The Pennsylvania State University The Graduate School

USING DUAL-POLARIZATION RADAR INFORMATION TO INVESTIGATE

CLEAR-AIR BOUNDARY LAYER ATMOSPHERIC PHENOMENA

A Thesis in Meteorology by John R. Banghoff

c 2019 John R. Banghoff

Submitted in Partial Fulfillment of the Requirements for the Degree of

Master of Science

May 2019 The thesis of John R. Banghoff was reviewed and approved∗ by the following:

David J. Stensrud Professor of Meteorology Head of the Department of Meteorology Thesis Co-Advisor

Matthew R. Kumjian Assistant Professor of Meteorology Thesis Co-Advisor

George S. Young Professor of Meteorology

Paul M. Markowski Professor of Meteorology Associate Head of Graduate Program

∗Signatures are on file in the Graduate School. Abstract

Dual-polarization radar provides a wealth of new information about the type, size, and orientation of scat- terers in the atmosphere. This radar information has been interrogated for its applications to hazardous weather, but a wealth of clear-air radar data exists that is significantly underutilized. The ability of Na- tional Weather Service WSR-88D radars to detect insects and other biota within the convective boundary layer (CBL) facilitates estimation of boundary layer depth and characterization of horizontal convective rolls (HCRs). Bragg scatter signatures in dual-polarization radar observations, which are defined by low differen- tial reflectivity (ZDR) values, are used as a proxy for CBL depth in 2014 over Central Oklahoma using data from the Twin Lakes (KTLX) WSR-88D. The 243 ZDR Bragg scatter and upper air sounding CBL depth estimates collected during this year have a correlation of 0.90 and a RMSE of 254 m. Additionally, a 10-year climatology of HCRs in Central Oklahoma indicates that HCRs occur on 75% of days during all months of the warm-season (April-September). HCRs typically form in the mid-morning and may persist throughout the day, transition to cellular convection, or develop from cellular convection before dissipating around sun- set. These results should facilitate future studies on convection initiation, HCR formation mechanisms, and model parameterization. The methods used to estimate CBL depth and identify and characterize HCRs are potentially applicable across a variety of geographic locations and seasons, and demonstrate the usefulness of clear-air radar data.

iii Table of Contents

List of Figures vi

List of Tables ix

Acknowledgments x

Chapter 1 Introduction 1

Chapter 2 Convective Boundary Layer Depth Estimation From S-Band Dual-Polarization Radar 3 2.1 Introduction ...... 3 2.2 Background ...... 4 2.3 Rawinsonde estimates of CBL depth ...... 5 2.4 Weather-radar based estimates of CBL depth ...... 6 2.5 Verification of WSR-88D-based estimates of CBL depth ...... 11 2.5.1 Application to locations outside of Oklahoma ...... 13 2.6 Operational implications and future work ...... 14

Chapter 3 A 10-year Warm-Season Climatology of Horizontal Convective Rolls and Cellular Con- vection in Central Oklahoma 18 3.1 Introduction ...... 18 3.2 Methods for Detection of Boundary Layer Circulations ...... 20 3.2.1 Identifying Boundary Layer Organization ...... 21 3.2.2 Differentiating HCRs from Cellular Convection ...... 23 3.2.3 HCR Characteristics ...... 24 3.3 Results ...... 24 3.3.1 10-Year Climatology ...... 24 3.3.2 Results from 2013-2017 ...... 25 3.4 Summary and Future Work ...... 29

Chapter 4 Conclusion 46

iv Bibliography 48

v List of Figures

2.1 Vertical profiles from the 0000 UTC KOUN sounding on 26 Sept. 2014 showing refractivity (N), potential temperature (θ), water vapor mixing ratio (q), and virtual potential tempera- ture (θv). The red dashed line represents estimated CBL depth based on maximum vertical gradients in each variable...... 6 2.2 Plan Position Indicator (PPI) of differential reflectivity (in dB, shaded according to scale) at 4.44◦ elevation on 11 May 2015 at 2345 UTC from the KTLX radar. Note the clear ring of lower ZDR values (blue color) indicative of a Bragg scatter layer. The radar is located at the origin...... 7 2.3 Quasi-vertical profiles of Z and ZDR for 20-21 May 2014 at KTLX. Note the daytime evolution of the CBL top characterized by reduced ZDR and the biota bloom overnight characterized by large Z and ZDR...... 9 2.4 Representation of Bragg scatter ZDR contamination by biota. For a given insect ZDR, an increase in the amount of insects leads to an increase in ZDR of Bragg scatter from 0 dB. The black contour in each plot represents the ratio between horizontal reflectivities for bugs and Bragg scatter resulting in a decrease in the ZDR of bugs by 0.5 dB. Such a difference is detectable by the algorithm used in the present study to estimate CBL depth from QVPs of ZDR...... 10 2.5 Time-height depiction of quasi-vertical profiles (QVP) of ZDR (in dB, shaded according to scale) at the 4.5◦ elevation angle for (a) 4 June 2014 and (b) 21 October 2014 at KTLX. Note the region of Bragg scatter characterized by low ZDR values. The estimated time series of minimum ZDR is represented by a white line (solid when clearly defined and dashed when interpolation is required)...... 11 2.6 Comparison of radar- and rawinsonde-derived CBL depth estimations for all usable days in 2014...... 12 2.7 ZDR QVP for 9 February 2017 in Minneapolis, MN (KMPX), 11 March 2017 Fairbanks, AK (PAPD), 7 May 2017 in Portland, OR (KRTX), 11 June 2017 in Albany, NY (KENX), 17 August 2017 in Tucson, AZ (KEMX), 4 September 2017 in Riverton, WY (KRIW), 2 October 2017 in Wilmington , OH (KILN), and 21 December 2016 in Tampa, FL (KTBW). The time series of minimum ZDR is manually traced with a white line. Rawinsonde estimates of CBL depth at 23 UTC are indicated by the black dot outlined in yellow. White shading indicates regions outside the temporal and spatial range of radar data...... 16 2.8 ZDR QVP (left) for 15 July 2014 and 30 November 2014 in Central Oklahoma (KTLX) showing a double layer of Bragg scatter. Legend is the same as Figure 2.7 excluding the daytime CBL depth estimate for clarity. Vertical profiles of refractivity, potential tempera- ture, mixing ratio, and virtual potential temperature (right) demonstrate vertical gradients of moisture/temperature characteristic of Bragg scatter signatures on radar...... 17

vi 3.1 Equivalent reflectivity factor at 1.4◦ (a) at 2142 UTC on 16 June 2014 at KTLX, showing a classic HCR signature with clearly-defined linear echoes and (b) at 1836 UTC on 29 September 2014 at KTLX, showing a classic cellular convection signature with clearly-defined circular echoes. Such echoes occur as the radar scans insects lofted in updrafts associated with HCRs. The associated absence of echoes represent locations of downdrafts where insects are vertically suppressed...... 21 3.2 0.5◦ Z (dBZ), 0.5◦ V (m s−1), and velocity azimuth display (VAD) computed between 35 and 45 km from KTLX during (a-c) a supercell thunderstorm on 1 June 2016, (d-f) a nocturnal boundary layer on 11 June 2016, and (g-i) HCRs on 22 June 2016. The variance (σ2) of residual radial velocity (observed winds minus VAD-estimated winds) is listed on each VAD plot. Notice the residual radial velocity variance (RRVV) is largest for the precipitation case and lowest for the HCR case. Lower variance implies increased uniformity of boundary layer winds...... 33 3.3 Time series of of residual radial velocity variances (RRVVs, m2 s−2) from VAD analysis for 29 July 2014 at KTLX. Velocity azimuth displays and RRVVs are calculated for range rings of 10, 20, 30, and 40 km distance from the radar (beam heights of 0.27, 0.53, 0.80, and 1.08 km respectively). The red bar indicates the algorithm-identified time range of boundary layer organization. Organization is defined when the variance among the 4 VAD RRVVs drops below 1 m4 s−4 implying a convergence of the various time series. The black bar indicates manually-identified boundary layer organization...... 34 3.4 Comparison of VAD RRVV analysis and manual analysis for start and end times of boundary layer organization. Organization departure is computed as TRRV V -Tmanual where T<0 indicates RRVV analysis times are earlier than manually-identified times. Note that timing from the RRVV method over-estimates the range of actual organization (i.e. RRVV analysis has earlier start times and later end times than found from the manual analysis). Departures for (a) start times and (b) end times from 134 days with organization in 2014 are included. . 35 3.5 (a) Cumulative 10-year warm-season climatology of HCRs in Central Oklahoma separated by month showing the percentage of days that exhibit boundary layer organization, widespread precipitation, and the absence of boundary layer organization (null cases), along with cases deemed indiscernible (unclear). (b) For each month, boundary layer organization days are separated into HCRs (left columnn) and cellular convection (right column). Transition cases (both HCRs and cells, so doubly represented), pure HCRs/cells and a mix of organization and precipitation are delineated. Note that a majority of days in each month have HCRs, and nearly 75% of all days have boundary layer organization...... 36 3.6 As in Figure 3.5, but separated by year. Data are based on visual observation of base re- flectivity between 1200 UTC and 0000 UTC from the Twin Lakes, OK (KTLX) WSR-88D radar...... 37 3.7 HCR duration for April-September of 2008-2017 at KTLX. Durations are broken down in (a) all HCR cases, (b) days where HCRs are the only boundary layer organization, (c) days when HCRs undergo transition to cellular convection, and (d) days when HCRs are formed via transition from cellular convection...... 38 3.8 Histogram of HCR timing during the warm-season from 2008-2017 at KTLX. All HCR cases that persist after 0000 UTC are grouped in the 2300 UTC bin (42 cases in 2014 with only 1 case persisting after 0100 UTC)...... 39

vii 3.9 (a) Wind direction calculated from the VAD wind at the onset of HCRs each day from April - September 2013-2017 at KTLX. (b) Histogram of the departure of HCR orientation from the mean wind direction for the days. Positive values indicate HCR orientation is to the right of the mean wind (counterclockwise). Note that there are 5 cases with departures above 30◦ not exceeding 50◦ (not shown)...... 40 3.10 Histograms of HCR wavelength and aspect ratio for all HCR days during the warm-seasons of 2013-2017 at KTLX. First and last hour wavelength and aspect ratio are plotted for pure HCR cases (a-d), HCR cases that transition to cellular convection (e-h), and HCR cases that transition from cellular convection (i-k)...... 41 3.11 Time series of box and whiskers plots for HCR (a) wavelength and (b) aspect ratio for all HCR days during the warm-seasons of 2013-2017 at KTLX. There number of cases for each hour is as follows: before 16 UTC: 58; 1600-1659 UTC: 127; 1700-1759 UTC: 134; 1800-1859 UTC: 119; 1900-1959 UTC: 90; 2000-2059 UTC: 100; 2100-2159 UTC: 93; 2200-2259 UTC: 110; after 2300 UTC: 220. Note that 7 cases have wavelengths above 15 km and 8 have aspect ratios above 10 after 2300 UTC (not shown)...... 42 3.12 Box and whisker plot of aspect ratio in the first hour of HCR activity and the last hour of HCR activity prior to any transition for each day and grouped by month for 2013-2017 (A=April, M=May, J=June, J=July, A=August, S=September). The corresponding average monthly boundary layer depth estimates are listed in the top right of each figure. Vertical black lines on the right figures correspond to the mean aspect ratio during the first hour. The black arrow denotes the change in aspect ratio from first hour to last hour...... 43 3.13 Boundary layer depth vs. roll wavelength as in Weckwerth et al. (1997) (their Figure 17). Plotted are lines of best-fit from Kuettner (1971) and Weckwerth et al. (1997) and observations of HCRs in Central Oklahoma during 2013-2017...... 44 3.14 Case study of boundary layer organization on 4 June 2015 at KTLX. Top row shows reflectivity and bottom row shows visible satellite imagery at the corresponding time. Note the transition from HCRs to cellular convection and back to HCR-like organization, except with a much larger wavelength. Black box represents the radar domain...... 45

viii List of Tables

2.1 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 ZDR-estimated CBL depths. Error is defined as the difference between CBL depth estimates...... 13

