chemistry-transport and chemistry-climate...
TRANSCRIPT
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