Fundamentals of Atmospheric Chemistry Modeling Guy P. Brasseur National Center for Atmospheric Research Boulder, CO Fundamentals of atmospheric chemistry modeling Model Philosophy Fundamantal Equations Types of models Numerical Solutions Examples of Model Results Data Assimilation and Inverse Modeling Acknowledgements Johann Feichter, MPI-M S. Freitas, INPE/CPTEC Claire Granier, CNRS and CIRES. Douglas Kinnison, NCAR John Mitchell, UKMO Tim Palmer, ECMWF Gabrielle Petron, NCAR Martin Schultz, MPI-M Philip Stier, MPI-M Part 1. Model Philosophy (General Issues) What is a Model? A model is: an idealized representation or abstraction of an object with the purpose to demonstrate the most relevant or selected aspects of the object or to make the object accessible to studies a formalized structure used to account for an ensemble of phenomena between which certain relations exist. Some kind of prototype, image, analog or substitute of a real system. An object that is conceptually isolated, technically manipulated and socially communicated. What is a Model? Our brain makes continuously models of what it perceives; these models may not capture the full complexity of a system and may be subjective. Exploratory models have been developed to help establish theories, and to build a consensus around these theories (ex: Quantum mechanics, relativity) Standard physical models are using mathematical representations of the established fundamental laws to predict the behavior of a system (ex. weather prediction). What is a Model? Models can be used to generate knowledge. They do not produce new concepts or laws that are not already included in the model formulation or input, but, by combining a large amount of information, they produce a system behavior that cannot be anticipated from simple considerations. Models are therefore used as diagnostic tools to analyze a system and understand observational data, or as prognostic tools to predict the behavior of a system under yet unknown situations. What is a Model? Models are often abstractions of reality, and are often associated with the concept of metaphor. They often capture limited aspects of the functioning of a system; they simplify reality and focus on a particular issue; they may not be fully “objective” and may “embellish” reality. Developing models can therefore be regarded as equivalent to writing essays in literature. In complex mathematical models, the solutions of the system are not easily obtained. Since in most cases, no solution exists, numerical approximations must be found. Supercomputers are needed to simulate the most complex systems. What is a Model? Purpose of models: To obtain a theoretically or practically manageable system by reducing its complexity and removing details that are not relevant for specific consideration. Citation by Alexander von Humbolt (The Cosmos): “By suppressing details that distract, and by considering only large masses, one rationalizes what cannot be understood through our senses”. What is a Model? Example 1: Architecture Representation of a building at the scales of a shoe box Wood+acryl instead of concrete, glas, etc. Overview of the object and its relation to the environment No details http://www.werk-plan.de/ What is a Model? Example 2: Fashion The ideal person to present a dress in the spirit of the designer True scale Flawless/perfect http:// What is a Model? Example 3: Climate Model Climate model are a mathematical abstraction of the observed real world Climate models use quantitative methods to simulate the interactions of the atmosphere, oceans, land surface, and ice They follow theoretical principles and observed relationships Model = simplified image representing the relevant features http://www.solarviews.com/cap/earth/ The Earth Simulator in Japan What is a Model? It is often assumed that a system is deterministic and therefore predictable once initial conditions are specified. de Laplace: The present state of the universe should be viewed as the effect of the past state and the cause of the state that will follow. von Humboldt: The structure of the universe can be reduced to a problem of mechanics. Modern view: Not all aspects of the natural and social behavior are predictable, and new formulations must developed (stochastic, systemic approaches, etc.) What is a Model? The deterministic assumption may be correct for certain processes (Newton’s apple), but may not be in other cases (turbulent flow). The weather is predictable for a limited time range (10-15 days, see Lorenz). Climate is believed to be predictable for a longer period, but this remains a debated question. Ensembles of simulations are performed to account for the internal variability of the model; means and variance are derived. Multi-model ensemble simulations are also performed to estimate the uncertainty in the predictions Ensemble of precipitation changes (Europe, winter) Precipitation changes (Europe, DJF) Different Types of Models Conceptual