Evaluation of wind resource uncertainty on energy production estimates for offshore wind farms

There is high potential to capture wind energy in offshore environments.¹ Recent infrastructure and energy diversification plans² have increased the desire to understand the wind energy resources on the outer continental shelves (OCS) of the US. The US aims to deploy an offshore wind capacity of 30 gigawatts (GW) by the year 2030 and a capacity of 110 GW by 2050.² In particular, the eastern coast has many lease areas already marked for offshore wind development, a proposed 16 wind farms with a total capacity of 26 GW.³ Chosen for their high mean wind speeds, these regions have the potential to account for a significant percentage of energy supply in the adjacent communities and total energy production in each coastal state.³ Compared to onshore environments, the offshore atmospheric boundary layer (ABL) experiences less diurnal variability and tends to have higher wind speeds due to lower levels of surface friction.⁴ These two traits of the offshore environment make it a valuable resource for energy harvesting.

The wind conditions in a given offshore area can be assessed using both field measurements and numerical data, such as from the Weather Research and Forecasting (WRF) numerical weather prediction (NWP) model. Field measurements, such as those from meteorological towers or Light Detection and Ranging (LiDAR), tend to be of a higher fidelity than numerical data given the lack, or limited number, of assumptions and simplifications needed to produce wind data. However, the cost associated with constructing and maintaining a measurement site is much higher than that associated with NWP.^5,6 Additionally, it is not always easy to obtain in situ measurements for a specific site. For example, site assessment for floating offshore wind farms is particularly challenging, requiring innovation in more expensive in situ measurement technologies, such as floating LiDAR.⁶ In such cases, there may be a trade-off between uncertain NWP, which models the exact wind farm site, and field measurements, which record data near but not directly at the site.

One particular site of interest is the Vineyard Wind 1 farm (VW1), which is scheduled to start delivering electricity in 2023. This will be the first commercial-scale offshore wind farm in the US.⁷ The location of this farm makes it an ideal candidate for the present study due to the presence of nearby, long-term LiDAR field measurements of wind conditions, as well as the existence of WRF NWP data for this site.

Previous studies have looked at the wind conditions⁸ and turbulence intensity (TI)⁹ for this particular area using LiDAR measurements from Woods Hole Oceanographic Institute's (WHOI) Air-Sea Interaction Tower (ASIT) at the Martha's Vineyard Coastal Observatory (MVCO). One finding of particular interest was that the TI in this area is relatively low, which would potentially lead to slower wake replenishment and subsequently higher wake losses relative to sites with more atmospheric turbulence.^10,11 In studying the turbulence characteristics in the VW1 lease area, it is important to understand how the turbulence impacts predictions. The power and AEP of a wind farm depend on a high-dimensional set of meteorological conditions and the farm design. To reduce the complexity of AEP estimation, which is the metric often used for wind farm design optimization, it is common to assume a fixed value of TI over the year.^12,13 This simplifying model assumption may introduce uncertainty into AEP and also predictions of the time-varying power production.

In conjunction with studies of the wind conditions in these areas, it is also important to quantify any uncertainty in predictions of power and AEP. Often the tools used for such predictions are analytical wake modeling frameworks,¹⁴ such as the FLOw Redirection and Induction in Steady State (FLORIS), a steady-state wake modeling software package.¹⁵ Uncertainty in analytical wake models can come from a number of sources, including uncertainty in the input wind conditions and uncertainty in the models themselves, such as parameter uncertainty and model-form uncertainty.¹⁶ Model parameter uncertainty has been studied for analytical wake models in FLORIS in Zhang and Zhao¹⁷ and in van Beek et al.¹⁸ Zhang and Zhao¹⁷ used Bayesian uncertainty quantification to quantify parameter uncertainty in an analytical wake modeling framework for the wake deflection, wake velocity, and wake expansion parameters. With the posterior distributions for the parameters, they were then able to use a stochastic wake modeling framework for turbine power predictions. van Beek et al.¹⁸ used variance-based sensitivity analysis to similarly quantify parameter uncertainty in an analytical wake modeling framework, in order to understand the sensitivity of the model to each parameter.

Input uncertainty pertaining to wind conditions has also been quantified, with a focus on wind direction^19–22 and wind speed.²³ In general, less attention has been paid to uncertainty in the turbulence when it is treated as an input parameter or to uncertainty in the source of the data, which is a significant source of uncertainty. As discussed above, in cases where in situ measurements are not available or if they are spatially or temporally limited in their extent, NWP data or non-local measurements can be used, but both of these data sources introduce additional uncertainty based on their shortcomings. Analyzing the impact of these uncertainties on predictions of wind farm metrics which drive decision-making is important for understanding the limitations of model predictions for wind farm design.

