Improving the Representation of Hail in the Thompson Microphysics Scheme

1. Introduction

The Thompson–Eidhammer (Thompson and Eidhammer 2014, hereafter TE14) bulk microphysics scheme runs operationally in the High-Resolution Rapid Refresh (HRRR; Benjamin et al. 2016) numerical weather prediction (NWP) model and is used extensively to aid in the prediction of aviation and societal hazards like aircraft icing (Thompson et al. 2017), convective storms (Clark et al. 2014), wintertime precipitation (Ikeda et al. 2013), and heavy precipitation and floods (Viterbo et al. 2020). To ensure that the prediction of various weather hazards can occur in real time, TE14 must be computationally efficient yet complex. Several interacting liquid and ice categories must be represented in the scheme, including cloud droplets and rain (both warm and supercooled), pristine ice, snow, and graupel/hail. These categories are simple representations, for computational efficiency, of liquid and ice in clouds. One simplification in TE14 is that graupel and hail are combined into a single rimed-ice category since they both grow by collecting supercooled water, or rime. Consequently, graupel and hail are indistinguishable in TE14. The TE14 rimed-ice category is essentially an average representation of both low-density graupel and high-density hail. This approach has been sufficient for predicting general convective storm characteristics like spatial distribution and diurnal cycle (Clark et al. 2014). However, it is insufficient for predicting more detailed microphysical storm characteristics and hazards such as hail size, density, and fall speed, which can be used to provide guidance on the timing and spatial extent of damaging hail.

From 1949 to 2006, annual property loss from hail damage in the United States was $852 million (U.S. dollars) (Changnon 2008). The extent of hail damage depends largely on hailstone size. Hailstones larger than 0.64 cm (0.25 in.) in diameter can cause crop damage (Changnon 1971); hailstones larger than 2.54 cm (1 in.) in diameter can cause roof damage (Marshall et al. 2002). Unsurprisingly, day-of and next-day predictions of hail-producing storms highlight regions where hail size is expected to be large. Hail size has traditionally been predicted based on environmental parameters like lapse rate, wind shear, temperature, height of the 0°C wet-bulb temperature level, and convective available potential energy (CAPE), which have been formulated into indices like the significant hail parameter (SHIP). Hail prediction may also be based on results from 1D hail growth models that use vertical profiles of appropriate NWP model output variables such as temperature, liquid water content, and vertical velocity, to directly predict hail growth in storms that contain sustained updrafts, e.g., HAILCAST (Adams-Selin and Ziegler 2016). These methods have shown reasonable accuracy (Herman et al. 2018; Adams-Selin et al. 2019; Gagne et al. 2017), but HAILCAST predicts some hail-size ranges better than others depending on how it is tuned (Adams-Selin et al. 2019), and SHIP struggles in environments with high shear and low CAPE (Herman et al. 2018).

Hail size can also be predicted directly by detailed microphysics schemes, like TE14, and there are several benefits of doing this. First, graupel/hail growth in these schemes is directly coupled to the storm dynamics, whereas the microphysics does not affect the dynamics in 1D growth models like HAILCAST. Second, a predicted hail size in the operationally run TE14 can be used to improve and supplement hail products like HAILCAST and SHIP, especially in environments where those methods are known to be ineffectual. Third, predicting hail size in TE14 can help improve understanding of hail growth in general and can help constrain hail-growth processes in models since hail-embryo initiation, hail-growth processes, and fallout and melting are all directly formulated in TE14. A current limitation to predicting hail size and other hail properties, like fall speed and density, in TE14 is the simple way that graupel and hail are combined into a single rimed-ice category. Modifications to TE14 are necessary so that hail can be distinguished from graupel and hail properties like size can be better predicted, both in-cloud and at the surface.

The graupel/hail hybrid category in TE14 is one-moment (cf. Rutledge and Hobbs 1984; Hong and Lim 2006); graupel/hail mass mixing ratio is the only prognostic variable for that category, and graupel/hail density is assumed to be constant. Graupel/hail density has been prescribed as 500 kg m⁻³, which is meant to represent a median value in the large range of observed graupel and hail densities (Heymsfield 1977; Knight and Heymsfield 1983). Bulk microphysics schemes like TE14 that prognose only one moment for graupel/hail generally use a constant y-intercept (hereafter intercept) parameter that is needed to diagnose the particle size distribution (PSD). Sensitivity studies have shown that using a constant intercept parameter and a constant density can significantly constrain predicted hail size: simulated storms either produced only pea-size or baseball-size hail (Gilmore et al. 2004). Partly for this reason, Thompson et al. (2004, 2008) implemented a diagnostic intercept parameter as a function of graupel/hail mass mixing ratio and supercooled rainwater (see Thompson 2013) to simulate sizes of both graupel—produced by heavily rimed snow—and higher density hail that may have been grown by freezing of large raindrops and subsequent wet growth. While the original relationship was developed ad hoc, it permits a relatively wide range of simulated convective storm characteristics, produces relatively realistic storm structures (Clark et al. 2014), and is computationally efficient for operational use.

While computationally more expensive, graupel/hail number mixing ratio, a second moment, can also be used as a prognostic variable, which provides more degrees of freedom to represent the PSD. In these two-moment schemes (e.g., Ferrier 1994; Reisner et al. 1998; Morrison and Pinto 2005; Milbrandt and Yau 2005) graupel/hail size is constrained by both mass and number. For a given mass, knowing the number of particles over which that mass is distributed provides an improved constraint on size. In one-moment schemes, size generally depends only on mass: size changes only when mass changes, assuming the intercept parameter and particle density are constant. In two-moments schemes, changes in number can cause changes in size. For example, the addition of numerous small, frozen raindrops into a distribution of large graupel particles will cause the mean size of the graupel to decrease. While a second moment can be used to constrain graupel/hail size, it cannot be used to directly distinguish graupel from hail.

A straightforward method to distinguish graupel from hail is to use separate categories for graupel and hail (e.g., Milbrandt and Yau 2005), to allow for differences in densities and fall speeds of the two categories. But this requires four prognostic variables to represent graupel and hail in a two-moment scheme. Some relatively new schemes (e.g., Mansell et al. 2010; Mansell and Ziegler 2013; Milbrandt and Morrison 2013; Morrison and Milbrandt 2015; Morrison et al. 2015, 2016; Milbrandt and Morrison 2016; Jensen and Harrington 2015; Jensen et al. 2017) predict ice particle properties during growth including rime density. The density of rimed ice can range from 50 to 900 kg m⁻³ (see Heymsfield 1977), and hail and ice pellets (newly frozen raindrops) typically have the highest densities and rimed snowflakes (graupel particles) typically have the lowest densities. Low-density graupel forms when snow collects supercooled cloud water slowly enough so that air bubbles become trapped among the rime. High-density hail forms when supercooled liquid is rapidly collected and relatively few air bubbles are trapped in the ice, producing a particle that has a density closer to that of bulk ice (920 kg m⁻³). Predicting graupel/hail density provides a natural way to distinguish graupel from hail based on how particles grow. Additionally, since density is a function of mass and volume and graupel/hail mass is already a prognostic variable in TE14, only one additional prognostic variable (volume) is needed to predict graupel/hail density.

