On polarimetric radar signatures of deep convection for model evaluation: columns of specific differential phase observed during MC3E

Abstract

The representation of deep convection in general circulation models is in part informed by cloud-resolving models (CRMs) that function at higher spatial and temporal resolution; however, recent studies have shown that CRMs often fail at capturing the details of deep convection updrafts. With the goal of providing constraint on CRM simulation of deep convection updrafts, ground-based remote-sensing observations are analyzed and statistically correlated for four deep convection events observed during the Midlatitude Continental Convective Clouds Experiment (MC3E). Since positive values of specific differential phase (K_DP) observed above the melting level are associated with deep convection updraft cells, so-called “K_DP columns” are analyzed using two scanning polarimetric radars in Oklahoma: the National Weather Service Vance WSR-88D (KVNX) and the Department of Energy C-band Scanning Atmospheric Radiation Measurement (ARM) Precipitation Radar (C-SAPR). KVNX and C-SAPR K_DP volumes and columns are then statistically correlated with vertical winds retrieved via multi-Doppler wind analysis, lightning flash activity derived from the Oklahoma Lightning Mapping Array, and KVNX differential reflectivity (Z_DR). Results indicate strong correlations of K_DP volume above the melting level with updraft mass flux, lightning flash activity, and intense rainfall. Analysis of K_DP columns reveals signatures of changing updraft properties from one storm event to another as well as during event evolution. Comparison of Z_DR to K_DP shows commonalities in information content of each, as well as potential problems with Z_DR associated with observational artifacts.

1. Introduction

a. Motivation

This study lays the groundwork for observational evaluation of cloud-resolving model simulations by quantifying statistical properties of objectively identified radar observables, namely specific differential phase (K_DP), and establishing their correlation with collocated retrieval of vertical winds, as well as precipitation rate, and lightning flash activity, which are also closely related to updraft properties. This will allow for future work to test approaches for comparing high-resolution simulations and observations that rely primarily on the strengths identified in the analysis of K_DP presented herein.

The microphysical properties of mature deep convection updrafts remain poorly quantified, at least in part because of sparse in situ measurements available from aircraft campaigns, which provide the only direct means of measuring hydrometeor mixing ratio, morphology, size distribution, and phase within strong updrafts (Heymsfield et al. 2002; Stith et al. 2002, 2004; Anderson et al. 2005; Stith et al. 2006; Lawson et al. 2010). A glaring result is the lack of observational data adequate to quantitatively constrain order-of-magnitude differences in condensate mixing ratios commonly predicted by cloud-resolving simulations of deep convection systems using differing microphysics schemes, where interaction of dynamics and microphysics schemes likely contribute to differences (Varble et al. 2011; Zhu et al. 2012; Collis et al. 2013; Varble et al. 2014; Varble 2014). This dearth of in situ measurements is furthermore unlikely to be quickly remedied owing to the difficulty of obtaining robust statistics by aircraft over sparsely distributed and rapidly evolving features. With research-grade simulations poorly constrained, it is extraordinarily difficult to robustly establish higher-order differences in updraft properties, such as those induced by changes in aerosol fields (see reviews by Levin and Cotton (2008) and Tao et al. (2012)), which have been hypothesized to influence climate via their influence on deep convection.

Instead of directly constraining hydrometeor concentrations, observations can be used to inform the microphysical processes present in deep convective updrafts. Perhaps the most promising sources of data now available for that task are scanning polarimetric radars, including those operated by the US National Weather Service and the Department of Energy’s Atmospheric Radiation Measurement (ARM) program (Ackerman and Stokes 2003; Mather and Voyles 2013). Such radars offer wide-domain and continuous coverage in time, but likely require an analysis approach that is suited to their strengths, which do not currently include robust retrieval of condensate mixing ratios within updrafts, for instance, but may include signatures associated with the microphysical processes of deep convection.

Within the high-resolution and global modeling community, radar reflectivity (typically horizontally polarized radar reflectivity Z_HH) has been effectively used, for example, to define convective and stratiform regions using the Steiner and Smith (1998) algorithm (e.g. Caniaux et al. (1995); Gray (2000); Lang et al. (2003); Mechem et al. (2006); Braun et al. (2010); Fridlind et al. (2012); Zeng et al. (2013); Mrowiec et al. (2015)). Additionally, contoured frequency with altitude (CFAD) plots of reflectivity are used to evaluate differences in modeled and observed storm microphysics and dynamics (Lang et al. 2003; Blossey et al. 2007; Matsui et al. 2009; Shi et al. 2010; Lang et al. 2011; Tao et al. 2014; Matsui et al. 2015). These methods have proven valuable in illustrating gross differences between modeled and observed storm characteristics; however, they do not provide specific information on, for example, the prevalence, spatial distribution, and strength of deep convective updrafts. There would be much potential value in an observational metric of deep convective storms that is capable of providing these data, providing that it could be effectively compared to analogous metrics calculated from numerical model simulations. The current work provides background for the use of columns of K_DP as an observational constraint on modeled deep convective updrafts.

This study focuses on polarimetric precipitation radar observations owing to their ability to provide unique information about hydrometeors involved in updraft microphysical processes (Bringi et al. 1996; Hubbert et al. 1998; Loney et al. 2002; Kumjian et al. 2014a). In particular, it focuses on the presence of elevated positive values of K_DP above the environmental 0 °C isotherm, which strongly suggests significant quantities of lofted liquid rain and/or water-coated ice, and thus, the presence of deep convection updrafts (Bringi et al. 1996; Hubbert et al. 1998; Loney et al. 2002). For a review of K_DP and other polarimetric variables, in the interest of space we refer the reader elsewhere (Doviak and Zrnić 1993; Zrnic and Ryzhkov 1999; Bringi and Chandrasekar 2001; Kumjian 2013)

Because the ultimate goal is to use these radar observations to constrain model simulations, we require that these observations be robust, both from the perspective of observational uncertainties, as well as from the perspective of forward modeling these observations. In both regards, the choice of K_DP is attractive. With regard to observational artifacts and uncertainty, K_DP is arguably more robust than Z_DR as an observational indicator of the presence of rain or liquid-coated ice particles above the melting level throughout the lifecycle of a convection cell. For example, results from Kumjian et al. (2014a) suggest that as hail mass becomes significant from the perspective of reflectivity, Z_DR is depressed despite the continued presence of both a convective updraft and rain above the melting level. In such cases, K_DP above the melting level is likely to better track the full lifecycle of a convection updraft. Additionally, K_DP-related rain rate statistics have been shown to have good fidelity, even for radar frequencies susceptible to attenuation errors (Giangrande et al. 2014). Z_DR is possibly preferable to K_DP as a signal of the initial stages of a deep convective updraft because it does not require significant concentrations of oblate hydrometeors, and is thus better able to characterize the initial evolution of an updraft where liquid hydrometeors may be present above the 0 °C isotherm in low concentrations.

