1. Introduction
The southerly, nocturnal, warm-season low-level jet (LLJ) of the U.S. Great Plains has been widely studied for decades because of its importance in many applications. Its role in transporting moisture northward from the Gulf of Mexico, thus contributing significantly to severe weather and precipitation during the agricultural season, has been well documented (e.g., Means 1954; Pitchford and London 1962; Mo et al. 1995; Higgins et al. 1997; Mitchell et al. 1995; Song et al. 2005; Pu and Dickinson 2014; Gebauer et al. 2018; Smith et al. 2019; Carroll et al. 2021). LLJs have also been shown to be efficient in transporting urban-generated pollutants away from urban centers at night (Banta et al. 1998, 2005; Klein et al. 2014). More recently wind energy has become an important application for meteorological information, and strong southerly LLJ winds at night can be an important resource for wind turbine operations.
These and other applications require accurate forecasts of LLJ properties as well as knowledge of long-term mean geographical distributions and variations of LLJ properties in the horizontal. For wind energy, quantitative wind information is needed for atmospheric layers above the surface occupied by the wind-turbine rotor blades (rotor layer) and such information would be most beneficial at accuracies of 0.1 m s−1 or better (Banta et al. 2013). The rotor layer of current land-based wind turbines generally extends somewhere between 40 and 150 m above ground level (AGL) or higher, where wind characteristics during LLJ conditions often differ significantly from those near the surface (Banta et al. 2013, 2018). Thus, quantitative characteristics of the vertical profile of the wind and turbulence below 200 m are of prime importance to wind energy, but profiles up to several hundreds of meters AGL are also needed to provide meteorological context. The variability of winds across wind farms, which may be 50–100 km or more across, under different conditions, is also of interest.
Several mechanisms have been proposed to explain evening LLJ accelerations in the Great Plains. The late-afternoon–early evening surface cooling and consequent decoupling of the flow above the surface from surface friction, which disrupts the daytime balance of forces and leads to ageostrophic accelerations and inertial oscillations of the flow aloft in the former convective boundary layer, was described by Blackadar (1957). Diurnal heating and cooling of the gradual east–west slope of the Great Plains, which generates diurnally varying pressure gradients and geostrophic wind cycles over the region, was proposed by Holton (1967). Using information from Nonhydrostatic Mesoscale Model (NAM) model runs, Parish and Oolman (2010) found that the strong heating differential, between the lower, cooler, moister regions of the eastern Great Plains and the higher, drier, hotter landscapes to the west, leads to a northerly thermal wind, resulting in the strongest southerly wind speeds near the surface, decreasing with height. The strength of LLJs was related to the magnitude of this east–west temperature differential. Understanding the relative effectiveness of each of the relevant mechanisms in producing the LLJ depends on understanding the nature of the evening decoupling processes, that is, the magnitude and evolution of the structure of the turbulent mixing profile in the nighttime stable boundary layer (SBL).
It is likely that more than one mechanism acts in concert to generate the Great Plains LLJ, which sometimes produces multiple maxima in the wind speed profile (Banta et al. 2002; Shapiro et al. 2016). Theoretical and numerical studies have addressed the relative contributions of the Blackadar versus the Holton versus thermal-wind mechanisms (Zhong et al. 1996; Shapiro et al. 2016; Fedorovich et al. 2017; Parish 2017). Shapiro and Fedorovich (2009, 2010) derived and solved a set of analytic equations for vertical profiles that included both decoupling and slope physics, and they found that both effects together could reproduce many aspects of the Great Plains LLJ structure and behavior. Many NWP modeling studies have generated LLJs that peaked above 400 m, which we will refer to as deep LLJs (e.g., Zhong et al. 1996; Smith et al. 2018).
NWP forecast models are important tools for providing wind forecasts, and in a companion paper we investigate the ability of the NOAA’s High Resolution Rapid Refresh (HRRR) model to represent LLJs. LLJ properties have not been well represented in models; for example, the maximum or nose in the wind profile has been too high, and either too weak (Storm et al. 2009) or too strong (Werth et al. 2011) in many attempts to simulate it. In a case-study simulation, Parish and Clark (2017) reported a jet at about the right height, but the corresponding speeds were too weak by several m s−1, and Mirocha et al. (2016) noted that “significant discrepancies occurred at various times for all of the simulations in relation to the observations,” within the subjet layer in their WRF LLJ runs. These errors have been blamed on the inadequate representation of sub-resolution-scale mixing processes, which are key to the development of LLJs during the evening transition (Mahrt 1998; Banta et al. 2003; Shapiro et al. 2016). Improvements in modeling LLJs depend on being able to accurately simulate the processes that generate them, including mixing processes in the SBL beneath the LLJ nose.
Studies during the Cooperative Atmosphere–Surface Exchange Studies (CASES-99) October 1999 field program in southeast Kansas (Poulos et al. 2002), and the Lamar Low-Level Jet Program of September 2003 (LLLJP-03; Kelley et al. 2004), were focused on SBL properties and processes, and thus addressed the relationship between the LLJ and SBL turbulence (Banta et al. 2003, 2006, 2007; Pichugina et al. 2008; Pichugina and Banta 2010). Analyses of these datasets showed modest veering in time from southeast to south-southwest through the subjet layer during the first 2–3 h after sunset, then little direction change for the rest of the night on most nights (Pichugina and Banta 2010). These results agreed with Lundquist (2003), who found no evidence for inertial oscillations, except for a postfrontal passage below 1000 m AGL during CASES-99 using 915-MHz profiler data, and Vanderwende et al. (2015), who also found modest LLJ veering in time (3° h−1). The absence of fully developed inertial oscillations would indicate that other processes in addition to the mechanism proposed by Blackadar must also be important in generating and maintaining the LLJ.
The existence of northerly jets is another issue addressed in LLJ studies. Whiteman et al. (1997), Song et al. (2005), and Carroll et al. (2019) found that these were most often post-cold-frontal, and Gebauer et al. (2017) studied these using the Shapiro and Fedorovich (2009) analytical model. In a typical summer, LLJs are mostly southerly, and northerly jets are infrequent (e.g., Carroll et al. 2019). In the present study, we focus on an intensive measurement campaign during August 2017, a month that saw an anomalously high incidence of cold fronts and jets having northerly or northeasterly component winds (Song et al. 2005).
