Convective Boundary Layer Depth Estimation from S-Band Dual-Polarization Radar
1. Introduction
The depth of the planetary boundary layer (PBL) varies from a few tens of meters at night to several kilometers during the day. This single measurement and its evolution provide useful information on PBL structure. Not surprisingly, PBL depth influences air quality, turbulence, and cloud development. Both wildfire behavior (Clements et al. 2007) and propagation of hazardous materials (Dabberdt et al. 2004) exhibit a strong dependence on PBL depth. Yet, observations of PBL depth come primarily from rawinsonde data collected only twice a day (0000 and 1200 UTC) at 97 locations across the United States. This network offers very poor spatial and temporal resolution; additionally, sounding data can be compromised by thunderstorms or saturated air encountered by the rawinsonde during its ascent. Estimates of PBL depth with better temporal resolution are attainable from 915-MHz vertical profilers (White 1993; Angevine et al. 1994), but these instruments are few in number. Although PBL depth estimates are provided by numerical models, these estimates can be off by a factor of 2, limiting their usefulness (Grimsdell and Angevine 1998; Bright and Mullen 2002; Stensrud and Weiss 2002). The combination of limited in situ measurements in space and time and inaccurate model predictions makes the observation and forecasting of PBL depth problematic.
Weather radar provides a dataset with higher spatiotemporal resolution than other instruments owing to the 159 continuously operating National Weather Service dual-polarization Weather Surveillance Radar-1988 Dopplers (WSR-88Ds). Weather radars, if useful for PBL depth estimation, would significantly improve the density of PBL depth observations and could facilitate routine observations of this important PBL characteristic. Previous studies have used legacy (single polarization) WSR-88D data to investigate PBL depth across a limited number of cases (Rabin and Doviak 1989; Heinselman et al. 2009). The implementation of the WSR-88D dual-polarization upgrade across the country by 2013 provides additional information to address the ambiguities associated with PBL depth signatures. In particular, the ability to differentiate between signatures caused by refractive index perturbations and biological scatterers may facilitate a more reliable technique to estimate PBL depth.
The current study focuses on the daytime PBL, which is often fully turbulent and will be referred to as the convective boundary layer (CBL). We will investigate the use of dual-polarization observations to provide an estimate of CBL depth as compared with CBL depth estimated from rawinsonde observations. Section 2 provides background and motivation for the use of radar data to detect Bragg scatter, which may be associated with the CBL top. Section 3 outlines the procedures used to determine CBL depth based on 0000 UTC rawinsonde data, followed by a discussion of how Bragg scatter can be used to determine CBL depth in section 4. To quantify the success of this methodology, a comparison of CBL depth estimation techniques is discussed in section 5 along with eight other example cases taken from dual-polarization WSR-88Ds in a variety of locations and seasons. Section 6 discusses important takeaways from this study and outlines future work.
2. Background
The top of the CBL is characterized by sharp vertical gradients of water vapor mixing ratio and temperature near the boundary between the CBL and the free troposphere. Both water vapor mixing ratio and temperature affect the refractive index of the atmosphere for electromagnetic waves at microwave frequencies. Thus, turbulent mixing of drier free-tropospheric air with moist air in the CBL at the CBL top can induce strong refractive index perturbations at a variety of spatial scales. These refractive index perturbations can scatter radiation. The turbulent perturbations in the refractive index on spatial scales of half the radar wavelength (for 10-cm WSR-88Ds, this corresponds to 5 cm) result in Bragg scattering, wherein the backscattered waves from these perturbations constructively interfere and lead to an enhancement in the received signal. This results in a local enhancement in radar reflectivity factor (reflectivity) at the CBL top (Weiss 1961; Doviak and Zrnić 1993; Melnikov et al. 2013).
Rabin and Doviak (1989) observed a persistent layer of enhanced reflectivity from the 10-cm National Severe Storms Laboratory Doppler radar, which they thought may have represented the CBL top. Later, Heinselman et al. (2009) sought to quantify the relationship between an elevated layer of high reflectivity and the top of the CBL. They assumed that slightly larger reflectivity values would be found at the top of the CBL, where moisture gradients generally are steepest. On 17 days with mainly clear skies and light winds, Heinselman et al. (2009) found that the height of the reflectivity maximum served as a suitable proxy for CBL depth but that the generality of this approach to other environments was unclear. Elmore et al. (2012) added solar insolation measurements in radar reflectivity–derived CBL estimates. This method yielded an improved estimation accuracy, but it was still limited in scope to summertime conditions in central Oklahoma. Using reflectivity alone to identify Bragg scatter at the top of the CBL is prone to contamination by bugs, birds, and other particulates (Heinselman et al. 2009; Melnikov et al. 2011, 2013), which can also produce enhanced reflectivity. Biological scatterers, however, tend to be highly nonspherical, whereas turbulent structures at 5-cm scales leading to Bragg scatter are assumed to be isotropic (Melnikov et al. 2011). Thus, retrieval of information about the shape, size, and distribution of scatterers in the observed region would assist with differentiating Bragg scatter from biological scatterers. Such a distinction would facilitate the use of radar data to detect Bragg scatter in a broader range of meteorological conditions.
