Stephen Ogden November 6, 2013

Finding Energy Pathways from a Tropical Energy Bubble to a Mid-Latitude Jet Using Wave Activity

Flux Vectors

Stephen OgdenNovember 6, 2013

Motivation Finding a way to quantify and track energy from

an energy bubble in the tropics to the mid-latitude Rossby wave train and the jets associated with it

Finding a better way to describe downstream development in the mid-latitude wave train

Explaining the connection between seemingly unconnected events in the tropical upper levels and mid-latitude low levels

Quantifying the energy provided by the bubble

What's The Energy Bubble? Convection in the tropics lifts high theta air to the

tropopause This inflates the space between isentropes, creating

an area of low static stability This is also a density anomaly compared to areas in

the mid-latitudes, creating a potential energy difference (measured as Jet Available Potential Energy, JAPE)

On maps, it is an anomalously high tropopause height and ridging in the tropics

Energy is accumulated above the equilibrium level, the straight isentrope above the polar jet and below the subtropical jet

Physical Reasoning Pieces of the tropical energy bubble can break

off and move towards the mid-latitudes, creating a potential energy gradient above the equilibrium level

When this gradient is tapped, energy is provided for the mid-latitude wave train

The amplified upper-level wave pattern that results is associated with stronger jet streaks

Stronger or new jet streaks are tied to enhanced kinetic energy conversion and an enhanced Sawyer-Eliassen circulation

More on Jet Streaks The Sawyer-Eliassen circulations can be enhanced by

providing low static stability air to the right entrance region of the jet (Lang, 2011)

This enhances the ability to have vertical motion in the circulations, allowing for an increase in the wind speed and extraction of energy from the bubble due to enhanced geopotential height gradients

From Tripoli (2013)

More on Jet Streaks II In addition, the vertical motion caused by non-

zonal jets serves to push the bubble along into the mid-latitude wave train

Vertical motions in the jet core squeeze the bubble (and energy) into the jet in SW flow and pull it out (and across the jet) in NW flow

Height patterns and anomalies. SW (NW) flow represented by arrows is geostrophic warm (cold) advection.

Downstream Energy Propagation in the Mid-Latitudes

After the bubble potential energy is converted to kinetic energy entering the mid-latitude jet, it must be converted back to potential energy to terminate the jet

That potential energy will develop a new trough below the equilibrium level in the wave pattern

The energy in the trough then creates a new jet streak afterwards, continuing the cycle

Not Always Directly Downstream Geostrophic wind rules seem

to partially contradict previous downstream work (Orlanski and Sheldon, 1995)

Why wouldn't a supergeostrophic area produce an enhanced jet over the top of a ridge?

And how would you shove energy into a jet exit region downstream of a ridge?

Does this also lead to recycling of bubble/ridge energy?

Modified from Orlanski and Sheldon (1995)

The Equations A set of equations describing vectors will show where the energy

is going Kinoshita and Sato (2013): A Formulation of Three-Dimensional

Residual Mean Flow Applicable Both to Inertia–Gravity Waves and to Rossby Waves

Describes wave activity flux vector components (equations 2.21a-f) in 3D compared to a time-mean flow

Does not use a specific dispersion relation to derive the flux, making it equally applicable to inertia–gravity and Rossby waves

The equations assume the following: Wave amplitudes are small and consistent There is no time mean derivative of any value Time mean vertical velocity is neglected

Wave Activity Flux Does not account for energy movement from

simple undisturbed wave propagation Wave activity flux is a measure of wave forcing Wave activity flux vector convergence implies

wave development/amplification and accumulation of energy

Vector divergence implies wave decay and loss of energy

Modifications/Adaptations Vertical (x3) components are ignored here, due

to their small magnitude The analysis is done on one level between the

tropical tropopause/subtropical jet and the polar tropopause/jet (250mb)

The assumption of small wave amplitudes is stretched, if not broken due to the depth of the waves depicted

