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  • View in gallery

    Skew T–logp plot of thermodynamic and wind data used in the model to initialize all simulations, modified from observed sounding data from the MC3E field campaign at 2030 UTC 23 May 2011, as explained in the text.

  • View in gallery

    Simulated reflectivity at 1 km AGL (shaded) and cold pool (black contour) throughout various times in the Control simulation. The axes are in grid points, but the plot window shifts in time to follow the storm as it progresses.

  • View in gallery

    (left) Simulated reflectivity at 1 km AGL (dBZ, shaded) and cold pool (contoured) and (right) theta perturbation at the surface (K) for the Control simulation at 205 min. The axes are in grid points.

  • View in gallery

    Time series of cold pool area for all 12 model simulations from the start of the cold pool until 50 min afterward.

  • View in gallery

    Time series of updraft (red) and downdraft (blue) maxima below 5 km for each simulation with the Control simulation in black for reference.

  • View in gallery

    Starting time of the cold pool for each simulation as noted.

  • View in gallery

    Integrated latent cooling of graupel sublimation (dashed red), graupel melting (solid red), hail sublimation (dashed blue), hail melting (solid blue), and rain evaporation (dotted green) up to 10 min prior to the start of the cold pool. Values are computed only within the 5 m s−1 downdraft forming the initial cold pool, and are normalized by the downdraft volume, for each case.

  • View in gallery

    Maximum downdraft speed forming the initial cold pool vs the total integrated latent cooling within the −5 m s−1 downdraft in the 10 min prior to cold pool formation, normalized by volume.

  • View in gallery

    Percent of total latent cooling contributed from each hydrometeor phase change in >5 m s−1 downdraft 10 min prior to initial cold pool formation.

  • View in gallery

    As in Fig. 7, but for >1 m s−1 downdrafts in contact with the cold pool in the 50 min after cold pool formation, and the ordinate now specified in units of joules.

  • View in gallery

    Integrated latent cooling of (a) all hydrometeor phase changes, (b) rain evaporation, (c) graupel sublimation and melting, and (d) hail sublimation and melting, in >1 m s−1 downdrafts sustaining the cold pool vs 50-min average cold pool expansion rate.

  • View in gallery

    Time series of average cold pool depth for all simulations, as described in the text.

  • View in gallery

    As in Fig. 11, but latent cooling contributions vs 50-min average cold pool depth.

  • View in gallery

    As in Fig. 11, but latent cooling contributions vs 50-min, spatially integrated cold pool buoyancy.

  • View in gallery

    Comparison of latent cooling by hydrometeor phase change for the Control simulation, but limiting calculations to particular vertical depths within the domain.

  • View in gallery

    Vertical cross sections of reflectivity, vertical velocity, and hydrometeor latent cooling for the Control simulation at 205 min through y = 65 as seen in Fig. 3. Black contours outline the 1 m s−1 downdraft, and the solid horizontal line indicates height of the melting level. Vertical axis is given in grid-level units. Note the difference in the scales for plots (c)–(g).

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An Investigation of Hydrometeor Latent Cooling upon Convective Cold Pool Formation, Sustainment, and Properties

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  • 1 University of Illinois at Urbana–Champaign, Urbana, Illinois
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Abstract

Downdrafts extending from convective clouds can produce cold pools that propagate outward, sometimes initiating new convection along their leading edges. Models operating at scales requiring convective parameterizations usually lack representation of this detail, and thus fail to predict this convective regeneration and longer episodes of convective activity. Developing such parameterizations requires an improved understanding of the physical drivers of cold pools, and detailed studies of the roles of all the contributing microphysical processes have been lacking. This study utilizes a set of 12 simulations conducted within a single convective environment, but with variability in the microphysical fields produced by varying parameters influencing warm-rain or ice processes. Time-integrated microphysical budgets quantify the contribution of each hydrometeor type to the total latent cooling occurring in the downdrafts that form and sustain the cold pool. The timing of the onset of the cold pool is earlier in cases with a stronger warm rain process, but both graupel and rain were equally as likely to be the dominant hydrometeor in the downdraft first forming the cold pool. Graupel sublimation is the dominant term in sustaining the cold pool in all simulations, but the evaporation of rain has the strongest correlation to the cold pool expansion rate, depth, and intensity. Reconciling the current results with past studies elucidates the importance of considering: graupel sublimation, the latent cooling only in downdrafts contributing to the cold pool, and latent cooling in those downdrafts at altitudes that may be significantly higher than the melting level.

© 2019 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Holly M. Mallinson, hmm2@illinois.edu

Abstract

Downdrafts extending from convective clouds can produce cold pools that propagate outward, sometimes initiating new convection along their leading edges. Models operating at scales requiring convective parameterizations usually lack representation of this detail, and thus fail to predict this convective regeneration and longer episodes of convective activity. Developing such parameterizations requires an improved understanding of the physical drivers of cold pools, and detailed studies of the roles of all the contributing microphysical processes have been lacking. This study utilizes a set of 12 simulations conducted within a single convective environment, but with variability in the microphysical fields produced by varying parameters influencing warm-rain or ice processes. Time-integrated microphysical budgets quantify the contribution of each hydrometeor type to the total latent cooling occurring in the downdrafts that form and sustain the cold pool. The timing of the onset of the cold pool is earlier in cases with a stronger warm rain process, but both graupel and rain were equally as likely to be the dominant hydrometeor in the downdraft first forming the cold pool. Graupel sublimation is the dominant term in sustaining the cold pool in all simulations, but the evaporation of rain has the strongest correlation to the cold pool expansion rate, depth, and intensity. Reconciling the current results with past studies elucidates the importance of considering: graupel sublimation, the latent cooling only in downdrafts contributing to the cold pool, and latent cooling in those downdrafts at altitudes that may be significantly higher than the melting level.

© 2019 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Holly M. Mallinson, hmm2@illinois.edu

1. Introduction

Deep cumulus convection plays a crucial role in the energy and hydrologic balance of the Earth system, and thus an understanding of the fundamental components of convection is necessary for weather and climate prediction across all time scales. However, the range of scales over which cloud processes occur presents significant modeling challenges. For example, modeled storms are sensitive to hydrometeor representation and their underlying assumptions because their formation, transport, and latent cooling influence, and are influenced by, the storm dynamics. As such, cloud microphysics and precipitation remain a weak point in all larger-scale models (IPCC 2013).

