Houze et al. (BAMS, 1989)

Johnson and Hamilton (1988)

Basic Equations: 2D Squall Line - Or, more simply, consider the 2D horizontal vorticity equation: where ⁄ *Also, no vortex tilting or stretching

2D Convective System Evolution: C/∆u << 1C/∆u ~ 1C/∆u > 1 Weak shear, strong cold pool: rapid evolution Strong shear, weak cold pool: slow evolution

“Optimal” condition for cold pool lifting C/∆u > 1 C/∆u = 1 C/∆u < 1 RKW Theory Rotunno et al. (JAS, 1988)

*Strength of Rear-Inflow Jet is proportional to CAPE Rear-Inflow Jets:

X Background and Definitions Mesoscale Convective System (MCS): an isolated, nearly contiguous region of thunderstorms, sometimes surrounded by an extensive region of moderate rainfall. Total size is usually km across. Bow-echo: a bow-shaped line of thunderstorms often containing strong surface winds. Mesoscale Convective Vortex: a lower-mid- tropospheric horizontal wind circulation derived from an area of convection (often an MCS) UTC 10 June, June, UTC 10 June, km

Now Consider a 3D Squall Line….without Coriolis: - ⁄ ⁄

Weisman and Davis (1998) f=0

How can we systematically produce the observed line-end vortex pattern?

Mature Phase: Line-end vortex mechanisms:

Vortex Tube Circulation:

Vertical Vorticity: …flux form Circulation: ⁄ ⁄ ⁄

⁄ ⁄

(Davis and Weisman, 1994; Weisman and Davis, 1998; Davis and Galarneau, 2009) …tilting of system-generated horizontal vorticity Rear-inflow jet

Role of Line-End Vortices Focuses and Intensifies Rear-Inflow Jet

Now Consider a 3D Squall Line….with Coriolis: -

⁄    f-flux

Derechos: Severe Lines of Thunderstorms Damage from straight-line wind Long swaths (> 400 km), long duration (> 6 h) Wide damage swaths ( km) Rapid movement: m/s 26 NOAA Storm Prediction Center Earthsky.org Csmonitor.com

Derecho: (Johns and Hirt 1987) Large CAPE Moderate Shear

29 June 2012 Derecho: 18 UTC21 UTC 00 UTC 03 UTC Composite Radar SPC Storm Reports

The 8 May 2009 “Super Derecho”: Morris Weisman NCAR/MMM Radar 17:56 UTC 05/08/09 (Paducah) Also: Lance Bosart, Clark Evans 8-10 h of Hurricane- Force Winds, Extensive Damage… SUNY Albany 9 April 2014

11 UTC (23 h) 13 UTC (25 h)15 UTC (27 h) Occluding Stage: 09 UTC (21 h)

06 UTC 07 UTC09 UTC 11 UTC 12 UTC 13 UTC 850 mb W (contoured) and Vertical Vorticity (shaded)

Vorticity Equation: Vertical Vorticity: tiltingstretching

…Tilting…Stretching 850 hPa Vorticity 07 UTC

900 hPa Horizontal Vorticity, SR Flow, W (shaded) With low-level jet from SW, streamwise horizontal vorticity evident in low-level environment…. 08 May 2009 Derecho

29 June 2012 versus 08 May 2009 Derechoes 29 June 2012 …Cold-pool dominant …Descending rear- inflow …Cyclonic mid-level vortex 08 May 2009 …Mesovortex dominant …Elevated rear-inflow jet …Warm-core vortex extending to surface Radar Reflectivity Model Reflectivity

29 June May 2009 Cape/Shear Intercomparison: CAPE: j/kg Shear: kts (10-15 ms-1) CAPE: j/kg Shear: kts (15-25 ms-1)

29 June May hPa Intercomparison: Low-Level Jet, west-east boundary, Lee trough   NO Low-Level Jet, NO west-east boundary

Summary: ….3 km WRF-ARW was capable of not only predicting the potential for two high-end Derecho events, but also was capable of distinguishing the differing mechanisms… 29 June 2012: Cold Pool dominant 08 May 2009: Mesovortex dominant ….These two cases may help clarify the differing environmental characteristics that contribute to these two archetypes: 29 June 2012: Extreme instability, modest unidirectional low-level shear 08 May 2009: Mid-trop baroclinicity, low- level jet, strong directional shear (streamwise at low-levels)

KT winds at ~1kft Base Reflectivity 1334z KSGF

Storm-Relative Velocity 1334z KSGF

Atkins et al. MWR (2004)

Wakimoto et al. MWR (2006)

U S = 20/2.5 f=0 t = 4 hr 50 km w, V z=3 km qr, V θ’ z=250 m continuous updraft no meso- vortices!

U S = 20/2.5 t = 4 hr 50 km w, V z=3 km qr, V θ’ z=250 m locational bias

Vorticity Equation: Vertical Vorticity: tilting stretching …integrate along a parcel’s path:

⁄

Weisman and Trapp (2003)

Trapp and Weisman (2003)

Wakimoto et al. MWR (2006)

Example of a “Serial” MCV/MCS Case 0915 UTC 27 May UTC 28 May UTC 28 May UTC 28 May UTC 29 May UTC 29 May 1998

IOP km

IOP hPa Widespread Instability m/s dBz X 1730 UTC 11 June Mean Wind Profile

Potential Vorticity: = 0 for isentropic motions Equivalent Potential Vorticity:

Long-time Behavior of MCSs (twice) L H H Warm Cool

Raymond and Jiang (JAS 1990) Conceptual Model of Isentropic Lifting within a Steady Balanced Vortex (e.g., MCV)

MCV Induced Lifting and Destabilization Fritcsh et al. 1994, MWR

Low-Level Jet Scenario

Flash-Flood-Producing Convective Systems Associated with Mesoscale Convective Vortices Russ Schumacher and Richard Johnson WAF (2008)