# Presentation: 200134

## Retrieving global sources of aerosols from MODIS by inverting GOCART model 

***Retrieving global sources of aerosols from MODIS by inverting GOCART****** ******model***** **

***INVERSION:*****         **_**Oleg Dubovik**_**1**** **
**   ****	****	****    ****Tatyana Lapyonok****2**
***MODIS******:******                 *****Yoram Kaufman****2,**
***GOCART:*****             Mian Chin****2****            **
**   ****	****                 ****Paul Ginoux****3**

***1- LOA/CNRS, University of Lille, France***
*** ***
***2-  NASA/GSFC, Greenbelt, MD, USA***
***3 - NOAA/GFDL, Princeton, NJ,  USA***

***INSPIRATION******:***

- Yoram Kaufman2

***Yoram J. Kaufman Symposium On Aerosols, Clouds and Climate***
*** ******NASA/GSFC, , May 30, 31, and June 1, 2007 ***

## The idea of the approach

**observations of ambient aerosol**

**INVERSION****:**
**(e.g. via adjoint model)**

**GOCART****:**
** ****meteorology**
** ****transport**
** ****chemistry**
** ****removal **
** ****emissions?**

_**Improved**_** sources (location and strength)**
** **
_**Improved**_** agreement of modeling with observations**** **
**Improved characterization of climate, air quality, etc.**

***The idea of the approach***

## Basic principle of inversion

**Least Square**
**Method** (m>n)

- Forward Model

- Matrix: m -lines, n- columns

**Criterion of solution optimization:**

_**Basic principle of inversion**_

## t

*X*

*∆**z*

*∆**y*

*∆**x*

*Y*

*Z*

**Vector of global **
**aerosol mass **

*X*

*∆**z*

*∆**y*

*∆**x*

*Y*

*Z*

*m( t+∆t*, *x*, *y*, *z )*

***         ******Vector elements - values of aerosol mass :****        *
*          **M**p**=m(t**i  **, x**j  **,** **y **k** , z**n**)****  (****p =1, ...., N**p****)******   ***
***	***
***	******Time and space coordinates***
***	****** ****z**n** = n ** ∆z**  **(n =1,...,N**z**)*
*	** **y**k** = k ** ∆y**   **( k =1,...,N**y**)*
*	** **x**i** =  j ** ∆x**   **( j =1,...,N**x **)*
*	** **t**i**  =  i ** ∆t**    **( i =1,...,N**t **)*
***            ***
***	***

***M***=

*m( t*, *x*, *y*, *z )*

***t***

_***Index convention: ***_
* **p = (i-1) N**x **N**y **N**z **+ (j-1) N**y **N**z **+ (k-1) N**z **+** **n*
* **N**p**=N**t **N**x **N**y **N**z *

***t***

*Z*

*X*

*Y*

## GOCART Model:Goddard Chemistry Aerosol Radiation and Transport Model 

- An atmospheric process model using assimilated meteorological fields from the Goddard Earth Observing System Data Assimilation System (GOES DAS)
- Including major types of aerosol, sulfate, dust, BC, OC, and sea-salt from both anthropogenic and natural sources
- Calculating aerosol composition, 4-D distributions, optical thickness, radiative forcing

**(spatial resolution 2****0 ****x 2.5****0****, time resolution 20 min)**

## Dimension of the Problem: 

-   Longitude Points (~144)
- X
-   Latitude Points (~91)
- X
-   Vertical Layers (~30)
- X
-   Time steps (~12 days)
-  = ~ 5,000,000

-   Longitude Points (~144)
- X
-   Latitude Points (~91)
- X
-   Time steps (~12 days)
-  = ~ 200,000

- 5,000,000 X 200,000

## Transport Inversion: 

- Aerosol
- Mass

- Transport
- Operator

**Source -**
- Aerosol Emission

- Measured Aerosol Mass

**Least Square**
**Method:**

## Steepest Descent Method: 

-   for p, steepest descent method is
- equivalent to LSM

- It converges as:

-              -has predominant diagonal due to local
-               character of aerosol transport

**???**

## “Transposed” ~ “Adjoint” Transport: 

- _For Transport:_
- 	-reversed order of time integration
- 	-reversed order of component processes
-   	(e.g., advection  backward advection,
-             falling  uplifting, updraft  falling)

- - _Adjoint_ (“Transpose”) Transport

- Transport Model:

- ?