With the implementation of dual-polarization capabilities for all NWS WSR-88Ds by 2013, new products and information are available to assist with identification of meteorological and nonmeteorological phenomena. For example, differential reflectivity 
3. Rawinsonde estimates of CBL depth
Rawinsondes provide one of the most reliable and best understood in situ observations of the atmosphere. Vertical profiles of sounding data have been used to determine CBL depth. Seidel et al. (2010) defined CBL depth as the height at which the maximum vertical gradient is achieved for the following variables: potential temperature θ, specific humidity q, and refractivity N. Another technique, commonly referred to as the parcel method, identifies the CBL depth as the height at which a parcel’s virtual potential temperature 
The method selected for use in this study combines the aforementioned methods and estimates CBL depth based on maximum vertical gradients in 
Vertical profiles from the 0000 UTC KOUN sounding on 26 Sep 2014 showing (from left to right) refractivity, potential temperature, water vapor mixing ratio, and virtual potential temperature. Estimated CBL depth based on maximum vertical gradients in each variable (red dashed line).
Citation: Journal of Atmospheric and Oceanic Technology 35, 8; 10.1175/JTECH-D-17-0210.1
This procedure was applied to all 0000 UTC soundings from Norman, Oklahoma (KOUN), during 2014. Data quality concerns including contamination by precipitation or saturated layers and missing soundings led to the elimination of 64 days. This method worked well for the remaining 301 days, although 49 days had multiple vertical gradient maxima that received careful manual inspection to subjectively determine the most appropriate CBL depth estimate. In most cases with multiple vertical gradient maxima, the lower maximum was closer to the 
4. Weather radar–based estimates of CBL depth
As described above, a Bragg scatter layer is often present near the top of the CBL, and is characterized by 
PPI of differential reflectivity (dB; shaded according to scale) at 4.44° elevation at 2345 UTC 11 May 2015 from the KTLX radar. Note the clear ring of lower 
Citation: Journal of Atmospheric and Oceanic Technology 35, 8; 10.1175/JTECH-D-17-0210.1
To map the diurnal variation of this Bragg scatter layer, which may be related to CBL depth, the QVP technique is applied (Kumjian et al. 2013; Ryzhkov et al. 2016). In this method, radar data are azimuthally averaged, and plotted with range converted into height. The height of the radar beam at each range gate is calculated assuming standard refraction (Doviak and Zrnić 1993, p. 21). QVPs are valid here because the CBL tends to be horizontally homogeneous.
A time series of these QVPs leads to a time–height profile of a given radar variable. Such a presentation maps the behavior of Bragg scatter in the PBL throughout the day. Figure 3 shows a QVP of Z and 
QVPs of Z and 
Citation: Journal of Atmospheric and Oceanic Technology 35, 8; 10.1175/JTECH-D-17-0210.1
The evolution of 
Representation of Bragg scatter 
Citation: Journal of Atmospheric and Oceanic Technology 35, 8; 10.1175/JTECH-D-17-0210.1
In the absence of insects or biota, Z and 
Assuming that a Bragg scatter layer is coincident with the top of the CBL during daytime conditions, the CBL depth is the height at which the local minimum of 
Time–height depiction of QVPs of 
Citation: Journal of Atmospheric and Oceanic Technology 35, 8; 10.1175/JTECH-D-17-0210.1
Despite the azimuthal analysis, the 
At a given time, QVPs with
Discontinuities, defined by pixels with
Isolated pixels, characterized by data points with fewer than two adjacent data points, are removed.
Once the filters are applied, smoothing via application of a running mean over five time and height steps provides further noise reduction to produce a clearer and less noisy evolution of QVP 
To facilitate a comparison between rawinsonde and radar-derived CBL depth estimates, the 2300 UTC 
5. Verification of WSR-88D-based estimates of CBL depth
CBL depths were estimated using the absolute maximum vertical gradients for rawinsonde data and the absolute minimum 
Comparison of radar- and rawinsonde-derived CBL depth estimations for all usable days in 2014.
Citation: Journal of Atmospheric and Oceanic Technology 35, 8; 10.1175/JTECH-D-17-0210.1
Bianco et al. (2008) investigated the variability in CBL depth estimation among experts at two locations and found RMSEs of 109 and 135 m. They then used several algorithms to estimate CBL depth with results indicating RMSEs between 152 and 424 m depending on the algorithm employed. Similar values of RMSE were found in Elmore et al. (2012). These values are comparable to the errors associated with the radar-derived CBL depth estimates found in the present study and indicate the feasibility of using Bragg scatter layers to estimate CBL depth.
Although data with which to compare radar-estimated CBL depths are limited during the day, the elevated Bragg scatter layer is observable throughout the daytime. Based on the demonstrated feasibility of using Bragg scatter to estimate CBL depth at one time during the day, and the previously noted similarities between the Bragg scatter layer and CBL depth behavior, it seems plausible that CBL depth estimation could be possible throughout the daytime hours. Though the results shown in this study are limited to central Oklahoma, this technique shows potential applicability to CBL depth estimation at all WSR-88D sites in real time, as suggested by Richardson et al. (2017a,b).
