Aggregated Convection, Tropical Cyclones, Aggregated Convection, Tropical Cyclones, and Climateand Climate

Kerry EmanuelKerry Emanuel

Program in Atmospheres, Oceans and ClimateProgram in Atmospheres, Oceans and Climate

Massachusetts Institute of TechnologyMassachusetts Institute of Technology

There are more things in heaven and earth, Horatio, than are dreamt of in your philosophy.

-- Climate physicist, to Horatio a climate modeler

We are such stuff as dreams are made on, and our little life is rounded by a sleep

Model Disagreement = Uncertainty:Is this true?

Climate understanding desert

Climate modeler

Skeptic

Specific Issues Addressed HereSpecific Issues Addressed Here

• Aggregated convection as an example Aggregated convection as an example of self-organized criticality (SOC)of self-organized criticality (SOC)

• Implications for climateImplications for climate• Implications for incidence of tropical Implications for incidence of tropical

cyclonescyclones• Tropical cyclone effects on the Tropical cyclone effects on the

meridional overturning circulationmeridional overturning circulation

Water vapor and convection are highly Water vapor and convection are highly inhomogeneousinhomogeneous

Frequency histogram of rawindsonde relative humidities from 1600 ascents at the tropical Pacific islands of Yap, Koror, Ponape and Majuro, January-May, 1994-95. Spencer and Braswell, Bull. Amer. Meteor. Soc., 1997.

What controls the distribution of What controls the distribution of water vapor and precipitation?water vapor and precipitation?

A critical problem in climate!A critical problem in climate!

A Partial List of Factors:A Partial List of Factors:

• Convective lofting of water

• Cloud and rain microphysics

• Subsidence

• Large-scale advection

Here we will consider the idealized problem of Here we will consider the idealized problem of what determines the distribution of humidity what determines the distribution of humidity

in radiative-convective equilibrium states.in radiative-convective equilibrium states.

• Generally derided as irrelevant to the real world (yet not a bad approximation to warm pool regions)

• Need to understand “simple” problems first• There are some surprises even in this “simple”

problem

Radiative-Moist Convective Radiative-Moist Convective EquilibriumEquilibrium

Radiative-Moist Convective EquilibriumRadiative-Moist Convective Equilibrium

Numerical Simulations of RC Numerical Simulations of RC EquilibriumEquilibrium

Vertically integrated water Vertically integrated water vapor at 4 daysvapor at 4 days

(Nolan et al., QJRMS, (Nolan et al., QJRMS, 2007)2007)

Sensitivity of relative humidity to cloud microphysics in radiative-Sensitivity of relative humidity to cloud microphysics in radiative-convective equilibrium (25 mb grid spacing, fixed SST)convective equilibrium (25 mb grid spacing, fixed SST)

Climate Sensitivity of Relative Humidity in Radiative-Climate Sensitivity of Relative Humidity in Radiative-Convective EquilibriumConvective Equilibrium

Understanding Free Tropospheric Humidity Influences Understanding Free Tropospheric Humidity Influences on Convection through Quasi-Equilibrium (QE) on Convection through Quasi-Equilibrium (QE)

ConceptsConceptsBoundary Layer QE (Raymond, 1995):

*0

*| |b

k b d e b m

hhH H C h h M w h h

t t

V

Moist static energyMoist static energy

PBL moist static energyPBL moist static energy

p vh c T L q gz

: 0

:

b

u d e

hBLQE

tMass Continuity w M M w

*0| | b

u kb m

h hM w C

h h

V

Smaller hm gives smaller Mu

Only yields cloud base mass flux!

large-scale

Note: Under global warming, increases slowly, while increases rapidly

*0| |k bC V h h b mh h

Temperature tendency of free atmosphere:Temperature tendency of free atmosphere:

* d du d rad

m

shM M w Q

t z

Need closure for Md:

1d p u

p

M M

precipitation efficiency

* d dp u rad

m

shM w Q

t z

Summary of BLQESummary of BLQEFree troposphere moisture affects convection Free troposphere moisture affects convection

by:by:

• Changing cloud base mass fluxChanging cloud base mass flux: Fewer downdrafts needed to balance surface fluxes and convergence when free troposphere is dry

• Affecting fraction of condensed water that Affecting fraction of condensed water that reaches surface: reaches surface: Precipitation efficiency is a function of humidity. Low humidity can reduce precipitation through entrainment and/or increased evaporation of precipitation

All of the preceding assumes that moist convection is statistically

homogeneous if lower boundary condition is constant.

Is this true?