3.1 Summary of HCR observations reported in the literature ...... 30

ix Acknowledgments

Funding for this work is provided by NSF Award AGS-1632850. This work would not have been possible without the countless hours of data crunching and code running by Jake Sorber to whom I am eternally grateful. To the great folks at Weather World who put up with my incessant shout out to horizontal convective rolls or cloud streets on air - thank you for humoring me. In all seriousness, thanks to the folks at Weather World for helping me improve my communication skills while working on my master’s degree. I’d also like to thank Barb Watson and all the folks at NWS State College for being flexible and patient as I worked to finish my thesis while working full time through the wettest year on record in State College. Special thanks to members of the RADAR research group at Penn State University for sharing code and providing insightful suggestions. And finally, a big thanks to Matt and Dave for their invaluable professional and personal mentoring over the last two years. I have learned so much and could never have imagined these 2+ years being as fruitful as they have been.

x Dedication

To the glory of God: Without His guidance, direction, and provision, these past two and a half years would have been significantly less fruitful or fulfilling. To my family: Thank you so much for your unwavering support and encouragement as I’ve pursued my passions and navigated this season of my career. To my colleagues at Penn State: Thank you for making my time here about so much more than research. I’ll always be grateful for the conversations we’ve had and the memories we’ve made.

xi Chapter 1

Introduction

The first observations of weather phenomena using surveillance radar occurred in the early 1940s by US Navy bombers. These aircraft used radar to detect German U-boats at night and it became clear that radar could also detect precipitation (Fletcher, 1990). This led to the use of radar to conduct weather reconnaissance out ahead of long-range bombers. Shortly thereafter, the usefulness of radar for detecting meteorological phenomena and severe weather became eminently clear. The first national network of weather surveillance radars (WSRs) in the United States was installed in 1957 as research efforts across the United States and abroad led to increased understanding of meteorological radar signatures (Lemon, 1977; Klemp and Rotunno, 1983). Later, in 1988, the national network of weather surveillance radars began to be updated to included Doppler capability and expanded, becoming known as the WSR-88D. This expansion led to continued research and improved accessibility of radar data that provided real-time scans of the atmosphere. Over the years, radar has played a significant role in lengthening average tornado warning lead time (Bieringer and Ray, 1996), improving quantitative precipitation estimates (Giangrande and Ryzhkov, 2008), and identifying severe hail (Witt et al., 1998), among many other applications. The implementation of dual-polarization radar, which started in 2011 and was completed at all WSR- 88D sites by 2013, produced an abundance of new information about the type, shape, orientation, and distribution of scatterers in the atmosphere. This information has led to identification and operational implementation of dual-pol products such as the hydrometeor classification algorithm (Park et al., 2009), tornado debris signature (Ryzhkov et al., 2005; Schultz et al., 2012; Bodine et al., 2013), precipitation type discrimination in winter (Kennedy and Rutledge, 2011; Thompson et al., 2014; Moisseev et al., 2015), and severe storm structure interrogation (Kumjian and Ryzhkov, 2008; Kumjian, 2013b). The usefulness of radar information for hazardous weather situations is well-documented and attracts a large portion of research efforts. Far less energy has been devoted toward exploring radar information on days without significant weather. During periods of quiet weather, so-called ”clear-air” days, operational meteorologists often work on research projects or catch up on non-weather-related activities, paying little or no attention to radar signatures. As such, there is a vast amount of clear-air radar data that is largely unexplored. The implementation of dual-polarization radar, an increasing interest in boundary-layer processes for modeling 2 and observation, and higher-spatiotemporal resolution radar information make investigation of clear-air radar data a worthwhile endeavor. Clear-air scans of the atmosphere currently complete a full volume scan every 10 minutes, with a 360◦ scan at 4 different elevation angles of up to 4.3◦. The usefulness of radar data to detect clear-air processes is based on radar’s ability to detect biota and refractive index gradients that exist in the atmosphere. Hardy and Gage (1990) provide a comprehensive review of the origin of clear-air radar applications from the 1930 through the 1980s. Past studies using clear-air radar data have investigated the depth of the boundary layer (Heinselman et al., 2009; Elmore et al., 2012) and boundary layer phenomena such as outflow boundaries (Mueller and Carbone, 1987), cloud streets (Christian and Wakimoto, 1989), horizontal convective rolls (Weckwerth et al., 1997), cellular convection (Young et al., 2002), and convergence lines (Wilson and Schreiber, 1986; Wilson et al., 1992) using legacy (single-polarization) radar. Others have looked at migration patterns of birds and insects using legacy radar (Gauthreaux Jr, 1970; Vaughn, 1985; Drake and Farrow, 1988; Achtemeier, 1991). Still, the breadth of clear-air radar studies pales in comparison to that of severe weather radar studies. Even fewer studies have leveraged dual-polarization data to investigate clear-air processes (Melnikov et al., 2011, 2013). The major clear-air phenomena that drive the present research are horizontal convective rolls and cellular convection in the boundary layer. Central Oklahoma is chosen as the location for this study because the atmosphere is insect-laden for much of the year. Through investigation of clear-air radar observations, a technique for estimating the depth of the daytime convective boundary layer is developed. A discussion of boundary layer behavior, dual-polarization radar signatures associated with the top of the boundary layer, an innovative method for monitoring the depth of the daytime convective boundary layer using dual-polarization radar, and a comparison of radar-derived boundary layer depth estimates with traditional weather balloon-based boundary layer depth estimates make up Chapter 2. Further, a 10-year investigation of horizontal convective roll behavior during the warm-season in Central Oklahoma is desirable in order to better understand boundary layer organization and benchmark planetary boundary layer schemes. Chapter 3 describes various characteristics of horizontal convective rolls including timing, evolution, frequency, and spatial distribution from a comprehensive 10-year warm-season data set. The combination of boundary layer depth estimates and horizontal convective roll analysis provides a wealth of new information about clear-air radar signatures. A summary of the important findings from this study are outlined in Chapter 4. Chapter 2

Convective Boundary Layer Depth Estimation From S-Band Dual-Polarization Radar

Note: This chapter in its entirety is in print as Banghoff et al. (2018).

2.1 Introduction

The depth of the planetary boundary layer (PBL) varies from a few tens of meters at night to several kilometers during the daytime. This single measurement and its evolution provide useful information on PBL structure. Not surprisingly, PBL depth influences air quality, turbulence, and cloud development. Wildfire behavior (Clements et al., 2007) and propagation of hazardous materials (Dabberdt et al., 2004) both exhibit a strong dependence on PBL depth. Yet observations of PBL depth come primarily from rawinsonde data collected only twice a day (0000 UTC 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 data set with higher spatiotemporal resolution than other instruments owing to the 159 continuously operating National Weather Service dual-polarization Weather Surveillance Radar- 1988 Doppler (WSR-88D) radars. Weather radars, if useful for PBL depth estimation, would significantly 4 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 2.2 provides background and motivation for the use of radar data to detect Bragg scatter, which may be associated with the CBL top. Section 2.3 will outline 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 2.4. In order to quantify the success of this methodology, a comparison of CBL depth estimation techniques is discussed in Section 2.5 along with 8 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.

2.2 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 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 refractive index on spatial scales of half the radar wavelength (for 10-cm WSR-88D radars, 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 (hereafter, reflectivity) at the CBL top (Weiss, 1961; Doviak and Zrni´c,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 the generality of this approach to other environments was unclear. Elmore et al. (2012) added solar insolation measurements into radar reflectivity-derived CBL estimates. This method yielded an improved estimation accuracy, but 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, 5 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-88D radars by 2013, new products and information are available to assist with identification of meteorological and non-meteorological phenomena. For example, differential reflectivity (ZDR) is commonly used to identify the shape or orientation of scatterers in the radar sampling volume (Seliga and Bringi, 1976; Kumjian, 2013a). For clear-air applica- tions, ZDR has proven useful in differentiating between enhanced reflectivity regions caused by Bragg scatter and those caused by biota in the daytime CBL (Melnikov et al., 2013). Biota tend to produce extremely large ZDR and low correlation coefficient (ρhv) values distinct from precipitation and other meteorological echoes owing to their non-spherical, irregular shapes. In contrast, the isotropic turbulent structures causing

Bragg scatter lead to ZDR near 0 dB and ρhv near 1.0 (Melnikov et al., 2011). Although reflectivity alone is unable to differentiate between Bragg scatters and biota, the combination of ZDR and ρHV has proven effective (Melnikov et al., 2013).

2.3 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,

θv, matches its surface value (Holzworth, 1964; Seibert et al., 2000). Alternatively, Coniglio et al. (2013) identified CBL depth as the height at which the parcel reached a virtual potential temperature value equal to the surface θv + 0.6 K. The method selected for use in this study combines the aforementioned methods and estimates CBL depth based on maximum vertical gradients in θv, θ, q, and N. The height at which the maximum vertical gradient for each variable occurs is calculated, and then CBL depth is defined as the modal height among the 4 variables. The technique for estimating CBL depth from each variable has errors as discussed in Seidel et al. (2010), but taking a modal approach helps minimize algorithm error. A modal approach is used because it eliminates outliers, whereas a mean approach would incorporate an outlier among the 4 profiles and skew the CBL depth estimate. An example using this technique is shown in Figure 2.1. Sharp vertical gradients in all 4 variables at a height of 1802 meters yield confidence that this layer is associated with the CBL top. This procedure was applied to all 0000 UTC soundings from KOUN during 2014. Data quality concerns including contamination by precipitation or saturated layers and missing soundings led to elimination of 64 days. This method worked well for the remaining 301 days, although 49 had multiple vertical gradient 6

θ N θ q v 3500

3000

2500

2000

1500 Height (m)

1000

500

0 0 200 400 300 310 320 0 5 10 300 310 320 Refractivity Potential Mixing Ratio Virtual Potential (N units) Temperature (K) (g kg -1 ) Temperature (K)

Figure 2.1. Vertical profiles from the 0000 UTC KOUN sounding on 26 Sept. 2014 showing refractivity (N), potential temperature (θ), water vapor mixing ratio (q), and virtual potential temperature (θv). The red dashed line represents estimated CBL depth based on maximum vertical gradients in each variable.

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 ZDR minimum in QVPs and was used as the CBL depth estimate.

2.4 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

ZDR near 0 dB and ρhv near 1. In a typical plan-position indicator (PPI) scan of ZDR, this Bragg scatter

layer shows up as a ring of reduced ZDR values encircling the radar (Figure 2.2). The ring of locally reduced

ZDR expands radially through the afternoon, indicating an increase in the altitude of the Bragg scatter layer. 7

◦ The large background ZDR values indicate the biota-filled CBL. This study uses the 4.5 elevation angle scan, which is the highest elevation angle in clear-air scanning modes (VCP 31 or 32), in order to minimize the influence of ground clutter (NOAA, 2017).

Figure 2.2. Plan Position Indicator (PPI) of differential reflectivity (in dB, shaded according to scale) at 4.44◦ elevation on 11 May 2015 at 2345 UTC from the KTLX radar. Note the clear ring of lower ZDR values (blue color) indicative of a Bragg scatter layer. The radar is located at the origin.

