China Flux 2019 Eddy Covariance Instrumentation 2.1 3.2... · 2019. 8. 15. · Eddy Covariance...

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China Flux 2019 Eddy Covariance Instrumentation

Ivan Bogoev, Larry Jacobsen, Eduard SwiatekBen Conrad, Bert Tanner

CAMPBELL SCIENTIFIC

China Flux 2019

Topic:The fundamental working principals and major field applications of sonic anemometer, CO2/H2O/trace gas analyzer, and atmospheric profile system

Contents a. How 3D sonic anemometer measures 3D wind b. Definition and calculation of sonic temperature c. Measurement working models of 3D wind speeds and sonic temperature d. Frequency response of sonic anemometer e. Optical principals of measuring CO2, H2O, and some trace gas species f. Spectrum absorption of CO2, H2O, and some trace gas species g. Beer-Bouguer Law h. Measurement working models of gas analyzer i. Frequency response of gas analyzer j. Applications of sonic anemometer, infrared gas analyzers in OPEC, CPEC and AP systems. k. Applications of laser trace gas analyzers in flux measurements.

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The beginning in 2002: Changbaishan

Passion, Dedication and Commitment to Flux Measurements



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Acknowledgements for contributions from:

T. Foken, J. Wingard, M. Aubinet, J. Kaimal, J. Finnigan,

R. Leuning, T. Horst, G. Burba, A. Grelle, R. Vogt, S. Oncley

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What is an eddy?“Eddies within eddies from near and far…”

Eddy Covariance Tall Tower Installation

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Eddy Covariance Measurement Principles

Vincent van Gogh “Starry Night” 1889 Google Art Project

“Vortices swirl around each star,Eddies within eddies from near and far…”

Mechanism of Turbulence Transfer - Eddies

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Mechanism of Turbulence Transfer Eddies and Scalars

Turbulent transport measured

by vertical wind and

• Temperature: Convection (Sensible Heat)

• Water Vapor: Evaporation (Latent Heat)

• CO2: Carbon Flux

• CH4: Methane Flux

• Horizontal Wind: Momentum Flux


w

scalar1 scalar2

flux1

flux2

u

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wscalar1 scalar2

flux1

flux2

u

Eddy Covariance Time Series

800 850 900 950 1000 1050 1100 1150 1200

Seconds

31

32

33

34

35

36

37

38

39

deg_

C

800 850 900 950 1000 1050 1100 1150 1200

-1.5

-1

-0.5

0

0.5

1

Sonic Temperature

(deg C)

Vertical Wind

(m/s)

m/s

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Reynolds decomposition of time series:

Reynolds averaging rules:


Ensemble Averaging: averaging over many realizations under identical conditions

Ergodic Hypothesis: time averages are equivalent to ensemble averages when the fluctuations are statistically stationary during the averaging time

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where: ρa is the dry air density, w is the vertical wind and s is the scalar (mixing ratio, temperature, etc.) overbar denotes average and prime denotes fluctuations

Assumptions: no divergence/convergence, no storage or accumulation of mass, average fluctuations are zero

Eddy flux:


Scalar definition of intensity of a constituent:

(A) in terms of molar density (mole m-3)

or mass density (kg m-3)

(B) in terms of mole fraction (mole mole-1) constituents partial pressure to the total pressure

or mass mixing ratio (kg kg-1) ratio of the mass of constituent to the mass of dry air

Only (B) are conserved quantities in the presence of changes in temperature, pressure and water vapor content

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Early Instruments for Atmospheric Turbulence and Wind Measurements

Wind vane with two perpendicular hot wire sensors

for measuring friction velocity (Obukhov, 1951)

Early Instruments for Eddy Covariance Measurements

Evapotron

Hot wire anemometer and psychrometer

Dyer (1965)

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Fluxatron

Propeller anemometer with fine wire thermometer

Dyer (1967)

Early Sonic anemometers

Businger (1969) University of Washington

Mitsuta & Hanafusa (1969) Kyoto University

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Fine wire PRT and spherical pressure probe for sensible heat flux measurements (Wesely 1970)

Early Sonic anemometers – orthogonal geometry

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History of the CSAT3 Sonic Anemometer

U.W. Sonic Anemometer (Zhang, Wyngaard, Businger and Oncley 1986)

Designed to reduce transducer shadowing for the horizontal wind components and increase the range of acceptable wind directions

University of Washington

Non-orthogonal design

Early Eddy-covariance System Designs

Hydra II

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History of the CSAT3 Sonic Anemometer

