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  • View in gallery

    TTUKa radar deployment schematics for (a) 14 Feb 2017 and (b) 12 Oct 2015. Mapped is the underlying mean sea level elevation (m) overlaid by the turbine (black circle) and tower (white square) locations, the radar sectors scanned, the mean wind direction during radar data collection (green arrow), and the DD analysis domain (shaded) in (b).

  • View in gallery

    The 14 Feb 2017 meteorological tower vertical profile of (a) virtual potential temperature (θV) (K) with time and (b) θV/z defined between 10 and 200 m [K (100 m)−1]. The value of θV/z at the numerically labeled vertical black lines is provided in Table 3.

  • View in gallery

    The 14 Feb 2017 meteorological tower time histories of the 10-min mean (a) wind speed, (b) wind direction, and (c) TI at both 116.4 and 158.2 m AGL. Mean magnitudes of wind speed and TI at the numerically labeled vertical black lines are provided in Table 3.

  • View in gallery

    The 12 Oct 2015 meteorological tower vertical profile of (a) virtual potential temperature (θV) (K) with time and (B) θV/z defined between 10 and 200 m [K (100 m)−1]. The value of θV/z at the numerically labeled vertical black lines is provided in Table 4.

  • View in gallery

    The 12 Oct 2015 meteorological tower time histories of the Obukhov length L at 2.44 m AGL. The value of L at the numerically labeled vertical black lines is provided in Table 4.

  • View in gallery

    The 12 Oct 2015 meteorological tower time histories of the 10-min mean (a) wind speed, (b) wind direction, and both (c) TI and TKE at 74.7 m AGL. Mean magnitudes of wind speed, TI, and TKE at the numerically labeled vertical black lines are provided in Table 4.

  • View in gallery

    TTUKa DD horizontal wind speed (m s−1) at (a) 1732:16 and (b) 1733:16 UTC 14 Feb 2017. The SCT was used to estimate the ABL wind field advection speed (19.34 m s−1) and direction (1.97°) between the DD volumes.

  • View in gallery

    The steps used to determine STI at a specific location within the measurement domain.

  • View in gallery

    (a) TTUKa DD horizontal wind speed (m s−1) and (c) STI at 1720:03 UTC 14 Feb 2017 and at an elevation of 158.2 m AGL. (b) STI analysis area at example grid points (blue rectangles); the analysis areas were constructed using a 30-s advection time window, an advection speed of 15.2 m s−1, and an advection direction of 1.2°. Spatial wind field analysis within these analysis areas are used to transform (a) to (c).

  • View in gallery

    (a) Zoomed-in image of Fig. 9c overlaid by the meteorological tower (white square) and the location of the individual STI values (red ×s) that will advect past the tower over the subsequent volume acquisition period. (b) The 48 STI values identified in (a) were used to develop an STI time history at the location of the meteorological tower (1720:03–1721:04 UTC).

  • View in gallery

    (a) The value of μerr (x axis) and σerr (y axis) using different STI analysis area widths and a 30-s advection time window. (b) The distance of the error points in (a) to the origin (0, 0) is equivalent to the RMSE value. Data plotted were from the 14 Feb 2017 deployment for the period 1701:55–1801:25 UTC at 158.2 m AGL.

  • View in gallery

    (a) STI and tower TI time histories on 14 Feb 2017 for the period 1701:55–1801:25 UTC at 158.2 m AGL. (b) As in (a), but the empirical corrections were applied to account for advection differences between 1714:19 and 1715:59 UTC. (c) As in (b), but with a static offset applied to account for the mean bias error in STI.

  • View in gallery

    (a) The ratio of TI to STI at 158.2 m AGL for the period 1701:55–1801:25 UTC 14 Feb 2017. (b) The ratio values in (a) plotted as a function of the mean wind speeds. The black line denotes the linear model that was fit to the distribution of ratio values and mean wind speeds.

  • View in gallery

    STI and tower TI time histories for the period 1701:55–1801:25 UTC at 116.4 m AGL. The plotted STI time history is reflective of the mean bias error correction.

  • View in gallery

    Error diagrams as plotted in Fig. 11. However, the error presented is consistent with STI analysis maps constructed using variable advection time windows and a 100-m width.

  • View in gallery

    (a) Schematic of TTUKa measurement height (blue line) with range overlaid by both the location (vertical green line) and instrumented levels (horizontal green line) of the meteorological tower. The red star indicates the 74.7 m AGL measurement range. (b) TTUKa radial velocities (m s−1) at 2237:56 UTC plotted with the 74.7 m AGL measurement range (red arc), the STI analysis area (black rectangle) and midpoint (red star), and the meteorological tower (white square).

  • View in gallery

    (a) STI and tower TI time histories for the period 2232:08–0052:30 UTC and (b) a 5-min running average of (a). The convective and stable ABL periods of data collection are shaded in red and blue, respectively.

  • View in gallery

    (a) The ratio of TI to STI for the period 2232:08–0052:30 UTC; data from the convective and stable ABL periods are plotted in red and blue, respectively. (b) The ratio values in (a) plotted as a function of the mean wind speeds. The black line denotes the linear model that was fit to the distribution of ratio values and mean wind speeds. The color lines denote the fitted linear model when data from only the convective or stable ABL were considered.

  • View in gallery

    Example measurement volume defined by the range and angular resolution of the scanning remote sensing instrument. The radial velocity estimate that is extracted from the measurement volume is assigned to the middle of the measurement volume.

  • View in gallery

    Linear model of STI as a function of the mean measurement range at 120, 140, 160, 180, and 200 m AGL. The models are plotted for 250-m measurement range bins that contain at least 20 000 STI measurements.

  • View in gallery

    STI within the (a) convective (2236:21 UTC) and (b) stable (0016:01 UTC) ABLs overlaid by contours of the SD measurement height (m AGL) and the location of the meteorological tower (white square) and wind turbine (black circle).

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Doppler Radar Measurements of Spatial Turbulence Intensity in the Atmospheric Boundary Layer

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  • 1 National Wind Institute, Texas Tech University, Lubbock, Texas
  • | 2 Department of Geosciences, Texas Tech University, Lubbock, Texas
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Abstract

Remote sensing instruments that scan have the ability to provide high-resolution spatial measurements of atmospheric boundary layer winds across a region. However, the time required to collect the volume of measurements used to produce this spatial representation of atmospheric winds typically limits the extraction of atmospheric turbulence information using traditional temporal analysis techniques. To overcome this constraint, a spatial turbulence intensity (STI) metric was developed to quantify atmospheric turbulence intensity (TI) through analysis of spatial wind field variability. The methods used to determine STI can be applied throughout the measurement domain to transform the spatially distributed velocity fields to analogous measurement maps of STI. This method enables a comprehensive spatial characterization of atmospheric TI. STI efficacy was examined across a range of wind speeds and atmospheric stability regimes using both single- and dual-Doppler measurements. STI demonstrated the ability to capture rapid fluctuations in TI and was able to discern large-scale TI trends consistent with the early evening transition. The ability to spatially depict atmospheric TI could benefit a variety of research disciplines such as the wind energy industry, where an understanding of wind plant complex flow spatiotemporal variability is limited.