In the present context, we define error as the difference between a prediction and a true value, while uncertainty is the representation of confidence in the prediction. The impact of assuming TI is a constant over the year is assessed here as error due to the availability of a ground truth comparison that leverages the distribution of TI. For the wind data source uncertainty, in the absence of a truth value for the wind flow at the planned wind farm site, we focus on uncertainty assessments. In general, uncertainty in the source of input wind data can come from a number of factors. Examples include uncertainty related to location if the measurements or data are not in situ, model uncertainty if the data are produced by a numerical model, and measurement uncertainty. In the present work, all three of these sources are present and are treated as uncertainties due to a lack of knowledge of a perfect ground truth. In approaching the problem in this way, we use forward uncertainty quantification to quantify uncertainty in the broadest possible terms by jointly accounting for all sources through a comparison of high fidelity LiDAR measurements that are not in situ and NWP data that are located within the site. In this way, model, site, and measurement uncertainty are simultaneously considered.

In this work, we study the effect of simplified or uncertain input wind conditions on AEP and farm efficiency through a simplified description of TI and uncertainty in the source of the wind condition input data, respectively. We compare the AEP estimates that result from three different wind datasets: (1) LiDAR measurements located near the wind farm, but not directly at the location; (2) NWP at the wind farm location; and (3) NWP at the LiDAR location. In comparing the LiDAR data adjacent to the farm site to the NWP at the farm site, we assess uncertainty stemming from a practical limitation for offshore wind energy site assessment: in situ data may not always be available at a site of interest, but NWP are more commonly available over a wider spatial and temporal extent. In addition to this practical consideration, we provide a supplementary comparison between the LiDAR measurements and the NWP predictions colocated at the LiDAR location to assess the model error stemming from the differences between in situ and NWP data. We also perform a final supplementary comparison between the NWP at the wind farm location and the NWP at the adjacent location to assess the impact of the site induced uncertainty in the NWP. For all comparisons, we analyze multiple heights in the ABL in order to understand how differing vertical trends in the datasets propagate to the prediction metrics for various candidate hub heights for offshore wind. Here we analyze turbine hub heights of 140, 160, and 180 m. This analysis is motivated by the range of hub heights of offshore wind farms that are both currently operating and in development. At present, there are offshore wind farms with hub heights ranging from below 100 m, such as Horns Rev,²⁰ up to the estimated 150 m hub height of the planned turbines for the Vineyard Wind 1 site. There is incentive to increase hub heights due to the decreased surface effects experienced higher in the atmosphere, leading to higher wind speeds.²⁴ As such, development plans for turbines with up to 200 m towers are under way.²⁵ Each future offshore wind site will select a hub-height during development based on a variety of factors including cost, AEP, and wind shear. This study seeks to elucidate to what extent wind data uncertainty impacts AEP and farm efficiency at several candidate hub-heights that may be considered for a given offshore wind farm.

We note that since the Vineyard Wind 1 farm is not yet constructed, we do not seek to validate any of the three particular datasets, but rather we seek to quantify the AEP and farm efficiency uncertainty introduced by the wind condition uncertainty and to understand the pertinent flow physics that drive the uncertainty.

The analytical wake modeling framework used in this work is presented in Sec. II A, and the wind data sources used to drive the model are presented in Sec. II B, along with a discussion of their advantages and drawbacks. The TI error results and the wind data source uncertainty results are presented in Secs. III A and III B, respectively. TI error is found to have minimal impact on AEP, while data source uncertainty can be larger than interannual variability. Wake model sensitivity is analyzed in Sec. III B 1 and the wind condition distributions are analyzed in Sec. III B 2 in order to explain the trends observed in the uncertainty results based on the flow physics and characteristics of the ABL. Finally, conclusions are provided in Sec. IV.

The input uncertainty in this work is quantified with respect to two quantities of interest: AEP and farm efficiency. This is accomplished using time series data of the input wind conditions to compute instantaneous farm power, and then averaging in time to compute these summary statistics. For the data source uncertainty, the full input distributions of wind speed, wind direction, and TI are used, while for the TI error, the full probability distributions are still used for wind speed and direction, but the median value of TI is used.