Convectively generated cold pools are an inseparable component in the convective storm life cycle. Cold pools form via latently cooled downdrafts that reach the surface and spread outward, often described as a density current (Simpson 1969; Charba 1974), displacing the surrounding warm, moist air (Goff 1976). The more buoyant environmental air is lifted along the edge of the cold pool (i.e., the gust front) and can generate a convective cloud (Goff 1976; Warner et al. 1980), thus making cold pools important for triggering new convection (Byers and Braham 1949; Purdom 1976; Weaver and Nelson 1982). Behind their leading edge, cold pools tend to suppress convection over their extent by strongly stabilizing the near-surface lapse rate (e.g., Trapp and Woznicki 2017). Despite their importance, a proper representation of cold pools in convection-permitting models awaits answers to unresolved questions.

Within GCM parameterizations, cold pool formation occurs once a sufficient amount of evaporation occurs (Rio et al. 2009; Park 2014). The cold pool propagation speed (C) is generally assumed to be equivalent to that of a density current, here given with more detail, e.g., Bryan et al. (2006); Bryan (2017):
C2=20H(B)dz,
where H is the cold pool depth, z is the height, and B is buoyancy expressed as
B=gθρθρ0θρ0g[θθ0+(1ϵ1)(qυqυ,0)qlqi],
where θρ is the density potential temperature, θ is the potential temperature, a prime denotes the deviation value from the environmental value at a given height, a subscript of 0 denotes environmental values at that height, qυ, ql, and qi are the mixing ratios of water vapor, cloud water, and cloud ice, respectively, and qυ,0 is the model base state water vapor mixing ratio. Both within this formula and within parameterizations, the cold pool depth is assumed to be uniform, and is related to the downdraft mass flux (Qian et al. 1998, Grandpeix and Lafore 2010, Del Genio et al. 2015). Recently, the idealized numerical modeling of Marion and Trapp (2019) lent some support to this approach, suggesting that, at least for supercell thunderstorms and their environments, the cold pool depth was strongly linked with updraft and downdraft widths, that were ultimately controlled by the storm environment (particularly the CAPE, vertical wind shear, and mixed-layer depth).

However, despite the fact that latent cooling from hydrometeor phase changes is the origin of the cold downdraft air producing the cold pool, current parameterizations lack any representation of their influence. Current knowledge, or at least consensus, regarding the most important microphysical influences is lacking. For a given hydrometeor mass, greater latent cooling results from ice sublimation than from rain evaporation or melting ice, but within a downdraft the former occurs farther from the ground, whereas melting ice, and especially evaporating rain, occurs closer to the ground. Thus, the latter two effects may be less offset by compressional warming within the downdraft, or entrainment into it, before that air reaches the ground.

Srivastava (1987) used a one-dimensional model to investigate the role of microphysical processes on downdraft initiation. When ignoring ice, stronger rain evaporation (resulting from smaller raindrop sizes and/or greater rain mass) led to stronger downdrafts. When including ice, the strongest downdrafts were caused by melting hail and its subsequent evaporation in environments having weak lapse rates; when the environmental lapse rate was stronger, the sublimation of small ice hydrometeors was most important. This simple model showed that hydrometeor properties such as phase and size play an important role in governing the formation of strong downdrafts, but their relative role can be modulated by the environment.

The sensitivity of downdraft intensity to various microphysical factors has been explored in many past studies. For example, several 3D modeling studies (e.g., McCumber et al. 1991; Gilmore et al. 2004; van den Heever and Cotton 2004; Cohen and McCaul 2006) have shown the importance of assumptions in the representation of ice phase hydrometeors, particularly graupel and hail. An observational analysis of latent cooling in High Plains thunderstorms by Knupp (1988) estimated the relative contributions of melting, evaporation, and sublimation to the downdraft, and found that melting graupel varied from 15% to more than 60% of the latent cooling. Some modeling studies have suggested that a stronger warm-rain process creates stronger downdrafts and subsequently stronger cold pools (e.g., Johnson et al. 1993; Villanueva-Birriel et al. 2014), but did not study this in detail.

A few numerical modeling studies have analyzed more details on the microphysical influences on cold pool formation, but have yielded conflicting results. These employed idealized simulations (but were often based upon soundings from real convective cases) that ignored radiation and land surface effects, to assist in isolating the microphysical effects. These studies are now briefly summarized.

Gilmore et al. (2004; hereafter G04) used a simple, single-moment microphysics scheme in 3D idealized simulations to investigate the sensitivity of accumulated precipitation and cold pool strength to assumptions about the large rimed ice category (set to either graupel or hail) in supercellular and multicellular storms. They varied the assumed number or density of the large rimed ice category to represent it as small graupel, large hail, or values in between these extremes. The coldest cold pools (i.e., minimum temperature) occurred in simulations having small hail, but the coldest area-averaged cold pools occurred in simulations having more graupel (although later in the simulation). G04 also found that simulations with stronger near-surface downdrafts resulted in colder cold pools. They evaluated domain-totaled source and sink rates for different hydrometeor categories, and a combined graupel/hail category. Although not discussed (or quantified) in terms of the actual latent cooling that would have been produced, their results (cf. their Figs. 6 and 7) suggest that cooling due to graupel/hail sublimation would have dominated over that from melting or rain evaporation.

Van den Heever and Cotton (2004, hereafter VC04) examined the impacts of the assumed mean hail diameter upon convective storm dynamics and precipitation, including cold pool characteristics, in 3D simulations of supercell thunderstorms typical of Oklahoma. They also used a single-moment microphysical scheme, but had separate classes for graupel and hail. The mean hail diameter (in an assumed negative-exponential distribution) was altered from 3 mm to 1 cm, holding all other conditions constant. A smaller mean hail diameter (with associated smaller fall speeds) increased hail melting and subsequently rain evaporation, enhancing latent cooling that forced stronger downdrafts, and cold pools that were deeper, more intense, and expanded faster. Although the relative contributions of latent cooling by other processes were not explored, the trend toward smaller rimed particles enhancing downdrafts and their cold pools is similar to that of G04.