There are other benefits of predicting graupel/hail density. Density affects fall speed; low-density rimed particles fall relatively slower than high-density ones. For particles of the same size, a particle with a density near 900 kg m⁻³ falls approximately 2.3 times faster than a particle with a density of 200 kg m⁻³ (Heymsfield and Wright 2014). This ultimately has an impact on the spatial distribution of precipitation (Milbrandt and Morrison 2013; Jensen et al. 2018; Han et al. 2019) and the amount and type of precipitation that reaches the surface, which affects convective storm characteristics such as propagation speed and strength through dynamical feedbacks from melting ice and evaporating rain (Morrison and Milbrandt 2011; Adams-Selin et al. 2013). Another benefit of predicting graupel/hail density is that ice pellets, high density ice that forms when liquid or partially frozen precipitation refreezes below a warm nose (air with T > 0°C) in wintertime conditions can be explicitly represented. Ice pellets at the surface indicate that there is freezing rain aloft, and they can also stick to aircraft and overwhelm deicing operations (Landolt et al. 2019). The ability to predict ice pellets directly can aid in the understanding of complex wintertime cloud systems and the prediction of hazardous wintertime precipitation.

The potential benefits of predicting both graupel/hail number concentration and density have led to the development of a new two-moment and predicted density graupel/hail category in TE14. In this formulation, graupel can be distinguished from hail, and hail size, density, and fall speed can be tracked during growth and fallout. Additionally, hail particle properties such as hail size, number concentration, fall speed, density, and reflectivity can be directly evaluated with observations, which can ultimately help constrain the formulation. Improving the representation of rimed ice particle properties in TE14 may also lead to improvements in predicted storm dynamics and propagation speed through microphysical feedbacks and improvements in the spatial distribution and type of precipitation at the surface.

The two-moment and predicted density graupel/hail scheme is more computationally costly to run since two new prognostic variables have been added, but as computational power increases, this more detailed microphysics could be run operationally. For now, the scheme can be used to explore the effects of predicting graupel/hail number and density on various cloud systems. Additionally, it can be used as a baseline to guide improvements to the one-moment graupel/hail category in TE14. In this regard, a new one-moment graupel/hail intercept parameter that is constrained by hail observations from Field et al. (2019) has also been developed and evaluated as a first step toward tuning a version of TE14 that can be used for hail prediction.

In this paper, the two-moment and predicted density graupel/hail formulation and the modified one-moment graupel/hail intercept-parameter formulation are first described. Weather Research and Forecasting (WRF) simulations of a case observed during the Plains Elevated Convection at Night (PECAN) field campaign, during which there were multiple hail reports across South Dakota and subsequently a mesoscale convective system (MCS), are run using the two-moment, the updated one-moment, and the original TE14 scheme. The three versions of the scheme are evaluated using radar observations, hail-size observations, and surface temperature and wind speed observations.

2. Modifications to the Thompson microphysics graupel/hail category

a. One-moment graupel/hail

The rimed ice category in the TE14 microphysics scheme is colloquially known as the graupel category. While it is meant to represent both graupel and hail, hereafter, for succinctness, this category will be referred to as graupel. The PSD for graupel is represented using a gamma distribution:

$N_g(D_g)=N_{0g}{D}_g^{\mu }\exp (-{\lambda }_g{D}_g),$(1)

where D_g is the graupel particle diameter, N_g(D_g) is the number concentration of graupel particles per diameter range ΔD_g, N_0g is the intercept parameter, λ_g is the slope parameter, and μ is the shape parameter. Currently, μ = 0 for graupel, which reduces to an inverse-exponential distribution. By integrating Eq. (1) over all sizes, the graupel number concentration can be derived as

$n_g=N_{0g}\frac{\Gamma (\mu +1)}{{\lambda }_g^{\mu +1}},$(2)

where Γ is the complete gamma function.

By integrating Eq. (1) over graupel mass, an equation for the slope parameter that relates mass, number and size is expressed as

${\lambda }_g={\left[\frac{\pi N_{0g}{\rho }_g\Gamma (\mu +4)}{6q_g{\rho }_a}\right]}^{1/(\mu +4)},$(3)

where q_g is the graupel mass mixing ratio (kg kg⁻¹), ρ_g is the graupel density that accounts for air bubbles trapped between frozen drops, reducing the density relative to that of bulk ice, and ρ_a is the density of air. Various characteristic distribution sizes can be calculated as functions of the slope parameter; for example, the median volume diameter of graupel assuming an inverse-exponential distribution is MVD_g ≈ 3.672/λ_g. Half of the total mass in a given distribution exists in sizes smaller than MVD_g.

From Eq. (3), a one-moment scheme that only predicts q_g requires assumed values or functions for both N_0g and ρ_g to calculate both λ_g (or size) and n_g. The original formulation (Thompson et al. 2004) was the simplest, using N_0g = 200/q_g and a constant density ρ_g = 500 kg m⁻³. The intent of using this N_0g relationship was to produce a PSD with a larger mean particle size as the mass of graupel increases. This is based on the idea that stronger updrafts are capable of supporting larger sizes and masses of ice particles.

Subsequently, the N_0g diagnostic formulation was modified to also depend on a second model variable, supercooled drop size (Thompson et al. 2008; Thompson 2013). This was done to account for wet growth of hail, during which small graupel rapidly collects supercooled liquid water and rapidly grows. A strong shift to larger graupel mean size in the presence of supercooled rain was attained by diagnostically forcing N_0g to lower values for larger supercooled raindrop sizes. This idea was ad hoc but produced satisfactory results from real-time experiments such as the National Oceanic and Atmospheric Administration’s (NOAA’s) Hazardous Weather Testbed (HWT; Clark et al. 2014) as well as daily operational use in the Rapid Refresh (RAP) and HRRR models. This one-moment graupel formulation is used in the aerosol-aware scheme, TE14, which is microphysics (MP) option 28 in the WRF Model. This version of the scheme will be referred to as MP28 (Fig. 1).

View Full Size

Values of N_0g and λ_g from T-28 hail observations (Field et al. 2019, orange dots) and from the MP38 simulation’s entire domain at 0300 UTC 20 Jun 2015 (gray dots) and the lowest model level only (k = 1, black dots). The λ_g–N_0g relationship used in MP28 is shown by the dashed blue line, and the relationship used in MP28-NEW is shown by the solid blue line. Blue markers are at every order of magnitude of mass concentration from 0.001 to 10 g m⁻³. Lines of constant reflectivity values (magenta, red, green, and cyan), constant mass concentration (solid black), and constant number concentration (dashed black) are labeled.

Citation: Monthly Weather Review 151, 9; 10.1175/MWR-D-21-0319.1

• Download Figure
• Download figure as PowerPoint slide

Field et al. (2019) used T-28 aircraft observations from various hail studies to show that graupel or hail PSDs have higher N_0g values as the mass mixing ratio increases, not the inverse, currently used in MP28. Simply, more hail mass is associated with higher hail number concentrations at all sizes. To try to improve the representation of the growth and evolution of hail constrained (as best as possible given the limitations of one-moment formulations) by observations, a new version of the intercept-parameter function has been developed (referred to as MP28-NEW, see Fig. 1):

${\text{Log}}_{10}(N_{0g})=3+\frac{2}{7}[{\text{Log}}_{10}(q_g)+8].$(4)

This relationship is fundamentally different from the one used in MP28 (Fig. 1); N_0g increases with increasing q_g in agreement with observations (Field et al. 2019, their Fig. 2). The formulation admittedly encompasses the higher values of N_0g and λ_g from the observations because tests (not shown) revealed that size and reflectivity values would otherwise become unreasonably large.