Models that help to assess the consequences of some hypotheses. These models are usually very simple and focused on some issue, but trigger interest and sometimes new research. There is no attempt to reproduce perfectly the real world. Examples: The Daisy model of Lovelock (the Earth acts as a thermostat). Detailed Models that try to reproduce as closely as possible the real world. Their success depends on the level of fidelity in representing real situations. Examples: Numerical Weather Forecast Models. What is a model? In geosciences, models are used to study the physical, chemical, and biological processes in the global environment, and to describe the complex nonlinear interactions and feedbacks that affect the Earth system. MPI-M EARTH SYSTEM MODEL MOZART Atmospheric Chemistry HAM Aerosols ECHAM5 JSBACH Land surface Atmospheric Physics MPI-OM Ocean Physics HAMOCC5 Ocean Biogeochemistry What is a Model? Simulation modeling represents a way to create virtual copies of the Earth in cyberspace. These virtual copies (often supported by computing devices) can be submitted to all kinds of forcings and experiments without jeopardizing the true specimen. For example, it is possible to explore the domains in the Earth system “phase space” that are reachable without creating catastrophic and irreversible damage to mankind. CO2 EMISSIONS PROFILES under the IPCC SRES scenarios Temperature change, A2 scenario Cubasch et al, 2001 Boundary and Initial Conditions The evolution of a system is often determined by processes that occurred prior to the temporal domain under consideration. This influence is expressed by initial conditions. Example: Current weather in numerical weather prediction models; Initial state can be based on observation, and may require complex and expensive data assimilation procedure. The evolution of a system depends also on external forcing. Example: winds at the surface of the ocean (for an ocean model) or surface emissions of chemical trace species in a chemical transport model. Regional (limited domain) models are very much affected by lateral boundary conditions. Boundary and Initial Conditions Initial conditions may have a strong influence at the beginning of the simulation, while boundary conditions may have the largest influence at a later stage of the integration. Weather prediction is a “initial value” problem (importance of the data assimilation to initialize the problem) Climate prediction is often regarded as a boundary condition problem. However, seasonal forecast is very dependent on the initial state of the system. Although the statistical mean of the climate system appears to be rather predictable, the details of the dynamical evolution of the system depends strongly on the initial condition (and other parameters). Ensembles of realizations must be produced. Part 2. Fundamental Equations Variables and Equations in an Atmospheric (Physical) Model Variables: Pressure p Density Temperature T Wind components (u, v, w) Equations: Momentum equation (3 components) Thermodynamic equation Continuity equation Equation of state (perfect gas) Fundamental Equations Momentum equations on a rotating sphere: Express the wind acceleration in response to different forces: gravity, gradient force, Coriolis force, dissipation Thermodynamic equation: Expresses the conservation of energy; importance of diabatic heating by absorption and emissions of radiative energy (solar and terrestrial), and of adiabatic processes (e.g., compression of air) Continuity equation: Expresses the conservation of mass Fundamental Equations Governing the Atmosphere Evolution v 1 v v p gk 2 v F visc t a (1), equation of motion a a v t (2), air mass conservation v Q t (3), first law of thermodynamics rn v rn Qrn t (4), water mass mixing ratio conservation s v s Qs (5), gases/aerosols mass mixing t ratio conservation Q represents the loss/production rate S. Freitas, CPTEC, Brazil Momentum Equation in an Inertial Frame dV/dt - (1 / )p [2 V ] geff ( / ) V 2 where V = (u, v, w) are the 3 components of the wind velocity p is the pressure (pressure gradient force) is the angular rotation velocity of the Earth (Coriolis force) geff is the effective gravity acceleration (corrected for the effect of the Earth’s rotation) is the air density t is time The last term accounts for viscosity in the fluid. Hadley Cell Circulation: Past, Present and Future Generalized atmospheric circulation in the Indian Ocean during the Northern Hemisphere summer Thermodynamic equation T T Q (d )w v T t z cp Heat advection Adiabatic heating Diabatic heating/cooling Sources of diabatic heating/cooling Absorption of solar radiation and energetic particles (e.g. ozone) Chemical heating through exothermic reactions (A + B -> AB + E) Collisions between ions and neutrals (Joule heating) IR cooling (e.g. CO2 and NO) Airglow Solar UV Energy Deposition in the Atmosphere Continuity Equation ( v) 0 t where is the mass density of air v is the wind velocity vector