August 2017 was the period of deployment of the Land–Atmosphere Feedback Experiment (LAFE; Wulfmeyer et al. 2018). Although primarily a daytime project, here we use this dataset, along with the longer-term network of five scanning Doppler lidars (DLIDs) at the Atmospheric Radiation Measurement (ARM) Southern Great Plains (SGP) atmospheric observatory, to characterize LLJ properties through the first 1 km AGL during the LAFE period. We compare these properties among sites to estimate the influence of the different surface types on the magnitude of variations of winds and LLJ parameters, and we use the longer-term 2016–21 dataset to put this month into perspective. We compare aspects of the LLJ for this period and location with findings from previous studies and construct temporal and vertical hodographs to gain insight into the structure and dynamics of the observed LLJs.
The present paper is organized as follows: section 2 provides information on the ARM research sites and instruments used for long-term and LAFE periods, including vertical and temporal resolution of wind and turbulence data from DLIDs at all sites that are important for the interpretation of the results. Section 3 describes wind flow conditions through a deep layer at the five SGP lidar sites over six summers (2016–21) and contrasts these findings with those observed during the LAFE experiment in August 2017. Section 4 focuses on measured LLJ properties, their relationship to the layer mean properties from section 3, the variability of LLJ characteristics among ARM DLID sites, and the evolution of nocturnal LLJ properties. Temporal and vertical hodographs for all five sites show similarities and differences in how these hodographs evolve at the different sites. The main results are summarized in section 6.
2. Background, research area, and Doppler lidar measurements
a. ARM SGP lidars
ARM SGP Doppler lidars are located at the well-instrumented central facility (C1) near Lamont, Oklahoma, and the four extended facilities E32, E37, E39, and E41. The sites are separated by 56–77 km and have different surface and vegetation types from cropland to grassland and pasture (Fig. 1a; Table 1). Wind turbines around SGP sites were deployed farm-by-farm over the years of lidar data collection. Project names and the beginning of wind-farm operations are provided on Fig. 1b.
(a) Location of Halo Streamline HR Doppler lidars at the ARM Climate Research SGP Facility (black circles) superimposed on the surface elevation map of the region from a 750-m-resolution HRRR simulation. Distances between the ARM central facility (C1) near Lamont and at the four extended facilities near Medford (E32), Waukomis (E37), Morrison (E39), and Peckham (E41) are indicated by black arrows. Small black squares indicate the horizontal grid points of the 3-km operational HRRR model where the primary land use type is cropland; locations with no small black squares have a primary land use type of pasture. [(a) is adapted from Wulfmeyer et al. (2018)]. (b) Google map of wind farms around SGP site provides names of wind projects. The colors indicate wind turbines of different capacities and owners (https://eerscmap.usgs.gov), and the beginning year of wind farm operations is given in parentheses.
Citation: Journal of Applied Meteorology and Climatology 62, 8; 10.1175/JAMC-D-22-0128.1
ARM Southern Great Plains facilities with Doppler lidar measurements.
These lidars are Halo Photonics Streamline scanning systems and had been in continuous operation since 2010 at C1, and from 2016 at the four extended facilities. These lidars provided multiyear profile data with temporal resolution of 15 min at C1 and 10 min at E32–E41 and a vertical resolution of 24 m (C1) and 26 m (E32–E41) for wind and respectively 5 min and 30 m for w turbulence profiles, from 90 m AGL up to ∼1.5 km aloft. Details of the deployment history, raw and processed data description, along with other valuable information and sample plots can be found in the Doppler lidar handbook (Newsom and Krishnamurthy 2022). (Lidar datasets at all five sites can be found at https://www.arm.gov/capabilities/observatories/sgp.)
b. LAFE instrumentation
A large array of additional instrumentation was deployed to site C1 during LAFE in July–September 2017 (Wulfmeyer et al. 2018; Meyers et al. 2018; Turner et al. 2018), to investigate interactions between different land surface types and the overlying atmosphere. Key instrumentation participating in LAFE, including the various types of scanning lidars, quantities measured, as well as scientific objectives of LAFE, is summarized in Wulfmeyer et al. (2018). Many of the instruments provided data continuously, but some, such as the Raman lidar, were operated in modes that optimized sampling of the lower daytime convective boundary layer. The complete list of all instruments deployed to the central facility (C1) during the LAFE campaign can be found in Wulfmeyer et al. (2018).
c. Doppler lidars: Wind and turbulence profiles
This paper focuses on the analysis of nighttime wind fields and LLJ characteristics obtained from the SGP Doppler lidar (SLID) long-term datasets at 5 sites and from the University of Hohenheim (UHOH) Doppler lidar (ULID) that operated during 13–31 August 2017 from C1. For this period the SLID measurements at C1 were switched to the vertical staring mode.
The ULID performed a continuous pattern of measurements referred to as “6-beam scans,” a 6-beam configuration whose sampling rate is 1-Hz and whose respective azimuthal angles are 0°, 60°, 120°, 180°, 240°, and 300°, oriented at 45° from zenith. These data were processed to derive profiles of the horizontal wind speed and direction with a temporal resolution of ∼1 min and vertical resolution of 26 m, also providing computed profiles of u and υ wind components and their uncertainties. The “6 beam” measurement technique allowed the computation of profiles of TKE, horizontal momentum, and variances of wind vector components, using the methods suggested by Sathe et al. (2015) and evaluated in Bonin et al. (2017).
Variables available from ULID during LAFE and the routine long-term SLID measurements are given in appendix A. This table also provides the temporal and vertical resolution of all profiles, and the minimum available (and plotted) profile heights.
Wind flow variables at C1 in August 2017, combined from SLID measurements (1–13 August) and ULID measurements (14–31 August), show (Fig. 2) high day-to-day variability with the strongest wind speeds during overnight period on 5, 16, 20–21 August, which were observed to come from the south (Figs. 2a,b). By the end of the month, the mostly north-northeasterly (NNE) winds tended to be weaker. Table 2 shows days grouped by the strength of the nocturnal wind speed in the first 1 km AGL (above ground level), along with the prevailing wind direction for these days.
(a) Wind speed, (b) wind direction, and (c),(d) vector wind components for 1–31 Aug 2017 from lidar measurement at the central facility (C1). White stripes indicate missing data. Wavy strips around day 14 indicate the transition from SLID (1–13 Aug) to ULID (14–31 Aug) measurements. The first available height from the SLID lidar is 90 m. Data from ULID (2 Hz) are averaged over 15 min to fit the temporal resolution of winds from SLID and are plotted from the third height of 53 m because of noisy data at the first two heights.
