j. h. lacasce norwegian meteorological institute oslo,...

Understanding thebuoyancy-driven circulation

J. H. LaCasce

Norwegian Meteorological Institute

Oslo, Norway

Understanding the buoyancy-driven circulation – p.1/39

Modelling climate change

Use general circulation models (GCMs)

e.g., double CO � and measure temperature change

But models parameterize processes, like:

� Sub-grid scale dissipation

� Tracer mixing

� Air-sea coupling

� Boundary conditions

Which approach is right? Why do different modelsgive different results?


Idealized models

Take a simplified system, and examine itsdependencies (e.g. boundary conditions) thoroughly

� Improve the GCMs

� Write simplified climate models

� Understand the physics


Idealized models

1) Meridional overturning circulation

2) Wind-driven oceanic variability


Global heat transport

Trenberth and Caron, 2001Understanding the buoyancy-driven circulation – p.5/39

Oceanic heat transport

Trenberth and Caron, 2001Understanding the buoyancy-driven circulation – p.6/39

Mean vs. eddies

Jayne and Marotzke, 2002Understanding the buoyancy-driven circulation – p.7/39

Model example

Te Raa and Dijkstra, 2002


Understanding the models

Questions:

� What drives the overturning (MOC)?

� How does MOC depend on mixing?

� On frictional parameterizations?

� On boundary conditions?


Models II

Marotzke, 1997


GeostrophyAtmospheric and oceanic motion governed by theNavier-Stokes equations

But simplified dynamics possible at larger scales,where the Coriolis force approximately balancespressure gradients

L


Geostrophy


Scaling theorye.g. Bryan and Cox, ’67, Nilsson et al., 2003

Assume: 1) Geostrophic flow:

��

��

� � ��

��

�

2) Hydrostatic balance

��

� � � ��


Scaling theory

3) Vertical advective-diffusive balance

��

��

� �

� � �

�

Yields:

� � � � ��

� � � � � ��


Scaling theory

Park and Bryan, 2000Understanding the buoyancy-driven circulation – p.15/39

Viscosity dependence

Huck et al., 1999


Scaling

Scaling theory approximately correct when constantmixing over the whole basin

Numerical simulations suggest mixing is intensifiednear the boundaries and viscosity-dependent

Observations (Polzin, Ledwell) also suggestboundary-intensified mixing

Scaling theory probably inadequate


Abyssal circulationStommel and Arons, 1960; Kawase, 1987

x


Equations

��

��

� ��

��

� �

� � � � ��

� � � � ��

� � � � � ��

�


Abyssal flowStommel and Arons, 1960

0 0.5 1 1.50

0.5

1

1.5

Stommel and Arons flow to uniform w0

Latit

ude

LongitudeUnderstanding the buoyancy-driven circulation – p.20/39

Abyssal solutions

Good:

� Dynamically plausible

� Predicted Deep Western Boundary current

� Viscosity dependence in boundary layer

Less good:

� Must specify upwelling

� Buoyancy driving produces purely baroclinicflow


Implied flow

0 0.5 1 1.50

0.5

1

1.5

Stommel and Arons flow to uniform w0

Latit

ude

Longitude

0 0.5 1 1.50

0.5

1

1.5

Latit

ude

Longitude

Implied surface flow


Model example

Te Raa and Dijkstra, 2002


Linear modelPedlosky, 1968,1969; Salmon, 1986

10y_0

1


Planetary Geostrophy

� ��

��

��

��

� � ��

��

��

��

��

��

��

��

� ��

��

� ��


Linear PG

� � � � � � � � � � � � � � � � � � � �

� � � � � �

Temperature equation becomes:

� � � ��

� � �

�

where

� �

��


Characteristics1) Flow driven by vertical mixing

2) Flow confined to surface boundary layer

about 500 m thick

3) Baroclinic velocities

4) Viscosity, lateral diffusion important only at west,North, South walls

5) Upwelling/downwelling occurs mostly near lateralboundaries


Diffusive viscosity

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

κV=κ

H=10−4, E=10−5

−1.5

−1

−0.5

0

0.5

1

1.5x 10

−3


Rayleigh viscosity

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

κV=κ

H=10−4, ε=0.01

−1.5

−1

−0.5

0

0.5

1

1.5x 10

−3


Boundary mixing

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

κV=κ

H=10−4, ε=.01; d=0.95

−1.5

−1

−0.5

0

0.5

1

1.5x 10

−3


Comparison to models

� SimilaritiesBoundary-intensified vertical velocitiesWestern boundary current with large �

� sensitive to viscosity and BCZonal thermocline flow with BT � �

� DifferencesSense of surface flowMagnitudes of vertical velocities


Models

Huck et al., 1999


Models

Marotzke, 1997


Models


Comparison to observations

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

κV=κ

H=10−4, ε=0.01

−1.5

−1

−0.5

0

0.5

1

1.5x 10

−3



Shetland

Rockall

Tro

ugh

Greenland Sea

Mohns Ridge

Jan Mayen Lofoten

Basin

Norwegian

Sea

Vøring

Plateau

Fram Strait

Reykja

nes

Rid

ge

Icel

and

Bas

in Faroes

Denmark

Strait

North Sea

Knip

ovic

hRid

ge

Barents

Sea

Svalbard

Greenland

IrelandEngland

Scotland

Norway

Iceland

Greenland Sea

Greenland

IrelandEngland

Scotland

Norway

Svalbard

Rockall

Tro

ughReykja

nes

Rid

ge

Mohns Ridge

Knip

ovic

hRid

ge

Lofoten

Basin

Barents

Sea

Norwegian

Sea

Icel

and

Bas

in

Vøring

Plateau

Iceland

Faroes

Shetland

North Sea

Jan Mayen

Denmark

Strait

Fram Strait

Orvik and Niiler, 2002Understanding the buoyancy-driven circulation – p.37/39


Skagseth and Orvik, 2002


Summary

� Idealized thermocline models capture someelements of observed circulation (Deep WesternBoundary Current, Norwegian Atlantic Current)

� But none (so far) capture the flow exhibited bymost numerical models

� Need for an improved analytical representation


j. h. lacasce norwegian meteorological institute oslo,...

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