Dawson et al. (2010, hereafter D10) analyzed differences in rain evaporation, size sorting, and the subsequent effect on cold pool strength by comparing 3D numerical simulations of an observed case of Oklahoma supercells using a single-moment scheme (nearly identical to that used by G04), and variations on a three-moment microphysical scheme that included separate categories of graupel and hail. Microphysical latent cooling budgets were computed within low-level downdrafts occurring from 4-km height (near the freezing level of the environmental sounding) to the surface. In contrast to G04 and VC04, rain evaporation was quantified as the most important process to cold pool development; latent cooling due to sublimating graupel was not examined, however.

D10, G04, and VC04 all had an emphasis upon investigating changes in the model solutions resulting from various aspects of microphysical parameterizations, useful to help interpret future simulations, but leaving questions about the dominant hydrometeor phase changes that control the development and characteristics of the cold pool. The differing results of the dominant latent cooling terms might result from the method of quantification itself: G04 quantified the latent cooling over the entire domain (that might include downdrafts not contributing to the cold pool), and D10 considered all downdrafts at and below the freezing level, which might also underestimate the contribution from sublimation at higher levels in the downdraft. In addition, the use of single-moment microphysics schemes by G04 and VC04 may limit the accuracy of their findings; D10 as well as numerous previous studies (e.g., Morrison et al. 2009; Lee and Donner 2011; Jung et al. 2012; Van Weverberg et al. 2012; Igel et al. 2015) have found that multimoment schemes significantly outperform single-moment schemes in convective clouds. The limitation of representing either only graupel, or only hail, by G04 precludes a comparison of their relative importance. While the D10 and VC04 studies explicitly stated their focus on changes due to the representation of rain and hail, respectively, they did not address any resulting impact upon, or comparison with graupel, nor quantify its contribution to latent cooling in the downdrafts. The contribution to latent cooling from sublimation is also not addressed in VC04, and only briefly mentioned in D10. Furthermore, while stronger downdrafts have been linked to stronger cold pools, a quantitative relationship between downdrafts and other cold pool properties (e.g., timing of formation, speed of expansion) has not been established.

This study investigates how microphysical latent cooling affects downdrafts and cold pool properties in higher-resolution, 3D numerical simulations based upon an observed case of multicellular convection in Oklahoma. Calculated budgets of latent cooling terms (rain evaporation, graupel melting, hail melting, graupel sublimation, hail sublimation) are limited to downdrafts that intersect the cold pool and thus are responsible for its formation or sustainment. Specifically, relationships are sought for the dominant microphysical cooling term that (i) influences the initial cold pool formation, (ii) sustains the cold pool, and (iii) determines cold pool strength, expansion rate, and depth.

2. Methodology

a. Model setup

This study uses Cloud Model 1 (CM1; Bryan and Fritsch 2002), a 3D idealized numerical model. An observed sounding from the Midlatitude Continental Convective Clouds Experiment (MC3E) field campaign (Jensen et al. 2016) at 2030 UTC 23 May 2011 in Purcell, Oklahoma, is used to initialize the model base state; the height of the 0°C level is approximately 4.5 km (600 hPa). Values of CAPE and 0–6-km bulk wind shear were 3521 J and 12 m s−1, respectively. The sounding was modified by decreasing temperatures by 1°C in the upper boundary layer (825–775 hPa) to remove CIN and allow convection to develop (Fig. 1). A grid spacing of 250 m (horizontal and vertical) is used over a domain size of 250 km × 250 km × 20 km. A 1-s time step is used and model results are output every 30 s. A Rayleigh dampening zone was placed from 17 to 20 km (top of the domain) to eliminate gravity waves interacting with the top rigid boundary. The lower boundary condition is free slip (i.e., without friction) for simplicity; thus the cold pool propagation speeds and expansion rates shown should be considered a theoretical maximum. Table 1 lists other model specifications used in this study for all simulations.

Fig. 1.
Fig. 1.

Skew T–logp plot of thermodynamic and wind data used in the model to initialize all simulations, modified from observed sounding data from the MC3E field campaign at 2030 UTC 23 May 2011, as explained in the text.

Citation: Monthly Weather Review 147, 9; 10.1175/MWR-D-18-0382.1

Table 1.

Model configuration used in this study.

Table 1.

b. NSSL microphysics scheme

The double-moment, 6-class NSSL microphysics scheme (Mansell et al. 2010) is used for all simulations. All hydrometeors are represented as three-parameter gamma distributions as discussed in Mansell et al. (2010), and use default values except when noted. Cloud droplets are nucleated according to the predicted supersaturation using a user-set leading CCN coefficient in the Twomey relationship (Twomey 1959). The ice nucleation parameterization of Phillips et al. [2008; their Eqs. (1) and (3), but applied for temperatures less than −30°C, and greater than −30°C, respectively] is used by default unless otherwise noted. Contact nucleation of ice, immersion freezing of raindrops, and rime splintering (Hallet and Mossop 1974) are also included unless noted. The scheme is preferable for this study because graupel and hail are included as separate hydrometeor classes with mass, number, and density predicted for each, the latter helping to improve fall speed estimates. Excessive size sorting of large hydrometeors is prevented by allowing sedimentation of the minimum number estimated from mass-weighted or reflectivity-weighted corrections to the number-weighted fall speeds, as described by Mansell (2010; Method I + II). Conversion of graupel to hail is limited so that only one-tenth of graupel mass is converted per time step once sufficient density (500 kg m−3) is reached, at temperatures less than −2°C to avoid erroneous conversion near the melting level.

c. Generation of multiple realizations

This study uses a set of 12 simulations (different realizations from the same initial environment) to investigate the relative importance of different hydrometeor types, and their associated latent cooling contributions in the downdrafts for determining cold pool characteristics. The aim is to create a set of simulations with similar dynamical storm evolution, but some variability in storm characteristics stemming from microphysical differences, to find relationships between microphysical processes, the downdrafts and subsequent cold pools. Slight alterations to the initial model parameters or processes influencing precipitation were made to the “control” simulation, including (i) decreasing or increasing the number of CCN, altering the warm-rain process; (ii) decreasing or increasing the graupel or hail shape parameter and hence broadening or narrowing the graupel or hail size distribution, respectively; and (iii) altering ice formation by decreasing or increasing the number of ice nuclei (IN) by multiplying by an “IN factor,” by disabling immersion freezing of raindrops, and/or by disabling rime splintering, the latter two with the purpose of slowing conversion of supercooled raindrops to graupel. Table 2 summarizes these differences in initial characteristics among the simulations, and the labels used to denote each.

