MOPITT Measurements of Tropospheric CO: Assimilation and Inverse Modeling MOPITT Measurements of Tropospheric CO: Assimilation and Inverse Modeling presented.

MOPITT Measurements of MOPITT Measurements of Tropospheric CO: Assimilation and Tropospheric CO: Assimilation and

Inverse Modeling Inverse Modeling presented by Boris Khattatov

Gabrielle Pétron, Jean-Francois Lamarque, Valery Yudin, David Edwards, and John Gille, National Center for Atmospheric Research, BoulderClaire Granier and Lori Bruhwiler, Service d'Aeronomie/NOAA

MOZART Team: G. Brasseur, M. Schultz, L. Horowitz, D. Kinnison, L. Emmons, S. Waters, P. Rasch, X. X. Tie, C. Granier, D. Hauglustaine, and others

US MOPITT Team: J. Gille, D. Edwards, C. Cavanaugh, J. Chen, M. Deeter, D.G. Francis, B. Khattatov, J-F Lamarque, L. Lyjak, D. Pacman, M. Smith, J. Warner, V. Yudin, D. Ziskin, and others

CA MOPITT Team: J. Drummond, G. Bailak, P. Chen, J. Kaminski, N. Mak, G. Mand, E. McKernan, R. Menard, B. Quine, B. Tolton, Z. Yu, L. Yurganov, J-S Zou, and others

! INPUTS: TYPE(ProfileType), INTENT(IN) :: Profile REAL(std) , INTENT(IN) :: NoData!! OUTPUTS: REAL(std), DIMENSION(:,:), INTENT(OUT) :: O!! LOCALS: INTEGER :: i,j,k! O(:,:) = 0.0 k=0 DO i=1,Profile_N_Lev-1 DO j=i+1,Profile_N_Lev k = k + 1 IF (k > SIZE(Profile%offDiag)) THEN CALL ABORT() ENDIF O(i,j) = Profile%offDiag(k) O(j,i) = Profile%offDiag(k) ENDDO ENDDO DO i=1,Profile_N_Lev O(i,i) = Profile%sigmaV(i)**2 ENDDO

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IntroductionIntroductionThe goal of this research project is to study global distributions and derive poorly known surface sources of CO from MOPITT data.

This is done via assimilation of MOPITT data and inverse modeling of CO emissions in the MOZART 2 model.

Data AssimilationData Assimilation

Mathematical basis of data assimilation is estimation or inverse problem theory:

“People were naked worms; yet they had an internal model of the world. In the course of time this model has been updated many times, following the development of new experimental possibilities or their intellect. Sometimes the updating has been qualitative, sometimes it has been quantitative. Inverse problem theory describes rules human beings should use for quantitative updating”

Albert Tarantola, Inverse Problem Theory

Norbert Weiner

Andrey Kolmogorov

1-D Estimation1-D Estimation

To optimally combine two pieces of information one has to know their uncertainties (errors).

Multiple DimensionsMultiple Dimensionsx is a vector, e.g.,

• concentrations of several chemicals at the same location• concentrations of the same chemical at different locations

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,latN lonNO....,lonlatO1, 1lat lonO

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If we know that element xi correlates with xj, we can infer information about xj from measurements of xi => error covariance matrices

Dynamic estimationDynamic estimation

Let’s assume we have a time dependent predictive model M: x(t+Dt) = M[ x(t) ]

The model tries to predict quantity x, which can be a scalar or a vector. Model simulations have uncertainty sx associated with them

Let’s also assume that there exist independent observations of quantity y, which is related to x via: y = H[ x ]

The uncertainty of measurements of y is sy

The problemThe problem

Model:

Observations:

Observational operator:

Problem: find the “best” x, which inverts

for a given y allowing for observation errors and other prior information

y = M(x)

z

z = H(y)

z = H(M(x))

0-D Example (a scalar x)0-D Example (a scalar x)

time

x

Let’s assume that we measure x directly, i.e., H = I

0-D Example (a scalar x)0-D Example (a scalar x)

time

x

0-D Example (a scalar x)0-D Example (a scalar x)

time

x

If we use optimal estimates of x as initial conditions for model integration we can improve model predictive skills. To do this systematically we need to be able to computethe time evolution of errors in the model