© 2019 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: James B Duncan Jr., james.b.duncan@ttu.edu

Abstract

Remote sensing instruments that scan have the ability to provide high-resolution spatial measurements of atmospheric boundary layer winds across a region. However, the time required to collect the volume of measurements used to produce this spatial representation of atmospheric winds typically limits the extraction of atmospheric turbulence information using traditional temporal analysis techniques. To overcome this constraint, a spatial turbulence intensity (STI) metric was developed to quantify atmospheric turbulence intensity (TI) through analysis of spatial wind field variability. The methods used to determine STI can be applied throughout the measurement domain to transform the spatially distributed velocity fields to analogous measurement maps of STI. This method enables a comprehensive spatial characterization of atmospheric TI. STI efficacy was examined across a range of wind speeds and atmospheric stability regimes using both single- and dual-Doppler measurements. STI demonstrated the ability to capture rapid fluctuations in TI and was able to discern large-scale TI trends consistent with the early evening transition. The ability to spatially depict atmospheric TI could benefit a variety of research disciplines such as the wind energy industry, where an understanding of wind plant complex flow spatiotemporal variability is limited.

© 2019 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: James B Duncan Jr., james.b.duncan@ttu.edu

1. Introduction

Fixed meteorological towers and nacelle-mounted anemometry are the primary measurement sources within a wind plant. However, because of both physical and financial constraints, these measurement systems are spatially limited and cannot adequately quantify wind plant complex flows. Scanning remote sensing instruments can alternatively provide high-resolution spatial measurements of atmospheric boundary layer (ABL) winds both horizontally and vertically across spatial footprints of tens to hundreds of square kilometers, and in recent years they have furthered the science and understanding of wind plant complex flows (e.g., Banta et al. 1999; Hill et al. 2010; Käsler et al. 2010; Hirth et al. 2012; Banakh and Smalikho 2013; Krishnamurthy et al. 2013; Hirth et al. 2015; Newsom et al. 2015; Hirth et al. 2016; Bodini et al. 2017). Despite the ability of scanning remote sensing instruments to develop three-dimensional maps of horizontal wind speed and direction, typical measurement revisit times inhibit the extraction of atmospheric turbulence information.

The measurement maps derived from scanning remote sensing instruments are produced by performing a series of sector scans, often across multiple elevation tilts, to collect a spatially distributed set (i.e., a volume) of measurements. Therefore, measurement revisit times vary greatly depending on the instrument [i.e., radio detection and ranging (radar), light detection and ranging (lidar), etc.], the measurement domain size, and the chosen scanning strategy. Using standard temporal analysis techniques (i.e., analyzing temporal wind field variability at a point), the ability to extract atmospheric turbulence information depends heavily on the sampling frequency of the anemometer. Although scanning strategies can be adapted to reduce measurement revisit times and enable the extraction of atmospheric turbulence information using standard temporal analysis techniques (e.g., Gunter et al. 2015), this is counterintuitive because it significantly reduces the size measurement volume and thus the spatial footprint of observation. Therefore, the question remains: To what extent, and with what methods, can scanning remote sensing instruments be used to determine atmospheric turbulence information?

The ability to extract atmospheric turbulence information from the spatially distributed velocity measurements derived from scanning instruments is an active area of research in the wind energy community (Calhoun and Heap 2006; Krishnamurthy et al. 2011; Sathe and Mann 2013; Barthelmie et al. 2014). Using velocity–azimuth and adapted range–height indicator scanning techniques, spatial analysis techniques have been previously established to enable the extraction of atmospheric turbulence intensity (TI) and turbulence kinetic energy (TKE) (e.g., Eberhard et al. 1989; Banta et al. 2006; Wang et al. 2015; Bonin et al. 2017). However, these methods require multiple data volumes; therefore, extended data collection periods (~10–20 min) are necessary. Furthermore, spatial structure functions can be used to extract atmospheric turbulence information such as the integral length scale and eddy dissipation rate (e.g., Banakh et al. 1999; Frehlich and Cornman 2002; Davies et al. 2004; Zhai et al. 2017). Analysis of spatial wind field variability has also been used by Aitken et al. (2014) to determine estimates of turbine inflow TI. While these methods enable the extraction of various atmospheric turbulence statistics, none of them provide a spatial depiction of the turbulence statistics being measured. Instead, these techniques nominally reduce the measurement maps down to a “virtual” tower, thereby removing the ability of the scanning remote sensing instruments to resolve spatial wind field structure.

Established herein is a spatial analysis technique that enables the extraction of atmospheric TI without requiring significant sacrifice to the spatial measurement domain. Through this method, a spatial turbulence intensity (STI) metric is used to transform the spatially distributed velocity fields to analogous measurement maps that characterize the embedded TI levels. Atmospheric TI is derived at individual locations by analyzing spatial, not temporal, wind field variability across defined analysis areas of a single scanned volume. The efficacy of STI was examined against in situ anemometry across a range of wind speeds and ABL stability regimes using both single-Doppler (SD) and dual-Doppler (DD) radar measurements. Using the established methods, the spatially distributed velocity field can be transformed to analogous measurement maps of STI. Within the wind energy industry, the ability to extract a spatial representation of atmospheric TI has significant implications. For example, these maps should support model validation efforts and help researchers better understand wind plant complex flow response to variations in atmospheric turbulence.

The following sections provide an overview of the instrumentation and data collection (section 2), detail the STI methods (section 3), examine STI efficacy (section 4), and provide a brief summary of the results (section 5).

2. Instrumentation and data collection summary

a. Instrumentation

Spatially distributed radial velocity measurements collected by Texas Tech University’s mobile pair of Ka-band Doppler radars (TTUKa; Hirth et al. 2012) were used in this study for STI validation. The TTUKa radars are long-range scanning remote sensing instruments that utilize a 0.33° half-power beamwidth, a nominal 15 m along-beam range gate spacing, and horizontal scan speeds of 30° s−1 to provide high-resolution spatial measurements of ABL winds across a region (additional technical specifications are provided in Table 1). Radar measurements were collected across two radar deployments using both SD (12 October 2015; Fig. 1a) and DD (14 February 2017; Fig. 1b) scanning strategies. Sector scans were performed at a single elevation tilt within the SD deployment, enabling the extraction of the radial wind field component at relatively rapid measurement revisit times (i.e., several seconds). Alternatively, DD strategies required the iteration of radar-coordinated sector scans across multiple elevation tilts in order to acquire a three-dimensional volume of information in about one minute. When performing DD scans, if the start of either radar volume (TTUKa1 or TTUKa2) differed by more than a few seconds, radar scanning was stopped, and the radar scans were resynced to ensure coordinated measurement volumes. In regions where the sector scans of each radar spatially overlapped (i.e., the DD domain) (Davies-Jones 1979), DD synthesis was performed to yield a full representation of the horizontal wind field (Lhermitte 1971).

Table 1.

TTUKa radar system technical specifications. Multiple values are provided if the radar specification used varied between the 12 Oct 2015 (SD) and 14 Feb 2017 (DD) deployments.

Table 1.
Fig. 1.
Fig. 1.

TTUKa radar deployment schematics for (a) 14 Feb 2017 and (b) 12 Oct 2015. Mapped is the underlying mean sea level elevation (m) overlaid by the turbine (black circle) and tower (white square) locations, the radar sectors scanned, the mean wind direction during radar data collection (green arrow), and the DD analysis domain (shaded) in (b).

