Climate ModelingClimate Modeling

Inez FungUniversity of California, Berkeley

Weather Prediction by Numerical ProcessWeather Prediction by Numerical ProcessLewis Fry Richardson 1922Lewis Fry Richardson 1922

Weather Prediction by Numerical ProcessWeather Prediction by Numerical ProcessLewis Fry Richardson 1922Lewis Fry Richardson 1922

• Grid over domain • Predict pressure,

temperature, wind

Temperature -->density Pressure

Pressure gradient Wind temperature

Weather Prediction by Numerical ProcessWeather Prediction by Numerical ProcessLewis Fry Richardson 1922Lewis Fry Richardson 1922

• Predicted: 145 mb/ 6 hrs

• Observed: -1.0 mb / 6 hs€

∂ps

∂t

First Successful Numerical Weather First Successful Numerical Weather Forecast: March 1950Forecast: March 1950

•Grid over US

•24 hour, 48 hour forecast

•33 days to debug code and do the forecast

•Led by J. Charney (far left) who figured out the quasi-geostrophic equations

ENIAC: ENIAC: <10 words of read/write memory<10 words of read/write memory

Function tables(read memory)

16 operations in each time step16 operations in each time step

Platzman, Bull. Am Meteorol. Soc. 1979

Reasons for success in 1950Reasons for success in 1950• More & better observations after WWII-->

initial conditions + assessment

• Faster computers (24 hour forecast in 24 hours)

• Improved physics - – Atm flow is quasi 2-D (Ro<<1) and is

baroclinically unstable – quasi-geostrophic vorticity equations– filtered out gravity waves– Initial C: pressure (no need for u,v) t ~30 minutes (instead of 5-10 minutes)

20072007

Bert BolinBert Bolin 5/15/1925 - 12/30/2007Founding Chairman of the IPCC…[student at 1950 ENIAC calculation]

Nobel Peace PrizeNobel Peace Prize to toVP Al Gore andVP Al Gore andUN Intergovt Panel for Climate ChangeUN Intergovt Panel for Climate Change

mass

energy

water vapor

momentum

)(

...),,,(

,...),(

)(

),(;

0)(

)(ˆ12

2

qonCondensatiEvapqutq

GHGCOqTfLW

aerosolscloudsfSW

TLHSHLWSWTutT

qTfRTp

ut

uFkgpuuutu

ℑ+−=∇•+∂∂

==

ℑ++++=∇•+∂∂

==

=•∇+∂∂

ℑ+++∇−=×Ω+∇•+∂∂

r

bbr

r

rrrrrr

ρρ

ρρ

ρ

AtmosphereAtmosphere

ℑ convective mixing

OceanOcean

momentum

mass

energy

salinity

€

∂ r

u 2∂t+

r u 2 • ∇

r u 2 + 2Ω×

r u 2 = −

1

ρ 0∇p +

r F +

r τ 0

wind stress{

∇ •r u 2 +

∂w

∂z= 0

0 = −∂p

∂z+ ρg; ρ = f (T, s )

∂T

∂t+

r u 3 • ∇T = Q

0

surface heating{

+ ℑ (T )

∂s

∂t+

r u 3 • ∇s =

s0ρ 0Δz

(E − P )0

freshwater flux1 2 4 4 3 4 4

+ ℑ (s)

Numerical Weather Prediction Numerical Weather Prediction ( ~ days)( ~ days)

Initial Conditions

t = 0 hr

Prediction t = 6 hr 12 18 24

•Predict evolution of state of atmosphere (t)

•Error grows w time --> limit to weather prediction

Seasonal Climate Prediction Seasonal Climate Prediction ( El – Nino Southern Oscillation )( El – Nino Southern Oscillation )

{ Initial Conditions}

Atm + Ocn t = 0

{Prediction}

t = 1 month 2 3

• Coupled atmosphere-ocean instability• Require obs of initial states of both atm & ocean, esp. Equatorial Pacific• {Ensemble} of forecasts • Forecast statistics (mean & variance) – probability• Now – experimental forecasts (model testing in ~months)

Continued Success Since 1950Continued Success Since 1950

• More & better observations

• Faster computers

• Improved physics

Modern climate Modern climate modelsmodels

• Forcing: solar irradiance, volanic aerosols, greenhouse gases, …

• Predict: T, p, wind, clouds, water vapor, soil moisture, ocean current, salinity, sea ice, …