The proposed VW1 farm design consists of 62 turbines spaced one nautical mile, or 8.5 rotor diameters apart. The turbines are General Electric Haliade-X 13.6 MW turbines, which have a rotor diameter of 218 m³⁵ and an estimated hub height of 150 m. The power and thrust curves are not publicly available for this turbine, so in this work, the IEA-15MW turbine is used as a representative turbine model. This turbine has a rotor diameter of 240 m and a hub height of 150 m.³⁵ We note that depending on the site, a candidate hub height of 180 m could accommodate a larger rotor diameter. However, we neglect these potential changes in rotor diameter in our analysis. The power and thrust coefficients are readily available in FLORIS v3.2. There are three distinct regions of the power and thrust curves shown in Fig. 1: region 1.5 in which the turbine starts to generate power at the cut-in wind speed (⁠ $3 m / s ≤ U ≤ 6.98 m / s$⁠), region 2 in which the coefficient of power C_p is constant (⁠ $6.98 m / s ≤ U ≤ 10.59 m / s$⁠), and region 3 in which the turbine is maintained to operate at the rated power until the cutout wind speed (⁠ $10.59 m / s ≤ U ≤ 25 m / s$⁠). Below the cut-in speed, the wind turbine produces zero power. We neglect the influence of wind speed and direction shear on wind turbine power production and thrust.^36,37 These regions will be discussed further in Secs. III B 1 and III B 2.

In this study, we consider three candidate wind resource assessment datasets from two sources: LiDAR data from the MVCO ASIT³⁸ and NWP data from NREL's long-term wind speed data,³⁹ which is a meteorological dataset generated with WRF⁴⁰ on a 2-km horizontal grid over the continental US. For the NWP data, two sites were used: one at the LiDAR location and one at the proposed farm location. Figure 2 shows the locations of the three datasets, with the coordinates of each site given in Table I. The ASIT where the LiDAR is located is just off the southern coast of Martha's Vineyard, as is the NWP dataset at this location. The other NWP location is within the Vineyard Wind 1 farm. For all three sources, the relevant quantities considered in this study are the wind speed, wind direction, and the ambient TI (referred to throughout the rest of this work simply as TI), as these are the ambient or freestream quantities input to FLORIS (see Sec. II A). In this study, we leverage these sites and data sources to provide estimates of the AEP and farm efficiency uncertainty stemming from different site assessment methodologies. Sections II B 1–II B 3 describe the different datasets and the associated practical limitations.

The field data were collected using a Windcube v2 vertically profiling LiDAR located on the main platform of the ASIT, which is 13 m (m) above sea level. Measurements were taken at 53, 60, 80, 90, 100, 110, 120, 140, 160, 180, and 200 m above sea level. The data used here are from 2017, 2018, and 2020, as these are currently the only full years of data. In the present work, the wind speed and direction data are averaged over 10-min windows. Additionally, a carrier-to-noise ratio of -23 dB was used to filter the raw data. Velocity variances, which are used to calculate TKE and TI, are calculated over 2-min intervals following the example of Bodini et al.⁸ These values are then additionally averaged over 10-min intervals in the calculation of TKE and TI, such that the averaging window matches that of the mean wind speed and wind direction. The shorter time window for the variance is used with the intention of capturing the smaller scale turbulence fluctuations that would be averaged out through a variance calculation over the full 10-min averaging window.

It is important to note that throughout this work, the temporal data range at each height in the NWP data has been matched to the temporal range at the same height in the LiDAR data. As shown in Fig. 3, there is a considerable range in the number of data points at each height, particularly above 140 m. Here, we have not fixed the number of data points across the considered heights to be the same, so as not to lose significant information regarding annually aggregated metrics of farm efficiency and AEP (data preserving approach). However, we recognize that the comparisons between different heights may be affected by biases in the data gaps. In studying the effect of fixing the temporal data range across all heights (data matching approach), we have found that while there is a quantitative effect, particularly on AEP, the qualitative results remain unaffected. Specifically, the trends with height that are discussed for data source uncertainty in Sec. III B remain the same, as does the fact that TI error is negligible when considering its impact on AEP. If the data were matched across all heights, approximately 25% of the data at a height of 140 m would be lost, which can bias the estimate of AEP. We assert that because this is due to an exclusion of data, the analysis as it has been conducted here presents a more accurate picture of the data source uncertainty and its effect on AEP at these lower heights where more data are available, rather than removing data at 140 m based on the availability at 180 m. Further quantitative details are provided in  Appendixes D. Again, we further note that the time instances are exactly matched between LiDAR and NWP at each individual height, but not necessarily across heights (i.e., data at 140 m may have different samples than 180 m, but at 140 m, LiDAR and NWP have identical time instances).