Table 2.

Differences in model realizations.

Table 2.

The control run uses a CCN value of 700 cm−3 and was run for 205 min. The warm-rain process is altered by decreasing or increasing the amount of CCN. Fewer CCN produce a faster warm-rain process by expediting collision–coalescence, whereas more CCN delay the onset of collision–coalescence and thus warm rain formation (e.g., Beard and Ochs 1993). When CCN were increased, the cold pool developed later, and the model run time had to be extended for consistent analysis with the other cases. Modifying the warm-rain process can also impact the production of ice hydrometeors, and thus does not alone indicate a dominant role in the latent cooling producing the cold pools. For example, smaller drops associated with increased CCN concentrations can be lofted higher, becoming supercooled and potentially creating more graupel and/or hail (e.g., Tao et al. 2007) that can then also alter the latent cooling associated with those hydrometeors.

Changes in the assumed underlying graupel or hail size distribution were made by altering the shape parameter (cf. Mansell et al. 2010). For most simulations, the graupel shape parameter is set to zero, yielding a negative-exponential distribution, except when increased to narrow it (Table 2). Similarly, the hail shape parameter is 0.5 for most simulations, but was increased or decreased for two simulations. A narrower/broader graupel or hail distribution (larger/smaller shape parameter) should decrease/increase fall speeds and size sorting, respectively.

Changes in ice processes are produced through varying the initial amount of IN by increasing or decreasing the leading coefficient in the Phillips et al. (2008) formula by a factor of 10 for temperatures greater than −30°C (Table 2). To try to severely limit the amount of ice being produced, and possibly encourage variations in the amount and sizes of graupel and hail produced, two additional simulations were run for the low IN case with either immersion freezing of raindrops disabled, or both immersion freezing and rime splintering disabled.

d. Microphysical budget calculations

Microphysical budgets are calculated to evaluate the relative quantity of latent cooling by each hydrometeor. The latent cooling terms calculated in this study are: graupel sublimation, graupel melting, hail sublimation, hail melting, and rain evaporation. (Contributions from phase changes in cloud water and ice, and snow, were found to be far less in this set of simulations.) These terms are calculated directly in the NSSL microphysics subroutine at each grid point during the CM1 integration by
Lxdqx=cpdT,
where Lx represents the latent heat due to the phase change, dqx represents the cooling from changes in the particular hydrometeor mixing ratio qx, cp is the specific heat of air in terms of constant pressure, and dT is the change in air temperature. Since cold pools are defined using θ, the equation can be manipulated using a simplified form of the Exner function. In this way, values can be expressed as an (isobaric) change in potential temperature (). For quantities integrated over long periods of time in the simulations, values are instead converted to joules (J) beginning with an alternate form of (3) and inserting the full form of the Exner function to obtain the following:
Lxdqx=dθ×cp(pp0)Rd/cp,
where p is total pressure, p0 is a constant pressure of 105 Pa, and Rd is the dry gas constant. The latent cooling output is then multiplied by the local air density and the grid box volume to convert the units to joules.

e. Defining the cold pool

While there is no unified definition for a cold pool in the literature, a majority of previous studies opt to use a form of potential temperature (θ); either potential temperature perturbation, θ′ (e.g., James et al. 2006; James and Markowski 2010; Morrison and Milbrandt 2011; Van Weverberg et al. 2012; Kalina et al. 2014; Peters and Schumacher 2015), equivalent potential temperature perturbation, θe′ (e.g., Dawson et al. 2010; Schlemmer and Hohenegger 2014), or density potential temperature perturbation, θρ′ (Grant and van den Heever 2015). Of these, variation in the threshold value used to define a cold pool also occurs, with some studies using a value of −1 K and others a value of −2 K. A number of other studies evaluate winds associated with the gust front to define the cold pool (Corfidi 2003, James et al. 2006; Redl et al. 2015). Because this study primarily focuses on the thermodynamic properties of downdrafts in deep convection, and for ease in comparison with past studies in the literature, a cold pool is defined as a parcel of air at the surface having θ′ less than or equal to −2 K. A less stringent threshold of −1 K made the fields too noisy, and using more stringent thresholds (e.g., −3, −4 K) did not greatly affect the results.

3. Results

a. Modeled storm morphology and dynamics

Modeled storms began as supercells (vertical vorticity values in updrafts between 0.01 and 0.07 s−1) before transitioning into a multicell cluster (Fig. 2) with a large, sweeping cold pool first developing along the backside of the storms, but then spreading southward and eastward (Fig. 3). This evolution is generally representative of all the simulations. The modeled storm evolution broadly follows that observed during MC3E for a subset of storms that occurred in north-central Oklahoma on 23 May 2011 (Borque et al. 2019, manuscript submitted to Mon. Wea. Rev., hereafter B19), reproducing general features of the convection and the production of an extensive cold pool. While the idealized nature of the simulations performed here precludes any meaningful direct comparison with individual storms on that day, comparison of the general features of the simulated cold pool will be made with the analysis of radar and Oklahoma mesonet data for this case by B19.

Fig. 2.
Fig. 2.

Simulated reflectivity at 1 km AGL (shaded) and cold pool (black contour) throughout various times in the Control simulation. The axes are in grid points, but the plot window shifts in time to follow the storm as it progresses.

Citation: Monthly Weather Review 147, 9; 10.1175/MWR-D-18-0382.1

Fig. 3.
Fig. 3.

(left) Simulated reflectivity at 1 km AGL (dBZ, shaded) and cold pool (contoured) and (right) theta perturbation at the surface (K) for the Control simulation at 205 min. The axes are in grid points.