Continuity equation for Chemical Species Mathematically describes the dynamical and chemical processes that determine the distribution of chemical species flux form: Transport i ( i v) Si t advective form : Chemical forcing f i S v f i i t a where, i is the mass (or number) density of species i a is the air mass (or number) density f i i is the mass (or volume) mixing ratio a Si is the production and loss rate of species i v is the wind velocity vector Chemical Composition of the Atmosphere Concentration of atmospheric trace gas i: di i i i i dt t emission t deposition t transport t chemistry Model Resolutions R15 T42 T85 T170 Orography Depending on the model resolution, the landscape will be resolved with more or less detail. Example: The altitude of the Alps is about 350 m in the T21 resolution (left)! At 1°x1° (right) the Alps extend to altitudes of about 1.2 km. Obviously, this will impact the flow of air! Note that even a 1x1 grid is far from sufficient to resolve valley flow. Vertical Coordinate System Vertical coorinates are usually given either as constant pressure levels (p), terrain following „“ levels, „hybrid“ coordinates (a mixture between p and ). Sometimes, z coordinates (alitudes) are used. The definition of coordinates is: p ps ... =0.985 =1 I.e. the actual pressure of a specific model level depends on the surface pressure for this grid box (and changes with time). The use of coordinates facilitates the formulation of the (physical) conservation equations (see Hartmann, 1994). Some models number the levels from top to bottom, in others it is bottomtop. Hybrid levels are defined as pi = A·p0+B · ps, where p0 is a constant reference pressure (100000 Pa). Some sub-grid process involved at gases/aerosols transportation 3D Eulerian model grid box mass inflow mass outflow z ~ 20-30 km convective transport by deep cumulus convective transport by shallow cumulus diffusion in the PBL source wet deposition dry deposition x ~ 10-100 km S. Freitas, CPTEC, Brazil Sub-grid Convective Transport Cloud venting is a very important mechanism transporting pollutants from the PBL to the upper levels, affecting the chemistry of troposphere and the biogeochemical cycles. 12km deep subsidence shallow 4 km updraft downdraft S. Freitas, CPTEC, Brazil updraft Updraft detrainment Static control: 1D cloud model Environmental subsidence Lateral entrainment Lateral detrainment Downdraft detrainment S. Freitas, CPTEC, Brazil Mass Conservation Equation 1 m ( z ) m ( z ) z m ( z ) m ( zb ) ( z ) m ( z ) : cloud base mass flux b ( z ) : normalized mass flux / : entrainment/detrainment mass rates ztop updraft downdraft zb,d zdet zb 1 S. Freitas, CPTEC, Brazil u 1 d Model output for PM2.5 column – Aug 2002 : South American and African biomass burning plumes From INPE/CPTEC, Brazil Part 3. Types of ChemicalTransport Models Types of (atmosphere) models Box (compartment) models: understand the principles of feedback cycles 0D (point) models: detailed analysis of the chemical tendencies for a given situation; analysis of sensitivities 1D column models: development of parameterisations 1D Lagrangian (trajectory) models: transport studies 2D (Eulerian) models: zonal mean state of the atmosphere (often in stratosphere) 3D (Eulerian) models: detailed description of several processes in time and space Box models Example: A very simplified box model of the global carbon cycle fossil fuel combustion 6 TgC/yr Atmosphere 615 TgC 60 90 61 92 Land Biosphere Surface Ocean 730 TgC 840 TgC 0.2 0.2 Sediments 90,000,000 TgC dmCO Atm 2 dt respiratio n photosynthesis ocean release ocean uptake fossil fuel emissions 0-D (point) models Idea: investigate the chemistry in an „air parcel“ without regarding advection or diffusion processes Long-lived compounds treated as boundary conditions; often run as „steady state“ simulation Advantage: computationally very fast, allows for comprehensive chemical mechanism, Monte Carlo simulations, etc. Disadvantage: does not take transport into account NOx O3 HO2 2-dimensional models This type of model has been used primarily in stratospheric applications, because there the assumption of zonally homogeneous fields is closer to reality than in the troposphere, where continents and emission sources produce large meridional gradients. Example: 3-dimensional Eulerian models This model type represents the most comprehensive, but also computationally most expensive type of models. The earth‘ atmosphere is divided into thousands of „grid boxes“ of more or less regular shape. Examples: Grid box boundaries over Europe for a „T21“ grid with 64x32 boxes globally (left), and a 1°x1° grid (right) Part 4. Numerical Solutions Numerics Equations, which do not have analytical solutions, are solved by numerical approximations. In global models, one uses Finite Difference Methods Finite Volume Methods Spectral Methods A Model Grid: Solving the equations on specified grid-points Finite Difference Methods In these methods, the