The Weather Research and Forecasting Model (WRF) is a mesoscale numerical weather prediction model that is widely used in wind energy assessment and forecasting applications, such as predicting the impact of climate change on wind power generation and creating wind energy production estimates offshore and onshore (Pryor et al., 2020b; Salvação and Soares, 2018; Prósper et al., 2019). A high-resolution WRF (v3.8.1) simulation is conducted using a nested domain where the outer domain (D01) spans 150×150, 12km×12km grid cells and encompasses much of the US Midwest, while the inner domain (D02), centered over Iowa, comprises 246×204, 4km×4km grid cells (Pryor et al., 2020c) (Fig. 2). This horizontal resolution has been found to be most optimal when simulating nocturnal LLJs when compared to higher (and lower) resolutions (Smith et al., 2018). A time step of 72 s is used for D01, while the time step in D02 is 24 s. A total of 57 vertical sigma layers are employed and there are 25 levels below approximately 530 m a.g.l. Below 250 m a.g.l., the vertical spacing is approximately 15 m. Analyses presented here use model output sampled once hourly (at the top of the hour) for December 2007 to May 2008 and thus consider over 4300 profiles for each grid cell within a sub-domain (D03) comprising 147×100 grid cells that encompasses the state of Iowa (Fig. 2). Iowa is selected as the focus for this work due to the high density of wind turbines (over 11 GW of installed capacity) (American Clean Power, 2020) and observational research that has indicated a high frequency of extreme positive wind shear, which may be associated with LLJs (Walton et al., 2014). Key physics settings in the simulation presented here parallel those used in a similar study of the Orinoco LLJ over South America (Jiménez-Sanchéz et al., 2019); i.e., the Mellor–Yamada–Nakanishi–Niino (MYNN) 2.5 (Nakanishi and Niino, 2006) PBL scheme is used, along with the MM5 surface layer scheme (Beljaars, 1995) and the Noah land surface model (Tewari et al., 2004). The MYNN scheme is selected as it has been validated previously for WRF simulations in the Great Plains and shown to adequately model the PBL height when compared to observations (Zhang et al., 2020). Further, studies of LLJs in the Great Plains indicate that nocturnal LLJ characteristics may be less sensitive to the scheme employed than vertical resolution; the MYNN scheme has been shown to have minimal mean absolute error when simulating key jet core conditions, particularly with fine vertical grid spacing and a high model top pressure level such as that utilized in this simulation (50 hPa) (Smith et al., 2018; Jahn and Gallus, 2018). Note that in all analyses presented herein, only wind speeds within the lowest 530 m of the atmosphere are considered. This implicitly limits the detection of LLJs to levels below that height.

The seasonal analysis of LLJ characteristics over Iowa is developed using a detection algorithm that employs a variable criterion of 20 %, applied to WRF output for all grid cells. This detection algorithm means that an LLJ is identified as present in a given profile if the wind speeds above and below the wind speed maximum have magnitudes that are at least 20 % below the maximum (jet core) wind speed. Thus, the threshold varies based on the maximum value in each wind speed profile. Cumulative density functions of atmospheric parameters conditionally sampled based on the presence or absence of an LLJ are used to describe the conditions associated with LLJs. Parameters are considered in the vertical length of 50 to 150 m a.g.l., representing the rotor span of a typical wind turbine (not modeled here) with a rotor radius of 50 m and hub height of 100 m.

The parameters considered are (a) mean turbulent kinetic energy (TKE) across the rotor plane derived by the PBL scheme, (b) wind speed at a nominal hub height of 100 m a.g.l., (c) the median Richardson number across the nominal rotor plane (RiRotor) specified as 50–150 m a.g.l. (Eq. 1) and (d) mean shear (α) across the nominal rotor plane (Eq. 2). 1RiRotor=2Z2-Z1gθZ2+θZ1θZ2-θZ1uZ2-uZ12+vZ2-vZ122α=UZ2-UZ1Z2-Z1, where U, u, v and θ represent wind speed U, wind speed components u and v, and virtual potential temperature, respectively, at height Z a.g.l. RiRotor∼0 is indicative of near-neutral stability, RiRotor>0.25 indicates stable conditions, and RiRotor<0 indicates unstable conditions (Grachev et al., 2013).

The RiRotor is similar to the bulk Richardson number (Stull, 1988) but describes the dynamical stability across the wind turbine rotor (Nunalee and Basu, 2014). RiRotor and wind shear are calculated across each sigma layer in the nominal wind turbine rotor plane (six sigma layers fall approximately within this range). Thus, positive and negative shear due to LLJs are described at multiple heights within the rotor plane. TKE is also calculated at each of the six heights within the rotor plane. Mean TKE and shear and median RiRotor are then calculated from these points to approximate the central tendencies of rotor plane characteristics during non-LLJ and LLJ events. All variables except RiRotor are computed using output sampled at an hourly time step, while RiRotor is computed using variables output at 3 h intervals.

