At the SGP Central Facility site, we consider observations from a Halo StreamLine lidar . We obtain horizontal wind speed data from full 360∘ conical scans by the lidar, which were performed approximately every 15 min, with 1 min needed to complete each scan. To obtain the horizontal wind speed from the line-of-sight velocity from these scans, we use the velocity–azimuth-display approach from . In doing this, the horizontal wind field is assumed to be homogeneous over the scan volume . As in , we discard any measurements that have a signal-to-noise ratio lower than -21 dB or higher than +5 dB, as well as any measurements from time periods with precipitation that may significantly lower the accuracy of the measurements. The wind speed data are then averaged to obtain hourly average data. For our study, we consider data from six range gates, which correspond to heights of 65, 91, 117, 143, 169, and 195 m a.s.l. Data at lower heights are not used because of poor data quality. The analysis of the lidar data reveals how the site experiences winds mainly from the south (see 91 m wind rose in Fig. a), with more variability observed in winter months. Many wind plants were built around the SGP site in the last decade. At the Central Facility site, the closest wind turbines are about 3.5 km away, and showed how the site is impacted by wind plant wakes for southerly flow, especially in nighttime stable conditions. We classify atmospheric stability using near-surface (4 m a.g.l.) observations from a sonic anemometer at the C1 site. We calculate the Obukhov length as 1L=-Tv‾⋅u*3k⋅g⋅w′Tv′‾, where k=0.4 is the von Kármán constant, g=9.81m s-2 is the acceleration due to gravity, Tv is the virtual temperature (K), u*=(u′w′‾2+v′w′‾2)1/4 is the friction velocity (ms-1), and w′Tv′‾ is the kinematic virtual temperature flux (Kms-1). All Reynolds decompositions are calculated with a 30 min averaging period . We consider stable conditions for 0≤L≤200 m, unstable conditions for -200≤L<0 m, and near-neutral otherwise. Figure b–d show 24×12 heat maps of the frequency of stable, unstable, and neutral conditions, respectively. A clear diurnal pattern emerges, with stable conditions being typical of the nighttime hours and unstable conditions occurring in daytime convective periods. Also, summer shows more extended unstable cases compared to winter months. On the other hand, near-neutral conditions are relatively rare at the site, occurring most often during morning and evening transitions. Finally, we consider measurements of sensible and latent heat fluxes from a flux station at the C1 site, which includes a sonic anemometer and an infrared gas analyzer, at 4 m a.g.l. Details on the calculation of the fluxes from these instruments are described in and follow the correction proposed in .

Offshore, we consider observations of wind speed from two floating lidars off the coast of New Jersey. The New York State Energy Research and Development Authority (NYSERDA) recently deployed ZephIR ZX300M lidars and made their data publicly available . The lidar on buoy E05 is located at 39.97∘ N, 72.72∘ W; the buoy E06 lidar is located at 39.55∘ N, 73.43∘ W. The lidar observations are provided as hourly averages, after proprietary quality checks are applied to the data. Wind speed and wind direction data for both lidars are available every 20 m from 60 to 200 m a.s.l. At these sites, wind mainly flows from the southwest and northwest, as is the case further east in this region , and it is generally stronger than what is observed at SGP, as shown in the wind rose at 100 m a.s.l. from lidar E05 in Fig. a. Due to the lack of observations from which atmospheric stability metrics can be calculated, we use WTK-LED data to classify atmospheric stability as a function of the bulk Richardson number from 0–200 m above the surface. The bulk Richardson number is calculated as 2Rib=gθv‾ΔzΔθv(ΔU)2+(ΔV)2, where g is the gravitational acceleration, θv‾ is the average absolute virtual potential temperature across the considered layer of thickness Δz, Δθv is the virtual potential temperature difference across the layer, and ΔU and ΔV are the changes in the horizontal wind components across that same layer. We use values of Rib>0.025 to classify stable conditions, Rib<-0.025 for unstable conditions, and all other values as near-neutral conditions. Figure b and c show the 24×12 heat maps of the frequency of stable and unstable conditions, respectively. While a clear diurnal pattern emerges when looking at similar plots at SGP, here we find little diurnal variability but a strong seasonal cycle. Summer months show the most instances of stable conditions, while winter months show primarily unstable conditions. Finally, near-neutral conditions account for up to half of the cases in certain times and show little variability across both the diurnal and annual scales.