Numerical simulations of RC equilibrium show that, Numerical simulations of RC equilibrium show that, under some conditions, moist convection self-under some conditions, moist convection self-

aggregates aggregates

Day 10 Day 50

From Bretherton et al. (2005)

Vertically integrated water vapor at 4 (a), 6 (b), 8 (c), and 10 (d) Vertically integrated water vapor at 4 (a), 6 (b), 8 (c), and 10 (d) daysdays

(Nolan et al., QJRMS, 2007)(Nolan et al., QJRMS, 2007)

Effect of Self-Effect of Self-Aggregation on Aggregation on

HumidityHumidity

(Bretherton et al. , 2005)

Nolan et al., QJRMS, 2007Nolan et al., QJRMS, 2007

Empirical Necessary Conditions for Self-Empirical Necessary Conditions for Self-Aggregation Aggregation (after Held et al., 1993; Bretherton et al.,

2005; Nolan et al.; 2007)

• Small vertical shear of horizontal wind• Interaction of radiation with clouds and/or

water vapor• Feedback of convective downdraft surface

winds on surface fluxes• Sufficiently high surface temperature

HypothesisHypothesis

• At high temperature, convection self-aggregates

• →Horizontally averaged humidity drops dramatically

• →Reduced greenhouse effect cools system• →Convection disaggregates• →Humidity increases, system warms• →System wants to be near phase transition to

aggregated state

Recipe for Self-Organized CriticalityRecipe for Self-Organized Criticality(First proposed by David Neelin, but by different (First proposed by David Neelin, but by different

mechanism)mechanism)

• System should reside near critical threshold for self-aggregation

• Convective cluster size should follow power law distribution

Toy ModelToy Model

PropertiesProperties• PBL quasi-equilibrium enforced• Bulk aerodynamic surface fluxes with convective gustiness• Albedo and emissivity simple weighted average of clear

and cloudy regions• Water vapor-dependent clear sky emissivity• Horizontally uniform temperature but variable moist static

energy (i.e. water vapor) at mid-level• Vertical motion calculated to enforce zero horizontal

temperature gradient• PBL moist static energy adjusted to yield zero domain-

averaged vertical motion• Slow horizontal diffusion of moisture at mid-level

ResultsResultsSelf-Aggregation Occurs for:Self-Aggregation Occurs for:

• Small or negative gross moist stability• Sufficiently large feedback between

convective gustiness and surface enthalpy fluxes

• Sufficiently high surface temperature

Example:Example:

Summary of Toy Model ResultsSummary of Toy Model Results• Self-aggregation driven by convective

gustiness at high temperature• No self-aggregation at low temperature• Aggregated state is much drier at mid levels• System tends towards self-organized criticality

(SOC)• Climate sensitivity of SOC state much lower

(0.04 K/Wm-2) than sensitivity of uniform convection (0.2 K/Wm-2)

Implications for Tropical Cyclones Implications for Tropical Cyclones and Climateand Climate

Tracks of all tropical cyclones, 1985-2005Tracks of all tropical cyclones, 1985-2005

Source: Wikipedia

Global TC Frequency, 1970-2006Global TC Frequency, 1970-2006

Data Sources: NOAA/TPC and NAVY/JTWC

Better Intensity Metric:Better Intensity Metric:

The Power Dissipation IndexThe Power Dissipation Index

0

3maxPDI V dt

A measure of the total frictional dissipation of kinetic energy in the A measure of the total frictional dissipation of kinetic energy in the hurricane boundary layer over the lifetime of the stormhurricane boundary layer over the lifetime of the storm

Atlantic Storm Maximum Power DissipationAtlantic Storm Maximum Power Dissipation(Smoothed with a 1-3-4-3-1 filter)

Po

wer

Dis

sip

atio

n In

dex

(P

DI)

Years included: 1870-2006

Data Source: NOAA/TPC

Atlantic Sea Surface Temperatures and Atlantic Sea Surface Temperatures and Storm Max Power DissipationStorm Max Power Dissipation

(Smoothed with a 1-3-4-3-1 filter)

Sca

led

Tem

per

atu

re

Po

wer

Dis

sip

atio

n In

dex

(P

DI)

Years included: 1870-2006

Data Sources: NOAA/TPC, UKMO/HADSST1

Feedback of Global Tropical Feedback of Global Tropical Cyclone Activity on the Climate Cyclone Activity on the Climate

SystemSystem

Strong Mixing of Upper Ocean

Direct mixing by tropical cyclones

Source: Rob Korty, CalTech

Emanuel (2001) estimated global rate of heat input as

1.4 X 1015 Watts

TC Mixing May Induce Much or Most of the Observed Poleward Heat Flux by the Oceans

Trenberth and Caron, 2001Trenberth and Caron, 2001

TC-Mixing may be Crucial for High-Latitude Warmth and Low-Latitude Moderation During Warm Climates,

such as that of the Eocene

Estimating Tropical Cyclone Estimating Tropical Cyclone Activity in Different ClimatesActivity in Different Climates

Our ApproachOur Approach• Step 1: Seed each ocean basin with a very large

number of weak, randomly located cyclones

• Step 2: Cyclones are assumed to move with the large scale atmospheric flow in which they are embedded

• Step 3: Run a coupled, ocean-atmosphere computer model for each cyclone, and note how many achieve at least tropical storm strength

• Step 4: Using the small fraction of surviving events, determine storm statistics.

