Section 6.7 Hot Issues

A: Genesis: review of the “marsupial paradigm”

Dunkerton et al 2009 : Today, available on the class website

Montgomery et al 2009: Friday

See: http://www.atmos-chem-phys-dicuss.net/9/19159/2009/acpd-9-19159-2009.html

The following slides were made available by Tim Dunkerton

B: Do tropical cyclones intensify by WISHE?

Montgomery et al, 2009: (Friday/Monday)

See: http://met.nps.edu/~mtmontgo/papers/M2.pdf

“Although some aspects of the transformation of atmospheric disturbances into tropical cyclones are relatively well understood, the general problem of tropical cyclogenesis remains, in large measure, one of the great mysteries of the tropical atmosphere.”

Kerry Emanuel, Divine Wind

Section 6.7 The “Marsupial Paradigm”, Dunkerton et al 2009

max at Z ~ 3-4 km

W.M. Gray, The formation of Tropical Cyclones, Meteorol. Atmos. Phys. 67, 1998.

Consideration of horizontal scales exposes thechallenging nature of the problem

• Planetary scale: 10000-40000 km– Madden-Julian Oscillation– Kelvin waves– Rossby & Rossby-gravity waves

• Synoptic scale: 2000-8000 km– Easterly waves– Hydrodynamic instability of the

ITCZ– Extratropical intrusions

• Meso-α: 200-2000 km– Inertia-gravity waves– Tropical wave critical layer– Isolated regions of recirculation

• Meso-β : 20-200 km– Tropical cyclones, hurricanes &

typhoons– Gravity waves– Mesoscale convective systems

• Meso-γ : 2-20 km– Vortical hot towers– Deep convective clouds– Squall lines

1

2

1: Forward enstrophy cascade

2: Inverse energy cascade

Tropical cyclogenesis in tropical waves:the marsupial paradigm

• Forecaster’s parlance: “surface low along the wave”• Theoretical interpretation: a critical layer exists in the lower

troposphere owing to the interaction of a tropical wave and the mean flow on which it propagates.

• Formation of a quasi-closed region of horizontal recirculation is a key piece of evidence, in addition to reversible undulations caused by passage of the wave.

• This region more often than not is invisible or incorrectly diagnosed in an Eulerian (Earth-relative) frame; a Lagrangian viewpoint is necessary.

• A generalized “Lagrangian boundary” around the quasi-closed gyre demarcates a protected region of the flow that is favorable to tropical cyclogenesis within a tropical wave.

Stable configuration:Darker shading = higher PV

Unstable configuration:Lighter shading = higher PV

Critical layer on the cover of a well-known textbook*

Adapted from Andrews et al., 1987

“Spaghetti on a fork”does not produce hurricanes

acting alone.

*held to the mirror; embellishments ours

• Marsupials are mammals in which the female typically has a pouch (called the marsupium, from which the name 'Marsupial' derives) in which it rears its young through early infancy.

• Our hypothetical pathway for genesis via tropical waves may be regarded as a marsupial theory of tropical cyclogenesis in which the “juvenile” proto-vortex is carried along by the “mother” wave until it is ready to be “let go” as an independent tropical disturbance.

Marsupial slogans

• “Ride the wave”– A wave-centric point of view is preferred over the Earth frame for

identification of Lagrangian boundaries.

• “Go with the flow”– Focus on critical surface / critical layer as locus of wave-mean flow

interaction & TC genesis.

• “Divide and conquer”– Identify manifolds of 2D horizontal flow on stratification isosurfaces,

critical points = separatrix, attracting & repelling node, center, etc.

• “Roadkill on the Rossby wave highway”– Vorticity debris is everywhere, but mostly irrelevant; focus instead on

gyre-pouch recirculation that is deep, local, rapid & persistent.

• “It’s a nasty world out there”– Tropical atmosphere is generally hostile to tropical cyclogenesis.

– Jule Charney / Jim Holton tropical “barotropic” scaling, independence of adjacent levels, Jim McWilliams “stratified turbulence”

Why a hostile world?

• Rotation must dominate deformation for shape-preservation. The Kelvin cat’s eye provides a sweet spot for development at its center, surrounded by deformational flow within & without.

• Vertical alignment requires LT pouch & favorable UT flow (a stochastic ingredient).

• Vertical shear is not necessarily detrimental to genesis (strong, yes; weak, perhaps)

• Saturation of the column may be disrupted by dry-air intrusion.• Owing to stratiform cloud processes it’s generally difficult to “turn the

tropical atmosphere upside down” and thereby drive a rotational system from below (due to convective heating).

• Another mature hurricane may be nearby.

The pouch protects and encourages development

• Dry & dusty air (e.g., Saharan Air Layer) stifles development.• Large vertical shear is generally inimical to genesis (e.g., El Niño).• Cyclonic vorticity resides in the wave critical layer equatorward of

the easterly jet axis.• This region is characterized by strong rotation and weak straining

deformation.• Vorticity and (if available) ambient moisture are entrained into the

gyre and additional moistening by deep convection within the gyre will tend to remain in the gyre.

• In addition to its cyclonic vorticity the gyre provides a strong focus for spontaneous aggregation of vortical building-blocks on the mesoscale, and segregation of cyclonic & anticyclonic anomalies.

• Preliminary evidence suggests a predominantly convective, as opposed to stratiform, vertical profile of heating in the gyre.

• Wave / vortex interaction within the CL is favorable to both.