## t

**Time Integration of **
**Transport Model:**
** **

*m(t**2**,x)=T(t**1**,x)(m(t**1**,x)+s (t**1**,x))∆t*

*m(t**2**,x)=T(t**1**,x)(m(t**1**,x)+s (t**1**,x))∆t*

*m(t**5**,x)=T(t**1**,x)(m(t**1**,x)+s (t**1**,x))∆t*

*                                                   *

***m****(t**3**,****x****)**=****T****(t**2**,****x****)(****m****(t**2**,****x****)+****s****(t**2**,****x****)**)∆t*

***m****(t**1**,****x****)**=****T****(t**0**,****x****)(****m****(t**0**,****x****)**+****s****(t**0**,****x****)**)∆t*

***m****(t**2**,****x****)**=****T****(t**1**,****x****)(****m****(t**1**,****x****)**+****s****(t**1**,****x****)**)∆t*

***t***

***transported mass:***
***m****(t,****x****) (t**0** ≤t ≤ t**max**)*

**OUTPUT**

**INPUT**

***initial mass:***
***m****(t**0**,****x****)*

***emitted mass:***
***s****(t,****x****)** **(t**0** ≤t ≤ t**max**)*

*t**i+1**= t**i**+∆t*

* **T**i* - operators of isolated
-  transport processes:
-         - advection,
-         - diffusion,
-         - convection,
-         - wet deposition,
-         - dry deposition, etc.

**Matrix equivalent:**

***M*** - vector of global aerosol mass,
***M***0 - vector of global aerosol mass at t0,
***S****** ***- vector of global aerosol emissions,
**T** - matrix defining mass transport

## (-t)

**Backward Time**
**Integration of Adjoint Transport Model:**
** **

*m(t**2**,x)=T(t**1**,x)(m)+s (t**1**,        ∆t*

***∆******s****p**(t**n**,x)**=****T***#*(t**n**,x)(****∆****p**(t**n**,x)**)∆t*

***(-t)***

***Solution Correction:***
***s****p+1**(t,x)=**** s****p**(t,x)-**** ∆s****p**(t,x)** *

**OUTPUT  **

**INPUT**

***   ******Residual obtained using s****p****(t,x):***
*** ∆****p**(t,x) **= *************(t,x)(****m****p**(t,x)- ****m*******(t,x))** (t**0** ≤t ≤ t**max**)*
***m****p**(t,x) -**** mass simulated using s****p****(t,x),***
***m*******(t,x) -**** mass measurements ***

*t**n-1**= t**n**- ∆t*

* **T**#**i* - adjoint operators of isolated transport processes:
-         - advection,
-         - diffusion,
-         - convection,
-         - wet deposition,
-         - dry deposition, etc.

**Matrix equivalent:**

-  ∆***S******p**** = ***T**T**C****-1 **∆** *****M****p*

***M***0 - vector of global aerosol mass at t0,
**T****T** - transpose of transport matrix T,
**C** -  measurement covariance matrix,
- ∆*** ******M****p* - vector of residuals (∆*** M****p* =***M(S****p****)***- ***M*************)***,

*                                                                   *

*                                                                    *

***∆******s****p**(t**n-2**,x)**= ****T***#*(t**n-2**,x)(****∆s****p**(t**n-1**,x)**+****∆****p**(t**n-2**,x)**)∆t*

***∆******s****p**(t**n-1**,x)**= ****T***#*(t**n-1**,x)(****∆s****p**(t**n**,x)**+****∆****p**(t**n-1**,x)**)∆t*

***∆******s****p**(t,x) (t**0**.≤ t ≤ t**max**)*

## Implementation of Steepest 

**Transport Model**

**Backward Time Integration of    **
**    ****Adjoint Transport Model**
***∆******s****p**(t,****x****)** *

**Backward Time Integration of**
** ****Adjoint Transport Model**

**Matrix Formulation:**

**Time Integration of**
**Transport Model**

*s**p=0**(t,****x****)*

*m(t**0**,****x****)*

*s**p**(t,****x****)*

***m****p**(t,****x****)*

**    ****Residual calculation:**
***∆****p**(t,****x****) = ******(t,****x****)(m**p**(t, ****x****)- m*****(t,****x****))*