With regards to observational uncertainties, Z_DR is sensitive to both radar calibration errors, as well as differential attenuation, which is caused by propagation of the signal through oriented hydrometeors (Aydin et al. 1989; Bringi and Chandrasekar 2001). K_DP is insensitive to both calibration and attenuation effects, although estimation of K_DP becomes complicated when backscatter differential phase is significant, as it is for particles that are large with respect to the radar wavelength (Aydin and Giridhar 1992; Carey et al. 2000; Giangrande et al. 2013), and K_DP may also be susceptible to cross-coupling effects (Hubbert et al. 2014).

For identification of deep updrafts, K_DP is preferred to radar reflectivity for a number of reasons. In deep convection, high reflectivity may indicate high concentrations of rain, ice-phase hydrometeors such as hail, graupel, and mixed phase hydrometeors. By comparison, elevated positive values of K_DP are generally related to liquid rain or liquid-coated hydrometeors which produce positive K_DP owing to their oblateness. Considering only rain, radar reflectivity, under the Rayleigh approximation, is proportional to the sixth moment of a drop size distribution. For the purposes of forward modeling observations, this results in strong and nonlinear sensitivity to assumptions in the modeled drop size distribution. By contrast, K_DP is approximately related to the 4th – 5th moment of the raindrop size distribution and is closely related to rain-rate (Sachidananda and Zrnic 1986; Ryzhkov and Zrnic 1996; Zrnic and Ryzhkov 1999; Cifelli and Chandrasekar 2010). This last point relates to the robustness of forward simulation of K_DP from model results. In the current study, it is hypothesized that use of K_DP instead of Z_DR will reduce forward modeling uncertainties related to raindrop size distribution assumptions because K_DP is less sensitive to variations in assumptions of the rain drop size distribution than either reflectivity or Z_DR.

The purpose of this study is to investigate the characteristics of K_DP as an observational signal of deep convective updrafts, in order to motivate its use as a constraint on numerical simulations. The focus is not on conclusively diagnosing the microphysical processes that produce K_DP columns, nor is it to use K_DP to study the dynamics of deep convection. Instead, K_DP columns observed in four mid-latitude deep convection storm systems are analyzed to answer the following questions: a) how does the signal of deep convection observed in the depth and volume of K_DP columns correlate with other metrics such as multi-Doppler wind retrievals and electrical storm activity? b) How do the relationships between K_DP columns and other metrics of deep convection vary from storm to storm and within evolving storms systems during their life cycles? Addressing these issues will improve understanding of how K_DP columns, and more generally, positive K_DP above the melting level, characterize deep convective storm systems and their lifecycles, to aid forecasters and provide information needed to use K_DP to evaluate numerical models.

b. Background

Two prominent examples of analysis and interpretation of K_DP columns can be found in Hubbert et al. (1998) and Loney et al. (2002). Hubbert et al. (1998) documented S-band observations of a supercell observed by the CSU-CHILL radar in Colorado and analyzed Z_DR, linear depolarization ratio (LDR), co-polar correlation ratio (ρ_hv) and K_DP signatures. The authors interpret the K_DP column as a signal of small drops (1–2 mm) shed by wet hailstones by virtue of its location on the fringe of the identified updraft. Loney et al. (2002) present S-band polarimetric radar observations of an Oklahoma supercell collocated with in-situ data collected from an aircraft. The aircraft sampled particle sizes along a path above the melting level through a region associated with roughly maximal K_DP values evident in CAPPI and vertical sections. Their results indicated radar observed elevated positive K_DP roughly co-located with the storm updraft, compared with K_DP forward-simulated from in situ data, which showed peaks on either side of the updraft. Recently, Homeyer and Kumjian (2015) performed a composite analysis of polarimetric radar observations of organized, cellular and supercellular deep convection across the Great Plains. This study showed the prevalence and consistency of K_DP and Z_DR columns in regions associated with convection that overshoots the altitude of the extratropical tropopause.

Electrical activity of storms has long been used as a signal of continental deep convection, to the extent that the word “thunderstorm” is used to describe such weather. It has been long understood that a dominant mechanism in separation of charge in thunderstorms is rebounding ice-ice collisions occurring between particles such as graupel and pristine ice in the presence of supercooled cloud water (Reynolds et al. 1957; Takahashi 1978; Jayaratne et al. 1983; Pereyra et al. 2000). Graupel is produced in regions where riming growth is dominant, in other words, regions of deep convection updrafts. Studies, for example, Deierling and Petersen (2008) have confirmed a strong link between updraft volume and total flash rate in storm systems, with Wiens et al. (2005) stressing the importance of using flash density, rather than raw VHF source density, as a measure of lightning activity.

The role of mixed-phase microphysics in the separation of charge suggests that polarimetric variables such as K_DP and Z_DR observed above the melting layer may be linked to lightning activity. Multiple studies have confirmed and elaborated on the relationship between lightning activity and multi-Doppler radar derived updrafts (Lang and Rutledge 2002; Tessendorf et al. 2007b,a; Deierling and Petersen 2008; Calhoun et al. 2013) and several have investigated the relationships between polarimetric variables and electrical activity in deep convection storms (Carey and Rutledge 1998; Tessendorf et al. 2005;Wiens et al. 2005; Bruning et al. 2007; Lund et al. 2009; Payne et al. 2010; Griffin et al. 2014).