Citation: Journal of Applied Meteorology and Climatology 58, 7; 10.1175/JAMC-D-18-0151.1

Located within the analysis domain of both radar deployments was a meteorological tower providing high-resolution (i.e., 50 Hz) wind, moisture, and thermal measurements and a wind turbine. Depending upon instrument availability and data quality during the analysis periods, wind measurements acquired using either a Gill R3–50 three-axis sonic anemometer or a Gill 200–27005 UVW anemometer (2.1-m distance constant) were used for STI validation. DD STI values were compared to the UVW-extracted turbulence statistics, while SD STI performance was measured against the sonic anemometer. Manufacturer suggested cosine corrections were applied to the UVW wind data and tilt corrections (Wilczak et al. 2001) were applied to the sonic anemometry. Temperature and moisture measurements provided by an RM Young 41382V sensor and thermal measurements by a sonic anemometer were used to determine ABL stability. A summary of the meteorological tower levels used in the presented analysis is provided in Table 2.

Table 2.

Description of the meteorological tower levels. The × indicates that the observation height was equipped with the instrument, and the SD/DD demonstrates whether the instrument was used for the 12 Oct 2015 (SD) or the 14 Feb 2017 (DD) deployment.

Table 2.

b. TTUKA radar deployments

The following sections provide an overview of the two radar deployments and ABL conditions (i.e., wind speed, turbulence, and stability classification) present during data collection. Deployment date selection was based upon data availability and the objectives of the measurement campaign. All ABL wind, turbulence, and thermal statistics provided in the data deployment sections were derived from 10-min windows that were temporally centered on the volume acquisition (SD or DD) completion time.

1) 14 February 2017

The pair of TTUKa radars were deployed on 14 February 2017 to the south (TTUKa2) and southwest (TTUKa1) of a meteorological tower to collect coordinated radar volumes comprising 60° sector scans across 14 elevation tilts (1.2°–2.5° in intervals of 0.1°). Upon the collection of an individual volume, which took on average 60.4 s to complete, editing of the volumetric radial velocity measurements was performed according to the three radar moments to ensure data quality and a Barnes objective analysis (OA) scheme (Barnes 1964) was used to transform the volumetric radial velocity measurements from their native polar coordinate system onto a Cartesian gridded DD domain. The DD domain was defined by a lateral grid spacing of 20 m and was vertically resolved at 116.4 and 158.2 m above ground level (AGL). These elevation levels are consistent with two of the instrumented levels of the meteorological tower. Within the DD domain, the interpolated radial velocity fields of each radar were combined via DD synthesis to yield the height-varying structure of the horizontal wind field. To improve DD wind field accuracy, intravolume advection corrections were used to account for the motion of turbulent features during the volume acquisition period (Duncan et al. 2019).

A total of 60 radar volumes were collected between 1701:55 and 1801:25 UTC during a period of light to moderate precipitation. During this period, ABL stability was considered to be near neutral as defined by the virtual potential temperature (θV) gradient (θV/z) between 10 and 200 m (Fig. 2a). This gradient denotes how conducive or suppressive the ABL is toward the development of turbulent eddies and can be used to estimate ABL stability. The ABL was considered to be statically stable, neutral, or unstable when the virtual potential temperature gradient was positive, approximately zero, or negative, respectively. Within the analysis period, the virtual potential temperature gradient exhibited a mean value of 0.034 K (100 m)−1 with fluctuations occurring between −0.032 and 0.13 K (100 m)−1 (Fig. 2b). These near-zero virtual potential temperature gradients indicated near-neutral ABL conditions.

Fig. 2.
Fig. 2.

The 14 Feb 2017 meteorological tower vertical profile of (a) virtual potential temperature (θV) (K) with time and (b) θV/z defined between 10 and 200 m [K (100 m)−1]. The value of θV/z at the numerically labeled vertical black lines is provided in Table 3.

Citation: Journal of Applied Meteorology and Climatology 58, 7; 10.1175/JAMC-D-18-0151.1

The prevailing wind conditions were also examined by analyzing mean wind speed and TI (Fig. 3). TI, defined as the ratio between the standard deviation (σ) and mean (μ) (i.e.,σ/μ) of the horizontal wind speed measurements, depicts the intensity of turbulent fluctuations in the wind relative to the mean flow. Mean wind speeds steadily increased during the data collection period at both elevations examined, increasing from 14.12 to 18.47 m s−1 at 116.4 m AGL and increasing from 14.39 to 18.84 m s−1 at 158.2 m AGL. Despite this increase in mean wind speed, TI did not exhibit any significant trends in magnitude. Instead, TI varied about a mean value of 0.086 at 116.4 m AGL and fluctuated about a mean value of 0.081 at 158.2 m AGL. Mean wind speed and the values of both θV/z and TI at various times during the data collection period (denoted by the numerically labeled black lines in Figs. 2 and 3) are provided in Table 3.

Fig. 3.
Fig. 3.

The 14 Feb 2017 meteorological tower time histories of the 10-min mean (a) wind speed, (b) wind direction, and (c) TI at both 116.4 and 158.2 m AGL. Mean magnitudes of wind speed and TI at the numerically labeled vertical black lines are provided in Table 3.

Citation: Journal of Applied Meteorology and Climatology 58, 7; 10.1175/JAMC-D-18-0151.1

Table 3.

The 14 Feb 2017 deployment mean wind speed (116.4 m|158.2 m AGL), TI (116.4 m|158.2 m AGL), and θV/z magnitudes. The values provided are valid for the 10-min period centered on 1712:57, 1725:10, 1737:21, and 1749:20 UTC, which correspond to the vertical black lines in Figs. 2 and 3.

Table 3.

2) 12 October 2015

TTUKa1 was deployed slightly north of its 14 February 2017 location on 12 October 2015 to capture changes in ABL wind field structure during the early evening transition (EET). Between 2332:08 and 0052:30 UTC, data were collected in a nonprecipitating environment, wherein the radar performed a total of 1791 sectors scans at a 1° elevation tilt with an average sector revisit time of 4.7 s. The orientation of the scanned sector relative to the governing wind direction from the northeast allowed the wind field to be well resolved in the vicinity of the meteorological tower (Fig. 1b). Upon editing of the radial velocity measurements to ensure data quality, a Barnes OA scheme was used to interpolate the polar radial velocity measurements onto a Cartesian gridded domain with a lateral grid spacing of 20 m.

During data collection, the ABL underwent the EET from the daytime convective to the nocturnal stable ABL. The convective ABL, defined by the virtual potential temperature gradient between 10 and 200 m, persisted from 2232:08 to 2327:53 UTC, while the stable ABL persisted for the remainder of the data collection period (i.e., until 0052:30 UTC) (Fig. 4). The mean virtual potential temperature gradient within the convective ABL was −0.17 K (100 m)−1, and after the transition to the stable ABL, the gradient increased to a mean value of 0.77 K (100 m)−1. The Obukhov length (L) was also used to determine ABL stability. Physically, L denotes the height AGL where buoyant factors first dominate mechanically driven shear in the generation of TKE (Stull 1988). The availability of three-axis sonic anemometer measurements during the data collection period enabled the derivation of L. The value of L was defined by
L=θυ¯u*3κg(wθυ¯),
where κ is the von Kármán constant, g is the gravitational acceleration constant, u* is the friction velocity, w′ is the turbulent component of the vertical wind speed, and the product wθυ¯ is the kinematic sensible heat flux. The overbar denotes a 10-min average value. Trends in L similarly capture ABL stability changes consistent with the EET (Fig. 5). Using stability classification criteria based on Panofsky and Dutton (1984) and Stull (1988), and further used in Wharton and Lundquist (2012), the transition between the daytime convective (i.e., −600 < L < 0) and nocturnal stable (i.e., 0 < L < 600) ABLs occurred at 2319:58 UTC. This transition time was approximately eight minutes prior to the time indicated by the value of the virtual potential temperature gradient. Although L provides insight into the convective, neutral, and stable ABLs, ABL stability classifications were based on the sign of the virtual potential temperature gradient.
Fig. 4.
Fig. 4.