• Very high spatial resolution:<1 deg lat/lon resolution~50 atm, ~30 ocn, ~10 soil layers

==> 6.5 million grid boxes

• Very small time steps (~minutes)

• Ensemble runs multiple experiments)

Model experiments (e.g. 1800-2100) take weeks to months on supercomputers

Continued Success Since 1950Continued Success Since 1950

• More & better observations

• Faster computers

• Improved physics

Earth’s Energy Balance, with GHGEarth’s Energy Balance, with GHG

COCO22, H, H22O, GHGO, GHG

Earth

70

95114

23

7

50 absorbed by sfc

Sun

30

20 absorbed by atm

100

Climate ProcessesClimate Processes• Radiative transfer:

solar & terrestrial

• phase transition of water

• Convective mixing

• cloud microphysics

• Evapotranspirat’n

• Movement of heat and water in soils

Climate ForcingClimate Forcing

change in radiative heating (W/m2) at surface for a given change in trace gas composition or other change external to the climate system

CO2

CH4

N2O

10,000 years ago

Climate FeedbacksClimate Feedbacks

Warming

Decrease snow cover;Decrease reflectivity of surfaceIncrease absorption of solar energy

Increase cloud cover;Decrease absorption of solar energy

Evaporation from ocean,Increase water vapor in atmEnhance greenhouse effect

J. Zwally

Greenland

Urgency: Rapid Melting Urgency: Rapid Melting of Glaciers --> accelerate of Glaciers --> accelerate

warmingwarming

Moulin

Will cloud cover increase or decrease with Will cloud cover increase or decrease with warming? warming? [models: decrease; warm air can [models: decrease; warm air can hold more moisture; +ve feedback]hold more moisture; +ve feedback]

A B + water vapor + longwave abs Warming

A C + water vapor + cloud cover + longwave abs - shortwave abs

275 280 285 290 295 3000

5

10

15

20

25

30

35

40

1 2 3 4 5 6

Temperature (K)

Sat

ura

tio

n V

apo

r P

ress

ure

(m

b)

A

B

Cliquid

vapor

AttributionAttribution

• are observed changes consistent with

expected responses to forcings

inconsistent with alternative explanations

Observations

Climate model: All forcing

Climate model: Solar+volcanic only

IPCC AR4 (2007)

Oceans: Bottleneck to warmingOceans: Bottleneck to warminglong memory of climate systemlong memory of climate system

• 4000 meters of water, heated from above

• Stably stratified • Very slow diffusion of

chemicals and heat to deep ocean

• Fossil fuel CO2: • 200 years emission,• penetrated to upper 500-

1000 m

Slow warming of oceans --> continue evaporation, continue warming

2121ststC warming depends on rate of COC warming depends on rate of CO2 2 increaseincrease

20thC stabilizn:CO2 constant at 380 ppmv for the 21stC

21thC “Business as usual”:CO2 increasing 380 to 680 ppmv

Meehl et al. (Science 2005)

Model Model predicted predicted change in change in

recurrence of recurrence of “100 year “100 year drought”drought”

years

2020s

2070s

Changes in the probability distribution Changes in the probability distribution as well the meanas well the mean

OutlookOutlook• More & better observations

• Faster computers

• Improved physics + Biogeochemistry: include atmospheric chemistry, land and ocean biology to predict climate forcing and surface climate forcing and surface boundary conditionsboundary conditions

mass

energy

water vapor

momentum

)(

...),,,(

,...),(

)(

),(;

0)(

)(ˆ12

2

qonCondensatiEvapqutq

GHGCOqTfLW

aerosolscloudsfSW

TLHSHLWSWTutT

qTfRTp

ut

uFkgpuuutu

ℑ+−=∇•+∂∂

==

ℑ++++=∇•+∂∂

==

=•∇+∂∂

ℑ+++∇−=×Ω+∇•+∂∂

r

bbr

r

rrrrrr

ρρ

ρρ

ρ

AtmosphereAtmosphere

ℑ convective mixing

Ship Tracks:Ship Tracks:- - more cloud more cloud condensation nucleicondensation nuclei- smaller drops- smaller drops- more drops- more drops- more reflective- more reflective- - energy balance energy balance

Climate Model’s View of Climate Model’s View of the Global C Cyclethe Global C Cycle