2. Data & Methodology

a. Data

1) KVNX S-band polarimetric radar

S-band polarimetric radar data was obtained from the National Weather Service WSR-88D (NEXRAD) Vance Oklahoma radar site (KVNX). This radar simultaneously transmits and receives electromagnetic waves with horizontal and vertical polarizations (STAR), meaning that measurements of cross-polarization variables such as LDR and cross-polar correlation coefficient (ρ_xh) are not possible using this radar. Level-II data from the National Climatic Data Center provides the variables horizontal reflectivity (Z_HH), differential reflectivity (Z_DR), differential phase (Ψ_DP), co-polar correlation coefficient (ρ_HV), and radial velocity. The radar operated in volume coverage patterns (VCP) 11, 212, 12, 212 for the four days, respectively; all modes featured 14 elevation scans performed in approximately 5 minutes. At the time of MC3E, KVNX had an angular resolution of 1 °for all elevations angles (lower angles had improved 0.5 °resolution) and 250 m range resolution.

K_DP is obtained from NEXRAD Level II differential phase data (Ψ_DP) using the Giangrande et al. (2013) algorithm as implemented in the Python ARMRadar Toolkit (Py-ART) (Heistermann et al. 2015). This algorithm assumes a monotonic increase in Ψ_DP, and is thus inappropriate for regions where negative K_DP is expected (such as in electrified ice fields or in the presence of conical graupel). Conversely, this algorithm is well-suited to using K_DP to identify the presence of rain, or liquid-coated hydrometeors lofted above the melting layer by strong convection updrafts, conditions where negative K_DP is not expected. Processing to retrieve Φ_DP and K_DP requires filtering that reduces range resolution to approximately 1 km for K_DP.

NEXRAD radar data, including the derived K_DP fields, are gridded using Py-ART gridding routines on a Cartesian grid with 1km horizontal and 500m vertical resolution. Care was taken in selecting the appropriate gridding algorithm to capture relevant detail while suppressing artifacts; we chose an inverse-distance weighted algorithm using a Barnes (1964) -like weighting function as in Collis et al. (2010) and Trapp and Doswell (2000). It should be noted that, at the time of MC3E, KVNX was the only operational NEXRAD radar in the region that was polarimetric. Future studies of large storm systems such as those observed during MC3E will no doubt benefit from enhanced spatial coverage of polarimetric NEXRAD radars.

2) C-SAPR C-band polarimetric radar

The Department of Energy (DOE) Atmospheric Radiation Measurement C-band ARM Scanning Precipitation Radar (C-SAPR) is a polarimetric 5 cm wavelength radar that was located near the ARM Southern Great Plains (SGP) site at Lamont, Oklahoma during this study. Like KVNX, it was run in STAR mode. The C-SAPR radar has approximately the same beam width as KVNX (approx. 1 °), but much improved range resolution (90 m vs. 250 m for KVNX). K_DP range resolution for C-SAPR is approximately 250 m due to filtering in the phase processing algorithm.

Data was analyzed on a Cartesian grid with 1 km horizontal and 500 m vertical resolution. Data was processed to derive K_DP from Ψ_DP, again using the Giangrande et al. (2013) algorithm. Z_DR suffered from problems associated with differential attenuation from heavy precipitation observed on all days, compounded by the sensitivity of C-band radar measurements to such effects, and Z_DR from C-SAPR was therefore not used in this study. Additionally, a polarimetric rainfall estimation based on specific attenuation was used to derive rain rates from C-SAPR polarimetric radar variables (Ryzhkov et al. 2014; Giangrande et al. 2014). Giangrande et al. (2014) analyzed these data and compared them with estimates from X-band polarimetric radars as well as rain gauges; C-SAPR rain rates were shown to be in good agreement with rain gauges. Here we analyze rain rates above the 40 and 90 mm hr⁻¹ thresholds to illustrate convective and particularly intense rain rates, respectively.

3) Multi-Doppler wind retrieval

The network of scanning precipitation Doppler radars at the ARM SGP site provides the capability to view the atmosphere from multiple different angles in under approximately 7 minutes. During MC3E, the coordination of this network was of highest priority at times when significant convection events were imminent or occurring. We briefly describe the multi-Doppler wind retrieval method here. For a full description of the method, see North et al. (2015). Fundamentally, the radial velocity observations from this network are ingested into a three-dimensional variational (3D-VAR) algorithm that minimizes a cost function defined as the sum of multiple independent constraints: radar Doppler radial velocity, mass continuity, a background field, and smoothness. Mass continuity in this case is the anelastic approximation for moist convection, and is a required constraint owing to inadequate sampling of vertical air motion by scanning Doppler radars. The background field provides a physical solution in data sparse regions, and the smoothness constraint is designed to reduce retrieval artifacts and extend properly constrained regions into poorly constrained regions. These four constraints are common in multi-Doppler wind retrieval literature. The analysis domain for these wind retrievals covers 100 × 100 km² around the SGP Central Facility and extends up to 10 km altitude, with a horizontal resolution of 500 m and a vertical resolution of 250 m. The radars used included the C-SAPR radar as well as two X-band (3 cm wavelength) ARM Scanning Precipitation Radars (X-SAPR) located near the central facility; the locations of these radars are shown in Fig. 1

Fig. 1.

Map of KVNX radar location with 200 km range ring (red square and ring), C-SAPR radar location with with 112 km range ring (blue square and ring), LMA array antennae locations and 200 km range ring (green asterisks and ring), and domain of multi-Doppler wind retrieval (black box) with location of X-SAPR radars (black squares).

4) Oklahoma lightning mapping array

The Oklahoma lightning mapping array (LMA) is a time-of-arrival based lightning mapping system that utilizes an array of very high frequency (VHF) antennas to provide a four-dimensional map of lightning activity in thunderstorms (MacGorman et al. 2008; Thomas et al. 2004). Vertical accuracy is limited at distances further than 100 km from the LMA and horizontal accuracy becomes limited at distances beyond 200 km from the LMA. For a given lightning strike, the LMA may detect between tens and thousands of VHF sources. As stated in Sec. 1B, results from Wiens et al. (2005) suggest that better correlation is found between convection storm statistics (such as updrafts) and flashes, rather than VHF sources. Clustering of VHF source into flashes was performed as suggested by MacGorman et al. (2008), with thresholds of 3 km and 0.25 s set for inclusion of a VHF source into a flash, and a minimum of 10 VHF sources required per flash. Data shown here represent the time and location of the first VHF source within a given flash. Collocated radar analysis is performed on data gridded from the Vance Oklahoma WSR-88D.

