atmospheric chemicalmodeling and data assimilation · atmospheric chemistry mechanisms are the most...

ESA-ESRIN, Frascati, Rome, Italy

18th – 29th August 20031

Atmospheric ChemicalAtmospheric Chemical ModelingModelingand and Data AssimilationData Assimilation

Boris Khattatov

Importance of Atmospheric ChemistryImportance of Atmospheric Chemistry

• Some atmospheric gases (CO2, H2O) trap infrared radiation emitted by the Earth’s surface. Increased concentrations of these gases are likely to lead to global warming since normally this this radiation would have escaped to space.

• Recent medical studies suggests a significant correlation between measured atmospheric pollutants and the rate of mortality recorded the following day.

• Ozone in the stratosphere is of paramount importance to existence of life on Earth due to its ability to absorb harmful ultraviolet rays.



IntroductionThe Earths atmosphere can be thought of as a combustion system where the energy of the sun drives a variety of chemical transformations.

The exact composition of the atmosphere is determined by a complex chemical mechanism that consists of hundreds to thousands of elementary chemical reactions.

Radiation

The process of absorption of a photon by a molecule results in achange in the energy level of the model. In the process the photon disappears.

Photons come in different “colors” or frequencies corresponding to different energies. “Blue” photons have more energy than “yellow” and more energy than “red”.

High energy photons can break molecules to pieces.



Radiation

Sometimes the energy of the photon is high enough to break the absorbing molecule into “pieces”.

Here are examples of photodissociation reactions:

Radiation



Stratospheric Chemistry

Rates of the photodissociation reactions depend on the amount of sunlight (number of photons) and absorption cross-section of the molecule.

These rates are often called photodissociation coefficients orphotolysis rates, J.

Photodissociation

2

[ ]2 [ ]

d OJ O

dt= ⋅2

2[ ]

[ ]d O

J Odt

= − ⋅



Some Photolysis Reactions

The most common bimolecular reactions are usually reactions of the type

Chemical Reactions

The rate of disappearance of reagents, equal to the rate of appearance of the products, is



Chemical Reaction Rates

Usually the rate k of a chemical reaction is a strong function of temperature:

Tri-molecular Chemical Reactions



Ozone ChemistryThe concentration of ozone in the stratosphere is determined by a balance between its production and loss rates.

In purely O2-N2 atmosphere, processes controlling ozone concentration are:

Ozone Chemistry

2 2 2 3 3 3

32 3 3 3

[ ]2 ( ) [ ] 1 [ ][ ] ( )[ ] 2 [ ][ ]

[ ]1 [ ][ ] ( )[ ] 2 [ ][ ]

d OJ O O k O O J O O k O O

dtd O

k O O J O O k O Odt

= ⋅ ⋅ − ⋅ + − ⋅

= ⋅ − − ⋅

J(O2)

k1

J(O3)

k2




Catalytic CyclesCertain trace gas species can destroy ozone catalytically:

Types of ozone destroying chemicals:NOx, Clx, HOx, Brx



Stratospheric ChemistryA more or less minimal set of stratospheric reactions:

k002: O + O3 = 2*O2; k003: O1D + O3 = 2*O2; k004: O1D + N2 = O + N2;k005: O1D + O2 = O + O2; k006: O1D + H2O = 2*OH; k007: O1D + H2 = H + OH; k008: O1D + CH4 = OH + CH3;k009: O + O2 + M = O3 + M; k016: OH + CO = CO2 + H; k017: CH4 + OH = CH3 + H2O; k019: H2 + OH = H2O + H; k020: H + O3 = O2 + OH; k021: H + HO2 = 2*OH; k022: OH + O = O2 + H; k023: OH + O3 = O2 + HO2; k024: OH + OH = H2O + O; k025: OH + HO2 = H2O + O2; k026: HO2 + O3 = 2*O2 + OH; k027: HO2 + O = O2 + OH; k028: HO2 + HO2 = H2O2 + O2; k029: H2O2 + OH = H2O + HO2; k030: H + O2 + M = HO2 + M; k031: CL + O3 = CLO + O2; k032: CL + CH4 = HCL + CH3; k033: CL + H2 = H + HCL; k034: CL + HO2 = O2 + HCL; k035: CL + HO2 = OH + CLO; k036: CL + H2O2 = HO2 + HCL; k038: CLO + O = CL + O2; k039: CLO + NO = CL + NO2; k040: CLO + OH = HO2 + CL; k041: CLO + HO2 = HOCL + O2; k042: HCL + OH = H2O + CL; k043: HCL + O = OH + CL; k044: HOCL + OH = H2O + CLO; k045: CLONO2 + O = CLO + NO3;