Citation: Monthly Weather Review 147, 9; 10.1175/MWR-D-18-0382.1

During the supercell stage in the simulations, the cold pools produced were shallow, spatially small, remained stationary or propagated opposite of storm motion, and dissipated quickly. (B19 were unable to identify any cold pools in the Oklahoma Mesonet data from the individual supercells observed on this day, also suggesting they were small or very transient.) These cold pools were not analyzed. Instead, the much larger, much more persistent cold pool resulting from the multicellular convection that developed later in the simulations was analyzed. The start of this cold pool was identified by the appearance of a −2 K surface potential temperature perturbation that was initiated by a low-level downdraft. Different simulations had different cold pool onset times. The 12 different realizations also produced cold pools of varying sizes and expansion rates (Fig. 4), but all simulations reached a minimum cold pool temperature of −10 K at some time.

Fig. 4.
Fig. 4.

Time series of cold pool area for all 12 model simulations from the start of the cold pool until 50 min afterward.

Citation: Monthly Weather Review 147, 9; 10.1175/MWR-D-18-0382.1

Derived radar reflectivity and vertical velocity extrema were compared as a brief investigation of any general changes in the storm dynamics among the 12 realizations. Visual comparison of the former (not shown) was very similar to that shown for the control case in Fig. 2. For the latter (Fig. 5), variance is seen in maximum updraft speeds with respect to the control run, but none of the storms were weakened to the point of being incapable of supporting hail growth, nor were any excessively large through the entire integration period. More variance is seen in the downdrafts as time progresses; this variance is due solely to microphysical effects (they are the only differences in the initial conditions among the simulations) and their feedbacks. As such, the variations to the model microphysics (Table 2) were successful in creating 12 different realizations of the 23 May 2011 convection that produce differences in downdraft strengths, which is useful in diagnosing the microphysical effects on cold pools.

Fig. 5.
Fig. 5.

Time series of updraft (red) and downdraft (blue) maxima below 5 km for each simulation with the Control simulation in black for reference.

Citation: Monthly Weather Review 147, 9; 10.1175/MWR-D-18-0382.1

b. Initiation time of cold pools

The cold pool first appeared for each simulation (Fig. 6) between 100 and 150 min in most simulations, but a trend is seen among the runs influencing the speed of the warm-rain process. A faster warm-rain process produced an earlier cold pool, whereas a slow warm-rain process significantly delayed its onset, due to its role in potentially creating the earliest rainfall. Manual analysis of each case showed that the cold pools were initiated by low-level downdrafts (<3.5-km height, typically), which appear to have resulted from precipitation greatly influenced by the warm rain process. Evaporating rain is the latent cooling mechanism that occurs nearest the ground, and has the least time to be counteracted by compressional warming of the descending air, or entrainment into the downdrafts.

Fig. 6.
Fig. 6.

Starting time of the cold pool for each simulation as noted.

Citation: Monthly Weather Review 147, 9; 10.1175/MWR-D-18-0382.1

c. Microphysical influences on initial cold pool formation

To address what hydrometeor type(s) and phase changes produce the initial cold pool, latent cooling budgets are calculated within a manually determined subset of the model domain within the 10 min prior to the start of the cold pool for each simulation. The domain subset encompasses the strongest downdraft that exists at the lowest model level near the region where the cold pool began, but broad enough to include its extent for the entire 10-min period leading up to the start of the cold pool, and ranges from 200 to 560 km2 among the different simulations. During this 10-min period, downdraft maxima at the lowest model level contributing to the initial cold pool varied among the simulations between 5 and 15 m s−1; latent cooling was calculated only within downdrafts at or exceeding 5 m s−1 and are presented in units of kelvin as described in section 2d. The vertical extent of the subdomain was limited to 5-km altitude.

Figure 7 shows the results of these calculations accumulated over the 10 min preceding the first appearance of the cold pool, since the effects of latent cooling are not instantaneously transferred to the cold pool. To account for differences in downdraft size among the different model runs, the integrated latent cooling is normalized by the volume of the respective downdrafts within which it is computed. As shown in Figs. 7d–f, slowing the warm rain process decreases the contribution of rain evaporation within the downdraft; it also increases the amount of graupel melting (and to a lesser extent graupel sublimation). As the warm rain process is slowed, more cloud water is available for graupel growth higher in the cloud (e.g., Tao et al. 2007), and that effect is reflected here in the amount of precipitating graupel in the downdraft.

Fig. 7.
Fig. 7.

Integrated latent cooling of graupel sublimation (dashed red), graupel melting (solid red), hail sublimation (dashed blue), hail melting (solid blue), and rain evaporation (dotted green) up to 10 min prior to the start of the cold pool. Values are computed only within the 5 m s−1 downdraft forming the initial cold pool, and are normalized by the downdraft volume, for each case.

Citation: Monthly Weather Review 147, 9; 10.1175/MWR-D-18-0382.1

As the graupel size distribution is shifted toward a little smaller (Fig. 7b) or much smaller sizes (Fig. 7c), the contribution of rain evaporation to the initial cold pool formation increases, demonstrating the effects of smaller hail that melts more quickly and can contribute to the rain evaporation term, particularly for the narrowest distribution (Fig. 7c). The resulting interplay of slower fall speeds as the graupel distribution is narrowed versus the relative effects of graupel melting and sublimation terms is more complex. For the narrowest graupel distribution, it appears that slower fall speeds can loft more graupel mass above the melting level in the updrafts, increasing rain evaporation relative to the melting term, while also encouraging more hail growth (and thus increasing those melting and sublimation terms relative to the control run).

As the hail size distribution is broadened or narrowed (Figs. 7g,h), the contribution from graupel changes significantly. A broader hail distribution reduces the sublimation of graupel, while a narrow distribution increases it while also decreasing the contribution from rain evaporation. It is hypothesized that the increase in graupel sublimation seen with the narrow hail distribution is the result of less competition with the smaller hail for collecting the available supercooled water.

When IN were decreased by various degrees (Figs. 7i–l), the contributions from the frozen hydrometeors also decreased by varying amounts, but not in a manner where the trends are easily explained. In the most limiting case (Fig. 7l), the contribution of melting hail increases as it likely has far less competition for growth with other frozen hydrometeors for collecting cloud water. When a factor of 10 more IN are initiated in the model (Fig. 7i), contributions from graupel and hail decrease. The interplay among the different hydrometeor types when various ice-nucleating processes are decreased or excluded are complex, and beyond the scope of this study, but do demonstrate that the microphysical alternations made to this set of realizations is creating differences that should also be reflected in the cold pool characteristics evaluated later in this study.