5) K_DP column analysis

K_DP columns were objectively identified from gridded C-SAPR and KVNX data. Gridded K_DP fields were integrated vertically within a 2-km slab above the melting level and smoothed using a Gaussian smoother in order to remove texture resulting from ray-to-ray processing of the K_DP field. From this processed two-dimensional field, regional maxima were identified and a watershed segmentation algorithm (a class of feature or “blob” detection algorithms) was used to identify the boundaries and horizontal extent of each K_DP column region (see Roerdink and Meijster (2001) for a review of watershed algorithms). This method allowed for the identification of K_DP columns of irregular shape, which may or may not share a boundary with other K_DP columns. Within the horizontal bound of each K_DP column, the maximum height of the K_DP > 0.75° km⁻¹ and Z_DR > 1.0 dB level was identified. These threshold were chosen based on values reported for K_DP and Z_DR columns in previous research (e.g., Loney et al. (2002)). The corresponding C-SAPR K_DP threshold of 1.5 ° km⁻¹ was increased to account for the inverse proportionality of phase shift to wavelength. Variations of 25% in each threshold were found to have insignificant effects on the conclusions in the paper.

In order to identify the maximum height of the Z_DR level explicitly associated with liquid water, additional requirements were made that this level occur where there is a negative vertical gradient in Z_DR (indicating the top of a vertically extended column of positive Z_DR) and that this level occur below the homogeneous freezing level (about 9.5 km above MSL on each day). These requirements were imposed so as to avoid finding levels associated with oblate ice hydrometeors found near the top of the stratiform ice deck that display elevated positive Z_DR. This method may still mid-identify regions of dendritic ice growth that occur between −10 and −20 °C as Z_DR columns due to the positive Z_DR of oblate ice; however, no such regions were found and no such contamination is expected in the cases studied here. K_DP and Z_DR volume above the melting level was calculated by summing the area included in the aforementioned K_DP and Z_DR thresholds, respectively, in a 3km slab above the melting level.

b. Meteorology

Four days during the Midlatitude Continental Convective Clouds Experiment (MC3E) were selected for analysis, each featuring deep convection over Oklahoma and southern Kansas. Some characteristics of storms observed on each day are listed in Table 1. These days were chosen because all featured deep convection and were sampled by aircraft, suitable for detailed model evaluation. The four cases displayed significant differences in organizational mode and intensity. In some cases, such as May 20 and May 24, the organizational morphology of the prevalent storm systems changed considerably during the observational period.

Table 1.

Summary of days considered in this study

Day	Times analyzed (UTC)	Melting level (km)	Storm type	Notes
April 25	0600–1200	3.6 km	Disorganized MCS
May 20	0200–1300	4.4 km	Trailing-stratiform MCS	Disorganized, isolated cells transition to organized squall-line MCS
May 23	2000–0500	4.2 km	Supercell	Record hail size for Oklahoma recorded during this storm system.
May 24	1900–0200	4.3 km	Supercell, Leading-Stratiform MCS	EF-5 tornado reported during this storm system.

1) April 25 2011, 0700 – 1100 UTC (late night – early morning local)

Storms initiated along a lower-tropospheric boundary associated with a weak surface low pressure system. The skew-T diagram indicates a linear 0–6 km shear of approximately 30 m s⁻¹ (Fig. 3) with strong upper-tropospheric westerly and southerly winds. Such a wind profile has been shown to favor linear squall line development with leading stratiform precipitation (Parker and Johnson 2000), and the storms that developed in southern Oklahoma were indeed of this type. However, the storms of interest were located in northern Oklahoma to southern Kansas, and developed along a weak low-level baroclinic zone. Convection cells in this region were initially oriented west to east, but organized into south-north oriented lines as they reached maturity. Evidence of both orientations can be seen in the mid-tropospheric radar plots in Fig. 2.

Fig. 3.

Soundings from the ARM SGP central facility for each of the four days. Times chosen are shortly before radar time series analysis in this study, except for May 23, which has a sounding from a time closer to storm maturity.

Fig. 2.

Examples of radar observations and analysis from KVNX on each of the four days in this study. Left panels show radar reflectivity at approximately the melting level. Middle panels show K_DP integrated in a slab above the melting level. Right panels show K_DP column objects identified by the algorithm described in this paper. Each object is color coded and the number of objects is listed in the plot title.

2) May 20 2011, 0700 – 1100 UTC (late night – early morning local)

This case exhibited cellular convection that developed in the early morning (local time) along a dry line generated on May 19 and with synoptic forcing for ascent provided by an approaching upper-level low pressure system. Storms subsequently organized into a linear mesoscale convection systems at approximately 0830 UTC. As on April 25, 0–6 km shear was approximately 30 m s⁻¹; however, on this day the surface winds were strongly southerly, and convection matured into “leading line, trailing stratiform” structures (Parker and Johnson 2000). A south-to-north oriented convection line with trailing stratiform can be clearly seen in the radar imagery in Fig. 2. Later soundings show a well-developed rear-inflow jet as is typical in such storms Biggerstaff and Houze (1991).

3) May 23 2011, 2100 – 0200 UTC (late afternoon – late evening)

On May 23, the upper level flow was nearly zonal, with a weak short-wave trough located just west of Oklahoma and a weak surface boundary extending from southwest Oklahoma into southeast Kansas. Cellular convection initiated along a dry line located in western Oklahoma, and exhibited anvils that expanded rapidly to the east and southeast. By the time the storm had reached maturity, upper level winds were oriented from northwest to southeast, promoting anvil expansion in that direction (see Fig. 3). Thick stratiform anvil structures can be clearly seen in the radar reflectivity in Fig. 2. Isolated convection in southern Oklahoma dissipated, while storms to the north organized along the surface boundary and eventually produced a northwest-to-southeast moving bow echo.

4) May 24 2011, 2000 – 0100 UTC (late afternoon – early evening)

In contrast to the previous day, convection on May 24 developed in association with an approaching upper level trough and deepening surface low pressure system. Convection initiated along the dry line at approximately 1830 UTC, rapidly moved east-northeast, and produced thick stratiform anvils that expanded to the north and east. Cellular and super-cellular features later organized into south-to-north oriented lines that continued to propagate eastward through the remainder of the evening (local time).

3. Summary of Results

a. Time series observations: KVNX, C-SAPR, LMA & Multi-Doppler updrafts

To illustrate one example of how K_DP, Z_DR, updraft mass flux and lightning flash rates contemporaneously evolve, time series are shown for a single day, May 23 2011. Time series for the other days analyzed here are made available as supplemental materials (supplemental figures S1 through S12).

