Heavy precipitation at a location = intensity x longevity

Common sources of heavy precipitation in U.S. Mesoscale convective systems and vortices Orographically induced, trapped or influenced storms Landfalling tropical cyclones

MCSs & precipitation facts Common types: squall-lines and supercells Large % of warm season rainfall in U.S. and flash floods (Maddox et al. 1979; Doswell et al. 1996) Initiation & motion often not well forecasted by operational models (Davis et al. 2003; Bukovsky et al. 2006) Boundary layer, surface and convective schemes “Achilles’ heels” of regional-scale models Improved convective parameterizations help simulating accurate propagation (Anderson et al. 2007; Bukovsky et al. 2006) Supercells often produce intense but not heavy rainfall Form in highly sheared environments Tend to move quickly, not stay in one place

U.S. flash flood seasonality Contribution of warm season MCSs clearly seen Number of events Maddox et al. (1979)

Linear MCS archetypes (e.g., squall-lines) 58% 19% Note in passing Parker and Johnson (2000) 5

Storm motion matters Doswell et al. (1996)

Forecasting MCS motion (or lack of motion…)

19980714 - North Plains

Some common “rules of thumb” ingredients CAPE (Convective Available Potential Energy) CIN (Convective Inhibition) Precipitable water Vertical shear - magnitude and direction Low-level jet Midlevel cyclonic circulations

Some common “rules of thumb” MCSs tend to propagate towards the most unstable air 1000-500 mb layer mean RH ≥ 70% MCSs tend to propagate parallel to 1000-500 mb thickness contours MCSs favored where thickness contours diverge MCSs “back-build” towards higher CIN Development favored downshear of midlevel cyclonic circulations “nothing succeeds like success”

70% RH rule of thumb Implication: Relative humidity more skillful than 70% layer RH 70% RH rule of thumb Implication: Relative humidity more skillful than absolute humidity RH > 70% # = precip. category Junker et al. (1999)

MCSs tend to follow thickness contours Implication: vertical shear determines MCS orientation and motion. Thickness divergence likely implies rising motion

Back-building towards higher CIN Lifting takes longer where there is more resistance

Corfidi vector method Propagation is vector difference P = S - C Therefore, S = C + P to propagate = to cause to continue, to pass through (space)

Schematic example System motion as shown

Schematic example We wish to forecast system motion So we need to understand what controls cell motion and propagation

Individual cell motion “Go with the flow” Agrees with previous observations (e.g, Fankhauser 1964) and theory (classic studies of Kuo and Asai) Cells tend to move at 850-300 mb layer wind speed* *Layer wind weighted towards lower troposphere, using winds determined around MCS genesis. Later some slight deviation to the right often appears Corfidi et al. (1996)

Individual cell motion Cells tend to move at 850-300 mb layer wind speed Cell direction comparable To 850-300 mb layer wind direction Corfidi et al. (1996)

Composite severe MCS hodograph Low-level jets (LLJs) are common Note P ~ -LLJ Bluestein and Jain (1985)

Propagation vector and LLJ • Many storm environments have a low-level jet (LLJ) or wind maximum • Propagation vector often anti-parallel to LLJ Propagation vector direction P ~ -LLJ Corfidi et al. (1996)

Forecasting system motion using antecedent information Cell motion ~ 850-300 mb wind Propagation ~ equal/opposite to LLJ S = C - LLJ

Evaluation of Corfidi method Method skillful in predicting system speed and direction Corfidi et al. (1996)

Limitations to Corfidi method Wind estimates need frequent updating Influence of topography on storm initiation, motion ignored Some storms deviate significantly from predicted direction (e.g., bow echoes) P ~ -LLJ does not directly capture reason systems organize (shear) or move (cold pools) Beware of boundaries! Corfidi (2003) modified vector method

Composite severe MCS hodograph Low-level shear influences storm organization & motion Angle between lower & upper shear also important (Robe and Emanuel 2001) 1000-500 mb shear of geostrophic wind is close to parallel to system motion These are severe squall lines, so weak lines already excluded. Lines stronger when shear above 500 mb does not interfere Bluestein and Jain (1985)

Low-level shear http://locust.mmm.ucar.edu/episodes

Potential vorticity Simplest form (see Holton. Ch. 4): absolute vorticity/depth is conserved for dry adiabatic processes. Equivalent to angular momentum conservation; stretching increases vorticity. This is a special case of Rossby-Ertel PV

Rossby-Ertel potential vorticity q incorporating: 3D vorticity vector, potential temperature gradient and Coriolis expressed as a vector (function of z only) In this formulation, mass x q is conserved between two isentropes even (especially!) if diabatic processes are changing the potential temperature Haynes and McIntyre (1987)

Rossby-Ertel potential vorticity q Here, we simplify a little bit and focus only on the vertical direction. The conserved quantity is mq. Holton’s version is derivable from Rossby-Ertel’s equation, where A is horizontal area. (Keep in mind ∆ is fixed between two isentropes.)

