A Strategy for Research in theApplication of Dynamic Data Assimilation

to Air Quality Forecasting

William R. Stockwell1,2, John M. Lewis2,3

and S. Lakshmivarahan4

Department of Chemistry, Howard University1; Division of Atmospheric Sciences, Desert Research Institute2; National Oceanic and Atmospheric Administration /National Severe Storm Laboratory3; School of Computer

Science, University of Oklahoma4

The Vision• To Provide the Nation with accurate and time-

resolved 4-day forecasts of ozone, PM2.5 and visibility.

EmissionsNOx

Biogenic Compounds

Hydrocarbons

ChemistryNO2 + h (+ O2) O3 O3 + NO NO2 + O2 HO + NO2 HNO3

Meteorology

Cloud Processes

Deposition

Environment

OzoneAerosols

Atmospheric Chemistry

Key to Data Assimilation is the Construction of a Background Error Covariance Matrix

How to determine the correlation between the errors for each variable when we don’t know the true state?

Note that for atmospheric chemistry the “true state” actually involves thousands of variables!

The development of a background error covariance matrix will require extensive parameterization of the chemistry.

>13>5>3>1>0

Emissionstons mile-2

NOx Emissions

U.S. EPA

>10>5>3>1>0

Emissionstons mile-2

VOC Emissions

U.S. EPA

>20>11>5>2>0

Emissionstons mile-2

Biogenic VOC Emissions

U.S. EPA

Biogenic Hydrocarbon Emissions

CH4

NO

NH3

isoprene -pinene

limonene -pinene

Tropospheric O3 ChemistryO3 Formation

NO2 + h O(3P) + NO O(3P) + O2 (+ M) O3 (+ M)

Ozone DestructionNO + O3 NO2 + O2

Steady-State Ozone Concentrations

d[NO]/dt = J[NO2] - k[NO][O3] 0

[O3] = {J / k} {[NO2] / [NO]}

Sun

HO Radical Production

O3 + h O(1D) + O2

O(1D) + N2 (+O2) O3

O(1D) + O2 (+O2) O3

O(1D) + H2O 2 HO

Sun

Alkane Oxidation

HO + CH3CH3 H2O + CH3CH2

CH3CH2 + O2 CH3CH2O2

CH3CH2O2 + NO CH3CH2O + NO2

CH3CH2O + O2 CH3CHO + HO2

HO2 + NO HO + NO2

Air Quality Equationscit = HVHci + [ ](ci)

zz

ci ( )hz K(ci/)

cit

+Chemistry

cit

+Emissions

cit

+Deposition

t = time ci = concentration of ith species VH = horizontal wind vector = net vertical entrainment rate z = terrain following vertical coordinate h = layer interface height = atmospheric density K = turbulent diffusion coefficient

Ozone Formation Chemistry

NONO2

h

HCHO, RCHO

HO

HO2

RO2

CO, VOC

H2O2 ROOH

O3

HNO3

NO2 PAN

from RO2

h

O3

from HO2

Ozone Formation

LOG(NOx, ppb)

ppb

-2-1

01

23

-10

12

34

LOG(VOC, ppbC)

100

200

O3

-2-1

01

23

LOG(NOx, ppb)

-10

12

34

LOG(VOC, ppbC)

2.5

5.0ppb

H2O2

HO

-10

12

34

LOG(VOC, ppbC)

-2-1

01

23

LOG(NOx, ppb)

0.20.40.60.8

ppt ppb

HNO3

10

20

-2-1

01

23

LOG(NOx, ppb)

-10

12

34

LOG(VOC, ppbC)

NOx and VOC Dependence

Relative Sensitivity of Ozone to Reaction Rate Constants. Initial total reactive nitrogen concentration is 2 ppb and total initial organic compounds is 50 ppbC.