Probability distributions for LLJ characteristics, including duration and the jet core height, are also examined. If an LLJ occurs in a grid cell, the cell is flagged for each hour of occurrence. To calculate duration, these flags are counted for each consecutive LLJ occurrence, representing the length of time in which output from a given grid cell indicates the presence of an LLJ.

Following development of the seasonal analysis, two sensitivity analyses are performed (Table 1). The first sensitivity analysis (A) examines the impact of different detection algorithms on the resulting LLJ analysis. LLJs are detected and characterized using both (i) fixed criteria, i.e., a difference in wind speed above and below the wind speed maximum quantified in absolute terms (Andreas et al., 2000; Banta et al., 2002), and (ii) variable criteria, i.e., a difference in wind speeds above and below the wind speed maximum expressed as a percentage of the wind speed maximum. Often, these two types of criteria are used in conjunction, requiring a fixed or variable threshold or a fixed and variable threshold to be met (Baas et al., 2009; Lampert et al., 2016). This study examines both definitions separately to define the LLJs extracted under both types of thresholds. The criteria are grouped into five classes based on strictness and usage in the literature, from the least strict (1 m s-1 fixed, 10 % variable) to the strictest (5 m s-1 fixed, 50 % variable) (Table 2). Threshold strictness increases across groups in increments of 1 m s-1 for fixed and 10 % for variable. Criteria group 2 features definitions most commonly used in tandem or uniquely in previous LLJ studies (2 m s-1 fixed, 20 % variable).

Sensitivity to the LLJ definition employed is first demonstrated irrespective of domain-wide variations in topography using the WRF grid cell with the highest LLJ frequency according to the seasonal study developed initially (43.7467∘ N, 92.2784∘ W). Results are presented in terms of the mean LLJ profiles and the marginal probability of LLJs produced by each criterion. From this, a relative frequency of disagreement is calculated between the two LLJ definitions in each criteria group, indicating how often definitions (for each level of strictness) identify different LLJ events (i.e., how frequently variable criteria identify LLJs when fixed criteria do not and the converse).

After the initial sensitivity is demonstrated, distributions of LLJ magnitude, duration and jet core height are compared across the entire domain for each LLJ detection algorithm. The domain-wide temporal LLJ frequency is compared for thresholds in criteria group 2 (2 m s-1 fixed, 20 % variable) to examine definition sensitivity across varying terrain for each criteria type.

Sensitivity analysis B is conducted to examine whether and by how much LLJ characteristics change with the vertical resolution at which the WRF output is sampled. Wind speed output is down-sampled to a half and a quarter of the simulation resolution to investigate effects of wind speed profile data resolution when all other factors are unchanged. Results of this analysis are presented in terms of the spatiotemporal mean LLJ wind speed profiles, magnitude of the LLJs, duration, fraction of LLJs that impinge upon the rotor plane (defined as heights from 50–150 m a.g.l.), and the spatial patterns of LLJ frequency and duration.

A clear jet core is evident when comparing spatiotemporal mean LLJ and non-LLJ profiles normalized by each profile's respective wind speed maximum (Fig. 3). The spatiotemporal mean LLJ core wind speed computed using wind speed values across each vertical layer for all hours from all grid cells is approximately 9.55 m s-1 and is centered at about 183 m a.g.l. Approximately 96 % of LLJs exhibit jet core wind speeds of 3–25 m s-1 and are thus likely to be associated with normal wind turbine operation. Over the analysis period of 6 months there is evidence of an LLJ in one or more grid cells on nearly 98 % of nights (between 18:00–06:00 LT – local time), and nearly 65 % of LLJs occur at night. Daytime LLJs are more frequent in the winter months (December–February). Approximately 40 % of winter LLJs occur during daytime hours as compared to 30 % during spring (March–May).

A total of 30 % of LLJs are evident only in individual hours, but 4 % have a duration of >10 h (Fig. 4a). The modal value of LLJ height in the vertical window considered is between 100–150 m a.g.l. (the upper extent of the nominal rotor plane), and approximately 39 % of LLJs have a wind speed maximum within the nominal rotor plane of 50–150 m (Fig. 4b).