Citation: Journal of Applied Meteorology and Climatology 62, 8; 10.1175/JAMC-D-22-0128.1
Classification of the LAFE (August) days by the nocturnal wind speed and the prevailing wind direction (“Dir”) in the first 1 km AGL from Doppler lidars operated from C1.
We can classify the study nights depending on their maximum wind speed, as strong (>12 m s−1), moderate (8–12 m s−1), and weak (<8 m s−1). Figure 3 shows 24-h time–height cross-sections of wind speed and direction along with the time series of those variables at seven heights from 117 to 714 m AGL for one sample day from each category. The differences in wind speed among the levels show the strong shear at night becoming near zero in the local morning after 1600 UTC. The direction time series show that the turning of the wind both with height and with time were mostly small through the 117–714 m layer, which was true for most nights, as further discussed below.
Diurnal variability of the wind field (a), (b) in the first 1 km AGL at site C1 and (c), (d) at the seven heights within this layer, shown for three days selected from each group: strong, southerly (20 Aug), moderate SE (25 Aug), and weak N and NE (30 Aug) overnight winds. Black and white horizontal bars at the bottom of (b) and (d) indicate night and day hours. Sunrise for 20, 25, and 30 Aug was at 0653, 0057, and 0701 CDT (UTC − 5 h); sunset for these days was at 1614, 1608, and 1601 correspondingly. White spots on 20 and 25 Aug above 800 m indicate missing data.
Citation: Journal of Applied Meteorology and Climatology 62, 8; 10.1175/JAMC-D-22-0128.1
Table 2 lists the nights in August 2017 that fell under each category. Those typical summer nights when the winds were predominantly southerly made up the strong-wind cases, whereas the postfrontal occurrences where easterly component flow predominated, which we will refer to as northeasterly (NE) nights, were the moderate-wind nights. The weak (4–8 m s−1) winds varied over a wide range of directions from northerly through westerly.
To characterize the anomalous nature of wind flows during LAFE, we will compare this period with winds from the 2016–21 summer months using the long-term SLID data at all sites (Fig. 4). In the next section 3a, we consider large-scale properties of the flow by looking at wind speed and direction averaged over a deep layer. In section 3b we look more closely at these properties during August 2017.
Distributions of 0000–1400 UTC wind speed and wind direction in the layer of 117–714 m at five SGP sites for the summer months of the six years from 2016 to 2021. Each site is shown by color according to the legend in the top row. Each plot consists of 15-min profiles at C1 and 10-min profiles at the other four sites. Sites with missing measurements are indicated for each month from August 2019 to 2021.
Citation: Journal of Applied Meteorology and Climatology 62, 8; 10.1175/JAMC-D-22-0128.1
3. Summertime nocturnal-wind properties through the SBL
Unlike typical summers when southerly flow dominates, southerly and northeasterly flow days from August 2017 had a roughly equal number of occurrences, allowing flow and LLJ properties to be contrasted between the regimes. The August 2017 LAFE study period was marked by an unusually large number of cold-front passages (including a day-long rain event on 11 August), which disrupted the typically frequent occurrence of southerly LLJs (the definition of LLJs and LLJ parameters is later explained in section 4a). Large-scale conditions during this month featured many days having a breakdown of the normal Bermuda high pressure system in the eastern United States, along with an unusually large incidence of hurricane and tropical cyclone systems in the western Gulf of Mexico (see the online supplemental material). To characterize the anomalous nature of wind flows during LAFE, we will compare this period with winds from the 2016–21 summer months using both the long-term SLID data at all five sites and ULID data at C1 from LAFE (Fig. 2).
a. Six summers (2016–21): 100–700-m layer-mean winds
Figure 4 shows the distributions of 0000–1400 UTC (period of observed LLJs) wind speed and direction averaged for the 117–714-m layer at the five SGP sites. Wind speeds had high frequencies in the range of 4–12 m s−1 for all months, which is important for the operations of the nearby wind farms (Fig. 1b) as these winds are in the ascending part of the power curves for most wind turbines (GE Energy 2009), and the power generated increases proportionally to the cube of the wind speed (Pichugina et al. 2019). Typical summertime months showed a strong, often monomodal peak in wind direction from the south; however, a noticeable secondary peak of northeasterly or easterly winds can be seen during some months, such as July 2018 and 2019. During the LAFE period (August 2017), the abnormal northeasterly peak was so large that it exceeded the southerly peak, although the southerly peak was broader (Fig. B1 of appendix B). The bimodal distributions of wind direction in August 2017 were also observed at 10 m from three flux stations as well as from sonic anemometer measurements at 25 and 60 m of a tall tower located at C1 (not shown). The patterns appeared similar from site to site for each month, but the highest and westernmost site (E37) showed the greatest frequency of strong (>12 m s−1) wind speeds during most months.
These basic month-to-month variations in mean winds are summarized more quantitatively in Fig. B2 of appendix B, which shows mean wind speeds and the number of points (integrated over the histograms in Fig. 4) for each month of the six summers. The plots are shown for all wind directions and two sectors [NE and south (S)]. Wind speeds from the total sample (Fig. B2a) were mostly 8–12 m s−1. Each year, the strongest winds were southerly (Fig. B2e) at all sites, whereas the northeasterly component sectors (Fig. B2c) tended to be weaker by 3–4 m s−1. Overall, the interannual variability of monthly mean summer winds in the 100–700-m layer was greater than the wind variability among sites (Fig. 4); namely, the variability was ∼4 m s−1 for the former and 1–3 m s−1 for the latter.
The next section provides details of wind flow variability among sites during August 2017.
b. LAFE period layer-mean wind-flow conditions
The dichotomy in wind direction between the normal and postfrontal regimes for the LAFE period is clear from the August 2017 wind roses for the first 700 m AGL—the layer most covered by lidar measurements at all sites (Fig. 5a). Higher frequencies of winds from NE and S and south-southeast (SSE) sectors than other directions at each site are highlighted by the dark yellow lines on C1.
Overnight (0000–1400 UTC) winds for August 2017 at the five SGP sites: (a) wind roses in the first 700 m AGL, (b) bistributions of wind speed in two sectors of wind direction, NE (33.7°–78.7°), and S and SE (146.2°–191.3°), which are highlighted by dark yellow lines at C1 (Fig. 6a, below), and (c) mean profiles in the same sectors as (b).