In order to map the diurnal variation of this Bragg scatter layer, which may be related to CBL depth, the quasi-vertical profile (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 Zrni´c,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 2.3 shows a QVP of Z and ZDR for 20-21 May 2014 at the KTLX radar. The diurnal evolution of Z is dominated by biota (Figure 2.3). 8

Around sunset (∼0000 UTC), Z values increase and are associated with a biota bloom, which occurs as bats, birds, and other airborne organisms become active. At sunrise (∼1200 UTC), a significant decrease in Z is evident as biota retreat. Interestingly, there is an elevated layer of enhanced Z, collocated with enhanced

ZDR, (at ∼1 km AGL) that persists after sunrise, which likely is associated with biota that remain airborne past sunrise. A second, weaker Z enhancement between 0.5 and 1 km AGL is collocated with low ZDR and thus is associated with the top of the growing CBL. After about 15 UTC, low-level Z and ZDR near the surface increase as insects and biota become more active within the CBL. A second layer of enhanced Z, indicated above the white line in the top panel of Figure 2.3, develops and is associated with Bragg scatter at the CBL top. Because Z is highly susceptible to contamination by biota, using it alone to track Bragg scatter can be difficult.

The evolution of ZDR is similar to that of Z, but ZDR can differentiate Bragg scatter from biological

scatterers more effectively. Around sunrise, two layers of low ZDR values are evident. The layer at about 1.5 km AGL that emerges around sunrise on both days is collocated with a region of low Z and could be associated with Bragg scatter in the residual layer that becomes visible as the higher-Z biota retreat. The second layer closer to the surface is likely Bragg scatter associated with the CBL top. Through the daytime hours, this layer continues to increase in altitude, reaching its peak just before sunset. Starting around

sunset, the low values of ZDR develop near the surface and stay near the surface over the nighttime hours. The behavior of this Bragg scatter layer matches the expected PBL diurnal evolution, as described by Stull (1988). For example, in the morning, as surface heating begins, the CBL deepens, ceasing its ascent just before sunset and leaving behind a residual layer. Overnight, a stable and persistent shallow PBL forms, which is indicated by the layer of low ZDR just above the ground. Given the similar evolutions of Bragg scatter layers in ZDR and the CBL, their behavior may be closely related. Theoretically, ZDR of Bragg scatter should be 0 dB; however, when mixed with biota that exhibit high ZDR, the total observed ZDR values may be positively biased. Figure 2.4 shows how different reflectivity contributions of insects (with

large intrinsic ZDR) and Bragg scatter (with intrinsic ZDR = 0 dB) combine to affect the total observed

ZDR. The contour in each panel shows when the total ZDR is reduced compared to pure insects by 0.5 dB, which we consider detectable with our algorithm. The total observed ZDR will be larger for larger reflectivity contributions from insects compared to the reflectivity contribution from Bragg scatter.

In the absence of insects or biota, Z and ZDR QVPs exhibit slightly different characteristics from those shown in Figure 2.3. Without insects or biota, which contaminate the ZDR field, the Bragg scatter region associated with the CBL top exhibits ZDR values near 0 dB and vertical gradients in ZDR are less pronounced. There were two such days in 2014 at KTLX without a clear signature of insects in the CBL. For these cases, a low-ZDR layer exists near the surface and deepens through the daytime hours. This pattern describes days with an insect-laden boundary layer as well; although the presence of insects does influence ZDR values, the Bragg scatter layer exists irrespective of insects or biota. 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 ZDR occurs in the QVPs at each time. Note that a non-uniform CBL top height across the radar domain would appear in QVPs as a wider layer of reduced ZDR because of the azimuthal averaging technique employed. Inspection of many diurnal cycles of ZDR indicates that there are two predominant patterns of ZDR that occur throughout the year. The first is characterized 9

Figure 2.3. Quasi-vertical profiles of Z and ZDR for 20-21 May 2014 at KTLX. Note the daytime evolution of the CBL top characterized by reduced ZDR and the biota bloom overnight characterized by large Z and ZDR.

by a local vertical minimum of ZDR aloft corresponding to the height of the CBL top (Figure 2.5a). The second is characterized by a sharp decrease in ZDR aloft (∼ 1.5 km AGL) with no clear subsequent increase in ZDR at even higher altitudes (Figure 2.5b). Identification of CBL height for the second case is more challenging than for the first owing to the much larger vertical extent of low ZDR, suggesting a very deep elevated layer of Bragg scatter.

Despite the azimuthal analysis, the ZDR QVP is noisy in many cases. Because of this, a simple quality control filter is developed and applied prior to estimating CBL depth. The filter implements the following steps:

1. ZDR < −2 dB (owing to ground clutter contamination from side lobes) are removed

2. Z > 0 dBZ and ρHV > 0.8, which indicate precipitation with larger Z values than typical of Bragg scatter, are removed (note that we tested the sensitivity of the Z threshold by making it 10 dBZ; this led to an insignificant increase of 5 m in the RMSE and no change in correlation in the subsequent analysis)

3. At a given time, QVPs with ZDR values < 2 dB through the entire column are removed (additional filter for light precipitation) 4. Discontinuities, defined by pixels with > 1 dB difference between adjacent data points, are removed 5. Isolated pixels, characterized by data points with less than 2 adjacent data points, are removed Once the filters are applied, smoothing via application of a running mean over five time and height 10

Figure 2.4. Representation of Bragg scatter ZDR contamination by biota. For a given insect ZDR, an increase in the amount of insects leads to an increase in ZDR of Bragg scatter from 0 dB. The black contour in each plot represents the ratio between horizontal reflectivities for bugs and Bragg scatter resulting in a decrease in the ZDR of bugs by 0.5 dB. Such a difference is detectable by the algorithm used in the present study to estimate CBL depth from QVPs of ZDR.

steps provides further noise reduction to produce a clearer and less noisy evolution of QVP ZDR during the daytime. The CBL depth can now be estimated by visual inspection, although a simple algorithm is used to find the minimum value of ZDR in the vertical profile at each time step and records the height at which that minimum occurs. A running mean is applied to the resulting time series of estimated CBL depth to eliminate large jumps and produce a smoother, and more realistic, behavior. CBL depth is only calculated during the day (1200 UTC-0000 UTC); Bragg scatter is often harder to identify overnight when biological 11

Figure 2.5. Time-height depiction of quasi-vertical profiles (QVP) of ZDR (in dB, shaded according to scale) at the 4.5◦ elevation angle for (a) 4 June 2014 and (b) 21 October 2014 at KTLX. Note the region of Bragg scatter characterized by low ZDR values. The estimated time series of minimum ZDR is represented by a white line (solid when clearly defined and dashed when interpolation is required).

scatterers dominate Z (and thus ZDR) and turbulence is often weaker. To facilitate comparison between rawinsonde and radar-derived CBL depth estimates, the 2300 UTC

ZDR profile is used to compare with the 0000 UTC National Weather Service rawinsonde from Norman, Oklahoma (launch time of ∼2300 UTC). The KTLX dual-polarization WSR-88D radar is located 23 km to the northeast of the KOUN rawinsonde site. This separation distance is well within the clear air sampling volume of KTLX, so the rawinsonde samples the same boundary layer. Precipitation, which contaminates

ZDR and makes both radar and rawinsonde CBL depth estimation impossible, occurred on 24 days. An additional 55 days were removed as a result of indiscernible Bragg scatter layers. In cases where the Bragg scatter layer become less discernible before 2300 UTC, a visual linear extrapolation of the Bragg scatter layer height was used to estimate CBL depth. Linear extrapolation generally works well an hour or two before sunset given that the CBL depth changes in a continuous and approximately linear fashion during this time as surface heating persists.

2.5 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 ZDR value for radar data on all days in 2014 at KOUN/KTLX. In order to evaluate the effectiveness of using radar data to estimate CBL depth, only days with discernible CBL estimates from both rawinsondes and radar were included in this analysis. Manual quality control of both methods led to 243 useful cases for analysis (62 from December, January, and February; 59 from March, April, and May; 62 from June, July, and August; and 60 from September, October, and November). Of the 122 erroneous 12 days, 10% did not have a 0000 UTC sounding, 50% had soundings that experienced a saturated layer (cloud/precipitation) near the surface, indicating that the CBL was indiscernible or absent, and 40% had inconclusive ZDR signatures. For the 243 usable days, the comparison between rawinsonde- and radar-derived CBL depth yielded a correlation of 0.90 and a RMSE of 254 meters (Figure 2.6). Bianco et al. (2008) investigated the variability in CBL depth estimation among experts at two locations and found RMSEs of 109 m 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.

CBL Depth Estimation Comparison 3500 Number of days plotted: 243 Correlation: 0.90 3000 RMSE: 254 m

2500

2000

1500

1000 Skew-T CBL Depth (m)

500 2014 KTLX 1:1 0 0 500 1000 1500 2000 2500 3000 3500 Z QVP CBL Depth (m) DR

Figure 2.6. Comparison of radar- and rawinsonde-derived CBL depth estimations for all usable days in 2014.

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 Bragg scatter layer and CBL depth behavior, it seems plausible that CBL depth estimation could 13 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).

2.5.1 Application to locations outside of Oklahoma

To explore whether or not an elevated layer of Bragg scatter can be used to estimate CBL depth in different geographic regions representing very different environmental conditions, data from 8 other WSR-88D sites are examined. These are: Minneapolis, MN (KMPX) in February; Fairbanks, AK (PAPD) in March; Portland, OR (KRTX) in May; Albany, NY (KENX) in June; Tucson, AZ (KEMX) in August; Riverton, WY (KRIW) in September; Wilmington, OH (KILN) in October; and Tampa, FL (KTBW) in December (Figure 2.7). The selected locations span meteorologically diverse regions and will test the applicability of techniques discussed herein. 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 addi- tion, specific days were selected with an intent to capture extreme weather conditions (e.g., Minneapolis in February and Tuscon in August). Care was taken to ensure the selected cases occurred in 8 different months to test seasonal applicability as well. The results are shown in Table 2.1 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. Re- sults indicate good agreement in environments with surface temperatures ranging from −17◦C to 36◦C and surface water vapor mixing ratio values ranging from 1 g kg−1 to 11 g kg−1.

Table 2.1. 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 ZDR-estimated CBL depths. Error is defined as the difference between CBL depth estimates.