Mathematical BasisMathematical Basis Arrange observations in vector z, Nz~102-104

Arrange model variables in vector x, Nx~104-106

Define “observational” operator H: transformation from model variables to observations (interpolation)

Invert (in the statistical sense) z = H(M(x))

X3

X1

X2

Z3

Z1

Z2

H

model space ~ 106 dimensions

observation space ~ 104 dimensions

The problemThe problem

Formally, find x that minimizes

B and O are the forecast and observational error covariances

J(x) = [z -H(M(x))]TO-1[z-H(M(x))] + [x - xa]TBa-1[x-xa]

Evolution of the PDF is governed by a differential equation (Fokker-Kolmogorov) which is impossible to solve in most

practical cases

Therefore, simplifications are necessary

ApproximationsApproximations

• PDFs are Gaussian:

B is the covariance matrix

PDF(x) ~ e-0.5(x-<x>)TB-1(x-<x>)

B = <(x-<x>)(x-<x>)T>

ApproximationsApproximations

.

Model can be linearized for small perturbations:

L is the linearization matrix

H(M[x(t) +x(t)]) ≈ H(M[x(t)]) + Lx(t)

L = dx(t + t)=

dx(t) dxdH(M(x))

LinearizationLinearization

For photochemically active gases, like CO, the relationship y=H(x) between x and y is non-linear

In order to solve the problem one needs to linearize the model and use iterative techniques for finding the solution

We assume that the model can be linearized with respect to the emissions for small perturbations:

H[x +x] ≈ H[x] + Lx

L = dy(t + t)=

dx(t) dxdH

LinearizationLinearization

So, H can be approximated using the linearization matrix. L can be obtained

1. Using finite differences -- by running the model N times (where N is the number of emission sources), once for each source while all but one source are set to zero., i.e., L~ Dy/Dx

2. By differentiating the computer code of the model, i.e., developing computer code that calculates matrix L for given x and y

LinearizationLinearization

1. Linearization via finite differences (L~ Dy/Dx):

Pros: straightforward to construct, easy to change models

Cons: takes a lot of CPU time

2. Linearization by differentiating the computer code of the model:

Pros: Small CPU requirements

Cons: complicated to construct, hard to switch models

The SolutionThe Solution

x = xa + K(z - H(M(xa)))

K = BaLT(L BaLT + O) -1

B = Ba - BaLT(L BaLT + O) -1LBa

Chemistry-Transport Model

Chemistry and Transport parameterizations

Initial 3-D CO distribution, y(t)

Final 3-D CO distribution y(t+Dt)

x

y(t + t) = M[y(t),x]

Chemistry-Transport Model Basic EquationBasic Equation

n – pollutant concentrationu,v,w – wind vector componentsD – diffusion coefficientP – production of pollutantL – loss of pollutant

+ u +v +w = D + +nt

ny

nz

nx

2nx2

2ny2

2nz2

+ P - L(n)

Chemistry-Transport Model 1. Emissions1. Emissions

+ u +v +w = D + +nt

ny

nz

nx

2nx2

2ny2

2nz2

+ P - L(n)

Chemistry-Transport Model 2. Advection2. Advection

+u +v +w = D + +nt

nx

2nx2

2ny2

2nz2

+ P - L(n)

ny

nz

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Chemistry-Transport Model 3. Convection3. Convection

+u +v +w = D + +nt

nx

2nx2

2ny2

2nz2

+ P - L(n)

ny

nz

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Chemistry-Transport Model 4. (Turbulent) Diffusion4. (Turbulent) Diffusion

+u +v +w = D + +nt

2nx2

+ P - L(n)

2ny2

2nz2

nx

ny

nz

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Chemistry-Transport Model 5. Chemistry5. Chemistry

+ u +v +w = D + +nt

ny

nz

nx

2nx2

2ny2

2nz2

+ P - L(n)

MOZART2 ModelMOZART2 Model

• 3-D global CTM MOZART 2

• 5° longitude by 5° latitude (T21) and higher (T42, T63)

• 28-60 levels

• Tropospheric chemistry, ~50 species

• ECMWF or NCEP dynamics

• Developed at NCAR and then at Max Plank

MOPITT MissionMOPITT Mission

The Measurement Of Pollution In The Troposphere mission is a joint CSA and NASA project. U. of Toronto leads the Canadian effort to contribute the instrument. NCAR leads the US effort do develop and apply data processing algorithms and provide science support

During the 5 year mission, MOPITT will provide the first long term, global measurements of carbon monoxide (CO) & methane (CH4) levels in the troposphere.