Band-passfilter for anomalypropagation

Low-pass filter for kinematic & dynamical fields

Low-frequency filter for wave critical latitude

Dunkerton et al., 2008 ACP

Trough axis

Best-trackgenesis

ERA-40TRMM 3B42NHC best-trackAug-Sep 1998-2001

Debby 2000: 850 hPa vorticity

Dunkerton et al., 2008 ACP

Debby 2000: 600 hPa vorticity

Dunkerton et al., 2008 ACP

Debby 2000: 850 & 600 hPa vorticity

The resting (Earth-relative) frame gives a misleadingpicture of the flow kinematics (not centered, or open).

Dunkerton et al., 2008 ACP

Dunkerton et al., 2008 ACP

Debby 2000: stream function, streamlines & trajectories

Hypothesis 1

• H1. Proto-vortex cyclonic eddies instrumental in TC formation are intimately associated with the parent wave’s critical latitude in the lower troposphere. The critical layer, formed as a result of the wave’s finite-amplitude interaction with its own critical latitude, is a region of cyclonic rotation and weak straining / shearing deformation in which synoptic and mesoscale anomalies move together and amplify on a nearly zero relative mean flow. This multi-scale interaction provides a dynamical pathway to “bottom-up” development of the proto-vortex from below.

• Counterpoint: in recent years tropical cyclogenesis has been visualized as a top-down process that begins with mid-level vortices spawned by mesoscale convective systems.

• Our new hypothesis (i) identifies the lower, not middle, troposphere as the locus of critical layer interaction and (ii) observes that mid-level vortices seldom exist without a surface signature in systems that are to undergo subsequent development.

Debby 2000: sfc-500 hPa saturation fraction

Dunkerton et al., 2008 ACP

Debby 2000: TRMM precipitation

Dunkerton et al., 2008 ACP

Hypothesis 2

• H2. The critical layer of the parent wave provides a set of quasi-closed material contours inside of which air is repeatedly moistened by convection, protected to some degree from lateral intrusion of dry air and impinging vertical shear, and (thanks to its location near the critical latitude) able to keep pace with the parent wave until the proto-vortex has strengthened into a self-maintaining entity.

• Counterpoint: mesoscale convective systems are typically characterized by a “top-heavy” heating profile, due to mixture of convective and stratiform cloud in the MCS lifecycle. This type of heating profile is important to the tropical general circulation, Madden-Julian Oscillation, and excitation of stratospheric gravity waves.

• Our new hypothesis regards the entrainment and containment of moisture by a closed recirculation region (CL pouch) as helping to saturate the column locally and thereby to develop within the gyre a preference for the convective type of heating profile that is able to drive low-level convergence & spin-up.

Fabio 2000: 850 hPa vorticity

Dunkerton et al., 2008 ACP

Fabio 2000: 600 hPa Okubo-Weiss parameter

Dunkerton et al., 2008 ACP

Vorticity squared minus squares of straining deformations

Fabio 2000: sfc-500 hPa saturation fraction

Dunkerton et al., 2008 ACP

Fabio 2000: TRMM precipitation

Dunkerton et al., 2008 ACP

Hypothesis 3

• H3. The parent wave is maintained and possibly enhanced by diabatically amplified eddies within the wave (proto-vortices on the mesoscale), a process favored in regions of small intrinsic phase speed.

• Counterpoint: diabatic Rossby waves are merely an illusion; we are instead seeing a flow induced by diabatic Rossby vortices in shear; the genesis sequence is mainly, if not entirely, a result of spontaneous vorticity aggregation and upscale (inverse) energy cascade.

• Our new hypothesis recognizes the essential “guiding hand” of large-scale dynamics (synoptic & meso-α) together with the kinematic and dynamical cooperation between what are essentially diabatic Rossby waves and diabatic Rossby vortices within the critical layer of the parent wave.

– Kinematic benefit: The induced flow by a point vortex “fits like a glove” within the cat’s eye of the parent wave (Andrews et al., 1987; Pozrikidis, 1997)

– Dynamical benefit: The effects of vorticity and heat sources on the parent wave are magnified in the recirculating region because parcels are trapped there (Held & Ting, 1990; Krishnamurti et al., 1994).

Waves precede (i) turbulence, (ii) vortices

• Every eddy is born of a (stable or unstable) wave.• Long-lived and / or unusually intense eddies / vortices represent

coherent structures that control and distort their surroundings while protecting themselves.

• Passive advection of vorticity that conserves extremum values cannot account for hurricane formation.

• Hurricane formation cannot account for the prior existence of a wave critical layer.

• It is unlikely that mesoscale processes responsible for hurricane formation could – if acting independently without any governance by the synoptic-scale flow – form an east-west array of hurricanes.

• Yet to be determined is whether the waves would exist, in any significant sense, without the help of mesoscale processes acting within.

Essence & spice

• Kelvin cat’s eye is the essential kinematic structure which is known given (i) wave phase speed, (ii) wave amplitude, (iii) meridional shear flow, and (iv) horizontal divergence vis-à-vis rotation.

• Wave refraction is an optional ingredient that imparts flavor to individual cases.– Wave compression or capture may cause concentration of wave action

in the direction of the wave vector.

– Wave tilting in the horizontal direction orthogonal to the wave vector represents a possible source of transient barotropic growth.

– Wave tilting in the vertical direction represents not only a possible source of baroclinic growth but (more importantly) a mechanism for favorable vertical alignment of the proto-vortex inside the pouch.

• Vertical shear therefore affects TC genesis in two fundamentally distinct ways: (i) convective organization & (ii) wave refraction.

Discussion