One-moment graupel (or any hydrometeor category) is inherently limited as shown in Fig. 1 because both N_0g and λ_g depend on q_g. One benefit of MP28 is that graupel size and number as a function of graupel mass span a wide range of values that include both graupel-like and hail-like particle. The scheme’s ability to capture these rimed particle types is predicated on a general assumption that graupel particles are smaller and more numerous than hailstones. This may be true at a particular time in a storm’s evolution. But the time-dependent growth of graupel and hail and the initiation of new hail embryos in strong updrafts causes mass, number, and size to increase concurrently. MP28-NEW addresses this problem; graupel size and number increase as mass increases. Changes in hail size and number during growth should be more realistically parameterized by MP28-NEW.

The intercept-parameter function used in MP28-NEW is also more hail-like than the one used in MP28 because it is shifted toward lower values of both N_0g and λ_g for a given graupel mass. For example, when q_g = 0.1 g m⁻³, graupel size and number concentration predicted by MP28 will be MVD_g = 2.5 mm and n_g = 0.2 L⁻¹, while graupel size and number concentration predicted by MP28-NEW will be MVD_g = 3.5 mm and n_g = 0.01 L⁻¹. When q_g > 1 g m⁻³, graupel number concentration is higher and graupel size is slightly smaller in MP28-NEW compared to MP28. The attempt to make the graupel category in TE14 more hail-like is similar in spirit to a user-defined switch in the Morrison scheme (Morrison et al. 2005). That scheme can be run in “hail” or “graupel” mode; in hail mode, both density and fall speed of rimed ice are increased. TE14 could also be run in hail mode without additional computational cost, using the modified intercept-parameter formulation, for ensemble prediction and other hail studies.

b. Two-moment and predicted density graupel/hail

Following the work of Mansell et al. (2010) and Milbrandt and Morrison (2013), two new predicted graupel variables were added to the TE14 microphysics scheme. These new additions are made such that they minimize added computational cost so that the scheme can be run operationally in the near future. The first variable added was the total graupel number mixing ratio—related to the number concentration by ρ_a—to eliminate the need for a constant or diagnostic calculation of N_0g. The second added variable is the volume mixing ratio b_g, which is similar to the mass mixing ratio except that it represents the volume of graupel particle mass that is occupied by a spherical shape (m³ kg⁻¹). Bulk density is calculated from the mass and volume mixing ratios, and during growth, density (e.g., rime density) is used to calculate volume changes. This scheme has been designated microphysics option 38 in the WRF model and, therefore, this scheme is referred to as MP38. The scheme will be available to the public in a future version of the official WRF repository. The graupel mass mixing ratio tendencies were not changed in MP38 compared to MP28. The addition of two new predicted variables means that two new sets of source/sink or tendency equations were added to the scheme. These number and volume source/sink equations are briefly described in the appendix.

The main benefit of using two moments to represent graupel is that n_g varies independently from q_g, allowing a large variety of graupel sizes and number concentrations for a given mass (see Fig. 1). Importantly, the hail-like particles from MP38 (as illustrated from the PECAN case) overlap the hail observations when plotted in N_0g–λ_g space, meaning that the model is appropriately capturing sizes and number concentrations of hail, in general, compared to hail observations (Field et al. 2019). While their data were from flights based out of Colorado, Kansas, and Oklahoma, there is no reason to expect large differences in hail sizes and number concentrations when comparing their observations to our model output in Fig. 1. Note that density also affects size since higher density particles are more compact (smaller) than lower density ones for a given mass.

Graupel density is constrained to be one of nine values in MP38 for using lookup tables for microphysical rate computations. These values are 50, 100, 200, 300, 400, 500, 600, 700, and 800 kg m⁻³. These densities cover the range of observed rimed ice densities and permit appropriate variability in the graupel particle fall velocity equations within lookup tables without being computationally burdensome. Graupel mass- and number-weighted fall speeds are calculated as functions of density using Best–Reynolds number calculations similar to Heymsfield and Wright (2014), but slightly modified (based on A. Heymsfield 2018, personal communication). A wide variety of observed particle fall speeds can be represented as a function of density, including fall speeds of low-density graupel and high-density hail (Fig. 2).

View Full Size

Fall speed plotted as a function of maximum particle diameter for observations of densely rimed dendrites and graupel (orange), hail (red), and high-density ice pellets (blue). Color-coordinated citations for each dataset are shown at the top left. The graupel fall speed formulation used in MP28 is shown by the black line. The graupel fall speed formulation used in MP38 that depends on density is shown by the gray lines.

Citation: Monthly Weather Review 151, 9; 10.1175/MWR-D-21-0319.1

• Download Figure
• Download figure as PowerPoint slide

3. PECAN case study

a. Description

The case study presented here took place from 19 to 20 June 2015, during the Plains Elevated Convection at Night (PECAN) field campaign (Geerts et al. 2017). An inaugural storm initiated at 1800 UTC 19 June 2015 in central South Dakota and produced hail in eastern South Dakota. Supercells were visible on radar at 0255 UTC in western South Dakota (Fig. 3a). The largest hail fell between 0220 and 0448 UTC with reported diameters ranging from 2 to 6 in. (Fig. 4). Individual storms eventually merged into a strong mesoscale convective system (MCS) that moved across South Dakota (Figs. 3b–d). By 0655 UTC, the MCS exhibited a bow echo structure on radar; it was still bowed and near the Minnesota border by 0825 UTC. There were no hail reports associated with the mature MCS—the last hail report was at 0448 UTC—that plodded across the state overnight. Any hail produced by the MCS while South Dakotans slept could have been simply unreported.

View Full Size

Composite NEXRAD radar images at (a) 0255, (b) 0455, (c) 0655, and (d) 0825 UTC 20 Jun 2015.

Citation: Monthly Weather Review 151, 9; 10.1175/MWR-D-21-0319.1

• Download Figure
• Download figure as PowerPoint slide

View Full Size

SPC hail reports from 1200 UTC 19 Jun 2015 to 1200 UTC 20 Jun 2015. The largest hailstone measured 6 in. (15.24 cm) in diameter and fell in western South Dakota. Several locations referred to in the text are marked by magenta stars.

Citation: Monthly Weather Review 151, 9; 10.1175/MWR-D-21-0319.1

• Download Figure
• Download figure as PowerPoint slide

c. Model setup

The WRF Model version 4.0 (Skamarock et al. 2019) is used. The WRF Model is nonhydrostatic and compressible and uses a third-order Runge–Kutta time integration.