0%

5%

10%

15%

20%

NO

2 +

hvO

3 +

NO

HO

+ N

O2

PAN

C

H3C

O3

+ N

O2

HO

2 +

NO

CH

3CO

3 +

NO

O3

+ hv

-> O

1DH

O +

CH

4O

1D +

H2O

O3

+ H

O2

O1D

+ N

2C

O +

HO

ALD

+ H

OC

H3O

2 +

NO

O1D

+ O

2H

O2

+ M

O2

HO

+ R

NO

3

HO

+ H

CH

OH

CH

O +

hv

-> H

O2

HO

+ K

ETH

O2

+ C

H3C

O3

HO

+ H

C5

HO

+ H

C3

HO

+ H

C8

HO

+ C

H3C

O3H

Oth

er R

eact

ions

Reaction

Rate constant for the O3 + NO reaction with upper and lower bounds.

Data from DeMore et al. (1997).

Z(m

)

-14

Z(m

)

0

5000

10000

15000

0.0 1 10-14 2 10k cm3 molecule -1 s-1

0

5000

10000

15000

1.1 1.2 1.3 1.4 1.5Uncertainty Factor

0

5000

10000

15000

0.0 2 10-11 4 10-11 6 10-11

k cm3 molecule -1 s-1

0

5000

10000

15000

2.0 2.5 3.0 3.5Uncertainty Factor

O3 + NO Reaction

O3 + NO Reaction

CH3O2 + HO2 Reaction

CH3O2 + HO2 Reaction

Uncertainties in rate parameters for HO• with alkenes.

The closed circles represent the nominal value while the crosses represent the approximate 1.

2 M

ethy

l - 1

- B

uten

e

2 M

ethy

l - 2

- B

uten

e

0.0

5.0 10-11

1.0 10-10

1.5 10-10

Ethe

ne

Prop

ene

1,3

But

adie

ne

Isop

rene

298 K

216 K

0.0

5.0 10-12

1.0 10-11

1.5 10-11

k H

O, c

m3 m

olec

ules

-1 s

-1k

HO

, cm

3 mol

ecul

es-1 s

-1

Mean values and 1 uncertainties of maximum incremental reactivity values for selected hydrocarbons determined from Monte Carlo simulations (Yang et al., 1995).

Yang et al., 1995

0.0

1.0

2.0

3.0

4.0

5.0

6.0

Form

alde

hyde

1,3-

But

adie

neP

rope

neIs

opre

neP

ropi

onal

dehy

deA

ceta

ldeh

yde

1,2,

4-TM

B

Eth

ene

3-M

-cyc

lope

nten

e

2-M

-2-B

uten

em

,p-X

ylen

eo-

Xyl

ene

2-M

-1-B

uten

eM

-cyc

lope

ntan

eTo

luen

eE

thyl

benz

ene

Eth

anol

ME

K2-

M-p

enta

neM

etha

nol

But

ane

2,2,

4-Tr

i-M-p

enta

ne

MTB

EB

enze

neE

than

eM

etha

ne

0E+00

2E+14

4E+14

6E+14

8E+14

200 300 400 500 600 700

Wavelength (nm)

DRI

Sunol

UC-Davis

Peterson Flux

Act

inic

Flu

x (p

hoto

ns s

-1 c

m -2

nm

-1 )

Comparison of Peterson flux with measured 4 actinic flux from UC-Davis, Sunol and DRI sites for

noon September 17, 2000.

0E+00

2E-03

4E-03

6E-03

8E-03

0 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96 102 108 114 120

Time (hr)

DRI

Sunol

UC-Davis

JNO

2 (s-1

)

September 17 September 18 September 19 September 20 September 21

Photolysis rate parameters of NO2 measured at UC-Davis, Sunol and DRI for episode September 17 to 21, 2000.

3-D Modeling Studies• Goal– Determine what spatial resolution is required to

effectively monitor lower tropospheric ozone from space.• Why?

– Satellite observations have the potential to provide an accurate picture of atmospheric chemistry. A key question when designing new satellite instruments is what spatial resolution is required to effectively monitor air quality from space.