If all the individual latent cooling terms are integrated over the 10 min prior to the cold pool initiation, the maximum strength of the corresponding downdraft does not necessarily coincide with that total latent cooling (Fig. 8). It was anticipated that for all simulations in a given environment, the total amount of latent cooling required to initiate a −2 K cold pool might be similar. The discreteness of model output (every 30 s) could explain some of the discrepancy with these expected relationships, as the first appearance of the cold pool is subject to the first time it was identified in the model output. There are also possible physical reasons for differences, even in the same storm environment, that include (i) the downdraft depth and thus the amount of adiabatic warming in the downdraft that is offsetting some of the latent cooling; (ii) entrainment of environmental air into the downdraft; and (iii) hydrometeor loading in the downdraft.

Fig. 8.
Fig. 8.

Maximum downdraft speed forming the initial cold pool vs the total integrated latent cooling within the −5 m s−1 downdraft in the 10 min prior to cold pool formation, normalized by volume.

Citation: Monthly Weather Review 147, 9; 10.1175/MWR-D-18-0382.1

Figure 9 shows the relative contribution of each process to the total latent cooling to summarize these trends. There is variation among the runs regarding the most important cooling term for the initiation of the cold pool; graupel and its associated latent cooling dominates in some instances (sublimation ranging from 10% to 45%; melting ranging from 22% to 37%), while evaporation of rain is most important in other cases (15%–64%). The contribution from hail is minimal in all model runs (less than 15%). If the latent cooling terms are simply combined in terms of evaporation, melting, or sublimation (not shown), the results are nearly the same because of the minor contribution of hail in all the simulations.

Fig. 9.
Fig. 9.

Percent of total latent cooling contributed from each hydrometeor phase change in >5 m s−1 downdraft 10 min prior to initial cold pool formation.

Citation: Monthly Weather Review 147, 9; 10.1175/MWR-D-18-0382.1

d. Hydrometeor properties and microphysical influences sustaining the cold pool

Understanding the microphysical processes that sustain the cold pool may provide useful information for predicting cold pool properties. To examine the phase change effects upon the cold pool evolution after initiation, each latent cooling process is now calculated for the first 50 min after the appearance of the respective −2 K cold pools at the model surface. Here, a different algorithm searches the entire model domain to identify the multiple, transient downdrafts that contribute to (i.e., are in contact with) the surface cold pool:

  • At each model output time (30-s interval) within these 50 min, the cold pool is identified (temperature threshold less than −2 K) at the lowest grid level, and any latent cooling is calculated within these grid boxes that have a downward vertical velocity at or exceeding 1 m s−1.
  • For each of those grid boxes, the latent cooling within any adjacent grid boxes at the next vertical level above (including diagonally) are identified and added to the totals from the first level; these grid boxes are also required to have a downward vertical velocity of 1 m s−1 or greater.
  • The algorithm continues searching additional vertical levels, moving upward and outward to adjacent grid boxes, to identify those located in the same downdrafts that intersect the surface cold pool, and their latent cooling contributions are added to the running total.
  • The calculation continues until the vertical level at which no more grid boxes are associated with downdrafts intersecting the cold pool.
Unlike the calculations presented in section 3b, here the latent cooling terms are not normalized by the downdraft volumes, nor are they limited to 5-km altitude. Units are transferred into joules as described in section 2c, as the amount of cooling in kelvin is no longer intuitive.

The results for all the simulations (Fig. 10) show that, unlike the results for the cold pool initiation shown in Fig. 7, graupel sublimation always dominates the latent cooling in the downdrafts responsible for the cold pool, and contributes 50% or more to the total latent cooling. The other contributions in decreasing order of importance are: rain evaporation (approximately 30% of the total), graupel melting (approximately 15% of the total), and finally hail melting and sublimation (combined approximately 5% of the total). While the relative magnitudes of individual cooling terms differ among the model realizations, the importance of graupel sublimation appears to be paramount, at least in this particular storm environment. The magnitudes shown here are comparable with those found by D10 for rain and hail terms.

Fig. 10.
Fig. 10.

As in Fig. 7, but for >1 m s−1 downdrafts in contact with the cold pool in the 50 min after cold pool formation, and the ordinate now specified in units of joules.

Citation: Monthly Weather Review 147, 9; 10.1175/MWR-D-18-0382.1

e. The influence of hydrometeors on cold pool characteristics

The results shown in Fig. 10 at the end of the 50 min, including the latent cooling due to a particular hydrometeor, or the total from all hydrometeor phase changes, is now related to cold pool properties over that same time period. Sublimation and melting are combined for graupel or hail, and the total combines all three terms. For all comparisons, the relationship improves when examining longer time scales; thus the analysis primarily uses 50-min averages since the cold pool start. No relationships are seen when examining the latent cooling ten minutes prior to the cold pool formation (i.e., Fig. 7) and the cold pool average characteristics 50 min later. Thus, for this set of simulations, the downdraft properties (and associated latent cooling within) that form the initial cold pool do not appear to influence the subsequent cold pool properties.

1) Expansion rate and propagation speed

An increase in cold pool area is seen shortly after the start time of the cold pool for all cases (e.g., Fig. 4). An analysis of the total cold pool area 50 min after its start in each model simulation relative to the respective latent cooling terms showed no discernable trends indicative of particular microphysical processes causing a more or less expansive cold pool. However, examining the 50-min averaged rate of the cold pool expansion (approximated by dividing the square root in the change of cold pool area by the model output time interval), does show a strong relationship with the quantified latent cooling budget. The correlation between average expansion rate and the total integrated latent cooling (Fig. 11a) is strong, and results primarily from the influence of the latent cooling from rain evaporation, having a r value of 0.94. The correlation with latent cooling due to graupel is also relatively high, and is partially reflected in the correlation with the rain evaporation, since melting graupel produces rain that can evaporate at lower levels. So, while the latent cooling of graupel dominates the downdrafts throughout the storm and does influence the amount of overall rainfall in the downdrafts, the amount of rain evaporation in the lower levels of the storm appears to be the best predictor of the average cold pool expansion rate. It is hypothesized that this is due to the fact that the latent cooling from rain evaporation occurs nearest the ground, or even within the cold pool, and thus its effects are more pronounced and less likely to be mitigated by compressional warming or entrainment into the downdraft.