Contours of wind speed, TKE, and TI are shown for 2017 (the year with the largest amount of continuous data) in Figs. 4–6. The data in all annual contours have been smoothed using a 30-day rolling average. These contours display seasonal and vertical trends that are an important point of comparison between the LiDAR and NWP datasets. In particular, TKE [Fig. 5(a)] and wind direction (see Fig. 19 in  Appendix A) display strong seasonal trends, with low TKE and winds from the southwest in late spring and summer and high TKE and winds from the northwest in the winter and early spring. TI exhibits similar seasonal changes, though to a slightly lesser degree than TKE due to its dependence on wind speed, which does not exhibit such strong seasonal trends. Notably, during late spring and summer, a persistent trend of TKE and TI increasing with increasing height emerges. As will be seen and discussed in Sec. II B 2, these vertical trends are not observed in the NWP data.

The trends in the NWP and LiDAR data diverge when analyzing the vertical variability in TKE and TI. In Figs. 5 and 6, the TKE and TI from NWP are largely monotonically decreasing as a function of height, regardless of the time of year. Figures 5(a) and 6(a) show that TKE and TI from the LiDAR exhibit some increasing behavior with height.

These vertical changes in TI are analyzed in Fig. 7 through calculation of the median TI (overall years) at each height filtered by season. The seasons here are defined as follows: winter is December, January, and February; spring is March, April, and May; summer is June, July, and August; and fall is September, October, and November. The strongest non-monotonic behavior in TI is observed in the summer in the LiDAR in Fig. 7(a). The gray lines on each plot show the median TI filtered by the stability conditions, where the Monin–Obukhov length from NWP MVCO is also used for LiDAR MVCO. In each dataset, when the conditions are unstable the median TI more closely follows the trend of the winter months and when the conditions are stable the median TI more closely follows the trend of the summer months. This illustrates that the vertical trends of increasing TI found in the LiDAR data are at least partially caused by the changing stability throughout the year.

This seasonality is in part due to the dominant wind directions in these months and the temperature of the wind relative to the sea surface temperature. In the winter months, the wind predominantly comes from the northwest, which is the direction of land in relation to the ASIT and the VW1 farm. This means that the wind is relatively cool and flows over a relatively warm ocean, leading to unstable conditions. In the summer, the wind predominantly comes from the southwest, and so the wind is coming from the warmer land or warmer ocean to flow over a relatively cooler ocean, leading to stable conditions. These stable conditions suppress the turbulence, but the presence of a neutral or weakly stratified residual layer above the stable boundary layer could possibly lead to the formation of a shear layer or low-level jet, which are known to exist in the Martha's Vineyard and Nantucket area at heights between 100 and 200 m based on analysis of data from the Coupled Boundary Layers Air-Sea Transfer Experiment in Low Winds (CBLAST-Low).⁴⁶ The increased shear production in this shear layer could potentially lead to higher TKE, which is a possible explanation for the observed trend of increasing TI in the summer months with height above the sea surface.

One further way to investigate the correlation between stability and vertical TI trends is through the analysis of the potential temperature θ profiles that can be obtained from the NWP data. Using the NWP MVCO dataset, the median potential temperature profiles (normalized by the potential temperature at ground level θ₀) are shown in Fig. 8, filtered by season [Fig. 8(a)], where the seasons are defined as detailed above, and filtered by the slope of TKE from the LiDAR MVCO data [Fig. 8(b)]. The slope of TKE is taken to be either strictly increasing or strictly decreasing above 140 m, following the trends observed in Fig. 7. Together with the median TI profiles shown in Fig. 7, the potential temperature profiles further illustrate that the increase in TKE and TI with increasing height is associated with increasingly stable conditions. Furthermore, these more stable boundary layer conditions are predominantly observed in the summer and spring (see  Appendixes B), which supports the hypothesis that these trends are associated with the presence of low-level jets that form above a stable boundary layer and result in high shear.