k046: CLONO2 + OH = HOCL + NO3; k047: CLONO2 + CL = CL2 + NO3; k048: CLO + NO2 + M =CLONO2 + M; k049: CLO + CLO + M = CL2O2 + M; k050: CL2O2 + M = 2*CLO + M; k053: NO2 + O = NO + O2; k054: NO + O3 = NO2 + O2; k055: NO + HO2 = NO2 + OH; k056: NO2 + O3 = NO3 + O2; k057: HNO3 + OH = NO3 + H2O; k058: HNO4 + OH = H2O + O2 + NO2; k060: NO2 + OH + M = HNO3 + M;k061: NO2 + HO2 + M = HNO4 + M; k062: NO3 + NO2 + M = N2O5 + M; k063: N2O5 + M = NO2 + NO3 + M; k064: HNO4 + M = HO2 + NO2 + M; k065: BR + O3 = O2 + BRO; k066: BR + HO2 = O2 + HBR; k068: BRO + O = O2 + BR; k069: BRO + HO2 = HOBR + O2; k070: BRO + NO = NO2 + BR; k071: BRO + BRO = 2*BR + O2; k072: BRO + CLO = BRCL + O2; k073: BRO + CLO = OCLO + BR; k074: HBR + OH = H2O + BR; k075: BRO + NO2 + M =BRONO2 + M

j001: O2 = 2*O j002: O3 = O2 + O j003: O3 = O2 + O1D j004: HO2 = O + OH j005: H2O2 = 2*OH j006: NO2 = NO + O j007: NO3 = NO2 + O j008: NO3 = NO + O2 j009: N2O5 = NO2 + NO3 j010: HNO3 = OH + NO2 j011: HNO4 = OH + NO3 j012: HNO4 = HO2 + NO2 j013: CL2 = 2*CL j014: OCLO = O + CLO j015: CL2O2 = 2*CL + OO j016: HOCL = OH + CL j017: CLONO2 = CL + NO3 j018: CLONO2 = CL + NO2 + O j019: BRCL = BR + CL j020: BRO = BR + O j021: HOBR = OH + BR j022: BRONO2 = BR + NO3 j026: HCL = H + CL


Photochemical rate of change equation for O:

2 3 2 2

3 2

3 2 2 2

2

[ ] 2* 001* 002* 004* 006*

007* 014* 018* 020*

- 002* * 004* 1 * 005* 1 * - 009* * *

- 022* * 024* * - 027* * - 038*

d Oj O j O j HO j NO

dtj NO j OClO j ClONO j BrO

k O O k O D N k O D O k O O M

k OH O k OH OH k HO O k C

= + + +

+ + + ++ ++

2 2

*

- 043* * - 045* * - 053* * - 068* *

lO O

k HCl O k ClONO O k NO O k BrO O

2 2 2 3 3 3

[ ]2 ( )* 1 * ( )* 2* *

d OJ O O k O O J O O k O O

dt= ⋅ − ⋅ + −



Stratospheric ChemistryA typical set of stratospheric chemical equations:

[ 1:] d[ H ]/d t= j026*HCL + k007*O1D*H2 + k016*OH*CO + k019*H2*OH - k020*H*O3 - k021*H*HO2 + k022*OH*O - k030*H*O2*M + k033*CL*H2

[ 2:] d[ OH ]/d t = j004*HO2 + 2*j005*H2O2 + j010*HNO3 + j011*HNO4 + j016*HOCL + j021*HOBR + 2*k006*O1D*H2O + k007*O1D*H2 + k008*O1D*CH4 - k016*OH*CO - k017*CH4*OH - k019*H2*OH + k020*H*O3 + 2*k021*H*HO2 - k022*OH*O - k023*OH*O3 - 2*k024*OH*OH - k025*OH*HO2 + k026*HO2*O3 + k027*HO2*O - k029*H2O2*OH + k035*CL*HO2 - k040*CLO*OH - k042*HCL*OH + k043*HCL*O - k044*HOCL*OH - k046*CLONO2*OH + k055*NO*HO2 - k057*HNO3*OH - k058*HNO4*OH - k060*NO2*OH*M - k074*HBR*OH