Track:Track:

850 2501 ,track V V V V

Empirically determined constants:

0.8, 10 ,u ms

12.5v ms

Example: 200 Synthetic TracksExample: 200 Synthetic Tracks

Present Climate: Spatial Distribution of Present Climate: Spatial Distribution of Genesis PointsGenesis Points

Observed

Synthetic

CalibrationCalibration

• Absolute genesis frequency calibrated to Absolute genesis frequency calibrated to North Atlantic during the period 1980-2005North Atlantic during the period 1980-2005

Genesis ratesGenesis rates

Downscale Global Eocene Downscale Global Eocene Simulations using CAM3 with Simulations using CAM3 with

Boundary Conditions Derived from Boundary Conditions Derived from Paleoclimate DataPaleoclimate Data(with Matt Huber)(with Matt Huber)

Global Annual Exceedence Frequency

300 Eocene Events300 Eocene Events

Incorporating Tropical Cyclone and Incorporating Tropical Cyclone and Convection Feedbacks in a Toy Convection Feedbacks in a Toy

ModelModel

As a first step toward understanding how this new picture of the thermohaline circulation might affect climate, we built a very simple two-column climate model that incorporates this effect plus the greenhouse effect and atmospheric heat transport. We ran this model until a steady state was achieved.(Emanuel, JGR, 2002)

Atmospheric FluxesAtmospheric Fluxes

• Convective fluxes determined so as to keep lapse rate moist adiabatic (Where profile is otherwise unstable); upper atmospheric layer dries out when convection is absent

• Strength of circulation determined so as to keep meridional temperature gradient at critical value

Ocean FluxOcean Flux

• Proportional to difference in ocean temperature between the two boxes

• Also proportional to a measure of hurricane activity in the tropical box

ResultsResults

For this particular choice of parameters, the model produces three overlapping climate regimes: hot, moderate and cold, as shown in this plot of polar air temperature.

The heavy lines show the poleward heat transport by the atmosphere, while the thin lines show the oceanic heat transport.

This graph shows a measure of hurricane activity in the three regimes.

Climate Manifold

Cold

Moderate

Hot

Atmospheric Circulation

Strong

Moderate

Monsoonal

Ocean Heat Flux

Weak or absent

Moderate

Very large

Pole-to-Equator s Gradient

Critical

Critical

Subcritical

Tropical Cyclone Activity

None

Moderate

High

Bottom Water

Temperature

Cold

Cold

Warm

Atmospheric CO2 Content

Low

Modest

Large

Tropical Convection

Shallow

Deep

Deep

Greenhouse Trapping

Small

Small to Moderate

Large

Implied Climate Regime

Characteristics

SST: elevated mixing to 360 meters – uniform SST: elevated mixing to 360 meters – uniform

10 x CO2 in both experimentsSource: Rob Korty, CalTech

Interactive TC-Mixing Moderates Tropical Warming and Interactive TC-Mixing Moderates Tropical Warming and Amplifies High-Latitude Warming in Coupled Climate ModelsAmplifies High-Latitude Warming in Coupled Climate Models

SummarySummary• Interaction between climate state and moist Interaction between climate state and moist

convection still not well understoodconvection still not well understood• At low values of wind shear, moist convection At low values of wind shear, moist convection

may self-aggregate when temperature is may self-aggregate when temperature is sufficiently highsufficiently high

• Aggregation leads to drier atmosphere, which Aggregation leads to drier atmosphere, which in turn cools systemin turn cools system

• System tends to self-organized critical state, System tends to self-organized critical state, which appears to be less sensitive to climate which appears to be less sensitive to climate forcingforcing

• Tropical cyclones are an example of organized Tropical cyclones are an example of organized convection and may also play a fundamental convection and may also play a fundamental role in driving the ocean’s meridional role in driving the ocean’s meridional overturning circulation overturning circulation

• Combination of TC-ocean feedback and moist Combination of TC-ocean feedback and moist convection may lead to hysteresis and multiple convection may lead to hysteresis and multiple equilibria of climateequilibria of climate

• Self-aggregation of convection and TC-ocean Self-aggregation of convection and TC-ocean feedback are poorly represented in or entirely feedback are poorly represented in or entirely missing from today’s GCMs missing from today’s GCMs

Vertical vorticity at z=2.2 km at days 11 (a), 12 (b) 13 (c) and 14 (d)

Which external parameters determine Which external parameters determine characteristic updraft speeds (and CAPE) in characteristic updraft speeds (and CAPE) in

radiative-convective equilibrium?radiative-convective equilibrium?

Answer: Answer: kinematic surface tension of water

g acceleration of gravity

Results of numerical simulations with a cloud-permitting model, Parodi and Emanuel (2006)

Daily-Mean Precipitation Versus Column-Relative HumidityDaily-Mean Precipitation Versus Column-Relative Humidity

Bretherton, Peters, and Back, 2004

Seasonal CyclesSeasonal Cycles

AtlanticAtlantic

Cumulative Distribution of Storm Lifetime Peak Cumulative Distribution of Storm Lifetime Peak Wind Speed, with Sample of 2946Wind Speed, with Sample of 2946 Synthetic Synthetic

TracksTracks

Captures effects of regional climate Captures effects of regional climate phenomena (e.g. ENSO, AMM)phenomena (e.g. ENSO, AMM)