Location Month Surface Water Rawinsonde ZDR (m) Error (m) Temperature Vapor (m) (◦C) Mixing Ratio (g kg−1) Minneapolis, MN February -17.3 1 882 900 -18 Fairbanks, AK March -13.3 1.37 1077 1009 68 Portland, OR May 17.4 4.84 1421 1870 -449 Albany, NY June 32.2 10.26 2187 2070 117 Tucson, AZ August 35.6 4.33 3023 3246 -223 Riverton, WY September 22.6 5.54 1755 1636 119 Wilmington, OH October 21.8 7.75 1259 1247 12 Tampa, FL December 17.4 11 593 813 -204 14

2.6 Operational implications and future work

Elevated layers of Bragg scatter, identified as local minima in ZDR, are found to rise from near the ground during the daytime, showing a diurnal evolution that parallels the expected behavior of CBL depth. Com- parison of these ZDR estimates of CBL depth to 243 rawinsonde observations yield an RMSE of 254 meters over central Oklahoma. The approach was tested across the country and throughout the year demonstrating that an elevated layer of Bragg scatter is coincident with with the top of the CBL across a variety of observed environmental conditions. Additionally, the use of an azimuthal average to estimate CBL depth provides a more representative measure of CBL depth than the point measurement made with a rawinsonde. 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 > 4.5◦ are not used for clear-air scanning (probably because they take additional time and have not previously been thought of as useful), inclusion of occasional higher elevation scans in a clear air scanning strategy would allow for more precise detection of the CBL depth based on Bragg scatter. The Radar Operations Center recently announced implementation of VCP 35, which will incorporate scans at the 5.1◦ and 6.4◦ elevation angle. Inclusion of these scans will provide more accurate estimates of CBL depth, and scans at even higher elevation angles would be useful in the future. 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 (Figure 2.8). In both cases, rawinsonde profiles also reveal 2 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, OH on 2 October 2017 presents an interesting Bragg scatter signature as well (Figure 2.7). 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 ILN on 2 October indicates easterly winds at the surface shifting to westerly in the residual layer. The 0000 UTC sounding at ILN 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. In the National Research Council report, Observing Weather and Climate from the Ground Up: A Na- tionwide 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.” To that end, Demoz et al. (2017) demonstrate the utility of the Automated Surface Observing Systems (ASOS) network ceilometers to detect CBL depth across the country. Owing to current 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 requires an extensive review process and may not be possible for several years. The use of dual-polarization radar to detect CBL depth 15 provides readily-available information for operational use as well as an extensive archive of > 4 years of radar data for use in further exploration and refinement of this method. 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 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. 16

Figure 2.7. ZDR QVP for 9 February 2017 in Minneapolis, MN (KMPX), 11 March 2017 Fairbanks, AK (PAPD), 7 May 2017 in Portland, OR (KRTX), 11 June 2017 in Albany, NY (KENX), 17 August 2017 in Tucson, AZ (KEMX), 4 September 2017 in Riverton, WY (KRIW), 2 October 2017 in Wilmington , OH (KILN), and 21 December 2016 in Tampa, FL (KTBW). The time series of minimum ZDR is manually traced with a white line. Rawinsonde estimates of CBL depth at 23 UTC are indicated by the black dot outlined in yellow. White shading indicates regions outside the temporal and spatial range of radar data. 17

Figure 2.8. ZDR QVP (left) for 15 July 2014 and 30 November 2014 in Central Oklahoma (KTLX) showing a double layer of Bragg scatter. Legend is the same as Figure 2.7 excluding the daytime CBL depth estimate for clarity. Vertical profiles of refractivity, potential temperature, mixing ratio, and virtual potential temperature (right) demonstrate vertical gradients of moisture/temperature characteristic of Bragg scatter signatures on radar. Chapter 3

A 10-year Warm-Season Climatology of Horizontal Convective Rolls and Cellular Convection in Central Oklahoma

3.1 Introduction

Horizontal convective rolls (hereafter HCRs or rolls) are common occurrences in the planetary boundary layer and influence boundary layer circulations, boundary layer structure, and initiation of deep convection. Numerous studies have investigated HCR behavior and documented typical HCR characteristics (Schuetz and Fritz, 1961; Angell et al., 1968; Kuettner, 1971; Lemone, 1973; Berger and Doviak, 1978; Reinking et al., 1981; Atkinson and Zhang, 1996; Young et al., 2002), but a robust HCR climatology has yet to be compiled. An increased understanding of HCR characteristics (frequency, spatial scale, orientation, and distribution) is needed, as high-resolution convection allowing models now produce HCR-type features; however, these model-generated HCRs may be caused by erroneous planetary boundary layer parameterizations and the circulations therein (Ching et al., 2014). Additionally, HCRs have been identified as an important factor in initiation of deep convection (Christian and Wakimoto, 1989; Wilson et al., 1992; Fankhauser et al., 1995; Weckwerth et al., 2008), primarily when interacting with boundaries such as dry lines, air mass fronts or those associated with sea breezes. The intent of this research is to develop a 10-year database of HCR characteristics that can be used to investigate a variety of outstanding questions related to HCR formation mechanisms, processes leading to convection initiation, and the accuracy of boundary layer parameterization schemes. The first observation of HCR circulations relied on viewing the flight patterns of soaring birds. When winds were weak, gulls would rise in a corkscrew pattern. When winds increased, however, birds would rise and soar over long horizontal distances (Woodcock, 1942). Based on this observation, Woodcock identified the elongated updraft regions that would later come to be associated with HCRs. Identification of this 19 phenomenon became very useful for glider pilots in the mid-20th century (Kuettner, 1959). The AMS Glossary defines HCRs as “counter-rotating horizontal vortices that commonly occur within the convective boundary layer.” (American Meteorological Society, cited 2019) Along the updraft portion of HCRs, rising air cools and may condense, resulting in cloud formation. These parallel lines of clouds are seen in visible satellite images and are called cloud streets (Kuettner, 1959). Cloud streets are particularly observable in the winter over oceans when cold continental air moves over the warmer ocean, and rising thermals are organized by the prevailing offshore winds into HCRs (Atlas et al., 1983, 1986). As their distance from the shoreline increases, HCRs often transition into cellular convection (Rothermel and Agee, 1980; Bakan and Schwarz, 1992; Atkinson and Zhang, 1996; Kristovich et al., 1999). Past studies document a number of HCR characteristics and note that the evolution of HCRs may be related to the depth of the boundary layer (Fankhauser et al., 1995). HCRs often form with sufficiently strong winds or wind shear (1 to 10 m s−1 km−1) in an unstable boundary layer, which is present when the surface is warmer than the air flowing over it (Atkinson and Zhang, 1996). Such conditions favorable for roll formation frequently occur over land in the warm season or over large lakes and oceans in the winter. Although all HCRs exhibit similar characteristics independent of the environment in which they form, there are some important differences. Rolls that form over land are called narrow rolls (class 1 in Atkinson and Zhang, 1996) because they are characterized by smaller aspect ratios (wavelength/boundary layer depth)(Young et al., 2002). Narrow rolls have an aspect ratio that is independent of boundary layer depth and tend to form in neutral or weakly unstable boundary layers and have aspect ratios of 1 to 4 (Atkinson and Zhang, 1996). In contrast, rolls that form over oceans or large lakes in the cold season tend to have much larger aspect ratios. So-called wide rolls (class 2 in Atkinson and Zhang, 1996) can have wavelengths of up to 30 km and aspect ratios of 10-20 (Atkinson and Zhang, 1996). Wide rolls exhibit aspect ratios that are closely correlated with boundary layer depth (Young et al., 2002). Another HCR characteristic that has been frequently investigated is roll orientation. Expressed as a departure from the mean boundary layer wind or wind shear vector, roll orientation tends to fall within 30◦ of the mean wind direction but most often is observed to occur within 10◦ (Etling and Brown, 1993; Atkinson and Zhang, 1996; Weckwerth et al., 1999). Though both satellites and radar have been used to study HCRs, the most robust way to identify boundary layer circulations is through the use of radar because of a radar’s ability to scan and detect boundary layer circulations even when clouds are not present in the atmosphere. Several studies have identified HCRs using radar observations (Angell et al., 1968; Berger and Doviak, 1978; Hildebrand, 1980; Reinking et al., 1981; Kelly, 1982; Christian and Wakimoto, 1989; Russell and Wilson, 1997; Weckwerth et al., 1997; Yang and Geerts, 2006). Christian and Wakimoto (1989) explore the linear features seen in equivalent reflectivity factor, hereafter reflectivity, associated with cloud streets. They determine that refractive index inhomogeneities associated with the top of the boundary layer are not responsible for these HCR-type features, and instead determine that biota lofted in the updrafts of HCRs produce enhanced reflectivity. In downdraft regions of HCRs, vertical transport of insects and particulates is downward, so reflectivity is lower. Thus, whenever HCRs are present, if there are sufficient biota in the atmosphere, a clear HCR signature of parallel higher- reflectivity bands is observable. Similarly, in the winter, HCRs can form lake-effect snow bands; in this case, the radar detects snowflakes along HCR updrafts. Many of the techniques that utilize radar data to 20 characterize rolls have been developed with data from HCR cases over the Great Lakes in winter. Subtle differences exist between HCRs over land and over water, as discussed earlier and in Atkinson and Zhang (1996), but the radar signatures associated with HCRs in both scenarios are comparable. As such, the techniques used to investigate radar data associated with lake effect HCR bands over the Great Lakes can be applied to overland HCR cases. A majority of our understanding of HCR evolution and characteristics has come from case studies con- sisting of a few to tens of HCR cases. An expanded and clearer understanding of HCR characteristics is vital as we seek to better quantify HCR behavior for use in improving and evaluating planetary boundary layer schemes in convection-allowing numerical weather prediction models. In order to accomplish this goal, the present study characterizes HCR structures and behaviors during the months of April through September over a 10-year period from 2008 to 2017 using observations from the Twin Lakes, OK, WSR-88D (KTLX). This study will provide valuable information with a scope that far exceeds any previous HCR observational study. Central Oklahoma is the location of choice because of the prevalence of insects during the warm- season, when the mean monthly temperatures are above above 16 ◦C. Additionally, the flat terrain and absence of significant beam blockage simplifies observation of boundary layer circulations. Frequent clear-air scanning provided by the KTLX radar, with full volume scans completed every 10 minutes, allows one to investigate the diurnal evolution of HCRs. The 10 years investigated in this study (2008-2017) reflect the most recent set of complete yearly radar data from the KTLX radar in Central Oklahoma. Section 3.2 describes the methods employed to develop a warm-season HCR climatology of boundary layer circulations using radar observations. Results from the climatology in Section 3.3 preface a summary of results and suggestions for future research in Section 3.4.

3.2 Methods for Detection of Boundary Layer Circulations

A low-level plan position indicator (PPI) display of reflectivity from KTLX on 16 June 2014 shows parallel linear regions of enhanced reflectivity indicative of HCRs in the boundary layer (Fig. 3.1a). Reflectivity values within the HCR updrafts in Fig. 3.1 are in the 5-20 dBZ range, consistent with previous studies (e.g. Christian and Wakimoto, 1989). Other types of boundary layer circulations are also observable with radar during the warm season. For example, cellular convection is observed on 29 September 2014 as indicated by roughly circular regions of enhanced reflectivity (Fig. 3.1b). Both PPIs demonstrate the relative ease of visually differentiating echoes associated with HCRs from other types of circulations owing to the linear orientation of parallel bands. Herein, we define “boundary layer organization” as being when HCRs and/or cellular convection are present (as inferred from radar imagery). On the contrary, when there is widespread precipitation or no clear reflectivity pattern, we consider this a lack of boundary layer organization. This characterization will be referenced throughout this manuscript and is a vital building block for the methods outlined next. The methods used in this study can be separated into the following steps: identifying boundary layer organization, differentiating HCRs from cellular convection, and investigating HCR characteristics. These methods were developed using the 2014 data set and are applied uniformly to all other years to complete the climatology. 21

Figure 3.1. Equivalent reflectivity factor at 1.4◦ (a) at 2142 UTC on 16 June 2014 at KTLX, showing a classic HCR signature with clearly-defined linear echoes and (b) at 1836 UTC on 29 September 2014 at KTLX, showing a classic cellular convection signature with clearly-defined circular echoes. Such echoes occur as the radar scans insects lofted in updrafts associated with HCRs. The associated absence of echoes represent locations of downdrafts where insects are vertically suppressed.

