely related to the weaker shear in the marine boundary layer. For example, reported shear values below the jet nose of close to 0.1 s⁻¹ over the Southern Great Plains, resulting in Ri of around 0.1.

We also computed dynamic stability for fixed layers, which allowed us to compare the distributions of shear and stability during LLJ hits (Fig. d–f) and correct rejections (Fig. g–i). The distributions of shear and stability for fixed layers during LLJ hits (Fig. d–f) were similar to the ones computed for the layer below nose height (Fig. a–c) with the model missing profiles with strong shear at the three sites and underestimating the frequency of high static stability and overestimating lower static stability at NANT. During correct rejections, high shear (>0.03 ms-1) and strong static stability (>0.015 Km-1) were hardly observed and the HRRR model did well in capturing the distribution of shear and stability (Fig. g–i). In contrast to LLJ hits, when low Ri (<0.5) values occurred at moderate to large static stability and large shear values, low Ri values during correct rejections mostly occurred when static stability was weak.

The model discrepancies in representing correct Bulk Richardson number regimes likely originate from two primary factors: (1) suboptimal regulation of the Prandtl number, and (2) insufficient calibration of near-surface mixing intensity relative to surface stability. Regarding the former, the stability functions for momentum SM and heat SH within the MYNN-EDMF framework govern the proportional mixing of momentum and heat, as expressed by the Prandtl number Pr=SM/SH. When Ri>0.1, SM exceeds SH and can trend toward infinity as Ri surpasses 1. Refined management of momentum mixing in this regime is expected to mitigate the overestimation of weak shear and the simultaneous underestimation of strong shear. Concerning the latter factor, the magnitude of near-surface mixing in the MYNN-EDMF is chiefly governed by the surface layer length scale ls, which is sensitive to the surface stability parameter ζ=z/L. Here, L represents the Obukhov length e.g. and z denotes the height above ground level. It is plausible that the regulation of ls requires distinct treatment over marine versus terrestrial surfaces. Alternatively, the estimation of ζ could be re-evaluated using flux-profile relationships specifically developed for stable marine environments. Continued investigation into these mechanisms may address the systematic underestimation of shear and LLJ intensity, as well as the positive bias in LLJ nose heights. Other sources of errors could be associated with the bulk surface flux algorithm used over water COARE3.0,, the detailed representation of the island soil temperature and moisture, and the representation of precipitation-induced surface sensible heat fluxes .