Methods for processing eddy covariance Methods for processing eddy covariance data: (re-)inventing the wheel. data: (re-)inventing the wheel.

Asko NoormetsAsko Noormets

IN

Measurements

10 Hz data of • 3D wind speed

• Tsonic

• H2O

• CO2

• Pressure

OUT

Fluxes

0.000556 Hz data of • Fc (carbon flux)

• LE (water flux)

• Hs (sensible heat flux)

Pro

cess

ing

Theoretical assumptions (D. Baldocchi, J. Finnigan et al.)

• Conservation of mass, i.e. input+output+storage=0

• Reynolds’ decomposition• Averaging done over long enough period (accommodate larger

eddies), and over short enough periods (not be affected by diurnal patterns)

uuu

Flux = change in mixing ratio (I)+ advection (II)+ flux divergence (vertical, lateral & longitudinal) (III)+ biological source/sink strength (IV)

Ideally:

I=0, II=0, III=0

In reality:

I II III 0

Measured covariance = true covariance + sensor bias

),,( zyxSy

F

x

F

z

F

t

cw

t

cv

t

cu

t

c

dt

cdB

yxz

I II III IV

''c

wF

Processing steps (D. Billesbach)

1. Replace spikes (>6) with the moving window mean.

2. Correct sonic temperature (CSAT) for humidity & pressure (IRGA).

3. Calculate deviations of each measurement from a 30-minute block average.

4. Calculate rotation angles using the block means (vmean = 0; wmean = 0).

5. Calculate all possible covariance pairs and rotated covariances.

6. Calculate density correction terms for LE and Fc (WPL).

7. Calculate the frequency correction factor for the sonic anemometer.

8. Calculate the frequency correction factor for the sonic anemometer and IRGA combination.

9. Adjust the WPL H term by the sonic frequency correction factor.

10. Adjust Fc and the WPL LE terms by the sonic-IRGA frequency correction factor.

11. Calculate final LE and Fc, that are rotated, adjusted for density and frequency bias.

******

*

Data processing

`

Coordinate rotation

u

vw

Rotation:

0''

