Wide Horizontal Convective Rolls over Land

David J. Stensrud aDepartment of Meteorology and Atmospheric Science, The Pennsylvania State University, University Park, Pennsylvania

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George S. Young aDepartment of Meteorology and Atmospheric Science, The Pennsylvania State University, University Park, Pennsylvania

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Matthew R. Kumjian aDepartment of Meteorology and Atmospheric Science, The Pennsylvania State University, University Park, Pennsylvania

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Abstract

Horizontal convective rolls (HCRs) with aspect ratios ≥ 5, called wide HCRs, are observed over land from WSR-88D radar reflectivity observations in clear air over central Oklahoma. Results indicate that wide HCRs are a natural part of the daily HCR life cycle, occurring most frequently from 1500 to 1700 UTC and from 2300 to 2400 UTC, with the HCRs having aspect ratios ∼ 3 during the rest of their lifetime. Wide HCRs are most likely to be observed from HCRs with lifetimes longer than 5 h. Results show that for HCRs lasting for more than 5 h, 12% have aspect ratios ≥ 5 during HCR formation, whereas 50% of have aspect ratios ≥ 5 at dissipation. An evaluation of radar observations from 50 cases of long-lived HCRs suggests the wide HCRs that occur in tandem with HCR formation early in the day develop in situ with a large aspect ratio. In contrast, the cases of wide HCRs that form late in the day most often appear to develop as specific HCR wavelengths are maintained while roll circulations with smaller wavelengths dissipate. These ephemeral wide HCRs over land deserve attention as the mechanisms leading to their formation are unclear.

Significance Statement

The atmospheric boundary layer extends from the ground up to a typical daytime height between 500 m and 3 km. Within this layer, the flow is often turbulent during the daytime, although there are common structures that help to organize the flow patterns. One of these structures is a field of horizontal counterrotating helical circulations, with parallel upwelling and downwelling zones. This study shows that the separation distance between these long parallel lines of upward and downward motion changes during the day and can be quite large when compared to the depth of the boundary layer, both early in the day and late in the day. Reasons for this behavior are unclear and deserve attention, as the boundary layer is where we spend our lives and has a large influence on our daily activities.

© 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: David J. Stensrud, david.stensrud@psu.edu

Abstract

Horizontal convective rolls (HCRs) with aspect ratios ≥ 5, called wide HCRs, are observed over land from WSR-88D radar reflectivity observations in clear air over central Oklahoma. Results indicate that wide HCRs are a natural part of the daily HCR life cycle, occurring most frequently from 1500 to 1700 UTC and from 2300 to 2400 UTC, with the HCRs having aspect ratios ∼ 3 during the rest of their lifetime. Wide HCRs are most likely to be observed from HCRs with lifetimes longer than 5 h. Results show that for HCRs lasting for more than 5 h, 12% have aspect ratios ≥ 5 during HCR formation, whereas 50% of have aspect ratios ≥ 5 at dissipation. An evaluation of radar observations from 50 cases of long-lived HCRs suggests the wide HCRs that occur in tandem with HCR formation early in the day develop in situ with a large aspect ratio. In contrast, the cases of wide HCRs that form late in the day most often appear to develop as specific HCR wavelengths are maintained while roll circulations with smaller wavelengths dissipate. These ephemeral wide HCRs over land deserve attention as the mechanisms leading to their formation are unclear.

Significance Statement

The atmospheric boundary layer extends from the ground up to a typical daytime height between 500 m and 3 km. Within this layer, the flow is often turbulent during the daytime, although there are common structures that help to organize the flow patterns. One of these structures is a field of horizontal counterrotating helical circulations, with parallel upwelling and downwelling zones. This study shows that the separation distance between these long parallel lines of upward and downward motion changes during the day and can be quite large when compared to the depth of the boundary layer, both early in the day and late in the day. Reasons for this behavior are unclear and deserve attention, as the boundary layer is where we spend our lives and has a large influence on our daily activities.

© 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: David J. Stensrud, david.stensrud@psu.edu

1. Introduction

Horizontal convective rolls (HCRs) are horizontally aligned, counterrotating vortices that often form across large horizontal regions when the mean boundary layer wind speed exceeds ∼6 m s−1 (Woodcock 1940; Weckwerth et al. 1997; Santellanes et al. 2021). HCRs extend from Earth’s surface to near the top of the planetary boundary layer and are observed over both water and land (Atkinson and Zhang 1996; Young et al. 2002). Analysis of tall-tower observations suggests that HCRs play an important role in the vertical transport of heat, moisture, and momentum within the boundary layer (LeMone 1973). HCRs also are known to be an important factor contributing to the initiation of deep convection (Wilson et al. 1992; Fankhauser et al. 1995; Xue and Martin 2006) and lake-effect snow (Kelly 1982; Kristovich 1993). Clouds may form in the updraft branch of the vortices, yielding parallel cloud bands called streets (Kuettner 1959) and making the visible identification of HCRs possible. Many of the early HCR studies use aircraft or satellite images to determine the presence of rolls and investigate the environmental conditions under which they form (Kuettner 1959; Planck 1966; Kelly 1982, 1984). Weather radars also observe HCRs, evident as linear bands of enhanced radar reflectivity factor (Hardy and Ottersten 1969; Konrad 1970; Christian and Wakimoto 1989; Weckwerth et al. 1997) due to an increased concentration of insects in regions of upward motion (Wilson et al. 1994; Geerts and Miao 2005). Banghoff et al. (2020) use operational WSR-88D radar observations to document warm-season HCRs in central Oklahoma over a 10-yr period and find that HCRs occur on more than 70% of days without precipitation. Most HCRs form by midmorning and last a few hours, although on some days HCRs persist until early evening.

