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Bistability of the climate around the habitable zone: a thermodynamic

investigationValerio Lucarini

Meteorological Institute, University of HamburgDept. Mathematics and Statistics, University of Reading

valerio.lucarini@uni-hamburg,de

R. Boschi, E. Kirk, N. Iro, S. Pascale, F. Ragone

Lorenz Center, 11/02/2014

Energy & Forcing – Perfect Model

NESS→Transient → NESS Applies to the whole climate and to to all climatic subdomains for atmosphere τ is small, always quasi-equilibrated

Forcing

τ

Total warming

2

Energy and GW – Actual GCMs

Not only bias: bias control ≠ bias final state

Forcing τ

3

L. and Ragone, 2011

Bias depends on climate state! Dissipation & Water

Steady State – Meridional Transports

4

TAO

20% uncertaintyamong models

L. and Ragone, 2011

5

Energies

Kinetic energy budget

Moist Static Potential Energy budget

Total Energy Budget

WDKPCdVK

),(2

WQdVP

HQ 21

HndSHdVE

ˆ

),( KPCW

WORK

DISSIPATION

FLUXES

6

Johnson’s idea (2000)

Partitioning the Domain (Eulerian approach)

Better than itseems!

QdVQdVWP

0Q 0Q

7

Long-Term averagesStationarity:

Work = Dissipation

Work = Input-Output

A different view on Lorenz Energy cycle

0 KPE

0

0

WWP

DWWK

0)( ),( )(

KDndissipatio

KACconversion

AGheatingaldifferenti

DW

W

efficiency

Results on IPCC GCMs

Hor vs Vert EP in IPCC modelsCollection of (weak. coup.) vertical columnsWarmer climate: Hor↓ Vert↑

8

vertinS

Smat dRnetsurf 1

TE

1TS

S

Smatvert

dRnet

TOA 1TES

Smat

hor

L., et al. 2011; 2014

Model Starter and

Graphic User Interface

Spectral Atmospheremoist primitive equations

on levels

Sea-Icethermodynamic

Terrestrial Surface: five layer soil

plus snow

Vegetations(Simba, V-code,

Koeppen)

Oceans:LSG, mixed layer,or climatol. SST

PlaSim: Planet Simulator

Key features• portable• fast• open source• parallel• modular• easy to use• documented• compatible

Fraedrich et al. 2005

Coupled with MITOGCMCESAM

10

Snowball HysteresisSwing of S* by ±10% starting from present climate hysteresis experiment!

Global average surface temperature TSWide (~ 10%) range of S* bistable regime -TS ~ 50 Kd TS/d S* >0 everywhere, almost linear

SB

W

L., Lunkeit, Fraedrich, 2010

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Thermodynamic Efficiencyd η/d S* >0 in SB regimeEffect of decreased static stability

d η/d S* <0 in W regimeSystem thermalized by efficient LH fluxes

η decreases at transitions System more stable

η=0.04

Δθ=10K

Let’s alter also [CO2]Parametric Analysis of Climate ChangeStructural Properties of the system (Boschi, et

al. 2013)Lower Manifold Upper Manifold

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η

CO2

S*

CO2

S*

A 3D picture - EP

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Be Smat Smin Smat W

Smat dV

H 1

T

dV 2

T

Parametrizations

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EP vs Emission Temperature

Purple Ω=ΩEBlack Ω=1/2ΩE

Parametrizations

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Efficiency vs Emission Temperature

Parametrizations

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Heat Transport vs Emission Temperature

No ice

D&B 2011

Just ice

Some ice

Change in Stratification

Polar Ampl.β

Polar Ampl. α

Shorter year - Phase Transition

17

Width bistability vs length year (L. et al. 2013)Fast orbiting planets cannot be in Snowball EarthHabitability

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Bistability, Efficiency, Etc.

19Boschi et al. 2014, unpublished

Water Vapour and Thermodynamics

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Yr(Earth days) 360 180 36 12 4 3 2.4 2 1.8 1.6 1.5 1.333 1

Very warm

Warm

Cold

DiffusivePlateau

Passive

Boschi et al. 2014, unpublish

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ConclusionsUnifying picture connecting Energy cycle to EP;Simplified 2D formula for studying GCMsSnowball hysteresis experiment Mechanisms involved in climate transitions;Analysis of the impact of [CO2] increaseGeneralized set of climate sensitivitiesAnalysis of impact of change on l.o.y.

Many challenges ahead:Analysis of GCMs performanceMelancholia/Edge StatesMultiscale, coarse graining effects

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Bibliography Boschi R., S. Pascale, V. Lucarini: Bistability of the climate around the

habitable zone: a thermodynamic investigation, Icarus (2013) Lucarini, V., K. Fraedrich, and F. Lunkeit, Thermodynamic Analysis of

Snowball Earth Hysteresis Experiment: Efficiency, Entropy Production, and Irreversibility. Q. J. R. Meterol. Soc., 136, 2-11 (2010)

Lucarini V., Thermodynamic Efficiency and Entropy Production in theClimate System, Phys Rev. E 80, 021118 (2009)

Lucarini, V., K. Fraedrich, and F. Ragone, 2011: New results on thethermodynamical properties of the climate system. J. Atmos. Sci., 68,2438-2458

Lucarini V., S. Pascale, R. Boschi, E. Kirk, N. Iro, Habitability andMultistability in Earth-like Planets, Astr. Nach. 334 576 – 588 (2013)

Lucarini V., Blender R., Herbert C., Pascale S., Wouters, J., Mathematical and Physical Ideas for Climate Science, arXiv:1311.1190 [physics.ao-ph] (2014)

Lucarini V. S. Pascale, Entropy Production and Coarse Graining of the Climate Fields in a General Circulation Model, Clim. Dyn. (2014)