AIR POLLUTION

ATMOSPHERIC CHEMICAL TRANSPORT MODELS

Why models?incomplete information (knowledge)spatial inference = predictiontemporal inference = forecasting

Mathematical models:provide the necessary framework for integration of our understanding of individual atmospheric processes.

Classification of atmospheric models :

Model Typical domain scale Typical resolution Microscale 200x200x100 m 5 m Mesoscale(urban) 100x100x5 km 2 km Regional 1000x1000x10 km 20 km Synoptic(continental) 3000x3000x20 km 80 km Global 65000x65000x20km 50 km

PHYSICAL LAWS

• Momentum equations

• Air conservation

• Water conservation

ixi

i FBx

p1

dt

du

0dx

)u(d

i

i

ijqi SD

dt

)q(di

• Energy conservation

• Reactive gas conservation

• Notations

)c(g)S(fDdt

)(diiji

ijxnci RD

dt

)c(di

z

Sw

y

Sv

x

Su

t

S

dt

dS

General circulation of the atmosphere

Dimension-based model classification

0-D and 1-D models:little information about a problem or poor data for validation

2-D models:an horizontal dimension is important

3-D models most complete answers are required

0-D models

• Account for– sources

– advection

– diffusion (entrainment/detrainment)

– reaction

– may be enhanced through a lagrangean approach

1-D and 2-D models

• 1-D models– ignore the horizontal

transport and processes

– only vertical processes are modeled

• 2-D models– ignore one horizontal

dimension

General methodology for air quality prediction

General methodology for air quality prediction (ctd.)

• Address the meteorological aspect of the problem

– determine (predict/ use meteorological products) the physical conditions (velocity fields temperatures, radiation etc)

• Identify the chemical processes and develop (include in the framework) numerical models to predict them

• Estimate the initial conditions and run the model in a predictive way

• Use observations to update the initial conditions and the state of the system

Assimilation of Data in Models

• Example– Data assimilation in a tropospheric ozone model

– Physical model

– Observations are provided by air quality monitoring stations and meteorological stations

– Special numerical technique are used to minimize Fobj

)c,...,c(F

)c(Dz

cw

y

cv

x

cu

t

c

ik1i

iiiii

Nt

1k

Ns

1i

2obs,ki

kiobj )cc(F

Assimilation of Data in Models (ctd)

• Minimization of Fobj requires the derivative of F with respect to the initial conditions

• Direct evaluation of the gradient is not feasible due to the large number of components in the initial field (ex. 200x200 km domain with 2km grid size)

• Consider the general model

• with the observations

• The objective function is then

),X(FX i1i

iii )X(HY

Nt

0ii

i1i

Tiiobj ))X(HY(W))X(HY(F

Assimilation of Data in Models (ctd)

• The gradient of the objective function

• The gradient may be efficiently evaluated starting from the left-hand side (i.e. in a reverse manner)

• Then Fobj can be minimized using a standard optimization procedure

N

0i

0ii1_i

Tiiobj FFHW))X(HY(2F

* * * * * * * * * * * ** * * * * * * ** * * * * * * ** * * * * * * *

Assimilation of Data in Models (ctd)

WRAP-UP

• The pollution (chemical) problem needs to be connected to the physical (meteorological) problem

• In short (medium) term forecasts dynamics dominates and need to be properly capture

• In long term (climatic) forecasts the effect of gases on energy budgets are most important

• Data may be readily used to correctly initialize the models and get additional insight