At SGP, we use WRF model data for 2018 from the preliminary National Renewable Energy Laboratory's (NREL's) Wind Integration National Dataset (WIND) Toolkit Long-term Ensemble Dataset (WTK-LED), which will update the original WIND Toolkit (WTK) . The main WRF attributes in the WTK-LED setup are summarized in Table . All the main setups that have been shown to have a major impact on modeled wind speed (e.g., the choice of the planetary boundary layer scheme and of the atmospheric forcing) are the same between the offshore and land-based domains. For some other setups, different choices are made between the two domains in order to optimize and tailor the numerical simulations to the specific needs of each domain. At both sites, the simulations are initialized every month, and each simulation is initialized 2 d prior to and run up to 1 d after the end of each month. The first day of each monthly run is used as spin-up time for the model, while the second and last days are used to combine monthly runs. Model output is available at 5 min resolution, and we average the data at hourly resolution to perform the validation analysis. We consider data from the closest 2 km grid cell to the location of the lidar (the difference in terrain height between this WRF grid cell and the actual lidar location is <3 m). To match the heights at which lidar observations are available, we linearly interpolate the WRF data from the two closest levels. Given the high near-surface resolution used (see Table ), we expect this linear interpolation to introduce only a small additional error to the analysis.

Offshore, we use WRF data from the offshore version of NREL's WTK-LED. A summary of the model setup is provided in Table . Similar to the land-based case, we select WTK-LED data from the closest grid cell to the location of each of the two floating lidars and linearly interpolate the WRF vertical levels to match the heights of the lidar data.

We use the state-of-the-art ERA-5 reanalysis product to compare its skill in assessing wind resources with that of the WTK-LED product. ERA-5 provides hourly average data at 137 vertical levels and an ∼31 km horizontal resolution. In our analysis, we consider vertical levels corresponding to heights of 54, 79, 106, 137, 170, and 205 m a.s.l. As done for WTK-LED, these heights are then linearly interpolated to match those of the lidar observations. We use data from the ERA-5 grid point which is closest in space to the considered lidars. recently showed that selecting the closest grid point generally leads to better reanalysis performance compared to a linear interpolation of the four surrounding grid points, while used a bilinear interpolation. The coordinates of the selected ERA-5 grid point at SGP are 36.5∘ N and 97.5∘ W; offshore, we use data from the 40∘ N, 72.75∘ W grid point to compare with the E05 lidar data and at 39.5∘ N, 73.5∘ W to compare with the E06 lidar data.

To quantify the skills of WTK-LED and ERA-5 in predicting the observed wind resource, we calculate, at all of the considered heights, five performance metrics.

In general, it is important to decompose a model error into bias, which quantifies the difference between modeled and observed data, and random error, which quantifies the variability of the modeled data around the mean. We decompose the root-mean-square error (RMSE) into a bias component and an “unbiased” or “centered” component of RMSE (cRMSE), following the approach in . We calculate bias as 3Bias=p‾-o‾, where p‾ is the mean of the modeled (by either WTK-LED or ERA-5) estimates and o‾ is the mean of the lidar observations. A perfect prediction would have a bias of 0. Next, we calculate the cRMSE as 4cRMSE=1N∑n=1N[(pn-p‾)-(on-o‾)]21/2, where N is the number of data points in the considered time series, and pn and on indicate the time series values of modeled and observed wind speed, respectively. A perfect prediction would have a cRMSE of 0.