[ 3:] d[ HO2 ]/d t = - j004*HO2 + j012*HNO4 - k021*H*HO2 + k023*OH*O3 - k025*OH*HO2 - k026*HO2*O3 - k027*HO2*O - 2*k028*HO2*HO2 + k029*H2O2*OH + k030*H*O2*M - k034*CL*HO2 - k035*CL*HO2 + k036*CL*H2O2 + k040*CLO*OH - k041*CLO*HO2 - k055*NO*HO -k061*NO2*HO2*M + k064*HNO4*M - k066*BR*HO2 - k069*BRO*HO2

[ 4:] d[ H2O2 ]/d t = -j005*H2O2 + k028*HO2*HO2 - k029*H2O2*OH - k036*CL*H2O2

[ 5:] d[ CL ]/d t= 2*j013*CL2 + 2*j015*CL2O2 + j016*HOCL + j017*CLONO2 + j018 *CLONO2 + j019*BRCL + j026*HCL - k031*CL*O3 -k032*CL*CH4 - k033*CL*H2 - k034*CL*HO2 - k035*CL*HO2 - k036*CL*H2O2 + k038*CLO*O + k039*CLO*NO + k040*CLO*OH + k042*HCL*OH + k043*HCL*O - k047*CLONO2*CL

[ 6:] d[ CLO ]/d t = j014*OCLO + k031*CL*O3 + k035*CL*HO2 - k038*CLO*O - k039*CLO*NO - k040*CLO*OH - k041*CLO*HO2 + k044*HOCL*OH + k045*CLONO2*O - k048*CLO*NO2*M - 2*k049*CLO*CLO*M + 2*k050*CL2O2*M -k072*BRO*CLO - k073*BRO*CLO

[ 7:] d[ HOCL ]/d t = - j016*HOCL + k041*CLO*HO2 - k044*HOCL*OH + k046*CLONO2*OH

[ 8:] d[ HCL ]/d t = - j026*HCL + k032*CL*CH4 + k033*CL*H2 + k034*CL*HO2 + k036*CL*H2O2 - k042*HCL*OH - k043*HCL*O

[ 9:] d[ CLONO2 ]/d t = - j017*CLONO2 - j018*CLONO2 - k045*CLONO2*O - k046*CLONO2*OH - k047*CLONO2*CL + k048*CLO*NO2*M

[10:] d[ OCLO ]/d t= - j014*OCLO + k073*BRO*CLO

[11:] d[ CL2O2 ]/d t = - j015*CL2O2 + k049*CLO*CLO*M - k050*CL2O2*M

[12:] d[ CL2 ]/d t = - j013*CL2 + k047*CLONO2*CL

[13:] d[ NO ]/d t = j006*NO2 + j008*NO3 - k039*CLO*NO + k053*NO2*O - k054*NO*O3 - k055*NO*HO2 - k070*BRO*NO

[14:] d[ NO2 ]/d t = -j006*NO2 + j007*NO3 + j009*N2O5 + j010*HNO3 + j012*HNO4 + j018*CLONO2 + k039*CLO*NO - k048*CLO*NO2*M - k053*NO2*O + k054*NO*O3 + k055*NO*HO2 - k056*NO2*O3 + k058*HNO4*OH - k060*NO2*OH*M - k061*NO2*HO2*M - k062*NO3*NO2*M + k063*N2O5*M + k064*HNO4*M + k070*BRO*NO - k075*BRO*NO2*M

[15:] d[ NO3 ]/d t = -j007*NO3 - j008*NO3 + j009*N2O5 + j011*HNO4 + j017*CLONO2 + j022*BRONO2 + k045*CLONO2*O + k046*CLONO2*OH + k047*CLONO2*CL + k056*NO2*O3 + k057*HNO3*OH - k062*NO3*NO2*M + k063*N2O5*M

