Boundary layer mechanisms in extra-tropical cyclones

© Crown copyright 2006

Boundary layer mechanisms in

extra-tropical cyclones

Bob Beare


Motivation

Boundary layer significantly reduces the depth of a cyclone (~50% reduction in growth rates, Valdes and Hoskins 1988).

Mechanism provides framework for understanding model changes. Drag Ekman pumping typically used at Met Office.

Conceptual models.

Recent research (Stephen Belcher, NWP seminar July 2005) indicates that potential vorticity (PV) should be considered also. Highlights warm sector and warm conveyor belt.

Aim: compare Ekman and PV approaches.


Boundary layer structure in extra-tropical cyclone

L

Potential temperature

Potential temperature

Height

Height

Warm sector

(stable)

Cold sector (unstable)


Ekman pumping

2*u

hBoundary layer stress

h

u*2

Geostrophic

wind

CoriolisPressuregradient

drag

2*

0 0

. ~e s

ukw

f f L Momentum balance &

continuity

2*| |s u L = horizontal scale

f0=Coriolis parameter

Convergent wind

L

u*=friction velocity


Ekman pumping

Convergence from boundary layer drag ascent (Ekman pumping) spin down by vortex squashing

Distribution of friction velocity Ekman pumping

Weakness: momentum budget only, what about thermodynamics?

2*

0

~eu

wf L


Potential vorticity

.PV

Potential temperature black, PV anomaly red, winds orange

Conservation when no heating or friction

Inversion (balance condition and boundary conditions)

.PV

Potential temperaturegradientAbsolute vorticity

Increasing


Potential vorticity in boundary layer

( ). .

D PV DF

Dt Dt

Heating from boundary layer:

Surface heat fluxes

Boundary layer stress: Ekman pumping contribution Horizontal potential

temperature gradients

All terms dependent on gradients in potential temperature.

Weakness: what about regions with zero gradient of potential

temperature (unstable layers)?


Summary

2*

0

~eu

wf L

.PV

Ekman pumping

Potential vorticity

Friction velocity

Horizontal scale

Coriolis paramter

Potential temperaturegradient

Absolute vorticity


Model set up

Met Office Unified model

Idealised: dry, only boundary layer scheme and dynamics operating.

Why idealised? Isolate boundary layer-dynamics interaction, control over jets and sea surface

temperature, framework for interpreting global model or NAE.

Met Office boundary layer scheme: separate treatment of stable and unstable boundary layers.

Limited area 18000 km x 9000 km, 45 km horizontal resolution, 10 minute time step.


Basic state


Triggering cyclogensis

Near surfacePotential

temperature

Upper level trough

Tropopause PV


Idealised UM cyclone lifecycle

Cold conveyor belt jet(height 1 km)

Warm seclusionShading friction velocity

> 0.5 m/s


Ekman pumping vs potential vorticity

Ekman pumpingmax 9 cm/s

Boundary layer averagedPV in warm sector


Distribution with stability

Unstable (cold sector) Stable (warm sector)

Peak friction velocity in neutral/ unstable boundary layer

h = boundary layer depth

L= Obukhov length

PV confined to stable boundary layers


Summary

Ekman pumping and boundary layer averaged PV in distinct locations: the cold sector/ seclusion region (unstable) and warm sector (stable) respectively.

Which sector of the cyclone contributes the most to the cyclone depth? Next switch off boundary layer mixing in each region.


Switching off boundary layer mixing

u*2 averaged over area of cyclone


PV inversion

Horizontal section

through domain

PV anomaly


Comparison with global model

Idealised UM Global N216

Friction velocity >0.5 m/s shaded, solid 20 m theta, dashed divides between stable and unstable BLs

Stable warm sector


Sensitivity to “operational” boundary layer and dynamics changes

PS 10 changes(stability

dependence)

Interpolation inSemi-lagrangian

scheme

Changes whichaffect the

neutral boundary layer


Conclusions

Unified model has been set up with an idealised jet, forming a realistic cyclone lifecycle.

Ekman pumping and potential vorticity in differentlocations at occlusion: Ekman in cold sector/occlusionand PV in warm sector.

Switching off mixing in unstable boundary layer(cold sector/ occlusion) has more impact than for stable

boundary layer (warm sector).

Operational type boundary layer mixing changes produce ~+/-2hPa change over 72 hours.


Future work

Invert warm sector PV to determine its impact on flow.

Harmonise PV and Ekman views via bottom boundary temperatures.

Revisit the role of the neutral boundary layermixing on cyclones.

CASE studentship with Reading University:Ian Boutle.

Boundary layer mechanisms in extra-tropical cyclones

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