One particularly useful and important parameter for describing HCRs is the aspect ratio, defined as the horizontal spacing of the linear updrafts (i.e., the wavelength) divided by the convective boundary layer (CBL) depth. Studies show that HCRs typically have aspect ratios < 5 (Atkinson and Zhang 1996), although HCRs with large aspect ratios (called wide HCRs) have been observed over water in association with cold-air outbreaks (e.g., Holroyd 1971; Walter 1980; Miura 1986). Results from many previous HCR studies are compiled by Young et al. (2002) in their review paper and show that a striking difference between the HCRs over water and land is that the overwater HCR aspect ratios increase with boundary layer depth, whereas the overland HCR aspect ratios vary little with boundary layer depth. Their results also suggest that although wide HCRs (aspect ratios > 5) are common over water, they have not been observed over land.

Theoretical and modeling studies suggest that wide HCRs are produced via an interaction between HCRs, boundary layer thermals, and gravity waves (Townsend 1965; Clark et al. 1986; Balaji et al. 1993; Melfi and Palm 2012). As HCRs develop, their circulations and embedded eddies perturb the overlying stable layer that exists at the top of the CBL, thereby acting to obstruct the flow in the stable layer, and gravity waves are formed. Once gravity waves are present the waves can influence the horizontal scale of the HCR vertical circulations. Depending upon environmental conditions, the gravity waves may have a longer wavelength than the HCRs, and thus provide a mechanism for the development of wide HCRs. Results from Melfi and Palm (2012) show good agreement between the HCR wavelengths estimated from the Townsend (1965) analytical model and observations for HCRs over the North Atlantic Ocean.

The 10-yr central Oklahoma HCR climatology of Banghoff et al. (2020) presents evidence of wide HCRs also being present over land, as well as HCR aspect ratios that vary with boundary layer depth over land. These wide HCRs over land are transitory, lasting an hour or two, in contrast to wide HCRs over water that can persist for days. The wide HCRs over land are seen both early in the morning with shallow boundary layers, and late in the day with deeper boundary layers (their Fig. 12). In the middle of the day, the aspect ratios reach a minimum near the value of 22 suggested by linear theory (Asai 1970; Kuettner 1971; Brown 1980). Thus, aspect ratios during the first half of the day decrease with boundary layer depth, whereas aspect ratios during the last half of the day increase with boundary layer depth, a strikingly different evolution of roll planform than seen with HCRs over water. The presence of wide HCRs over land and aspect ratios that vary on an hourly time scale deserve further exploration.

The goal of this study is to document in greater detail the evolution of wide HCR cases seen in the Banghoff et al. (2020) dataset and explore whether there are environmental clues that can identify the physical process that leads to the dramatic increase in aspect ratio associated with these HCRs over land. Section 2 describes the data and methods used in the analysis. Results of the analyses are presented in section 3, followed by a discussion in section 4.

2. Data and methods

a. HCR dataset

The 10-yr warm-season HCR and cellular convection dataset created by Banghoff et al. (2020) using WSR-88D radar observations from central Oklahoma is used as the beginning point for this research. The dataset includes the start and end times of HCR fields from 1 April to 30 September with calculations of aspect ratios at these two times for the years 2013–17, as well as information on any transitions to and from cellular convection. To simplify the analysis, we select days where a field of HCRs extends across the radar volume and is the dominant circulation pattern, thereby neglecting all transition cases in which cellular convection dominates for part of the day. We also define wide HCRs as those having an aspect ratio ≥ 5 at any point during their lifetime, based on suggestions by both Atkinson and Zhang (1996) and Young et al. (2002) that HCRs over land typically have aspect ratios < 5.

With these criteria in mind, an investigation of the Banghoff et al. (2020) dataset from 2013 to 2017 (when dual polarization radar data are available) reveals that wide HCRs are more likely to occur from HCRs with longer lifetimes. Out of the 100 days with HCR lifetimes ≥ 5 h, there are 23 wide HCR events (23%). In contrast, out of the 242 days with HCR lifetimes < 5 h, there are only 17 wide HCR events (∼7%). Thus, the occurrence of wide HCRs is over 3 times more likely for longer-lived HCRs. The longer-lived HCRs have a mean start time of 1700 UTC (1100 LT; subtract 6 h for LT), with mean aspect ratios increasing from 3.5 at start time to 7.8 at end time. A similar increase in mean aspect ratio is seen in the wide HCR cases associated with shorter HCR lifetimes. These results help explain why wide HCRs over land have not been observed previously, as they only occur on 4% of the days during the warm season, and the large aspect ratios are more apparent late in the day. It takes a multiyear climatology, such as that conducted by Banghoff et al. (2020), to observe these behaviors.

Because one of our research goals is to determine whether there are environmental clues to the increase in aspect ratio that leads to wide HCRs, it is important to select HCR days that span the spectrum of pure HCR events in Banghoff et al. (2020). Thus, we select 50 long-lived HCR events, with preference given to the longest lifetimes, making sure that 10 events represent cases of wide HCRs. The shortest-lived HCR is 5 h, and the longest-lived HCR is 9 h in the 50 cases, with an average HCR lifetime of 7.6 h.

b. Dual-polarization radar observations

Radar observations from the Twin Lakes, Oklahoma (KTLX) dual-polarization WSR-88D radar are used to provide observations on times of HCR formation and dissipation, HCR wavelength, and CBL depth. The values of HCR wavelength and CBL depth then are used to calculate HCR aspect ratio.

The presence of a field of HCRs is determined using a 1.5° elevation angle plan position indicator (PPI) display of the KTLX equivalent radar reflectivity factor (hereafter reflectivity) observations. This elevation angle is chosen to avoid issues with ground clutter and thereby provide the clearest observation of the CBL circulations. The linear reflectivity features associated with HCRs are visually identified by animating the PPIs during the daytime hours. This same approach to HCR identification is used by Banghoff et al. (2020). The WSR-88D radars likely sample HCRs earlier and later in the daytime hours compared to satellites because clouds are not needed to identify the HCR patterns in reflectivity observations.