Consistent with expectations, LLJs are more prevalent during stable conditions as indicated by cumulative density functions of RiRotor, conditionally sampled by the presence or absence of an LLJ (Fig. 5a). Approximately 15 % of LLJs occur during hours when RiRotor<0.25, but the spatiotemporal median RiRotor is 0.87 when the detection algorithm indicates the presence of an LLJ. Conversely, 60 % of non-LLJ profiles occur with RiRotor<0.25, and the median non-LLJ RiRotor is 0.15. Also consistent with a priori expectations, LLJ events are associated with substantially lower TKE within the rotor plane. The median TKE within the rotor plane when LLJs are identified is 0.056 m2 s2, while the non-LLJ median rotor plane TKE is 0.37 m2 s2 (Fig. 5b). Almost two-thirds (61 %) of LLJs exhibit wind speed maxima above the rotor plane. Thus, a greater diversity (i.e., wider distribution) of wind shear conditions occur during LLJs (Fig. 5d), and there is evidence that very-near-surface (i.e., low-altitude) LLJs can induce negative shear across the nominal rotor plane (Gutierrez et al., 2017). Wind speeds at the nominal hub height of 100 m a.g.l. are higher on average during non-LLJ conditions (Fig. 5c), with a median of 9.24 m s-1 when compared to the LLJ median of 8.02 m s-1. This is likely due to a complex combination of the following factors: (a) the LLJ selection criteria are more readily met at lower wind speeds (Sect. 3.2); (b) microscale to mesoscale features (i.e., locally forced LLJs) are less readily established under conditions with strong synoptic forcing that generates high geostrophic wind speeds (Mortarini et al., 2018); and (c) depending on the precise height under consideration and the depth of the boundary layer, stable stratification may result in decreased vertical exchange of momentum (Barthelmie et al., 2013).

The mean duration and frequency of LLJs exhibit a clear dependence on geographical location and season (Fig. 6). On average, LLJs last slightly longer and occur more frequently in the winter months. The mean duration averaged over space and time is 3.6 h in winter and 3.4 h in spring. In spring, the northeast of Iowa experiences the highest frequency of LLJs, with the detection algorithm using a 20 % variable threshold detecting LLJs on up to 20 % of hours. The mean LLJ duration in this season and region of Iowa approaches 4.5 h. Conversely, the western part of the state is characterized by higher terrain elevation and larger terrain variability and exhibits a wintertime maximum of both LLJ duration and frequency (27 % of hours) (Fig. 6) consistent with formation of LLJs resulting from drainage-flow-induced gravity waves (Prabha et al., 2011; Udina et al., 2012).

Mean wind vectors at a nominal wind turbine hub height of ∼100 m a.g.l. under LLJ and non-LLJ conditions suggest marked differences in both the mean wind direction in winter and spring and the mean wind directions (averaged in polar space) associated with LLJ and non-LLJ conditions (Fig. 6a and b). The mean winter flow direction for both LLJs and non-LLJs exhibits a westerly component for all grid cells considered, while easterly flow components are more common during the spring months. Rotor plane wind directions during LLJ events exhibit more spatial variability than during non-LLJ events. Springtime LLJs exhibit less spatial variability in wind direction than winter LLJs, coinciding with the increased frequency of winter LLJs compared to spring LLJs. Springtime LLJs are most frequently associated with northeasterly flow over the northeast of the state, while winter LLJs are most frequently associated with southwesterly flow in the northwest of the state. Analyses of the seasonality and spatial variability in mean LLJ wind directions indicate that, during winter over the western portion of the state, LLJs are predominantly associated with southerly wind directions, while over eastern Iowa the LLJs are associated with more northerly flow (Fig. 6a). Conversely, springtime LLJs over almost all of the state are dominated by easterly wind directions and are generally of substantially shorter duration over the western half of Iowa (Fig. 6).

This variation in LLJ intensity and duration by season and location may reflect differences in LLJ genesis mechanisms. The western portion of Iowa exhibits substantially more complex terrain and thus may be subject to stronger thermal (radiative) and dynamic forcing at the meso- and microscales. Consequently, this region may be subject to density-driven slope and valley winds that may induce LLJs via the Holton mechanism, particularly during winter (Holton, 1967). The increase in LLJ frequency in the northeast during the spring is also associated with an increase in LLJ speed when compared to LLJ wind speeds for the region in winter and may have a greater forcing contribution from the Blackadar mechanism (Blackadar, 1957).