Citation: Journal of Applied Meteorology and Climatology 62, 8; 10.1175/JAMC-D-22-0128.1
Distributions of wind speed (Fig. 5b) for the S and SSE sector show a broader range of speeds and a larger fraction of winds greater than 11 m s−1, as compared with the NE wind regime. August-mean profiles (Fig. 5c) for these sectors show LLJ shapes having maxima around 200 m (NE) and 225–300 m (S and SSE) AGL. The NE winds at the 200-m jet height were 7.8 m s−1 at the western E32 and E37 sites, as compared with 8.2 m s−1 at the other sites, and speeds continued to be about 0.5 m s−1 weaker above. The difference in S and SSE winds among sites varied with height AGL, the western sites being comparable to the others below 500 m, but 1 m s−1 stronger above 500 m. At LLJ heights the winds at the southern (E37, E39) sites (∼10 m s−1) were ∼1 m s−1 stronger than those at the northern (E32, E41) sites (∼9 m s−1).
Overall, no significant differences were found between the wind relationships at different sites when comparing 0000–1400 UTC and the 24-h (0000–0000 next day UTC) periods (Table 3) at eastern and western sites as well as the southern and northern sites. A high correlation was found for winds in the larger layer 90–714 m AGL for both the 0000–1400 (R2 = 0.84–0.85) and 24-h (R2 = 0.83–0.84) periods.
Spatial variability of wind speed in the 90–714 m layer between east and west SGP sites and between north and south SGP sites for 0000–1400 UTC hours and over the diurnal cycle. The number (count) of profiles in August 2017 was used for the calculation of the correlation coefficient squared (R2) between wind speed at two sites and the coefficients of the linear fit (y = A + Bx). Mean and standard deviation (STD) are computed over two periods (0000–1400 UTC) and (0000–0000 next day UTC).
In wind energy operations, winds at the hub heights of wind turbines have often been used to estimate the power production of a wind farm. In August 2017, wind roses of the 117-m wind speed (appendix C) show similar patterns for the 0000–1400 UTC and the 24-h (0000–0000 next day UTC) periods at all sites, with stronger S–SSE winds, and a significant frequency of NE winds. The high frequency (>70%) of 4–12 m s−1 winds was observed within the layer at 90 and 117 m AGL—the layer of hub heights of modern wind turbines (appendix D). The very weak wind (0–4 m s−1) group is also included in this table to indicate how often turbines may not operate due to winds below cut-in values (GE Energy 2009). The range of these cases (20%–28%) means that turbines would not have been harvesting winds for about 104–202 h in August 2017. Such slack conditions are good for maintenance and repair operations if they can be forecasted.
4. Low-level jet properties during LAFE (August 2017)
a. LLJ statistics from lidar measurements
Wind-profile measurements from scanning Doppler lidars at the five SGP sites obtained with high temporal (10–15 min) and vertical (∼21 m) resolutions are used to statistically characterize LLJ properties (Fig. 6a) including jet-speed maxima (ULLJ), the height of these maxima (ZLLJ), wind direction at this height (DLLJ), and overnight evolution of these parameters for different wind speed regimes (as illustrated in Fig. 3).
(a) Definition of LLJ parameters. The red point indicates the LLJ strength (ULLJ) and the LLJ height (ZLLJ) automatically detected in each 15-min wind profile. The LLJ direction (DLLJ) is the value in wind direction profile found for this time and at this height. (b) Categories of wind profiles frequently observed from lidar measurements during the previous experiments in the Great Plains (from Pichugina and Banta 2010). (c) Time–height plot of wind speed on 19 Aug 2017 at C1. Black symbols indicate the LLJ evolution. (d) Sample wind speed profiles most observed during dusk (0000–0300 UTC), nighttime (0300–1000 UTC), and morning-transition (1200–1400 UTC) periods on 19 Aug.
Citation: Journal of Applied Meteorology and Climatology 62, 8; 10.1175/JAMC-D-22-0128.1
The occurrence of LLJs in each wind speed profile was estimated by an automated procedure that detects wind speed maxima (ULLJ) with a decrease of at least 2 m s−1 at vertical levels both above and below the level of the peak value (ZLLJ), the criteria proposed in Andreas et al. (2000).
Similar to the other parts of the Great Plains (Banta et al. 2002, 2003; Kelley et al. 2004; Gebauer et al. 2018; Smith et al. 2018, 2019; Carroll et al. 2019), summer LLJs at SGP sites generally formed over a 3-h period after sunset [2030–2130 central daylight time (CDT), 0230–0330 UTC]. In August 2017 LLJs at SGP sites were frequently identified during 0000–1400 UTC from various shapes (Fig. 6b) of wind profiles (Pichugina and Banta 2010). The “classic” LLJ (Fig. 6d, 0900 UTC), single-maximum shapes occurred often during stable boundary layer (BL) conditions at 0300–1000 UTC for many nights, although sometimes such profiles were observed up to 1200 UTC. Multiple maxima in the wind speed profile were occasionally observed after dawn, during morning-transition (1000–1400 UTC) hours (Fig. 6d, 1400 UTC), under neutral, near-neutral, or unstable conditions at the surface. This structure was generally related to the growing early morning shallow convective boundary layer eroding the LLJ layer from below.
In addition to the nocturnal evolution, LLJ parameters were analyzed for three periods: evening transition (0000–0300 UTC), nighttime (0300–1000 UTC), and morning transition (1000–1400 UTC). Stability was estimated by the Monin–Obukhov length LMO obtained from sonic-anemometer measurements at the 25- and 60-m levels of a tower installed at C1 (appendix E). An example of diurnal wind speeds in the first kilometer AGL on 19 August illustrates LLJ development through the night (Fig. 6c).
Nighttime winds on this day were southerly and moderate (8–13 m s−1) in the first 700 m AGL, the strongest LLJ speeds occurring at ∼200 m at 0800–1100 UTC. Sample profiles from each period (Fig. 6d) illustrate both how the algorithm estimates LLJ properties and how the wind profiles develop from a late-afternoon (0000–0300) mixed-layer through a nighttime (0300–1000) LLJ and to the (1000–1400) morning transition profiles (where in these unstable-BL profiles, the upper maximum is indicated).