1) May 23 2011, 2000–0500 UTC (May 24 2011)

Time series of bulk polarimetric radar analysis from KVNX data collected on May 23 2011 are shown in Fig. 4. K_DP volume above the melting level shows very little signal until approximately 2120 UTC, when it increased dramatically, peaking just before 2200 UTC. Between 2200 and 2330, K_DP volume above the melting level remained elevated, while experiencing considerable fluctuations. Subsequently, K_DP volume decreased before showing three sharp increases peaking at 0045, 0145, and again at 0400 UTC, respectively. There is inconsistency in terms of the relationship between K_DP volume observed above the melting level and K_DP area at the surface. In particular, the period between 2120 and 2330 UTC showed greater K_DP area at the surface relative to above the melting layer, when compared with the period between 2330 UTC and 0200 UTC. C-SAPR data from storms on May 23rd (Fig. 5) agreed well with KVNX in both magnitude and timing of the presence of K_DP observed above the melting level, but data are temporally limited for this case because of a radar malfunction. Rain rates above both the 40 and 90 mm h⁻¹ thresholds are well correlated with one another and generally followed the evolution of K_DP volume above the melting level, though limited data exists for comparison.

Fig. 4.

Analysis of polarimetric observations from the S-band Vance WSR-88D radar on May 23, 2011. Top panel: area with K_DP > 0.75 °km⁻¹ at each level (filled colors), volume with K_DP > 0.75 °km⁻¹ above the melting level (gray line), and melting level (dotted line). Second panel as in first panel, however for Z_DR > 1 dB. Third panel: number of K_DP columns detected (black and area of each column (red). Fourth panel: maximum height of the K_DP > 0.75 ° km⁻¹ contour for each K_DP column (colored histogram), median height (gray line) and melting level (dotted line). Fifth panel: as in the fourth panel, except for the maximum height of the Z_DR > 1 dB contour for each K_DP column. Domain is red circle in Fig. 1.

Fig. 5.

Analysis of polarimetric observations from the C-SAPR radar on May 23, 2011, as in Fig. 4, except with K_DP volume threshold increased to 1.5 ° km⁻¹ and with Z_DR analysis omitted, owing to radar characteristics (see text). Domain is blue circle in Fig. 1.

Z_DR volume above the melting level is seen to have increased before elevated positive values of K_DP became evident. This finding is in agreement with use of Z_DR columns as an early observational signal of deep convection updrafts (Bringi et al. 1991). Z_DR volume above the melting level followed the general trend of K_DP volume, but maxima were not always contemporaneous. For example, the peak in K_DP volume at 0145 UTC is visible in Z_DR volume, but its shape and strength relative to other peaks is different than for K_DP. K_DP column heights are generally higher than on April 25 or May 20, though lower than May 24, with a mode in the height distribution at about 6 km, or almost 2 km above the melting level. Z_DR volume above the melting level is generally much greater than K_DP volume above the melting level. This can be explained, in part, by noting that K_DP, unlike Z_DR, requires significant concentrations of liquid hydrometeors, and may therefore be absent in cases where size sorting produces low concentrations of large droplets, for example. However, choice of K_DP and Z_DR thresholds is likely also a factor in comparison between respective volumes above the melting level. There are generally more K_DP columns that exceed 7 km in height during the later period of the storm system (after 0000 UTC) compared with the earlier period of the storm system. K_DP columns detected in the C-SAPR radar show generally good agreement with KVNX in median column height.

LMA flash analysis, shown in Fig. 6 together with polarimetric radar analysis from KVNX show that total lightning flash activity appears to lag local maxima in K_DP volume in time, but generally appears better correlated temporally with Z_DR volume above the melting level. Total flash activity peaks at values greater about equal to those observed on May 20, despite much lower values of K_DP volume above the melting level.

Fig. 6.

As in Fig. 4, however top panel shows time-height histogram of lightning flash initiation from the LMA (filled colors), together with time histogram of total flash rate (white line) and median height of initiation (gray line). Domain is overlap of yellow and red circles in Fig. 1.

Comparison of K_DP from C-SAPR with multi-Doppler wind retrievals is shown in Fig. 7. Lag correlation (not shown) peaks at r_τ = 0.93 when updraft mass flux at 0°C precedes the onset of K_DP volume above the melting level by at approximately 14 minutes (compared to a correlation of r = 0.79 for zero lag). This appears to echo results shown in Fig. 6, where the presence of K_DP volume above the melting level can be seen to lag both lightning activity and Z_DR volume above the melting level. One may hypothesize by extension that updraft statistics might be correlated with Z_DR above the melting level on this day, and thus in this case, Z_DR may better track the early updraft than K_DP. Whether or not this is the case, the fact that a lag in correlation between K_DP above the melting level and other observational metrics is observed on this day, but not others, suggests that this lag may be related to storm morphological and microphysical properties unique to the May 23 case.

Fig. 7.

Updraft (w > 1m=s) mass flux at four levels from multi-Doppler wind retrieval, K_DP > 1.5°/km volume above the melting level and K_DP “supercooled mass” from the C-SAPR radar (see text) on May 23 2011. Domain is black square in Fig. 1.

b. Statistical correlations

In order for meaningful comparison to be made between observations and simulations, aggregated statistics of relationships between storm-relevant variables should be employed. This reduces the effects of spatial and temporal phase errors related to the timing and propagation of the simulated storm system. We note, however, that it is unreasonable to assume that a linear correlation provides the best statistical analysis for relationships that are undoubtedly non-linear, and so Spearman rank correlation coefficients (ρ) are shown together with Pearson correlation coefficients (r).

Fig. 8 shows volumes which exceed the K_DP > 0.75 ° km⁻¹ threshold in a 2 km slab above the melting level compared with similar volumes observed at low levels (a 2 km slab above the surface). The K_DP volume above the melting level can be considered a K_DP signal associated with deep convection updrafts, whereas the low level volume is more closely related to convective rain rates. The two quantities plotted together thus provide a basis for insight into how much of convective rainfall is associated with deep convection updrafts, in essence providing a measure of convective intensity at a given time as well as the likelihood of mixed-phase processes in deep convection. In Fig. 8 these data are presented for each time observed using the KVNX radar, with all plots sharing an axis ratio of 1:4.5 between K_DP volume above the melting level and K_DP volume at low levels. In addition, data from each day are scaled so that plots are directly comparable, allowing for both comparison of ratio of low-level K_DP to high-level K_DP as well as temporal evolution of that ratio and low and high K_DP volumes. In these figures, points closer to the lower-right section of the plots can be considered more closely associated with concurrent deep convective updrafts than points closer to the upper-left section.