Horizontal wavelength is determined by measuring the distance between the centers of 3 parallel linear reflectivity lines as displayed on the PPI (an example is shown in Fig. 1). The distances are measured at multiple locations across the HCR field displayed on the PPI and used to subjectively determine a consensus separation distance. Although the KTLX observations are available every 10 min or so, HCR wavelengths vary more slowly, so hourly time intervals are used. The horizontal wavelength is smaller earlier in the day (Fig. 1a) when the CBL is shallow and increases during the daytime hours. The change in wavelength from 1700 to 2000 UTC (1100 to 1400 LT) is not large (cf. Figs. 1a,b) in contrast to the change from 2000 to 2400 UTC that has a visually evident increase in wavelength (cf. Figs. 1b,c). The observations show that HCRs can meander, and the width of the high-reflectivity zone can vary, leading to some uncertainty in the wavelength calculations. The orientation of the HCRs, as identified by the angle of the parallel reflectivity lines, can change during the day as the CBL deepens, which alters the vertical wind shear in the CBL, and as the low-level winds evolve owing to mesoscale and synoptic-scale processes.

Fig. 1.
Fig. 1.

Example of method to determine HCR horizontal wavelength between the centers of three linear reflectivity features. Red lines indicate the center of the outermost of the three linear reflectivity features at (a) 1704, (b) 2008, and (c) 2341 UTC 5 Jul 2015 using the KTLX WSR-88D radar at 1.5° elevation angle. The white circle represents the 30-km range from the radar.

Citation: Monthly Weather Review 150, 11; 10.1175/MWR-D-22-0014.1

CBL depth is estimated from a quasi-vertical profile (QVP; Kumjian et al. 2013; Ryzhkov et al. 2016) of differential reflectivity (ZDR), following Banghoff et al. (2018). This approach takes advantage of the presence of Bragg scatter at the top of the CBL, which is characterized by ZDR values near 0 dB and leads to a local minimum in the vertical profile of ZDR (Fig. 2). The local minimum in ZDR that rises from near the ground at 1400 UTC and reaches depths of around 1400 m by 2200 UTC represents the top of the CBL. As with horizontal wavelength, the CBL depth is calculated every hour when an HCR field is present.

Fig. 2.
Fig. 2.

QVP of ZDR (shaded in dB according to scale) for 5 Jul 2015 between 1200 and 0000 UTC 6 Jul. The white line follows the local minimum value of ZDR that signals the top of the growing CBL. The change in data density around 1640 UTC is when the WSR-88D radar scanning strategy changes from precipitation to clear-air mode.

Citation: Monthly Weather Review 150, 11; 10.1175/MWR-D-22-0014.1

By combining the estimates of HCR wavelength and CBL depth one can calculate the HCR aspect ratio (wavelength/depth) at each hour an HCR is present. Aspect ratios of 222.828 are suggested by linear theory (Asai 1970; Kuettner 1971; Brown 1980), and so we expect this value of aspect ratio will be frequently observed in the data. For the 5 July 2015 case shown in Fig. 1, the aspect ratio is 4 at 1700 UTC, decreases to just below 3 at 2000 UTC, which matches the value expected from linear theory, and then increases to 5.5 at 2400 UTC. Observations indicate that the aspect ratio increases from 3.9 to 5.5 during the final hour before HCR demise shortly after 2400 UTC.

An estimate of the uncertainty in the aspect ratio calculation is made by comparing HCR wavelengths across the PPI at numerous observation times. The HCRs meander and the width of the higher reflectivity zone changes throughout the day, leading to measurement uncertainties of ∼300 m in HCR wavelength. In addition, there are uncertainties in the CBL depth determined from the QVP. A comparison with the CBL depth determined from the 0000 UTC rawinsonde observations launched from Norman, Oklahoma (within the KTLX radar volume), indicates a root-mean-square error of 86 m for the 50 cases studied. Taken together these two measurement uncertainties combine to yield an uncertainty in the HCR aspect ratio of ∼0.5.

The WSR-88D radar observations of reflectivity and radial velocity also are used to explore the spatial scales seen in the cross-roll direction associated with the HCRs. Radar observations from the ∼4.5° elevation angle are mapped to a radar-relative Cartesian coordinate system. All points within a narrow polygon of size 2 km in the along-roll direction and 60 km in the cross-roll direction are gathered. Since the HCRs in the dataset tend to align in the south–north direction, the polygon is placed 20 km to the north of the radar site, with the HCR orientation angle estimated using the mean wind direction determined from the velocity azimuth display (VAD) technique (Browning and Wexler 1968). Data points contained within the polygon are gathered such that all points within each 150-m increment in the cross-roll direction are averaged. This results in mean observations every 150 m that extend in the cross-roll direction for 60 km and pass through many HCR circulations. An autocorrelation function is applied to the data and spatial scales are evaluated.

c. Surface and sounding observations

Surface observations from the Oklahoma Mesonet (Brock et al. 1995; McPherson et al. 2007) and 0000 UTC rawinsonde observations launched from Norman, Oklahoma, are used to provide in situ observations for each case. Following the methods described in Brotzge and Crawford (2000) and used in Santellanes et al. (2021), observations from three Oklahoma Mesonet stations (Norman, Shawnee, Spencer) underneath the clear-air sensing umbrella of KTLX are used to calculate three-station mean values of 10-m wind speed, friction velocity, Obukhov length (L), sensible heat flux (SHF), solar radiation, and Richardson number every 5 min. The 5-min observations then are averaged over hourly intervals. The hourly mean values of L are combined with the CBL depth (Zi) to calculate the free convective scaling velocity and −Zi/L, which is typically ≤25 for HCRs (Deardorff 1976). Further details on these calculations are discussed in Brotzge and Crawford (2000) and Santellanes et al. (2021).

The 0000 UTC rawinsonde observations from Norman, Oklahoma (KOUN), are used to calculate the mean wind and wind shear over the depth of the CBL, over the 500-m layer immediately above the boundary layer, as well as the bulk Richardson number and Brunt–Väisälä frequency of the 500-m layer immediately above the boundary layer. The wind shear perpendicular (ΔV) to the HCR orientation is calculated in the 500-m layer immediately above the CBL. The sounding launch location also is located within the clear-air sensing umbrella of KTLX.

d. Methods

Once the hourly values of HCR aspect ratios are calculated for each day, we explore relationships between these values and the available observations, with a focus the aspect ratios and observations from the end of each day when the wide HCRs form. As a first step, correlations between the end time aspect ratios and the available observations are calculated. The combined daily data also are sorted by aspect ratio and the 10 days with the smallest end time aspect ratio and the 10 days with the largest end time aspect ratio are examined by using the mean values of all the observations in the two 10-day groups and compared.

