an introduction to coupled models of the …an introduction to coupled models of the...

An Introduction to Coupled Models of the

Atmosphere–Ocean System

Jonathon S. [email protected]

Saturday, September 28, 13

mailto:[email protected]

mailto:[email protected]

Atmosphere–Ocean Coupling1. Important to climate on a wide range of time scales

• Diurnal to seasonal: coastal climates

• Interannual to decadal: El Niño and other oscillations

• Long time scales: deep ocean uptake of heat and carbon dioxide

2. Strongest in the tropics, where the circulation is thermally direct

• Tropical wind stress is controlled by SST, leading to a strong positive wind–thermocline–SST feedback

• In mid-latitudes, much weaker relationship between SST and surface wind stress

3. Many key uncertainties and challenges remain


Outline

1. A hierarchy of coupled atmosphere–ocean models

2. Constructing coupled energy balance models

3. Constructing coupled general circulation models

4. Simple models of coupled atmosphere–ocean variability

5. Can general circulation models simulate this variability?

Part 2

Part 1


Part 1:Coupled Atmosphere–Ocean Models


3-dimensional 2-dimensional

0-dimensional1-dimensional

A Hierarchy of Models

global mean

(�,', z) (�,'); (', z); (�, z)

(�); ('); (z)Saturday, September 28, 13



more complex

less complex


global mean

(�,', z) (�,'); (', z); (�, z)




less parameterization

more parameterization


global mean

(�,', z) (�,'); (', z); (�, z)


The Simplest Climate Model

surface

0-dimensional

Ts =4

rQ(1� ↵)

4

�T 4s

Q

4(1� ↵)

energy balance modelSaturday, September 28, 13

Adding an ‘Atmosphere’

surface

atmosphere�T 4

e

�T 4e

1-dimensional

�T 4s

Q

4(1� ↵)

Ts =4

rQ(1� ↵)

4+ �T 4

e



surface

atmosphere�T 4

e

�T 4e

1-dimensional

�T 4s

Q

4(1� ↵)

Ts =4

r2Q(1� ↵)

4

=Q

4(1� ↵)


surface

lower atmosphere

�T 4e

�T 4e

1-dimensional

upper atmosphere�T 4

e


Q

4(1� ↵) �T 4

s

Ts =4

r3Q(1� ↵)

4

2�T 4e

2�T 4e


surface

�T 4e

1-dimensional

1

2

3

4

n-1

n


Q

4(1� ↵)

Ts =4

r(n+ 1)Q(1� ↵)

4

�T 4s n�T 4

e


Adding an ‘Ocean’

µdT

dt= S �OLR(T, c)

thermal capacityof the ocean

absorption bythe atmosphere

absorbed solarradiation

Dµ = cp⇢D

= (1� c)�T 4

1-dimensional



µdT

dt= S �OLR(T, c)

Dµ = cp⇢D

radiative forcing

equilibrium still balances and T S OLR

= (1� c)�T 4

1-dimensional



µdT 0

1

dt= ��T 0 +�F

radiative forcing

D

�F = S �OLR

1-dimensional

� =@OLR

@T= 4(1� c)�T 3

deviation from equilibrium:T 0 = T � Teq


Response to Climate Forcing


T 0(t) = T 0(0)e(�t/⌧)

⌧ =µ

�



Simulating Climate Variability

Held et al., J. Climate 2010

full climate model

one-box ocean model


A Layered Ocean

µ1dT 0

1

dt= ��T 0

1 � (T 01 � T 0

2) +�F

µ2dT 0

2

dt= (T 0

1 � T 02)

diffusion to / from the deep ocean

1-dimensional



fast response



fast response

slow response



Held et al., J. Climate 2010

global warming climate projection

abrupt return to pre-industrial


A Layered Ocean1-dimensional

can be modified to study CO2 uptake by the ocean


From Global to Zonal Mean


1-dimensional

ocean

⇢cp@T (')

@t= S(')�OLR(') + F(')

' north polesouth pole

S OLR

F

Meridional Energy Transport


2-dimensional

atmosphere

ocean

⇢cp@T (')

@t= S(')�OLR(') + F(')

' north polesouth pole

Meridional Energy Transport


Coupled Energy Balance Models1. 0- to 2-dimensional (global mean to latitude–height)

2. The atmosphere...

• Determines the radiation balance

• Contributes to horizontal energy transport

3. The ocean...

• Provides thermal inertia and/or CO2 storage, stabilizing the climate

• Contributes to horizontal energy transport

4. Models are suitable for studying climate sensitivity over a wide range of parameters and over long time scales.

5. Can supplement fully coupled model simulations


water conservation equation

equations of motion

thermodynamic equation

ATMOSPHERE

radiation turbulence clouds

conservation of water & salt

conservation of momentum

conservation of energy



equations of motion


ATMOSPHERE


salt conservation equation

equations of motion


turbulence sea ice

OCEAN






equations of motion


ATMOSPHERE


radiation

sensible heat

wind stress

friction evaporation

precipitation


equations of motion


turbulence sea ice

OCEAN





ATMOSPHERE

OCEAN

requires high temporal resolution

Different Requirements

requires high spatial resolution


OCEAN

Simplify One, Simulate the Other


equations of motion


ATMOSPHERE


swamp ocean: infinite source of water vapor


OCEAN



equations of motion


ATMOSPHERE


slab ocean: horizontally diffusive mixed layer stores heat and supplies water vapor