Partitioning the Energy Transfer The bubble provides some fraction of the mid-

latitude Rossby wave train energy That potential energy is converted to kinetic and

then potential energies present in the wave train The bubble can be quantified as JAPE, a density

anomaly at a level in the tropics as compared to the mid-latitudes

Conversion can be isolated by defining a box and subtracting out KE fluxes in/out, leaving the KE change due to energy conversion

The Case Cause: Hurricane Michelle (min. 934mb, late

Oct-early Nov 2001) Effect: An intense cyclone over Algeria and the

Mediterranean Sea (min. 989mb, early to mid-Nov 2001)

Connection: Tracers released in the eyewall of Hurricane Michelle end up in a jet associated with the cyclone

The Tropopause Level View (0Z 5 Nov)

A weak jet has formed on the north side of the bubble

B

Putting the Vectors To Use (0Z 5 Nov)

The Atlantic is mostly quiet as the bubble moves through the tropics

B

The Tropopause Level View (12Z 5 Nov)

B

T1D C

B

T1

As energy moves through the jet, some of it develops a trough to the north

Putting the Vectors To Use (12Z 5 Nov)

D CB

T1

Energy moves from a bubble associated with Michelle into the entrance region of a jet on its northern side, moving toward the exit region

The Tropopause Level View (0Z 7 Nov)

BT1

DCC

The bubble pushes northeast as its energy moves through the jet

Putting the Vectors To Use (0Z 7 Nov)

BT1

DCC

More energy exits the bubble into the entrance region

The Tropopause Level View (0Z 8 Nov)

DC

CDC

T1 B

An intense jet has wrapped around the north side of the bubble

Putting the Vectors To Use (0Z 8 Nov)

DC

CDC

T1 B

Energy is now moving en masse from the bubble through multiple jets

The Tropopause Level View (0Z 9 Nov)

DCD

CC

C

T2B

The jet is now 160kts, with the trough growing as well

Putting the Vectors To Use (0Z 9 Nov)

DCD

CC

C

T2B

Massive amounts of energy are pouring out of the bubble toward the west

Energy is also pouring into the trough from the jet

The Tropopause Level View (0Z 10 Nov)

DC D

C C

CD

CT2

B

The bubble is now rapidly deflating, seen in its lower tropopause

The trough and jet are fully developed

Putting the Vectors To Use (0Z 10 Nov)

DC D

C C

CD

CT2

B

Energy begins leaving the trough toward the south

The Tropopause Level View (0Z 11 Nov)

DC

DCC

T2BC

The bubble is almost gone

Downstream development has extended into northern Africa

Putting the Vectors To Use (0Z 11 Nov)

DC

DCC

T2BC

The bubble has lost almost all of its energy

Statistics of the Energy Transfer The amount of potential energy (as JAPE) in

the bubble before interaction (calculated at 12Z 2 Nov) is 1.97x10^10J

Total energy converted from potential to kinetic in the mid-latitude wave train throughout the bubble interaction (12Z 2 Nov-18Z 8 Nov) is 2.11x10^10J

Based on this calculation, the bubble contributes a large fraction of the mid-latitude wave train energy!

Summary The wave activity flux vectors show energy moving through a

jet on the north side of the bubble, pulling the bubble into the mid-latitudes

The vectors show energy converging into jet entrance regions and diverging out of jet exit regions in the mid-latitudes, deflating the bubble and inflating troughs

The net effect is that energy moves into a trough and jet that lead to the surface cyclone, fueled by energy from a bubble associated with Hurricane Michelle as expected

But the energy must go through multiple other jets and build troughs before it can end up in the final trough and jet

Kinoshita and Sato's wave activity flux equations work well despite the stretching of the “small perturbation amplitude” assumption

The bubble provides much of the energy to the amplified mid-latitude wave train and associated jets

Potential Long-Term Future Work See if the behavior/location of these bubbles

can be related to things like the major oscillations, ENSO, etc.

Investigate how the global energy bubble would change in a changing climate

Quantify such changes as compared to energy extracted from baroclinicity

Model the effects of modifying the bubble (adding/subtracting energy, moving location, etc.)