Two gravity wave parameters also are explored using the rawinsonde observations. The first is from the analytic gravity wave solution of Townsend (1965) and described in Melfi and Palm (2012) in which the horizontal wavelength λg of a gravity wave is estimated as λg = 2πΔV/N, in which we assume that the gravity wave crests and troughs align with the HCRs. The second parameter is a nondimensional product and is proportional to any wavelength of gravity waves generated by flow over the rolls: ΔV/(NZi). These two gravity wave parameters are compared with the available HCR observations.

3. Results

a. Aspect ratios

The estimates of HCR wavelength and CBL depth are used to calculate hourly values of aspect ratio from the 50 long-lived HCR cases and results reveal that the variation of aspect ratio during the daytime hours (Fig. 3a) largely duplicates the results from Banghoff et al. (2020). This favorable comparison increases the confidence in our estimation methods as Banghoff et al. (2020) used data from over 400 days. However, their analysis is limited as they also only use aspect ratios at HCR start and end times, whereas our analysis has hourly values of aspect ratio for all 50 days. Median hourly values of aspect ratio are around 4 when the HCRs first develop, decrease to a value of 3 during the middle of the day, and then increase again to values above 4 late in the day. Wide HCRs occur most frequently from 1500 to 1700 UTC and from 2300 to 2400 UTC (Fig. 3a). These large-aspect-ratio HCRs are not observed in the middle of the day in the 50 cases selected.

Fig. 3.
Fig. 3.

Time series of box-and-whisker plots for HCR aspect ratio calculated for each hour of the day between 1500 and 2400 UTC for all 50 cases and displayed in (a) UTC and (b) a dimensionless roll time (varies from start time = 0 to end time = 1). The red horizontal line inside each box is the median; the bottom and top box edges indicate the 25th and 75th percentiles, respectively; the whisker length is 1.5 times the interquartile range; and the red plus signs are outliers. The solid blue horizontal line is the aspect ratio of 22 suggested by linear theory. In (a) the number of cases at each hour is less than 50 early and late in the day, as not all HCRs develop by 1500 UTC or last until 2400 UTC. In (b) the number of cases at each hour is less than 50 during the middle of the day but equal to 50 at roll time = 0, 1.

Citation: Monthly Weather Review 150, 11; 10.1175/MWR-D-22-0014.1

Because HCR start and end time hours vary from case to case, a dimensionless roll time is defined in which time = 0 is the first hour of HCR existence and time = 1 is the last hour of HCR existence. The time of observations between the first and last hours are linearly interpolated between the start and end times. Bins of 0.1 roll-time units are created and the mean observation time of each bin is calculated with aspect ratio values grouped into each bin accordingly. Results of this temporal rescaling are displayed in Fig. 3b and show the same general evolution as seen in Fig. 3a for UTC times, with larger values of aspect ratio early and late during the HCR lifetime. However, it is notable that the third quartile of aspect ratios at roll time = 0 is smaller than at 1500 UTC, indicating that HCRs that form at 1500 UTC more often have larger aspect ratios than HCRs that form later. A similar situation occurs late in the day as the third quartile of aspect ratios at roll time = 1 is smaller than at 2400 UTC, indicating that HCRs that still exist at 2400 UTC more often have larger aspect ratios than those that dissipate before this time. This analysis further suggests that environmental conditions early and late in the day may play a role in the development of wide HCRs.

A more detailed investigation of the daily evolution of aspect ratio reveals that 12% of long-lived HCRs have aspect ratios ≥ 5 during HCR formation, whereas 50% of these HCRs have aspect ratios ≥ 5 at the end of the day. Only 6% of the long-lived HCRs have aspect ratios ≥ 5 at both start and end times, whereas 46% of the long-lived HCRs have aspect ratios < 5 from formation to dissipation.

The data also show that HCRs typically are not observed before 1500 UTC, and the latest time of HCR development is 1900 UTC in the 50 cases. Oklahoma Mesonet data (not shown) indicate that positive SHF starts to warm the boundary layer at least 1–2 h prior to HCR formation, whereas the maximum value of SHF during the HCR lifetime varies considerably among the cases, from values of 50 to over 500 W m−2. Values of −Zi/L are less than 25 for 86% of the days when calculated during the middle of the day and typically become smaller as the day progresses. Radar-estimated CBL depths vary from 300 to 1400 m at the time of HCR formation, although most cases have CBL depths < 1000 m at HCR formation. Daytime maximum CBL depth during which HCRs are observed varies from 1000 to 2800 m.

A wide-HCR event is selected as an example to provide better context and more detailed information on the evolution of the HCRs. A wide-HCR field develops both early and late in the day on 26 July 2014 (Fig. 4). HCRs are first observed around 1600 UTC with an aspect ratio of 5.5, indicating a wide HCR, and an hour later the HCR aspect ratio has only decreased to 4.6. The HCR field has well-defined linear reflectivity structures stretching from southwest to northeast across the entire clear-air sensing domain of the radar. CBL depths are around 500 m at the time of HCR formation, with the local minimum in ZDR clearly defined in the QVP (not shown). Mean hourly SHF values from the Oklahoma Mesonet sites are between 150 and 200 W m−2, with −Zi/L values near 15. The radar observations show that the HCRs form with a large aspect ratio; there is no evidence in the radar reflectivity observations of rolls starting with a smaller aspect ratio and then increasing rapidly in aspect ratio over the first few minutes of roll existence.

Fig. 4.
Fig. 4.

HCR case from 26 Jul 2014 from the KTLX WSR-88D radar at (a) 1703, (b) 2009, and (c) 2333 UTC at 1.5° elevation angle. Red lines indicate the center of the linear reflectivity features seen that stretch from southwest to northeast. The yellow circle in (c) highlights an area in which reflectivity bands with small values of aspect ratio are observed, but only in this localized area.