In this analysis, an LLJ detection algorithm using a variable threshold of 20 % is applied to output from the WRF simulation using the original vertical resolution, output sampled from every second level and output sampled from every fourth vertical level (Table 5, Fig. 11). The profiles are not linearly interpolated between vertical layers; the LLJs can only exhibit maxima at heights at the 25, 13 and 7 vertical layers considered (to parallel the extraction of LLJ profiles from observational data in which there are a number of fixed data points). The spatiotemporal mean LLJ core wind speed differs markedly according to the vertical resolution (Table 5). When the model output is sampled at one-quarter of the simulation vertical resolution, the mean maximum (jet core) wind speed is 1 m s-1 lower than when the LLJ detection algorithm is applied to output at the model resolution (i.e., all 25 levels below 531 m a.g.l.) (Fig. 11, Table 5). Output down-sampled to one-quarter resolution also exhibits a substantially lower mean LLJ core height (156.43 m) than when the analysis is applied to output at full resolution (182.64 m). This reduction in the height of the wind speed maxima results in a higher percentage of LLJ cores falling within the nominal wind turbine rotor plane of 50–150 m a.g.l. The spatiotemporal mean duration and frequency of LLJs are also lower in the reduced-resolution output (Table 5).

The usage of a polynomial interpolation to account for lower output resolution when extracting LLJs is shown to reduce sensitivity in LLJ characteristics (Table 6). Winter wind speed output at full resolution is firstly analyzed for LLJs under the 20 % variable criterion. From this, wind speed profiles corresponding with identified LLJs are sampled at quarter resolution (resulting in wind speed profiles comprised of seven vertical layers). A sixth-degree polynomial is then fit to each of these wind speed profiles to extrapolate the non-linear LLJ shape between wind speed values at each layer. After creation of the polynomial, the quarter-resolution height above ground level for each profile is linearly interpolated to that of the full-resolution output (25 layers). These linearly interpolated height values are then input into the polynomial function for each wind speed profile to extrapolate the quarter-resolution output into full-resolution output. These profiles (extrapolated to full resolution from quarter resolution) are then input into the LLJ detection algorithm (20 % variable), and resulting ensemble characteristics are compared to LLJ characteristics from full-resolution profiles and the original down-sampled quarter-resolution profiles.

LLJ characteristics (particularly jet core height) are sensitive to the model output resolution, but spatial variability appears to be less sensitive. The temporal mean LLJ frequency and duration in each WRF grid cell, as extracted from quarter-resolution and full-resolution output, are normalized relative to their respective domain-wide maximum values (Fig. 12). This process defines the domain-wide variations in LLJ frequency and duration for full-resolution and quarter-resolution output irrespective of the numerical values of each. The resulting normalized LLJ frequency and durations for both resolutions allow for comparison of spatial variability. Most regions (irrespective of terrain elevation) display low sensitivity to reductions in resolution (Fig. 12). Maximum positive and negative differences between normalized frequency and duration range from approximately -0.05 to 0.16, respectively. Regions of maximum spatial variability differences occur sporadically throughout the domain and do not correspond with terrain elevation. Regardless of these areas of high variability difference, the spatial patterns of LLJ frequency and duration are comparatively insensitive to the down-sampling of vertical resolution for most of the domain. Further, regions identified as having the highest frequency and temporal mean duration (the highest 5 % of each quantity) of LLJs are similar when the LLJ detection algorithm is applied to output at the original vertical resolution and one-quarter vertical resolution (Fig. 12a). However, there is more divergence in spatial variation in LLJ duration than frequency when these contours are considered (Fig. 12b). This potentially indicates that inter-study comparisons of regions of high LLJ frequency (and less so duration) may be possible, even under reduced vertical resolution of observational data and/or model output.

Ensemble LLJ characteristics display sensitivity to the resolution of wind speed profiles, but this can be mitigated through extrapolating the wind speed profile to higher resolution through a polynomial fit. This sensitivity appears to be consistent across the domain and irrespective of terrain complexity as regions of highest LLJ frequency and duration are preserved when LLJs are extracted from full-resolution wind speed profiles and manually down-sampled wind speed profiles. Though a 20 % variable criterion is utilized for this sensitivity study, it is possible that usage of a different criterion might affect the results and increase the efficacy of the polynomial fit in resolving lower-resolution LLJ profiles. For example, for higher-wind-speed LLJs (wind speed maximum > 17 m s-1) that are extracted by the fixed criterion, shear across the rotor plane remains relatively constant (Aird et al., 2020). In contrast, LLJs exhibiting lower wind speed maxima, as are more commonly extracted by the variable criterion (wind speed maximum between 5 and 11 m s-1), exhibit a nearly linear decrease in rotor plane shear with an increase in height above ground level These differences are attributed to lower jet core maximum heights for LLJs extracted with variable criteria (Figure 9). Thus, it is possible that extrapolating the LLJ profile from lower-resolution wind speed profiles as extracted from a fixed criterion would prove to be more effective due to more constant shear and higher wind speed maxima.