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Hail trajectory modeling is a popular tool to explore how environment and storm characteristics allow or prohibit large hail growth. However, trajectory models are complex and computationally expensive: storm dynamics relevant to hail growth are inextricably linked such that ``cause’' and ``correlation” are difficult to distinguish. Therefore, we develop a novel hail trajectory model that can be used to untangle hail growth processes. Toward this end, we explore the vertical structure of vertical velocity and liquid water content in updrafts and define analytic functions that approximate the thermodynamic prediction of these quantities. These analytic profiles are used, along with a temporal updraft-pass parameterization to define a 2D updraft (defined in height and time) in which hailstones can grow. Hail growth in this 2D updraft is fully defined by a set of 16 scalar parameters that act as turnable knobs to produce unique hail trajectories. This article is Part I of a series using this modeling framework to explore the nature of hail growth. Here, we define the model and test its ability to produce realistic hail trajectories and hail sizes through a Monte Carlo simulation with physical couplings maintained. The size distribution from 1 billion simulated trajectories is exponential and has maximum hail size of 25.7 cm. Stochasticity in the model’s representation of hail fall speed and cross-sectional area is explored and produces some variability in the resulting hailstone sizes. The model produced and evaluated here will be used in further studies to identify how environment, updraft, and hail embryo characteristics individually impact hail growth. 

This is Part II of a multi-part series exploring the fundamental nature of hail growth through a toy model developed in Part I. The toy model uniquely parameterizes all hail growth processes by single-valued parameters with great computational efficiency. The parameters are uncoupled so that environment, storm, and hail embryo characteristics, and their impact on hail growth, can be studied independently---a task 3D trajectory models cannot perform because of their highly coupled nature. Three Monte Carlo simulations were run to compare hail growth from small and large hail embryos, and coupled and uncoupled model parameters. Hail with maximum dimension ($$D$$) $$\le25.71$$ cm grew in the physically coupled small-embryo simulation, $$D\le33.59$$ cm hail grew in the physically coupled large-embryo simulation, and $$D\le44.97$$ cm hail grew in the uncoupled large-embryo simulation. The largest hailstones from the three Monte Carlo simulations took similar trajectories, accumulating a large proportion of their mass both while suspended and during their fall. Analysis of model parameters corroborate current hail growth theory, indicating three necessary ingredients for large hail: (1) a favorable embryo size and location, (2) a long residence time in a water-rich updraft, and (3) a balance between updraft vertical velocity and hailstone fall speed. The sensitivity of hail size to these parameters is analyzed: a hailstone's potential size is limited by its updraft-pass duration and the available amount of supercooled liquid water, but hail size is most sensitive to the balance between its fall speed and its encountered updraft vertical velocity. 

Abstract Modeled hail trajectories have previously been studied in individual observed supercells or in simulated supercells with similar background environments. To explore the impact of changing updraft structure on hail formation from a different perspective, this study analyzes detailed hail trajectories in a large ensemble of time-averaged supercell-like updrafts. The updrafts are created with an idealized heat source, which allows the systematic investigation of the full range of updraft widths and intensities reported in the literature. The simulations exhibit a dominant hail trajectory pathway with a single ascent and a curved horizontal trace. However, a systematic shift in the trajectories and in their start and end locations is found with increasing updraft intensity and updraft width. Furthermore, wider updrafts but with only moderate intensity provide optimal conditions for the hail of most sizes. The exception is giant hail, which requires both wide and intense updrafts. This result is partially linked to the occurrence of an alternative trajectory pathway characterized by the recycling of hailstones (1–4 cm) in the back-sheared anvil region, which then grew to giant size after reentering the updraft. 

Abstract Data obtained during the NSF-funded Experiment of Sea Breeze Convection, Aerosols, Precipitation, and Environment (ESCAPE) field campaign and conventional observations are used to evaluate the physical mechanisms responsible for convection initiation (CI) over coastal Texas during the 2 June 2022 intensive observational period. Failed CI attempts first occurred about 1300 UTC (8 am local time, LT) along a decaying land breeze located parallel to and offshore of the Texas coastline. Subsequent successful CI, which occurred around 1430 UTC (9:30 am LT), required the assistance of gravity waves that formed as an upstream MCS cold pool perturbed the stable lower troposphere. Upon the interaction between the leading radar-detected gravity wave and the offshore remnants of the land breeze, convective cells developed along the length of the offshore boundary. Outflow from this line of cells moved inland and initiated new convective cells resulting in widespread convection over the coastal zone that continued past 2000 UTC (3:00 pm LT). Results from this work illustrate the complex chain of mechanisms that can lead to CI over coastal regions, and emphasizes the challenges encountered by forecasters in predicting coastal CI. 