Fig. 11.
Fig. 11.

Integrated latent cooling of (a) all hydrometeor phase changes, (b) rain evaporation, (c) graupel sublimation and melting, and (d) hail sublimation and melting, in >1 m s−1 downdrafts sustaining the cold pool vs 50-min average cold pool expansion rate.

Citation: Monthly Weather Review 147, 9; 10.1175/MWR-D-18-0382.1

Calculating a true cold pool propagation speed from the simulations is challenging, given the heterogeneity of the cold pool as well as the complexities in constructing an objective numerical algorithm to calculate its speed relative to the sheared environmental winds. Thus, estimates of the cold pool propagation speed were instead made based on the southward advance of the cold pool’s leading edge over the last 35 min of the 12 simulations. These estimated average propagation speeds varied from near 3 m s−1 up to 6 m s−1 while being opposed by the 15 m s−1 southerly environmental winds near the surface; B19 estimated a value from Oklahoma mesonet observations and MC3E radar data analysis on this day near 6 m s−1. No clear relationship emerged between these average propagation speed estimates and the microphysical differences in the simulations.

2) Depth

Cold pool depth is calculated using a “bottom-up” approach, starting at the lowest model grid level and searching upward to find the heights where the θ′ threshold of −2 K fails to be met. Its accuracy is thus limited by the grid spacing (250 m). Air that is being latently cooled by −2 K or more within downdrafts reaching higher altitudes within the storm would be considered within the cold pool in this approach, and thus produces a positive bias in the estimated cold pool depth values. The limited model grid spacing also produces a positive bias; tests with a stretched grid (not shown) having 100-m grid spacing in the lowest 4 km produced average depths 300–550 m lower, but trends among the simulations were not changed.

Because the expanding cold pool is not homogeneous in depth, spatially averaged values are used in the analysis (Fig. 12). While the average depth increases in time, significant fluctuations exist even in an individual simulation. This variability is indicative of the transitory nature of the downdrafts (and their vertical extent) that contribute to the cold pool. B19 estimated average cold pool depth on this day from an analysis of multiple MC3E radar datasets and found generally increasing values from ~0.7 to 2.7 km over their analysis period. The peaks in average depth shown in Fig. 12 represent times where cold pool depth was increased by more numerous low-level downdrafts, that later decayed. B19 also found transient maximum values over 5-km altitude; the maximum depth found in the simulations was approximately 5 km for nine simulations and greater than 6 km for the remaining three simulations. When time-averaging the values shown in Fig. 12, the strongest positive correlation is between evaporating rain and the time-averaged cold pool depth (Fig. 13b), as also found for the expansion rate.

Fig. 12.
Fig. 12.

Time series of average cold pool depth for all simulations, as described in the text.

Citation: Monthly Weather Review 147, 9; 10.1175/MWR-D-18-0382.1

Fig. 13.
Fig. 13.

As in Fig. 11, but latent cooling contributions vs 50-min average cold pool depth.

Citation: Monthly Weather Review 147, 9; 10.1175/MWR-D-18-0382.1

3) Intensity

“Cold pool intensity” is usually expressed as a relative quantity with stronger cold pools being those that have colder surface values of θ′ (or the chosen variable for representing a cold pool). This is not a useful quantification in the context of this study, as all model simulations reach a minimum cold pool temperature of −10 K. Other metrics such as representing the strength as a percentage of the −2 K cold pool area occupied by a colder threshold (i.e., what percent of the cold pool is “strong”, for example having θ′ < 6 K, as observed in the Oklahoma Mesonet observations by B19, for the day on which the simulations are based) did not demonstrate a strong relationship with the latent heating calculations (r values < 0.56). If the cold pool intensity is instead evaluated as the 50-min average of the 3D spatial integral of negative buoyancy within the −2 K cold pool [B, using Eq. (2) and integrated up to heights near 6 km], the cold pool intensity indeed shows a strong correlation with the total latent cooling, and is essentially most correlated with the rain evaporation term (Fig. 14).

Fig. 14.
Fig. 14.

As in Fig. 11, but latent cooling contributions vs 50-min, spatially integrated cold pool buoyancy.

Citation: Monthly Weather Review 147, 9; 10.1175/MWR-D-18-0382.1

4. Conclusions

Because of the complexities surrounding microphysical processes and their effects on storm dynamics, an understanding of how cold pools are coupled to the microphysics has remained elusive. Previous studies have primarily focused on differences in cold pools resulting from the use of different microphysical parameterization schemes, or parameters used in those schemes. Given that different schemes have different underlying assumptions, questions remain regarding the role of particular microphysical processes in determining cold pool characteristics, the answers to which could improve the representation of cold pools and cold pool–induced convection within parameterizations used for larger-scale weather and climate models.

Using a set of 12 model simulations representing different realizations of multicellular convection in the same environment, but with varying hydrometeor characteristics, the dominant microphysical processes within downdrafts forming and sustaining the cold pool were identified, and some relationships between latent cooling associated with particular hydrometeor types and cold pool properties were found. Within downdrafts forming the initial cold pool, variability existed among the dominant hydrometeor phase changes governing the cooling: in some simulations, graupel sublimation/melting dominated and in others, rain evaporation. In all runs there was a minimal contribution from hail sublimation/melting. With respect to sustainment of the cold pools over a longer time period (50 min), graupel sublimation was always the dominant cooling term, with secondary contributions by rain evaporation and melting graupel, and minimal contributions from melting or sublimating hail.

However, many cold pool characteristics were most correlated with the amount of rain evaporation. The speed of the warm-rain process in these simulations significantly influenced the onset time of the cold pool, with a slower warm-rain process delaying its onset, and a faster warm-rain process speeding it. The overall amount of rain evaporation in the downdrafts sustaining the cold pool, including rain resulting from melting graupel and hail, correlated extremely well with the average cold pool expansion rate, and the spatially and temporally averaged cold pool depth and intensity.