• How?– Perform meteorological (MM5) and air chemistry (CAMx)

model simulations at 4, 8, 12, and 16km resolutions.– Produce variograms with the GSLIB Geostatistical

Software Library to calculate the spatial length scales of ozone.

C.P. Loughner, D.J. Lary, L.C. Sparling, P.de Cola, and W.R. Stockwell

• The horizontal range or smallest distance where there is no dependence on concentrations in other locations in the east-west and north-south directions were found to be 60 km.

• For a satellite platform to effectively monitor lower tropospheric ozone, the Nyquist sampling theorem tells us that it should have a spatial resolution of at least 30 km but preferably near 15 km.

• Future work – use same method to determine spatial resolution for other air quality species and find ideal temporal resolutions for air quality species

Lewis et al., 1989, BAMS 70, 24-29

GUFMEX Ship Track

Daytime Aerosol Formation

Source NO

NO + HO2 NO2 + HO

HO + NO2 (+M) HNO3 (+M)

HNO3 +NH3 NH4NO3 (aerosol)

NH4NO3 Deposition

kE

k1

k2

k3

kd

Rate Expressions for Daytime Aerosol Formation

d NO dt

kE k1 NO HO2

d NO2 dt

k1 NO HO2 k2 NO2 HO

d HNO3 dt

k2 NO2 HO k3,R NH4NO3 k3F HNO3 NH3

d NH4NO3 dt

k3F HNO3 NH3 k3R NH4NO3 kd NH4NO3

For our simple model assume:

[HO] and [HO2] are constant.

NO + HO2 NO2 + HO is a fast reaction.

HNO3 +NH3 NH4NO3 (aerosol)can be treated as net reaction:HNO3 +NH3 NH4NO3

The model becomes:

Source NOx

NOx HNO3

HNO3 Aerosol

Aerosol Depos.

Source A

A B

B C

C Deposition

kE

k1

k2

kd

d A dt

kE k1 A

d B dt

k1 A k2 B

d C dt

k2 B kd C

d Deposition dt

kd C

Chemistry Only Model Simplifies to:

Integrate withRunge-Kutta method.

0

10

20

30

40

Dep

ositi

on

0.0

0.5

1.0

1.5

2.0

2.5C

once

ntra

tion

0 1 2 3 4 5 6Time

[A]

[B]

[C]

Chemistry Only

Atmospheric Chemistry is Affected by Meteorology

H (Inversion - Mixing Height)

Typically air pollutants near the Earth’s surfaceare confined within the “boundary layer”.

The boundary layer may expand during thedaylight hours diluting mixture.

d A dt

kEH

d A dt

dHdt

[A]H

Emission RateAdjusted for H

Dilution Rate

d A dt

kEH

k1[A] dHdt

[A]H

d B dt

k1[A] k2[B] dHdt

[B]H

d C dt

k2[B] kd[C]H

dHdt

[C]H

dDepCdt

kd[C]H

Modified Atmospheric Chemistry Equations

H

Surface

Average Layer

z (A

ltitu

de)

Potential Temperature

HInversion Height

H wH

wS

wHeat Flux

Driedonks 1982

Profile of Potential Temperature and Heat Flux in a Mixed-Layer Model

ddz

Mixed-Layer Model Equations

d dt

1 k CTVo o H

d Hdt

w kCTVo o

d dt

dHdt

w

d dt

“T Jump”

Mixing Height

Average Potential Temperature of Layer

•Surface o

•Air layer •Difference at top •Surface wind-speed Vo

•Vertical wind velocity w•Mixing layer height H

286

288

290

292

294

Tem

pera

ture

(K)

0 120 240 360 480 600 720 840 960 1080 1200Time (Min)

GUFMEX Surface Layer Temperature

MeasuredFit

0

500

1000

1500

2000

Mix

ing

Hei

ght (

m)

