# Satellite-based inversion of NOx emissions using the

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```					Satellite-based inversion of NOx emissions using the adjoint of CMAQ

Amir Hakami, John H. Seinfeld (Caltech) Qinbin Li (JPL) Daewon W. Byun, Violeta Coarfa, Peter Percell (UH) Adrian Sandu, Kumaresh Singh (VaTech)

CMAS, 10/18/2006

• Inverse modeling is our primary approach for reducing model prediction uncertainties.
– Among all model parameters, emission uncertainties play the most significant role.

• Inverse modeling requires sensitivity information. When a large number of model parameters are inverted, adjoint sensitivity analysis provides an efficient tool.
– Variational methods have been widely used in meteorology and oceanography. – 4D-Var applications in atmospheric modeling is receiving increasing attention. – Adjoint analysis has been recently implemented in CMAQ.

CMAS 10/18/2006

4D-Var formulation

•

Cost function is defined as:
J  J Observations  J Background  1 CDCMAQ  CDSCIA T O 1 CDCMAQ  CDSCIA   1 E  Eb T B 1 E  Eb 2 2









– The first part of the cost function is a measure of distance (mismatch) between the model predictions and observations. The second term penalizes deviations from background (a-priori) estimates. – The weight factor is used to assign proper emphasis on the observations. – Gradients of the cost function with respect to the control variables,  J   , are calculated during backward calculations. – The cost function is minimized iteratively using a quasi-Newton optimization algorithm (LBFGS).

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4D-Var formulation (II)

• Instead of adjusting absolute emissions, optimal emission scaling factors are found. Normalized gradients are used in the optimization:
J  k  Ek J Ek

• Cost function is re-defined as:
J 1 CDCMAQ  CDSCIA  T O1 CDCMAQ  CDSCIA  1 f 1T Bn1 f 1 2 2 f ,k  max k , 1  k 

– By using scaling factors, relative changes are compared at various locations. Also, zero-emission cells will not be assigned emissions as a result of optimization.

CMAS 10/18/2006

Application
• • • • CMAQ-ADJ with CB-IV chemical mechanism. 3-day simulation (6/20/20056/22/2005). 36 km horizontal resolution (45x46), 23 vertical layers. 3-D time-independent, emission scaling factors (47610 control variables). Independent background error covariance matrix with 100% uncertainty. Time-dependent boundary conditions from GEOS-Chem global model (ozone, NO, NO2, PAN, HNO3). SCIAMACHY tropospheric NO2 column densities used as observations.
CMAS 10/18/2006

•
•

•

4d-Var test

• Inversion with pseudoobservations (identical twin experiment) where the true answer is known. • After 15 iterations scaling factors are approximately recovered. • Not a realistic case, as abundance of (pseudo-) observations helps the assimilation.

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SCIAMACHY NO2 tropospheric columns

• One overpass per day during 3-day period.
– Observational time rounded to closest advection time.

Day 1

Day 2

Day 3

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Mapping CMAQ to SCIAMACHY grid

T CDCMAQ  K trop H CCMAQ  where

H  Hv Hh

K trop  K
• •

AMF AMFtrop

CMAQ grid cells are interpolated horizontally and vertically to produce concentrations that correspond to SCAIMACHY averaging kernel. Adjoint of mapping operators is used in forcing term propagation in backward calculations.
J Obs, k  1 T K k H v ,k H h ,k CCMAQ,k  CDSCIA,k 2 2Ok





2

k 

1 T T T H h ,k H v ,k K k K k H v ,k H h ,k CCMAQ,k  CDSCIA,k 2 Ok




CMAS 10/18/2006

Model Predictions vs. SCIAMACHY retrievals

Day 1

Day 2

Day 3

SCIA

CMAQ

(x 10-15)

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• • Adjoint variables indicate regions of influence on the cost function. NO2 is generally considered a short-lived species. As a result other investigators have corrected the mismatch in model predictions by adjusting (only) the local emissions. This assumption appears to be an oversimplification, particularly at finer scales.
NO

PAN

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Cost function reduction

Cost function minimization
700

600

Cost function

500

400

300 0 5 10 15 20 25 30 35 40 45 50

Iteration number

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Assimilated results: Day I

After

SCIA

Before

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Assimilated results: Day II

After

SCIA

Before

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Assimilated results: Day III

After

SCIA

Before

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Scaling factors

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Independent verification (day IV)

After

SCIA

Before

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Conclusions

• Adjoint analysis provides an efficient tool for fine scale inversion of chemically active species and their precursors emissions. • In general, CMAQ underestimates SCIAMACHY retrievals, leading to significantly scaled-up emissions. • For column density assimilation, inclusion of lightning emissions seems necessary. • Even though emissions scaling factors are mostly local to the retrievals, the effect of emissions carry-over into the following day can be sizable. • Emissions scaling results in improved model prediction, even for days that were not included in the inversion.

CMAS 10/18/2006

Future work

• Inclusion of lightning emissions. • Addition of other parameters to the control variables. Boundary conditions can also be scaled. • Addition of ground-level observations of NO2. • Multi-pollutant assimilation.

CMAS 10/18/2006

Acknowledgements

• This work was supported by funding from:
– NSF-ITR – JPL

CMAS 10/18/2006

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