Citation: Monthly Weather Review 150, 11; 10.1175/MWR-D-22-0014.1

As the CBL deepens during the morning, the horizontal wavelength remains nearly the same, leading to the aspect ratio dropping until a value below 3 is reached at 1800 UTC. Mean hourly SHF is 220 W m−2 at this time, with a mean −Zi/L value of 32, which larger than typically expected for HCRs. If instead of calculating the hourly mean we average the minimum value of L from the three Mesonet stations at each 5-min observation time, then the hourly mean −Zi/L value decreases to 16. The aspect ratio hovers around 3 for the next several hours as the CBL continues to deepen and as the HCR wavelength increases. At 2000 UTC, the aspect ratio remains near the oft-cited value of 3 (Fig. 4b), with twice the horizontal wavelength and over 3 times the CBL depth (1800 m) than observed at HCR formation. Hourly mean SHF is slightly over 200 W m−2 with a −Zi/L value of 35 (averaging the minimum values of L yields a −Zi/L of 15). The linear reflectivity lines at 2000 UTC are wider and are harder to discern in the lower portion of the CBL closer to the radar, suggestive of widespread insects within the CBL. However, the linear structures are clearly discernable farther away from the radar where beam heights are greater. Close examination of the radar observations suggests the presence of cellular convection in addition to HCRs, although the linear HCR features dominate the PPI.

The HCR aspect ratio remains near 3 until 2200 UTC, after which time the aspect ratio increases to over 15 by 2300 UTC (Fig. 4c) with a CBL depth of 2100 m, hourly mean SHF of 80 W m−2 and −Zi/L of 32 (averaging the minimum values of L yields a −Zi/L of 19). The HCR orientation also has shifted such that the rolls are aligned in more of a south–north direction than seen previously. The aspect ratio stays at 15 for the next hour before the HCR field dissipates shortly after 2400 UTC (this is the largest aspect ratio HCR observed from all 50 cases). Mean SHF values are positive throughout the HCR lifetime with a maximum value of 273 W m−2 at 1840 UTC. Visible satellite imagery over central Oklahoma (not shown) indicates that no clouds develop in association with the HCRs for this case.

The increase in HCR aspect ratio after 2200 UTC 26 July 2014 is seen most clearly by animating the radar PPIs (animation 20140726Z_H.mov in the online supplemental material); our visual analysis suggests that the linear reflectivity bands associated with a specific horizontal wavelength are maintained while the other bands in between these dominant bands dissipate. For example, at 2333 UTC there are three main reflectivity lines stretching southwest to northeast across the radar domain that yield the aspect ratio of 15 (Fig. 4c). However, there are suggestions of weaker or dissipating HCRs with smaller values of aspect ratio (highlighted within the yellow circle in Fig. 4c). Similar behavior is suggested in the modeling results of Clark et al. (1986) as the HCRs respond to the gravity waves forced by the HCR circulations. In the radar observations, the narrow and weaker HCR bands are only apparent in a small portion of the radar domain, suggesting that they are localized HCRs and not part of the larger field of wide HCRs. Even when lower reflectivity values are examined for signs of the linear reflectivity bands, the WSR-88D radar observations suggest that the smaller aspect ratio bands have largely disappeared. This evolution is observed in many of the cases examined, in which the dominant linear reflectivity feature is associated with a large value of aspect ratio, but within the HCR field there are localized areas in which weaker reflectivity bands with smaller values of aspect ratio are present, suggestive of remnants from earlier reflectivity structures.

Examples of other wide HCRs show the variety of the reflectivity features seen in the observations (Fig. 5). All observations are from late in the day between 2250 and 2400 UTC, and satellite observations (not shown) indicate the lack of visible cloud streets for these cases. Some days have very regularly spaced linear reflectivity features that cover the entire clear-air radar domain. Other days have suggestions of weaker linear reflectivity features associated with HCRs having a smaller value of aspect ratio. The 12 July 2014 case shows three very wide reflectivity structures that are over 10 km in width. Closer examination of the evolving reflectivity structures suggests that several HCR bands merge to form the wide reflectivity structures seen (animation 20140712Z_H.mov in supplemental material). This evolution may resemble the wide HCRs discussed by Brümmer (1999).

Fig. 5.
Fig. 5.

Wide HCR cases valid late in the day for various cases in the dataset. All HCRs depicted have values of aspect ratio > 5. Red lines indicate placement and orientation of the linear reflectivity features that are used to estimate the horizontal wavelength.

Citation: Monthly Weather Review 150, 11; 10.1175/MWR-D-22-0014.1

Calculations of hourly mean values of −Zi/L for the hour centered on roll initiation time yields only 6 days with −Zi/L > 25 as HCRs formed, with 42 being the largest value in the dataset. The mean value for the 44 cases with −Zi/L < 25 at HCR formation is 11. As the CBL deepens during the morning hours and into the afternoon, the values of −Zi/L tend to increase. By 2100 UTC, there are 23 days with −Zi/L > 25, with 146 being the largest value in the dataset. The mean value for the 27 days with −Zi/L < 25 is 12, very similar to the value for roll onset. Late in the day, near the time of HCR demise, the values of −Zi/L decrease as SHF decreases.

Young et al. (2002) show that while overland HCRs have a near-constant aspect ratio as the CBL deepens, overwater HCRs increase in aspect ratio as the CBL deepens (their Fig. 4). Data from the 50 cases in this study suggest both behaviors occur when long-lived HCRs are observed at the end of the day prior to dissipation. Aspect ratios increase with CBL depth for some days but not others (Fig. 6). For the HCRs in which aspect ratio increases with CBL depth, the increase in aspect ratio per 1000-m increase in CBL depth is nearly twice the slope shown by Young et al. (2002) and the best-fit lines have different intercept values. Observations of these wide HCRs over land further indicate that their formation occurs rapidly, either with HCR formation at the start of the day or within a few hours of HCR demise at the end of the day. This evolution does not represent a slow increase in aspect ratio as CBL depth increases, but rather a rapid transition near the time of boundary layer transitions from stable to unstable or unstable to stable. Although the number of cases is not large, these results certainly suggest that overland HCRs are more complex than previously considered.