space derivative are replaced by finite difference approximations, and the solutions are produced on specified grid points. For example, df/dx is approximated by at grid point xj [f(xj + dx) – f(xj – dx)]/ 2 dx with a truncation error of O(dx2), if dx is the grid size Different algorithms exist to solve the differential equation df/dx = F (f(x), x). Explicit methods (F is evaluated at point x) require very small step dx to provide stable and accurate solutions; Implicit methods (F is evaluated at point x + dx) are more difficult to solve, but the solution is unconditionally stable. Spectral Methods On the sphere, functions can be expressed as a combination of periodic functions such as an infinite Fourier expansion. In practical cases, only a limited number of terms are retained (truncation). Thus, the contributions of the basis function beyond a certain wavenumber are ignored. The fields are expressed by the coefficients of the Fourier series. Spectral General Circulation Models frequently use a spherical harmonics basis for the horizontal expansion of scalar fields with associated Legendre functions. Typical truncations are T21, T42, T63, T106, T170 and beyond. Model Resolution R15 T42 T85 T170 Solving the continuity equation for N chemical species N species leads to N coupled non-linear equations which rarely have an analytic solution. System is solved with numerical methods at discrete locations (“grid-points”) Differentials replaced by finite differences Finite resolution (time or space) implies some transport processes are unresolved (e.g. diffusion) Chemistry and transport handled as separate operations Part 3. Numerical Solutions 1. Transport 2. Chemistry 3. Surface Processes Advection •Desired properties of an advection scheme: • accuracy • stability • mass conservation • monotonicity (shape preservation) • positive definite fields • local • efficient •Reviews of transport algorithms are given by Oran and Boris (1987), Rood (1987), etc. •Three groups of algorithms: •Eulerian •Lagrangian •Semi-Lagrangian Advection I: Eulerian Methods Assume a property (such as the concentration) than is transported in direction x with a constant velocity c example : one - dimensional advection equation F 0 t x flux F c solved e.g. by the ' leap - frog' method : t n n F F j1 j1 x Stable if Courant - Friedricks - Lewy (CFL) n1 n1 j j condition is satisfied : c t 1 x Advection I: Eulerian Methods Courant-Friedrichs-Lewy (CFL) condition: c t x Const , with Const 1 The time step must be small enough, so that an air parcel does not pass through more than 1 grid box during one time step. This is a major restriction for many global models beacuse near the pole, the CFL condition is often violated unless very small timesteps are adopted. Eulerian methods are routinely used in regional models. Solution: Modified grids towards high latitudes or other algorithms Advection I: Eulerian Methods Other discretizations are possible: The Euler forward (explicit) scheme is unconditionally unstable The Upwind method is diffusive The Leapfrog method is not monotonic Improved methods: Smolarkiewicz, Bott, Prather. The CFL condition must be verified to ensure stability. Only nonlinear algorithms produce stable solutions, maintain steep gradients, and preserve monotonicity. Advection I: Eulerian Methods The Prather Scheme In this method, the transported property (tracer mixing ratio) is expressed in each grid box by a quadratic function in the x, y, and z directions (including cross terms). This function is decomposed into orthogonal polynomials over each grid box. Zeroth, first and second order moments are calculated over each box. Transport is performed sequentially in the 3 directions x, y, and z. The first step is to decompose the moments for each gridbox between the fraction for the gridbox that will be moved by advection into the neighboring box, and the fraction that will remain in the original box. Advection I: Eulerian Methods The Prather Scheme In the second step, which represents the advection in 1 direction, new moments are calculated in each grid box through the addition of the moments calculated at the previous timestep in the two adjacent sub-grid boxes that contribute to the tracer in a grid box at the new timestep. Dividing of the moments in a given grid box in submoments, and reforming the moments (by addition of submoments) after an advection step, guarantees conservation of moments (i.e., mass) during the advection process. Advection II: Lagrangian Methods In Lagrangian schemes, distinct air parcels, in which tracers are assumed to be homogeneously mixed, are followed as they are displaced by the winds. In the absence of source/sinks processes, the tracer mixing ratio remains constant in the air parcel. Lagrangian methods are relatively simple in concept and are not subject to spurious diffusion. Errors can, however, accumulate over the integration. Typically 100,000 parcels are used in a global transport model. Parcels