The domain includes 780 west–east and 860 north–south grid boxes centered at 42.5°N and 100.5°W (Fig. 5). A total of 72 stretched vertical levels are used. The horizontal grid spacing is 3 km, which is used operationally in the convection-allowing HRRR model. Simulations were run for 24 h using 6-hourly ERA-Interim data for initial/boundary conditions, starting from 1200 UTC 19 June 2015, with a 12-s time step.

View Full Size

The WRF domain is outlined in red.

Citation: Monthly Weather Review 151, 9; 10.1175/MWR-D-21-0319.1

• Download Figure
• Download figure as PowerPoint slide

The Rapid Radiative Transfer Model for GCMs (RRTMG) long- and shortwave radiation schemes (Iacono et al. 2008), the YSU planetary boundary layer (PBL) scheme (Hong et al. 2006), and the NOAH land surface model (LSM, Chen et al. 1996) are used. Three versions of the microphysics scheme are used: the operationally run Thompson–Eidhammer scheme (MP28), the Thompson–Eidhammer scheme with a modified one-moment graupel intercept-parameter formulation [Eq. (4), MP28-NEW], and the Thompson–Eidhammer scheme with two-moment and predicted density graupel (MP38).

4. Radar evaluation

The lowest-model level simulated 10-cm reflectivity fields during both the discrete storm and MCS phases are shown in Fig. 6. Discrete storms are apparent at 0200 UTC in western South Dakota from the reflectivity fields plotted for all three simulations (Figs. 6a–c). MP28 and MP28-NEW produce storms with what appear to be hook echoes and large regions of 45–50 dBZ. In contrast, storms produced by MP38 appear to lack hook echoes at this specific time. These storms contain large regions with reflectivity values greater than 50 dBZ, consistent with the observed supercells (Fig. 3a).

View Full Size

Lowest model level simulated reflectivity at 0200 UTC for (a) MP28, (b) MP28-NEW, and (c) MP38 and at 0700 UTC from (d) MP28, (e) MP28-NEW, and (f) MP38. The white stars in (d)–(f) mark the location of KFSD. Cross sections shown in Figs. 7 and 8 are plotted along the dashed white line in (c) and (f), respectively.

Citation: Monthly Weather Review 151, 9; 10.1175/MWR-D-21-0319.1

• Download Figure
• Download figure as PowerPoint slide

There are some qualitative differences in both the supercell and MCS reflectivity fields plotted for the three scheme versions at 0200 and 0700 UTC (Fig. 6), and these differences are a result of changes to the graupel category. The southernmost supercell in west-central South Dakota produced by MP38 at 0200 UTC has higher reflectivity values in the core than the supercells produce by MP28 and MP28-NEW. Another difference is that the leading-edge convection of the MCS at 0700 UTC produced by MP28 extends the farthest south into northern Nebraska. MP28-NEW produces an MCS that looks similar to the one produced by MP28 though it does not extend into Nebraska. The MCS produced by MP38 has wider leading-edge convection than the MCSs produced by the one-moment graupel schemes. The MCS produced by MP28 has propagated the farthest east and is almost at KFSD by 0700 UTC. Radar observations show that the MCS actually reached KFSD by 0825 UTC (Fig. 3d).

The detailed graupel characteristics are examined using the MP38 simulation to showcase that scheme’s added details. The supercell produced by MP38 is characterized by reflectivity values near the convective core that exceed 55 dBZ (Fig. 7a, near 102.5°W). The graupel associated with these high reflectivity values has mass concentrations that exceed 1 g m⁻³ (Fig. 7b), MVD_g values that generally exceed 5 mm (Fig. 7c), and high densities (Fig. 7d), particularly adjacent to the convective updraft, where a bounded weak echo region is apparent and below the melt level. All three simulations also produce an MCS with classic squall-line reflectivity features (Biggerstaff and Houze 1991). Leading-edge convection is associated with reflectivity values greater than 40 dBZ from the surface to 11 km above mean sea level (MSL, Fig. 8a, near 96°W). There is a transition zone directly behind (west of) the leading-edge convection and a region of stratiform precipitation with enhanced reflectivity values (>30 dBZ) compared to those in the transition zone. Graupel is the dominant frozen hydrometer type in the leading convection, where mass concentrations exceed 1 g m⁻³ (Fig. 8b) and number concentrations are as high as 10 L⁻¹ (Fig. 8c).

View Full Size

Vertical cross sections of (a) reflectivity, (b) graupel mass concentration, (c) graupel number concentration, and (d) graupel density plotted along the dashed white line in Fig. 6c. The black, magenta, and white contours in (c) are MVD_g values of 3, 5, and 7 mm.

Citation: Monthly Weather Review 151, 9; 10.1175/MWR-D-21-0319.1

• Download Figure
• Download figure as PowerPoint slide

View Full Size

Vertical cross sections of (a) reflectivity, (b) graupel mass concentration, (c) graupel number concentration, and (d) graupel density plotted along the dashed white line in Fig. 6f. The black contour in (c) is an MVD_g value of 2 mm.

Citation: Monthly Weather Review 151, 9; 10.1175/MWR-D-21-0319.1

• Download Figure
• Download figure as PowerPoint slide

These higher mass and number concentrations in the leading convection are associated with reflectivity values greater than 40 dBZ. Graupel densities in the leading convection are as high as 600 kg m⁻³ (Fig. 8d). This is from the addition of high-density, newly frozen raindrops—that freeze in convective updrafts—to the graupel category and the subsequent collection of large supercooled drops, which results in increased graupel densities compared to densities in the stratiform region. Graupel in the stratiform region exists in relatively low mass and number concentrations (Figs. 8b,c) and this graupel is low density graupel, or rimed snow that has collected small supercooled cloud droplets. Note that graupel density also increases as graupel melts; it is assumed that some of the high-density meltwater soaks into the particle. The spatial distribution of graupel number and density look qualitatively accurate in this simulation of an MCS.

Histograms of radar reflectivity

Normalized histograms of reflectivity values are shown in Figs. 9 and 11 for radars observations at Rapid City, South Dakota (KUDX), and Sioux Falls, South Dakota (KFSD). These histograms are directly compared to those for each simulation to evaluate each MP version compared to observations and examine the effects of the graupel parameterization on the reflectivity structure. The KUDX radar detected individual storms before they merged into an MCS, and the KFSD radar detected the MCS as it approached the Minnesota border. Radar reflectivity values less than −10 dBZ are removed because of nonmeteorological scatterers like ground clutter contamination, and these values are also removed from the model output. The elevation of the KUDX radar is approximately 1000 m MSL, whereas the elevation of the KFSD radar is approximately 400 m MSL. This difference is taken into account; the KUDX and KFSD radar evaluations are performed at similar heights above ground level (AGL). To account for timing offsets between the observations and the model, histograms are created using KUDX radar reflectivity values from 0210 to 0530 UTC and simulated reflectivity values from 0100 to 0400 UTC. Histograms of KFSD radar reflectivity values are from 0733 to 0930 UTC, and histograms of simulated reflectivity values are from 0600 to 0900 UTC.

View Full Size

Histograms of reflectivity for KUDX radar observations (blue) and for MP28 at (a) 10, (b) 8, (c) 4, (d) 3, and (e) 2 km MSL. (f)–(j),(k)–(o) As in (a)–(e), but for MP28-NEW and MP38, respectively. The elevation of the KUDX radar is approximately 1000 m MSL.