Fig. 6.
Fig. 6.

HCR aspect ratio vs CBL height for the last hour of HCR observation. Note that there are two different relationships suggested by the dashed black and solid red lines.

Citation: Monthly Weather Review 150, 11; 10.1175/MWR-D-22-0014.1

b. Environmental influence

To determine whether environmental conditions have any obvious influence on wide HCR formation, both Oklahoma Mesonet observations and 0000 UTC Norman, Oklahoma, soundings are used. Oklahoma Mesonet three-station mean values of 10-m wind speed, SHF, friction velocity, solar radiation, and L, as well as the free convection scaling velocity and −Zi/L, are collected and averaged over the final hour of HCR lifetime for each case day. Mean boundary layer and inversion layer parameters from the 0000 UTC Norman soundings are computed. Finally, the HCR aspect ratio at the final hour of HCR lifetime is noted. Correlations between the final hour of HCR lifetime aspect ratio and the available surface and rawinsonde observations valid at the same time then are calculated to determine whether any linear relationships exist that would suggest an environmental characteristic that influences the formation of these wide HCRs.

Results from the Oklahoma Mesonet derived observations indicate that the correlations between HCR end time aspect ratio and the surface observations at HCR end time are small, with the largest correlations less than 0.3 (not shown). Differences in the 10 days with largest and smallest aspect ratios also are small (<10% of the mean value) for the surface observations. There is no clear signal of environmental influence as observed at the surface on wide HCR formation.

Examination of parameters derived from the 0000 UTC soundings from Norman, Oklahoma, are only slightly more encouraging. The largest correlation magnitude calculated is between the HCR wavelength and the CBL depth, with a correlation of −0.24 (Table 1). When comparing the 10 smallest- and 10 largest-aspect-ratio HCR cases near their end times (Table 1), we find that the mean CBL depth for the 10 largest aspect ratio cases is 365 m lower than the mean CBL depth for the 10 smallest aspect ratio cases (Table 1). In addition, the mean wind shear in the 500-m layer above the CBL and perpendicular to the HCR orientation angle is 0.008 s−1 for the largest aspect ratio cases and only 0.005 s−1 for the smallest aspect ratio cases. When the total wind shear is combined with vertical potential temperature gradient in the layer, the bulk Richardson number is smaller for the cases with the largest aspect ratio, although the individual values of bulk Richardson number span similar ranges.

Table 1

Values of mean observations from 10 days with smallest HCR aspect ratios and 10 days with largest HCR aspect ratios calculated from the 0000 UTC Norman, Oklahoma, soundings with CBL depth calculated using the virtual potential temperature profile. Correlation coefficient is calculated between the 0000 UTC observations and HCR aspect ratios near roll dissipation time for all 50 cases.

Table 1

The Townsend (1965) analytic model provides an expression for the expected wavelength (m) for a gravity wave forced by CBL circulations. Unfortunately, the calculated wavelengths are not correlated with either observed HCR aspect ratio (Table 1) or wavelength (r = 0.02) late in the day. The largest calculated wavelength is just over 3.2 km, whereas observations indicate wavelengths as large as 15 km. Results further indicate that the second gravity wave parameter ΔV/(NZi) increases by 25% for large-aspect-ratio cases compared to small-aspect-ratio cases, although the correlation between the gravity wave parameter and HCR aspect ratio at the end of the day is only 0.06. Thus, none of the sounding parameters, dimensional or nondimensional, exhibit a strong linear relationship to HCR aspect ratio. It may be that the gravity wave scale is independent of the source region characteristics, as suggested by Balaji et al. (1993).

The evolution of CBL depth during the final few hours of HCR lifetime also is examined. The trends are categorized into steady CBL depths, decreasing CBL depths, or increasing CBL depths during the 3-h prior to the HCR end time. Results indicate steady and decreasing CBL depths occur in roughly 36% of the cases each, with the remaining 26% having increasing CBL depths. This suggests that changes in CBL depth are not influencing wide HCR formation.

Finally, we hypothesize that if gravity waves near the top of the CBL produce the wide roll circulations, then there may be evidence of these waves in the radar observations preceding the formation of the wide rolls, with the signal appearing first in the radial velocity data. This hypothesis is explored using the mean radar reflectivity and radial velocity observations from within a polygon that stretches across a 60-km length in the cross-roll direction. An autocorrelation function is applied to the data and spatial scales are evaluated for both the reflectivity and radial velocity observations for every volume scan from 1500 to 2400 UTC. Six wide roll cases are explored using this approach. Unfortunately, the autocorrelation results fail to show any clear signal of gravity wave activity preceding the formation of the wide rolls. Values of autocorrelation are relatively large across many horizontal scales early in the day, likely capturing structures within the turbulent boundary layer, and then later in the day are largest for spatial scales representative of HCRs, but with a fair amount of noise (not shown) across successive volume scans. Different polygon sizes, averaging windows, and elevation angles are tested, but none show any conclusive signals.

4. Discussion

Wide HCRs, defined here as HCRs with aspect ratios ≥ 5, are observed over land from WSR-88D radar reflectivity observations in clear air over central Oklahoma. These HCRs are observed either early in the morning during HCR formation or late in the day near HCR dissipation and last for a few hours at most. Wide HCRs are not observed during the middle of the HCR lifetime. Results indicate that 12% of HCRs that persist for more than 5 h have aspect ratios ≥ 5 during HCR formation, whereas 50% of these long-lived HCRs have aspect ratios ≥ 5 at the end of the day. A visual examination of the radar reflectivity observations from 10 wide roll cases observed at the end of the day suggests three formation pathways: wide HCRs occur as specific HCR wavelengths are maintained while roll circulations with smaller wavelengths dissipate (most common, and also suggested in the modeling study of Clark et al. 1986); wide HCRs develop as the wavelength increases rapidly across the roll field; and wide HCRs occur when several HCR bands merge together to form wide reflectivity bands with larger aspect ratio.