3.2.1 Identifying Boundary Layer Organization

The visual appearance of radar reflectivity PPI displays on days with boundary layer organization (defined as times when cellular convection and/or HCRs are present) is distinctly different from days without organiza- tion or with precipitation. A number of methods were evaluated to automate the identification of boundary layer organization using either reflectivity or radial velocity observations, including spatial autocorrelation (Weckwerth et al., 1997) and harmonic analysis (Bloomfield, 2004). The use of autocorrelation and harmonic analysis sought to leverage the periodic behavior of reflectivity for a given radial radar scan. For HCRs, the dominant wavelength of radial reflectivity should maximize for a radial perpendicular to roll orientation and minimize for a radial parallel to roll orientation. For cells, however, there would be very little azimuthal variability in wavelength. Either of these methods could, in theory, identify HCR wavelength and orienta- tion as well. Unfortunately, hybrid HCR/cell cases and heterogeneous signatures across the domain result in inconsistent success using autocorrelation and harmonic analysis, and both methods were abandoned. The method that is found to be most successful at identifying boundary layer organization is based on the velocity azimuth display (VAD) (Browning and Wexler, 1968). The VAD method can be used to estimate wind speed and direction from radial wind observations at a fixed range from the radar. Kelly (1982) uses the VAD technique to identify perturbations in the velocity field associated with circulations of HCRs over Lake Michigan. He finds that HCR circulations produce perturbations in a uniform horizontal wind field, which 22 result in deviations from the VAD best-fit curve. Kelly (1982) quantifies the perturbations by computing residual radial velocity at all radials (radar-derived radial velocities minus VAD best-fit line). This VAD residual radial velocity calculation is effective for quantifying wind perturbations in a single volume scan. In order to investigate boundary layer winds over time, we compute the variance of residual radial velocities (σ2) for each volume scan and produce a time series. Larger residual radial velocity variance, hereafter RRVV, implies larger perturbations in the wind field. Based on Kelly (1982), one might expect RRVV to be higher when boundary layer organization is present owing to HCR wind perturbations. To determine the RRVV characteristics of HCRs, it is helpful to investigate VADs for several different features: precipitation, nocturnal boundary layer, and HCRs (Fig. 3.2). The black line in each VAD (right column) is the sinusoidal fit to the radial velocity observations from radar (blue dots) as a function of azimuth; a purely sinusoidal variation in azimuth represents a perfectly uniform wind field across the radar domain. For the precipitation case (Fig. 3.2a-b), the storm’s flow field causes significant departures from the sinusoidal best-fit line, resulting in rather large residual radial velocities and large σ2. As a result, σ2 values remain large for the duration of the supercell’s lifetime. The nocturnal boundary layer case (Fig. 3.2c-d) exhibits a much more uniform observed wind field, though notably less uniform than the case for HCRs (Fig.3.2e-f). These results imply that radial velocity departures from a sinusoidal best fit are larger when boundary layer organization is absent (precipitation and at night). The idea that a wind field with precipitation is more perturbed than one with HCRs is intuitive, but the enhanced perturbation of a nocturnal boundary layer is less clear at first - especially because of the emphasis on wind field perturbations caused by HCRs in Kelly (1982). We attribute the enhanced wind field perturbations at night to boundary layer decoupling and stabilization. Mahrt (2007) describes “internal gravity waves, microfront-like structures, horizontal modes, and a complex variety of other signatures, perhaps resulting from superposition of different modes” that occur at night in a stable boundary layer. Such structures perturb the wind field in irregular ways and result in increased RRVV. During the day, however, as wind speeds increase and and the boundary layer becomes well-mixed, we hypothesize that these mesoscale structures become muted. As such, the wind field in the radar domain becomes more uniform resulting in reduced RRVV when organization is present. Although HCRs and cells perturb the wind field, the associated perturbations are much smaller than those caused by precipitation and nocturnal mesoscale phenomena. Inspection of a much wider range of radar signatures and VAD-derived winds in this study corroborates the finding that RRVVs from VAD winds are smaller when boundary layer organization is present. An example of the reduction in RRVV due to boundary layer organization is shown in Figure 3.3. VAD winds and RRVV are computed for ranges of 10, 20, 30, and 40 km from the radar to span the depth of the boundary layer (these ranges correspond to beam heights of 0.27, 0.53, 0.80, and 1.08 km). RRVV is calculated over all azimuth angles for each radar scan between 1200 UTC and 0000 UTC. Boundary layer organization is suggested when the variance lines from each range segment are similar. Similarity is determined by calculating the variance of the 4 RRVVs at each time increment. The threshold for organization is when the variance among the 4 time series is less than 1 m4 s−4. In this example, organization is suggested from 1400 UTC to shortly after 2000 UTC. Comparison against the manual identification of boundary layer organization from reflectivity PPI displays (black line) shows that the RRVV method over predicts the duration of organization. 23

The RRVV method is verified against all manually-identified boundary layer organization events in 2014 (Fig. 3.4). VAD RRVV-defined start and end times are compared with manually identified start and end times to compute the difference between them, with positive values indicating an overestimate of boundary layer organization duration. Out of the 179 days in the warm season in 2014, 143 days are identified manually as having boundary layer organization. The RRVV method correctly identifies 140 days with boundary layer organization, with only 3 days on which organization was observed but not diagnosed. Additionally, the mean and median departures for start and end time are positive, indicating that the method diagnoses boundary layer organization ∼ 2.5 h earlier than observed and maintains organization ∼ 30 minutes after it dissipates. With the aforementioned evaluation in mind, this method is then used to identify days on which boundary layer organization is present for all 10 years of the climatology. This method significantly reduces the time and effort spent on manual analysis by filtering ∼20% of the cases (those with precipitation as the dominant weather condition). Only days on which the RRVV method identifies organization are subjected to manual inspection.

3.2.2 Differentiating HCRs from Cellular Convection

Once boundary layer organization (HCRs, cellular convection, or a combination of both) is diagnosed, it is desirable to differentiate between HCRs and cellular convection. Visually, HCRs and cellular convection have distinct differences (Fig. 3.1). HCRs are aligned in linear reflectivity patterns with much larger along- wind extent than cross-wind extent. Cellular convection, however, has a more symmetric reflectivity pattern with many hexagon-like structures. Over the times when boundary layer organization is identified using the VAD RRVV threshold, reflectivity PPIs take at 1.4◦ elevation angle are generated and visually inspected to identify the characteristics of HCRs and cellular convection. The 1.4◦ elevation scan is used to reduce the effects of ground clutter while maximizing the range of boundary layer sampling. Several computational methods were tested in an attempt to differentiate cellular and HCR reflectivity patterns. Autocorrelation, as in Weckwerth et al. (1997), is found to be useful for differentiating between the most ideal HCR and cellular convection cases, but it does not work as well for cases with less clear-cut or hybrid radar signatures. Ultimately, the development of robust computational methods proved time consum- ing and unreliable owing to the continuum over which HCRs and cellular convection manifest themselves. Instead, the identification of HCR start and end time for the remainder of the climatology was conducted manually by visual inspection of all radar imagery during the interval over which boundary layer organization was suggested by the VAD RRVV method. Times are recorded for the onset of HCRs or cellular convection, transitions between both modes, and the dissipation of HCRs and cellular convection. Boundary layer orga- nization is only recorded if rolls or cellular convection persist for at least 30 minutes. If no boundary layer organization is observed, the day is classified as a null case. After all PPI images are investigated and roll/cellular convection cases classified, a final visual check is performed using a loop of radar images each day from 1200 UTC - 0000 UTC. The purpose of this visual check has two purposes: to verify the timings of HCRs and cellular convection evolution; and to identify days on which precipitation is observed or the radar imagery is too complex to effectively classify. The latter task involves independent identification of the occurrence of rolls, cellular convection, precipitation, null cases, 24 or complex features for each day. Based on these results, we then classify individual days into the following categories: Rolls, Cells (cellular convection), Rolls to Cells, Rolls and Precipitation, Cells and Precipitation, Precipitation, Null Case, and Unclear. This classification process results in the climatology that is presented in Section 3.3.1.

3.2.3 HCR Characteristics

The orientation of the roll axis with respect to the mean wind, the roll wavelength, and the roll aspect ratio are important properties for describing HCRs. In order to estimate HCR wavelength and orientation, 1.4◦ reflectivity images are produced for each volume scan within the identified HCR lifetime. The VAD method is used to identify the mean wind direction; the roll orientation with respect to the VAD wind is determined manually. HCR wavelength is also determined manually by counting the number of updraft regions over a 20 to 100 km distance depending on the horizontal extent of HCRs. Wavelength and orientation are determined for the first and last hour of HCR lifetime. Convective boundary layer depth is estimated for the first and last hour of HCR lifetime using differential reflectivity (ZDR) following Banghoff et al. (2018). Finally, wavelength and boundary layer depth are used to determine aspect ratio (wavelength/boundary layer depth) for the first and last hour of HCR lifetime.

3.3 Results

There are 1830 days during the months of April through September over the 10-year period 2008-2017. Of those days, 5 did not have any radar data and 18 had missing radar data for part of the day, resulting in 1807 complete days of KTLX radar data. Boundary layer organization (HCRs and/or cellular convection) is observed on 1382 days (76.5%) with HCRs observed on 1072 days (59.3%). The remaining days include precipitation (313 days or 17.3%), null cases in which no coherent structure is observed (108 days or 6.0%), and radar signatures that are too complex or ambiguous to effectively classify (20 days or 1.1%). Thus, HCRs or cellular convection occur on 76% of the days during this 10-year period, and if the days with precipitation are removed, then over 92% of the days have some form of boundary layer organization for part of the day.

3.3.1 10-Year Climatology

Figure 3.5 shows the monthly climatology for the period 2008-2017. Boundary layer organization occurs on at least 66% of days in each month across the 10-year period, peaking at 83% in July. A majority of the days with precipitation occur in April and May (Figure 3.5a). Separating boundary layer organization by organization type reveals that HCRs occur on a majority of days in each month throughout the warm-season (Fig. 3.5b). Additionally, about one-third of the HCRs undergo transition to or from cellular convection (Fig. 3.5b); these transitions happen more frequently later in the warm-season, during July, August, and September. Separating the climatology by year yields further insights (Fig. 3.6). July 2011 and July 2012 fully consist of days that exhibit boundary layer organization. Additionally, 2015 has the lowest percentage of days with boundary layer organization (66%), whereas 2011 has the largest percentage of days (87%). July 25 and August have the highest frequency of HCR to cellular transition cases, which is especially evident in 2010-2013. In addition, a majority of purely cellular convection days occur in the second half of the warm season. We hypothesize that this is due to generally weaker winds (as in Atkinson and Zhang (1996)) and larger sensible heat flux observed during these months. The majority of HCR fields (individual roll circulations are not tracked in this study) last less than 4 hours, but some HCR fields can persist for longer than 9 hours (Fig. 3.7). Roll duration is most commonly between 1 and 3 hours, with much reduced instances of durations between 4 and 9 hours. When HCRs are the only type of boundary layer organization on a given day, HCR duration is uniformly distributed from half an hour to 8 hours with a drop off in frequency between 8 and 9.5 hours (Fig. 3.7b). When HCRs undergo a transition either from or to cellular convection, the HCR field generally persists for <4 hours (Fig. 3.7c-d). Transitions from HCRs to cellular convection are more common than transitions from cellular convection to HCRs, with 415 cases of the former and 239 of the latter. Analysis of HCR diurnal evolution (Fig. 3.8) shows that HCRs can develop as early as 1438 UTC (0938 local time) and persist past 0000 UTC (1900 local time). All HCR cases that persist after 0000 UTC are grouped in the 2300 UTC bin. Of the 137 days that exhibited boundary layer organization in 2014, 42 had organization after 0000 UTC. Of these days, organization only persisted past 0100 UTC on 1 day. Owing to the organization and download process of WSR-88D data, it is assumed that boundary layer organization dissipates around 0000 UTC for simplicity. Based on the aforementioned 2014 analysis, error acquired by this assumption is considered negligibly small. HCRs formed as late as 2200 UTC, corresponding to very short- duration HCR events. After formation, some HCRs undergo a transition to cellular convection, most often in the early afternoon (1700-1900 UTC; 1200-1400 LT). Cellular convection also can transition to HCRs, often late in the day. About half of the observed cases of transition from cellular convection to HCRs occur on days when HCRs are the first mode of boundary layer organization earlier in the day. The other half of HCR cases develop after cellular convection is the first mode of boundary layer organization. Finally, HCRs and cellular convection dissipate around sunset as surface heating subsides and boundary layer organization is no longer sustained. Sunset times in Central Oklahoma during the warm season range from 0015 UTC to 0149 UTC.

