Modeling approach to regional flux inversions at WLEF Modeling approach to regional flux inversions at WLEF Marek Uliasz Department of Atmospheric Science.

Modeling approach to regional flux inversions at WLEF

Modeling approach to regional flux inversions at WLEF

Marek UliaszDepartment of Atmospheric Science

Colorado State University

Who needs data?Who needs data?or

CSU RAMSCSU RAMS

LPD modelLPD model

influence functionsinfluence functionsfor concentrationfor concentration for vertical fluxfor vertical flux

Bayesian inversionBayesian inversion

modeling frameworkmodeling framework

*

00 0 0

*00

0 0 0

* * * *

0 00 0 0 0 0 0

( )

ˆ ˆ( ) ( )

yx

yx

y x

x y

LLT

z

LL H

t

L LT H T H

W E S Nx x L y y L

C

C qdxdydt

C C dxdydz

uC C u C C dydzdt vC C vC C dxdzdt

influence function for concentration measurements C*influence function for concentration measurements C*

concentration sample

*

00 0 0

*00

0 0 0

* * * *

0 00 0 0 0 0 0

( )

ˆ ˆ( ) ( )

yx

yx

y x

x y

LLT

z

LL H

t

L LT H T H

W E S Nx x L y y L

C

C qdxdydt

C C dxdydz


surface fluxes



*

00 0 0

*00

0 0 0

* * * *

0 00 0 0 0 0 0

( )

ˆ ˆ( ) ( )

yx

yx

y x

x y

LLT

z

LL H

t

L LT H T H

W E S Nx x L y y L

C

C qdxdydt

C C dxdydz


surface fluxes

initial concentration



*

00 0 0

*00

0 0 0

* * * *

0 00 0 0 0 0 0

( )

ˆ ˆ( ) ( )

yx

yx

y x

x y

LLT

z

LL H

t

L LT H T H

W E S Nx x L y y L

C

C qdxdydt

C C dxdydz


surface fluxes

initial concentration

inflow fluxes



0 100 200 300 400 500 600 700 800 900 1000 1100

-200

-100

0 03:00

0 100 200 300 400 500 600 700 800 900 1000 1100

-200

-100

0 09:00

0 100 200 300 400 500 600 700 800 900 1000 1100

-200

-100

0

y

[km

]

15:00

0 100 200 300 400 500 600 700 800 900 1000 1100

x [km]

-200

-100

0 21:00

R-tracer

1E-011

5E-011

1E-010

5E-010

1E-009

influence functions for surface fluxes: 1D PBLinfluence functions for surface fluxes: 1D PBL

0 100 200 300 400 500 600 700 800 900 1000 1100

-200

-100

0 03:00

0 100 200 300 400 500 600 700 800 900 1000 1100

-200

-100

0 09:00

0 100 200 300 400 500 600 700 800 900 1000 1100

-200

-100

0

y

[km

]

15:00

0 100 200 300 400 500 600 700 800 900 1000 1100

x [km]

-200

-100

0 21:00

R-tracer

1E-011

5E-011

1E-010

5E-010

1E-009

0 100 200 300 400 500 600 700 800 900 1000 1100

-200

-100

0 03:00

0 100 200 300 400 500 600 700 800 900 1000 1100

-200

-100

0 09:00

0 100 200 300 400 500 600 700 800 900 1000 1100

-200

-100

0

y

[km

]

15:00

0 100 200 300 400 500 600 700 800 900 1000 1100

x [km]

-200

-100

0 21:00

A-tracer

1E-011

5E-011

1E-010

5E-010

1E-009

influence functions for surface fluxes: 1D PBLinfluence functions for surface fluxes: 1D PBL

WLEF tower – July 1997influence function for passive tracer

4 8 5 0 5 2 5 4 5 6 5 8 6 0 6 2 6 4 6 6 6 8 7 0 7 20

0.5

1

1.5

2

hei

gh

t [k

m]

4 8 5 0 5 2 5 4 5 6 5 8 6 0 6 2 6 4 6 6 6 8 7 0 7 2

sam pling tim e [hours]

0

0.5

1

1.5

2

hei

gh

t [k

m]

0

0.08

0.16

0.24

0.32

0.4

D=100km

D=500km

influence functions for inflow fluxes: 1D PBLinfluence functions for inflow fluxes: 1D PBL

4 8 5 0 5 2 5 4 5 6 5 8 6 0 6 2 6 4 6 6 6 8 7 0 7 20

0.5

1

1.5

2

hei

gh

t [k

m]

4 8 5 0 5 2 5 4 5 6 5 8 6 0 6 2 6 4 6 6 6 8 7 0 7 2

sampling time [hours]

0

0.5

1

1.5

2

hei

gh

t [k

m]

0

0.08

0.16

0.24

0.32

0.4

D=100km

D=500km

30m sample 1100m sample

0 6 12 18 24local time [hours]

-16

-14

-12

-10

-8

-6

-4

-2

0

2

4

6C

O2

flu

x [

mol

m-2

s-1 ]