0

0

wv

w

v

Fc+wpl+storage, July

- w/o rotation

- rotated

s i t e=mhw

f c_sum

- 1. 2

- 1. 1

- 1. 0

- 0. 9

- 0. 8

- 0. 7

- 0. 6

- 0. 5

- 0. 4

- 0. 3

- 0. 2

- 0. 1

0. 0

0. 1

0. 2

0. 3

0. 4

t i me

0. 0 0. 1 0. 2 0. 3 0. 4 0. 5 0. 6 0. 7 0. 8 0. 9 1. 0

s i t e=mr p

f c_ sum

- 1. 5

- 1. 4

- 1. 3

- 1. 2

- 1. 1

- 1. 0

- 0. 9

- 0. 8

- 0. 7

- 0. 6

- 0. 5

- 0. 4

- 0. 3

- 0. 2

- 0. 1

0. 0

0. 1

0. 2

0. 3

0. 4

t i me

0. 0 0. 1 0. 2 0. 3 0. 4 0. 5 0. 6 0. 7 0. 8 0. 9 1. 0s i t e=pb

f c_ sum

- 0. 8

- 0. 7

- 0. 6

- 0. 5

- 0. 4

- 0. 3

- 0. 2

- 0. 1

0. 0

0. 1

0. 2

0. 3

0. 4

0. 5

0. 6

t i me

0. 0 0. 1 0. 2 0. 3 0. 4 0. 5 0. 6 0. 7 0. 8 0. 9 1. 0s i t e=yhw

f c_sum

- 0. 8

- 0. 7

- 0. 6

- 0. 5

- 0. 4

- 0. 3

- 0. 2

- 0. 1

0. 0

0. 1

0. 2

0. 3

0. 4

0. 5

t i me

0. 0 0. 1 0. 2 0. 3 0. 4 0. 5 0. 6 0. 7 0. 8 0. 9 1. 0

s i t e=yr p

f c_ sum

- 0. 9

- 0. 8

- 0. 7

- 0. 6

- 0. 5

- 0. 4

- 0. 3

- 0. 2

- 0. 1

0. 0

0. 1

0. 2

0. 3

t i me

0. 0 0. 1 0. 2 0. 3 0. 4 0. 5 0. 6 0. 7 0. 8 0. 9 1. 0

Fc+wpl+storage, November

- w/o rotation

- rotated

s i t e=mhw

f c_ sum

- 0. 30

- 0. 28

- 0. 26

- 0. 24

- 0. 22

- 0. 20

- 0. 18

- 0. 16

- 0. 14

- 0. 12

- 0. 10

- 0. 08

- 0. 06

- 0. 04

- 0. 02

0. 00

0. 02

0. 04

0. 06

0. 08

0. 10

t i me

0. 0 0. 1 0. 2 0. 3 0. 4 0. 5 0. 6 0. 7 0. 8 0. 9 1. 0

s i t e=mr p

f c_ sum

- 0. 5

- 0. 4

- 0. 3

- 0. 2

- 0. 1

0. 0

0. 1

t i me

0. 0 0. 1 0. 2 0. 3 0. 4 0. 5 0. 6 0. 7 0. 8 0. 9 1. 0s i t e=pb

f c_ sum

- 0. 20

- 0. 18

- 0. 16

- 0. 14

- 0. 12

- 0. 10

- 0. 08

- 0. 06

- 0. 04

- 0. 02

0. 00

0. 02

0. 04

0. 06

0. 08

0. 10

0. 12

0. 14

0. 16

0. 18

0. 20

0. 22

0. 24

0. 26

0. 28

0. 30

0. 32

t i me

0. 0 0. 1 0. 2 0. 3 0. 4 0. 5 0. 6 0. 7 0. 8 0. 9 1. 0s i t e=yhw

f c_ sum

- 0. 14

- 0. 12

- 0. 10

- 0. 08

- 0. 06

- 0. 04

- 0. 02

0. 00

0. 02

0. 04

0. 06

0. 08

0. 10

0. 12

0. 14

0. 16

0. 18

0. 20

0. 22

0. 24

0. 26

0. 28

t i me

0. 0 0. 1 0. 2 0. 3 0. 4 0. 5 0. 6 0. 7 0. 8 0. 9 1. 0

s i t e=yr p

f c_ sum

- 0. 23

- 0. 22

- 0. 21

- 0. 20

- 0. 19

- 0. 18

- 0. 17

- 0. 16

- 0. 15

- 0. 14

- 0. 13

- 0. 12

- 0. 11

- 0. 10

- 0. 09

- 0. 08

- 0. 07

- 0. 06

- 0. 05

- 0. 04

- 0. 03

- 0. 02

- 0. 01

0. 00

0. 01

0. 02

0. 03

t i me

0. 0 0. 1 0. 2 0. 3 0. 4 0. 5 0. 6 0. 7 0. 8 0. 9 1. 0

Respiration, with () and without () coordinate rotation

s i t e=mhw

r espi r

0. 10

0. 11

0. 12

0. 13

0. 14

0. 15

0. 16

0. 17

0. 18

0. 19

t i me

0. 0 0. 1 0. 2 0. 3 0. 4 0. 5 0. 6 0. 7 0. 8 0. 9 1. 0

s i t e=mhw

r espi r

0. 012

0. 013

0. 014

0. 015

0. 016

0. 017

0. 018

0. 019

0. 020

0. 021

0. 022

0. 023

0. 024

0. 025

0. 026

0. 027

0. 028

0. 029

0. 030

0. 031

0. 032

0. 033

0. 034

t i me

0. 0 0. 1 0. 2 0. 3 0. 4 0. 5 0. 6 0. 7 0. 8 0. 9 1. 0

July

November

Rotation effect (rerel):

- uncorrected flux

- wpl-corrected

- wpl- & storage-corrected, gapfilled

mont h=7

r ot eff 4

- 1. 1

- 1. 0

- 0. 9

- 0. 8

- 0. 7

- 0. 6

- 0. 5

- 0. 4

- 0. 3

- 0. 2

- 0. 1

0. 0

0. 1

0. 2

0. 3

0. 4

0. 5

0. 6

0. 7

0. 8

0. 9

t i me

0. 0 0. 1 0. 2 0. 3 0. 4 0. 5 0. 6 0. 7 0. 8 0. 9 1. 0

mont h=11

r ot eff 4

- 3

- 2

- 1

0

1

2

3

t i me

0. 0 0. 1 0. 2 0. 3 0. 4 0. 5 0. 6 0. 7 0. 8 0. 9 1. 0

rotated

rawrotated

Fc

Fc-Fc

relre

July

November

AQ parameters, MHW

- w/o rotation

- rotated

0

1

2

3

4 6 8 10

Month

Pmax

0

0.001

0.002

0.003

0.004

4 6 8 10

Month

Alpha

-0.3

-0.2

-0.1

0

4 6 8 10

Month

Resp

iration

Comparison of three methodsFc, July 21-26, 2002

C-1-rot. vs. C-2-roty = 0.6413x - 0.1867

R2 = 0.4917

-2

-1

0

1

2

-2 -1 0 1 2

SAS-1-rot. vs. C-2-roty = 0.855x - 0.1399

R2 = 0.6819

-2

-1

0

1

2

-2 -1 0 1 2

SAS-1-rot. vs. C-1-rot.y = 0.943x - 0.0164

R2 = 0.6933

-2

-1

0

1

2

-2 -1 0 1 2

Comparison of three methods, July 21-26, 2002

-2

-1

0

1

2

7/21 7/22 7/23 7/24 7/25 7/26 7/27

2 rotations, C+

1 rotation, C+

1 rotation, SAS

Comparison of three methodsLE, July 21-26, 2002

C-1-rot. vs. C-2-rot.y = 0.6856x + 28.778

R2 = 0.7051

0

100

200

300

400

500

600

0 100 200 300 400 500 600

SAS-1-rot. vs. C-2-rot.y = 0.7248x + 23.361

R2 = 0.728

0

100

200

300

400

500

600

0 100 200 300 400 500 600

SAS-1-rot. vs. C-1-rot.y = 0.9477x + 2.8615

R2 = 0.7988

0

100

200

300

400

500

600

0 100 200 300 400 500 600

Uncertainties remain

Flux = change in concentration (I)+ advection (II)+ flux divergence (vertical, lateral & longitudinal) (III)+ biological source/sink strength (IV)

Ideally:

I=0, II=0, III=0

In reality:

I II III 0

Measured covariance = true covariance + sensor bias

(high- and low-pass filtering

spectral correction factors 1.04-1.36 for Fc and LE)

),,( zyxSy

F

x

F

z

F

t

cw

t

cv

t

cu

t

c

dt

cdB

yxz

For more comprehensive overview:

Finnigan JJ, Clement R, Malhi Y, Leuning R, Cleugh HA (2003) A re-evaluation of long-term flux measurement techniques - Part I: Averaging and coordinate rotation. Boundary-Layer Meteorology 107, 1-48.