may “bunch up” in certain areas and leave others without parcels to track. This problem is avoided in the Semi-Lagrangian methods where at every new time step, one examines the back trajectory of the parcel that arrives at a given grid point of the model. Advection III: Semi-Lagrangian Transport In semi-Lagrangian transport schemes, a backward trajectory is computed for each corner point of a grid cell. The new mixing ratio f of species i is then computed by interpolation („remapping“) of the concentration field of timestep t0 onto the model grid at timestep t. Arrival point AP (x,t) (x0,t0) Thus fAP (x,t) = fDP (x0, t0) The location of the upstream departure point is found by solving the equation dx/dt = v (x, t). This equation has to be solved iteratively since v varies with along the back trajectory that needs to be determined. Departure point DP Advection III: Semi-Lagrangian Transport x 0 x t v(x,t)dt tt (x, t) trajectory Accuracy depends greatly on Interpolation scheme used. Common in modern GCMs (x0, t-∆t) Advection III: Semi-Lagrangian Methods The accuracy of the semi-Lagrangian scheme depends on the accuracy of The determination of the location of the departure point (DP) The determination of the tracer mixing ratio at the DP, and hence on the interpolation scheme that is used. A linear interpolation leads to excessive smoothing. Cubic interpolation is preferred, but is computationally expensive. The major advantage of the SLT method is that it is not restricted by the CFL condition, and the timestep is chosen by accuracy considerations. It gives minor phase errors, minimizes computational dispersion, preserves shapes and can handle sharp discontinuities The major disadvantage of the SLT scheme is that it does not formally conserve integral invariants such as total mass or energy. Advection III: Conservative SemiLagrangian Methods To address this issue, rather than considering variables at specific grid points, one can transport integral quantities or average values over finite cell volumes (or cell areas in the case of 2-D formulations). In finite-volume-based Semi-Lagrangian methods, the value of the advected field at a new time level is just the average value of the departure cell defined by its upstream position at the previous timestep. Lin and Rood (1996) have developed a mass conservative finite volume semi-Lagrangian method, in which the boundaries (“ departure walls” rather than “departure points”) of the grid volumes are transported to the next step (“arrival walls”). Mass is conserved in the box during a timestep. The CFL restriction does not apply. Un-resolved transport: Diffusion example : one - dimensional diffusion equation K t x x K 0 is the so - called diffusion coefficient Fully explicit solution : n n1 j j t K n n n 2 2 j1 j j1 x only stable if 2Kt 2 1 x Fully implicit solution : n n1 j j t K n1 n1 n1 2 2 j1 j j1 x For more than one dimension, each dimension is treated separately Part 3. Numerical Solutions 1. Transport 2. Chemistry 3. Surface Processes Chemistry: Solving df/dt = S/ Simplest method is fully explicit : f n1 f n t S(t n ,f n ) / a Euler Forward f n1 expressed in terms of known quanities Requires very small time - steps. Fully implicit is stable for any t : f n1 f n t S(t n1 ,f n1 ) / a Euler backward However, S contains non - linear terms, and accuracy is comprimised for large t. Iterative techniques are often used to improve the accuracy of implicit methods. Prominent is the Newton-Raphson iteration which requires that the Jacobian matrix of the chemical system be calculated. The convergence is achieved for sufficiently small timesteps Chemical forcing (S) (i.e. production and loss) First-order forcing Photolysis, airglow, … S(f,x,t) a e(x,t) A(x,t) f B(f,x,t) f External forcing Independent of f Non-linear forcing Bi-molecular and tri-molecular reactions For N species, A and B are NxN matrices Chemistry: Solving df/dt = S/ Shimazaki writes the source term S(f , x, t ) a e(x, t ) B(f , x, t ) f and f(nm11) [f n e (f(nm)1 x , t n 1 )t ] /[1 B(f(nm)1 , x , t n 1 )t ] Iterations (m) are performed for nonlinear cases. Hesstvedt proposes a semi-analytic solution fi n 1 (fi ) ss [fi (fi ) ss ] exp( Bi (fi n , t n 1 )t n where (fi )ss ei ( x, t ) / Bi (fi n 1 , x, t ) is the steady-state value. Iterations may be needed. Chemistry: Solving df/dt = S/ A multi-step method very appropriate for “stiff” systems has been developed by Gear (1971). This algorithm is composed of the so-called backward difference formulas up to order six. The method is extremely robust and stable but does require solving nonlinear algebraic systems (like Euler backward algorithm). Time step and order of the method are continuously adapted to meet user-specified solution error tolerances. Codes require much computer memory and tine; not practical for multi-dimensional models. Quasi steady state approximation If the loss of a chemical species is much faster than its production (and fast