CO 2 f luxapproxobs

respiration flux

assimilation flux

NEE constrains

used in inversion calculations: NEE=R+AR=R0

A=A0cvegRAD/(RAD+200)R0,A0 – unknown parameters to be estimatedRAD, cveg – from RAMS

CW

1000 km

x

z

D

q

sam

ple

s

D D D

q0

Two-Tower Inversions

• R is very well estimated

• A isn’t bad• NEE very hard to

estimate with unknown inflow

• Best estimates when towers are spaced optimally w.r.t. travel time (daytime)

0 40 80 120 160 200

0

25

50

75

100R fluxA fluxnet CO2 flux

0 40 80 120 160 200

0

25

50

75

100

RM

SE

/flu

x [%

]

0 40 80 120 160 200d - distance between towers [km]

0

25

50

75

100

2x400m towers

400m+30m towers

2x30m towers

200 400 600 800 1000

x [km]

200

400

600

800

1000

y [k

m]

W LEF tower - single level (76m)

200 400 600 800 1000

x [km]

200

400

600

800

1000

W LEF tower - all levels

Climatology of influence functions for August 2000

influence functions derived from RAMS/LPD model simulations passive tracer different configurations of concentration samples - time series from - a single level of WLEF tower - all levels of WLEF tower - WLEF tower + six 76m towers

200 400 600 800 1000

x [km]

200

400

600

800

1000

all towers

0.010.020.050.10.20.51251020

[ppm/umol]

Regional inversionsRegional inversions

reduction of uncertainty in flux estimationreduction of uncertainty in flux estimation

pseudo-data generation and ensemble inversion pseudo-data generation and ensemble inversion

0 300 600 900 1200

0

300

600

900

1200 N

E

S

W

Configuration of source areaswith WLEF tower in the centerof polar coordinates

Example of estimation of NEE averaged for August 2000 Bayesian inversion technique using influence function derived from CSU RAMS and Lagrangian particle model flux estimation for source areas in polar coordinates within 400 km from WLEF tower (better coverage by atmospheric transport) NEE decomposed into respiration and assimilation fluxes: R=R0, A=A0 f(short wave radiation, vegetation class) inversion calculations for increasing number of concentration data (time series from towers) NEE uncertainty presented in terms of standard deviation derived from posteriori covariance matrix inflow CO2 flux is assumed to be known from a large scale transport model in further work, concentration data from additional tower will be used to improve the inflow flux given by a large scale model

0

1

2

3

4

0

1

2

3

4

a-p

rio

ri N

EE

un

cert

ain

ty

0

1

2

3

4

NE

E e

sti

ma

tio

n u

nce

rtai

nty

[m

ol/s

/m2]

d istance [km]0-100100-200200-300300-400

W LEF 76m(single level) W LEF all levels W LEF all levels

+ 6 additional towers

N N NE S W E S W E S W

DIRECTIONAL SECTOR

0

1

2

3

0

1

2

3

a-p

rio

ri N

NE

un

cert

ain

ty

0

1

2

3

NE

E e

sti

ma

tio

n u

nce

rta

inty

[m

ol/s

/m2 ]

distance [km]0-100100-200200-300300-400

1 ppm 2 ppm 3 ppm

N N NE S W E S W E S W

DIRECTIONAL SECTOR

E F F E C T O F D A T A -M O D E L M I S M A T C H E R R O R ( a ll tow er s)

CSU RAMSCSU RAMS

LPD modelLPD model

influence functionsinfluence functionsfor concentrationfor concentration for vertical fluxfor vertical flux

Bayesian inversionBayesian inversion

modeling frameworkmodeling framework

Signature of Lake Superior inWLEF tower CO2 concentration data

Attempt to validate transport modeling

Example of using influence function to analyze observational data

… following data analysis by Noel R. Urban:

2000 WLEF data: CO2 concentration lake and land sectors determined by 396m wind direction wind speed < season median daytime only 10:00-17:00

… following data analysis by Noel R. Urban:

2000 WLEF data: CO2 concentration lake and land sectors determined by 396m wind direction wind speed < season median daytime only 10:00-17:00

200 300 400 500 600 700 800 900 1000 1100

X [km]

200

300

400

500

600

700

800

900

1000

1100

Y [

km]

200 300 400 500 600 700 800 900 1000 1100

X [km]

200

300

400

500

600

700

800

900

1000

1100

Y [

km]

200 300 400 500 600 700 800 900 1000 1100

X [km]

200

300

400

500

600

700

800

900

1000

1100

Y [

km]

Repeating analysis for all available CO2 data 1996-2001

0 2 4 6 8 10 121

0.8

0.6

0.4

0.2

0

0.2

0.4

0.6CO2 concentration difference: lake-land

month

0.433

0.964

delta396 m

delta244 m

delta122 m

delta76 m

delta30 m

111 m

Repeating data analysis for August 2000

0 50 100 150 200 250 300 350 4000

0.1

0.2

0.3

0.4

0.5

0.6

0

delta k

39630 levelk

n 743

nlake 66

nland 46

problems: a lot of missing wind data at 396m (only 62% of wind data available during 1996-2001 daytime hours) sectors poorly represent land or water source areas

problems: a lot of missing wind data at 396m (only 62% of wind data available during 1996-2001 daytime hours) sectors poorly represent land or water source areas