The absence of these vertical TI trends in the NWP datasets is likely due to the fact that they occur in relatively stable conditions, which are a known to be more sensitive to PBL parameterization.⁴⁷ As discussed in Sec. II B 2, the level 2.5 MYNN PBL scheme is used to generate the NWP data. While PBL schemes are capable of capturing low-level jets in stable conditions, in general, many PBL schemes (including MYNN) have been shown to overpredict boundary layer height and underpredict near surface gradients in wind speed.⁴⁸ In the present case, the vertical TI trends in the LiDAR are observed below 200 m, which is indicative of a fairly shallow boundary layer with a low-level jet closer to the surface than the PBL scheme predicts in this case. The fidelity of WRF to predict LLJs is, in general, is site-specific, and depends on the vertical resolution used in WRF and the PBL parameterization.⁴⁹ We refer to others studies that focus on leveraging WRF to predict LLJs.^49–51 The implication of this is that the parameterization of the boundary surface layer physics makes it difficult to accurately capture the stable boundary layer behavior due to the small scales associated with these flows.⁵² 

Error and uncertainty in the predictions of AEP and farm efficiency are quantified in two ways. In the first, error related to simplifying TI assumptions is considered by comparing the AEP and farm efficiency predictions using the median TI in a given year (a common practice in wind farm AEP assessment^12,13) and the predictions using the instantaneous values of TI. The second method assesses uncertainty based on the comparison between the predictions made with the two different sources of wind data. For these latter results, only the comparison between the LiDAR MVCO and the NWP data located at the VW1 site are presented in Sec. III B. Comparisons made between the LiDAR MVCO and the NWP data located at MVCO are shown in Subsection 1 of  Appendix E.

For both the TI error and data source uncertainty, multiple heights in the ABL are analyzed in order to understand how the differing vertical trends discussed in Sec. II B 3 between the LiDAR and NWP datasets affect the predictions of AEP and farm efficiency when considering different candidate hub heights. Given the differing vertical trends, particularly in the turbulence statistics, analyzing multiple heights provides quantitative insight into what extent these differences affect aggregated farm metrics that drive decision-making, and at which heights they influence predictions most for a given metric. The results suggest that generally AEP uncertainties are highest closer to the surface, suggesting opportunity for future work in improving planetary boundary layer modeling and predictions to reduce uncertainty. It should be noted that due to the lack of wind speed shear present in the FLORIS simulations, the metrics calculated at different heights represent the outputs of different, independent FLORIS runs. The wind speed, direction, and TI measured at a particular height above the surface are given as inputs to the wake model, which outputs farm power. The mean farm power at a particular height is then used to calculate AEP and farm efficiency at that height. The height is then effectively only changing through the changes in the input conditions at a given candidate hub height. Throughout the figures in Sec. III, hub height of the IEA 15 MW turbine is denoted with a vertical dashed gray line.

Figure 11 shows $RMSE P TI$ [Fig. 11(a)] and $RMSE η ¯ TI$ [Fig. 11(b)]. As a comparison, the uncertainty shown in Fig. 9 is $O ( 0.1 )$%. This is at least 10 times smaller than the RMSE for both LiDAR MVCO and NWP VW1, and while large scale metrics like AEP and mean farm efficiency might not show sensitivity to TI in the aggregate, instantaneous farm power and instantaneous farm efficiency do display sensitivity to TI. The results for MAE are summarized in Table II. For both AEP and mean farm efficiency, MAE is an order of magnitude greater than percent error. This highlights the sensitivity of 10-min averaged farm power to TI, in contrast to the negligible impact that TI has on AEP.

Relatedly, analytical wake models are often used to evaluate the potential of wind farm control to increase energy production.^12,13 Since the potential for wake steering to increase power depends on the time-varying wind conditions,^33,54 it is likely that the errors associated with assuming the median TI may be relevant for wake steering evaluation. Analysis of the impact of this simplifying assumption on wake steering should be carried out in future work.

In analyzing the error from TI, it is also important to consider how this error compares to any interannual variability. This comparison is shown in Fig. 12 for AEP and farm efficiency predicted using median TI. The gray shaded region represents the interannual variability, which is found by calculating AEP and farm efficiency over the period of one year for 2017, 2018, and 2020 and then taking the maximum and minimum values out of the three years as the bounds at each height. The symbols are the mean values of AEP and farm efficiency predicted using the median TI and the error bars show the error due to the simplified TI description based on the absolute error at each height given by $| M TI ¯ − M TI |$⁠. For both LiDAR MVCO and NWP VW1, the AEP uncertainty from TI [Figs. 12(a) and 12(b)] is within the bounds of the interannual variability. The farm efficiency error above 160 m for LiDAR MVCO falls outside the bounds of the interannual variability [Fig. 12(d)], while for NWP VW1 TI error is less than interannual variability for all candidate hub heights. Since the farm efficiency metric represents wake loss magnitude, these results suggest that TI error can impact wind farm design optimization, which focuses on minimizing wake effects. The impact of TI error on AEP is less than interannual variability for all heights, and therefore does not have a statistically significant impact on AEP at this site.