The 12 Oct 2015 meteorological tower vertical profile of (a) virtual potential temperature (θV) (K) with time and (B) θV/z defined between 10 and 200 m [K (100 m)−1]. The value of θV/z at the numerically labeled vertical black lines is provided in Table 4.

Citation: Journal of Applied Meteorology and Climatology 58, 7; 10.1175/JAMC-D-18-0151.1

Fig. 5.
Fig. 5.

The 12 Oct 2015 meteorological tower time histories of the Obukhov length L at 2.44 m AGL. The value of L at the numerically labeled vertical black lines is provided in Table 4.

Citation: Journal of Applied Meteorology and Climatology 58, 7; 10.1175/JAMC-D-18-0151.1

ABL wind conditions at 74.7 m AGL responded heavily to the EET (Fig. 6). Given the availability of sonic anemometry, TKE was also analyzed in conjunction with TI to examine the evolution of ABL turbulence within the EET. As opposed to TI, TKE incorporates buoyant contributions to turbulence that are strongest in the vertical dimension. TKE was defined as 0.5(σu2+συ2+σw2), where σu2, συ2, and σw2 denote the variance of the turbulent wind field component in the along-wind, lateral, and vertical dimensions, respectively. Mean wind speed, TI, and TKE exhibited their peak magnitudes in the convective ABL before steadily decreasing in magnitude as the ABL became increasingly stable. Upon transition to the stable ABL at 2327:53 UTC, the mean wind speed stopped decreasing and instead began to fluctuate about a mean value of 7.48 m s−1. Despite mean wind speeds roughly stabilizing, both TI and TKE did not reach their minimum value until later in the data collection period. TKE reach a minimum value of 0.0065 at 0044:51 UTC and TI reach a minimum value of 0.013 at 0046:45 UTC. Mean wind speed and the values of θV/z, L, TI, and TKE at various times during the data collection period (denoted by the numerically labeled black lines in Figs. 4, 5, and 6) are provided in Table 4.

Fig. 6.
Fig. 6.

The 12 Oct 2015 meteorological tower time histories of the 10-min mean (a) wind speed, (b) wind direction, and both (c) TI and TKE at 74.7 m AGL. Mean magnitudes of wind speed, TI, and TKE at the numerically labeled vertical black lines are provided in Table 4.

Citation: Journal of Applied Meteorology and Climatology 58, 7; 10.1175/JAMC-D-18-0151.1

Table 4.

The 12 Oct 2015 deployment mean wind speed (74.7 m AGL), TI (74.7 m AGL), TKE (74.7 m AGL), θV/z, and L (2.44 m AGL) magnitudes. The values provided are valid for the 10-min period centered on 2253:57, 2326:53, 2356:54, and 0026:56 UTC, which correspond to the vertical black lines in Figs. 4, 5, and 6.

Table 4.

3. STI determination methods

A wind speed time history as measured by a fixed anemometer is traditionally used to quantify atmospheric TI. Scanning instruments are not commonly used because measurement revisit times are typically insufficient to quantify TI using long-established temporal analysis techniques. However, enhanced estimates of the ABL wind field advection velocity (Duncan et al. 2019) can be used to spatially identify the wind field within a measurement domain that will be measured at a point over some time interval. Therefore, if given a spatial depiction of ABL winds and an accurate estimate of ABL wind field advection, spatial analysis of the identified wind field should denote temporal wind field variability at that point. The question then becomes, To what extent can spatial wind field variability as measured by scanning remote sensing instruments be used to determine atmospheric TI? The following subsections detail the methods used to investigate this question.

a. Spatial correlation technique

Taylor (1938) asserted that ABL wind field advection can be attributed to the local mean wind speed and direction of the flow. However, the validity of this hypothesis has been shown to depend on the turbulent characteristics of the ABL wind field (Lappe and Davidson 1963; Willis and Deardorff 1976; Del Álamo and Jiménez 2009; Higgins et al. 2012; Cheng et al. 2017; Duncan et al. 2019). Furthermore, there is ambiguity with how to define these mean characteristics from volumetric measurements (i.e., should they be a point-, area-, or volume-averaged velocity estimate?). Therefore, the uncritical use of Taylor’s hypothesis to denote ABL wind field advection should be avoided.

A spatial correlation technique (SCT) was used in this study to determine enhanced estimates of the ABL wind field advection velocity (Duncan et al. 2019). This technique enables a direct estimate of ABL wind field advection by tracking the motion of an isolated portion of the wind field (IWF; red rectangle in Fig. 7) across the advection analysis area (AAA; black rectangle in Fig. 7) of successive measurement maps (i.e., SD or DD) using normalized cross correlation. Application of these methods to the DD horizontal wind speeds between 1732:16 and 1733:16 UTC 14 February 2017 at 158.2 m AGL is provided in Fig. 7. An advection speed of 19.34 m s−1 and an advection direction of 1.97° were derived. This advection speed was 2.47 m s−1 faster than the AAA mean wind speed and 0.92° to the left (i.e., counterclockwise) of the AAA mean wind direction. Considering the entire 14 February 2017 analysis period, the advection speed at 158.2 m AGL was on average 0.51 m s−1 slower than the AAA mean wind speed and 1.42° to the left (i.e., counterclockwise) of the AAA mean wind direction. The same advection patterns (i.e., slower than the area mean wind speed and counterclockwise of the area mean wind direction) were observed at 116.4 m AGL and also when the advection was compared to the IWF mean wind speed and direction. These estimates of ABL wind field advection were also used to perform the 14 February 2017 DD wind field intravolume advection corrections.

Fig. 7.
Fig. 7.

TTUKa DD horizontal wind speed (m s−1) at (a) 1732:16 and (b) 1733:16 UTC 14 Feb 2017. The SCT was used to estimate the ABL wind field advection speed (19.34 m s−1) and direction (1.97°) between the DD volumes.

Citation: Journal of Applied Meteorology and Climatology 58, 7; 10.1175/JAMC-D-18-0151.1

b. STI analysis areas

Spatial wind field analysis is required to extract atmospheric TI at locations within the measurement domain. However, in order to reliably discern atmospheric TI, it is not sufficient to simply spatially analyze the wind field within the measurement domain that will be measured at a point over some time interval. This is partially due to the temporal sampling frequency yielded by the space-to-time conversion process, which depends upon the ABL wind field advection speed and the lateral grid spacing of the measurement domain. To more accurately determine atmospheric TI from the spatial measurement maps, spatial wind field variability is examined across an STI analysis area.