Fig. 8.

Scatter plot of K_DP > 0.75 °km⁻¹ volume above the melting level and K_DP > 0.75 °km⁻¹ volume in the bottom two kilometers above the surface. Colors indicate observation time, with darker colors indicating later observation times. Each plot is scaled identically, with a ratio of 1.4.5 for the axes of K_DP above the melting level and K_DP at low levels, respectively. Due to this scaling, units are not shown.

Data from April 25 in Fig. 8 show a generally high ratio of K_DP at low level to K_DP at high levels. This is in keeping with other metrics such as lightning and updraft mass flux that suggest that convection was weaker on this day compared with others. May 20, on the other hand, displays great variability in this deep convection K_DP ratio, in agreement with conclusions from lightning data as well as K_DP column heights recorded at this time (see supplemental time-series plots S5–S8 for details). Specifically, the relationship between low-level K_DP and high-level K_DP shows a stronger deep-convective updraft signature before 0730 UTC which is associated with the more intense lightning and higher K_DP columns observed during this time, associated with largely disorganized cellular and multi-cellular convection. This is in contrast to the strongly organized convection of the trailing-stratiform MCS that follows. Thus, in cases such as May 20 where convective morphology changes so dramatically, K_DP volume alone is insufficient to characterize the intensity of deep convection, although both the ratio of high and low-level K_DP signals as well as the heights of K_DP columns do provide some indication of these changes. May 23 also features variability in the relationship observed between high- and low- level K_DP. In this case, later cells appear to be more characteristic of deep convective updrafts. May 24 features a generally smaller ratio of K_DP at low levels to K_DP at high levels, indicating consistent deep convective updrafts, in agreement with both lightning frequency and updraft mass flux, which are the highest of the four days considered. Later times show slightly increased deep convection character as well as higher K_DP columns (see comparison in Fig. 9), a shift which is contemporaneous with the shift in storm morphology from supercellular storms to an intense leading-stratiform squall line. It bears noting that increased organization on this day is associated with an increased intensity of K_DP and lightning metrics shown here, the opposite of the trend found for May 20.

Fig. 9.

Histogram of K_DP column-top height as detected by the KVNX radar (a) and the C-SAPR radar (b), for the four days of the study. Also shown as white and black lines in panel (a) are subjectively selected sub-samples of the full histogram, to demonstrate non-stationarity of K_DP column height statistics.

Fig. 9 shows K_DP column heights as detected by KVNX and C-SAPR for each of the four days investigated. As previously discussed, results from KVNX suggest that May 24 features the strongest convection of the four days, followed by May 23, May 20 and April 25, in roughly that order. Heights of K_DP columns range from just above the melting layer to 5 km above the melting layer, in the case of some K_DP columns detected on May 24. The tails of these distributions are uncertain, as beam-width effects may result in significant exaggeration of the maximum height of features far from the radar. Assuming a simple linear model of resolution and uncertainty error that increases with distance, cumulative probability distributions of K_DP column height were calculated. The heights of the 10% (20%) probability levels (i.e., 10% (20%) probability of a given column height exceeding this value) are 5.7 km (5.3 km) for April 25, 7.3 km (6.6 km) for May 20, 6.8 km (6.3 km) for May 23 and 7.6 km (7 km) for May 24. These values are suggested as conservative estimates of maximum column heights recorded, given uncertainties caused by increased resolution error with distance from the KVNX radar.

Results from C-SAPR (also shown in Fig. 9) match KVNX results quite well despite differences in radar domain and resolution. Modes of the K_DP column height distributions are generally in very good agreement. K_DP column heights recorded in the KVNX data for May 20 suggest that the heights of K_DP columns may vary significantly within the course of a day in accordance to changing morphology and intensity of convection. For example, in the case of May 20, a decrease in both height and variability of K_DP column heights is related to a change from disorganized convection cells to a trailing-stratiform MCS with generally less intense convection. On May 24, a similar organizational process occurs, with distinct supercellular storms merging into a leading-stratiform squall line after 2230 UTC. In this case the change in storm morphology to a linearly organized state is associated with an increase in intensity of the metrics here associated with deep convection.

Multi-Doppler wind retrieval-derived updraft mass flux at the environmental −10° C level shows good (r > 0.8) correlation with C-SAPR K_DP volume above the melting level for April 25, May 20 and May 23 (Fig. 10). May 24 shows poor correlation, likely attributable to issues with wind retrieval on this day, including severe attenuation of X- and C-band radars as well as problems with Doppler de-aliasing. In some cases, K_DP is shown to correlate better with updraft mass flux at different levels. For example on April 25, K_DP volume is better correlated with updraft mass flux at the −20°C and −30°C levels and on May 20, K_DP volume is best correlated with updraft mass flux at the 0°C level (see Fig. 7 as well as supplemental Figs. S4, S8, S12). We decline to offer a hypothesis on this peculiarity, as a conclusive answer might require a detailed analysis of uncertainties in the multi-Doppler wind retrievals for each day studied, which is beyond the scope of the current study.

Fig. 10.

Updraft mass flux at −10° C from multi-Doppler wind retrieval vs. K_DP > 1.5 ° km⁻¹ volume above the melting level. Domain is black square in Fig. 1. Colors as indicated in legend, where linear correlation coefficients are also provided.

K_DP volume above the melting level, as detected by C-SAPR, is well correlated with intense surface rain rates estimated via the R(A) method of Ryzhkov et al. (2014); Giangrande et al. (2014). These values are shown together in Fig. 11. All days show correlation coefficients of r > 0.75.

Fig. 11.

C-SAPR K_DP > 3.5 ° km⁻¹ volume above the melting level vs. domain-averaged rain rates for rain above 90 mm h⁻¹, derived using specific attenuation (Ryzhkov et al. 2014; Giangrande et al. 2014). Domain is blue circle in Fig. 1.