As a third performance metric, we calculate the square of the Pearson's correlation coefficient between observed and modeled wind. The correlation coefficient r measures how strong the correspondence between two variables is, and it is calculated as 5r=1N∑n=1N(pn-p‾)-(on-o‾)σpσo, where σp and σo are the standard deviations of the modeled and observed data, respectively. A perfect prediction would have a correlation coefficient of 1.

Next, we use the Earth mover's distance (EMD), also known as the Wasserstein distance , which measures the difference between two distributions. EMD is calculated as the area between two cumulative distribution functions (here, modeled and observed wind speed). This metric is an improvement on the bias metric and will catch cases where bias may be zero, despite having different modeled and observed wind speed distributions. The distribution of a perfect prediction would have an EMD of 0.

Last, we compare the standard deviation of the observed wind speed with what is predicted by WTK and ERA-5.

In Fig. , we compare the mean wind profiles from all three data sources at SGP and the NYSERDA E05 lidar. (Results from the E06 lidar are included in the Supplement because no major differences between the results from the two lidars were found.) In each panel, the solid lines indicate the mean wind profile, and the shaded bands around them represent ± the standard deviation of the data. On average, the wind resource is stronger offshore. At both sites, the ERA-5 mean wind profile underestimates the observed wind resource. Conversely, WTK-LED shows a limited overestimation of the mean wind profile at the land-based site and a slight underestimation offshore. However, in all cases, a large variability emerges so that a more detailed investigation, beyond an annual average, is required.

We then consider the five mean performance metrics introduced in Sect. 2.4 for both WTK-LED and ERA-5 calculated at the two sites (Fig. ). The WTK-LED-predicted wind speed profiles show a limited positive bias (∼+0.5ms-1) at the land-based location and a slight negative bias (∼-0.5ms-1) offshore. However, ERA-5 shows a significant negative bias at both locations, especially at SGP, where the bias is ∼-1.5ms-1. In general, we find little variability with height, with just a minor degradation of the bias with height for both WTK-LED and ERA-5. When considering the cRMSE, however, we find an opposite situation, with ERA-5 outperforming WTK-LED at both locations at all heights. We find satisfactory correlation at both sites, once again with ERA-5 providing marginally better values. The offshore location shows larger values (r2>0.85 for both ERA-5 and WTK-LED at all heights), likely because of the positive effects of the simpler topography on the skills of both data sources. Interestingly, we find a minor increase in r2 with height, especially at SGP. When looking at the EMD, WTK-LED significantly outperforms ERA-5 at both sites, once again with the offshore site showing better results for both data sources compared to the land-based location. Finally, when comparing the modeled and observed wind speed standard deviations, we find no clear winner between WTK-LED and ERA-5 at SGP, whereas offshore WTK-LED provides more accurate results. Given the difference in relative performance between WTK-LED and ERA-5 when considering different metrics, we will investigate the impact of wind direction, atmospheric stability, diurnal, and seasonal cycles in the next sections to investigate the potential reasons for such variability.

To assess whether the relative performance between ERA-5 and WTK-LED holds in all atmospheric stability conditions, we segregate the data at both sites. As detailed in Sects. 2.1.1 and 2.2.1, we classify atmospheric stability at SGP based on the near-surface observed Obukhov length, while offshore we base our classification on the WTK-LED-modeled bulk Richardson number, in absence of direct observations from which atmospheric stability parameters can be derived. We then calculate the vertical profiles of the five performance metrics for each stability class at the two sites (Fig. ). The relative performance between ERA-5 and WTK-LED observed from the mean profiles with no data segregation still holds in all stability conditions: WTK-LED outperforms ERA-5 for bias EMD and, at the offshore site, standard deviation, while ERA-5 shows a better performance when considering cRMSE and r2. When analyzing how the performance of each data source varies with atmospheric stability, interesting considerations emerge.

At SGP, WTK-LED shows the best agreement with observations in unstable conditions, with a near-zero bias and EMD at all considered heights, and its lowest values of cRMSE. However, stable cases seem the most challenging to model for WTK-LED, as also noticed by with respect to the challenges for WRF to accurately model the frequent nocturnal low-level jets in the region. ERA-5 also performs well in unstable conditions, but ERA-5's stable cases outperform neutral conditions, which show worse performance in terms of bias, cRMSE, and EMD. Little variability with stability emerges when considering the r2 metric.