The STI analysis area is composed of an along-wind (longitudinal) and a crosswind (lateral) dimension. The longitudinal axis is aligned parallel to the ABL wind field advection direction, the crosswind axis is oriented normal to the ABL wind field advection direction, and the analysis area is centered about some location of interest (e.g., a Cartesian grid point). This location of interest (i.e., the STI analysis area midpoint) serves as the reference point for comparison of STI to the in situ tower TI measurements used for STI validation (section 4). For DD measurements, the longitudinal length of the area is determined by multiplying a user-defined time window (i.e., the advection time window, e.g., 30 s) by the ABL wind field advection speed. The longitudinal axis depicts the portion of the wind field that will advect past the location of interest over the specified time interval. Turbulence can be idealized as consisting of varying size turbulent eddies. Therefore, the user-defined time interval governs the largest turbulence scales resolved by STI, whereas the smallest turbulence scales resolved (discussed in further detail in section 4c) are limited by the specifications of the remote sensing instrument used. For SD measurements, measurement height varies with range as a function of the elevation tilt angle; therefore, the STI analysis area will comprise measurements from various heights AGL. Because of wind shear, these measurement height differences can impact the spatial wind field variability estimate derived from the STI analysis area. Therefore, a longitudinal length that varies between scans depending on the ABL wind field advection speed is not appropriate for SD STI determination. Instead, a fixed longitudinal length that corresponds to a specific height layer (e.g., ±3 m AGL) about a user-defined elevation of interest should be used. The STI analysis area lateral width is also defined as a fixed value and was set to 100 m in the presented analysis. Justification for this width is provided in section 4a.

Once the STI analysis area is set, the ratio between the standard deviation (σ) and mean (μ) (i.e.,σ/μ) of the wind field measurements (SD or DD) within the analysis area is used to quantify STI. The TI type resolved by STI (i.e., horizontal, longitudinal, etc.) depends on the nature of the resolved wind field (e.g., horizontal velocities, radial velocities). The steps used to determine STI are further documented in Fig. 8. A novelty of this technique is the ability to develop an analysis area about each grid point within the measurement domain (Fig. 9b) in order to transform the spatially mapped velocity fields (Fig. 9a) to analogous STI measurement maps (Fig. 9c). The utility of STI is independent of the TTUKa radar technology. The methods could be applied to spatially distributed measurements acquired from any scanning remote sensing instrument (e.g., lidar) providing like data coverage. However, differences in instrument spatiotemporal resolution will require that the method efficacy be reexamined.

Fig. 8.
Fig. 8.

The steps used to determine STI at a specific location within the measurement domain.

Citation: Journal of Applied Meteorology and Climatology 58, 7; 10.1175/JAMC-D-18-0151.1

Fig. 9.
Fig. 9.

(a) TTUKa DD horizontal wind speed (m s−1) and (c) STI at 1720:03 UTC 14 Feb 2017 and at an elevation of 158.2 m AGL. (b) STI analysis area at example grid points (blue rectangles); the analysis areas were constructed using a 30-s advection time window, an advection speed of 15.2 m s−1, and an advection direction of 1.2°. Spatial wind field analysis within these analysis areas are used to transform (a) to (c).

Citation: Journal of Applied Meteorology and Climatology 58, 7; 10.1175/JAMC-D-18-0151.1

4. STI validation efforts

Atmospheric TI is traditionally defined using 10-min average estimates of σ and μ. This temporal averaging period is used because it is sufficiently short to assume a stationary μ value (Holmes 1997). Depending on measurement domain size, the STI metric could be used to discern a 10-min TI value. However, because of the lateral extent of the TTUKa measurement domain and spatially varying SD measurement heights, 10-min STI extractions were not performed. Instead, the ability of STI to discern the intensity of turbulent eddies consistent with smaller (i.e., sub-10-min) scales of motion was examined. DD STI efficacy was examined using advection time windows from 30 to 180 s in 30-s intervals, and SD STI validation comprised advection time windows ranging from 42.3 to 84.6 s with a mean value of 62.0 s. The SD advection time windows were based on a 343.8- m fixed longitudinal length (corresponding to a ±3-m height layer) and the estimated ABL wind field advection speeds. This fixed longitudinal length was selected to limit the impact of vertical wind shear on the estimation of STI and to ensure that the STI value extracted was representative of the height AGL of the STI analysis area midpoint. Although a ±3-m height layer was used for SD STI validation, this layer could be adapted in future work depending on the scanning strategies employed and the ABL wind shear. The following sections detail the methods used for STI validation and provide the corresponding results.

a. 14 February 2017 DD STI comparisons

Using ABL wind field advection estimates derived from the SCT, DD STI measurement maps (e.g., Fig. 9c) were constructed. For validation of these measurement maps, individual STI values were compared to TI measurements from the collocated meteorological tower. While it makes sense to simply compare the STI value nearest the meteorological tower to a TI value derived from the same advection time window on a volume-by-volume basis, this would only yield 60 validation points for the entire analysis period, thus limiting STI validation. Therefore, methods were established to evaluate multiple estimates of STI within each DD volume.

For each DD volume, space-to-time extractions were made to identify individual STI values (at 20-m intervals, i.e., consistent with the DD grid spacing) that would advect past the collocated meteorological tower over the subsequent volume acquisition period (Fig. 10a). For validation of a single upstream STI value, the following steps were performed. First, the ABL wind field advection speed was used to determine the “arrival time” of the STI value. This arrival time denotes the time when the identified STI analysis area midpoint would reach the tower, and therefore was defined as the upstream distance of the STI analysis area midpoint divided by the ABL wind field advection speed. Based upon this arrival time, an analogous TI value was determined. The analogous tower TI value was defined using standard definitions for horizontal TI (i.e.,σ/μ) based upon both the STI arrival time and the advection time window (i.e., the temporal period analyzed to extract TI was the advection time window centered on the STI arrival time). This time period was analyzed to ensure the wind field measured by the tower anemometer was similar to the wind field contained within the STI analysis area. Using the distribution of STI arrival times, a DD volume time history of both STI and the analogous tower TI was developed (Fig. 10b).

Fig. 10.
Fig. 10.

(a) Zoomed-in image of Fig. 9c overlaid by the meteorological tower (white square) and the location of the individual STI values (red ×s) that will advect past the tower over the subsequent volume acquisition period. (b) The 48 STI values identified in (a) were used to develop an STI time history at the location of the meteorological tower (1720:03–1721:04 UTC).

Citation: Journal of Applied Meteorology and Climatology 58, 7; 10.1175/JAMC-D-18-0151.1

An extended period of TTUKa measurements collected between 1701:55 and 1801:25 UTC were used to validate STI at both 116.4 and 158.2 m AGL. However, prior to performing STI validation, STI sensitivity to the analysis area width was examined using a 30-s advection time window and width values of 40 through 200 m in 20-m intervals. The mean (μerr) and standard deviation (σerr) of the STI error (i.e.,TISTI) distribution was calculated for each width value to discern STI sensitivity to the analysis area width and also to determine the analysis area width that should be used to examine STI efficacy. Co-opted from the error diagrams in Kalverla et al. (2019), μerr was plotted against σerr at 158.2 m AGL in Fig. 11a for each width examined. The distance of each error point (μerr,σerr) to the origin (i.e.,μerr2+σerr2) is equivalent to the root-mean-square error (RMSE) (Fig. 11b). Although the RMSE was typically smaller for larger analysis area widths, simply identifying the analysis area width that minimized the RMSE (i.e., 180 m) was not sufficient for width optimization. A principal objective of the STI measurement map is to accurately depict the local area wind conditions (i.e., preserve the spatial structure of the flow). To preserve the spatial representativeness, or precision, of individual STI estimates within the measurement domain, it is imperative to foremost identify the STI analysis area width that minimizes σerr. Minimizing μerr is a secondary objective of the analysis area width selection (partially because μerr can be mitigated by removing the mean bias). The σerr value reached a minimum (0.014) with STI analysis area widths of 90 and 100 m. However, the μerr value was minimized with a 100-m width, and therefore this width was used to construct the STI measurement maps used in validation. Error analysis at 116.4 m AGL similarly supported the use of a 100-m width.