Distributions of LLJ properties in August 2017 (Fig. 7a) show the highest frequency of strong (>12 m s−1) jets during nighttime hours (0300–1000 UTC), and a significant portion of the jet maxima for all 3 periods was located at 200–300 m. Monthly mean profiles normalized by ZLLJ (Fig. 7b) illustrate LLJ-profile shapes having strongest ULLJ during the nighttime hours. Distributions of DLLJ show two prevalent (NE and S–SSE) directions for each period. Mean LLJ statistics from Fig. 7a (Table 4) show a significant number of LLJ profiles with a mean frequency of 38%, 74%, and 59% for the evening transition, nighttime, and morning transition hours. The most frequent stability conditions for the evening, nighttime, and morning hours in August 2017 were (Fig. 7). very stable (19%, 34%, and 29%) and stable (17%, 19%, and 24%), respectively.
(a) Distribution of LLJ parameters in August 2017 from measurements at C1 for three periods (000–0300, 0300–1000, and 1000–1400) and over 0000–1400 UTC. (b) Monthly-mean profiles of wind speed at C1 normalized by the height of LLJ (ZLLJ), shown for each of three periods. (c) The frequency (%) of the stability classes based on the LMO (appendix E) from sonic anemometer data at 25 and 60 m of an 80-m tower for the periods defined in (a).
Citation: Journal of Applied Meteorology and Climatology 62, 8; 10.1175/JAMC-D-22-0128.1
Mean LLJ statistics for August 2017 at C1 (Fig. 7a) are shown for different periods: late-afternoon (0000–0300), nighttime (0300–1000) LLJ, the morning transition (1000–1400, where in these unstable-BL profiles, the upper maximum is indicated), and overnight (0000–1400 UTC).
b. Spatial variability of LLJ parameters in August 2017
Wind-flow patterns among the sites for 23 August LAFE IOP 11 are shown in Fig. 8, which shows that many details of LLJ evolution varied among sites. Differences are evident in the timing of the LLJ, the maximum height of the jet nose, and the strength and depth of LLJs (Fig. 8f). This day of primarily easterly winds is characterized by a disturbance at ∼ sunset (e.g., 0100–0400 UTC at E37 and E32, then 0500–0700 UTC at E39) and shown here, as it was an important day for other LAFE studies.
(a)–(e) Time–height cross sections of wind speed on 23 Aug 2017 from lidar measurements at five SGP sites, as labeled. The panels for each site are plotted following the location of the sites (Fig. 1) to better illustrate the connection of wind flow and LLJ difference to the site’s position (S–N and W–E) and surface types. The height of the LLJ is indicated by black symbols for 0000–1400 UTC. (f) Time series of the LLJ properties ULLJ, ZLLJ, DLLJ at five sites (colors as indicated at the top of each plot). The gold-dashed box outlines the period of very stable (vS) and stable (S) boundary layer conditions observed on 23 Aug.
Citation: Journal of Applied Meteorology and Climatology 62, 8; 10.1175/JAMC-D-22-0128.1
Figure 9a shows LLJ wind roses for August 2017 at the five SGP sites. The predominant LLJ directions were from the south or northeast, and the strongest jets (darkest blue shading) were from the south (cf. Gebauer et al. 2017; Carroll et al. 2019), consistent with the layer-averaged mean winds (Fig. 5). Small site-to-site differences can be seen in the prevailing direction of the southerly flow occurrences: the westernmost sites show mostly southwesterly LLJ-nose directions, whereas the mode for E41 was southerly and for C1 and E39, SSE. Distributions of ULLJ (Fig. 9b) are similar in shape and monthly mean values (9.8–10.2 m s−1). The distribution of LLJ directions (Fig. 9b) at the jet nose shows a significant NE component in addition to the more normal southerly [SSE through south-southwest (SSW)] jets, again consistent with the ∼100–700-m layer mean wind speed (Fig. 5). Site-to-site variability is evident in the shapes and mean values (261–304 m for ZLLJ) of the bimodal distributions of ZLLJ and the wind direction (DLLJ) at the height of LLJs.
(a) Wind roses of ULLJ in August 2017 at five SGP sites for 0000–1400 UTC. (b) Distributions of LLJ parameters over 0300–1400 UTC in August 2017 at five sites.
Citation: Journal of Applied Meteorology and Climatology 62, 8; 10.1175/JAMC-D-22-0128.1
Interannual comparisons of LLJ parameters (Fig. 10) show that in general, jet speeds were smallest in 2017, but for each year agreed within ∼2 m s−1 among the sites, with jet height varying over ∼100 m. Similar to Fig. 9b, a closer relative agreement is seen in the strength (ULLJ) and direction (DLLJ) of LLJs between sites for all years than in the height (ZLLJ) of LLJs, where, for example, larger (∼200 m) differences can be seen between E37 and E41 in August 2016 (after 1000 UTC). Mean wind directions at all sites and years showed modest veering from southeasterly at the evening transition toward the S and southwest (SW) by 1400 UTC. The modest LLJ veering in the evening hours was also observed from CASES-99 and LLLJP-03 (e.g., Pichugina and Banta 2010). Overall, in the LAFE month of August 2017, LLJs at all five sites were weaker, lower, and more easterly relative to other years.
August-mean LLJ properties at five sites for 2016–21; LLJ parameters (top) ULLJ, (middle) ZLLJ, and (bottom) DLLJ at each site are shown by color lines according to the scale in the top-right panel. Missing data in 2019 and 2020 at some sites are due to instrument maintenance.
Citation: Journal of Applied Meteorology and Climatology 62, 8; 10.1175/JAMC-D-22-0128.1
c. Relationship between turbulence and LLJs
All mechanisms for generating nocturnal LLJs require an abrupt reduction of vertical turbulent momentum-flux divergence at sunset. Although the turbulent fluxes are reduced by at least a factor of 10, they do not go to zero. Likely, the magnitude of the fluxes—and as a consequence, the magnitude of this reduction—as well as the structure of the postsunset flux profile through the SBL play key roles in the nighttime balance of forces. NWP models need to get this right, and it is, therefore, important to investigate the turbulence structure of the nighttime SBL, in an attempt to understand the role of the turbulence profile in the dynamics of the LLJ. Turbulence parameterizations are acknowledged weaknesses of NWP models, so for studies of these processes, accurate measurements of mean and turbulent momentum profiles are required to advance understanding of LLJ–SBL dynamics and to assess the credibility of model results.