Another source of uncertainty that is pertinent to the siting and design of new wind farms is the uncertainty associated with the source of the wind data. As discussed in Sec. II B, there are advantages and drawbacks of each data source, namely, the NWP data site is located within the Vineyard Wind 1 farm, though it lacks some of the accuracy of the LiDAR data, while the LiDAR is located $∼ 25$ km away from the wind farm. As a result of these considerations, in this study, neither one of these datasets can be considered as more or less accurate than the other, however, the discrepancy between their predictions can be used as a measure of uncertainty, as is done in the present work.

As in Sec. III A, we consider how the wind data source uncertainty compares to interannual variability. Figure 15 shows the comparison of the interannual variability with the data source uncertainty for AEP and farm efficiency, where the uncertainty here is $ε AEP LiDAR , NWP VW 1$ and $ε η ¯ LiDAR , NWP VW 1$ [Eq. (19)], as shown in Fig. 14. For farm efficiency, above 150 m, the data source uncertainty is greater than the interannual variability for both datasets. For AEP, at 140 m data source uncertainty exceeds interannual variability for both LiDAR MVCO and NWP VW1, and for LiDAR MVCO interannual variability is additionally exceeded at 160 m. This indicates that data source uncertainty contributes to these predictions at various candidate hub heights, and should be quantified when making these aggregate predictions.

In order to understand the trends with height observed in Secs. III A and III B—particularly the data source uncertainty in Sec. III B—it is important to understand the variable sensitivities of the present FLORIS configuration. The sensitivity analysis is carried out through variable hold out tests, in which one variable is held fixed while the other two are allowed to change according to their full joint distribution. The results of these tests are presented in Fig. 16. As a first point of observation, it can be seen that AEP is most sensitive to changes in wind speed, with changes in TI and wind direction being relatively small in comparison. This means that when analyzing the variability with height in AEP data source uncertainty, the wind speed distributions will be the main driver of these trends. This is in line with the well-accepted notion that wind resource potential is primarily driven by the wind speed, but also that TI and wind direction are non-negligible.

Farm efficiency is a slightly more complicated function of wind speed, wind direction and TI, with very strong wind speed region dependence. In regions 1.5 and 3, farm efficiency depends largely on wind speed. When the turbines are operating in region 2, though, there is no dependence on wind speed (in an idealized sense), since the coefficients of thrust and power are approximately constant, and instead, TI and wind direction become important. Figure 16(f) exhibits minima when the wind direction is aligned or partially aligned with the directional layout of the farm. The oscillatory changes with wind direction happen over very short periods according to Figs. 16(e) and 16(f), leading to the conclusion that while farm efficiency is sensitive to wind direction, unless the wind direction distribution has a very strong and very narrow peak, it is not possible to neatly separate out the influence of this variable. Additionally, changes in wind direction over a given time period should average out, making farm efficiency mostly insensitive to the full distribution of this variable. As a result of this and the lack of dependence of farm efficiency on wind speed in Region 2, TI becomes very important in Region 2 when considering farm efficiency.

The differences in the predictions from the LiDAR MVCO data and the NWP VW1 data are due to differences in the distributions of wind speed, TI, and to a lesser extent wind direction. These distributions are shown in Fig. 17 for the candidate hub heights. Looking first at wind speed in Figs. 17(a)–17(c), the distributions from the two data sources appear to be converging with increasing height. This can be analyzed further through an inspection of the statistics in Figs. 18(a)–18(c), in which the mean wind speed and, to a lesser extent, wind speed standard deviation of the two data sources are converging with increasing height. As discussed in Sec. III B 1, the calculation of AEP is largely driven by wind speed, such that as the distributions of wind speed become more similar, the AEP also converges.

Farm efficiency is more sensitive to changes in TI and wind direction, particularly when the wind speed is in Region 2. Figures 17(g)–17(i), show that the TI distributions for the two datasets are fundamentally different, while the wind direction distributions [Figs. 17(d)–17(f)] and statistics [Figs. 18(d)–18(f)] exhibit less divergence. The NWP VW1 data exhibits a bimodal TI distribution. This bimodality in the TI distributions is strongly correlated with stability (see  Appendix C). The lower peak occurs in stable conditions and the higher peak occurs in unstable conditions. While Fig. 17(h) exhibits bimodality in the LiDAR MVCO TI distribution at 140 m, it is much less pronounced than in the NWP VW1 data. As such, in Figs. 18(g)–18(i), there is divergence of the mean, standard deviation, and skewness of the NWP VW1 and LiDAR MVCO TI distributions with increasing height, particularly at hub height of the IEA 15 MW turbine and higher. These statistics, coupled with the sensitivity analysis in Sec. III B 1, show that while the wind speed distributions become more alike with increasing height, when the wind speeds are in region 2, the divergence of the TI distributions with height leads to diverging trends in farm efficiency.

