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.)

PLAN 1/ Some basics about atmospheric modelling 2/ From simple (box) to complex chemistry- climate models 3/ Use of models in the analysis of observations

HOW TO MODEL ATMOSPHERIC COMPOSITION? Solve continuity equation for chemical mixing ratios C i (x , t) Eulerian form: U = wind vector  C      i P i = local source U C P L Lightning  i i i t of chemical i Lagrangian form: Transport L i = local sink dC dt   i P L Chemistry i i Aerosol microphysics Volcanoes Fires Land Human Ocean biosphere activity

HOW TO SOLVE CONTINUITY EQUATION? The atmospheric evolution of a species X is given by the continuity equation  [ X ]      E ( [ U X ]) P L D  X X X X t Deposition (wet, dry) emission transport local change in chemical production and loss (flux divergence; concentration (depends on concentrations U is wind vector) with time of other species) This equation cannot be solved exactly e need to construct model (simplified representation of complex system) Improve model, characterize its error Design Design model; make Define Evaluate observational assumptions needed model with problem of system to test to simplify equations observations interest model and make them solvable Apply model: make hypotheses, predictions

SIMPLEST MODEL: ONE-BOX MODEL Atmospheric “box”; spatial distribution of X Chemical Chemical within box is not resolved production loss Inflow F in Outflow F out L P X D E Deposition Emission dm   dt        Mass balance equation: sources - sinks F E P F L D in out m   F Atmospheric lifetime:  out Fraction lost by export: f     F L D F L D out out 1 F L D 1 1 1       out Lifetimes add in parallel:     m m m export chem dep 1     Loss rate constants add in series: k k k k  export chem dep

NO 2 has atmospheric lifetime ~ 1 day: strong gradients away from combustion source regions Satellite observations of tropospheric NO 2 columns

CO has atmospheric lifetime ~ 2 months: mixing around latitude bands Satellite observations of CO mixing ratio at 850 hPa

CO 2 has atmospheric lifetime ~ 100 years: global mixing, very weak gradients Assimilated observations of CO2 mixing ratio

SIMPLEST MODEL: ONE-BOX MODEL Atmospheric “box”; spatial distribution of X Chemical within box is not resolved Chemical production loss Inflow F in Outflow F out L P X D E Deposition Emission dm   dt        Mass balance equation: sources - sinks F E P F L D in out m   F Atmospheric lifetime:  out Fraction lost by export: f     F L D F L D out out 1 F L D 1 1 1       out Lifetimes add in parallel:     m m m export chem dep 1     Loss rate constants add in series: k k k k  export chem dep

SPECIAL CASE: SPECIES WITH CONSTANT SOURCE & 1 st ORDER SINK & NO TRANSPORT -> ANALYTICAL SOLUTION dm S         kt kt S km m t ( ) m (0) e (1 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 m g S/k: quasi steady state

EXAMPLE : GLOBAL BOX MODEL FOR CO 2 (Pg C yr -1 ) SIMPLE CASE: NO ATMOSPHERIC CHEMISTRY & NO TRANSPORT (GLOBAL) IPCC [2001] IPCC [2001]

PUFF MODEL: FOLLOW AIR PARCEL MOVING WITH WIND C X ( x, t ) In the moving puff, dC wind dt     X E P L D C X ( x o , t o ) …no transport terms! (they’re implicit in the trajectory) Application to the chemical evolution of an isolated pollution plume: C X,b C X dC dt       X E P L D k ( C C ) In pollution plume, dilution X X b ,

TWO-BOX MODEL defines spatial gradient between two domains F 12 m 2 m 1 F 21 dm dt       1 E P L D F F Mass balance equations: 1 1 1 1 12 21 (similar equation for dm 2 /dt ) If mass exchange between boxes is first-order: dm dt       1 E P L D k m k m 1 1 1 1 12 1 21 2 e system of two coupled ODEs (or algebraic equations if system is assumed to be at steady state)

EULERIAN MODELS PARTITION ATMOSPHERIC DOMAIN INTO GRIDBOXES This discretizes the continuity equation in space Solve numerically continuity equation for individual grid-boxes • Detailed chemical/aerosol models can presently afford -10 6 gridboxes • In global models, this implies a horizontal resolution of ~ 1 o (~100 km) in horizontal and ~ 1 km in vertical • 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) • Transport large number of points with trajectories from input meteorological data base (U) + random turbulent component (U’) over time steps D t • Points have mass but no volume • Determine local concentrations as the number of points within a given volume position • Nonlinear chemistry requires Eulerian mapping at t o + D t every time step (semi-Lagrangian) U’ D t PROS over Eulerian models: • no Courant number restrictions U D t • no numerical diffusion/dispersion position • easily track air parcel histories t o • invertible with respect to time CONS: • need very large # points for statistics • inhomogeneous representation of domain • convection is poorly represented • nonlinear chemistry is problematic

LAGRANGIAN RECEPTOR-ORIENTED MODELING Run Lagrangian model backward from receptor location, with points released at receptor location only backward in time • Efficient cost-effective quantification of source influence distribution on receptor (“footprint”)

BACK ON EULERIAN MODELS …

OPERATOR SPLITTING IN EULERIAN MODELS Reduces dimensionality of problem • Split the continuity equation into contributions from transport and local terms:       C C dC   i i i           t t dt TRANSPORT LOCAL   dC     i Transport advection, convection: U C   i   dt TRANSPORT  Local chemistry, emission, deposition, aerosol processes:   dC   i C C P ( ) L ( )   i i   dt LOCAL … and integrate each process separately over discrete time steps:  D   ( ) (Local)•(Transport) ( ) C t t C t i o i o 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)

SPLITTING THE TRANSPORT OPERATOR • Wind velocity U has turbulent fluctuations over time step D t :   U ( ) t U U '( ) t Time-averaged Fluctuating component component (stochastic) (resolved) • Split transport into advection (mean wind) and turbulent components:    C air density 1       i U C K C    K turbulent diffusion matrix i i t advection turbulence (1 st -order closure) • Further split transport in x, y, and z to reduce dimensionality. In x direction:     C C 1 C     i i i u ( K ) U ( , , ) u v w      xx t x x x turbulent advection operator operator

SOLVING THE EULERIAN ADVECTION EQUATION   C C   i i u   t x • 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 u D t/ D x < 1 … limits size of time step • Addressing other requirements (e.g., positivity) introduces non-linearity in advection scheme