[16:] d[ HNO3 ]/d t= - j010*HNO3 + 2*k001*N2O5*H2O(a) - k057*HNO3*OH + k060*NO2*OH*M

[17:] d[ HNO4 ]/d t= - j011*HNO4 - j012*HNO4 - k058*HNO4*OH + k061*NO2*HO2*M - k064*HNO4*M

[18:] d[ N2O5 ]/d t = - j009*N2O5 -k001*N2O5*H2O(a) + k062*NO3*NO2*M - k063*N2O5*M

[19:] d[ O ]/d t= 2*j001*O2 + j002*O3 + j004*HO2 + j006*NO2 + j007*NO3 + j014*OCLO + j018*CLONO2 + j020*BRO - k002*O*O3 + k004*O1D*N2 + k005*O1D*O2 - k009*O*O2*M - k022*OH*O + k024*OH*OH - k027*HO2*O - k038*CLO*O - k043*HCL*O - k045*CLONO2*O - k053*NO2*O -k068*BRO*O

[20:] d[ O1D ]/d t = j003*O3 -k003*O1D*O3 - k004*O1D*N2 - k005*O1D*O2 -k006*O1D*H2O - k007*O1D*H2 -k008*O1D*CH4

[21:] d[ O3 ]/d t = - j002*O3 - j003*O3 -k002*O*O3 - k003*O1D*O3 + k009*O*O2*M - k020*H*O3 - k023*OH*O3 - k026*HO2*O3 - k031*CL*O3 - k054*NO*O3 - k056*NO2*O3 - k065*BR*O3

[22:] d[ CH4 ]/d t = - k008*O1D*CH4 - k017*CH4*OH - k032*CL*CH4

[23:] d[ BR ]/d t = j019*BRCL + j020*BRO + j021*HOBR + j022*BRONO2 - k065*BR*O3 -k066*BR*HO2 + k068*BRO*O + k070*BRO*NO + 2*k071*BRO*BRO + k073*BRO*CLO + k074*HBR*OH

[24:] d[ BRO ]/d t = - j020*BRO + k065*BR*O3 - k068*BRO*O - k069*BRO*HO2 - k070*BRO*NO - 2*k071*BRO*BRO - k072*BRO*CLO - k073*BRO*CLO - k075*BRO*NO2*M

[25:] d[ HOBR ]/d t = -j021*HOBR + k069*BRO*HO2

[26:] d[ HBR ]/d t = k066*BR*HO2 - k074*HBR*OH

[27:] d[ BRONO2 ]/d t = - j022*BRONO2 + k075*BRO*NO2*M

[28:] d[ BRCL ]/d t = - j019*BRCL + k072*BRO*CLO

[29:] d[ H2O ]/d t = -k006*O1D*H2O + k017*CH4*OH + k019*H2*OH + k024*OH*OH + k025*OH* HO2 + k029*H2O2*OH + k042*HCL*OH + k044*HOCL*OH + k057*HNO3*OH + k058*HNO4*OH + k074*HBR*OH

Photochemical Models

3

[ ] 2* 001* 002* 004* ....2 3 2

( )

...

... ...

d Oj O j O j HO

dt

d(t)dt

HOH

NOOO

= + +

=

=

xf x

x

rr

r



An Example of Model Simulations

Numerical Solution

( )

( ) ( ) ( )

d(t)

dtt t t

(t)t

=

+ ∆ −=

∆

xf x

x xf x

rr

r rr

( ) ( ) ( )t t t (t) t+ ∆ = + ⋅ ∆x x f xr r r

In reality this simple scheme won’t work and more sophisticatednumerical schemes are required.



Atmospheric chemistry mechanisms are the most computationally intensive components of photochemical models of the atmosphere.

This computational burden is partly due to the fact that atmospheric chemical kinetic systems are very “stiff”, i.e. they include reactions ranging from very fast to very slow; this requires theuse of elaborate numerical integration schemes (“stiff solvers”).

The development of a photochemical mechanism that accurately describes atmospheric chemistry while being computationallyefficient is a difficult undertaking.

Speeding up the chemistrySpeeding up the chemistry• A number of attempts have been made to parameterize theand speed up chemical calculations.

• In recent years (~1999) High Dimensional Model Representations or Fully Equivalent Operational Models were shown to have some success.

