Analysis of TraceP Observations Using a 4D-Var Technique

Tianfeng Chai, Greg R. CarmichaelCenter for Global and Regional Environmental Research, University of Iowa

Dacian N. Daescu Portland State University

Adrian SanduVirginia Ploytechnic Institute and State University

Background Significant advances have been made in Chemical

Transport Models

Large amounts of atmospheric chemistry observations are becoming available, but sometimes difficult for the conventional methods to use

Data assimilation has shown its capability in providing optimal analysis by integrating model analysis and measurements in meteorology, oceanography, and other fields

Why not apply data assimilation to atmospheric Chemistry? Number of variables Stiff system

Chemical Transport Model

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

Δ 2 Δ 2 Δ 2 Δ Δ 2 Δ 2 Δ 2[ Δ ]M t t t t t t tt t t X Y Z Z Y XT T T C T T T

Use operator splitting to solve CTM

where chemical reactions are modeled by nonlinear stiff terms

iiii ccDcPcf )()()(

iiiii EcfcKcut

c

)()(1

TraceP field experiment

Shown are measured CO along the aircraft flight path, the brown isosurface represents modeled dust (100 ug/m3), and the blue isosurface is CO (150 ppb)shaded by the fraction due to biomass burning (green is more than 50%).

Basic idea of 4D-Var

0 0 b 1 0 b obs 1 obs

0

1 1( )

2 2

NT Tk k k kk

k

J c c c B c c c c R c c

•Define a cost functional

•Derive adjoint of tangent linear model

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

λ λ( λ ) ρ (ρ )λ φ

ρTi i

i iiu K F c

t

Where is 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.

ii c

J

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

4D-Var application

Observations

Forward CTM model evolution

Backward adjoint model integration

Optimization

Cost function

Gradients

Update control variables

Checkpointing files

Computational aspects

Parallel Implementation using our PAQMSG library

The parallel adjoint STEM implements a distributed checkpointing scheme

Sensitivity analysis

In sensitivity analysis, the cost functional is chosen as

),(3

FinalO tChejucJ

The adjoint variables then give the sensitivities of ozone concentration at Cheju at the final time step to different chemical species at different time steps,

Influence functions (over Cheju O3 concentration at 0:0:00 UT, 3/07/01) of O3, NO2, HCHO at -48, -24 hr

Data assimilation test

Assimilation window

6 hours starting from 0:0:0 GMT on March 1st

Observations O3 and/or NO2 concentrations at the end of the assimilation window at all grid points from the reference run

Control variables

initial concentrations of O3 or NO2

Initial guess reference initial values increased by 20%

Data assimilation results

The evolutions of cost function and RMS error of the control variable during the optimization procedure. The results are normalized by their pre-assimilation values. Several tests are shown using different control (CTRL) and observed (OBS) variables.

•Timing : Assimilation/Forward = 2.2

Conclusions and future work

The current 4D-Var system is able to give detailed sensitivity analysis

The 4D-Var system can successfully reduce the cost function to recover the initial condition using Twin experiments

Using observations to adjust emissions (choosing emissions as control variables) is undergoing

We plan to use the current system in air quality forecast applications

•This work is supported by NSF Grant ITR/AP&IM 0205198.