At the offshore site, slightly different considerations apply. While unstable conditions still show the best performance in terms of cRMSE, stable and neutral cases outperform unstable conditions when considering bias and EMD, with again little variability in terms of correlation. For ERA-5, unstable cases show the best performance across all the considered metrics, followed by neutral conditions and, last, stable periods.

Different wind direction regimes could also have an impact on the relative performance of WTK-LED and ERA-5. In general, we find that both WTK-LED and ERA-5 are capable of accurately representing the observed wind direction distributions at the considered locations (see histograms in the Supplement). At SGP, the wind is mainly from the south or north (wind rose in Fig. ), with a strong seasonal variability as summer months experience mostly southerly flow, whereas in winter a broader range of wind directions is observed. At the offshore location, the winds are mostly from the northwest or the southeast (wind rose in Fig. ), once again with a significant seasonal variability (as described in ), with summer seeing mostly southwesterly winds and winter experiencing mostly northwesterlies. Based on these dominant wind regimes, we show in Fig.  vertical profiles of the five performance metrics with data segregated by wind direction. At SGP, we include northerly (315–45∘) and southerly (135–225∘) flow; at the E05 lidar, we show results for northwesterly (270–360∘) and southwesterly (180–270∘) winds.

At SGP, both WTK-LED and ERA-5 show a better performance for northerly flow, when looking at bias, cRMSE, and EMD. In terms of correlation, southerly flow cases are marginally better for both data sources, but with a very limited difference. As will be detailed in Sect. 3.5, the worse performance for southerly flow at the site can be connected to potential wind turbine and wind plant wake effects, which impact the SGP observational site for southerly winds.

At the offshore site, WTK-LED shows better skills when modeling southwesterly flow, whereas ERA-5 is more accurate at representing northwesterly flow. This is true across all performance metrics.

To further investigate the reasons for WTK-LED displaying a worse performance in its cRMSE and r2 compared to ERA-5, we analyze the average diurnal cycle in wind speed at both locations (Fig. ). A clear diurnal variability emerges at both locations, with higher wind speeds occurring at night (SGP) or evening (offshore). At SGP, this variability is consistent with the frequent nocturnal low-level jets that have been observed at the site . We find that ERA-5 well captures the amplitude of the observed diurnal cycle with a negative bias that remains nearly constant throughout the average day. By contrast, WTK-LED overestimates the amplitude of the average diurnal cycle, especially at the land-based location. At SGP, we find that WTK-LED significantly overestimates the nocturnal high wind speeds, whereas it slightly underestimates the daytime wind regime. Offshore, a nearly opposite situation occurs as WTK-LED exhibits skill in predicting the strong nocturnal winds but marginally underestimates the weaker daytime winds. This exaggeration of the diurnal cycle by WTK-LED leads to its worst performance, compared to ERA-5, when considering the cRMSE and correlation coefficient at both locations.

To further break down the temporal variability of the relative performance of WTK-LED and ERA-5, we look at the diurnal and seasonal variability of bias, cRMSE, r2, and EMD at both test sites. To do so, we build 24×12 heat maps of the four metrics by partitioning data by both hour of day and month. We show results for the land-based test case in Fig. ; the offshore test case is shown in Fig. . We show results at 91 m a.g.l. at SGP, at 100 m offshore, considered as a proxy for wind turbine hub height, and we note that no significant variability of the metrics with height was found. At SGP, the analysis of bias confirms what was seen in Fig.  – that ERA-5 displays a negative bias for all months and hours, whereas WTK-LED shows mostly a positive bias during the night and a negative bias during the daytime, thus confirming that WTK-LED overestimates the diurnal cycle throughout the year. While the daytime bias performance of WTK-LED does not change significantly throughout the year, we find a larger positive bias in summer nights, whereas in winter the bias is smaller. As mentioned in the previous section, this could connect to the seasonal variability of the wind regimes at the site, where summer months show dominant winds from the south, whereas winter experiences a larger variability of wind directions. When looking at the differences in the cRMSE between WTK-LED and ERA-5, we find more instances where WTK-LED shows higher cRMSE values than ERA-5 during the nighttime than the daytime. As already noted for bias, we find a worse WTK-LED performance during nighttime in summer months also in terms of cRMSE, correlation, and EMD. In general, WTK-LED shows significantly better performance than ERA-5 in terms of EMD during the daytime, whereas there are several instances during the nighttime, especially in the late spring and summer months, where ERA-5 outperforms WTK-LED.

