1. Introduction and motivation
Vertical velocity w plays a critical role in many atmospheric processes. Within the daytime continental convective boundary layer (CBL) over flat terrain, variations in w are generally associated with thermals generated by surface heating, turbulence induced by wind shear, or a combination of both processes. The thermals lead to rapid mixing of heat, moisture, momentum, and trace gases over the depth of the layer, and the role of individual thermals has been well documented (e.g., Lenschow and Stephens 1980; Greenhut and Khalsa 1987; Williams and Hacker 1992). If a thermal rises high enough that it reaches its lifting condensation level, then the water vapor in the thermal will condense and a cloud-topped boundary layer will form. A wide range of studies have focused on the analysis of the cloud-topped boundary in both continental (e.g., Berg and Kassianov 2008; Berg et al. 2011; Fang et al. 2014) and maritime (e.g., Bretherton and Wyant 1997; Ghate et al. 2014) conditions.
Distributions of w are a key part of many cumulus parameterizations used in regional and global models. For example, some approaches explicitly use joint distributions of temperature and w (Larson et al. 2012), and others use the variance of w (Bretherton et al. 2004). Other parameterizations use closure assumptions related to the cumulus mass flux, which is tightly coupled to the speed of the convective updrafts for deep convection (Kain and Fritsch 1990) as well as for mixtures of deep and shallow convection (Kain 2004; Berg and Stull 2005; Berg et al. 2013).
There are relatively few long-term measurements of w statistics within the CBL. Most studies have focused on the analysis of a relatively small number of measurements from aircraft (e.g., Lenschow et al. 1980; Lenschow and Sun 2007) or remotely piloted aircraft (Martin et al. 2014). These studies are episodic, and, while the measurements are highly useful, it is difficult to know how representative they are. Even studies with routine aircraft observations (Vogelmann et al. 2012) still only have a relatively small number of flights. Other studies have utilized tower data to examine w statistics (e.g., Wyngaard et al. 1971; Wood et al. 2010; Liu et al. 2011). The short height of the towers (relative to the depth of the daytime boundary layer), however, has caused some researchers to focus on the analysis of shallow internal boundary layers (e.g., Smedman and Högström 1983). Other approaches that have been applied include tank studies (Deardorff and Willis 1985) or large-eddy simulation (e.g., Deardorff 1974; Lenschow et al. 2012; Darbieu et al. 2015) to document changes in the w statistics with altitude. Coherent Doppler lidar (CDL) data have been used more recently to document not only the w variance 
The long-term deployment of CDLs by the U.S. Department of Energy’s Atmospheric Radiation Measurement (ARM) Climate Research Facility (Mather and Voyles 2012) gives a unique opportunity to address these shortcomings and to provide a long-term dataset that can be analyzed to document the behavior of 
This paper is organized in the following way: Details of the instrument systems used in the study, including the CDL as well as other instruments, are described in section 2. Section 3 presents analyses and results that are focused on changes in w statistics as a function of time of day as well as a range of other variables, such as season, wind direction, static stability, friction velocity (surface shear stress), and wind shear across the boundary layer top. Overall, systematic differences in the variance, skewness, and kurtosis are found that are related to changes in these variables.
2. Instruments
a. Coherent Doppler lidar
A detailed description of the configuration and operation of the Halo Photonics CDL deployed at the ARM Southern Great Plains (SGP; Sisterson et al. 2016) Central Facility site is presented by Pearson et al. (2009) and Newsom (2012). In brief, the system uses a near-IR laser (wavelength of 1.5 μm) that is sensitive to the backscatter from aerosol and clouds to provide measurements of radial velocity and attenuated backscatter. As configured at the SGP, the CDL has a height resolution of 30 m but can be set to have a resolution between 18 and 60 m. It is important to note that the maximum range of the CDL is limited by the presence of aerosol, which generally limits retrievals of w statistics to the heights within the boundary layer, which has implications in the analysis of the data presented in this study. The CDL is configured to stare vertically for the majority of the time. Once every 15 min, the unit performs plan position indicator scans that are used to compute the mean wind profile on the basis of the traditional velocity–azimuth display algorithm (Browning and Wexler 1968; Banta et al. 2002).