Abstract Hail research and forecasting models necessarily involve explicit or implicit—and uncertain—physical assumptions regarding hailstones’ shape, tumbling behavior, fall speed, and thermal energy transfer. Whereas most models assume spherical hailstones, we relax this assumption by using hailstone shape data from field observations to establish empirical size–shape relationships with reasonable degrees of randomness considering hailstones’ natural shape variability, capturing the observed distribution of triaxial ellipsoidal shapes. We also incorporate explicit, random tumbling of individual hailstones during their growth to simulate their free-falling behavior and the resultant changes in cross-sectional area (which affects growth by hydrometeor collection). These physical attributes are incorporated in calculating hailstones’ fall speeds, using either empirical relationships or analytical relationships based on each hailstone’s Best and Reynolds numbers. Options for drag coefficient modification are added to emulate hailstones’ rough surfaces (lobes), which then modifies their thermal energy and vapor exchange with the environment. We investigate how applying these physical assumptions about nonspherical hail to the Penn State hail growth trajectory model, coupled with Cloud Model 1 supercell simulations, impacts hail production and examine the reasons behind the resulting variability in hail statistics. The choice of hailstone size–mass relation and fall speed scheme have the strongest influence on hail sizes. Using nonspherical, tumbling hailstones reduces the number of large hailstones produced. Applying shape-specific thermal energy transfer coefficients subtly increases sizes; the effects of lobes vary depending on the fall speed scheme used. These physical assumptions, although adding complexity to modeling, can be parameterized efficiently and potentially used in microphysics schemes. Significance StatementIn numerical modeling of hailstorms, we usually consider hailstones to be spherical to simplify calculations, but in nature, hailstones generally are not spheres and can be rather lumpy and have spikes. The purpose of this study is to examine how the model result would change when nonspherical hailstone shape is implemented. We examine the relationship between hailstone shape and physical processes during hail growth in effort to explain why these changes occur and offer insights on how nonspherical hailstone shape may be parameterized in bulk microphysics schemes. 

Previous work has shown that differential reflectivity ZDR observations from National Weather Service dual-polarization Doppler weather radars (WSR-88Ds) provide accurate estimates of convective boundary layer (CBL) depth when compared with depth estimates from 0000 UTC rawinsonde observations. We extend this work by launching small rawinsondes, called Windsonds, to study ZDR signals throughout the daytime hours. Results show that it can be difficult to identify CBL depth from ZDR alone when biological scatterers are absent. The exploration of other radar variables leads to the use of azimuthal ZDR variance to help in identifying CBL characteristics. A variable that combines both ZDR and azimuthal ZDR variance, called DVar, allows for improved signal identification using the quasi-vertical profile (QVP) method. Furthermore, the QVP channel width is found to be closely tied to the overall entrainment zone (EZ) structure. Results show that the centers and vertical extents of channels of reduced DVar in QVPs correlate well with sounding-observed CBL depth and EZ depth, respectively, across all stages of CBL development and in both clear and cloud-topped CBLs. The QVP approach tends to fail in identifying CBL and EZ depths when the vertical gradient in moisture above the CBL is small. Additionally, we compare the observed EZ depth to various EZ parameterizations and show that the parameterizations generally underestimate EZ depth. We conclude that the ability of WSR-88Ds to sample the CBL should be leveraged to increase our knowledge of CBL properties. Significance Statement: The boundary layer is the lowest layer of Earth’s atmosphere and influences many weather-related phenomena. During the day, sunlight warms the surface and the convective boundary layer (CBL) forms. Even though CBL characteristics are important for accurate weather forecasts, current methods of observing the CBL are severely lacking. This study investigates the potential of using dual-polarization weather radars to expand CBL observations. We also evaluate how well simplified CBL models predict certain CBL characteristics and how they could be improved in the future. 

Convective boundary layer (CBL) depth can be estimated from dual-polarization WSR-88D radars using the product differential reflectivity ZDR because the CBL top is collocated with a local ZDR minimum produced by Bragg scatter at the interface of the CBL and the free troposphere. Quasi-vertical profiles (QVPs) of ZDR are produced for each radar volume scan and profiles from successive times are stitched together to form a time–height plot of ZDR from sunrise to sunset. QVPs of ZDR often show a low-ZDR channel that starts near the ground and rises during the morning and early afternoon, identifying the CBL top. Unfortunately, results show that this channel within the QVP can occasionally be misleading. This motivated creation of a new variable DVar, which combines ZDR with its azimuthal variance and is particularly helpful at identifying the CBL top during the morning hours. Two methods are developed to track the CBL top from QVPs of ZDR and DVar. Although each method has strengths and weaknesses, the best results are found when the two methods are combined using inverse variance weighting. The ability to detect CBL depth from routine WSR-88D radar scans rather than from rawinsondes or lidar instruments would vastly improve our understanding of CBL depth variations in the daytime by increasing the temporal and spatial frequencies of the observations. Significance Statement: The daytime convective boundary layer (CBL) can increase in depth from a few hundred to a few thousand meters between sunrise and sunset and is strongly connected to temperature changes at Earth’s surface. Unfortunately, current observations of CBL depth primarily consist of measurements from twice daily rawinsonde launches at 97 locations across the United States. As a result, CBL depth observations lack fine spatial and temporal resolution and miss the daily cycle of CBL growth. This study seeks to fill the gaps in CBL depth observations by developing an automated method to estimate CBL depth from dual-polarization WSR-88D radar observations with a temporal resolution as fine as 5–10 min. These observations will greatly enhance our ability to observe and monitor CBL depth in real time. 

