# Presentation: 790092

## MOPITT Measurements of Tropospheric CO: Assimilation and Inverse Modeling presented by Boris Khattatov

- Gabrielle Pétron, Jean-Francois Lamarque, Valery Yudin, David Edwards, and John Gille, ***National Center for Atmospheric Research, Boulder***
- Claire 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*

## Introduction

**Introduction**

**	**The 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 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 Estimation

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

## Multiple Dimensions

- x is a vector, e.g.,
-  concentrations of several chemicals at the same location
-  concentrations of the same chemical at different locations

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

## Dynamic estimation

**Let’s assume we have a time dependent predictive model**** ****M:  x(t+****D****t) = M[ x(t) ]**
**The model tries to predict quantity ****x****, which can be a scalar or a vector. Model simulations have uncertainty**** ****s****x**** ****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**** ****s****y**

## The 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)

**time**

**x**

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

## 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 Basis

**Arrange observations in vector ****z, N****z****~10****2****-10****4**
**Arrange model variables in vector ****x, N****x****~10****4****-10****6**
**Define “observational” operator ****H****: transformation from model variables to observations (interpolation)**
**Invert (in the statistical sense)  ****z = H(M(x))**** **

- model space ~ 106 dimensions

- observation space ~ 104 dimensions

## The  problem

**Formally, find**** ****x**** that minimizes**
**B**** and ****O**** are the forecast and observational error covariances**

**J(x) = [z -H(M(x))]****T****O****-1****[z-H(M(x))] + [x - x****a****]TB****a****-1****[x-x****a****]**

## 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

## Approximations

-  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****>**

## Approximations

- .
- Model can be linearized for small perturbations:

**L** is the linearization matrix

**H(M[x(t) +********x(t)]) ≈ H(M[x(t)]) + L********x(t)**

**L =**

**dx(t + ********t)**

**=**

**dx(t)**

**dx**

**dH(M(x))**

## Linearization

**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] + L********x**

**L =**

**dy(t + ********t)**

**=**

**dx(t)**

**dx**

**dH**

## Linearization

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

## Linearization

**1. Linearization via finite differences (****L~ ****D****y/****D****x****):**
**	**_*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 Solution

**x = x*****a***** + K(z - H(M(x*****a*****)))**

**K = B*****a*****L****T****(L**** ****B*****a*****L****T ****+ O)***** *****-1**
**B = B*****a***** - B*****a*****L****T****(L**** ****B*****a*****L****T ****+ O)***** *****-1****LB*****a***

## Chemistry-Transport Model 

- Chemistry and Transport parameterizations

- Initial 3-D CO distribution, **y(t)**

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

**x**

**y(t + ********t) = M[y(t),x]**

## Chemistry-Transport Model Basic Equation

- n – pollutant concentration
- u,v,w – wind vector components
- D – diffusion coefficient
- P – production of pollutant
- L – loss of pollutant

-      + u      +v      +w       = D         +         +

-  + P - L(n)

## Chemistry-Transport Model 1. Emissions

-  + **P **- L(n)

## Chemistry-Transport Model 2. Advection

-      +**u       +v      +w**       = D         +         +

-  + P** **- L(n)

## Chemistry-Transport Model 3. Convection

-      +**u       +v      +w**       = D         +         +

-  + P** **- L(n)

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

-      +u       +v      +w       = **D**         +         +

-  + P** **- L(n)

## Chemistry-Transport Model 5. Chemistry

-  + **P - L(n)**

## MOZART2 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 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 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 Preliminary 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, MOZART 2

## MOPITT Data

## Assimilation of MOPITT CO

## Instantaneous Isosurface of CO, MOPITT Assimilation

## Isosurface of CO, MOZART2

## CO, March-December 2000

## Inverse Modeling

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

- yo

- ym

- MOPITT

- MOZART

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

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

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

- -100

- 0

- 100

- -60

- -40

- -20

- 0

- 20

- 40

- 60

-  Latitude

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

- -100

- 0

- 100

-  Longitude

- -60

- -40

- -20

- 0

- 20

- 40

- 60

-  Latitude

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

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

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

- -100

- 0

- 100

- -60

- -40

- -20

- 0

- 20

- 40

- 60

-  Latitude

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

- -100

- 0

- 100

-  Longitude

- -60

- -40

- -20

- 0

- 20

- 40

- 60

-  Latitude

## CO “colors”, day 2

## CO “colors”, day 65

## CO “colors”, day 85

## CO “colors”, 4 months

## MOPITT 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 priori CO emissions, August 2000

## CO MOPITT inversion August 2000

## CO MOPITT inversion, August 2000

## Slide 48