The LLJ generates a strong shear zone and thus strong shear-generated turbulence between the LLJ nose and the surface. It is essential to distinguish between the height of the LLJ speed maximum, or jet nose ZLLJ, and the height of the turbulent SBL Zh. Mahrt et al. (1979) noted that ZLLJ represents an “upper bound to the vertical extent of turbulent transport,” because of the peak in stability (Ri) at this level, and refer to it as the top of the “momentum boundary layer.” Referring to ZLLJ as an “upper bound” recognizes that significant turbulence does not always extend up to this level. Other studies have attempted to equate the jet nose with the top of the SBL Zh. For weakly stable SBL conditions Banta et al. (2006) showed a high correlation between ZLLJ and minima in the turbulent velocity-variance profile. But Banta et al. (2002) noted that wind speed profiles can have many shapes, some having multiple maxima. The height of the first wind speed maximum above the surface in Banta et al. (2002, 2003), which was not always the absolute maximum speed (i.e., ZLLJ), was considered a good representation of the depth of the surface-based shear layer, and by inference of Zh itself (also Balsley et al. 2006).
Pichugina and Banta (2010) showed that the relationship between ZLLJ and Zh was even more nuanced. Because of the lack of directional shear with height and the relative flatness of the terrain, they were able to use lidar along-wind scans in elevation (vertical-slice or “RHI” scans) to profile the mean wind speed and streamwise variance, which was found to be approximately equal to TKE for stable conditions (Banta et al. 2006; Pichugina et al. 2008). The advantages of this scanning approach were that each scan took ∼30 s (or less) to complete. Each 10-min averaging period thus contained a large sample of points from at least 20 scans, so that even using 5- or 10-m vertical binning, the analysis produced smooth profiles of the wind speed and variance. They used the minimum in the variance profile to define Zh and related this to features in the mean speed, shear, and curvature profiles. They found three shapes (Fig. 6b) to the wind speed profile, the one in which the wind profile (type 1) has a distinct nose that corresponds to the top of the SBL Zh from the variance profile, and a second (type 2) that has a distinct surface-based layer of strong shear and turbulence but does not have a distinct nose because the profile above this layer has constant speed with height. The third profile shape (type 3) showed a layered structure to the shear and turbulence, where the strongest values are within a ground-based layer that lies beneath the second layer of weaker (but still positive) shear and weaker turbulence aloft. For these profiles, the maximum jet speed is at the top of the upper layer at ZLLJ, but the SBL Zh reaches only the top of the lower, strong-shear layer, so in this case, the two do not coincide. The scaling of SBL properties by LLJ speed and height previously proposed (Banta et al. 2003) should be interpreted as the mean speed and height at the top of the turbulent boundary layer Zh (which would be ZLLJ when the two coincide), as also found for stable conditions in the Netherlands by Vogelezang and Holtslag (1996).
Many Great Plains studies have found ZLLJ maxima at 400–500 m or more (e.g., Whiteman et al. 1997; Bonin et al. 2020). These deep jets are certainly well above Zh, the height to which significant surface-generated turbulence is likely to extend in stable conditions. In measured summertime Great Plains LLJ profiles of sufficient data quality, the layered type-3 profile, where the jet nose is higher than the top of the SBL (e.g., Bonin et al. 2020), is seen more often than in CASES-99 and LLLJP-03. Figure 11a shows an example of an LLJ profile from 23 August 2017, where the depth of the stronger, surface-based turbulence does not extend up to ZLLJ, but its top can be associated with a kink in the mean vertical shear of the profile, as in the type-3 profiles. The weaker, shallower LLJs observed during the CASES-99 experiment may reflect the lack of strong surface heating in October at higher elevations of the western Great Plains, such that the east–west temperature differential was too weak to routinely activate an effective thermal-wind mechanism (Parish and Oolman 2010). Conceptually, we may consider the lower, strong-shear layer as a layer where surface-based, mechanically generated turbulence dominates, but the intensities are much weaker than daytime turbulence, enabling the Blackadar-jet maximum to form at Zh. The upper layer is where surface-based shear (and turbulence) weakens to the extent that other larger-scale drivers (such as slope effects and thermal wind, which do not support such large shears), take over (Banta et al. 2002), such that the wind speeds continue to increase with height, but not so strongly as below Zh.
(a) Sample profiles of TKE (blue), the horizontal velocity variance (green), and wind speed profiles (black) for 0700 UTC 23 Aug at C1. The TKE and Uvar data were available from “6-beam” ULID measurements during LAFE. The first minimum of the turbulence indicates the SBL (stable boundary layer) top. The second minimum corresponds to the strongest LLJ height (ZLLJ) as indicated by the red symbol. (b) Profiles for 0600, 0900, and 1200 UTC for this night illustrate the most observed cases during the very stable (vS) boundary conditions when the minimum of shear-generated turbulence coincides with the ZLLJ, except 0700 UTC 23 Aug, which is similar to a stable (S) BL.
Citation: Journal of Applied Meteorology and Climatology 62, 8; 10.1175/JAMC-D-22-0128.1
During LAFE, some of the 15-min profiles under stable conditions show type 1 structure when ZLLJ coincides with the height of the minimum turbulence as illustrated by sample profiles (Fig. 11b), but most of the profiles, especially for the deep LLJs, exhibited type 3 structure.
d. Turning of the wind: Temporal and spatial hodographs
1) Temporal hodographs
After the postsunset drop in the intensity of vertical mixing in the ABL, the horizontal winds above the heights where the LLJ nose forms follow an inertial oscillation (IO) in time about the geostrophic wind according to the theory proposed by Blackadar (1957). The amplitude of the IO decreases with a height from its peak value at the jet nose, and its period corresponds to a half-pendulum day T = 2π/(2ω sinϕ) (∼20 h in Oklahoma), where ω is Earth’s rotational frequency and ϕ is the latitude. The IO wind oscillation rotates anticyclonically (clockwise, Northern Hemisphere) from its late-afternoon direction, which is at an angle down the pressure gradient, to a direction aligned with the geostrophic wind (normal to the pressure gradient) after ¼ period, when it reaches maximum speed. The wind then continues to rotate but at decreasing speeds, as it is now blowing toward higher pressure, until after the morning transition the next day when the daytime balance of forces is restored and the winds become well mixed. Idealized LES model runs have reproduced this behavior (Fedorovich et al. 2017).