Abstract Convection initiation (CI) remains a formidable forecasting challenge, particularly along the coast. Examining Houston, Texas, radar observations of isolated cells’ CI spatiotemporal patterns for Junes from 2017 to 2022 revealed three patterns: cells forming exclusively over land (LAND), over coastal waters (GULF), or domainwide, initiating first over land (DW-L) or the water (DW-G). CI and dissipation times varied by regime. LAND events tended to typify the diurnal cycle, whereas GULF events tended to initiate overnight; both had durations < 10 h. In contrast, DW events began overnight and lasted until evening, with durations often exceeding 10–15 h. Synoptic-scale composites for each regime revealed only minimal forcing for ascent, suggesting the local environment’s importance for CI. Composite vertical profiles for CI locations revealed surface-based CAPE > 1500 J kg⁻¹and CIN > −40 J kg⁻¹for each regime. LAND had the hottest and driest lowest 1 km AGL, but was moistest between 1 and 2 km, suggesting LAND parcels originating below 1 km may be susceptible to entrainment and require moister midlevels for successful CI. We also found conditional instability below 1 km AGL for all regimes but a stable layer for GULF and neutral layers for LAND and DW-G between 1 and 2 km. This indicates saturation of air parcels within this layer is insufficient for CI, and mechanical lifting (e.g., sea breeze) would be necessary for CI. Indeed, all regimes featured potential instability throughout the lowest 4 km. However, only the LAND regime had a coastal density gradient conducive to sea-breeze formation; this indicates other lifting mechanisms may be important in the other regimes. Significance StatementForecasting the timing and location of storm formation is a major challenge, particularly in coastal areas. We endeavor to understand storm formation patterns in the Houston, Texas, area, with the main goal of better understanding how precursor atmospheric conditions may favor or disfavor such storm formation. We find four spatial patterns of storm formation: only over the land, only over coastal gulf waters, or over both land and gulf (but starting over land or the gulf). Average large-scale and local conditions were similar for each regime, with only subtle differences in their low-level temperature and humidity profiles. Results suggest that small-scale features like sea breezes thus are required for initiation, but only the LAND regime has sea-breeze-favorable conditions. 

Abstract Supercell storms are commonly responsible for severe hail, which is the costliest severe storm hazard in the United States and elsewhere. Radar observations of such storms are common and have been leveraged to estimate hail size and severe hail occurrence. However, many established relationships between radar-observed storm characteristics and severe hail occurrence have been found using data from few storms and in isolation from other radar metrics. This study leverages a 10-yr record of polarimetric Doppler radar observations in the United States to evaluate and compare radar observations of thousands of severe hail–producing supercells based on their maximum hail size. In agreement with prior studies, it is found that increasing hail size relates to increasing volume of high (≥50 dBZ) radar reflectivity, increasing midaltitude mesocyclone rotation (azimuthal shear), increasing storm-top divergence, and decreased differential reflectivity and copolar correlation coefficient at low levels (mostly below the environmental 0°C level). New insights include increasing vertical alignment of the storm mesocyclone with increasing hail size and a Doppler velocity spectrum width minimum aloft near storm center that increases in area with increasing hail size and is argued to indicate increasing updraft width. To complement the extensive radar analysis, near-storm environments from reanalyses are compared and indicate that the greatest environmental differences exist in the middle troposphere (within the hail growth region), especially the wind speed perpendicular to storm motion. Recommendations are given for future improvements to radar-based hail-size estimation. 

Abstract. The layered structures inside hailstones provide a direct indication of their shape and properties at various stages during growth. Given the myriadof different trajectories that can exist, and the sensitivity of rime deposit type to environmental conditions, it must be expected that manydifferent perturbations of hailstone properties occur within a single hailstorm; however, some commonalities are likely in the shared early stagesof growth, for hailstones of similar size (especially those that grow along similar trajectories) and final growth near the melting level. Itremains challenging to extract this information from a large sample of hailstones because of the time required to prepare cross sections andaccurately measure individual layers. To reduce the labour and potential errors introduced by manual analysis of hailstones, an automated method formeasuring layers from cross section photographs is introduced and applied to a set of hailstones collected in Melbourne, Australia. This work ismotivated by new hail growth simulation tools that model the growth of layers within individual hailstones, for which accurate measurements ofobserved hailstone cross sections can be applied as validation. A first look at this new type of evaluation for hail growth simulations isdemonstrated.