Observations of Wall Cloud Formation in Supercell Thunderstorms During VORTEX2’’
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4278 MONTHLY WEATHER REVIEW VOLUME 143 CORRESPONDENCE Comments on ‘‘Observations of Wall Cloud Formation in Supercell Thunderstorms during VORTEX2’’ PAUL MARKOWSKI,YVETTE RICHARDSON,MATTHEW KUMJIAN,ALEXANDRA ANDERSON-FREY, GIOVANNI JIMENEZ,BRANDEN KATONA,ALICIA KLEES,ROBERT SCHROM, AND DANA TOBIN Department of Meteorology, The Pennsylvania State University, University Park, Pennsylvania (Manuscript received and in final form 31 March 2015) 1. Introduction drastic effect on the temperature perturbation associ- ated with a given pressure perturbation. AGN’s Eq. In a recent article, Atkins et al. (2014, hereafter (1), subject to their assumptions, becomes AGN) nicely synthesize mobile radar and stereo pho- togrammetric data in a study of the wall clouds observed 0 0 T p in the 5 June and 11 June 2009 supercells intercepted by T 5 s , (1) p the second Verification of the Origins of Rotation in as Tornadoes Experiment (VORTEX2). They conclude where T0 and p0 are the temperature and pressure that the lifting of rain-cooled air originating in the perturbations, respectively; and Ts and pas are the base- storms’ forward-flank precipitation regions contributed state temperature and pressure, using AGN’s symbol- to wall cloud formation, as Rotunno and Klemp (1985) ogy. AGN infer 2.28C of cooling for a 6–7-hPa pressure found in a numerical simulation of a supercell thun- drop, which implies a lowering of the cloud base by derstorm. However, AGN also conclude that a dynamic approximately 270 m. Equation (1) predicts T0 ; 30 K pressure deficit associated with rotation within the in a strong tornado (assuming p0 ; 100 hPa), which 5 June wall cloud contributed significantly to cloud would correspond to temperatures near or below lowering. Moreover, it was found that both wall clouds freezing within many tornadoes. comprised air parcels from not just the forward-flank Unavoidably, density perturbations accompany tem- precipitation region, but also from the environmental perature perturbations. For the problem at hand, the first inflow, and that some other parcel trajectories into the law of thermodynamics provides the relationship between 5 June wall cloud originated from the rear-flank down- pressure and temperature changes: draft (RFD). Below we offer an alternative inter- pretation of some of their results. dT dp q 5 c 2 a . (2) p dt dt 2. The lowering of the cloud base owing to rotation The variables q, cp, T, a, and p are the specific heating AGN use the linearized ideal gas law to relate pres- rate, specific heat at constant pressure, temperature, 5 sure, density, temperature, and water vapor perturba- specific volume, and pressure, respectively. For q 0, tions [see their Eq. (1)]. Though neglecting the effects dT a of water vapor on pressure perturbations is fairly in- 5 . (3) dp c consequential, neglecting density perturbations has a p This expression is perhaps used most often to obtain the lapse rate of temperature within a vertically displaced Corresponding author address: Dr. Paul Markowski, Department of Meteorology, The Pennsylvania State University, 503 Walker parcel, but it also can be used as a general expression to Building, University Park, PA 16802. link pressure and temperature changes that occur during E-mail: [email protected] any dry adiabatic process, such as the dynamic lowering DOI: 10.1175/MWR-D-15-0126.1 Ó 2015 American Meteorological Society Unauthenticated | Downloaded 09/25/21 02:55 AM UTC OCTOBER 2015 C O R R E S P O N D E N C E 4279 of pressure that occurs as vorticity increases. A tem- and Ray 1985).] Assuming AGN used Neumann perature change of DT 520.78C is obtained for boundary conditions, the magnitude of the retrieved 21 21 3 21 Dp 527 hPa, cp 5 1005 J kg K , and a 5 1m kg pressure perturbations (e.g., AGN’s Figs. 2b and 4b) (a needs to be averaged during the process). The tem- cannot be interpreted as pressure deficits relative to perature change is less than one-third of that estimated the environment without first adding a constant to by AGN; the implied lowering of the cloud base is the pressure fields. Though the constant is unknown, similarly reduced to less than one-third of the AGN one strategy would be to require p0 ; 0 along the estimate. AGN’s overestimate of the temperature drop southern and eastern boundaries of the dual- and cloud-base lowering stems from the erroneous Doppler domain. constant-density assumption. In AGN’s Figs. 2b and 4b, it appears that p0 might be too negative (i.e., a positive