compared to the length of a day), it is generally a reasonable assumption to assume that it is in „dynamic steady state“, i.e. dX/dt = 0. Example: dO 1D jO1D O3 k1 O 1D M k2 O 1D H 2 O dt dO 1D 0 dt thus O D 1 jO1D O3 k1M k2 H 2O Validity of QSSA reasonable good Chemical Families A „trick“ to make the QSSA approach work for longer-lived species as well is the definition of chemical „families“: Species are grouped together so that the fast reactions don‘t change the group concentration. Example: NOx = NO + NO2 Emissions NO +O3, +HO2 +h NO2 +OH, deposition dNO Emissions j NO2 NO2 NOk1 O3 k 2 HO 3 dt dNO2 NO k1 O3 k 2 HO 3 j NO2 NO2 k3 NO2 OH deposition dt dNOx dNO dNO2 Emissions k3 NO2 OH deposition dt dt dt Lagrangian models Lagrangian (or trajectory) models are in fact 3-dimensional in that they take account of the horizontal and vertical transport of an air parcel. „We define a transition probability density Q(X0,t0|X,t), such that the probability that the fluid element will have moved to within volume (dx,dy,dz) centered at location X at time t is Q(X0,t0|X,t) dx dy dz.“ (Jacob, 1999) t0 t While this approach implicitely accounts for small-scale processes like diffusion or convection, it has disadvantages, because it neglects mixing of air parcels, and the quantity Q is not directly observable. One way of using the lagrangian technique efficiently is the particle model, where Q is approximated by a large number of pointlike particles (~10000), and a trajectory for each particle is computed using stochastic methods to simulate diffusion. Example: Stohl et al., 2000. Part 3. Numerical Solutions 1. Transport 2. Chemistry 3. Surface Processes Model surface description Rstomatal ∫(PAR, soil moisture) z (~ 30 m) z0 depth (~ 60 m) Sea Sea ice Wet surface Bare soil Snow/ice 5 soil layers 3.750 (~ 300 km) Soil moisture Surface exchanges: emission-deposition d c c c dt t em ttchem turb t t chem dep ttemiss Atmospheric model surface layer ~ 60 m chemistry turbulence Vegetation model dry deposition emissions Vegetation and wet skin fraction crown-layer ~ 0.5-15 m canopy-soil layer Emissions (1) In current models, emissions are typically specified as monthly mean mass fluxes. These are read from file and interpolated to time t. The compilation of emissions inventories is a labour-intensive task, and these inventories still constitute one of the major uncertainties in modeling. Today, first attempts have been made to estimate emissions based on satellite and insitu observations and using „inverse“ models. Emissions (2) Typical categories of „bottom-up“ emissions inventories include: fossil fuel combustion biofuel combustion vegetation fires biogenic emissions (plants and soils) volcanic emissions oceanic emissions agricultural emissions (incl. fertilisation) etc. Example emissions inventory after gridding Emissions of Carbon Monoxide Emissions of Nitrogen Oxides Vegetation fire emissions „biomass burning“ Classic approach: use forest fire statistics, observations of „fire return intervals“, and average parameters for fuel load and burning efficiency, and derive a climatological inventory. Disadvantage: vegetation fires occur episodically and exhibit a large interannual variability. New approach: Use satellite observations of burned areas and measured or model-derived parameters for the available biomass and the fire behaviour. The Global Wildfire Emission Model (GWEM) J. Hoelzemann Ei A F EFi area combustion burnt efficiency fuel load emission factor Biomass Burning NOx Emissions, September Monthly Carbon Monoxide Emission Estimation for 2002 Hybrid remote sensing fire products: GOES WF_ABBA AVHRR and GOES (INPE) MODIS (NASA) September August Freitas et al 2005 Duncan et al.2003 EDGAR 3.2 Anthropogenic NOx Emissions Chemical Weather seen from Space (Dry) Deposition Transport of gaseous and particulate species from the atmosphere onto surfaces in the absence of precipitation Controlling factors: atmospheric turbulence, chemical properties of species, and nature of the surface Deposition flux: F vd C vd: deposition velocity C: concentration of species at reference height (~10 m) Resistance analog 1 vd Ra Rb Rc Ra = aerodynamic resistance. Rb = quasi laminar boundary layer resistance Rc = canopy resistance atmosphere Ra Rb Rc surface Seinfeld & Pandis, 1998 Dry deposition velocity Ra Resistance of: Rb Resistance of: dynamic sublayer 1 Vd Ra Rb Rc Rc Resistance of: wet surface interfacial sublayer vegetation sublayer laminary sub-layer stomata dry surface Wet deposition Cloud Water evaporation nucleation dissolution rain formation particles in air reactions below-cloud scavenging evaporation evaporation chemical reactions gaseous species in air below-cloud scavenging Rain, snow evaporation chemical reactions interception Wet deposition after Seinfeld&Pandis, 1998 Part 4. Examples MOZART-2: Model set-up Uses analysed winds (e.g. ECMWF, NCEP) or climate model output (T, q, u, v, ps, ...) Standard chemistry scheme comprises of 65 species and 170 reactions. Chemistry is easily adaptable by means of a preprocessor code Runs efficiently on almost any computer platform (parallel and vectorized) Flexible output specification; postprocessing tools available Brasseur et al., JGR, 1998; Horowitz et al., JGR, 2004. Parameterisations Model physics according to Rasch et al., 1997 Boundary layer: Holtslag and Boville, 1993 Advection: Lin and Rood, 1996 Convection: Zhang and McFarlane, 1995; Hack, 1994 Dry deposition: Wesely, 1989, Hess et al., 2000 Scavenging: Giorgi ad Chameides, 1985; Brasseur et al., 1998 Lightning NOx production: Price, Penner, and Prather, 1997 Model resolution and computer resources Regular grid, standard resolution approx. 