• Experience shows that up to second-order terms in the expansion below are satisfactory for many high-dimensional practical systems.



Photochemical ModelsPhotochemical Models

3

, ( Ä ) ( )

H

OHt t (t)...

...O

= + =

x x M x

Reaction rates,p

Concentrationsof chemicals

at time tx(t)

ModelM

Concentrationsof chemicalsat time t+∆∆ t

x(t+∆∆ t)

Photochemical Box ModelPhotochemical Box Model

NO

O

O3

NO

O

O3

M

time ttime t+∆t



Knowing probability density functions is necessary for properimplementation of data assimilation.

NO

O

O3

NO

O

O3

M

time ttime t+∆t

Evolution of probability density functions is very hard to computein practice due to high dimensionality of the model space. Therefore…

Probability Density FunctionsProbability Density Functions

ApproximationsApproximations

•PDFs are Gaussian:

B is the covariance matrix.

•Model can be linearized for small perturbations:

10.5( ) ( )( ) ~

( )( )T

TPDF e −− −< > −< >

=< − < > − < > >

x x B x xx

B x x x x

M x x M x L x

Lx

x

M

x

[ ( ) ( )] [ ( )] ( )

( )( )

t t t t

d t td t

dd

+ ≈ +

=+

=

δ δ∆

L is the linearization matrix.



ApproximationsApproximations

•PDFs are Gaussian:

B is the covariance matrix.

•Model can be linearized for small perturbations:

10.5( ) ( )( ) ~

( )( )T

TPDF e −− −< > −< >

=< − < > − < > >

x x B x xx

B x x x x

M x x M x L x

Lx

x

M

x

[ ( ) ( )] [ ( )] ( )

( )( )

t t t t

d t td t

dd

+ ≈ +

=+

=

δ δ∆

L is the linearization matrix.



Tangent Linear ModelTangent Linear ModelThe linearization matrix (tangent linear model) L describes time evolution of small perturbations to the model state :

δ δx L x( ) ( )t t t+ =∆

t3NN

232221

131211

tt3 ......................................................

=

∆+ O......

OHH

L

LLLLLL

O......

OHH

It also determines time evolution of error covariances:T( ) ( )t t t+ ∆ = ⋅ ⋅B L B L

Calculating L

( )d

(t)dt

=x

f xr

r

( ) ( ) ( )t t t (t) t+ ∆ = + ⋅∆x x f xr r r

( ) ( ) ( )

t t t(t)

t+ ∆ −

=∆

x xf x

r rr

( ) ( ( ))( ) ( )

d t t d t td t d t

+ ∆ = ⋅ ∆x f xx x



Calculating L

[ ] 2* 001* 002* 004* ....2 3 2

d Oj O j O j HO

dt= + +

...

...

...

3

H

OH

NO

O

O

=

xr

( ) ( ( ))( ) ( )

d t t d tt

d t d t+ ∆

= ⋅ ∆x f x

x x

, 3

( ( ))002;

( ) O O

d tj

d t=

f xx

, 2

( ( ))004;

( ) OHO

d tj

d t=

f xx

Calculating L – Implicit Solver

( ) ( )) ( )t t (t t t t+ ∆ + + ∆ ⋅ ∆ =x f x xr r r

( ) ( ) ( )

t t t(t t)

t+ ∆ −

= + ∆∆

x xf x

r rr

2

2

( )( , , , , )

( )

d t t d dfunc t

d dd t

→

→

+ ∆= ∆

x f fx f

x xx

0( ) ( ) )) ( )d

t t t (t t (t t td

+ ∆ + ⋅∆ + ⋅ + ∆ − ⋅∆ =f

x f x x xx

r r r r

2

2

( ) ( )( ) ))

( ) ( )odd t t d d d t t

t (t t (t t td t d d d d t

+ ∆ + ∆+ ⋅∆ + ⋅ + ∆ − ⋅ ∆ + ⋅ ⋅∆ =

fx f f xx x I

x x x x x

r rr r

r r



• Coding f by hand is hard, time consuming and error-prone.

• Coding df/dx “by hand” is even harder.

• Coding d2f/dx2 by hand is next to impossible.

• If chemical scheme changes, code needs to be recreated.