Rossby-Ertel PV For a dry adiabatic process, the mass between two isentropes cannot change. Thus, the only way to increase the cyclonic vorticity  is to move the object equatorward (decreasing f) OR decrease its horizontal area A. Now, consider a more relevant example…

Start with a stably stratified environment, with no initial horizontal variation. Define two layers, bounded by these three isentropes. We are dealing with horizontal layers. Horizontal area A is not relevant.

m1 and m2 are the initial masses residing in these two layers. q1 and q2 are the initial PVs. mq can be transported horizontally but not vertically. So m1q1 and m2q2 will not change.

Introduce a diabatic heat source, representing convection. The potential temperature in the heated region increases. This effectively moves the isentrope 2 downward.

Now there is less mass in the lower isentropic layer, and more mass in the upper layer. Because mq is conserved between any two isentropes, q has increased in the lower layer because m has decreased there. q has NOT been advected vertically.

The increased q in the lower layer represents a positive PV anomaly (+PV). Because q has increased,  is enhanced and a cyclonic circulation is induced. In the upper layer, decreased q means -PV and an induced anticyclonic circulation.

MCVs as PV anomalies Combination: uplift & destabilization on Here they work together Combination: uplift & destabilization on windward side AND downshear side Raymond and Jiang (1990)

Composite analysis of MCV heavy rain events • Based on 6 cases poorly forecasted by models • Composite at time of heaviest rain (t = 0h) • Heaviest rain in early morning • Heaviest rain south of MCV in 600 mb trough 600 mb vorticity (color), heights and winds. Map for scale only Schumacher and Johnson (2008)

Schumacher’s situation Tends to result in very slow-moving, back-building convection south of MCV

Back-building Ground-relative system speed ~ 0 Schumacher and Johnson (2005) Doswell et al. (1996)

Evolution of the heavy rain event At t + 6h (morning): rain decreases as LLJ weakens 600 mb vorticity, 900 mb winds & isotachs Schumacher and Johnson (2008)

South Plains LLJ Enhanced southerly flow over South Plains Most pronounced at night Responsible for moisture advection from Gulf & likely a major player in nocturnal thunderstorms and severe weather

Bonner (1968) - LLJ occurences meeting certain criteria most frequent in Oklahoma - most frequent at night

Explanations for LLJ Oscillation of boundary layer friction (mixing) responding to diurnal heating variation Vertical shear responding to diurnally varying west-east temperature gradients owing to sloped topography Cold air drainage down the Rockies at night Topographic blocking of some form

Bonner (1968) observations of wind speed vs Bonner (1968) observations of wind speed vs. height for days in which nocturnal LLJ appeared at Ft. Worth, TX wind speed max just below 1 km MSL (about 800 m AGL) at midnight and 6AM local time note increased low-level shear

Bonner (1968) observations of Ft. Worth wind at height of wind max. • wind weaker, more southerly during afternoon • nighttime wind stronger, more from southwest, elevation lower

Episodes of MCSs & predictability Hovmoller diagrams reveal westward- propagating MCSs Note “envelope” of several systems with “connections” Carbone et al. (2002)

MCV role in predictability Carbone et al. (2002)

“Training lines” of cells • In Asia, stationary front could be the Mei-Yu (China), Baiu (Japan) or Changma (Korea) front • Motion along the front and/or continuous back- building Schumacher and Johnson (2005)

Record 619 mm in 15 h at Ganghwa, Korea X shear Lee et al. (2008) Sun and Lee (2002)

2-3 April 2006

New cell initiation ahead of squall-lines One possible trapping mechanism: the storm anvil Fovell et al. (2006)

Trapping mechanism Trapping can occur when a layer of lower l2 resides over a layer with higher values More general Scorer parameter (c = wave speed) Lowered l2 can result from decreased stability or creation of a jet-like wind profile Storm anvil does both

New cell initiation ahead of squall-lines …and can create clouds Fovell et al. (2006)

New cell initiation ahead of squall-lines …some of which can develop into precipitating, even deep, convection Fovell et al. (2006)

New cell initiation ahead of squall-lines 14 km 150 km Fovell et al. (2006)

Tropical Storm Erin (2007) http://en.wikipedia.org/wiki/Image:Erin_2007_track.png

Erin’s redevelopment over Oklahoma Emanuel (2008) http://www.meteo.mcgill.ca/cyclone/lib/exe/fetch.php?id=start&cache=cache&media=wed2030.ppt

Erin inland reintensification Hot and wet loamy soil can rapidly transfer energy to atmosphere Previous rainfall events left Oklahoma’s soil very wet Need to consider antecedent soil moisture and soil type Emanuel (2008) see also Emanuel et al. (2008)

Soil T as Erin passed Emanuel (2008)

Summary A critical view of some ideas, tools relevant to heavy precipitation forecasting Emphasis on factors operational models do not handle particularly well CAPE & CIN, MCS development and motion, surface and boundary layer conditions Philosophical rather than detailed summary