CHEMISTRY-TRANSPORT AND

CHEMISTRY-CLIMATE MODELLING

Slimane BEKKI, LATMOS

(Thank you to Daniel Jacob great website, Harvard Univ.)

1/ Some basics about atmospheric modelling

2/ From simple (box) to complex chemistry-

climate models

3/ Use of models in the analysis of observations

PLAN

HOW TO MODEL ATMOSPHERIC COMPOSITION? Solve continuity equation for chemical mixing ratios Ci(x, t)

Fires Land

biosphere

Human

activity

Lightning

Ocean Volcanoes

Transport

Eulerian form:

ii i i

CC P L

t

U

Lagrangian form:

ii i

dCP L

dt

U = wind vector

Pi = local source

of chemical i

Li = local sink

Chemistry

Aerosol microphysics

HOW TO SOLVE CONTINUITY EQUATION?

Define

problem of

interest

Design model; make

assumptions needed

to simplify equations

and make them solvable

Evaluate

model with

observations

Apply model:

make hypotheses,

predictions

Improve model, characterize its error

The atmospheric evolution of a species X is given by the continuity equation

This equation cannot be solved exactly e need to construct model

(simplified representation of complex system)

Design

observational

system to test

model

[ ]( [ ])X X X X

XE X P L D

t

U

local change in

concentration

with time

transport

(flux divergence;

U is wind vector)

chemical production and loss

(depends on concentrations

of other species)

emission Deposition (wet, dry)

SIMPLEST MODEL: ONE-BOX MODEL

Inflow Fin Outflow Fout

X

E

Emission Deposition

D

Chemical

production

P L

Chemical

loss

Atmospheric “box”;

spatial distribution of X

within box is not resolved

out

Atmospheric lifetime: m

F L D

Fraction lost by export: out

out

Ff

F L D

Lifetimes add in parallel:

export chem dep

1 1 1 1outF L D

m m m

Loss rate constants add in series: export chem dep

1k k k k

Mass balance equation: sources - sinks in out

dmF E P F L D

dt

NO2 has atmospheric lifetime ~ 1 day:

strong gradients away from combustion source regions

Satellite observations of tropospheric NO2 columns

CO has atmospheric lifetime ~ 2 months:

mixing around latitude bands Satellite observations of CO mixing ratio at 850 hPa

CO2 has atmospheric lifetime ~ 100 years:

global mixing, very weak gradients

Assimilated observations of CO2 mixing ratio

SIMPLEST MODEL: ONE-BOX MODEL

Inflow Fin Outflow Fout

X

E

Emission Deposition

D

Chemical

production

P L

Chemical

loss

Atmospheric “box”;

spatial distribution of X

within box is not resolved

out

Atmospheric lifetime: m

F L D

Fraction lost by export: out

out

Ff

F L D

Lifetimes add in parallel:

export chem dep

1 1 1 1outF L D

m m m

Loss rate constants add in series: export chem dep

1k k k k

Mass balance equation: sources - sinks in out

dmF E P F L D

dt

SPECIAL CASE: SPECIES WITH CONSTANT SOURCE

& 1st ORDER SINK & NO TRANSPORT

-> ANALYTICAL SOLUTION

( ) (0) (1 )kt ktdm SS km m t m e e

dt k

Steady state

solution

(dm/dt = 0)

Initial condition m(0)

Characteristic time = 1/k for

• reaching steady state

• decay of initial condition

If S, k are constant over t >> , then dm/dt g 0 and mg S/k: quasi steady state

EXAMPLE : GLOBAL BOX MODEL FOR CO2 (Pg C yr-1)

SIMPLE CASE: NO ATMOSPHERIC CHEMISTRY & NO TRANSPORT (GLOBAL)

IPCC [2001] IPCC [2001]

PUFF MODEL: FOLLOW AIR PARCEL MOVING WITH WIND

CX(xo, to)

CX(x, t)

wind

In the moving puff,

XdCE P L D

dt

…no transport terms! (they’re implicit in the trajectory)

Application to the chemical evolution of an isolated pollution plume:

CX

CX,b

,( )Xdilution X X b

dCE P L D k C C

dt In pollution plume,

TWO-BOX MODEL

defines spatial gradient between two domains

m1 m2

F12

F21

Mass balance equations: 1

1 1 1 1 12 21

dmE P L D F F

dt

If mass exchange between boxes is first-order:

11 1 1 1 12 1 21 2

dmE P L D k m k m

dt

e system of two coupled ODEs (or algebraic equations if system is

assumed to be at steady state)

(similar equation for dm2/dt)