Results indicate that differences in available environmental observations between small aspect ratio and large aspect ratio HCRs are negligible (less than 10% difference) for most parameters. The exceptions are CBL depth, the mean wind shear in the 500-m layer above the CBL and perpendicular to the HCR orientation angle, and the bulk Richardson number (see Table 1), although the differences are not large. Predicted HCR wavelengths from the Townsend (1965) analytic model are not correlated with the observed HCR wavelengths and the correlation also is negligible for a second gravity wave parameter that is examined. We further searched for indications of gravity waves in the radar radial velocity observations when wide HCRs are present and found none. Thus, while the development of wide HCRs seen in the radar reflectivity observations from late in the day follows the general evolution seen in the modeling results of Clark et al. (1986) there is no quantitative evidence linking the observed HCR widening to gravity waves. It is likely that observations at finer scales are needed to observe accurately the HCR environment and any wave features associated with wide HCRs. Exploring the development of wide HCRs over land using large-eddy simulations also would be beneficial.

The radar observations show that a linear relationship exists between the aspect ratios for some wide rolls over land and CBL depth. A similar linear relationship between HCR aspect ratio and CBL depth has been found for wide HCRs in association with cold-air outbreaks over water. However, the evolution from aspect ratios near 3 to large aspect ratios occurs in a few hours over land, which appears very different than the slow progression to larger aspect ratios seen over water.

While this study asks more questions than are answered regarding how these wide aspect ratio HCRs form, our results suggest that wide HCRs occur with some regularity over land. If this HCR evolution is produced via gravity waves, as seen in modeling studies, then these waves may persist into the evening hours and could influence convection initiation and/or convection organization. Further study of HCRs in the very early morning and late afternoon with targeted observations or modeling studies is needed to clarify the physical mechanisms of these interesting yet ephemeral wide HCRs over land and explore their potential impact on cloud formation and evolution.

Acknowledgments.

Funding for this work is provided by NSF Award AGS-1632850. Special thanks to Keenan Eure and Paul Mykolajtchuk at Penn State University for helping with radar observations for the cases. We greatly appreciate the helpful and constructive comments of Dr. Margaret LeMone and two anonymous reviewers.

Data availability statement.

The 10-yr warm-season climatology of HCRs, cells, and nulls is openly available on The Pennsylvania State University Data Commons at https://doi.org/10.26208/9d63-5p83 as cited in Stensrud et al. (2019). WSR-88D radar data are freely available from the National Center for Environmental Information. Soundings are freely available from the University of Wyoming sounding web page. Oklahoma Mesonet observations are available from the Oklahoma Climatological Survey.

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Supplementary Materials

Save
  • Asai, T., 1970: Stability of a plane parallel flow with variable vertical shear and unstable stratification. J. Meteor. Soc. Japan, 48, 129139, https://doi.org/10.2151/jmsj1965.48.2_129.

    • Search Google Scholar
    • Export Citation
  • Atkinson, B. W., and J. W. Zhang, 1996: Mesoscale shallow convection in the atmosphere. Rev. Geophys., 34, 403431, https://doi.org/10.1029/96RG02623.

    • Search Google Scholar
    • Export Citation
  • Balaji, V., J.-L. Redelsperger, and G. P. Klassen, 1993: Mechanisms for the mesoscale organization of tropical cloud clusters in GATE Phase III. Part I: Shallow cloud bands. J. Atmos. Sci., 50, 35713589, https://doi.org/10.1175/1520-0469(1993)050<3571:MFTMOO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Banghoff, J. R., D. J. Stensrud, and M. R. Kumjian, 2018: Convective boundary layer depth estimation from S-band dual-polarization radar. J. Atmos. Oceanic Technol., 35, 17231733, https://doi.org/10.1175/JTECH-D-17-0210.1.

    • Search Google Scholar
    • Export Citation
  • Banghoff, J. R., J. D. Sorber, D. J. Stensrud, G. S. Young, and M. R. Kumjian, 2020: A 10-year warm-season climatology of horizontal convective rolls and cellular convection in central Oklahoma. Mon. Wea. Rev., 148, 2142, https://doi.org/10.1175/MWR-D-19-0136.1.

    • Search Google Scholar
    • Export Citation
  • Brock, F. V., K. C. Crawford, R. L. Elliott, G. W. Cuperus, S. J. Stadler, H. L. Johnson, and M. D. Eilts, 1995: The Oklahoma Mesonet: A technical overview. J. Atmos. Oceanic Technol., 12, 519, https://doi.org/10.1175/1520-0426(1995)012<0005:TOMATO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Brotzge, J. A., and K. C. Crawford, 2000: Estimating sensible heat flux from the Oklahoma Mesonet. J. Appl. Meteor., 39, 102116, https://doi.org/10.1175/1520-0450(2000)039<0102:ESHFFT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Brown, R. A., 1980: Longitudinal instabilities and secondary flows in the planetary boundary layer: A review. Rev. Geophys. Space Phys., 18, 683697, https://doi.org/10.1029/RG018i003p00683.

    • Search Google Scholar
    • Export Citation
  • Browning, K., and R. Wexler, 1968: The determination of kinematic properties of a wind field using Doppler radar. J. Appl. Meteor., 7, 105113, https://doi.org/10.1175/1520-0450(1968)007<0105:TDOKPO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Brümmer, B., 1999: Roll and cell convection in wintertime Arctic cold-air outbreaks. J. Atmos. Sci., 56, 26132636, https://doi.org/10.1175/1520-0469(1999)056<2613:RACCIW>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Christian, T. W., and R. M. Wakimoto, 1989: The relationship between radar reflectivities and clouds associated with horizontal roll convection on 8 August 1982. Mon. Wea. Rev., 117, 15301544, https://doi.org/10.1175/1520-0493(1989)117<1530:TRBRRA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Clark, T. L., T. Hauf, and J. P. Kuettner, 1986: Convectively forced internal gravity waves: Results from two-dimensional experiments. Quart. J. Roy. Meteor. Soc., 112, 899925, https://doi.org/10.1002/qj.49711247402.