***s****p+1**(t,****x****)=**** s****p**(t,****x****)-**** ∆s****p**(t,****x****)*

**Solution correction:**

**p-th Approximation **
**of Solution:**

**Initialization (***p*=0**):**

**Implementation of Steepest **
**Descent Method via Adjoint **
**               ****Modeling**

**IF (p < p****max****)**

**yes**

**no**

- END

## Testing of inversion

**Testing of inversion**

**Assumed**
**emission**

**Initial **
**guess**

**Retrieved**
**(40 iterations)**

- Emission Sources

**Notes:**
Retrieval from GOCART AOT

## August 28, 2000 (107 kg of mass/day)

**Assumed**
**Emission**

**Retrieved**** **
**Emission**

- _inverting model output:_
- Black Carbon

- August 28, 2000 **(10****7**** kg of mass/day)**
- (two weeks inversion)

## Optical Thickness

**August 28, 2000**

******BC****(0.55)**
**simulated by GOCART using**
**assumed emission**

******BC****(0.55)**
**simulated by GOCART using retrieved emission**

******fit ****< ~****0.007 ****(for instantaneous ********values)**** **

## Optical Thickness(real coverage)

**Optical Thickness****(real coverage)**
**August 28, 2000**

******BC****(0.55)**
**simulated by GOCART using**
**assumed emission**

******BC****(0.55)**
**simulated by GOCART using retrieved emission**

******fit ****< ~****0.009 ****(for instantaneous ********values)**** **

## August 28, 2000 (108 kg of mass/day)

**Assumed**
**Emission**

**Retrieved**** **
**Emission**

- August 28, 2000 **(10****8**** kg of mass/day)**
- (two weeks inversion)

- _inverting model output:_
- Desert Dust

## Optical Thickness

**August 28, 2000**

******dust****(0.55)**
**simulated by GOCART using**
**assumed emission**

******dust****(0.55)**
**simulated by GOCART using retrieved emission**

******fit ****< ~****0.008 ****(for instantaneous ********values)**** **

## Model  Observations

**2****o********2.5****o****,~20 min**
_***Components:***_
** ****BC ****hydrophilic**
** ****BC ****hydrophobic**** **
** ****OC ****hydrophilic**
** ****OC ****hydrophobic**
** ****sulfates**
** ****dust ****(size d.)**
** ****sea salt **
**  ****(fine, coarse)**

***Model ************ Observations***

***24 hours constant emissions***
_***Components:***_
** ****M****fine****(*****x*****;*****y*****;*****z*****;*****t*****)**
**(BC + OC + sulfates + fine dust + fine sea salt)**** **
** ****M****coarse****(*****x*****;*****y*****;*****z*****;*****t*****)**
**(coarse dust + coarse sea **
**salt)**

***GOCART ******output****** ***

**Aerosol Optical thickness****: **
******(*****x*****;*****y*****;*****t*****)**
**1****o********1****o****,**
**global coverage in ~2 days**
_***Components:***_
** ********fine****(0.55********m)**
******coarse****(0.55********m)**
** **

***MODIS******products****** ***

- 

***Extra - assumptions ******in the inversion***

***A priori constraints****** ***

***Using GOCART  emissions***** *****as a priori estimates***
***(~ assimilation)***

## Steepest Descent Methodwith a priori constraints: 

-   for p, steepest descent method is equivalent to
**multi-term LSM**** ****(Dubovik 2004, Dubovik and King, 2000)**

**A priori estimates**
**correction**
***METHODS: ******Kalman filter*****,**
***Rogers optimal estimates,***
***Twomey,... ***

**Correction by a priori **
**limitation of derivatives**
***METHODS: ***
***Phillips-Tikhonov-Twomey***

## MODIS Aerosol Product for 24 hours

**MODIS Aerosol Product for 24 hours**

**MODIS ********total******
**(Total  AOD ****(****degraded to 2****0 ****x 2.5****0 ****)**

**MODIS ********fine******
**(Fine Mode AOD ****(****degraded to 2****0 ****x 2.5****0 ****)**

## August 28, 2000 (107 kg of mass/day)

**Assumed**
**Emission**

**Retrieved**** **
**Emission**

- _inverting model output sub-sampled _
- _according to actual MODIS coverage:_
- Black Carbon

- August 28, 2000 **(10****7**** kg of mass/day)**
- (two weeks inversion)