3.3.2 Results from 2013-2017

For the analysis of orientation, horizontal wavelength, and aspect ratio, only data from 2013-2017 are used. These years have a complete set of dual-polarization radar data available, which facilitates estimation of boundary layer depth using differential reflectivity (ZDR) following the methods of Banghoff et al. (2018). Because dual-polarization radar was not implemented at KTLX until October 2012, the years 2008-2012 are excluded from the orientation, wavelength and aspect ratio analysis. HCR characteristics have been investigated in numerous case studies, and observations of HCR wave- length, boundary layer depth, and roll orientation reported. A summary of results from several representative previous studies is shown in Table 2.1. HCRs have previously been observed with horizontal wavelengths ranging from 2 to 18 km, boundary layer depths from 0.6 to 2.2 km, aspect ratios of 1 to 13, and orientation angles generally within 10◦ of the mean boundary layer wind. For the sake of comparison, it is important 26

to note that many of the listed HCR observations are from studies of cold air outbreaks over water. Based on the work of Atkinson and Zhang (1996) and Young et al. (2002), it is expected that such cool-season cases would have somewhat larger wavelengths and aspect ratios compared to warm-season cases. Overland warm-season cases in previous studies have exhibited wavelengths of 2 to 6.5 km and aspect ratios around 3.1. The environmental wind orientation on HCR days and HCR orientation angle departure from the mean wind orientation for the warm-seasons of 2013-2017 are shown in Figure 3.1. Wind directions are computed using the VAD method with radial velocities averaged over the range of 15 to 25 km from the radar cor- responding to a beam height of 0.39 km to 0.66 km. Note that the radar detects the motion of insects, not necessarily the wind (Vaughn, 1985; Drake and Farrow, 1988; Chapman et al., 2011). If insects are not passive tracers, which is possible for large insects such as locusts and butterflies, the radar will detect migration direction and not necessarily wind direction. A majority of wind orientations on HCR days occur near 180◦ with a peak just below 180◦, corresponding to south-southeasterly flow. These wind orientations are representative of typical of warm-season wind direction distributions in Central Oklahoma (United States Department of Agriculture National Water and Climate Center, cited 2019). HCR orientation angle departure is computed by taking the HCR orientation angle minus the VAD mean wind direction. Positive values indicate HCR orientation counterclockwise from the mean wind. Results show that the average HCR alignment is slightly to the left of the mean wind (clockwise, negative departure values) with 98% of cases exhibiting orientation departures <30◦, and 79% aligning within 10◦ (Fig. 3.9). There were 6 cases with orientation departures greater than 30◦ (not shown) but none exceeded 50◦. The orientation angle departure distribution is approximately symmetric around 0◦, suggesting there is not a preferred departure in the counterclockwise or clockwise direction. HCR orientation departures in the present study mirror previous HCR review papers (Atkinson and Zhang, 1996; Young et al., 2002) and case studies listed in Table 2.1. For the present study, the wavelength and aspect ratio analysis is separated into three separate categories: pure HCRs (242 cases), HCRs before transition to cellular convection (pre-transition, 176 cases), and HCRs after transition from cellular convection (post-transition, 103 cases) for a total of 521 HCR cases on 465 days (56 days with HCRs before and after cellular convection). This separation lends itself to discerning important differences between all three types of HCR manifestation. Wavelength and aspect ratio values for the first and last hour of roll duration are investigated (Fig. 3.10). HCR wavelengths are generally between 2 and 8 km in the first hour across all modes (Fig. 3.10a-b, e-f, i-j). All modes undergo an increase in wavelength with time, referred to as cell broadening, from the first to last hour of duration. HCRs that occur before a transition to cellular convection have the shortest average wavelengths throughout their life cycle (2.66 km in the first hour and 3.32 km in the last hour for 175 cases; Fig. 3.10e-f). Shorter wavelengths are observed because these HCRs occur earlier in the day and do not have as much time to undergo cell broadening. On the contrary, HCRs that form after transition from cellular convection have the longest average wavelengths throughout their life cycle (4.53 km in the first hour and 6.97 km in the last hour for 103 cases; Fig. 3.10i-j). HCRs have wavelengths of up to 30 km, but most wavelengths are less than 10 km. There were a total of 44 HCR cases with wavelengths > 10 km (2 pre-transition cases, 19 pure HCR cases, 1 before transition, and 22 after transition; total of 8.5% of all 27

HCR cases). Wavelengths > 20 km occurred on 7 days (6 pure HCR and 1 after transition; 1.3% of all HCR cases) with all of such HCRs observed after 2200 UTC. This result suggests that the upper bound of HCR wavelength is not dependent on the number of transitions between modes of organization in a given day. The 44 cases with wavelengths exceeding 10 km diverge from the narrow, or so-called ”class 1”, rolls associated with overland cases as described in Atkinson and Zhang (1996). These observations also exceed values previously reported for overland cases, and are more characteristic of wavelengths associated with cold-season HCR cases over water, or so-called ”wide roll” cases (Kelly, 1984; Atkinson and Zhang, 1996; Young et al., 2002; Yang and Geerts, 2006). That some overland HCR cases have wavelengths characteristic of wide rolls is novel. Additionally, the overlap in HCR characteristics between overland and cold-season overwater cases across the entire continuum of wavelengths further supports the idea that HCR structure is similar across narrow and wide rolls as suggested by Young et al. (2002). A subset of days in this climatology experience a dual transition in which rolls transition to cellular convection and then transition back to roll-like features late in the day. Such a process has not been previously reported in the literature. Of the 886 days in the 10-year climatology with rolls as the first mode of boundary layer organization, 13.9% underwent a dual-transition (11.5% of all days in the 10-year period). In dual-transition cases, the resultant roll-like features tend to have higher reflectivities and wider wavelengths compared to those of initial roll occurrence. Such signatures imply wider circulations and may also be an indication of stronger updrafts (larger concentration of lofted bugs). One such example of this dual transition is discussed in a case study at the end of this section. Observed aspect ratios are generally between 1 and 8 and less variable than wavelength across the three modes (Fig. 3.10c-d, g-h, k-l). Aspect ratios increase from the first hour to last hour of HCR duration for pure and post-transition HCRs (3.12 in the first hour and 3.94 in the last hour for 232 pure HCR cases; 2.92 in the first hour and 4.28 in the last hour for 101 post-transition HCR cases). This implies that wavelength increases by a larger proportion than boundary layer depth during pure and pre-transition HCR lifetime. The aspect ratios of pre-transition HCRs decrease through HCR lifetime (3.48 in the first hour and 2.54 in the last hour for 172 pre-transition HCR cases; Fig. 3.2g-h), implying that wavelength increases by a lesser proportion than boundary layer depth. Aspect ratios up to 22 are observed, with aspect ratios > 10 in 11 cases (1 first hour HCR before transition, 9 last hour pure HCRs, and 2 last hour HCRs after transition; 2.1% of all HCR cases). A temporal analysis of wavelength and aspect ratio provides a clear understanding of the evolution of and interaction between both variables (Fig. 3.11). There is a clear upward trend in wavelength values from 15 UTC to 23 UTC for all HCR cases in 2013-2017 (Fig. 3.11a). The expansion of HCR wavelength during the day, also called cell broadening, is well-documented (Atlas et al., 1983; Chang and Shirer, 1984; Miura, 1986). The range of wavelengths observed at each hour also increased during the day, suggesting there may be a relationship between HCR wavelength and HCR duration. For example, HCR wavelengths during the 23 UTC hour include rolls that have persisted for less than 1 hour and several hours. A dependence of HCR wavelength on HCR duration would explain the wider range of observed wavelengths later in the day. Aspect ratio is at a maximum (on average) early in the morning during the first hour of roll formation and then decreases, reaching a minimum during the early afternoon (1700-1900 UTC; 1200-1400 LT; Fig. 3.11b). During the morning hours, there is a relatively slow increase in wavelength, so the decreasing aspect ratio 28

implies a more rapid increase in boundary layer depth during the same period. Later in the afternoon aspect ratio increases simultaneously with wavelength. By extension, boundary layer depth must be relatively constant during this time period. The rapid increase and successive flattening out of boundary layer depth derived from this analysis is quite consistent the pattern of boundary layer evolution described by Stull (1988) and shown from radar observations in Banghoff et al. (2018). Combining aspect ratio values from all three modes and separating by month yields information about the seasonal variability of HCRs (Fig. 3.12). There are at least 59 cases included from each month and as many as 106 for the period 2013-2017. During the first hour of HCR evolution, there is a gradual increase in aspect ratio from April until July followed by a drop off in August and September. Aspect ratio values for the last hour have a similar monthly trend with an increase from April until July followed by a decrease. Notably, mean aspect ratio increases from the first hour to last hour of HCR duration in 5 of 6 months (excluding May; Fig. 3.12). Last-hour boundary-layer depth exhibits a similar trend to those of the first hour, with a decrease from April until August and an increase thereafter. The cases from May again deviate as boundary layer depth is less than that of April and June. The last-hour aspect ratio data also exhibits an inverse relationship to boundary-layer depth. Multiplication of average aspect ratio by boundary layer depth indicates that monthly wavelength trends mirror those of aspect ratio. Weckwerth et al. (1997) show HCR wavelength and boundary-layer depth (their Figure 17) for a variety of case studies. This plot is duplicated here as Fig. 3.13, along with the idealized relationship from Kuettner √ (1971) that assumes an aspect ratio of 2 2 based on theoretical calculations using critical Rayleigh number. Results from the present study are overlayed and indicate that first hour HCRs exhibit generally smaller aspect ratios than those in either of the previous studies. Observed values remain within the range of aspect ratios reported in the literature (Table 2.1). The last hour HCR characteristics have much more spread. It appears there may be a bi-modal aspect ratio trend for all HCR cases, though. The first follows the line found by Weckwerth et al. (1997), and the second follows a line with a slope that is slightly shallower than that of Kuettner (1971). Thus far, a discussion of narrow HCRs, cellular convection, and transitions between the two have been discussed. A case study is used to illustrate these various modes and to show differences between narrow HCRs and the observed overland wide rolls that occur late in the day. The case study should also help lay the framework for future investigation of boundary layer organization using radar data with a well-defined example of HCRs that undergo a dual transition to cellular convection and then back to HCRs. Although several days in 2013-2017 could have been used to illustrate boundary layer evolution, 4 June 2015 is selected based on the clarity of radar and satellite data. The high temperature on this day was 32 ◦C with mostly sunny skies and no precipitation. Winds were from the south at 5-7 m s−1 with gusts to 12 m s−1. No surface fronts were in the vicinity. Radar and visible satellite imagery from three different times on 4 June 2015 in Central Oklahoma depict the mean boundary layer organization structures (Fig. 3.14). At approximately 1715 UTC, the KTLX radar begins to show an HCR pattern in reflectivity at the 0.5◦ elevation scan (Fig. 3.14a). These linear features are oriented approximately SSW-NNE along the mean wind direction. The wavelength of these HCRs is approximately 2.5 km. At this point in the day, the boundary layer depth is 0.9 km, below the LCL, yielding an aspect ratio of 2.8. Given that the LCL was approximately 1500 m, boundary layer circulations are not deep enough to 29 produce clouds at this time, as confirmed in visible satellite imagery (Fig. 3.14d). A few hours later, at approximately 1946 UTC, the boundary layer depth is ∼1.5 km and radar reflectivity shows various non-linear patterns of enhanced reflectivity characteristic of cellular convection (Fig. 3.14b). The approximately circular updraft regions indicate that cellular convection has begun and HCR transition has occurred or is occurring. Note that linear features are still evident in the reflectivity field, but there are fewer coherent linear downdraft regions. The radar image at 1946 UTC illustrates the challenges of applying automation to HCR versus cellular convection discrimination. It is difficult even for the human eye to differentiate between both modes. The visible satellite imagery at 1945 UTC shows cloud streets have developed across the eastern half of Oklahoma. Approximately half of the radar domain encompasses the area where clouds have formed (Fig. 3.14e). As sunset approaches (2320 UTC), the mode of boundary layer organization shifts again, this time back to HCRs, with wavelengths closer to those of wide (class 2) rolls as in Atkinson and Zhang (1996). Enhanced reflectivity regions aligned S-N are now thicker and farther apart than earlier in the day (Fig. 3.14c). The wavelength of these updrafts is approximately 9 km. At this point, cloud streets have dissipated across most of eastern OK, but clouds have formed across south central Oklahoma with a classic “string-of-pearls” structure as discussed in Kuettner (1971) (Fig. 3.14f). Dual-transition cases, like the one presented in this case study, effectively encompass the range of HCR modes observed in the warm-season in Central Oklahoma. Boundary layer organization (either rolls or cells), often develops in the late morning or early afternoon in a relatively shallow boundary layer. Through the day, as surface heating persists and the boundary layer deepens, cellular convection or HCRs may persist through the entire day or undergo transition to the other mode. HCR wavelengths often increase owing to the deepening of the boundary layer and expansion of circulations. HCRs that undergo transition to cellular convection in the afternoon also occasionally experience a second transition later in the day back to HCRs. As pure HCRs evolve or when HCRs form a second time late in the day, wavelengths often become larger, and sometimes significantly larger than wavelengths observed earlier in the day. Finally, as sunset approaches and surface heating slows down, boundary layer circulation dissipates and the presence of HCRs or cellular convection on radar becomes indiscernible.