• Automatic chemical “compilers” are not too difficult to create and several already exist (http://acd.ucar.edu/~boris/0D.htm)

LinearizationLinearization MatrixMatrix

• The exact past state of the system cannot be inferred from present observations.

L is severely rank deficient for∆t > few hours.

• Observations of only a small subset of chemicals are necessary to precisely determine the future state.



Singular Value Decomposition Singular Value Decomposition (SVD) Spectrum of (SVD) Spectrum of LL

Photochemical ModelPhotochemical Model

• H, OH, HO2, H2O2, NO, NO2, NO3, N2O5, HNO3, HNO4, Cl, ClO, HOCl, HCl, ClONO2, O, O(1D), O3, CO, CH4, N2O, H2, H2O, and aerosol.

• ~100 chemical and photodissociation reactions.

• The tangent linear and adjoint models are automatically generated and integrated along with the original model. http://acd.ucar.edu/~boris/Content/3D.htm



In practice chemical solvers must be coupled with dynamical, radiation transfer, land surface and other modules in order to properly simulate the chemical composition of the atmosphere.

Chemistry-Transport Models

Chemistry-Transport ModelBasic EquationBasic Equation

2 2 2

2 2 2 ( )n n n n n n n

u v w D P L nt x y z x y z

∂ ∂ ∂ ∂ ∂ ∂ ∂+ + + = + + + − ∂ ∂ ∂ ∂ ∂ ∂ ∂

n – chemical concentrationu,v,w – wind vector componentsD – diffusion coefficientP – chemical productionL – chemical loss



Chemistry-Transport Model1. Production1. Production

2 2 2

2 2 2( )

n n n n n n nu v w D L n

t x y z x yP

z ∂ ∂ ∂ ∂ ∂ ∂ ∂

+ + + = + + + − ∂ ∂ ∂ ∂ ∂ ∂ ∂

Chemistry-Transport Model2. Advection2. Advection

2 2 2

2 2 2 ( )n n n n

D P L nt x y

n n nu v w

x y z z ∂ ∂ ∂ ∂

+ = + + + − ∂ ∂ ∂ ∂

∂ ∂ ∂+ +

∂ ∂ ∂



Chemistry-Transport Model3. Convection3. Convection

2 2 2

2 2 2 ( )n n n n

D P L nt x y

n n nu v w

x y z z ∂ ∂ ∂ ∂

+ = + + + − ∂ ∂ ∂ ∂

∂ ∂ ∂+ +

∂ ∂ ∂

Chemistry-Transport Model4. (Turbulent) Diffusion4. (Turbulent) Diffusion

2 2 2

2 2 2 ( )n n n

Dx y

n n n nu v w P L

zn

t x y z ∂ ∂ ∂

+ +∂ ∂ ∂ ∂

+ + + = +∂ ∂ ∂−

∂ ∂ ∂ ∂



Chemistry-Transport Model5. Chemistry5. Chemistry

2 2 2

2 2 2( )

n n n n n n nu v w D

t x y z xP

y zL n

∂ ∂ ∂ ∂ ∂ ∂ ∂+ + + = + + + ∂ ∂ ∂ −

∂ ∂ ∂ ∂

Global Model GridGlobal Model Grid



Practicalities (1)Practicalities (1)• Computer programs representing 3-D CTMs are very complex. They consist of thousands lines of code and many modules (radiation, chemistry, large-scale transport, sub-gridparameterizations (e.g., convection, boundary layer), land surface models…

• Entire scientific careers have been spent developing foundationsof a particular module.

• These programs are written by many scientists, post-docs, andgraduate students with different programming styles and skills and over many years.