OCEAN



equations of motion


ATMOSPHERE


dynamical model of the surface layer


Surface Layer Dynamics

EkmanCurrents

Internal WaveRadiation

Wells, 2012

Langmuir Circulation

PenetratingSolar Radiation

Evaporation

SolarRadiationPrecipitation

WindStress

Wave–CurrentInteractions

Sea Spray

Wave Breaking

MixedLayerDepth


Surface Layer Dynamics

EkmanCurrents

Internal WaveRadiation

Wells, 2012

Langmuir Circulation

PenetratingSolar Radiation

Evaporation

SolarRadiationPrecipitation

WindStress

Wave–CurrentInteractions

Sea Spray

Wave Breaking

MixedLayerDepth

HorizontalHeat Transport



stochastic atmosphere

ATMOSPHERE


equations of motion


turbulence sea ice

OCEANSaturday, September 28, 13


equations of motion


ATMOSPHERE



equations of motion


turbulence sea ice

OCEAN






equations of motion


ATMOSPHERE



equations of motion


turbulence sea ice

OCEAN




earliest fully-coupled models: alternating time steps



equations of motion


ATMOSPHERE



equations of motion


turbulence sea ice

OCEAN




aquaplanet: no lateral boundary conditions


The CouplingATMOSPHERE

OCEAN

increasingpressure

~10m

increasingdepth

~10m

∆x ~ 100–300km

∆x ~ 30–100km

sea ice

fluxes of heat, momentum,and water at the surface


radiation

sensible heat

wind stress


precipitation


equations of motion


ATMOSPHERE



equations of motion


turbulence sea ice

OCEAN





radiation

sensible heat

wind stress


precipitation


equations of motion


ATMOSPHERE



equations of motion


turbulence sea ice

OCEAN




coupling shock followed by gradual equilibration


radiation

sensible heat

wind stress


precipitation


equations of motion


ATMOSPHERE



equations of motion


turbulence sea ice

OCEAN




coupling shock followed by gradual equilibrationclimate drift


Climate Drift1. Can complicate studies of climate change signal

2. Careful initialization crucial for coupled models

• Run each component model several times

• Observationally constrain variables at the interface

3. Empirical “flux corrections”

• Calibration of coupled model with surface variables (temperature, salinity, momentum, etc.) constrained to observed climatologies

• Apply calculated ‘corrections’ as artificial fluxes during coupled simulations to prevent drift away from a realistic climate state

• Requires very long (~1000 yr) initialization runs of the ocean component

• Gradually being replaced by direct flux coupling techniques



equations of motion


ATMOSPHERE


radiation

sensible heat

wind stress


precipitation


equations of motion


turbulence sea ice

OCEAN






equations of motion


ATMOSPHERE


radiation

sensible heat

wind stress


precipitation


equations of motion


turbulence sea ice

OCEAN




can be appliedregionally as well as

globally.


Coupled Model Intercomparisons1. Study the response of coupled atmosphere–ocean

models to idealized climate forcings

2. Main sources of model spread include

• Cloud processes and interactions with radiation

• Cryospheric processes (sea and land ice)

• Deep ocean processes (i.e., the slow response)

• Atmosphere–ocean interactions

3. Often supplemented by Monte Carlo-type simulations using a single model framework


Simulation of Surface Temperature

IPCC AR4

•contours: observations•shading: error in multi-model mean

typical model error


Simulation of Precipitation

IPCC AR4

observations

multi-model mean


Simulation of Precipitation

IPCC AR4

observations

multi-model mean

double ITCZ

ITCZ + SPCZ


Simulation of Sea Ice

IPCC AR4

observed extent

number of models (out of 14) simulating at least 15% ice cover


Coupled AOGCMS1. Essential for full representation of the climate system

2. Coupling is a major technical challenge

• AGCMs have different requirements than OGCMs

• Climate drift due to the coupling can distort the magnitude of climate feedbacks and responses to climate forcings

3. Coupled models are improving rapidly

• Increasing computational power enables finer resolutions

• Improvement in parameterizations of atmosphere–ocean interactions and introduction of new coupling techniques

• Conversion of flux correction techniques to direct flux coupling

• Still substantial inter-model spread and differences relative to observations


Part 1:Modeling Coupled Atmosphere–Ocean Variability: El Niño–Southern Oscillation


What is ENSO?under normal conditions, convection is

centered in the western Pacific

noaa.govSaturday, September 28, 13



under El Niño conditions, convection shifts eastward to the central Pacific




under La Niña conditions, convection shifts even further toward the west


How SST Changes

ocean mixed layer

upwelling ofcold water

heat fromatmosphere


Why SST Controls Precipitation

ocean mixed layerwarm SST


Why SST Controls Precipitation

ocean mixed layerwarm SST

low SLP


deep ocean

Changes in the Thermocline

ocean mixed layer


deep ocean


ocean mixed layer

climatological wind direction


deep ocean


ocean mixed layer

climatological wind direction

the density of seawater in the mixed layeris less than the density in the deep ocean,so the bottom depth increases more than

the height of the sea surface.


deep ocean


ocean mixed layer

regional eastward wind anomaly


deep ocean


ocean mixed layer

regional eastward wind anomaly

Kelvin waves communicate the anomaly in the depth of the thermocline across

the entire ocean basin.