To investigate whether strong updrafts appear in the vicinity of K_DP columns, a joint histogram of K_DP column heights as detected by the C-SAPR radar and coincident maximum updraft speed, as retrieved by multi-Doppler wind analysis is shown in Fig. 12. Maximum retrieved updraft speed (w > 1 m s⁻¹) is collected in the 3D columnar region defined by the 2D K_DP column object boundaries. K_DP column height shows a weak correlation (r = 0.37) with multi-Doppler retrieved updraft speed. One hypothesis for this weak correlation is that true correlations between these variables may occur with some spatial and temporal lag. Loney et al. (2002), for example, noted that updrafts and the hydrometeors that produce K_DP columns are likely spatially distinct features, at least in the absence of resolution-broadening of the K_DP column. Furthermore, updrafts are likely to be tilted, or even helical depending on shear and storm helicity; these effects are likely to impact the location and shape of polarimetric features of deep convection updrafts (e.g. Kumjian and Ryzhkov (2009)). A more robust approach may be to search for updrafts in the spatial region surrounding a K_DP column, or to analyze the full lifecyle of K_DP columns from a Lagrangian perspective. This last approach would also reveal any correlations between K_DP and updraft strength that lag in time. A stronger correlation is observed between K_DP column area and maximum updraft speed, but this may be partly explained by noting that no matter the region chosen, larger areas are more likely to result in a greater maximum updraft speed than smaller areas.

Fig. 12.

Joint histogram of K_DP column top height from the C-SAPR analysis and multi-Doppler derived maximum updraft speed detected within K_DP column region (left). Joint histogram of K_DP column area from the C-SAPR analysis and maximum updraft speed. Data aggregated from April 25, May 20, May 23 and May 24 cases within the domain of the multi-Doppler analysis. Linear correlation coefficients provided within panels.

Each day featured widely varying K_DP column heights as well as substantial variability in K_DP volume, updraft and lightning statistics; however, common characteristics can be identified for each day. Fig. 13 shows a clear relationship between K_DP column height and K_DP column area for columns detected by KVNX. C-SAPR results, also shown in Fig. 13, generally match these results, although column areas are not as great as in the KVNX data, likely because the poorer resolution of the KVNX data exaggerates column size and also results in the apparent merging of columns. Spread in the joint distribution of K_DP column area and height can be explained either by resolution effects or variations in the area-height relationship over the lifecycle of a convection cell or both. Evaluating this last possible explanation requires analysis of the full lifecycle of convective cells in a Lagrangian framework.

Fig. 13.

Comparison of K_DP > 0.75° km⁻¹ contour heights and K_DP column areas for K_DP columns detected by the KVNX radar (top) and C-SAPR radar (bottom). Linear (r) and rank (ρ) correlation coefficients provided within panels.

K_DP column height is also correlated with height of coincident Z_DR features (Fig. 14. This correlation indicates that when K_DP columns are present, Z_DR columns also tend to be present. Z_DR height tends to be lower than K_DP height partly from anomalous reduction of Z_DR values from differential attenuation or the presence of hail in the radar volume or both. Analysis of K_DP and Z_DR volumes above the melting level (see top two panels of Fig. 4) suggest that deep convective signatures of K_DP and Z_DR evolve semi-independently. As such, it is likely that the presence of K_DP and Z_DR columns are not strictly contemporaneous or spatially collocated and one may draw similar conclusions from previous studies (Loney et al. 2002; Kumjian et al. 2014a).

Fig. 14.

Comparison of K_DP >0.75° km⁻¹ and Z_DR > 1 dB contour heights for K_DP columns detected from KVNX radar observations. The dotted red line indicates the 1:1 line. Linear correlation coefficients (r) and rank correlation coefficients (ρ) are provided within panels.

Finally, the relationships between lightning total flash rate and K_DP and Z_DR volumes are shown in Fig. 15 to further explore the relationship between the polarimetric signals associated with mixed-phase processes in deep convection updrafts and lightning, a phenomenon physically linked with such processes in continental convection. For all four days, a positive correlation is found between K_DP volume above the melting level and total flash density, though correlation is only moderate and highly variable across the four days studied (for an example of collocation of lightning flashes and K_DP columns, see supplemental Figure S13). Interestingly, data from both May 20 during the disorganized phase of convection before 0730 UTC and data from May 23 indicates a lagged correlation (not shown) of approximately r = 0.6 at 10 minutes lag (i.e., lightning peaks 10 minutes after K_DP volume above the melting layer does, on average). This lagged correlation underscores a need for treatment of the full updraft lifecycle in order to better ascertain the relationships between lightning, K_DP above the melting level, and updraft strength. Z_DR volume above the melting level also shows correlation with flash rates on all days except May 20, where resolution effects produce anomalously large Z_DR volume above the melting layer. On May 24, periods of substantial differential attenuation and the possible presence of hail in the radar volume results in many samples with copious lightning flash activity, but relatively small Z_DR volume above the melting level.

Fig. 15.

Comparison of K_DP > 0.75° km⁻¹, Z_DR > 1 dB volumes and total lightning flash rate measured by KVNX and the Oklahoma LMA, respectively, for the four days studied here. Points are colored according to relative time during the period of interest. All plots in a given row share a common axis ratio between x- and y-axes. Linear correlation coefficients are provided in each panel. Data after 2315 UTC on May 24 were not included in calculation of correlation owing to possible failure of the LMA at this point.

4. Discussion

The strong link seen between K_DP observed above the melting level and updraft statistics in 3 out of 4 cases supports our working hypothesis that K_DP is a useful proxy for deep convection updrafts. Detail of the K_DP signal also elucidates information relevant to changing storm morphology and, likely, updraft microphysics. Lightning flash rates also show that K_DP and lightning flash activity do not always display a simple covariance, and the relationship between these variables may depend on the morphological characteristics of the convection that produces them. For example, early disorganized convection cells on May 20 appear more electrically active for a given K_DP volume above the melting level. This especially active period, in turn, occurs at a time when K_DP volume above the melting level is large relative to K_DP volume at low levels, indicating an increased deep convective character of the storm system. This early phase of storm activity on May 20 also displays lagged correlations between K_DP volume and lightning flash activity. Similarly lagged relationships are seen for observations onMay 23, but not significantly for April 25 orMay 24. We hypothesize that lagged correlation occurs at the scale of individual updraft cells, and thus may not be evident in cases where many cells exist at varying points in their lifecycles. In cases such as early May 20 and throughout May 23, overall lag may be evident by virtue of updraft cells with temporally correlated lifecycles. On May 20 it is unclear what causes this correlation; however, on May 23 multiple convection cells initiate almost simultaneously along a dry line, in comparison with organized MCS squall lines occurring later on May 20 and late on May 24 that consist of many updraft cells at different stages of their lifecycles.