1.9°1.9° (19296 grid boxes), 31 vertical levels 1000-10 hPa Code allows for arbitrary regular grid. Tested between 3.8°3.8° (9648 grid boxes) and 1.1°1.1° (256128 grid boxes) Hybrid coordinates (sigma-pressure) for vertical grid Standard run uses about 4GB memory and needs 120 CPU hours for one simulation year (8 CPUs, NEC SX-6) Results from simulation May 2003 Ozone Lindenberg, May 2003 1890 CO emissions 2000 2100- A2 1890 NOx emissions 2000 2100-A2 Surface Ozone July 1890 Surface Ozone July 2000 Surface Ozone July 2100 A2 Scenario SRES CO Changes in the surface concentration between 2000 and 2100 July Scenario A2 No climate change NOx O3 AEROSOLS HAM: The Aerosol Model Component • Resolves aerosol distribution by seven log-normal modes • Components: Sulfate, Black Carbon, Organic Carbon, Sea Salt, Dust composition mixing state size distribution HAM - Aerosol Representation Considered Compounds: Sulfate Black Carbon Organic Carbon Sea Salt Mineral Dust Resolve aerosol size-distribution by 7 log-normal modes Each mode is described by three moments 2. ECHAM5-HAM Global Aerosol Distribution 3.1 Global Distribution Part 5. Inverse Modeling Data Assimilation and Inverse Modeling Data are often used to independently verify model results. However, data can also be used to constrain a model. Recognizing that errors are associated with both observational data and models, the most probable solution is probably located “between” the observational data and the model values. Key in the search for the optimal value is the quantitative estimate of these errors. Data assimilation procedures are now applied to chemical quantities measured for example from space. Data Assimilation and Inverse Modeling Forward models often attempt to calculate relatively well-known quantities based on poorly quantified data. Example: When calculating the atmospheric concentration of chemical species based on specified emissions, the atmospheric concentration is much better known than the emissions used to ‘force’ this “forward” model Therefore, what is often more interesting is to derive the emissions from our knowledge of the atmospheric concentration: This refers to inverse modeling. Principle of Inverse Modeling The discrepancies between the observed and the modeled CO distributions are used to optimize poorly known parameters in the model – here, CO surface emissions. March 2000 Total column of CO : MOZART2 (top) and MOPITT (bottom) MAR MOZART2, CO-column, scale=1.e17 60 40 27.5 .0 25 25 .0 20. 0 22.5 17 .5 20 20. 0 15.0 30.0 17.5 0 20. 25.0 .5 22 20 .0 17 .5 0 25. 27 .5 15.0 22.5 0 15.0 12.5 17 .5 12.5 -20 27.5 -40 -60 -100 22.5 17 .5 25.0 0 20. .5 27 20.0 .5 .0 273 0 .5 22 22 .5 17 .5 0 20. .5 17 0 15. 15 .0 0 25 .0 .0 25 20 CO-column, scale=1.e17 25 .0 27 .5 100 22.5 40 MAR MOPITT, 25. 0 22 .5 60 0 Longitude 20.0 -20 12 .5 -40 17. 5 0 15. .0 10 10.0 -60 -100 0 Longitude 100 Modeled distribution of [CO] 2. Observed distribution of [CO] Tropospheric Chemistry and Transport discrete equations Inverse modeling 1. A priori Emissions xb 3. MOPITT data product Hypothesis Transport in the model is perfect (for the CMDL/IMAGES inversion) Statistics of the observations known (mean and cov matrix) Statistics of the a priori sources known All Errors are gaussian and independent Chemistry weakly non linear. CO sink not optimized. a posteriori sources close ENOUGH to a priori no big change in [OH] Use linearized version of the model Synthesis Inversion No : number of observations Ne : number of emission variables to be optimized Ne < No to have an over-determined problem Monthly Emissions are aggregated over continents or oceans (see next slide) Observation Matrix M : ymodel=Mx M links the sources to [CO] at observed locations [CO]model|station j = S Mji . xi = S [CO]ji Observations observations Ascension Island total modeled [CO] with xb 100 + agricultural waste burning and fuel wood use 90 + forest and savanna burning over Southern Africa + forest and savanna burning over Southern America + forest and savanna burning in Northern Hemisphere and Oceania + technological activities 80 70 [CO] ppbv Modeled total [CO] 60 50 40 30 + vegetation/soil 20 oceanic emissions 10 0 1 2 3 4 5 6 7 Month 8 9 10 11 12 Problem in timing !!! Biomass