Citation: Monthly Weather Review 151, 9; 10.1175/MWR-D-21-0319.1

• Download Figure
• Download figure as PowerPoint slide

1) KUDX

KUDX histograms are shown in Fig. 9; there are three columns, one for each MP version, and five rows for five different altitudes: 10, 8, 4, 3, and 2 km MSL. The top two rows show reflectivity values in the upper levels of discrete convective cells, and the bottom three rows show reflectivity values near and below the melting level.

At 10 km MSL near KUDX, the normalized histogram of radar reflectivity values is narrow with positive skewness and a peak at 16 dBZ (Fig. 9a, blue). Similarly sized ice particles are the dominant hydrometeor type in the upper levels and anvils of discrete storms. Relatively larger hydrometers are lofted to 10 km MSL in convective cells, resulting in a tail of reflectivity values up to 56 dBZ.

The histogram of simulated reflectivity values for MP28 is too flat, but it correctly peaks at 16 dBZ (Fig. 9a). In contrast, the MP28-NEW histogram has a narrow peak, but the peak value is at 10 dBZ, 6 dBZ lower than where the observed peak value occurs (Fig. 9f). The MP28-NEW histogram is also too flat for high reflectivity values. There is a prominent tail of reflectivity values greater than 48 dBZ, and these reflectivity values occur too frequently. This means that a fraction of hydrometeors lofted to 10 km MSL in storms simulated by MP28-NEW are too large. The histogram of reflectivity values for MP38 is most similar to the observed one (Fig. 9k). The MP38 histogram is narrow and positively skewed, albeit the peak value is, like MP28-NEW, at 10 dBZ. The tail of relatively high reflectivity values (>32 dBZ) is shaped similarly to how it is in histogram of observations: frequencies steadily decrease with increasing reflectivity.

The only difference between MP28 and MP28-NEW is the graupel intercept-parameter formulation, which ultimately affects the partitioning of graupel in the upper levels of discrete storms. Graupel in MP28-NEW is relatively larger and faster falling (more hail-like) than graupel in MP28. Graupel particles in MP28-NEW are therefore lofted to 10 km MSL only in the strongest updrafts. The areal extent of graupel is therefore reduced in MP28-NEW. At 0200 UTC at 10 km MSL, the area that contains graupel in the entire domain, conditionally sampled for mass mixing ratios greater than 0.1 g kg⁻¹, is 51 588 km² in MP28 and 11 682 km² in MP28-NEW. The area that contains snow, conditionally sampled for mass mixing ratios greater than 0.1 g kg⁻¹, is 330 651 km² in MP28 and 328 887 km² in MP28-NEW. The areal extent of graupel at 10 km MSL is reduced by 77% in MP28-NEW while the areal extent of snow is only reduced by 0.5%. The large reduction in the area occupied by graupel without a concurrent reduction in the area occupied by snow results in a relative increase in the frequencies of snowlike reflectivity values near 10 dBZ, in better agreement with observations.

The benefits of using the two-moment and predicted density graupel category are apparent from the histogram of reflectivity values for MP38 at 10 km MSL (Fig. 9k). This improvement over the one-moment graupel schemes is expected since graupel number, size, and fall speed are better represented in MP38, leading to a more accurate representation of the particle properties of graupel lofted to 10 km MSL in simulated discrete storms. Interestingly, the areal extent of graupel for MP38 at 0200 UTC at 10 km MSL, conditionally sampled for mass mixing ratios greater than 0.1 g kg⁻¹, is 9378 km², similar to areal extent for MP28-NEW. This suggests that MP28-NEW results in an improvement in the representation of graupel in convective updrafts.

At 8 km MSL, the histogram of radar reflectivity values are similar to the one at 10 km MSL (Figs. 9a,b; blue). The peak reflectivity value increases from 16 to 20 dBZ with decreasing altitude and slightly broadens since growth and fallout are producing more disparate particles. All three histograms from the three MP versions improve the peak reflectivity from 10 to 8 km MSL (Figs. 9b,g,l). The MP38 histogram still appears to be most similar to the histogram of observations, again, particularly for reflectivity values greater than 32 dBZ.

At and below the melting level, which is near 4 km MSL (see Fig. 8), the histograms of radar reflectivity values are dominated by precipitation-sized particles (Figs. 9c–e, blue). The peak reflectivity value at all altitudes below the melting level is at approximately 32 dBZ. The shapes of the histograms of radar reflectivity values are also similar at these three altitudes. One difference between these histograms is that the simulation histograms become increasingly flatter between 40 and 48 dBZ with decreasing altitude.

All three simulations struggle to produce reflectivity histograms that look like the observed ones at and below the melting level (Fig. 9, bottom three rows). Histograms from all simulations are generally too flat. The MP28 histogram at 3 km MSL appears to best match the observations, but mostly at this single altitude (Fig. 9d). The MP28 histogram shape changes drastically from 4 to 3 km MSL: the peak value shifts from 44 to 34 dBZ. This reduction in the relatively higher reflectivity values is also seen to a lesser degree for MP28-NEW and MP38, and is likely caused, in part, by melting graupel. As graupel mass rapidly decreases from melting, size also quickly decreases in one-moment schemes as a result of the intercept-parameter formulation. The rapid decrease in graupel size from 4 to 3 km MSL from melting is more apparent for the one-moment graupel schemes than MP38.

A significant challenge exists when simulating melting snow or graupel in bulk microphysics schemes, irrespective of single or double-moment species: the a priori choice of the gamma distribution shape parameter, especially zero (inverse exponential) is enforced during melting. In fact, since the vast majority of the smallest ice melts rapidly, the distribution is far from inverse exponential, and, as temperature increases only the larger tail of the distribution remains unmelted yet bulk schemes “recast” the distribution into the same form as unmelted snow/graupel. Regardless, a benefit of MP38 over the one-moment graupel schemes is the added degrees of freedom for both graupel mass and number tendencies using observations to improve microphysical process parameterizations such as melting. We also note that discrepancies between the observed and simulated histograms could also be, in part, from the simulated storms being too weak since the simulations cannot resolve the strongest vertical velocities when using 3-km horizontal grid spacing. Finally, the simulated storms near KUDX may not be representative of the actual storms due to model errors in storm initiation location and timing and model errors in the environment conditions (Figs. 3 and 6).

A statistically robust method to compare histograms of radar reflectivity to histograms of simulated reflectivity is to create quantile–quantile (qq) plots. The benefit of qq plots is that they can be used to determine if two datasets have similar distributions by plotting the quantiles of one dataset against the quantiles of another. If the values plotted come from the same distribution, i.e., if the histograms of observed and simulated reflectivity values are the same, the qq plot will be linear. Deviations from a theoretical reference line plotted along constant quantile values highlight where the two datasets have different distribution properties. Note that two distributions can have the same shape but be offset in values; the theoretical reference line does not necessarily have to be one to one.

Quantile–quantile plots for KUDX histograms are shown in Fig. 10. There are five qq plots, one for each altitude. The pluses show the observed (abscissa) and simulated (ordinate) reflectivity values for the same quantile. The dotted–dashed lines show the theoretical quantiles that the reflectivity values would follow if they came from the same distribution. The gray shaded regions span the 10th–90th percentile of the radar observations.