In this paper, multiple sources of input uncertainty have been analyzed that are pertinent to wind farm siting and design. Wind data from two sources—NWP data and LiDAR data—have been used as inputs to a Gaussian wake model in FLORIS in order to calculate AEP and farm efficiency for the Vineyard Wind 1 farm off the coast of Martha's Vineyard. While the observed LiDAR data are of a higher fidelity, they were collected $∼ 25$ km from the location of the wind farm. The NWP data studied here were located within the wind farm, making these two datasets good points of comparison for assessing input wind condition uncertainty.

For both the LiDAR MVCO and NWP VW1 data, input uncertainty owing to simplifying TI was studied. This consisted of using the median value of TI over a period of one year and comparing this against the AEP and farm efficiency calculated using the full joint distribution of TI, wind speed, and wind direction over a full year. While the TI percent errors in AEP and farm efficiency were less than 1%, an analysis of the RMSE and MAE in the farm power as a percentage of AEP and the farm efficiency as a percentage of mean farm efficiency showed that these errors were 1 to 2 orders of magnitude higher than the percent error in AEP and farm efficiency. This illustrates that calculations of AEP and mean farm efficiency hide much of the error that comes from using median TI values, and that for more detailed analyses of wind farms that look specifically at farm power, such as for wind farm flow control evaluation, the use of median TI can introduce larger errors. Additionally, it should be noted that the turbulence model used in the Gaussian wake model is simple. As such, TI error is indicative of the model's sensitivity to changing values of TI, as opposed to the overall problem's sensitivity to atmospheric turbulence. The turbulence model-form uncertainty is not captured in this work, and further study is required to understand the influence of turbulence as it pertains to the use of more descriptive and complex models.

Data source uncertainty was shown to be much larger than the TI error for AEP, with a maximum value of 3.7% at 140 m. In general, the impact of TI error on AEP was negligible. Its impact is smaller than interannual variability for all candidate hub-heights considered, and therefore, can be considered statistically insignificant at this site. In comparing the data sources, AEP uncertainty decreased strongly with height, reaching 0.4% at 180 m. This was shown to be the result of AEP being strongly driven (in the present wake modeling configuration) by the character of wind speed, and the wind speed distributions, for the LiDAR MVCO and NWP VW1 datasets. The mean values of wind speed converged with height, resulting in the convergence of the estimated AEP with height. Farm efficiency exhibited lower uncertainty values, with a maximum value of 0.7%, but generally the farm efficiency uncertainty was outside the bounds of interannual variability. Farm efficiency also displayed strong height trends, with the two data sources diverging from 140 to 180 m. This was shown to be the result of the similarity in the wind speed distributions coupled with the divergence of the TI distributions with increasing height above 140 m. Future work should assess the impact of wind condition uncertainty on wake minimizing wind farm design through optimization under uncertainty. Additionally, while this work has focused on input uncertainty, model parameter and model-form uncertainty also contribute to the overall prediction uncertainty. Understanding the relative impact of each source of error will be important for the informed design of wake modeling and farm optimization tools.

K.S.K. acknowledges funding from the MIT Energy Initiative. M.F.H. acknowledges funding from the National Science Foundation (Fluid Dynamics program, Grant No. FD-2226053) and partial support from the MIT Energy Initiative and MIT Civil and Environmental Engineering. All simulations were performed on Stampede2 supercomputer under the XSEDE Project No. ATM170028.

The authors have no conflicts to disclose.

Kerry S. Klemmer: Formal analysis (equal); Investigation (equal); Methodology (equal); Software (equal); Validation (equal); Visualization (equal); Writing – original draft (equal). Emily P. Condon: Formal analysis (equal); Investigation (supporting); Methodology (equal); Software (equal); Validation (lead); Writing – original draft (supporting); Writing – review & editing (supporting). Michael F. Howland: Conceptualization (equal); Funding acquisition (equal); Project administration (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Figure 19 shows the wind direction contours for the three datasets. In late spring and summer, the wind predominant comes from the southwest and in winter and early spring, the wind predominantly comes from the northwest.

The annual and diurnal stability trends are analyzed in Fig. 20 with heat maps of the frequency of stable and unstable conditions over the diurnal and annual cycle for the two NWP datasets for 2017. These heat maps further display the trend of stable summer conditions and unstable winter conditions, particularly for NWP VW1.