The time series of w from the CDL clearly shows the presence of convective updrafts and downdrafts during convective periods (Fig. 1). These data can be combined directly to form probability density functions (PDFs) of uncorrected w (w values that include instrument noise). An ARM value-added product has been developed that takes the 1-Hz data (as shown in Fig. 1) and computes values of the higher-order moments of the w distribution (variance, skewness, and kurtosis) derived from the CDL data with a time resolution of 30 min (Newsom et al. 2015). Each 10-min value is not independent, however, because it is computed using a moving 30-min average. Thus, we only use every third value reported in our analysis. One key step in the processing of CDL data is the removal of instrument noise from the lidar’s variance estimates. In our processing, the instrument noise is estimated using the method that is described by Lenschow et al. (2000) and Pearson et al. (2009). In this approach, the noise contribution to the raw radial velocity variance is determined from a time series analysis of the radial velocity data. Once the instrument noise is determined, it is subtracted from the raw variance, leaving only the atmospheric contribution. Calculation of the third- and fourth-order moments is handled differently. These quantities are computed directly by first removing radial velocities corresponding to wideband signal-to-noise ratios (wSNR; Iwai et al. 2013) below 0.008.
Time–height cross section of uncorrected w (shading), zi (black line), and intervals and heights used for computing sample PDFs (colors) and PDFs of w for the respective time and heights on 18 Jul 2015.
Citation: Journal of Applied Meteorology and Climatology 56, 9; 10.1175/JAMC-D-16-0359.1
Even with the noise compensation, it is well known that CDL w variance measurements are biased toward lower values because of the spatial-averaging effect caused by the laser pulse width and the range-gate size. Preliminary analysis of field data collected during a recent field campaign at the Boulder Atmospheric Observatory (Lundquist et al. 2017) suggests that the ARM CDL w variance estimates are negatively biased by approximately 9% when the range-gate size is 30 m (Newsom et al. 2017).
Long-term averages of 
The CDL can also be used to measure the cloud-base height and to estimate cloud fraction, because it is very sensitive to the backscatter from cloud drops and ice crystals. The ARM CDLs estimate cloud-base heights from the wSNR data using a matched-filter approach (Newsom et al. 2015). The ARM SGP site has a number of other instruments from which data are combined to provide detailed information about the clouds above the site; these instruments include cloud radars and laser ceilometers (Clothiaux et al. 2000) that have been used in previous studies (e.g., Dong et al. 2005; Berg and Kassianov 2008). In this study, the cloud-base-height estimates are used to mask out regions affected by clouds, because we are most interested in the identification of periods that are cloud free rather than in the details of the cloud field that can be determined from the other systems deployed at the site.
One key component of our analysis is the scaling of height by the boundary layer depth zi. In the case of CDL systems, the w variance can be used to estimate the value of zi by applying a threshold value. In our study, we experimented with the threshold value of 0.04 m2 s−2, as suggested by Tucker et al. (2009). This method has the advantage that it applies a direct measure of the turbulence intensity and is less susceptible to the presence of residual layers that can fool lidar retrievals of zi that are based on only the aerosol backscatter. At the SGP site, however, this threshold often resulted in an estimate of zi that was too large because of gravity waves or other weak coherent vertical motions above the convective boundary layer. Definition of a single threshold is also difficult when the turbulence intensity can vary greatly during the day or over different seasons. With these considerations in mind, the boundary layer depth is defined in this study by using a threshold of normalized variance (
b. Radar wind profiler
Data from the 915-MHz radar wind profiler (RWP; Muradyan et al. 1998) operated at the SGP are, in many ways, complementary to the data collected by the CDL, albeit with a much higher first range gate and coarser height and time resolution. The RWP, however, has a greater vertical range and provides measurements to heights well above zi on many occasions. For this reason, RWP data are used to compute the wind shear across the boundary layer top using differences in the wind speed measured at 1.1zi and 0.9zi. This choice of heights is somewhat arbitrary, but the goal of this specific analysis is to break the data into cases with relatively large and small amounts of wind shear across the boundary layer top, which should not be overly sensitive to the exact heights that are selected. Data from the RWP are collected using high and low power settings to form hourly consensus averages. In this analysis, only data from the lower power setting are used because they have finer spatial resolution. Additional details of the operation of the RWP at the ARM sites are presented by Coulter (2012).
c. Surface measurements
Data from the eddy-covariance (ECOR; Cook 1997) system deployed at the ARM SGP are used to compute the sensible heat flux and typical scaling velocities, including w* and the friction velocity u* {
The calculation of w* also requires mean potential temperature. The ECOR system reports temperature as measured by the sonic anemometer, but it can be biased (Cook 2016). Therefore, in our calculation, we utilize the mean temperature measured by the weather station (Holdridge and Kyrouac 1993) deployed near the ECOR system rather than the mean temperature derived from the sonic anemometer.
