Fourdimensional Variational 4DVar Chemical Data Assimilation Using STEM

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Four-dimensional Variational (4D-Var) Chemical
Data Assimilation Using STEM
Tianfeng Chai Center for Global and Regional
Environmental Research University of Iowa
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Outline

• Introduction to 4D-Var data assimilation
• Early applications using Trace-P data
• Target-oriented adjoint sensitivity analysis
• New development for ICARTT data
• Model background error statistics
• 4D-Var Implementation of background error
  statistics using TSVD
• Top-down emission inversion

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Data assimilation Model Observation
To understand and/or forecast air pollution, we
need

• Measurements, samplings of the reality
• Chemical Transport Models (CTMs), describing the
  physical and chemical processes
• Data assimilation techniques, optimally integrate
  models and observations
• Background (a priori) error statistics
• Observation error statistics
• Model error information

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Data assimilation
(new)
dx
(old forecast)
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Challenges in chemical data assimilation

• A large amount of variables (100 concentrations
  of various species at each grid points)
• Memory shortage (check-pointing required)
• Various chemical reactions (gt200) coupled
  together (lifetimes of species vary from seconds
  to months)
• Stiff differential equations
• Chemical observations are very limited, compared
  to meteorological data
• Information should be maximally used, with least
  approximation
• Highly uncertain emission inventories
• Inventories often out-dated, and uncertainty not
  well-quantified

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Computational aspects

• Parallel Implementation using our PAQMSG library
• The parallel adjoint STEM implements a
  distributed checkpointing scheme

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Chemical Transport Model

• 3D atmospheric transport-chemistry model
  (STEM-III)

where chemical reactions are modeled by
nonlinear stiff terms

• Use operator splitting to solve CTM

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Basic idea of 4D-Var

• Define a cost functional

which measures the distance between model output
and observations, as well as the deviation of the
solution from the background state

• Derive adjoint of tangent linear model

Where fis the forcing term, which is chosen so
that the adjoint variables are the sensitivities
of the cost functional with respect to state
variables (concentrations), i.e.

• Use adjoint variables for sensitivity analysis,
  as well as data assimilation

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4D-Var application with CTMs
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Trace-P DC-8 and P3-B flights on 3/7/2001

• Simulated region East Asia
• Simulated time interval 12 hours (starting at
  00000 GMT 3/7/01)
• Meteorological fields given by RAMS
• Grid size 90 60 18
• Horizontal resolution 80 Km 80 Km
• Control parameters initial concentration
• Optimization algorithm L-BFGS-B

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DC-8 O3 observations and model predictions
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Effect on P3-B O3 model predictions
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Adjoint sensitivity analysis
Direct sensitivity analysis is a source-oriented
approach.
Adjoint sensitivity analysis is a
receptor/target-oriented approach.
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Influence functions (over Cheju O3 concentration
at 0000 UT, 3/07/01) of O3, NO2, HCHO at -48,
-24 hr
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Sensitivity Analysis
Adjoint sensitivities identify key species
affecting model predictions (NOy of P3-B).
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Selecting control variables
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NO and NO2 predictions after assimilating NOy
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Cone of influence Target 1600 GMT 8/6/04
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ICARTT
International Consortium for Atmospheric Research
on Transport and Transformation of Pollutants
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Observational error

• Observational Error
• Representative error
• Measurement error

• Observation Inputs
• Averaging inside 4-D grid cells
• Uniform error (8 ppbv)

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Air Quality Forecasts for NMC method
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NMC method

• Substitute model background errors with the
  differences between 24hr, 48 hr, 72 hr forecasts
  verifying at the same time
• Calculate the model background error statistics
  in three directions separately

• Equivalent sample number 811,890

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NMC method results

• Equivalent sample number 360,840

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NMC method results
Vertical correlation
Horizontal correlation
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Observational (Hollingsworth-Lönnberg) method
results
i
j
Rij
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Implementation using TSVD
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Vertical correlation of model errors, Z (left)
and Zq (Right, after TSVD truncation).
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Assimilated observations
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RMS error changes of model predictions
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DC-8 Ozone and model results
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P3 Ozone measurements and model results
Quantile-quantile measurements and model results
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Ron-Brown ozone and model results
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Assimilating satellite data
We are now assimilating MODIS (AOD), MOPITT
(CO), SCIAMACHY (column NO2) to constrain model
and estimate emission
Terra
http//www-misr.jpl.nasa.gov/

• Satellite data
• Global coverage
• Year-round operation

http//eosweb.larc.nasa.gov
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STEM SCIAMACHY tropospheric NO2 column
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Mean SCIAMACHY tropospheric NO2 column in
July-August,2004
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STD/Mean of tropospheric NO2 column
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NOx emission scaling factor
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Summary and future work

• 4D-Var data assimilation system developed for
  STEM is able to assimilate chemical observations
  into CTM
• generate better reanalysis
• target-oriented sensitivity analysis
• Top-down emission estimation
• Background model error has been analyzed using
  NMC and observational approaches.
• The utilization of the model error statistics in
  chemical data assimilation through TSVD improves
  model analysis and air quality forecasting.
• Adjusting initial concentration and emission
  inventories simultaneously in assimilation is
  being tested

This work is supported by NSF, NASA, and NOAA
grants
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Thank you!
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Introduction

• Understanding model uncertainty is crucial in
  chemical data assimilation
• Model uncertainties are studied using STEM
  forecasts during ICARTT
• Model error correlation covariance through NMC
  approach
• Model error variance through observational
  approach
• This information is then utilized in 4D-Var
  chemical data assimilation experiments
• Truncated Singular Value Decomposition used to
  solve ill-conditioning
• Validation is performed by withholding
  independent observations from the data
  assimilation tests. The effect of such chemical
  data assimilation on improving air quality
  forecasts is also evaluated.

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Sensitivities
O3
CO
NO2
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Assimilating multiple species
Measurement uncertainties O3 8 NO
20 NO2 20 HNO3 100 PAN 100 RNO3 100
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Assimilating multiple species
(In lower panels, green lines shows the effect of
more iterations)
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Predictability as Measured by Correlation
Coefficient Met Parameters are Best
lt 1km
O3 predicted better than CO
Performance decreases with altitude
Carmichael et al., JGR, 2003