constant might need to be added to the retrieved p0 field), given the min- 3. Nonuniqueness of retrieved pressure fields imum p0 of 28to210 hPa (these pressure perturba- The pressure retrieval employed by AGN likely in- tions are several hPa lower than those occurring in volves inverting (on a given horizontal plane) numerically simulated supercell wall clouds, even in high- resolution simulations) and how limited the areal extent 2 0 2 0 0 0 › p › p of positive p is within the cool outflow. Concerning this =2p 5 1 , (4) h ›x2 ›y2 second point, where positive p0 exists, its magnitude is very weak, with virtually no regions within the outflow where the rhs of Eq. (4) is obtained from the dual- having p0 . 1 hPa. Doppler-derived three-dimensional wind field and the Navier–Stokes equations, such that 4. Dynamic versus nonhydrostatic pressure 0 ›p ›u perturbations 52r 1 v Á $u 2 f y 2 F , (5) ›x ›t u AGN (p. 4829) refer to the diagnosed pressure per- › 0 ›y p turbations as ‘‘nonhydrostatic dynamic’’ pressure per- 52r 1 v Á $y 1 fu 2 Fy , (6) ›y ›t turbations. We believe this terminology could create some confusion. r 5 r where (z) is a reference density profile, f is the The dynamic pressure perturbation, as defined by 5 y Coriolis parameter, v (u, , w) is the velocity, and Klemp and Rotunno (1983), among others, is related to (Fu, Fy) are the horizontal components of turbulent the wind field via drag (usually neglected or parameterized from the velocity field). =2 0 52$ Á r Á $ 1 r z pd ( v v) f , (7) Though AGN do not say what boundary conditions were used, in our experience, Eq. (4) is usually solved where z is the vertical vorticity and the variation of f with 0 by applying Neumann boundary conditions on the latitude has been neglected. Given this definition of pd, 0 horizontal boundaries of the dual-Doppler domain the total pressure perturbation is the sum of pd and a › 0 › › 0 › 0 (e.g., Hane and Ray 1985)because p / x and p / y pressure perturbation due to the buoyancy (B) field, pb, 0 5 0 1 0 are known along the boundaries via Eqs. (5) and (6). that is, p pd pb, where Dirichlet boundary conditions (such as p0 5 0along 0 ›rB the boundaries) are typically not a viable option; al- =2p 5 . (8) 0 b › though p 5 0 might be a satisfactory assumption along z the southern and eastern boundaries of a dual-Doppler Alternatively, p0 can be decomposed into hydrostatic wind synthesis region surrounding a storm, this assump- 0 0 (ph) and nonhydrostatic (pnh) parts, that is, tion is less credible along the western and northern 0 5 0 1 0 p ph pnh. In this framework, following Davies-Jones boundaries because these boundaries are likely to reside (2003), in cool outflow and high pressure. › 0 If Neumann boundary conditions are used, then the ph 0 0 52r g (9) retrieved p field is not unique; it is only known to ›z within a constant in a given horizontal plane. [Note, however, that horizontal gradients of p0 are unique, and 0 2 h 0i h 0i as is the field of p p ,where p is the horizontal 0 0 0 =2 52=2 2 $ Á r Á $ 1 r z average of the retrieved p at each level (e.g., Hane pnh hph ( v v) f , (10) Unauthenticated | Downloaded 09/25/21 02:55 AM UTC 4280 MONTHLY WEATHER REVIEW VOLUME 143 where g is the acceleration due to gravity and r0 is the However, these trajectories appear to be behind the density perturbation (r0 52Br/g). outflow boundary per AGN’s Fig. 13, which implies 0 0 Although pd and pnh are similar in some circum- they likely have been cooled and humidified too. In- stances [e.g., see Fig. 2.6 in Markowski and Richardson deed, the mobile mesonet observations in AGN’s 0 0 (2010), which depicts pd and pnh fields associated with a Fig. 15 indicate potential temperatures and water vapor 0 0 21 density current], in other situations pd and pnh are mixing ratios of 301–303 K and 10.8–11.1 g kg ,re- dissimilar [e.g., see Fig. 2.7 in Markowski and spectively, in the region of these trajectories. The en- 0 0 Richardson (2010), which depicts pd and pnh fields as- vironmental inflow sounding shown in AGN’s Fig. 16 sociated with a rising warm bubble]. Reference to a has a surface potential temperature and water vapor 2 nonhydrostatic dynamic pressure perturbation does mixing ratio of 36.28C (309.4 K) and 10.4 g kg 1,re- not seem appropriate because only part of the non- spectively. It might be more appropriate to charac- 0 hydrostatic pressure perturbation is related to pd;the terize the air parcels following the inflow trajectories as 0 rest is attributable to pb, which is virtually certain to be outflow parcels, given their potential temperature nonzero beneath a thunderstorm updraft.