As shown in Sec. III B 2, the TI distribution for NWP VW1 exhibits strong bimodality, which is strongly correlated with stability. Figure 21(a) shows the TI distribution for NWP VW1 at 140 m filtered by unstable, stable, and neutral conditions. Here, neutral stability is defined as $| L | ≥ 500$⁠, where L is the Monin–Obukhov length defined in Eq. (13). Figure 21(b) shows the distribution of $1 / L$⁠. Both Figs. 21(a) and 21(b) illustrate that in the NWP VW1 dataset there are relatively few neutral conditions, which leads to this strong bimodal trend.

As stated in Sec. II B 1, the availability of data over the 3 year period decreases with increasing height (see Fig. 3). Throughout this work, we have used all the data available at each height (relative to the availability of the LiDAR dataset). This was done in order to preserve the quantity of data at 140 and 160 m relative to 180 m, where there is lower availability. Again, we emphasize that in all results in the study, the data samples are matched between LiDAR and NWP datasets exactly, but that the data are not necessarily matched across different heights. Here, we show a comparison of the error and uncertainty between the data preserving approach, described above and used throughout the study, and a data matching approach, where the temporal range of the data across all heights is matched (limited by the availability of the LiDAR data).

Figures 22–24 show the changes in TI percent error, farm power and farm efficiency RMSE, and TI error compared with interannual variability, respectively. Table III summarizes the differences for the TI percent error and farm power and farm efficiency RMSE as a percentage of AEP and mean farm efficiency at 160 m. Overall, the errors from TI still have a negligible effect on AEP. There is a larger difference between the data preserving and data matching approaches on the modeled farm efficiency, as the impact of TI error relative to interannual variability increases. The error from TI exceeds interannual variability for LiDAR MVCO at 140 m when the data are matched across heights. This is in addition to the exceedance at 180 m, which was already present in the data preserving approach. The general trend in the comparison between the TI error and interannual variability for NWP VW1 farm efficiency is similar in both cases, with slightly higher errors when the data are matched.

For the data source uncertainty, the qualitative trends with height are preserved, with lower uncertainties in both AEP and farm efficiency across all heights when the data matching approach is employed. Using the data preserving approach, data source uncertainty exceeds interannual variability for AEP for LiDAR MVCO at 140 and 160 m, while it does not exceed interannual variability at any height using the data matching approach. Data source uncertainty exceeds interannual variability for AEP for NWP VW1 at 140 m using both approaches. Using the data preserving approach, data source uncertainty exceeds interannual variability for farm efficiency for both LiDAR MVCO and NWP VW1 at 160 and 180 m, and it exceeds interannual variability using the data matching approach for 160 and 180 m as well. These differences are summarized in Table IV for 160 m and shown in Figs. 25 and 26. The important feature of the analysis is to ensure that the data are matched between LiDAR and NWP at a given height to ensure the differences between model output are only driven by data source uncertainty rather than biased sampling. The analysis using the data preserving approach shown in the main manuscript presents a more accurate picture of the data source uncertainty and its effect on AEP at these lower heights where more data are available, rather than removing data at 140 m based on the availability at 180 m.

We provide two additional comparisons in order to approximately parse two components of the wind data source uncertainty: (1) a comparison between LiDAR MVCO and NWP MVCO to assess NWP model error at the MVCO site and (2) a comparison between NWP MVCO and NWP VW1 to assess site error within the NWP model.

We compare the predictions of AEP and farm efficiency for the LiDAR MVCO and the NWP MVCO datasets in order to study the error stemming from differences between in situ measurements and NWP. Note that due to the nature of NWP, this model error is site specific and cannot be taken as the model error at the VW1 site. Figure 27 shows the predictions of AEP and farm efficiency, and Fig. 28 shows the percent error (normalized by LiDAR MVCO predictions) between the two datasets. The vertical trends observed for farm efficiency are very similar to those found in Fig. 14, though the differences between the two colocated MVCO datasets are typically smaller than those found between the LiDAR MVCO and NWP VW1 datasets.

We compare predictions of AEP and farm efficiency for the NWP VW1 and NWP MVCO datasets in order to study the error stemming from differences in between sites. Figure 29 shows the predictions of AEP and farm efficiency, and Fig. 30 shows the percent error (normalized by NWP VW1 predictions) between the two datasets. Overall, these differences are smaller than those found between LiDAR MVCO and NWP VW1.