On most LAFE nights the turning of the wind in time appeared small at all vertical levels (Fig. 4d), in agreement with previous studies. The IO theory is concerned with departures from geostrophic, which is difficult to determine with accuracy, so Fig. 12 shows the behavior of the wind direction as a departure from its 0000 UTC value (cf. Klein et al. 2015; Bonin et al. 2020) at several vertical levels on an expanded direction axis. Shown are time series of wind directions for the five sites on three southerly flow nights and two northeasterly flow nights. For each night the values at the five sites tracked each other rather closely (mostly within 10°), especially on 21 August and the NE flow nights, although instances of flow disruptions at individual locations can be seen, for example, at site E32 from 0500 to 0700 UTC and after 10 UTC 21 August when significant wind shifts (50° and 100°, respectively) occurred at the lower levels. The 21 August ramp events from lidar measurements and LES are analyzed in a separate study. Similarly, such flow disruptions can be seen at times during the night at site E41 on 20 August at the lower levels.
Directional deviation from 0000 UTC direction for (a) southerly and (b) northeasterly winds at five heights (117, 221, 365, 455, and 584 m) through the boundary layer with the most frequent LLJs. Winds at each SGP site are indicated by colors according to legends at the bottom panels.
Citation: Journal of Applied Meteorology and Climatology 62, 8; 10.1175/JAMC-D-22-0128.1
The NE-flow nights tended to show a steady turning through the night, which was smallest at the lowest 116-m level and which for most of the sites amounted to less than 20° over the entire 12-h (0000–1200) period. For the southerly flow nights, any turning tended to occur in the first 6 h, after which the direction remained constant or in some cases reversed. As was the case for the NE-flow nights, the nightly rotation was mostly less than 20°, but again, happening in the first 6 h of 19–20 August. Vanderwende et al. (2015) also found small-magnitude (3° h−1) rotations through the night farther north in Iowa. For these cases, the normal expected strong IO-theory rotation thus clearly did not continue through the night. It is worth noting that all five sites behaved similarly so that each site was representative of regional LLJ evolution.
Temporal hodographs at constant height (Fig. 13) show that at 117 m, which was generally within the turbulent SBL, the evolution of the wind tended to be largely disorganized. At 455 m AGL, above the jet nose, clockwise rotation was found on most nights. On 22 August, the hodograph showed an IO-like rotation, with peak speeds occurring at ∼0500–0600 UTC. Although other southerly nights did have indications of a clockwise rotation, it was not always so obviously IO-like; for example, 22 August had a small rotation in direction but mostly accelerated to >15 m s−1 through the night. NE-flow nights also had a mostly disorganized flow evolution at 117 m, but at 455 m, some nights, such as 25 August, did have IO-like rotation, although the peak speeds were often later than 06 UTC. On many NE-flow nights, the resemblance to the IO was less clear, such as on 24 August shown here. Thus, nights could be found having temporal hodographs that conformed to the IO pattern, but not consistently: many nights having well-formed LLJs did not clearly exhibit this behavior.
Temporal hodographs for (a) southerly and (b) easterly winds at two heights (117 and 455 m) illustrate clockwise rotation in time of winds at four SGP sites located at (west to east) 66–77 km and (north to south) 56–57 km.
Citation: Journal of Applied Meteorology and Climatology 62, 8; 10.1175/JAMC-D-22-0128.1
Overall, the rotational amplitudes were small on most nights. If these small rotations had been observed at only one location, it might be easy to dismiss their validity as not significant, nonrepresentative, or due to instrument uncertainty, but they were measured at all five sites. This smallness of the rotations means either that the late afternoon geostrophic departures were small, which we regard as unlikely, or that other factors or forces were important in the evolution of the LLJs besides pure IO physics. Such factors most likely include a significant role for height-dependent vertical mixing and/or processes contributing to a time-dependent geostrophic wind (e.g., Parish et al. 1988).
2) Vertical hodographs
Vertical hodographs, shown for three times (0000, 0400, and 0600 UTC) in Fig. 14, reveal the vertical structure of the winds between 117 and 714 m AGL. In the late afternoon at 0000 UTC (top row), the strong mixing produced mostly small differences in the winds with height. Later in the evening at 0400 and 0600 UTC, the winds in the lower levels all blew from a similar direction, forming a linear hodograph configuration in which the wind speed increased with height but without significant change in direction. The near constancy of wind direction with height within the SBL below the jet nose has been previously noted in late summer and fall in southeast Colorado and Kansas (Pichugina and Banta 2010). Above this layer of uniform wind direction, the winds veered, giving the vertical hodograph a hooked appearance. This pattern was true for both the southerly and NE-flow nights. We note that Grachev et al. (2005) previously found evidence for Ekman turning in the very stable, very shallow boundary layer that persisted for many weeks in the Arctic, but we did not find such behavior within the overnight SBLs studied here.
Vertical “hooked” hodographs for southerly winds on 16, 21, and 22 Aug at four SGP sites. The first level represented in each hodograph was at 117 m, and the top level was 714 m AGL.
Citation: Journal of Applied Meteorology and Climatology 62, 8; 10.1175/JAMC-D-22-0128.1
3) Other hodograph behavior
Temporal hodographs from weaker wind nights (e.g., Fig. 15a) showed indications of veering, but not well organized and having less site-to-site coherence. Figure 15b shows an anomalous example of a temporal hodograph where the rotation turned counterclockwise with height at site E41 at 0400 UTC, then intensified and appeared at all the sites by 0600 UTC. [Although Van de Wiel et al. (2010) found instances of such reverse rotations on many nights by considering departures from an alternative reference wind profile, this was the only instance of counterclockwise rotation with the height that we found in the LAFE-period dataset.] Vertical hodographs also showed considerable variability among nights.
Cases of unusual (“interesting”) (a) temporal and (b) vertical hodographs.
Citation: Journal of Applied Meteorology and Climatology 62, 8; 10.1175/JAMC-D-22-0128.1
5. Conclusions
Doppler-lidar profiles of wind speed and direction were available at the central site during the intensive lidar deployment of LAFE, which was embedded in the SGP array of Doppler lidars. The availability of the 6-yr dataset from the five-site SGP array allowed the LAFE findings at the central site to be put into their spatial and temporal context. The layer-averaged nighttime winds showed a bimodal histogram in direction, with a predominant southerly peak and a secondary northeasterly peak that was usually much smaller. Southerly winds were stronger than the northeasterlies by more than 4 m s−1 on average. Geographic variations were noted: on southerly wind nights, the winds blew strongest at the highest, westernmost sites by 2 m s−1, whereas on the northeasterly flow nights, the easternmost sites had the highest wind speeds by a similar margin.