3. Selection criteria
A number of different criteria are used to select specific time periods used in the analysis, including thresholds related to the cloud fraction and the wSNR. Given that this study is focused on cloud-free conditions, we required that the cloud fraction computed from the CDL be less than 0.001 (derived from the fraction of time over a 0.5-h interval in which a cloud was detected by the CDL at any height between 100 and 9600 m). Note that using this definition leads to the inclusion of clear periods in an otherwise cloudy day. This treatment maximizes the number of points used in the analysis. Future studies may wish to apply more stringent criteria. A wSNR threshold was applied to ensure sufficient signal strength. Different wSNR thresholds were applied for the variance (0.007) and skewness and kurtosis (0.02). These different thresholds were used because the higher-order moments are inherently noisier and benefit from a higher value of wSNR while using a smaller threshold for the variance allows us to include more data points in the analysis. Using a larger wSNR threshold has the side effect of reducing the number of observations of skewness and kurtosis and leads to some differences in the number of observations within specific height ranges. Two other preliminary selection criteria are also applied to the CDL time series, including requiring that the value of sensible heat flux be positive and that the value of zi be greater than 0.2 km. These two criteria are applied to ensure that the boundary layer was truly convective. A number of different selection criteria that are focused on specific processes within the CBL, such as the season, time of day, stability, shear stress, and wind shear across the boundary layer top, are also applied, forming the basis of the analysis that is presented in the next section. In total, several thousand individual 1-h periods were selected for analysis.
4. Analysis and results
Over the course of any given day, the cycles of 
Time–height cross section of 
Citation: Journal of Applied Meteorology and Climatology 56, 9; 10.1175/JAMC-D-16-0359.1
Composites of 
Composite time series of (top) 
Citation: Journal of Applied Meteorology and Climatology 56, 9; 10.1175/JAMC-D-16-0359.1
Although the composites, such as those shown in Fig. 3, provide information about the variation of the w statistics, additional insight can be gained by carefully investigating their sensitivity to a number of different factors, including the time of day, the wind direction, the season, u*, static stability, and wind shear at the top of the boundary layer. These sensitivity studies are presented in the next sections.
a. Variation with time of day
The intensity of turbulence within the boundary layer clearly changes with time during the day, but scaling parameters such as w*, combinations of w* and u* (Moeng and Sullivan 1994), and zi are frequently used to make profiles of normalized key variables that are invariant with time (e.g., Stull 1988; Moeng and Sullivan 1994). Analysis of the CDL data allows us to investigate the performance of the scaling more carefully. Profiles of the median 
Profiles of median (a) 
Citation: Journal of Applied Meteorology and Climatology 56, 9; 10.1175/JAMC-D-16-0359.1
The 
As compared with 
All of the median values of 
b. Variation with mean wind direction
The area around the SGP is surrounded by a combination of pasture and cropland with relatively little topographic variability (Sisterson et al. 2016), and it is perhaps surprising that the profiles of 
Profiles of median 
Citation: Journal of Applied Meteorology and Climatology 56, 9; 10.1175/JAMC-D-16-0359.1
The results presented on the right-hand side of Fig. 5 highlight the rapid decrease in the number of good observations between normalized heights of 0.8zi and 1.0zi. This decrease is largely associated with the maximum range of the CDL and the relatively small amounts of aerosol loading near the boundary layer top. The median value of zi between 1100 and 1700 LT is 1.40 km, and the 75th and 90th percentiles are 1.64 and 1.85 km, respectively. We see that there are many instances in which the unit will struggle to retrieve high-quality w statistics near the boundary layer top. This is one reason why RWP data are applied in section 4f to examine the impact of wind shear across the boundary layer top on the turbulence in the boundary layer.
c. Variation with season
One advantage of a long-term dataset is the ability to investigate the variability of important parameters across different seasons. In this case, we have divided the data into 3-month blocks, and values of 
Profiles of (a) 
Citation: Journal of Applied Meteorology and Climatology 56, 9; 10.1175/JAMC-D-16-0359.1
d. Variation with u*
The surface stress, as represented by u*, is found to be related to the variability in the vertical profiles of w turbulence statistics. Values of u* have been computed using data from the sonic anemometer deployed at the ARM SGP site, and the distribution of u* is presented in Fig. 7. The data have been sorted into three difference classes according to the observed values of u*: one for u* of less than 0.28 m s−1, one for values that are greater than 0.59 m s−1, and one intermediate class. These values represent the 15th and 85th percentiles of the u* distribution, and the range is roughly consistent with the thresholds applied in Lenschow et al. (2012), where u* was found to range between 0.16 and 0.52 m s−1.