EULERIAN MODELS PARTITION ATMOSPHERIC DOMAIN

INTO GRIDBOXES

Solve numerically

continuity equation for

individual grid-boxes

• Detailed chemical/aerosol models can

presently afford -106 gridboxes

• In global models, this implies a

horizontal resolution of ~ 1o (~100 km)

in horizontal and ~ 1 km in vertical

This discretizes the continuity equation in space

• Chemical Transport Models (CTMs) use external meteorological data as input

• General Circulation Models (GCMs) compute their own meteorological fields

JUST AN INTERVAL ON

LAGRANGIAN MODELS

IN EULERIAN APPROACH, DESCRIBING THE

EVOLUTION OF A POLLUTION PLUME REQUIRES

A LARGE NUMBER OF GRIDBOXES

Fire plumes over

southern California,

25 Oct. 2003

A Lagrangian “puff” model offers a much simpler alternative

LAGRANGIAN APPROACH: TRACK TRANSPORT OF

POINTS IN MODEL DOMAIN (NO GRID)

UDt

U’Dt

• Transport large number of points with trajectories

from input meteorological data base (U) + random

turbulent component (U’) over time steps Dt

• Points have mass but no volume

• Determine local concentrations as the number of

points within a given volume

• Nonlinear chemistry requires Eulerian mapping at

every time step (semi-Lagrangian)

PROS over Eulerian models:

• no Courant number restrictions

• no numerical diffusion/dispersion

• easily track air parcel histories

• invertible with respect to time

CONS:

• need very large # points for statistics

• inhomogeneous representation of domain

• convection is poorly represented

• nonlinear chemistry is problematic

position

to

position

to+Dt

LAGRANGIAN RECEPTOR-ORIENTED MODELING

Run Lagrangian model backward from receptor location,

with points released at receptor location only

• Efficient cost-effective quantification of source

influence distribution on receptor (“footprint”)

backward in time

BACK ON EULERIAN MODELS…

OPERATOR SPLITTING IN EULERIAN MODELS

i i i

TRANSPORT LOCAL

C C dC

t t dt

… and integrate each process separately over discrete time steps:

( ) (Local)•(Transport) ( )i o i oC t t C tD

• Split the continuity equation into contributions from transport and local terms:

Transport advection, convection:

Local chemistry, emission, deposition, aerosol processes:

(

ii

TRANSPORT

ii

LOCAL

dCC

dt

dCP

dt

U

) ( )iLC C

These operators can be split further:

• split transport into 1-D advective and turbulent transport for x, y, z

(usually necessary)

• split local into chemistry, emissions, deposition (usually not necessary)

Reduces dimensionality of problem

SPLITTING THE TRANSPORT OPERATOR

• Wind velocity U has turbulent fluctuations over time step Dt:

( ) '( )t t U U UTime-averaged

component

(resolved)

Fluctuating component

(stochastic)

1( )i i i

xx

C C Cu K

t x x x

• Further split transport in x, y, and z to reduce dimensionality. In x direction:

( , , )u v wU

• Split transport into advection (mean wind) and turbulent components:

1ii i

CC C

t

U K

air density

turbulent diffusion matrix

K

advection turbulence (1st-order closure)

advection

operator

turbulent

operator

SOLVING THE EULERIAN

ADVECTION EQUATION

• Equation is conservative: need to avoid

diffusion or dispersion of features. Also need

mass conservation, stability, positivity…

• All schemes involve finite difference

approximation of derivatives : order of

approximation → accuracy of solution

• Classic schemes: leapfrog, Lax-Wendroff,

Crank-Nicholson, upwind, moments…

• Stability requires Courant number uDt/Dx < 1

… limits size of time step

• Addressing other requirements (e.g., positivity)

introduces non-linearity in advection scheme

i iC Cu

t x

LOCAL (CHEMISTRY) OPERATOR:

solves ODE system for n interacting species

1,i n

1( ) ( ) ( ,... )ii i n

dCP L C C

dt C C C

System is typically “stiff” (lifetimes range over many orders of magnitude)

→ implicit solution method is necessary. Needs to be conservative and fast

• Simplest method: backward Euler. Transform into system of n algebraic

equations with n unknowns

( ) ( )

( ( )) ( ( )) 1,i o i oi o i o

C t t C tP t t L t t i n

t

D D D

DC C

( )ot t DC

Solve e.g., by Newton’s method. Backward Euler is stable, mass-conserving,

flexible (can use other constraints such as steady-state, chemical family

closure, etc… in lieu of DC/Dt ). But it is expensive. Most 3-D models use

higher-order implicit schemes such as the Gear method.

For each species

SPECIFIC ISSUES FOR AEROSOL CONCENTRATIONS

• A given aerosol particle is characterized by its size, shape, phases, and

chemical composition – large number of variables!