MOPITT MissionMOPITT Mission

The field-of-view of MOPITT is 22 x 22km and it views four fields simultaneously. The field of view is also continuously scanned through a swath about 600 km wide as the instrument moves along the orbit.

This Study Used This Study Used Preliminary MOPITT DataPreliminary MOPITT Data

The MOPITT instrument and the measurement technique are unique: lessons are being learned for the first time in both instrument operation and data processing

The US and Canadian MOPITT Teams work very hard on identifying and removing potential problems in the retrieved CO data and recently succeeded in delivering first data to NASA

The released data (internal version V4.6.2) is considered beta; individual profiles might contain noise that needs to be understood better

This study used V4.3.1 – all data were binned in 5x5 degree bins

Instantaneous Isosurface of CO, Instantaneous Isosurface of CO, MOZART 2MOZART 2

MOPITT DataMOPITT Data

Assimilation of MOPITT COAssimilation of MOPITT CO

Analysis Model

Instantaneous Isosurface of CO,Instantaneous Isosurface of CO, MOPITT Assimilation MOPITT Assimilation

Isosurface of CO, MOZART2Isosurface of CO, MOZART2

CO, March-December 2000CO, March-December 2000

Inverse ModelingInverse Modeling

The discrepancies between observations and model results can be used to optimize poorly known parameters in the model – e.g., surface emissions.

yo ymMOPITT MOZART

March 2000 : Total column of COMarch 2000 : Total column of CO MOZART2 (top) and MOPITT (bottom) MOZART2 (top) and MOPITT (bottom)

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

-100 0 100-60

-40

-20

0

20

40

60

Lati

tud

e

MAR MOPITT, CO-column, scale=1.e17

-100 0 100 Longitude

-60

-40

-20

0

20

40

60

Lati

tud

e

July 2000: Total column of COJuly 2000: Total column of CO MOZART2 (top) and MOPITT (bottom) MOZART2 (top) and MOPITT (bottom)

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

-100 0 100-60

-40

-20

0

20

40

60

Lati

tud

e

JUL MOPITT, CO-column, scale=1.e17

-100 0 100 Longitude

-60

-40

-20

0

20

40

60

Lati

tud

e

CO “colors”, day 2CO “colors”, day 2

CO “colors”, day 65CO “colors”, day 65

CO “colors”, day 85CO “colors”, day 85

CO “colors”, 4 monthsCO “colors”, 4 months

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MOPITT CO InversionMOPITT CO Inversion

We performed first inversion experiments using a finite-differences constructed linearization of the MOZART 2 model

MOPITT August observations of CO at 500mb were used to constrain model surface emissions of CO for August 2000

a prioria priori CO emissions, CO emissions, August 2000August 2000

CO MOPITT inversion CO MOPITT inversion August 2000August 2000

CO MOPITT inversion, CO MOPITT inversion, August 2000August 2000

! INPUTS: TYPE(ProfileType), INTENT(IN) :: Profile REAL(std) , INTENT(IN) :: NoData!! OUTPUTS: REAL(std), DIMENSION(:,:), INTENT(OUT) :: O!! LOCALS: INTEGER :: i,j,k! O(:,:) = 0.0 k=0 DO i=1,Profile_N_Lev-1 DO j=i+1,Profile_N_Lev k = k + 1 IF (k > SIZE(Profile%offDiag)) THEN CALL ABORT() ENDIF O(i,j) = Profile%offDiag(k) O(j,i) = Profile%offDiag(k) ENDDO ENDDO DO i=1,Profile_N_Lev O(i,i) = Profile%sigmaV(i)**2 ENDDO