DVX(N)=(VX(NU,M,L)-Vx(ND,m,l))/2.0DVY(N)=(VY(NU,M,L)-Vy(ND,m,l))/2.0DDVX(N)=VX(NU,M,L)+Vx(ND,m,l)-2.0*VX(N,M,L)DDVY(N)=VY(NU,M,L)+Vy(ND,m,l)-2.0*VY(N,M,L)A11=-VX(N,M,L)*(VX(n,ms,l) -VX(N,MN,L))/SX1A12=-VY(N,M,L)*(VX(N,m,le) -VX(N,m, lw))/SX2A1(n)=A11+A12B11=-VX(N,M,L)*(VY(N,ms,l) -VY(N,MN,L))/SX1B12=-VY(N,M,L)*(VY(N,m,le)-VY(N,m, lw ))/SX2B1(n)=B11+B12C1(n)=-VX(N,M,L)*((eps(n,ms,l) -.5*(vx(n,ms,l)**2 +

* vy(n,ms,l)**2))-(eps(n,mn,l)-.5*(vx(n,mn,l)**2+* vy(n,mn,l)**2)))/sx1C2(n)=-Vy(N,M,L)*((eps(n,m,le)-.5*(vx(n,m,le)**2 +

* vy(n,m,le)**2))-(eps(n,m, lw )-.5*(vx(n,m, lw)**2+* vy(n,m, lw)**2)))/sx2DT=(TEMP(NU)-TEMP(ND))/2.0

c DUMUT(N)=(UMUT(NU) -UMUT(ND))/2.0DKMKT=(KM(NU)+KT(NU) -KM(ND) -KT(ND))/2.0DDT=TEMP(NU)+TEMP(ND)-2.0*TEMP(N)

C3(n)=KM(N+KT(N))*DDT+DT*DKMKT)/PRES(N)C3(n)=C3(n)**0.71*TIN(N)/(TIN(N)**0.71*TEMP(N))

C3(n)=C3(n)+(KT(NU)*SCHT(NU) -KT(ND)*SCHT1(ND))*GRAV**2/(PRES(N)*CP(N)*2.0)C51(n)=OM(N)*(cp(nu)*temp(NU)-cp(nd)*temp(ND)

1)/(2.0*PRES(N))

Practicalities (2)Practicalities (2)This normally leads to un-readable, un-documented and un-manageable codes, like the piece shown on the right:

These codes are prone to errors and make it hard to introduce new modules orto bring in data assimilation.

Earth system modeling has become a tightmix of computer sciences, mathematics, physics and chemistry, with computer sciences component becomingmore and more important, if not crucial.



Examples of CTM SimulationsExamples of CTM Simulations

MOZART2 ModelMOZART2 Model

•3-D global CTM MOZART 2

•50 longitude by 50 latitude (T21) and higher (up to ~10)

•28-60 levels

•Tropospheric chemistry, ~50 species

•ECMWF or NCEP dynamics

•Developed at NCAR and then at Max Plank

•Will be shareware with web download very soon.http://acd.ucar.edu



An example of MOZART model An example of MOZART model simulations of global COsimulations of global CO

IsoIso--surface of CO from MOZART 2 surface of CO from MOZART 2 model, Marchmodel, March--December 2000December 2000



An Example of Air Quality An Example of Air Quality Simulations with MOZARTSimulations with MOZART

CO emitted by Colorado for 6pm CO emitted by Colorado for 6pm December 7 2000December 7 2000



Animation of CO emitted by Colorado for Dec 1Animation of CO emitted by Colorado for Dec 1-- 20 20 20002000

What controls tracer distribution?What controls tracer distribution? M A C C M 3 - T 4 2 C O 8 0 4 1 8

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• Zonal mean CO• LS-advection • Convection • Vertical diffusion

• Chemistry

1.

2. 3.

4. 5.



MOZART2:MOZART2: ZonalZonal mean CO, different convective mean CO, different convective schemesschemes

May, CO, ZM-con, NCEP

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May, CO, ZM-con, ECMWF

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May, CO, ZMncl-con, ECMWF

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Sensitivity of theSensitivity of the zonalzonal mean CO to the mean CO to the equatorial surface fluxesequatorial surface fluxes


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Total column of CO, MOZART2 (top) and Total column of CO, MOZART2 (top) and observations (bottom).observations (bottom).

JUN MOZART2, CO-column, scale=1.e17

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• Methods of data assimilation provide a unified mathematical framework for objective analysis of discrepancies between model results (our theoretical knowledge) and observations (the reality).

• Such analysis should lead to advances in our understanding of the environment.

• Practical applications of data assimilation in studies of atmospheric chemical composition will be discussed atthe next lecture.

atmospheric chemicalmodeling and data assimilation · atmospheric chemistry mechanisms are the most...

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