Bjerknes Feedback1. Winds flow from low SST to high SST...

2. ...leading to a shallower thermocline under low SST and a deeper thermocline under high SST...

3. ...leading to cooling in the region of low SST and warming in the region of high SST...

4. ...reinforcing and strengthening the winds...

changes in sea surface temperature

zonal wind stress in equatorial Pacific

changes in depth of thermocline

+


Describing ENSO

noaa.gov

Sea surface temperature anomalies invarious regions serve as indices


El Niño–Southern Oscillation

ENSO varies on interannual timescales,with a period of 2–7 years.


Typical Effects of El Niño on Winter Climate

Typical Effects of La Niña on Winter Climate


Seasonal Climate Forecasts


Seasonal Climate Forecasts

Even with current understanding,ENSO predictions are highly uncertain


What Is ENSO?1. An unstable nonlinear oscillator?

• Delayed oscillator: changes in thermocline are out of phase with changes in wind stress.

• Recharge oscillator: a warm event (El Niño) leaves the equatorial thermocline shallower and the sea surface colder than normal (La Niña). The reservoir of warm water is then refilled over time.

2. A stable system with non-normality?

• Small disturbances grow and then decay

3. A combination of these two?


Simple Models1. Coupled shallow-water atmosphere and ocean on an

equatorial ß-plane

• Gill-type atmospheric model (quasi-geostrophic with a simple thermal forcing)

• Ocean model assumes a well-mixed surface layer, no mean currents, and a deep ocean at rest (a ‘one and a half ’ layer model).

2. Results

• Coupling of the tropical atmosphere and ocean can produce unstable coupled modes with interannual periods (Hirst, 1986)

• Propagating signals on the equatorial thermocline are an important part of the ENSO response (Wakata and Sarachik, 1991)

• The propagating signals strongly depend on the shape of the thermocline and the distribution of the upwelling

• Can achieve unstable coupled modes under constant (annual mean) conditions


The Zebiak–Cane Model

atmosphere

upper layer

An anomaly model – the climatological annualcycle is specified for both atmosphere & ocean!

modified Gill-type shallow water model

surface winds respond to SST

surface layer

deep oceanu = v = w = 0

wind-driven convergence and divergence

thermocline depth responds to wind stress; determines temperature of entrained water

linear reduced-gravitymodel


Simulated SST Anomalies

Zebiak and Cane, Mon. Wea. Rev., 1987noaa.govSaturday, September 28, 13

Development of El Niño

Zebiak and Cane, Mon. Wea. Rev., 1987

1 2

3 4

December March

June December




Zonalwind stress

anomaly

Thermoclinedepth

anomaly




Zonalwind stress

anomaly

Thermoclinedepth

anomaly

El Niño




Zonalwind stress

anomaly

Thermoclinedepth

anomaly

El Niño

La Niña


The Zebiak–Cane Model1. ENSO is an oscillation of the coupled atmosphere–

ocean system

2. All of the necessary interactions take place in the tropical Pacific

3. The rapid response of the surface layer to the atmosphere is crucial

4. The basin-wide response down to the thermocline is the core of the interannual variability

5. ENSO is a combination of a positive (Bjerknes) feedback and the basin-scale dynamic response


Simulation of the Tropical Pacific

Sun et al., J. Climate, 2006

simulations of SST


Simulation of the Tropical Pacific

Bellenger et al., Clim. Dyn., submitted

model constrained by observations (reanalysis)

older models

newer models


Simulation of SST Variability

Guilyardi et al., BAMS, 2009

standard deviation of SST


Simulation of ENSO Amplitude

Guilyardi et al., BAMS, 2009preindustrial 2xCO2


Simulation of ENSO Seasonality

Bellenger et al., Clim. Dyn., submitted

older models

newer models

observations

month


Simulation of ENSO

Bellenger et al., Clim. Dyn., submittedSaturday, September 28, 13

Modeling ENSO1. Simple coupled models can produce unstable modes

2. Surface layer dynamics play a key-role in generating ENSO variability, which extends across the tropical Pacific to the depth of the thermocline

3. The exact ENSO mechanisms are still uncertain, and ENSO is difficult to predict at seasonal timescales

4. Coupled models still have difficulty simulating ENSO

• Problems remain not only in simulations of coupled variability, but even in simulations of the mean climate of the tropical Pacific

• The CMIP5 model ensemble offers some improvement relative to the CMIP3 model ensemble


an introduction to coupled models of the …an introduction to coupled models of the...

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