Fig. 11.
Fig. 11.

(a) The value of μerr (x axis) and σerr (y axis) using different STI analysis area widths and a 30-s advection time window. (b) The distance of the error points in (a) to the origin (0, 0) is equivalent to the RMSE value. Data plotted were from the 14 Feb 2017 deployment for the period 1701:55–1801:25 UTC at 158.2 m AGL.

Citation: Journal of Applied Meteorology and Climatology 58, 7; 10.1175/JAMC-D-18-0151.1

Using a 30-s advection time window, STI and tower TI time histories derived from each DD volume were combined at each constant-height plane examined for comparison. At 158.2 m AGL, the STI and tower TI time histories each comprised 2888 measurements (~47.3 per DD volume), with an average arrival time difference of 1.25 s (Fig. 12a). TI fluctuated rapidly about a mean value of 0.045 within the analysis period, while STI exhibited a mean value of 0.037. Furthermore, STI performed reasonably at discerning second-by-second variability in TI as evidenced by a correlation coefficient R of 0.59. Negatively impacting R were differences in the two TI measures between 1714:19 and 1715:59 UTC. Visual inspection suggests that this discrepancy was not due to TI being insufficiently resolved within the STI maps, but rather the space-to-time extractions not adequately identifying the turbulent features that would advect past the tower between 1714:19 and 1715:59 UTC (i.e., a turbulent feature was located slightly east of the path denoted by the space-to-time conversion methods). To verify this, the ABL wind field advection direction that governs the space-to-time extractions was incrementally increased by one degree from +1° to an offset +10° (i.e., resulting in clockwise rotation of the upstream path denoted by the space-to-time conversion methods). With an advection direction offset of +7° applied, the discrepancy between STI and TI during this period was significantly reduced (Fig. 12b). Other instances of advection differences inhibiting STI validation efforts may also have existed within the analysis period; however, empirical advection corrections were only applied for this period. The empirical correction was applied to establish that errors between STI and TI might not always be indicative of poor STI performance and also to demonstrate the difficulties in STI validation.

Fig. 12.
Fig. 12.

(a) STI and tower TI time histories on 14 Feb 2017 for the period 1701:55–1801:25 UTC at 158.2 m AGL. (b) As in (a), but the empirical corrections were applied to account for advection differences between 1714:19 and 1715:59 UTC. (c) As in (b), but with a static offset applied to account for the mean bias error in STI.

Citation: Journal of Applied Meteorology and Climatology 58, 7; 10.1175/JAMC-D-18-0151.1

With this empirical correction applied, STI exhibited a mean bias error of only −0.008. This underestimation of TI can be primarily attributed to volume-averaging effects (discussed further in section 4c). When a static offset was used to account for this mean bias error (Fig. 12c), the RMSE between STI and TI was reduced to 0.013. The ratio between TI and STI was also analyzed at 158.2 m AGL (Fig. 13a) to examine STI sensitivity to wind speed. During the analysis period, mean wind speeds (based on the advection time window) steadily increased from 12.92 to 21.19 m s−1, while the ratio between TI and STI varied between 0.49 and 4.27 about a mean value of 1.27. Despite this general increase in mean wind speed, the ratio between TI and STI remained relatively steady (Fig. 13b). A linear model was fit to the distribution of ratio values as a function of wind speed to demonstrate this. The slope of the linear model (0.011) indicates that STI efficacy within the neutral ABL was not sensitive to variations in wind speed for the wind speed range examined.

Fig. 13.
Fig. 13.

(a) The ratio of TI to STI at 158.2 m AGL for the period 1701:55–1801:25 UTC 14 Feb 2017. (b) The ratio values in (a) plotted as a function of the mean wind speeds. The black line denotes the linear model that was fit to the distribution of ratio values and mean wind speeds.

Citation: Journal of Applied Meteorology and Climatology 58, 7; 10.1175/JAMC-D-18-0151.1

The ability of STI to replicate second-by-second variability in TI was slightly reduced at 116.4 m AGL. The R value at this elevation was 0.49, with the largest differences occurring between 1729:34 and 1730:34 UTC. During this 1-min period, STI underestimated TI by an average of 55.3%. Contributing heavily to this underestimation was a significant difference in the value of μ used to determine the two TI measures; on average, μSTI exceeded μTI by 1.31 m s−1. Although less significant, similar discrepancies for this period were observed at 158.2 m AGL. However, despite the discrepancy in μSTI and μTI between 1729:34 and 1730:34 UTC at both 116.4 m AGL and 158.2 m AGL, μSTI was able to resolve variations in μTI with an R2 value of 0.88 at 116.4 m AGL and an R2 value of 0.92 at 158.2 m AGL. Considering the entire analysis period, STI exhibited a mean bias error of −0.013, attributed to averaging effects of the remotely sensed measurement volume. Volume-averaging effects are expected to be enhanced at lower elevations because the turbulent length scales are on average smaller. With a static offset applied to account for this mean bias error, the STI and tower TI time histories at 116.4 m AGL are shown in Fig. 14. Similar to at 158.2 m AGL, STI efficacy demonstrated little sensitivity to variations in wind speed. The linear model fit to the distribution of ratio values (TI/STI) as a function of wind speed exhibited a slope value of −0.027. A statistical summary of STI performance using varying moving average windows (60, 300, and 600 s) is provided in Table 5.

Fig. 14.
Fig. 14.

STI and tower TI time histories for the period 1701:55–1801:25 UTC at 116.4 m AGL. The plotted STI time history is reflective of the mean bias error correction.

Citation: Journal of Applied Meteorology and Climatology 58, 7; 10.1175/JAMC-D-18-0151.1

Table 5.

STI performance statistics at both 116.4 and 158.2 m AGL. The first- and second-order moments (i.e., mean and standard deviation) of STI are not reflective of any mean bias error correction. However, the other statistics provided at both elevations include the respective mean bias error correction, and at 158.2 m AGL empirical corrections were applied to account for turbulence feature advection between 1714:19 and 1715:59 UTC. Also provided are corresponding statistics using a 60-, 300-, and 600-s running average (RA).

Table 5.

Results presented thus far demonstrate the ability of STI to discern TI based on a 30-s advection time window. However, a strength of the STI framework is the ability to adapt this advection time window to discern TI attributable to different size turbulent eddies (i.e., those contained within the advection time window). To examine this ability, STI efficacy was investigated across a range of advection time windows from 30 to 180 s in 30-s time intervals. Analysis of STI performance at larger advection time windows was inhibited by the size of the DD domain. Regardless, trends in μerr, σerr, and the RMSE demonstrate improved STI performance with larger advection time windows (Fig. 15). The value of σerr decreased by 36.5% between advection time windows of 30 and 180 s, while only incurring a 0.0017 increase in the μerr. Also, the RMSE value decreased from 0.017 when using a 30-s advection time window to 0.014 when using a 180-s advection time window. The improved performance of STI at larger advection time windows can be partially attributed to the sensitivity of STI to the remote sensing instrument specifications.