5. Discussion

Because this study yielded differing results from prior research (G04, VC04, and D10) an attempt to reconcile some of these differences is now presented. D10 calculated latent cooling within the 0.5 m s−1 downdrafts, whereas this study used a more stringent threshold of 1 m s−1. Tests conducted using a weaker downdraft threshold (not shown) suggest only slight increases in the magnitude of rain evaporation and graupel sublimation occur. More importantly, a 4-km upper vertical limit to the latent cooling calculations was used by D10, whereas this study (and G04) performed these calculations through the vertical extent of the domain. Figure 15 illustrates the differences in results that occur when different vertical limits are applied for the control case simulated here, and two notable points emerge. First, rain evaporation dominates the total latent cooling in the downdrafts contributing to the cold pool when the calculations are restricted to lower levels; a changeover to graupel dominating the latent cooling terms occurs at higher levels. Second, there is little difference in latent cooling values in the downdrafts when increasing the depths of the calculations above 6 km. Examination of a sample cross section of the control case (Fig. 16) shows that nearly all of the latent cooling occurs below this altitude (Figs. 16c–g, corresponding to vertical level 25), even though downdrafts often extend much higher into the storm (Fig. 15b). Thus, it appears that the vertical extent of the latent cooling due to hydrometeor phase changes in forming the cold pool can be limited to midlevels of the storm, but care must be exercised in setting this vertical limit for a particular storm and/or environment to include levels where sublimation of graupel and hail may be important.

Fig. 15.
Fig. 15.

Comparison of latent cooling by hydrometeor phase change for the Control simulation, but limiting calculations to particular vertical depths within the domain.

Citation: Monthly Weather Review 147, 9; 10.1175/MWR-D-18-0382.1

Fig. 16.
Fig. 16.

Vertical cross sections of reflectivity, vertical velocity, and hydrometeor latent cooling for the Control simulation at 205 min through y = 65 as seen in Fig. 3. Black contours outline the 1 m s−1 downdraft, and the solid horizontal line indicates height of the melting level. Vertical axis is given in grid-level units. Note the difference in the scales for plots (c)–(g).

Citation: Monthly Weather Review 147, 9; 10.1175/MWR-D-18-0382.1

The results of G04 and VC04 suggested that more numerous, smaller rimed particles created stronger and deeper cold pools. G04 concluded that representing the large rimed ice as smaller graupel rather than larger hail created stronger cold pools, which is also consistent with the findings of this study in that latent cooling associated with hail was a minor factor compared to graupel. VC04 concluded that greater hail melting, accomplished by smaller hailstones, produced deeper cold pools. When comparing the magnitude of hail melting alone to the average cold pool depth in the 50 min after cold pool formation (not shown), a positive trend does exist (r value of 0.68) in these results to support that finding, although here much stronger trends were associated with graupel or rain (Fig. 13), which VC04 did not examine.

This study does suggest that consideration of the microphysics of deep convection may be necessary to accurately represent cold pools and their effects in parameterizations used in larger-scale weather and climate models. In particular, the timing of the onset of the cold pools appeared to be very dependent upon the speed of the warm rain process; the latter could in turn be parameterized based upon local CCN values and cloud base temperatures from an environmental sounding. The amount of graupel produced in the storms appears to help modulate the sustainment of the cold pool; it would ultimately be related to the amount of IN (unfortunately not well quantified), the amount of liquid water above the melting level, and also the competition with any hail. Models using microphysical schemes that only predict one rimed hydrometeor category may have more difficulty in this regard. Large amounts of rainfall near the ground, whether produced by warm-rain or melting graupel and hail, would seem to be a good predictor of the average expansion rate, cold pool depth, and (negative) buoyancy, and would be predicted by most microphysical schemes.

While trying to avoid shortcomings of previous studies, and to reconcile differences seen in other studies, the presented research still has limitations that future work is needed to resolve, particularly to assist in building a robust parameterization of cold pools. In this study, a single environment was used for all simulations, and thus more work is needed to investigate the generality of the results, particularly in different regimes of vertical static stability and/or vertical humidity profiles. Srivastava (1987) found ice sublimation increased with stronger lapse rates, but ice melting increased with weaker lapse rates. The lapse rates for the environment in the current study are moderate, at approximately 5.5 K km−1 from 500 to 600 hPa (melting level), and approximately 6.5 K km−1 between 800 and 600 hPa, but indicate that the results could differ in a more stable environment. Other cases also need to be simulated in environments with different degrees of vertical wind shear to understand the magnitude of the cold pool response to variations in storm dynamics and morphology versus the microphysics, and to determine which might ultimately have a greater influence on cold pool properties. Such a study is planned, and will provide further insight that could aid in the development of more realistic cold pool parameterization schemes.

Because of the large number of high-resolution simulations that was required to produce the variability needed to find relationships among the microphysical variables studied here, performing the entire set of simulations again with other microphysics parameterizations was impractical. Additional studies using other microphysical schemes should be done to ensure the generality of the findings here, but caution must also be applied when using microphysical schemes that may not represent all of the important processes. Given that many schemes only contain one rimed ice category, more work is needed to understand how best to implement these findings into a cold pool parameterization.

Acknowledgments

The authors wish to thank Drs. Jeff Trapp and Steve Nesbitt, as well as Dr. Paloma Borque and Geoff Marion, for their constructive comments throughout the completion of this work. The authors also wish to thank Dr. George Bryan of the National Center for Atmospheric Research (funded by the National Science Foundation) for developing and maintaining CM1, and Dr. Ted Mansell of the National Severe Storms Laboratory (funded by the National Oceanic and Atmospheric Administration) for developing and maintaining the NSSL microphysics scheme. The comments and suggestions from three anonymous reviewers and Editor Dr. Hugh Morrison greatly improved this work. All simulations were run on the Blue Waters Supercomputer, which is supported by the National Science Foundation, the National Center for Supercomputing Applications, and the University of Illinois at Urbana–Champaign. This work was supported by the U.S. Department of Energy’s Atmospheric Systems Research program, Award DE-SC0014101.

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