294

295

296

297

298

299Po

tent

ial T

empe

ratu

re (K

)

0 1 2 3 4 5 6Time (hr)

0.0

2.5

5.0

7.5

10.0

12.5

Dep

ositi

on

0.0

0.5

1.0

1.5

2.0C

once

ntra

tion

0 1 2 3 4 5 6Time

[A]

Deposition

[B]

[C]

Initial Conditions for Monte Carlo Simulations

Initial chemical concentrations constant.[A] o = 1.0; [B] = 0.0; [C] = 0.0

Surface pressure (Po) varies between 950 and 1050 millibar.

Initial potential temperature of surface (o) and initial average potential temperature of air layer (o) varies between 295 and 305 K under the constraint that o > o.

Initial temperature jump ()o varies between 0.1 and 0.3 K.

Initial surface wind-speed (Vo)varies between 3. and 7 m/s.

Vertical velocity (w) varies between 0.0 and 0.2 m/s.

Initial mixing layer height (H) varies between 100 and 500 m.

0

50

100

150

200

Freq

uenc

y

0 2000 4000 6000 8000H

0

50

100

150

200

0 2000 4000 6000 80000

25

50

75

100

Perc

entil

e0 2000 4000 6000 8000

H

Mixing Height

0

100

200

300

400

500

Freq

uenc

y

0 1 2 3 4[A]

0

100

200

300

400

500

0 1 2 3 40

25

50

75

100

Perc

entil

e0 1 2 3 4

[A]

Emitted Species [A]

0

200

400

600

800

Freq

uenc

y

0.0 0.5 1.0 1.5 2.0[B]

0

200

400

600

800

0.0 0.5 1.0 1.5 2.00

25

50

75

100

Perc

entil

e

0.0 0.5 1.0 1.5 2.0[B]

Reacted Species [B]

0

50

100

150

200

Freq

uenc

y

0.75 0.80 0.85 0.90 0.95 1.00[C]

0

50

100

150

200

0.75 0.80 0.85 0.90 0.95 1.000

25

50

75

100

Perc

entil

e0.75 0.80 0.85 0.90 0.95 1.00

[C]

Aerosol Species [C]

0

100

200

300

400

500

Freq

uenc

y

0 20 40 60 80Deposition

0

100

200

300

400

500

0 20 40 60 800

25

50

75

100

Perc

entil

e0 20 40 60 80

Deposition

Deposition

How well could model parameters be determinedfrom “observations”?

For example, could deposition parameter (Kd) andsurface potential temperature (o) be determined fromobservations of the potential temperature of air layer ()and chemical concentrations [A] and [B]?

Test by calculating cost function while varying Kd and .

Cost = (i - obs)2 + ([A]i - [A]obs)2 +([B]i - [B]obs)2

0.05

0.10

0.15

0.20

Kdep

296

298

300

302

304

Surface Pot Temp

0

1000

2000

3000

4000

5000

0 1000 2000 3000 4000Temp_C_and_D_Total_Cost

Cost = (i - obs)2 + ([A]i - [A]obs)2 +([B]i - [B]obs)2

Cost Function for Kd and o.

KdSurface PotentialTemperature, o

Cost

Conclusions• The development of a Background Error Covariance Matrix

will require extensive parameterization of the chemistry.• The chemistry of the real atmosphere involves thousands

of chemical species.• Each species (in principle) requires a continuity equation.• There is significant uncertainty in the chemical parameters.• Lack of knowledge and computational resources require

that the chemistry to be simplified.• The atmospheric system is nonlinear and this leads to

complex behavior that is nontrivial even for models with only 7 variables (3 meteorological and 4 chemical).

Conclusions

• Sensitivity analysis supports the idea that simplifications can be made.

• Future research needs to be focused on improving the operational air quality forecasts.

• But experiments with simple, “toy” models may provide some valuable insights into the interactions of meteorology and chemistry.