View Full Size

Quantile–quantile (qq) plots for KUDX observations and MP28 (red), MP28-NEW (green), and MP38 (blue) at (a) 10, (b) 8, (c) 4, (d) 3, and (e) 2 km MSL. A description of qq plots is given in the text. The shaded regions span the 10th–90th percentile of the KUDX radar reflectivity values.

Citation: Monthly Weather Review 151, 9; 10.1175/MWR-D-21-0319.1

• Download Figure
• Download figure as PowerPoint slide

As expected, at 10 and 8 km MSL, the MP38 qq plots are nearly linear and are close to a one-to-one line (Figs. 10a,b; blue). Thus, the various data quantiles from the observations and the simulation are close to each other in terms of their reflectivity values, and the distributions are similar. The MP28 and MP28-NEW qq plots deviate from linear at 22 dBZ at 10 km MSL and 26 dBZ at 8 km MSL. Thus, these histograms of reflectivity are more different from the observed ones than the MP38 histogram is at these altitudes. Additionally, the theoretical lines (red and green dotted–dashed lines) are steeper than a one-to-one line meaning that a given quantile would occur at a different value for the observed reflectivity compared to the simulated reflectivity. This figure shows a clear improvement in the distribution of reflectivity values for MP38 at 10 and 8 km MSL.

At 4, 3, and 2 km MSL, the qq plots are generally similar with no microphysics scheme version standing out as consistently the best in terms of the total distribution of simulated reflectivity values (Figs. 10c,d,e). As expected, the MP28 histogram best matches the KUDX radar reflectivity histogram at 3 km MSL: that qq plot is almost linear across the 10th–90th percentile of the radar observations (Fig. 10d, red).

Ultimately, both MP28-NEW and MP38 result in some improvements in the representation of discrete storms compared to MP28. The representation of ice at 10 and 8 km MSL in discrete storms for this case is clearly improved when using MP38. This scheme also results in an improvement in the relative frequencies of the highest reflectivity values at 10, 8, and 4 km MSL. The sizes of the largest particles at these altitudes are best represented by MP38. MP28-NEW results in some improvements in the distribution of reflectivity values at 10 and 8 km. This improvement coincides with a significant reduction in the areal extent of graupel aloft.

2) KFSD

Histograms of radar reflectivity values at 9.4 and 7.4 km MSL near KFSD, during the MCS phase, are similar to the KUDX histograms. The KFSD histograms are narrow, positively skewed, and they have a peak at 14 dBZ at 9.4 km MSL and 20 dBZ at 7.4 km MSL (Figs. 11a,b; blue).

View Full Size

As in Fig. 9, but for KFSD. The elevation of the KFSD radar is approximately 400 m MSL.

Citation: Monthly Weather Review 151, 9; 10.1175/MWR-D-21-0319.1

• Download Figure
• Download figure as PowerPoint slide

The simulation results at 9.4 km MSL (9 km AGL) are the same as the results from the KUDX radar evaluation at 10 km MSL. The MP38 simulation produces the best distribution of reflectivity values at 9.4 km MSL (Figs. 11k and 12a). The MP28-NEW simulation produces a histogram peak at 9.4 km MSL that looks qualitatively better than the peak produced by the MP28 simulation (Figs. 11a,f). At 7.4 km MSL, the histograms of reflectivity values for MP28 and MP28-NEW appear to be similar (Figs. 11b,g and 12b). Again, MP38 results in an improvement in the width, peak, and upper tail of the reflectivity histogram (Fig. 11l), and the MP38 histogram quantiles are close to one-to-one with the observed quantiles (Fig. 12b).

View Full Size

As in Fig. 10, but for KFSD.

Citation: Monthly Weather Review 151, 9; 10.1175/MWR-D-21-0319.1

• Download Figure
• Download figure as PowerPoint slide

At and below 3.4 km MSL, KFSD histograms of radar reflectivity values (Figs. 11c–e; blue) are different than the KUDX histograms. The KFSD histograms are representative of precipitation from an MCS. There is a more prominent peak at 32 dBZ caused by the dominance of a wide region of stratiform precipitation, and this peak is seen at all three altitudes at and below the melting level. Additionally, the maximum reflectivity values below the melting level are lower for the KFSD histograms (56 dBZ) compared to the KUDX histograms (64 dBZ). Thus, the largest hydrometeors are smaller during the MCS phase, as expected since supercells are generally better at producing relatively larger hail than MCSs.

In contrast to the KUDX evaluation, histograms of simulated reflectivity values for all three MP versions below the melting level have peaks near 32 dBZ, close to the value of the observed peaks (Fig. 11, bottom three rows). The MP versions also have a better handle on the histogram shape and width below the melting level during the mature MCS phase. While all three simulations result in similar histogram shapes, MP38 and MP28-NEW result in an improvement in the relative frequencies of reflectivity values greater than 44 dBZ compared to MP28 at both 2.4 and 1.4 km MSL (Fig. 11, bottom two rows). These higher reflectivity values do not occur frequently enough in the MCS simulated by MP28. Since the rain formulation, including evaporation, is the same in all three MP versions, these improvements in MP28-NEW and MP38 are again attributed to the changes made to the graupel category, which through melting affects raindrop sizes and reflectivity values. Generally, below the melting level, qq plots from all three simulations are again nearly identical (Figs. 12c–e). Overall, no simulation stands out as producing a histogram of reflectivity values that is significantly more similar or different to the histogram of radar observations.

5. Hail-size evaluation

The three MP versions are further evaluated for their ability to predict hailstone diameter aloft and at the surface. Storm Prediction Center (SPC) storm reports of hail provide information on the timing, location, and size of hail at the surface either from in situ reports or estimated by radar. Of course, hail can go unreported at night and away from population centers, and sizes can be misreported because of melting. In fact, the comments on the 6-in. hailstone observed during this case reveal that some melting occurred before measurement. Hail size can also be estimated from radar using the maximum estimated hail size (MESH) algorithm (Witt et al. 1998). This method can provide spatially and temporally continuous estimates of maximum hail potential, but it can underestimate hail size at times, like in storms in strong, deep-layer shear.

a. Storm reports

MAX_HAILK1 is plotted for each simulation over 24 h, from 1200 UTC 19 June 2015 to 1200 UTC 20 June 2015 (Fig. 13). Additionally, normalized histograms of hail size using bins that are 0.5 in. wide to account for the coarse resolution of hail reports are also shown. All three simulations produce a main hail swath across southeastern Montana and into South Dakota, almost exactly where the swath was observed. Observed hail sizes along this swath were routinely larger than 5.08 cm. Predicted hail diameters along this swath are roughly 2.54–3.81 cm for MP28, 1.90–2.54 cm for MP28-NEW, and 3.81–5.08 cm for MP38.

View Full Size

MAX_HAILK1 plotted from 1200 UTC 19 Jun 2015 to 1200 UTC 20 Jun 2015 for (a) MP28, (b) MP28-NEW, and (c) MP38. SPC hail reports are plotted with + symbols. Normalized histograms of hail diameter (starting at 2.5 cm) for storm reports (gray), MAX_HAILK1 (orange), and HAIL_99TH (cyan) are also plotted for each simulation.