Application to locations outside of Oklahoma
To explore whether an elevated layer of Bragg scatter can be used to estimate CBL depth in different geographic regions representing very different environmental conditions, data from eight other WSR-88D sites are examined: Minneapolis, Minnesota (KMPX), in February; Fairbanks, Alaska (PAPD), in March; Portland, Oregon (KRTX), in May; Albany, New York (KENX), in June; Tucson, Arizona (KEMX), in August; Riverton, Wyoming (KRIW), in September; Wilmington, Ohio (KILN), in October; and Tampa, Florida (KTBW), in December (Fig. 7). The selected locations span meteorologically diverse regions and will test the applicability of techniques discussed herein.
The 
Citation: Journal of Atmospheric and Oceanic Technology 35, 8; 10.1175/JTECH-D-17-0210.1
Potential days for an analysis at each location were identified based on 0000 UTC upper-air soundings with a distinct temperature inversion and steep moisture gradient characteristic of the CBL top. In addition, specific days were selected with an intent to capture extreme weather conditions (e.g., Minneapolis in February and Tucson in August). Care was taken to ensure the selected cases occurred in eight different months to test seasonal applicability as well. The results are shown in Table 1 and indicate that an elevated layer of Bragg scatter is a good estimate of CBL depth across all seasons in a variety of environmental conditions. The results are comparable to those found in central Oklahoma and demonstrate the potential widespread application of this methodology to a variety of locations, times of year, and meteorological conditions. The results indicate good agreement in environments with surface temperatures ranging from 
Weather conditions and algorithm performance are listed for locations outside of Oklahoma. 0000 UTC rawindsonde surface temperature and mixing ratio are shown next to rawinsonde- and 
6. Operational implications and future work
Elevated layers of Bragg scatter, identified as local minima in 
Detection of Bragg scatter associated with the top of the CBL is most effective with a higher antenna elevation angle. At a lower elevation angle, the radar beam will take longer to pass through the layer of Bragg scatter, thus making it appear wider on the PPI scan. At higher elevation angles, the Bragg scatter layer will be narrower, as seen by the radar. Though scans at angles 
Interesting behavior of Bragg scatter was observed in a few cases during 2014 in Oklahoma. On 15 July and 30 November, two layers of Bragg scatter were observable late in the day (Fig. 8). In both cases, rawinsonde profiles also reveal two layers of sharp gradients in moisture and temperature. These examples demonstrate that Bragg scatter regions may also exist outside of the CBL top, as in Melnikov et al. (2013). The case from Wilmington on 2 October 2017 presents an interesting Bragg scatter signature as well (Fig. 7). The temporally constant CBL depth observed based on Bragg scatter seems to deviate from the expected steady daytime deepening of the boundary layer. Further investigation of the 1200 UTC sounding at KILN on 2 October indicates easterly winds at the surface shifting to westerly in the residual layer. The 0000 UTC sounding at KILN on 3 October indicates southerly winds and warmer CBL. Based on these observations, it appears the CBL may have been advected across a boundary. This explanation justifies the presence of a steady-state CBL depth and deviation from the expected surface-heat-flux-driven deepening of the CBL.
(left) The 
Citation: Journal of Atmospheric and Oceanic Technology 35, 8; 10.1175/JTECH-D-17-0210.1
In the National Research Council report Observing Weather and Climate from the Ground Up: A Nationwide Network of Networks, the current limitations associated with CBL depth monitoring are highlighted as a major concern (NRC 2009). One recommendation states, “As a high infrastructure priority, federal agencies and their partners should deploy lidars and radio frequency profilers nationally at approximately 400 sites to continually monitor lower tropospheric conditions” (NRC 2009, p. 10). To that end, Demoz et al. (2017) demonstrate the utility of the Automated Surface Observing System (ASOS) network of ceilometers to detect CBL depth across the country. Owing to current Federal Aviation Administration (FAA) restrictions on how the data are used, however, ASOS ceilometers do not currently transmit backscatter in real time, although the information can be collected and used to estimate CBL depth. A change in data procedures for ASOS is feasible, but it requires an extensive review process and may not be possible for several years. The use of dual-polarization radar to detect CBL depth provides readily available information for operational use as well as an extensive archive of 
The value of real-time monitoring of CBL depth and structure for air quality forecasts, fire weather, model initialization, and convection initiation has been documented by numerous previous studies. Various field campaigns have mapped the CBL depth during the day with increased temporal resolution relative to current methods. Implementation of CBL depth estimation across the country using the WSR-88D network could provide data with greater temporal and spatial resolution compared to current techniques. The use of radar data will result in a denser network of CBL depth estimates, but it could also assist with human forecasting of severe weather, improve forecasts through assimilation into weather models, and equip the public with better preparation for air quality and fire weather concerns.
Acknowledgments
Funding for this work is provided by NSF Award AGS-1632850. Special thanks to members of the RADAR research group at Pennsylvania State University for sharing code and providing insightful suggestions. This work is part of the first author’s master’s thesis at The Pennsylvania State University. Constructive comments from three anonymous reviewers led to improvements in the manuscript and are greatly appreciated.
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