3.4 Summary and Future Work

Boundary layer organization is readily observed using WSR-88D radar data owing to the detection of insects lofted by boundary layer thermals. The widespread availability of radar data on clear air days lends itself well to investigating boundary layer organization and HCR behavior. We performed an analysis of 10 years of clear-air WSR-88D data over central Oklahoma and identified and characterized horizontal convective rolls and cellular convection during the warm-season (April-September). Results indicate that HCRs or cellular convection, grouped here as boundary layer organization, occur on 76% of the warm season days in Oklahoma. HCR wavelengths are typically between 2 and 10 km, but can be as large as 30 km, and 82% of HCRs exhibit increasing wavelength during their lifetime with an additional 15% maintaining constant wavelength. HCRs align, on average, approximately parallel to the mean boundary layer wind, but can align as much as 50◦ to the right or left of the mean wind (98% within 30◦ and 79% within 10◦). A majority 30

Table 3.1. Summary of HCR observations reported in the literature

Reference Nature of study Wavelength PBL Aspect HCR (km) Depth Ratio Orientation Angell et al. (1968) Radar tracking of tetroons 4 1.4 2.9 =19 in SE Idaho, clear air Atlas et al. (1983) Cold air outbreak in NY 3-10 1.0-1.4 3-7 φ=0 and NJ Atlas et al. (1986) Cold air outbreak along 1-2 0.6-0.8 1.3-3.3 φ=0 the coasts of the mid- Atlantic states Berger and Doviak (1978) Dual Doppler radar data 4 1.5 2.7 φ = 20 near Norman, OK Hildebrand (1980) Dual Doppler radar data 4-4.8 1-1.4 3.4-4 φ=0 from Central Oklahoma Kelly (1982) Lake effect snow over Lake 3.5-7.5 1.3 2.7-5.8 =0 Michigan Kelly (1984) Cold air flow over Lake 1.5-13.7 0.9-2.1 1.0-9.1 =-10 - 10 Michigan Kropfli and Kohn (1978) Dual-Doppler radar data 5 - - - near St. Louis, MO Kuettner (1971) Measurements from satel- 2-8 0.8-2 2-4 =0-10 lite phots and raobs over tropical Atlantic, Florida, Wisconsin, Gulf of St. Lawrence, and Georgia Lemone (1973) Tower and/or aircraft 1.3-6.5 0.6-2.3 2.16-6.5 =10-20 probes over Great Lakes and in Oklahoma; clear air Reinking et al. (1981) Dual Doppler radar data 2-6 1.1-1.5 avg 2.7 φ=10-20 near Chickasha, OK Weston (1980) Visible satellite imagery 2.5-9 - avg 3.2 φ=-25-25 and rawinsondes over England Yang and Geerts (2006) Cold air flow over Lake 2.5-18 1.1-1.37 2-13 φ=-10 Michigan  = counterclockwise from inversion level geostrophic wind φ= counterclockwise from mean BL wind

of HCRs, however, align within 10◦ of the mean wind, which matches the findings in past studies (Table 2.1). This study, however, includes 462 cases, which far exceeds any previous work and bolsters confidence in these results. HCRs are observed to persist as the only mode of boundary layer organization for a given day or undergo transition to or from cellular convection. Pure HCRs occur on 471 days during the 10-year climatology (26% of all days, 34% of all days with boundary layer organization, and 44% of days with HCRs). The most 31 common transition observed between modes of boundary layer organization occurs when HCRs develop prior to a transition to cellular convection. This occurs on 415 days over the 10-year climatology (23% of all days, 30% of days with boundary layer organization, and 39% of days with HCRs). A less common, though repeatable transition, involves the transition from cellular convection to HCRs late in the day (often within an hour or two of sunset). This transition occurs on 239 days, with 129 of those HCRs reforming after a transition to cellular convection earlier in the day. HCRs that form for the first time on a given day following a transition from cells account for 6% of all days, and 8% of days with boundary layer organization, and 10% of all days with HCRs. The occurrence of HCRs with wavelengths greater than 10 km and up to 30 km late in the day represents a unique finding from this study. Such large wavelengths have been observed in previous studies, but only over water during the cold season (Table 3.1). The HCRs are representative of wide rolls observed over water during cold air outbreaks as described in Young et al. (2002), but deserve further investigation. Young et al. (2002) notes a major difference between narrow and wide rolls is the number of thermal updrafts responsible for sustaining the roll circulation. He suggests that narrow rolls are usually sustained by a single updraft with embedded smaller-scale turbulent fluctions, whereas wide rolls are generally accompanied by multiple thermals within a given updraft. A modeling study using a large eddy simulation (LES) framework could prove useful at elucidating the dynamic and thermodynamic factors that influence the formation of these HCR-like features late in the day. Previous studies have used LES to simulate rolls, but model energetics and computational constraints have led to conflicting results (Glendening, 1996; Weckwerth et al., 1997). A high-resolution, large-domain, high-lid radiative boundary condition LES, as suggested by Young et al. (2002), could be used to investigate this overland wide roll phenomena. The combination of HCR wavelength data and boundary layer depth estimates based on the method of Banghoff et al. (2018) from April through September in 2013-2017 provide additional insights into HCR characteristics. Boundary layer depths observed when HCRs or cellular convection is present range from about 500 m to 2 km and deepen during the day. Aspect ratios (wavelength/boundary layer depth) increase during the day for 5 out of 6 months over the 5-year period. Aspect ratios are most often between 1 and 8 with values of up to 22 observed. The present study investigates aspect ratio for the first and last hour. A temporal analysis of wavelength and boundary layer depth would be useful to determine the relative importance and diurnal variation of both variables as they relate to aspect ratio. The VAD residual radial velocity variance method effectively identifies boundary layer organization, but the goal of differentiating between HCRs and cellular convection remains unmet. Several methods to automatically determine HCR characteristics were tested, but none performed satisfactorily compared to manual methods. The use of Fast Fourier Transforms and spatial correlation as in Weckwerth et al. (1997) sought to leverage the periodic structure of reflectivity for HCRs. Radial scans perpendicular to roll orientation result in a sinusoidal reflectivity pattern as the radar beam passes through alternating updrafts and downdrafts. In principle, applying a Fast Fourier transform or spatial autocorrelation to the resultant radial plot of reflectivity can help identify the wavelength of HCRs. Another method involved transforming the format of radar data from polar to Cartesian coordinates. Such a process facilitates shifting of images perpendicular to roll orientation to quantify correlation at various horizontal displacements. Each of the aforementioned methods, in principle, would have distinctly different responses for rolls and open cells. 32

All methods proved promising but not widely successful. One explanation for this lack of success may be that radar data are plotted for a given elevation angle, which results in sampling of different parts of the convective structures at differing ranges. As such, the boundary layer structure is not planar and may skew the periodicity of HCR structure. In addition, the 2014 and 2015 data sets were run through a series of artificial intelligence/image processing software using convolutional neural nets to attempt to identify HCRs with some degree of success. They showed some skill in differentiating obvious roll cases from obvious cellular convection cases, but less skill in differentiating marginal cases. It would be worthwhile to use the full 10 years of boundary layer organization radar imagery to develop and test an image processing algorithm that could be used expedite the HCR identification process in other years or locations. A next step is investigating roll and cellular convection formation mechanisms. Previous studies have investigated the role of parallel, convective, and inflection point instability in HCR formation and charac- teristics, but it is still unclear which mechanism is more important (Lemone, 1973; Brown, 1980; Stensrud and Shirer, 1988). Cloud cover has also been implicated in HCR formation mechanisms and bears further investigation as in Sykes et al. (1988). Parsing out a single formation mechanism for rolls has proven diffi- cult owing to the complexity of boundary layer processes, the similarity of shear and wind directions in a well-mixed boundary layer, and computational limitations. Future research in this area should be two-fold: utilizing high-resolution surface observations from a mesonet or similar network in order to investigate a wide range of boundary layer characteristics, and leveraging improved computational capabilities for LES studies that focus on roll formation mechanisms and secondary transition roll-like generation over land. Now that typical HCR initiation and dissipation times, frequency, wavelength, and aspect ratio are quantified, these results can be used to compare against the occurrence of HCR-like signatures in high- resolution model output (Ching et al., 2014). Similar climatologies could be developed in different locations across the country, especially if a more robust algorithm could be developed to automate identification of the presence of HCRs on radar. The rapidly increasing amount and availability of meteorological observations is a treasure trove for gaining a better understanding of HCR formation mechanisms and characteristics in the future. 33

Figure 3.2. 0.5◦ Z (dBZ), 0.5◦ V (m s−1), and velocity azimuth display (VAD) computed between 35 and 45 km from KTLX during (a-c) a supercell thunderstorm on 1 June 2016, (d-f) a nocturnal boundary layer on 11 June 2016, and (g-i) HCRs on 22 June 2016. The variance (σ2) of residual radial velocity (observed winds minus VAD-estimated winds) is listed on each VAD plot. Notice the residual radial velocity variance (RRVV) is largest for the precipitation case and lowest for the HCR case. Lower variance implies increased uniformity of boundary layer winds. 34

10 5-15km 9 15-25km 25-35km 8 35-45km Variance Organization 7 Manual Organization

6

5

4

3 Residual Velocity Variance

2

1

0 12 14 16 18 20 22 00 Time (UTC)

Figure 3.3. Time series of of residual radial velocity variances (RRVVs, m2 s−2) from VAD analysis for 29 July 2014 at KTLX. Velocity azimuth displays and RRVVs are calculated for range rings of 10, 20, 30, and 40 km distance from the radar (beam heights of 0.27, 0.53, 0.80, and 1.08 km respectively). The red bar indicates the algorithm-identified time range of boundary layer organization. Organization is defined when the variance among the 4 VAD RRVVs drops below 1 m4 s−4 implying a convergence of the various time series. The black bar indicates manually-identified boundary layer organization. 35