Citation: Monthly Weather Review 151, 9; 10.1175/MWR-D-21-0319.1

• Download Figure
• Download figure as PowerPoint slide

The effect of using a more hail-like intercept-parameter in MP28-NEW is that the spatial area over which hail is predicted to reach the surface increases (Figs. 13a,b). Interestingly, more hail does not translate to larger hail in this case, apparent from the histograms of hail sizes. MP38, on the other hand, produces hail at the surface over a similar spatial area as MP28, but the predicted sizes of hail are larger. In fact, MP38 is the only scheme that accurately produces diameters larger than 3.81 cm and reasonably represents the observed hail-size distribution at the surface when using HAIL_99TH to predict hail size (Fig. 13c). HAIL_99TH sizes (mass based) are larger than HAIL_MAXK1 sizes (number based) in MP38, the two-moment scheme. These two formulations result in similar hail sizes in the one-moment schemes since number is more highly constrained by mass in those schemes. Readers should also be reminded that reported hail sizes have inherent biases and that isolated hail-size reports may not be representative of entire storm characteristics.

The timing and location of large and potentially damaging hail (>2 in. in diameter) is shown for MP38 alongside storm reports of those hail sizes to evaluate the scheme’s ability the warn for this hazard (Fig. 14). An early storm produced hail in central South Dakota between 1600 and 1700 UTC 19 June 2015 (blue plus), and the model produces this storm, but it is east of where it occurred and 4–5 h late. Between 2300 and 0200 UTC, large hail was observed in Montana and swaths of large hail were observed in western South Dakota. The timing and location of this 2-in. and larger hail, including the large hail swaths in western South Dakota are, for the most part, accurately represented by MP38. MP38 produces 2-in. hail after 0400 UTC 20 June 2015 in North and South Dakota but mostly at sporadic, single grid locations. MP38 also produces large hail in Minnesota during the MCS phase, after 0700 UTC, that was not directly observed, though again, overnight hail can at times go unreported.

View Full Size

MP38 HAIL_99TH conditionally sampled for diameters larger than or equal to 2 in. (5.08 cm) and plotted by time. SPC hail reports conditionally sampled for diameters larger than or equal to 2 in. are plotted with + symbols.

Citation: Monthly Weather Review 151, 9; 10.1175/MWR-D-21-0319.1

• Download Figure
• Download figure as PowerPoint slide

b. Hail size estimated from radar

Hail size is also estimated from radar using the MESH algorithm, based on Witt et al. (1998), in which hail size is estimated by integrating radar observations between two specified vertical levels. MESH is used to evaluate predicted maximum hail size in each vertical column, MAX_HAIL2D, and predicted maximum hail size at the surface, MAX_HAILK1 and HAIL_99TH. MAX_HAIL2D provides an estimate of the maximum hail size potential from the model. If MAX_HAIL2D at some location is above the melting level, then it is an estimate of the current maximum hail size that has grown but not yet melted.

An example of MESH calculated from KDUX radar observations from 0210 to 0530 UTC is shown in Fig. 15a. Narrow regions or swaths of hail with diameters larger than 4 cm are surrounded by broader regions of smaller hail. Model output of hail sizes from each simulation is calculated from 0100 to 0400 UTC to account for some timing offsets in storms near the radar. MP38 is the only MP version that produces narrow swaths of large hail sizes surrounded by large regions of relatively smaller hail sizes aloft (Fig. 15b). Again, the benefit of added complexity to the graupel category is that a larger spread in hail size is predicted. While MP28 and MP28-NEW were shown to produce similar hail sizes at the surface (Figs. 13a,b), MP28-NEW produces larger sizes aloft (Figs. 15c,d), which ultimately results in the increase in the spatial area over which hail is predicted to reach the surface.

View Full Size

(a) MESH plotted for KUDX radar observations from 0210 to 0530 UTC. MAX_HAIL2D for (b) MP38, (c) MP28-NEW, and (d) MP28. All model output is from 0100 to 0400 UTC.

Citation: Monthly Weather Review 151, 9; 10.1175/MWR-D-21-0319.1

• Download Figure
• Download figure as PowerPoint slide

Histograms of hail sizes (diameters) calculated from both MESH and for the three MP versions (using MAX_HAIL2D, HAIL_99TH, and MAX_HAILK1) are compared at both KUDX (Fig. 16) and KFSD (Fig. 17). MESH calculated from KUDX radar observations produces an inverse-exponential distribution of sizes up to approximately 4 cm. Interestingly, the histogram of MAX_HAIL2D for MP28 matches this histogram of KUDX MESH values extremely well (Fig. 16a), albeit somewhat masked by plotting relatively frequency (cf. Fig. 15). MP28-NEW produces hail sizes larger than 1 cm in diameter too frequently aloft compared to MESH (Fig. 16b). MP38 produces a histogram of hail sizes aloft that is similar to the MESH histogram, but diameters from 0.5 to 1.5 cm occur too frequently (Fig. 16c).

View Full Size

Histograms of MESH for KUDX radar observations (blue). Histograms of MAX_HAIL2D (orange) for (a) MP28, (b) MP28-NEW, and (c) MP38. Histograms of MAX_HAILK1 (orange) and HAIL_99TH (gray) for (d) MP28, (e) MP28-NEW, and (f) MP38.

Citation: Monthly Weather Review 151, 9; 10.1175/MWR-D-21-0319.1

• Download Figure
• Download figure as PowerPoint slide

View Full Size

As in Fig. 16, but for KFSD.

Citation: Monthly Weather Review 151, 9; 10.1175/MWR-D-21-0319.1

• Download Figure
• Download figure as PowerPoint slide

Comparing histograms of MAX_HAIL2D to predicted hail-size values at the surface gives a sense of the impact of melting on the hail size distribution. All three MP versions produce surface hail-size distributions (Figs. 16d–f) that are quite obviously different from the distributions of hail size aloft. At the surface, MP28 hail sizes are slightly larger than MP28-NEW hail sizes, and the MP28 hail-size distributions are slightly wider. Maximum hail diameter at the surface is as large as approximately 3.5 cm for MP28 and 2.5 cm for MP28-NEW (Figs. 16d,e); both values are smaller than the maximum hail size from MESH, which is approximately 8 cm (Fig. 15a). As mentioned, MP38 produces the widest hail-size distributions at the surface, and MP38 is the only version that produces sizes larger than 3.5 cm (Fig. 16f). The relative frequency of occurrence of these large sizes is too high compared to the KUDX MESH histograms; this could result from underrepresenting hail sizes smaller than 1 cm in diameter at the surface in all three schemes.

During the MCS phase of the storm near KFSD, hail sizes of up to 2 cm are predicted by MESH (Fig. 17), though there were no hail reports near the KFSD radar. Histograms of MAX_HAIL2D for both MP28 (Fig. 17a) and MP38 (Fig. 17c) are similar to histograms of KFSD MESH values, though both versions produce hail larger than 2 cm in diameter aloft, with MP38 producing the best distribution of hail sizes aloft. The MP28-NEW MAX_HAIL2D histograms are significantly too flat (Fig. 17b).