    • Search Google Scholar
    • Export Citation
  • Deardorff, J. W., 1976: Discussion of ‘Thermals over the sea and gull flight behavior’ by A. H. Woodcock. Bound.-Layer Meteor., 10, 241246, https://doi.org/10.1007/BF00229293.

    • Search Google Scholar
    • Export Citation
  • Fankhauser, J. C., N. A. Crook, J. Tuttle, L. J. Miller, and C. G. Wade, 1995: Initiation of deep convection along boundary layer convergence lines in a semitropical environment. Mon. Wea. Rev., 123, 291314, https://doi.org/10.1175/1520-0493(1995)123<0291:IODCAB>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Geerts, B., and Q. Miao, 2005: A simple numerical model of the flight behavior of small insects in the atmospheric convective boundary layer. Environ. Entomol., 34, 353360, https://doi.org/10.1603/0046-225X-34.2.353.

    • Search Google Scholar
    • Export Citation
  • Hardy, K. R., and H. Ottersten, 1969: Radar investigations of convective patterns in the clear atmosphere. J. Atmos. Sci., 26, 666672, https://doi.org/10.1175/1520-0469(1969)26<666:RIOCPI>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Holroyd, E. W., III, 1971: Lake-effect cloud bands as seen from weather satellites. J. Atmos. Sci., 28, 11651170, https://doi.org/10.1175/1520-0469(1971)028<1165:LECBAS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Kelly, R. D., 1982: A single Doppler radar study of horizontal-roll convection in a lake-effect snow storm. J. Atmos. Sci., 39, 15211531, https://doi.org/10.1175/1520-0469(1982)039<1521:ASDRSO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Kelly, R. D., 1984: Horizontal roll and boundary-layer interrelationships observed over Lake Michigan. J. Atmos. Sci., 41, 18161826, https://doi.org/10.1175/1520-0469(1984)041<1816:HRABLI>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Konrad, T. G., 1970: The dynamics of the convective process in clear air as seen by radar. J. Atmos. Sci., 27, 11381147, https://doi.org/10.1175/1520-0469(1970)027<1138:TDOTCP>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Kristovich, D. A. R., 1993: Mean circulations of boundary-layer rolls in lake-effect snow storms. Bound.-Layer Meteor., 63, 293315, https://doi.org/10.1007/BF00710463.

    • Search Google Scholar
    • Export Citation
  • Kuettner, J., 1959: The band structure of the atmosphere. Tellus, 11, 267294, https://doi.org/10.3402/tellusa.v11i3.9319.

  • Kuettner, J., 1971: Cloud bands in the Earth’s atmosphere: Observations and theory. Tellus, 23, 404426, https://doi.org/10.3402/tellusa.v23i4-5.10519.

    • Search Google Scholar
    • Export Citation
  • Kumjian, M. R., A. V. Ryzhkov, H. D. Reeves, and T. J. Schuur, 2013: A dual-polarization radar signature of hydrometeor refreezing in winter storms. J. Appl. Meteor. Climatol., 52, 25492566, https://doi.org/10.1175/JAMC-D-12-0311.1.

    • Search Google Scholar
    • Export Citation
  • LeMone, M. A., 1973: The structure and dynamics of horizontal roll vortices in the planetary boundary layer. J. Atmos. Sci., 30, 10771091, https://doi.org/10.1175/1520-0469(1973)030<1077:TSADOH>2.0.CO;2.

    • Search Google Scholar
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  • McPherson, R. A., and Coauthors, 2007: Statewide monitoring of the mesoscale environment: A technical update on the Oklahoma Mesonet. J. Atmos. Oceanic Technol., 24, 301321, https://doi.org/10.1175/JTECH1976.1.

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  • Fig. 1.

    Example of method to determine HCR horizontal wavelength between the centers of three linear reflectivity features. Red lines indicate the center of the outermost of the three linear reflectivity features at (a) 1704, (b) 2008, and (c) 2341 UTC 5 Jul 2015 using the KTLX WSR-88D radar at 1.5° elevation angle. The white circle represents the 30-km range from the radar.

  • Fig. 2.

    QVP of ZDR (shaded in dB according to scale) for 5 Jul 2015 between 1200 and 0000 UTC 6 Jul. The white line follows the local minimum value of ZDR that signals the top of the growing CBL. The change in data density around 1640 UTC is when the WSR-88D radar scanning strategy changes from precipitation to clear-air mode.

  • Fig. 3.

    Time series of box-and-whisker plots for HCR aspect ratio calculated for each hour of the day between 1500 and 2400 UTC for all 50 cases and displayed in (a) UTC and (b) a dimensionless roll time (varies from start time = 0 to end time = 1). The red horizontal line inside each box is the median; the bottom and top box edges indicate the 25th and 75th percentiles, respectively; the whisker length is 1.5 times the interquartile range; and the red plus signs are outliers. The solid blue horizontal line is the aspect ratio of 22 suggested by linear theory. In (a) the number of cases at each hour is less than 50 early and late in the day, as not all HCRs develop by 1500 UTC or last until 2400 UTC. In (b) the number of cases at each hour is less than 50 during the middle of the day but equal to 50 at roll time = 0, 1.

  • Fig. 4.

    HCR case from 26 Jul 2014 from the KTLX WSR-88D radar at (a) 1703, (b) 2009, and (c) 2333 UTC at 1.5° elevation angle. Red lines indicate the center of the linear reflectivity features seen that stretch from southwest to northeast. The yellow circle in (c) highlights an area in which reflectivity bands with small values of aspect ratio are observed, but only in this localized area.

  • Fig. 5.

    Wide HCR cases valid late in the day for various cases in the dataset. All HCRs depicted have values of aspect ratio > 5. Red lines indicate placement and orientation of the linear reflectivity features that are used to estimate the horizontal wavelength.

  • Fig. 6.

    HCR aspect ratio vs CBL height for the last hour of HCR observation. Note that there are two different relationships suggested by the dashed black and solid red lines.

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