In comparison with other summertime 2016–21 months, August 2017, the period of deployment, showed an anomalously large number of post-cold-frontal days, characterized at night by a higher frequency of northerly through easterly LLJs than normal, a departure from the southerly winds and LLJs typical of summertime conditions in this region. Flow and LLJ properties could be compared for the same month, and the results echoed the results of the longer-term averages. Mean winds and LLJ speeds were stronger for the southerly flows than northeasterly flows by several m s−1, reflecting a significantly higher frequency of winds stronger than 12 m s−1. Under the southerly flow, speeds at the westernmost sites were ∼1 m s−1 stronger than at the other sites.
The availability of frequent wind profiles at high vertical resolution allowed the construction of temporal and vertical hodographs over the study region. At levels within the SBL, the temporal hodographs showed a disorganized pattern, most likely due to the stronger mixing below the LLJ nose. Many nights where LLJs were observed featured the expected veering above the SBL. The total turning of the wind with time through the nights, however, was less than would be expected for a pure IO following an afternoon of strong convective heating through the Oklahoma ABL, which should generate a strong ageostrophic wind component at sunset. This indicates that mechanisms other than IO physics play a role in generating and maintaining the LLJ wind profile, such as turbulent mixing, thermal wind, or an evolving geostrophic wind.
Vertical hodographs of the wind profile in the SBL below the LLJ nose indicated dramatic increases in speed with height, but the direction was uniform, leading to a linear hodograph in this layer. This provides evidence for significant vertical mixing of the winds in the SBL at night, but of course at intensities much less than daytime convective mixing. The turning of the wind with height was thus less than expected from Ekman theory, suggesting the influence of variable turbulent mixing with height. Above the SBL, veering with height above the linear trace within the SBL produced a hook-shaped hodograph. The similarity of the temporal and vertical hodographs from site to site reinforces their validity and shows that these were regional behaviors.
Acknowledgments.
This study was conducted as part of LAFE. This research was supported in part by NOAA Cooperative Agreements NA17OAR4320101 and 375 NA22OAR4320151, the U.S. Department of Energy’s Atmospheric System Research, an Office of Science Biological and Environmental Research program, under Grant DE-SC0020114, as part of the Atmospheric Radiation Measurement Program and Atmospheric System Research Program, and the NOAA Oceanic and Atmospheric Research Office of Weather and Air Quality, the NASA Water and Energy Cycle Program, the German Federal Ministry of Education and Research (BMBF), and the University of Hohenheim. We gratefully acknowledge the efforts of the ARM Southern Great Plains managers and Pacific Northwest National Laboratory staff for maintaining and operating that site both during this campaign and over the last three decades.
Data availability statement.
Datasets from scanning Doppler lidars at five SGP sites used during this study are openly available from the ARM SGP Archive (https://www.arm.gov/capabilities/observatories/sgp; Shippert et al. 2016).
APPENDIX A
Temporal and Vertical Resolutions of the Lidar Measurements
Temporal and vertical resolutions of the data available from ULID during LAFE and of the routine long-term SLID measurements are given in in Table A1.
List of turbulence and wind flow variables obtained from SLIDs during the long term (2016–21) and from ULID measurements during LAFE (August 2017) along with the temporal and vertical resolutions of profiles. The last column shows the first available height of the profile and (in parentheses) the lowest height used to plot the figures in this paper. SLID designates the ARM SGP Doppler lidar of long-term, baseline observations at five SGP sites, and ULID indicates the Hohenheim Doppler lidar observations during LAFE.
APPENDIX B
More Details on Wind Speed and Direction
Figure B1 provides the distribution of nighttime winds for August 2017, the LAFE period. Wind speeds from the total 6-year sample were mostly 8–12 m s−1 (Fig. B2a). Each year, the strongest winds were southerly at all sites (Fig. B2e), whereas the northeasterly component sectors tended to be by 3–4 m s−1 weaker (Fig. B2c). The southerly winds (Fig. B2f) were most frequent (25%–60%) for all months and years. During the LAFE, the mean southerly winds were weaker relative to other months and years (except July 2018), whereas the northeasterly component winds were comparable to the other months. The frequency of northeasterly winds during August 2017 was larger (∼22%) in comparison with other months.
Distributions of 0000–1400 UTC wind direction in the layer of 117–714 m at five SGP sites in August 2017, illustrating two prevalent wind directions: 67.5° and 172.5°. The embedded table shows the mean wind at each site for these direction peaks.
Citation: Journal of Applied Meteorology and Climatology 62, 8; 10.1175/JAMC-D-22-0128.1
(a) The monthly-mean wind speed and (b) the number of points used in Fig. 4 for the summer months of 2016–21. Each site is shown by color according to the legends in (a) and (b). Also shown are (left) wind speed and (right) the number of points (%) for the (c),(d) NE (45° ± 22.5°) and (e),(f) S (180° ± 22.5°) sectors of wind direction. Missing data at some sites are due to instrument maintenance.
Citation: Journal of Applied Meteorology and Climatology 62, 8; 10.1175/JAMC-D-22-0128.1
APPENDIX C
Wind Roses of Overnight and Diurnal Winds
Figure C1 shows wind roses of overnight (0000–1400 UTC; top panel) and diurnal (0000–0000 next day UTC) winds at approximately 100 m from lidar measurements at five SGP sites for August 2017.
August 2017 wind roses of 117-m wind speed at the five SGP sites for the (a) 0000–1400 UTC and (b) 0000–0000 next day UTC periods.
Citation: Journal of Applied Meteorology and Climatology 62, 8; 10.1175/JAMC-D-22-0128.1
APPENDIX D
Wind Speed Frequencies
The frequencies and percents of wind speed that were observed for different parts (ranges) of a power curve of a “virtual” wind turbine are shown in Table D1.
The total number (count) and percentage (%) of 15-min (at site C1) and 10-min (at sites E32, E37, E39, and E41) wind speed data points in August 2017 at 90 and 117 m and over a layer of 90–140 m is shown for different wind categories at each site. The categories are selected for a power curve of a virtual wind turbine, and data are taken for the diurnal cycle of 0000–0000 next day UTC.
APPENDIX E
Stability Classification
Table E1 provides the stability classes resulting from classification using the Monin–Obukhov length as obtained from sonic-anemometer measurements at 25 and 60 m AGL.
Classification of the nocturnal boundary layer stability by the Monin–Obukhov length LMO (Gryning et al. 2007).
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