Slimane BEKKI, LATMOS (Thank you to Daniel Jacob great website, - - PowerPoint PPT Presentation

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:

i i i i

C C P L t        U

Lagrangian form:

i i i

dC P L dt  

U = wind vector Pi = local source

• f 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

• bservations

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

• bservational

system to test model

[ ] ( [ ])

X X X X

X E 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

• f 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

• ut

Atmospheric lifetime: m F L D    

Fraction lost by export:

• ut
• ut

F f F L D   

Lifetimes add in parallel:

export chem dep

1 1 1 1

• ut

F L D m m m          

Loss rate constants add in series:

export chem dep

1 k k k k      Mass balance equation: sources - sinks

in

• ut

dm F 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

• ut

Atmospheric lifetime: m F L D    

Fraction lost by export:

• ut
• ut

F f F L D   

Lifetimes add in parallel:

export chem dep

1 1 1 1

• ut

F L D m m m          

Loss rate constants add in series:

export chem dep

1 k k k k      Mass balance equation: sources - sinks

in

• ut

dm F E P F L D dt       

 

SPECIAL CASE: SPECIES WITH CONSTANT SOURCE & 1st ORDER SINK & NO TRANSPORT

• > ANALYTICAL SOLUTION

( ) (0) (1 )

kt kt

dm S S 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,

X

dC E 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

,

( )

X dilution X X b

dC E 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

dm E P L D F F dt      

If mass exchange between boxes is first-order:

1 1 1 1 1 12 1 21 2

dm E 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

• i
• C t

t C t  D  

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

Transport advection, convection: Local chemistry, emission, deposition, aerosol processes: (

i i TRANSPORT i i LOCAL

dC C dt dC P dt                   U ) ( )

i

L  C 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 U

Time-averaged component (resolved) Fluctuating component (stochastic)

1 ( )

i i i xx

C C C u K t x x x            

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

( , , ) u v w  U

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

1

i i i

C C C t          U K

air density turbulent diffusion matrix    K

advection turbulence (1st-order closure) advection

• perator

turbulent

• perator

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 i

C C u t x      

LOCAL (CHEMISTRY) OPERATOR: solves ODE system for n interacting species

 

1, i n 

1

( ) ( ) ( ,... )

i i i n

dC P 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

• i
• i
• i
• C t

t C t P t t L t t i n t  D    D   D  D C C

( )

• t

t  D C

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

• nly 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

• bs. -> 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