Biophysics+ BGC

AtmosphereCO2 = 280 ppmv (560 PgC) + …

Ocean Circ.+ BGC

37400 Pg C 2000 Pg C

90± 60±

TurnoverTurnoverTime of CTime of C101022-10-103 3 yryr

TurnoverTurnovertime of Ctime of C101011 yryr

FFFF

Prognostic Carbon CyclePrognostic Carbon Cycle

€

DCa

Dt= (FF + Def + Foa c

air− sea_flux1 2 3 + Fba c )

atm− land _ flux1 2 3

0

+ ℑ (Ca )

DCo

Dt= −Foa c

0+ P − L

biology1 2 3 + ℑ (Co )

∂Cb _ livek

∂t= −α k Fab ↓

photosynthesis{

0

−Cb _ live

k

τ livek

mortality1 2 3

∂Cb _ deadk

∂t=

Cb _ livek

τ livek

mortality1 2 3

+ Fjk

j

∑ −Cb _ dead

k

τ deadk

decomposition1 2 3

Atm

Ocean

Land-live

Land-dead

Warm-wet

Warm-dry

T, Soil Moisture Index}

Regression of NPP vs T

Photosynthesis decreases with carbon-climate coupling

Fung et al. Evolution of carbon sinks in a changing climate. PNAS 2005

21st C Carbon-Climate Feedback: 21st C Carbon-Climate Feedback: = Coupled minus Uncoupled = Coupled minus Uncoupled

Changing Carbon Sink CapacityChanging Carbon Sink Capacity

With SRES A2 (fast FF emission): as CO2

increases•Capacity of land and ocean to store carbon decreases (slowing of photosyn; reduce soil C turnover time; slower thermocline mixing …)•Airborne fraction increases --> more warming

Fung et al. Evolution of carbon sinks in a changing climate. PNAS 2005

CO2 Airborne fractionCO2 Airborne fraction=atm increase /=atm increase /Fossil fuel emissionFossil fuel emission

Continued Success Since 1950Continued Success Since 1950

• More & better observations: –initial conditions, –Analysis --> improve physics–assessment of model results

• Faster computers

• Improved physics

Initial Condition: Initial Condition: Numerical Weather PredictionNumerical Weather Prediction

Challenge• Diverse, asynchronous

obs of atm• Find the current state of

the atm at tn

• Model --> forecast for tn+1

Practice• Ensemble forecast -->

– mean state,

– uncertainty in forecast Kalnay 2003

Approach: Data AssimilationApproach: Data Assimilation

yo

x=[T, p, u,v, q, s, … model parameters]

obs yo

tn-1 tn

yo

xbModel: xb

n = M(xa

n-1)xa

Find best estimate of x (xa

n) given imperfect model (xb

n) and incomplete obs (yo)

Approaches to Merge Data + ModelApproaches to Merge Data + Model

• Optimal analysis• 3D variational data assimilation• 4D var• Kalman Filter• Ensemble Kalman Filter• Local Ensemble Transform Kalman

Filter• …

Observations: The A-TrainObservations: The A-Train

1:26

TES – T, P, H2O, O3, CH4, COMLS – O3, H2O, COHIRDLS – T, O3, H2O, CO2, CH4

OMI – O3, aerosol climatology

aerosols, polarization

CloudSat – 3-D cloud climatologyCALIPSO – 3-D aerosol climatology

AIRS – T, P, H2O, CO2, CH4

MODIS – cloud, aerosols, albedo

OCO - - CO2

O2 A-band ps, clouds, aerosols

Coordinated Observations

5/4/20024/28/2006

7/15/2004

12/18/2004

Challenge: assimilating ALL data simultaneously in high-resolution climate model to understand interactions

Outlook: Research challengesOutlook: Research challenges

Climate Change ScienceClimate Change Science::

High resolution climate projections 1800-2030:

• Project impact on water availability, ecosystems, agriculture, at a resolution useful to inform policy and strategies for adaptation and carbon management

• Articulation of uncertainties and risks

Outlook: Research challengesOutlook: Research challenges

Adaptation and Mitigation

• Production and consumption energy efficiency

• Alternative energy• Carbon capture & sequestrat’n - scalable?• Geo-engineering - potential harm vs

benefitsMaturity

Need a new generation of models where climate interacts with adaptation and mitigation strategies to guide, prioritize policy decisions

http://www.ipcc.ch

4th Assessment4th AssessmentReport 2007Report 2007

WGI: ScienceWGI: Science

WGII: ImpactsWGII: Impacts

WGIII: Adaptation WGIII: Adaptation and Mitigationand Mitigation