At the offshore lidar location, ERA-5 shows a negative bias for all months and hours, similar to what was seen at SGP. WTK-LED displays more occurrences of positive biases in spring and summer months, especially at night, whereas a limited negative bias is observed during the winter months at all hours. The overestimation of the observed diurnal cycle by WTK-LED is therefore more typical of summer months. However, little variability emerges when considering the relative performance of WTK-LED and ERA-5 in terms of the cRMSE, at both diurnal and annual scales. In fact, in the majority of cases, WTK-LED displays a higher cRMSE than ERA-5 but without any clear seasonal or diurnal pattern, thus making the interpretation of the results murkier compared to the land-based case. Looking at the heat map for the EMD, a consistent seasonal or diurnal pattern is not clear, either. However, WTK-LED generally outperforms ERA-5 in terms of EMD, with its best performance in the spring.

As already mentioned, the land-based location, during 2018, is influenced by the presence of a large number of wind power plants in its vicinity (see map in Fig. ). As shown by , wakes from wind plants in the vicinity affect the lidar measurements at the C1 location when the wind is flowing from the south, and wake effects tend to be stronger in stable conditions. Because the WTK-LED predicts stronger winds at night than the lidar observes, some of the exaggerated diurnal cycle could be due to the fact that the WTK-LED does not incorporate effects from wind power plants. To further investigate this possibility, Fig.  shows the hub-height wind speed average diurnal cycle at SGP for southerly flow (i.e., when the wind turbines are directly upwind of the lidar, panel a) and northerly flow (i.e., when the lidar measurements are unaffected by the wind power plants, panel b). We find that WTK-LED overestimates the hub-height wind speed especially for southerly flow, while only a marginal overestimation is observed for the less frequent northerly flow. This result suggests how wind power plant wakes, which are not represented by WTK-LED, could contribute to its strong overestimation of wind speed during stable conditions, which is consistent with the results presented in the previous sections. Based on the quantification of the wake impacts on the SGP C1 lidar in , wakes reduce wind speeds at C1 by up to 0.7 ms-1 and can therefore explain about a third of the WRF nighttime overestimation of wind speed at the site.

The ability of WTK-LED of accurately representing soil moisture could also contribute to explaining the overestimation of the diurnal cycle at SGP, as the variability of surface fluxes can change atmospheric turbulence and, as a consequence, drag . In Fig. , we compare the average diurnal cycle in sensible and latent heat fluxes from near-surface observations at SGP and from the WTK-LED. We find that WTK-LED overestimates the sensible heat flux during the day, while at night the WTK-LED prediction is, on average, quite accurate. The diurnal cycle of latent heat flux, on the other hand, is quite accurately modeled by WTK-LED throughout the day, on average, with a minor delay compared to the observed one. These results suggest that the exaggerated strong sensible heat flux by WTK-LED during the day (potentially caused by issues in the WTK-LED land use/land cover) is consistent with the WTK-LED's slight underprediction in the mean diurnal cycle of hub-height wind speed between 16:00–23:00 UTC, as a strong sensible heat flux would increase turbulence and drag. Soil moisture seems instead accurately modeled in WTK-LED given the relatively accurate latent heat flux values, so that the effects on the exaggerated diurnal cycle in hub-height wind speed are likely negligible .