Fig. 15.
Fig. 15.

Error diagrams as plotted in Fig. 11. However, the error presented is consistent with STI analysis maps constructed using variable advection time windows and a 100-m width.

Citation: Journal of Applied Meteorology and Climatology 58, 7; 10.1175/JAMC-D-18-0151.1

b. 12 October 2015 SD STI comparisons

Slight modifications were made to STI validation methods to accommodate differences between SD and DD data collection techniques and accompanying OA. The biggest difference that needed to be accounted for was the 13.4-m height difference between the intersection point of the gridded domain with the meteorological tower at 61.6 m AGL and the nearest instrumented tower level at 74.7 m AGL (Fig. 16a). Therefore, STI values in the immediate vicinity of the turbine were not suitable for validation. Instead, comparisons were made to STI values extracted at a commensurate tower elevation (74.7 m AGL) on average 793.2 m upstream of the tower (denoted by the red arc in Fig. 16b). For each SD sector scan, the ABL wind field advection speed and direction was used to determine STI at SD grid points located along the 74.7-m elevation arc and further to identify the STI value that would subsequently advect past the meteorological tower. Once this STI value was identified, an arrival time could be determined (advection to the tower took on average 139.2 s) and an analogous tower TI defined (i.e., the temporal period analyzed to extract TI was the advection time window centered on the STI arrival time). Because a single radar resolves the radial wind field component, SD STI validation was made against the longitudinal TI value (i.e.,σlon/μlon).

Fig. 16.
Fig. 16.

(a) Schematic of TTUKa measurement height (blue line) with range overlaid by both the location (vertical green line) and instrumented levels (horizontal green line) of the meteorological tower. The red star indicates the 74.7 m AGL measurement range. (b) TTUKa radial velocities (m s−1) at 2237:56 UTC plotted with the 74.7 m AGL measurement range (red arc), the STI analysis area (black rectangle) and midpoint (red star), and the meteorological tower (white square).

Citation: Journal of Applied Meteorology and Climatology 58, 7; 10.1175/JAMC-D-18-0151.1

The SD velocity measurements collected on 12 October 2015 were used to investigate the ability of STI to discern TI trends across the EET. Time histories of STI and tower TI derived from the 1791 SD sector scans collected between 2232:08 and 0052:30 UTC both demonstrate trends in TI consistent with the EET (Fig. 17a). Within the convective ABL, STI was able to effectively capture TI variability consistent with the passage of turbulent transients. A 5-min running average of the two TI measures, defined by an R2 value of 0.65, highlights this ability (Fig. 17b). With no temporal averaging filter applied, the mean bias error was reduced by 52.5% relative to the DD analyses to a value of −0.0042. This reduction in TI underestimation can be partially attributed to enhanced lateral wind field variability within the convective ABL, which acts to increase σSTI and combat volume-averaging effects. Volume-averaging effects may also be inherently magnified within the DD wind fields because volume-averaging is being combined from two misaligned measurement perspectives. However, as ABL stability increased with the progression of the EET, a distinct bias between STI and TI developed. Despite correctly depicting a general decrease in TI with the development of the stable ABL, STI exhibited a mean bias error of +0.015 from 2358:46 to 0052:30 UTC. The inability of STI to properly track these lower TI levels could be partially attributed to enhanced wind shear within the stable ABL and the emergence of “speckle” in the radial velocity return (speckle can occur when the number of scatterers per measurement volume is reduced). Both wind shear and radar speckle can enhance σSTI and therefore increase the value of STI. Other discrepancies (e.g., between 2246:26 and 2247:06 UTC and 2335:51 and 2336:46 UTC) might be due to wind field evolution occurring between the location of radar and tower measurement, or improper ABL wind field advection estimation. A summary of STI performance relative to ABL stability is provided in Table 6.

Fig. 17.
Fig. 17.

(a) STI and tower TI time histories for the period 2232:08–0052:30 UTC and (b) a 5-min running average of (a). The convective and stable ABL periods of data collection are shaded in red and blue, respectively.

Citation: Journal of Applied Meteorology and Climatology 58, 7; 10.1175/JAMC-D-18-0151.1

Table 6.

STI performance statistics for both the convective and stable periods of the analysis domain. The first- and second-order moments (i.e., mean and standard deviation) of STI are not reflective of any mean bias error corrections, whereas the other statistics provided include the stability-respective mean bias error correction. Also provided are corresponding statistics using a 60-, 300-, and 600-s running average (RA).

Table 6.

The ratio between TI and STI was analyzed across the EET to further examine STI sensitivity to wind speed, and also to quantify how this sensitivity might depend on ABL stability (Fig. 18). Within the convective ABL, mean wind speeds ranged between 6.17 and 10.61 m s−1, but in general, wind speed decreased during the data collection period with the progression of the EET and the stable ABL. Despite this trend in wind speed, the ratio between TI and STI within the convective ABL exhibited little sensitivity to wind speed as demonstrated by a slope of −0.062 that was derived from the fitted linear model. However, within the stable ABL, analysis suggests some STI sensitivity to wind speed. The fitted linear model within the stable ABL exhibited a slope of −0.19, but it should be mentioned that STI also exhibited a distinct decreasing trend during this period. Therefore, changes in the ratio cannot be solely attributed to wind speed differences within the stable ABL. While not examined, a more apt comparison might be to exclude what appears to be a transitional period occurring between the convective and stable ABLs. Regardless, the ratio between TI and STI appears to be more sensitive to changes in ABL stability than changes in wind speed.

Fig. 18.
Fig. 18.

(a) The ratio of TI to STI for the period 2232:08–0052:30 UTC; data from the convective and stable ABL periods are plotted in red and blue, respectively. (b) The ratio values in (a) plotted as a function of the mean wind speeds. The black line denotes the linear model that was fit to the distribution of ratio values and mean wind speeds. The color lines denote the fitted linear model when data from only the convective or stable ABL were considered.

Citation: Journal of Applied Meteorology and Climatology 58, 7; 10.1175/JAMC-D-18-0151.1

c. STI sensitivities

STI is sensitive to the turbulent structure of the resolved wind field, and therefore can be impacted by several factors. Three such factors are 1) the details of the OA technique used to interpolate the radar data from their native polar coordinate system to the Cartesian analysis grid, 2) the underlying remotely sensed measurement resolution, and 3) the relative alignment of the measurement volume with the wind. While other considerations exist that can also impact the turbulent structures resolved, the impact of these three factors on STI are examined in more detail below.

1) OA techniques (KNN impacts)

The interpolation methods employed in any OA scheme will determine the turbulent structures resolved. A modified Barnes interpolation scheme was used in the presented analyses, wherein the traditional Barnes weighting function was applied to a finite number [i.e., k nearest neighbor (KNN)] of observations within the user-specified volume of interest (VOI). This KNN constraint was primarily applied for computational purposes and manipulated according to data availability. Increasing the value of KNN can enhance the robustness of the assigned radial velocity estimate, but in doing so it also acts as a low-pass filter. Thus, variations in the KNN value can directly impact the resolvable scales of motion and STI.