Modeling approach to data analysis: RAMS simulation: (August 2000, 2 nested grids)

LPD model influence functions

Modeling approach to data analysis: RAMS simulation: (August 2000, 2 nested grids)

LPD model influence functions

200 300 400 500 600 700 800 900 1000 1100

X [km]

200

300

400

500

600

700

800

900

1000

1100

Y [

km]

0

0.001

0.005

0.01

0.05

0.1

0.5

1

Influence function: August 2000, entire domain

200 300 400 500 600 700 800 900 1000 1100

X [km]

200

300

400

500

600

700

800

900

1000

1100

Y [

km]

0

0.001

0.005

0.01

0.05

0.1

0.5

1

Influence function: August 2000, land

200 300 400 500 600 700 800 900 1000 1100

X [km]

200

300

400

500

600

700

800

900

1000

1100

Y [

km]

0

0.001

0.005

0.01

0.05

0.1

0.5

1

Influence function: August 2000, water

200 300 400 500 600 700 800 900 1000 1100

X [km]

200

300

400

500

600

700

800

900

1000

1100

Y [

km]

0

0.001

0.005

0.01

0.05

0.1

0.5

1

Influence function: August 2000, land

0 124 248 372 496 620 7440

0.2

0.4

0.6

0.8

"land" sector: 120-320 deg1

0

land_landi

land_alli

land_water i

land_alli

7440 i

0 124 248 372 496 620 7440

0.2

0.4

0.6

0.8

"lake" sector: 340-45 deg

lake_landi

lake_alli

lake_water i

lake_alli

i

0 124 248 372 496 620 7440

0.2

0.4

0.6

0.8

"land" sector: 120-320 deg

land_landi

land_alli

land_water i

land_alli

i

0 124 248 372 496 620 7440

0.2

0.4

0.6

0.8

"lake" sector: 340-45 deg1

0

lake_landi

lake_alli

lake_water i

lake_alli

7440 i

0 100 200 300 400 500 600 7000

2

4

6"land" sector: 120-320 deg

land_landi

lake_landi

i

0 100 200 300 400 500 600 7000

2

4

6"lake" sector: 340-45 deg

lake_landi

lake_water i

i

0 100 200 300 400 500 600 7000

2

4

6"land" sector: 120-320 deg

land_landi

lake_landi

i

0 100 200 300 400 500 600 7000

2

4

6"lake" sector: 340-45 deg

6

0

lake_landi

lake_water i

7440 i

what 400m tower sees in “land” and “lake” sectors in August 2000

Applying modeling approach to data analysis for August 2000

0 100 200 300 400 500 600 700 8000

0.2

0.4

0.6

0.8

hours

0.998

1.622 103

landday396 i lakeday396( )

i

7430 i

Relative contribution from Lake Superior and all land areas

0 100 200 300 400 500 600 700 8000

0.2

0.4

0.6

0.8

hours

landday396 i lakeday396( )

i

i

rows c396( ) 744

nnn2 c396 landday396 0.8( ) 458

nnn2 c396 lakeday396 0.5( ) 27

nnn2 c396 lakeday396 0.6( ) 9

nnn2 c396 lakeday396 0.7( ) 2


0.1 0.2 0.3 0.4 0.54

2

0

2

4lake-land CO2 concentration [ppm]

fraction of Lake Superior contribution

3.976

2.041

sum2 c396 lakeday396 cc( ) sum2 c396 landday396 0.8( )( )


0.60.2 cc


0.1 0.2 0.3 0.4 0.54

2

0

2



3.976

2.041



0.60.2 cc


0.1 0.2 0.3 0.4 0.54

2

0

2



3.976

2.041



0.60.2 cc

0.1 0.2 0.3 0.4 0.50

100

200

300number of obs data analyzed


221

4

nnn2 c396 lakeday396 cc( )

nnn2 c244 lakeday244 cc( )

0.60.2 cc

0 100 200 300 400 500 600 7000

0.2

0.4

0.6

0.8

lakeday396 i

i

0 100 200 300 400 500 600 700

340

360

380

c396( )i

i

time series analysis?

lake contributionlake contribution

CO2concentrationCO2concentration

RAMS/LPD simulations for WLEF areaRAMS/LPD simulations for WLEF area


Summer 2000Summer 2000





Pseudo-data inversions using the Ring of Towers (Summer 2000)









Real data inversions using the Ring of Towers (Summer 2004)









Data analysis using influence functionsData analysis using influence functions

Modeling approach to regional flux inversions at WLEF Modeling approach to regional flux inversions at WLEF Marek Uliasz Department of Atmospheric Science.

Documents

wlef data

concentration measurements

observational data

co2 concentration lake

available co2 data

repeating data analysis

wind data available

additional tower