Histograms of (a) u*, (b) w*, and (c) −zi/L for periods used in the analysis of w statistics. The dashed lines in (a) and (c) indicate thresholds used for separating cases with small and large values.
Citation: Journal of Applied Meteorology and Climatology 56, 9; 10.1175/JAMC-D-16-0359.1
Significant differences are found in the vertical profiles of 
Profiles of (a) 
Citation: Journal of Applied Meteorology and Climatology 56, 9; 10.1175/JAMC-D-16-0359.1
e. Variation with stability
The static stability can be represented with the parameter −zi/L, where L is the Obukhov length. In their study, Lenschow et al. (2012) used a threshold value of 30 to separate moderately unstable conditions and very unstable conditions. The same threshold is applied in this study. The median value of 
As in Fig. 8, but for very unstable (red) and moderately unstable (black) conditions.
Citation: Journal of Applied Meteorology and Climatology 56, 9; 10.1175/JAMC-D-16-0359.1
PDFs of w for very unstable (red) and moderately unstable (black) conditions observed with the CDL.
Citation: Journal of Applied Meteorology and Climatology 56, 9; 10.1175/JAMC-D-16-0359.1
f. Variation with wind shear
The suite of instruments deployed at the SGP Central Facility provides a unique opportunity to examine changes in w turbulence statistics with changes in the wind shear across the boundary layer top. Rather than use the wind shear calculated from the CDL, we have used data from the RWP. As pointed out earlier, the number of good CDL observations drops off quickly near the boundary layer top. This drop-off makes the calculation of the wind shear across the boundary layer top difficult. The RWP retrieves wind profiles through the boundary layer on a more regular basis (although the number of points used in the analysis is still relatively small) with a vertical resolution of 60 m. The wind shear is simply calculated as the difference in wind speed between 0.9zi and 1.1zi, and directional shear is ignored in this approach. Small and large values of shear are defined to be −0.6 and 1.4 m s−1, respectively. These values are approximately the 30th and 70th percentiles of the observed shear values derived from the RWP. The impact of the wind shear on the 
As in Fig. 8, but for large (red) and small (black) amounts of wind shear across the boundary layer top.
Citation: Journal of Applied Meteorology and Climatology 56, 9; 10.1175/JAMC-D-16-0359.1
5. Summary and conclusions
This study helps to fill a void associated with a lack of long-term observations of the characteristics of turbulence over the depth of the cloud-free CBL. We utilized 1 yr of data collected using the CDL deployed at the ARM SGP site to document the characteristics of 
Standard boundary layer scaling parameters were used to normalize the CDL observations; although profiles of 
The w statistics were found to be sensitive to season, u*, static stability within the boundary layer, and wind shear across the boundary layer top, although the details of the sensitivity changed depending on the variable of interest. The largest values of 
Long-term datasets, like the CDL data generated by the ARM Program, provide a unique opportunity to extend our understanding to include a wider range of meteorological conditions than has been possible in the past. In addition to insights gained about the vertical structure of turbulence in the boundary layer, studies such as this one can be used to evaluate parameterizations used in regional- and global-scale models. Future efforts will focus on combining data from the CDL with other instruments at the ARM sites to link the turbulence statistics with the thermodynamic properties and to examine bulk models of entrainment flux, such as those proposed by Sorbjan (1991, 2005), Conzemius and Fedorovich (2006), and Wulfmeyer et al. (2016).
Acknowledgments
This research was supported by the Office of Science of the U.S. Department of Energy as part of the Atmospheric Radiation Measurement (ARM) and Atmospheric System Research (ASR) programs, including partial support of authors Berg and Newsom via Grant KP1701000/57131 and author Turner via Grant DE-SC0014375. We thank Dr. Hailong Wang of Pacific Northwest National Laboratory for a careful review of the manuscript. The Pacific Northwest National Laboratory is operated for DOE by the Battelle Memorial Institute under Contract DE-A06-76RLO 1830. The data used in this paper are available from the ARM data archive (http://www.arm.gov) or from the corresponding author.
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