As previously mentioned our results suggest that analysis of K_DP columns above the melting level is useful for characterizing deep convection. Height of K_DP columns, likely related to the lifecycle of individual updraft cells, reveal variability that tracks other metrics of storm intensity, in particular on May 20 and May 24 where particularly high K_DP columns are observed when lightning flash activity peaks, for example. Nevertheless, further work is planned to better ascertain fundamental spatial characteristics of K_DP columns and other polarimetric features of deep convection, and are mentioned in the Conclusion. Perhaps unsurprisingly we find that radar resolution strongly affects measures of K_DP columns. For example, C-SAPR typically detects a greater number of smaller K_DP columns than KVNX. These results are also in agreement with results from Loney et al. (2002), in which radar perception of a K_DP column fails to capture the fine-scale structure of hydrometeor fields detected in-situ.

It should be noted that Z_DR sometimes shows good agreement with lightning as well, such as for the storms on April 25 and May 23. In particular, Z_DR above the melting level may be better suited to revealing the early appearance of deep convection than K_DP above the melting level. On April 25, May 23 and May 24, Z_DR volume above the melting level increases to appreciable values (approx. 100 km²) 30 to 60 minutes before K_DP volume does. This earlier detection may result from Z_DR-column producing convective updrafts that quickly produce large raindrops in relatively low concentrations through droplet recirculation pathways (Kumjian et al. 2014b). Considerable values of liquid water content that might result in elevated K_DP only occur later as the microphysical processes that produce them become active. These processes may include droplet shedding by wet hail, as suggested by Hubbert et al. (1998), or the formation of mixed-phase hydrometeors (e.g., small wet hail), as suggested by Loney et al. (2002), or lofting of supercooled rain produced by warm-rain processes.

Particularities endemic to the measurement of Z_DR present problems for its use in mapping the lifecycle of a convection updraft cell. Differential attenuation effects caused by transmission of the radar beam through volumes containing oblate particles may anomalously reduce Z_DR, for example between 0900 and 1000 UTC on May 20, or just after 2000 UTC on May 24 (see supplemental Figs. S5 and S9). At other times, the presence of hail as a dominant scatterer may result in small Z_DR, despite the continued presence of liquid hydrometeors; it is this feature that is implicated in the “death” of the Z_DR column in Kumjian et al. (2014b). Finally, degraded resolution causes anomolous values of Z_DR due to non-uniform beam filling when strong spatial gradients of hydrometeors are observed far from the radar Ryzhkov (2007). These effects were only found to be significant onMay 20, and are partly responsible for the poor correlation between Z_DR volume and lightning on May 20 shown in figure 15. These effects may not be as pronounced for K_DP because they are likely removed during phase processing.

Lagged correlations between K_DP and both updraft mass flux and lightning flash rates, observed primarily early on May 20 and throughout May 23 strongly suggest that correlations between K_DP and other aspects of deep convective storm activity occur on the lifecycle of an updraft cell rather than the lifecycle of a storm system, which may comprise many convective updrafts in various stages of maturity. Storm-wide analysis may serve to underestimate these relationships, as multiple updraft cells may be present at differing stages of their lifecycles. Cell-tracking may allow a more complete characterization of K_DP as a signal of deep convection updrafts. We hypothesize that only by tracking individual updraft cells within larger storm systems can definitive answers be found concerning the variability of K_DP columns within a single storm system as well as between different storm systems. Future work will investigate these ideas, with detailed comparison between modeled and observed updraft cells.

5. Conclusions

In this study observations by C- and S-band polarimetric radars of four storm systems during the MC3E field campaign were analyzed to investigate the characteristics of enhanced positive specific differential phase (K_DP) above the melting level to motivate its use as an observational metric of deep convection updraft properties. The volume above the melting level where K_DP > 0.75 °km⁻¹ and K_DP > 1.5 °km⁻¹ from KVNX and C-SAPR radars, respectively, were recorded. In addition, K_DP columns thought to be proxies for deep convection updraft were identified. These data were then statistically compared with lightning flash activity, Z_DR from KVNX, precipitation estimates from the C-SAPR radar, and updrafts retrieved using two X-band radars and the C-SAPR radar.

K_DP volume was found to correlate well with retrieved updraft mass flux in 3 out of 4 cases, with some evidence that K_DP lags peak updraft mass flux by approximately 14 minutes. K_DP volume also shows a strong relationship with flash rate; here again there is some indication that lightning flash rates may lag K_DP volume by approximately 10 minutes. K_DP column heights were shown to be variable between days studied and also show variability within a single day, in accordance with changes in storm morphology. Despite this, consistent statistical relationships are seen between K_DP column height and column horizontal area. Intense rain rates (above 90 mm h⁻¹) correlate well with K_DP volume, in contrast to more moderate convective rain rates (above 40 mm h⁻¹). This difference indicates that K_DP is best correlated with especially intense convection, and may not track moderate deep convection activity as well. Finally, Z_DR volume shows similar correlations as K_DP, with Z_DR at times a better indicator of the early stages of deep convection, as well as more moderate convection. Conversely, when convection is more intense, Z_DR may suffer from artifacts related to differential attenuation and other factors. These findings suggest the combined use of Z_DR and K_DP columns to characterize deep convection updrafts.

Loney et al. (2002) note that significant radar resolution degradation may preclude the use of K_DP and Z_DR to ascertain the structure of hydrometeor fields. Comparison between K_DP columns detected by C-SAPR and KVNX further support this result, and suggest that NEXRAD radars may be inappropriate for determining fundamental scales of such features because of inadequate range resolution. Work has begun comparing the spatial statistics of polarimetric radar features observed at varying radar resolutions alongside high-resolution modeled simulations of deep convection in order to answer questions such as: What is the fundamental size of a K_DP or Z_DR column? How closely are these columns spaced from one another? What is the variability of these metrics between and within storm systems? How do characteristics of simulated updrafts and forward-modeled polarimetric properties compare with those observed?