burning South Africa The solution xa of the inverse problem minimizes a cost function 1 1 J (x) (M(x) y) O (M(x) y) (x xf ) Bf (x xf ) T T Symbol Signification Dimension xa a posteriori emissions Ne xf a priori emissions Ne y Observed concentrations No Bf COV Errors on the a priori emissions Ne*Ne Ba COV Errors on the a posteriori emissions Ne*Ne O COV Errors on the observed concentrations No*No M Model Operator + Linear Interpolation = Observation Matrix ymodel=Mx No*Ne J (x) (M(x) y)T O1 (M(x) y) (x xf )T Bf 1 (x xf ) Weights ~“Inverse of Uncertainties” [Distance ( [CO] modeled – [CO] observed )]2 [Distance (a priori emission – a posteriori emissions)]2 Simple Geometry Observed [CO] A priori modeled CO A posteriori modeled CO xa M(xa) xf EMISSIONS space y M(xf) Observation space Optimal Interpolation Analytical solution xa exists for linear problem (or weakly non-linear) x a x f K ( y Mx f ) K B f M (MB f M O) T T y-Mxf : residual 1 B a = ( I - KM )B f Ba : a posteriori uncertainties for xa = “new information” K : gain matrix K (Ne*No) projects the residual in the emissions space Comparison of MOZART results with in situ CMDL data CMDL data post prior + a priori modeled [CO] * a posteriori modeled [CO] Conclusions The combined use of MOPITT data together with the MOZART model and a priori inventories for CO emissions = promising tool for the optimization of CO sources. Several prominent features are reproduced : biofuel in Asia. biomass burning in Australia. change in the timing of biomass burning emission peak in SH. • The optimized emissions have been validated using independent data Thank you! The End Bibliography Holton, J.R., An Introduction to Dynamic Meteorology, Academic Press, San Diego,1992. Peixoto, J.P., and Oort, A.H., Physics of Climate, Springer, New York, 1992. Jacobson, M.Z., Fundamentals of atmospheric modeling, Cambridge University Press, Cambridge, New York, 1999. Brasseur, G.P., Orlando, J.J., and Tyndall, G.S., Atmospheric Chemistry and Global Change, Oxford University Press, Oxford, New York, 1999. Hartmann, D.L., Global Physical Climatology, Academic Press, San Diego, 1994. Durran, D.R., Numerical Methods for Wave Equations in Geophysical Fluid Dynamics, Springer, New York, 1998. Impact of Climate Change on Tropospheric Temperature and Water Vapor Concentration 2000 to 2100 SRES A2 Scenario Temperature Water vapor Impact of Climate Change on NOx Production by Lightning 2000 to 2100 SRES A2 Scenario CO Impact of Climate Change on the Chemical Composition of the Atmosphere (July) 2000 to 2100 SRES A2 Scenario NOx Ozone The ECHAM5-HAM Aerosol Model Sulfur Chemistry ECHAM5 (Roeckner et al., 2003) HAM (Stier et al., 2004) (Feichter et al., 1996) MOZART Chemistry (Horowitz et al., 2003) Size-Dependent Dry- and Wet-Deposition (Ganzeveld et al., 1998; Slinn and Slinn, 1982; Stier et al., 2004) Online emissions of Dust, Sea Salt, and DMS (Tegen et al., 2002; Schulz et al., 2002; Kettle and Andreae, 2000) Aerosol Microphysics M7 (Vignati, Wilson, and Stier, 2004) • • • • • Nucleation of sulfate particles Condensation of sulfate on existing particles Coagulation Inter-modal transfer Thermodynamical equilibrium with water vapour Radiation Module (Boucher and Stier) Cloud Microphysics - Aerosol Activation (Lohmann et al., 1999; Lohmann, 2002; Zhang et al., in press; Lin and Leaitch, 1997; A.-Razzak and Ghan, 2000) 2. ECHAM5-HAM Simulations with the ECHAM5-HAM aerosol-climate model: • Resolution horizontal: T63 1.8 x 1.8 on Gaussian grid vertical: 31 levels from surface up to 10 hPa • Nudging to ECMWF ERA-40 meteorology for year 2000 • AEROCOM year 2000 emission inventory Evaluation of Number Densities Aircraft-campaign composite profiles of aerosol number-concentrations Scotland (27/09/-12/10/2000, 9W-4E, 57N-61N) Chile (23/03/-14/04/2000, 84W-69W, 59S-51S) Measurement data by courtesy of Andreas Petzold and Andreas Minikin (DLR) 3.1 Global Distribution Microphysical Coupling of the Global Aerosol Cycles Response to omission of SO2 emissions from fossil-fuels, industry, and bio-fuels: Annual-mean column-integrated mass change 3.2 Microphysical Coupling Microphysical Coupling of the Global Aerosol Cycles Response to omission of SO2 emissions from fossil-fuels, industry, and bio-fuels: Increased burden of black carbon Increased absorption Decreased internal mixing of black carbon with sulfate Reduced absorption cross-section 3.2 Microphysical Coupling Global annual mean surface air temperature (deviation from 1961-1990) [°C] SRES B1 GHG‘s = const SO4 (anthr.)=0 Constant concentrations (GHG‘s + SO4) observed simulated year Aerosol-Cloud interactions Warm Indirect Aerosol Effects + Lohmann et al. (1999) Glaciation Indirect Aerosol Effect Cloud albedo _ + Cloud cover and lifetime _ Precipitation _ Cloud droplets Lohmann (2002) + + Mixed particles + Ice crystals + Cloud nuclei Aerosol Microphysics + + Aerosols + Emissions + Ice nuclei Chemistry Aerosol Dynamics 4. Aerosol-Cloud Interactions