## Optical Thickness

**Optical Thickness**
**August 20-28, 2000**

******BC****(0.55)**
**simulated by GOCART using**
**assumed emission**

******BC****(0.55)**
**simulated by GOCART using retrieved emission**

******fit ****< ~****0.009 ****(for instantaneous ********values)**** **

## August 20-28, 2000(107 kg of mass/day)

**Assumed**
**Emission**
**BC+OC+Sulfates**

**Retrieved**** **
**Emission**
**Single Fine mode aerosol**

- _inverting model output sub-sampled _
- _according to actual MODIS coverage:_
**Fine Mode Aerosol**

- August 20-28, 2000**(****10****7**** kg of mass/day)**
- (two weeks inversion)

## Optical Thickness

**August 28, 2000**
- (two weeks inversion)

******BC****(0.55)+ ********OC****(0.55)+ ********sulfates****(0.55) simulated by GOCART using**
**assumed emission**

******BC****(0.55)**
**simulated by GOCART using retrieved emission**

******fit ****< ~****0.02 ****(for instantaneous ********values)**
** ********MODIS****= ****0.03+0.05 ******

## August 28, 2000 (108 kg of mass/day)

**Assumed**
**Emission**

**Retrieved**** **
**Emission**

- _inverting model output sub-sampled _
- _according to actual MODIS coverage:_
- Desert DUST

- August 28, 2000 **(10****8**** kg of mass/day)**
- (two weeks inversion)

## Optical Thickness

**August 28, 2000**

******BC****(0.55)**
**simulated by GOCART using**
**assumed emission**

******BC****(0.55)**
**simulated by GOCART using retrieved emission**

******fit ****< ~****0.006 ****(for instantaneous ********values)**** **

## August 20 - 28, 2000

**MODIS Observations**
**(opt. thickness)**

**Retrieved**** **
**Emission**

_***Fine Mode Aerosol:***_
- Black Carbon +
- Organic Carbon +
- Sulfate + ...

## Optical Thickness

**Optical Thickness**
**(August 20-28, 2000)**

******fit ****< ~****0.04 ****(for instantaneous ********values)**
******MODIS****= ****0.03+0.05 ******

**MODIS+AERONET Observations**
**(Fine Mode opt. Thickness,**
**(****degraded to 2****0 ****x 2.5****0 ****)**

**Model output **
**using retrieved **
**emission**

**9 day average, Optical Thickness**
**retrieval is ****NOT CONSTRAINED**** to the land**

## Emission Sources

**Sulfates + BC +OC**

**Retrieved**** Emission**
**(total fine aerosol)**

**Combination** of satellite hotspots (TRMM and ATSR), satellite burned area (MODIS), and a biogeochemical model (CASA)
- Guido van der Werf
- Jim Collatz

**Emission Sources**
**COMPARISON**

**Notes:**
Retrieval from MODIS AOT, all parameters

## August 20 - 28, 2000

**Desert Dust**
**(mass)**

_***Coarse Aerosol:***_
- Desert Dust +
- Sea Salt + etc.

**Retrieved ****emissions**** **
**Coarse Aerosol**
**(mass)**

## Optical Thickness

**MODIS AOD**
**(Coarse Mode AOD ****(****degraded to 2****0 ****x 2.5****0 ****)**

**Model output **
**using retrieved **
**emission**

******fit ****< ~****0.05 ****(for instantaneous ********values)**** **

## February 2001

**February 2001**

_***Fine Mode Aerosol:***_
**Monthly retrievals**

**May 2001**

**July 2001**

## Vermote et al. 2007

**OC & BC 0.5° (MG)**
**Inverted emissions**

**FRP CMG 0.5° (MW)**
**Fire Radiative Power**

**Fossil Fuel Emissions**
- OC & BC adjusted for anthropogenic sources

***Vermote et al. 2007***

***Vermote et al. 2007***

- FRP (Fire Radiative Power)

## Estimating the Emission Factor

***Vermote et al. 2007***

## Perspectives :

-  improved coverage- retrievals over bright surfaces - sensitivity to aerosol type- sensitivity to vertical profile - sensitivity to aerosol source    variability

-  inverting multi-instrument data:MODIS + MISR + POLDER+ APS ...

-  Deriving regional emissions from        geostationary observations               (METEOSAT)

-  retrievals over bright surfaces - sensitivity to aerosol type - sensitivity to vertical profile

-  inverting data from: MISR,     POLDER, APS,CALISPO, etc.

-  higher time resolution - higher spatial resolution

- INVERSION REFINEMENTS: 	- using “a priori” knowledge about emissions;	- inverting satellite radiances