To determine these effects, OA and STI derivations at both 116.4 and 158.2 m AGL were performed using the following KNN values: 1, 2, 10, 20, and 40. A grid-averaged STI value measured across the DD domain was then determined at each elevation level for the analysis period (Table 7), confirming an inverse relationship between KNN and STI. Increasing KNN from just 1 to 5 saw an 8.93% decrease in the grid-averaged STI value at 116.4 m, and a 9.00% decrease at 158.2 m AGL. When KNN was increased to 40, the grid-averaged STI value at both elevations examined was reduced in excess of 20% relative to that extracted using a KNN value of one. Hence, a nearest-neighbor approach (i.e., KNN value of one) is optimal for STI analyses, as the interpolation inherent to any scheme will act to smooth wind field variability and reduce STI.

Table 7.

Grid-averaged STI value for the analysis period as a function of KNN at both 116.4 and 158.2 m AGL.

Table 7.

2) Measurement volume resolution

The scales of motion resolved by a remote sensing measurement system depend on the measurement volume resolution. This measurement volume is governed by the along-beam range gate spacing and the horizontal and vertical beamwidths of the emitted pulse. For pulsed remote sensing instruments, the length of the measurement volume is determined by hardware constraints and remains fixed with measurement range. However, the measurement volume expands in both the horizontal and vertical dimensions as a function of the beamwidth. Angular resolution (i.e., SA) is defined by
SA=2R×sinΘ2,
where R is the measurement range and Θ is the antenna beamwidth. The TTUKa radars emit a circular beam (0.33° dB beamwidth) that laterally and vertically spreads at a rate of 5.76 m km−1. An example measurement volume is provided in Fig. 19.
Fig. 19.
Fig. 19.

Example measurement volume defined by the range and angular resolution of the scanning remote sensing instrument. The radial velocity estimate that is extracted from the measurement volume is assigned to the middle of the measurement volume.

Citation: Journal of Applied Meteorology and Climatology 58, 7; 10.1175/JAMC-D-18-0151.1

To examine STI sensitivity to measurement volume size, STI was analyzed as a function of the mean measurement range between TTUKa1 and TTUKa2. Because tower comparisons were not required for this sensitivity analysis, the DD domain was modified enabling analyses at 20-m height intervals between 120 and 200 m. At each elevation level, a linear model was fit to the distribution of STI values derived within the analysis period and measurement domain as a function of measurement range. These linear fits are shown in Fig. 20 for 250-m measurement range bins (e.g., between 5000 and 5250 m) that contain at least 20 000 STI measurements. STI was inversely proportional to measurement range at each elevation examined, albeit this sensitivity decreased with height. These results are consistent with the expectation that turbulent length scales generally increase with height. Thus, as the measurement volume increases with range, the ability to resolve smaller turbulent scales prevalent at lower elevations is reduced. Intersection between the fitted linear models (e.g., at 5625 m between the 120- and 140-m AGL models) suggests that STI may not be able to discern height-respective TI variations at these ranges. Beyond this range, STI measurements should not be relied upon except to denote relative (i.e., increasing or decreasing) TI trends. In addition to modifying the turbulent structures resolved, measurement volume expansion with range will increase errors associated with spatial coverage and intensity.

Fig. 20.
Fig. 20.

Linear model of STI as a function of the mean measurement range at 120, 140, 160, 180, and 200 m AGL. The models are plotted for 250-m measurement range bins that contain at least 20 000 STI measurements.

Citation: Journal of Applied Meteorology and Climatology 58, 7; 10.1175/JAMC-D-18-0151.1

STI sensitivity to measurement volume size is instrument specific. For instance, scanning lidar emit a pulse that does not appreciably widen with range (i.e., negligible beamwidth). Therefore, STI sensitivity to measurement range will be mitigated by application of the methods to lidar-estimated velocity fields. However, typical lidar scan speeds and along-beam range resolutions (Grund et al. 2001) may impact STI in other ways, and further inhibit the derivation of three-dimensional STI measurement maps.

3) Relative alignment of the measurement volume with the wind

Atmospheric turbulence is anisotropic, meaning that its three-dimensional structure exhibits directional dependencies. Therefore, measurement volume alignment relative to the wind will impact both the turbulence structures sampled and the accuracy of STI. Optimal alignment would necessitate the long axis of the measurement volume be aligned parallel to the wind direction. This maximizes the ability of the remote sensing instrument to resolve longitudinal variability in the flow that contributes to TI. Increasing off-axis alignment is expected to decrease the wind variability resolved, thereby reducing the ability of STI to discern TI. This sensitivity to measurement volume alignment suggests that, in addition to measurement range, DD STI might depend on the respective look angles of the remote sensing instruments used. More research is required to definitively answer this question.

5. Summary and discussion

Scanning remote sensing instruments enable a spatial representation of ABL winds with high spatial resolution and coverage. However, measurement revisit times are typically insufficient to extract atmospheric turbulence information using traditional temporal analysis techniques. To combat this limitation, a STI metric was developed to estimate atmospheric TI by performing spatial analysis of the wind field. A principal advantage of STI is that it can be readily determined at individual locations within the measurement domain, thereby enabling a spatial characterization of atmospheric TI in both the horizontal and vertical dimensions of the ABL from a single scanned volume. The ability to extract a spatial representation of atmospheric TI has significant implications for the wind energy industry, where a comprehensive understanding of the spatial structure of atmospheric turbulence within the wind plant is limited. STI measurement maps have the potential to support wind plant modeling efforts and also allow the turbulent structure of wind plant complex flows to be studied. As an example, Fig. 21 demonstrates changes in wind turbine wake STI in response to changes in ABL stability.

Fig. 21.
Fig. 21.

STI within the (a) convective (2236:21 UTC) and (b) stable (0016:01 UTC) ABLs overlaid by contours of the SD measurement height (m AGL) and the location of the meteorological tower (white square) and wind turbine (black circle).

Citation: Journal of Applied Meteorology and Climatology 58, 7; 10.1175/JAMC-D-18-0151.1

STI efficacy was examined in this study against in situ point measurements across a range of wind speeds and ABL stability regimes using both SD and DD measurements. STI validation was at times inhibited by advection differences between that derived and observed, as well as wind field evolution occurring between radar and tower measurement times. Nonetheless, STI was able to reasonably resolve TI magnitudes, capture rapid TI fluctuations, and discern large-scale TI trends consistent with the EET. Because remote sensing instruments derive their velocity estimates from a measurement volume as opposed to a point, STI was subject to volume-averaging effects. This bias was pronounced within the neutral ABL, albeit a slight mean bias error correction allowed STI to closely parallel TI variability. Within the convective ABL, enhancements to lateral wind field variability acted to mitigate volume-averaging effects. The impacts of volume-averaging were also reduced within the stable ABL because turbulent length scales typically grow with increasing ABL stability. The ratio between TI and STI was relatively independent of wind speed, but it did exhibit sensitivity to ABL stability. Furthermore, sensitivity analysis suggests that the measurement domain may need to be constrained in order to preserve STI effectiveness. The magnitude of this constraint, and other STI sensitivities, will depend upon the specifications of the remote sensing instrument used. More research is needed to determine how various scanning strategies and emitted pulse characteristics may improve STI effectiveness.

Acknowledgments

Funding for this study was provided by the National Science Foundation Award CBET-1336935.

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