• Aerosol size distribution in a model is either decomposed in size bins

(and so as many tracers) or only its moments (integrals over size) are

treated by the model (assuming a certain shape for the size distribution,

typically a log-normal).

• If evolution of the size distribution is not resolved, continuity equation

for aerosol species can be applied in same way as for gases

• Simulating the evolution of the aerosol size distribution requires

inclusion of nucleation/growth/coagulation terms in Pi and Li, and size

characterization either through size bins or moments.

Typical aerosol

size distributions

by volume

nucleation

condensation coagulation

INFLUENCE DU SCENARIO GES SUR LA COUCHE D’O3

“INTERACTIVE” ATMOSPHERIC CHEMICAL COMPOSITION

MOVIE

MODEL PROJECTIONS

An other motivation …

INFLUENCE OF CO2 ON STRATOSPHERIC O3

WMO, 1998

Temporal evolution of column O3 Projections by 2-D chemistry-climate model (Cambridge)

Halogen Halogen

CO2

CO2 constant

INFLUENCE OF IPCC GHG SCENARIOS ON O3

Temporal evolution of

column ozone Projections: multi-model

mean (chemistry-climate)

Different colours:

different scenarios of

greenhouse gases

evolution (GHG: CO2, CH4,

N2O)

Eyring et al., 2014

INFLUENCE OF STRATOSPHERIQUE O3 ON CLIMATE

ON THE USE OF CTM IN THE

ANALYSIS OF OBSERVATIONS

TIME EVOLUTION OF HCl COLUMN (INDICATOR OF

STRATOSPHERRIC CHLORINE LOADING)

AT JUNGFRAUJOCH (47°N)

What is going on between 2004 and 2010?

STRATOSPHERIC HCl ANOMALY DUE TO

ATMOSPHERIC CIRCULATION CHANGES

CTM varying dyn.

CTM fixed

dynamics

JUNGFRAUJOCH NY-ALESUND

Anomaly found at all NH sites except tropics Nothing at SH sites

ANTARCTIC OZONE MEASUREMENT STATIONS (SAOZ, DOBSON, BREWER, DOAS)

How can we estimate ozone losses from these observations?

TIME EVOLUTION OF PARAMETERS USED

TO ESTIMATE OZONE LOSSES AT DDU IN 2007

Ozone loss = Measured ozone – CTM passive ozone

TIME EVOLUTION OF VORTEX OZONE LOSS

ESTIMATED AT DIFFERENT STATIONS

solid black line:

mean ozone loss

Kuttippurath et al., ACP, 2010

Anomalies relative to the

1964‐1978 reference period

Black (ODS): CTM with changing ODS

Blue (cODS): CTM with ODS

held constant at 1960s values

Yellow: ground-based observations

Good agreement between ODS CTM

and observations.

Attribution (halogen-induced loss)

based on observations alone is

difficult and risky

TIME EVOLUTION OF TOTAL OZONE ANOMALIES

Shepherd et al., Nature, 2014

TIME EVOLUTION OF HALOGEN-INDUCED O3 LOSS

Halogen-induced O3

loss started in the 60s

Big negative O3 anomaly

after volcanic eruptions

only in ODS CTM

Ozone recovery but very

small (difficult to claim

it because of decadal

dynamical variability)

TIME EVOLUTION OF TOTAL OZONE ANOMALIES Anomalies relative to the

1964‐1978 reference period

Black (ODS): CTM

with changing ODS

Blue (cODS): CTM

with ODS fixed to 60s

Yellow: ground-

based obs.

Red: Satellite

Good agreement

between ODS CTM and

obs. -> attribution

TIME SERIES OF MONTHLY ZONAL MEAN H2O

AT 100 hPa OVER 20°S-20°N FOR 1988-2010

How can we

correct biases to

merge data &

derive trend?

Used CTM H2O as

transfer function

Note that no

evidence of long-

term trend in CTM

with respect to

SAGE or SCIA

TIME SERIES OF MONTHLY ZONAL MEAN H2O

AT 100 hPa OVER 20°S-20°N FOR 1988-2010

How can we

correct biases to

merge data &

derive trend?

Used CTM H2O as

transfer function

Note that no

evidence of long-

term trend in CTM

with respect to

SAGE or SCIA

Hegglin et al., Nature, 2014

CONSISTENCY BETWEEN TROPICAL TEMPERATURE

AND LOWER STRATOSPHERIC H2O

(16 months overlap)

T anomalies are

correlated with

CTM H2O

anomalies and

with merged

satellite H2O

anomalies

Correlation drift

with merged

HALOE-MLS

Temperature &

H2O from CTM,

Merged satellite,

Merged

HALOE/MLS

THANK YOU