30 (a) Mean: -136.25 Mean: 47.04 Median: -148 (b) Median: 55 # of days: 134 # of days: 134 25

20

15 # of days

10

5

0 -600 -400 -200 0 200 400 600 -600 -400 -200 0 200 400 600 Organization Start Time Departure (minutes) Organization End Time Departure (minutes)

Figure 3.4. Comparison of VAD RRVV analysis and manual analysis for start and end times of boundary layer organization. Organization departure is computed as TRRV V -Tmanual where T<0 indicates RRVV analysis times are earlier than manually-identified times. Note that timing from the RRVV method over-estimates the range of actual organization (i.e. RRVV analysis has earlier start times and later end times than found from the manual analysis). Departures for (a) start times and (b) end times from 134 days with organization in 2014 are included. 36

100 Boundary Layer Organization Rolls to Cells Rolls 90 (a) Precipitation (b) Null Case Rolls and Precipitation Unclear Cells 80 Cells and Precipitation

70

60

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40

% of days in the month 30

20

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0 Apr May Jun Jul Aug Sept Apr May Jun Jul Aug Sept Month Month

Figure 3.5. (a) Cumulative 10-year warm-season climatology of HCRs in Central Oklahoma separated by month showing the percentage of days that exhibit boundary layer organization, widespread precipitation, and the absence of boundary layer organization (null cases), along with cases deemed indiscernible (unclear). (b) For each month, boundary layer organization days are separated into HCRs (left columnn) and cellular convection (right column). Transition cases (both HCRs and cells, so doubly represented), pure HCRs/cells and a mix of organization and precipitation are delineated. Note that a majority of days in each month have HCRs, and nearly 75% of all days have boundary layer organization. 37

Figure 3.6. As in Figure 3.5, but separated by year. Data are based on visual observation of base reflectivity between 1200 UTC and 0000 UTC from the Twin Lakes, OK (KTLX) WSR-88D radar. 38

150 80 (a) All HCRs (b) Pure HCRs 70 125 60 100 50

75 40

# of days 30 50 20 25 10

0 0 80 80 (c) HCRs that transition to Cells (d) HCRs that Transition from Cells 70 70

60 60

50 50

40 40

# of days 30 30

20 20

10 10

0 0 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 Duration (hours) Duration (hours)

Figure 3.7. HCR duration for April-September of 2008-2017 at KTLX. Durations are broken down in (a) all HCR cases, (b) days where HCRs are the only boundary layer organization, (c) days when HCRs undergo transition to cellular convection, and (d) days when HCRs are formed via transition from cellular convection. 39

450 Roll Formation 400 Rolls Transition to Cells Rolls Transition from Cells 350 Roll Dissipation

300

250

200 # of days

150

100

50

0 14 15 16 17 18 19 20 21 22 23 Time (Hours UTC)

Figure 3.8. Histogram of HCR timing during the warm-season from 2008-2017 at KTLX. All HCR cases that persist after 0000 UTC are grouped in the 2300 UTC bin (42 cases in 2014 with only 1 case persisting after 0100 UTC). 40

160 0 (a) (b) Mean: -1.62 330 30 140 Median: -2.23 # of days: 456 120 300 60 50 100 25 80 270 90 60 # of days 40 240 120 20

210 150 0 180 -30 -20 -10 0 10 20 30 Roll Orientation Departure ( °)

Figure 3.9. (a) Wind direction calculated from the VAD wind at the onset of HCRs each day from April - September 2013-2017 at KTLX. (b) Histogram of the departure of HCR orientation from the mean wind direction for the days. Positive values indicate HCR orientation is to the right of the mean wind (counterclockwise). Note that there are 5 cases with departures above 30◦ not exceeding 50◦ (not shown). 41

Pure HCRs HCRs Before HCRs After Transition to Cells Transition From Cells 125 80 25 (a) Average: 2.93 km (e) Average: 2.66 km (i) Average: 4.53 km 100 Total # of Days: 241 Total # of days: 175 20 Total # of Days: 103 60

75 15 First 40 Hour 50 10

20

Number of Days 25 5

125 80 25 (b) Average: 5.51 km (f) Average: 3.32 km (j) Average: 6.97 km 100 Total # of Days: 241 Total # of Days: 173 20 Total # of Days: 103 60

75 15 40 Last 50 10 Hour

20 25 5 Number of Days

0 0 0 0 5 10 15 20 25 30 0 5 10 15 20 25 30 0 5 10 15 20 25 30 Wavelength (km) Wavelength (km) Wavelength (km)

50 60 30 (c) Average: 3.12 (g) Average: 3.48 (k) Average: 2.92 50 25 40 Total # of Days: 232 Total # of Days: 172 Total # of Days: 101 40 20 30 30 15 First 20 Hour 20 10 10 Number of Days 10 5

50 60 30 (d) Average: 3.94 (h) Average: 2.54 (l) Average: 4.28 40 Total # of Days: 232 50 Total # of Days: 170 25 Total # of Days: 101 40 20 30 30 15 Last 20 20 10 Hour

Number of Days 10 10 5

0 0 0 0 5 10 15 20 25 0 5 10 15 20 25 0 5 10 15 20 25 Aspect Ratio ( ) Aspect Ratio ( ) Aspect Ratio ( )

Figure 3.10. Histograms of HCR wavelength and aspect ratio for all HCR days during the warm-seasons of 2013- 2017 at KTLX. First and last hour wavelength and aspect ratio are plotted for pure HCR cases (a-d), HCR cases that transition to cellular convection (e-h), and HCR cases that transition from cellular convection (i-k). 42

15 10 (a) (b)

9 13

8

11 7

9 6

5 7 Aspect Ratio Wavelength (km)

4 5

3

3 2

1 1 15 16 17 18 19 20 21 22 23 15 16 17 18 19 20 21 22 23 Time (UTC) Time (UTC)

Figure 3.11. Time series of box and whiskers plots for HCR (a) wavelength and (b) aspect ratio for all HCR days during the warm-seasons of 2013-2017 at KTLX. There number of cases for each hour is as follows: before 16 UTC: 58; 1600-1659 UTC: 127; 1700-1759 UTC: 134; 1800-1859 UTC: 119; 1900-1959 UTC: 90; 2000-2059 UTC: 100; 2100-2159 UTC: 93; 2200-2259 UTC: 110; after 2300 UTC: 220. Note that 7 cases have wavelengths above 15 km and 8 have aspect ratios above 10 after 2300 UTC (not shown). 43

First Hour Last Hour

Average PBL depth: 1.37 km Average PBL depth: 1.68 km Total # of cases: 79 Total # of cases: 78 A

Average PBL depth: 1.22 km Average PBL depth: 1.55 km Total # of cases: 58 Total # of cases: 59 M

*Outlier: 12.5

Average PBL depth: 1.19 km Average PBL depth: 1.56 km Total # of cases: 106 Total # of cases: 106 J

*Additional Outlier: 16.1

Average PBL depth: 1.08 km Average PBL depth: 1.47 km Total # of cases: 106 Total # of cases: 105 J

*Outliers:10, 11.4, 19.4, 20

Average PBL depth: 1.09 km Average PBL depth: 1.32 km Total # of cases: 77 Total # of cases: 76 A

Average PBL depth: 1.15 km Average PBL depth: 1.55 km Total # of cases: 79 Total # of cases: 79 S

*Additional Outlier: 16.5 0 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 Aspect Ratio Aspect Ratio

Figure 3.12. Box and whisker plot of aspect ratio in the first hour of HCR activity and the last hour of HCR activity prior to any transition for each day and grouped by month for 2013-2017 (A=April, M=May, J=June, J=July, A=August, S=September). The corresponding average monthly boundary layer depth estimates are listed in the top right of each figure. Vertical black lines on the right figures correspond to the mean aspect ratio during the first hour. The black arrow denotes the change in aspect ratio from first hour to last hour. 44

15 Kuettner(1971) Weckwerth(1997) Weckwerth(1997) First Hour Last Hour

10

5 Roll Wavelength (km)

0 0 0.5 1 1.5 2 2.5 3 3.5 Boundary Layer Depth (km)

Figure 3.13. Boundary layer depth vs. roll wavelength as in Weckwerth et al. (1997) (their Figure 17). Plotted are lines of best-fit from Kuettner (1971) and Weckwerth et al. (1997) and observations of HCRs in Central Oklahoma during 2013-2017. 45

Figure 3.14. Case study of boundary layer organization on 4 June 2015 at KTLX. Top row shows reflectivity and bottom row shows visible satellite imagery at the corresponding time. Note the transition from HCRs to cellular convection and back to HCR-like organization, except with a much larger wavelength. Black box represents the radar domain. Chapter 4

Conclusion

The usefulness of National Weather Service WSR-88D radars is well-documented for hazardous weather conditions, but the results presented herein demonstrate the value of radar data for investigation of clear-air weather phenomena as well. Over the 10-year period from 2008-2017, 69% of the days during the warm season were precipitation-free. At least 30 minutes of boundary layer organization (cellular convection or horizontal convective rolls) was observed on a total of 89% of days. Although clear-air weather conditions are typically not hazardous, boundary layer structure associated with clear-air processes affect air pollution, wildfires, and convection initiation. The results presented herein demonstrate two applications of radar data to investigate clear air phenomena: convective boundary layer (CBL) depth estimation and boundary layer organization (horizontal convective rolls (HCRs) or cellular convection) characterization. Convective boundary layer depth estimation is possible because gradients in temperature and moisture exist at the top of the CBL. Historically, CBL depth estimation in the United States has been conducted by launching rawinsondes twice daily into the atmosphere at 97 locations. Given that the CBL is not well- developed at 1200 UTC when rawinsondes are launched, the 0000 UTC launch provides the only reasonable estimate of CBL depth. In this study, we have shown that WSR-88D dual-polarization radar is able to detect the refractive index gradient at the top of the boundary via a local reduction in ZDR values to near zero. The 159 WSR-88Ds located across the United States that scan the atmosphere continuously every day provide much higher spatiotemporal-resolution boundary-layer depth estimates compared to those of rawinsondes. The methods used to estimate CBL depth are shown to be effective in a variety of locations and environmental conditions. Eventually, extension of this algorithm to automatically estimate CBL depth across the country in real-time is desired. Another application of radar information in clear-air environments is the identification and characteri- zation of horizontal convective rolls (HCRs) and cellular convection. Analysis shows that boundary layer organization occurs on 76% of the days and HCRs occur on 59% of the days during the warm season (April- September) in central Oklahoma. Observations of wavelength, orientation, aspect ratio (wavelength/CBL depth), and timing of roll evolution matches previous findings but provides a significantly larger sample size than any previous work. The reported HCR characteristics can be used to investigate planetary boundary 47 layer schemes used in numerical modeling and validate model generation of HCR-like features as in Ching et al. (2014). Additionally, the methods developed for this study provide a foundation for designing an algorithm to automatically identify HCR circulations as sampled by radar. Expansion of these HCR iden- tification methods to other locations across the country or other modes of HCRs (Great Lakes or over the ocean) would provide further insights. Dual-polarization radar provides a wealth of information about clear-air boundary layer processes not previously explored in such detail. Future work in this area is promising and, with the help of convolutional neural nets or other advanced technology, may lead to greater efficiency and accuracy for characterizing boundary layer phenomena. Incorporation of CBL depth estimates or HCR characteristics in numerical models through the use of data assimilation could significantly improve model representation of boundary layer structure. Clear air days are a dream for operational meteorologists because of the ability to catch up on projects or complete required training. But with the implementation of dual-polarization radar information and the increased spatial resolution of numerical weather models, the weather community may benefit greatly from investigation of clear-air phenomena in the months and years to come. Bibliography

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