At the surface near the KFSD radar, there is no hail predicted by MP28, which has completely melted (Figs. 17d and 13a). Evidently the slightly smaller hail in MP28 falls slow enough to melt completely as compared to the other two experiments with larger hail sizes. The histograms of hail sizes at the surface for MP38 are broader than radar-derived with generally too large sizes (Fig. 17f). The hail-size histograms for MP28-NEW (Fig. 17e) are narrower at the surface than aloft, and provide the best estimate of surface hail sizes of all three MP versions, up to 2 cm in diameter, in agreement with MESH. These MP28-NEW hail-size histograms are also narrower than the ones near KUDX; MP28-NEW for this case is able to produce relatively larger hail sizes from supercells and relatively smaller hail sizes from an MCS at the surface. Analysis of more cases will be needed to see if this can be done consistently. These results suggest that predicted hail size aloft (MAX_HAIL2D) is currently a valuable variable and should be used in conjunction with predicted hail sizes at the surface when evaluating these MP versions using MESH. Note that this type of evaluation should be repeated for more cases and ultimately be used to improve the one- and two-moment melting parameterizations.

6. Cold-pool evaluation

Temperature and wind speed from the three simulations are compared to temperature and wind speed from ASOS sites across South Dakota when the MCS was mature. This comparison is done to evaluate how changes to graupel particle properties, which ultimately affect melting and rain production, affect cold-pool dynamics. Four ASOS sites (shown in Fig. 4) that extend from central to eastern South Dakota and were influenced by the MCS are used. Model values from a 3 × 3 grid surrounding the closest model grid location to a given ASOS site are used for comparison.

Generally, all three simulations produce an MCS with similar cold-pool dynamics, though there are some differences between the simulations. At Pierre, South Dakota (KPIR), the farthest west ASOS site used, the MCS passed at 0600 UTC and was accompanied by 22 m s⁻¹ winds (Fig. 18a). The simulated systems pass through KPIR 2 h too early, though all simulations capture the approximate maximum wind speed of 25 m s⁻¹. Interestingly, MP28-NEW produces an MCS with an outflow that is colder by approximately 1°C than outflows produced by the other two MP versions yet arrived at KPIR slightly later than the other two. Minor positional differences of convective elements a few hours earlier may explain some of these discrepancies.

View Full Size

Temperature and wind speed from ASOS (black dots) and 2-m temperature and 10-m wind speed for MP28 (orange), MP28-NEW (magenta), and MP38 (blue) at (a) KPIR, (b) K9V9, (c) KHON, and (d) KFSD. Model values are shaded using a 3 × 3 grid (9 total grid points) around the approximate location of each ASOS. The station locations are shown in Fig. 4.

Citation: Monthly Weather Review 151, 9; 10.1175/MWR-D-21-0319.1

• Download Figure
• Download figure as PowerPoint slide

The observed MCS passed though Chamberlain, South Dakota (K9V9), between 0630 and 0700 UTC, Huron, South Dakota (KHON), just before 0800 UTC, and Sioux Falls, South Dakota (KFSD), at 0830 UTC. In general, the simulated MCSs pass these locations approximately 2 h early. At KPIR and K9V9, the temperature decreases (from the MCS passage) approximately 3°C too much in the simulations, though the cooling that occurs in the model at KHON and KFSD is similar to what was observed. At KFSD the passage of the MCS produces less of a temperature decrease and weaker winds compared to the other ASOS sites. All simulations capture this weakening of the cold pool. The simulated MCSs pass through KFSD at different times: the MP28 MCS propagates the fastest, and the MP28-NEW MCS is the slowest. There is about an hour difference between the MP28 and MP28-NEW MCSs. A plausible explanation derives from hail that falls faster than graupel; therefore, it spends less time in the atmosphere melting, ultimately reaching the surface while producing less rain aloft. Less rain aloft means less evaporation, and this weakens the cold pool and slows storm propagation (Adams-Selin et al. 2013). The MCS that produces the most hail at the surface (see Fig. 13) should be the slowest, which is the MCS predicted by MP28-NEW.

7. Summary and conclusions

The graupel/hail category in the Thompson–Eidhammer microphysics framework has been modified with the goal of improving the ability to predict the location and size of hail in convective storms and at the surface. Two versions, a more complex two-moment and predicted density graupel category version and a simple one-moment version, based on observations, have been developed and implemented into the WRF model.

In the two-moment and predicted density graupel formulation (MP38), number is predicted that provides an additional degree of freedom allowing for more graupel/hail size variability, and density is predicted that directly affects fall speed and can help differentiate graupel from hail aloft. A key benefit of MP38 for the case simulated here is that the distribution of reflectivity values at the upper levels (9 km AGL) of convective storms is improved. The particle properties of relatively low-density graupel lofted to these altitudes are better represented in storms when using MP38 compared to the one-moment schemes. Additionally, MP38 produces a wider variety of graupel/hail sizes. This ultimately results in a wider range of predicted hail sizes at the surface including large, damaging hail, an improvement for this case compared to the one-moment versions that currently are much more limited in their ability to predict a wide range of hail sizes.

A key benefit of MP28-NEW is that it is based roughly, as much as a one-moment scheme can be, on observations. M28-NEW produces hail over a larger area at the surface compared to MP28, but this hail is not significantly larger. MP28-NEW does lead to a slight improvement in the distribution of upper-level reflectivity values compared to MP28. This improvement coincides with a decrease in the spatial area occupied by graupel aloft since graupel in MP28-NEW is larger, faster-falling (more hail-like) than in MP28 and is only lofted to the tops of the strongest convective cores. Interestingly, the relative amount of graupel in the upper levels of convective storms predicted by MP38 agrees better with MP28-NEW than MP28. MP28-NEW could be considered for use in a multiphysics ensemble to provide probabilistic hail forecasts. Predicting hail sizes from one-moment schemes is more difficult than two-moment schemes since there are fewer degrees of freedom. Results from this study show that additional metrics or additional tuning of hail-size formulations are needed to better predict large and damaging hail sizes using the one-moment MP28 or MP28-NEW.

Histograms of MAX_HAIL2D for MP28 and MP38 compared relatively well to histograms of MESH values in terms of relatively frequency yet may still have a bias in amount of occurrence. Histograms of simulated reflectivity (Fig. 9) evolve too drastically below the melting level compared to observations for discrete storms, and histograms of predicted hail sizes also evolve noticeably when comparing MAX_HAIL2D to the surface values (Fig. 16). This suggests that the parameterizations of melting of graupel/hail and growth of large hail may need further refinement. For now, predicted hail size aloft (MAX_HAIL2D) is currently a valuable variable and should be used in conjunction with predicted hail sizes at the surface to constrain expected hail sizes from the microphysics scheme versions.

Further evaluation of MP28-NEW and MP38 during hazardous weather testbeds and for other cases should be a top priority to continue preparing these schemes and their hail-prediction abilities for operational use.

Data availability statement.

Radar data and SPC hail reports are provided by NOAA. ASOS data are provided by the Iowa State archive. Simulations performed here are stored on CISL’s campaign storage.