Slide by T. Foken

Transformation Matrices

Conversion from orthogonal to non-orthogonal coordinates

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Sonic Anemometer Measurement Principles


d

Out UparUperp

U

t = distance/speed

tout = d/(c + Upar)

c is speed of sound

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d

c

Back

UparUperp

U

tout = d/(c + Upar)

tback = d/(c - Upar)

Upar = d/2 (1/tback – 1/tout)

c = d/2 (1/tback + 1/tout)

Speed of Sound Measurement and Cross-Wind Correction

Acoustic Virtual Temperature is determined using Gas constant and Specific heat for dry air

Implemented in the firmware of the CSAT3

e=0dry air

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Accuracy of Acoustic Temperature Measurement

The distance (d) between the transducer faces needs to be measured accuratelyA deviation of 0.1 mm (a thickness of a sheet of paper) will result in a temperature error of about 0.3K

Research grade anemometers can resolve 0.002K

Transducer delays need to be calibrated over the entire operating temperature range

Acoustic Virtual Temperature Measurement

Speed of sound in humid air

Acoustic Temperature depends on the humidity of the air Acoustic Temperature>Air TemperatureAcoustic Temperature approximates virtual temperature

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Acoustic Virtual Temperature Measurement

Standalone sonic anemometer are not able to measure true air temperatureThe sonic virtual temperature spectrum is contaminated by water valor fluctuations scaled by absolute temperature q – specific humidity [kg kg-1] (moist air)

Sonic heat flux need a latent heat flux correction

The perfect instrument idea: all measurements are in the same volume IRGASON can provide true air temperature because of the synchronized and co-located water valor measurement

Fast-response Acoustically derived Air Temperature Measurement

IRGASON can provide true air temperature because of the synchronized and co-located water vapor measurement

e240 260 280 300 320 340

240

260

280

300

320

340XY plot

slope = 1.0014 R2 = 0.99994

Air Temperature [K]

Tso

nic H

um

idity

Cor

rect

ed

[K]

T1:1

240 260 280 300 320 340

-0.4

-0.2

0

0.2

0.4

0.6Residuals plot

Air Temperature [K]

Tpr

obe

- T

soni

c hum

idity

cor

rect

ed

[K]

InstantaneousMean

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Wind Offset and Distance Calibration: Temperature range -30 to +50 deg. C Piezoelectric transducers are resonant devices and have certain delay when excited. These delays are accounted during calibration in a zero-wind environmental chamber.

-30 -20 -10 0 10 20 30 40 50

degC

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

m/s

X

Y

Z

Maximum Offset Error < ±8.0 cm s-1

(ux, uy), < ±4.0 cm s-1

(uz)

Sonic Anemometer Calibration

Sonic Anemometer Calibration

Wind Offset and Distance Calibration: Temperature range -30 to +50 deg. C

Maximum Offset Error < ±8.0 cm s-1

(ux, uy), < ±4.0 cm s-1

(uz)

Zero-wind box with dry air

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Sonic Anemometer Coordinate Rotations

What is the frame of reference?It is difficult (or impossible) to align the sonic coordinate system with an objective frame relative to the local flow field (not gravity)If the sonic is not oriented with the stream flow there will be cross-contamination between u’ and w’z-axis should be perpendicular to the mean streamlines surface (and parallel to the scalar concentration gradient)

A B C


Rotation around z-axis (yaw angle) aligns to mean (30 min) wind direction

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Rotation around new y-axis (pitch angle) nullifies mean vertical wind


Rotation around new x-axis (roll angle) nullifies w’v’ NOT RECOMMENDED ANYMORE

Rotations are applied for each averaging period

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Long-term Planar FitAligns the z-axis perpendicular to the long-term (weeks) mean streamline plane (long data set when the position of the sonic does not change.

Planar regression on wind components in the sonic coordinate system:

b0 accounts for instrument offsetb1 and b2 define the orientation of the long-term streamline plane


Long-term Planar FitR1: around z-axis, with α nullifies mean crosswindR2: around y-axis with βPF

R3: around x-axis with γPF

Mean long term vertical velocity =0 , but not short term (30 min)

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Transducer-Shadow Effects

Difficult to characterize in turbulent conditions because there is no standard

Transducer-Shadow Effects

L/d ratio 17.2 Acoustic paths oriented at a zenith angle of 30 degrees while other designs the angle is 45 degrees with L/d ratio of 9

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Experiment to Evaluate Transducer-Shadow Effects. What is the optimal geometry?

After Wyngaard and Zhang (1985)

Correction derived in a wind tunnel under laminar flow conditions, but there is no standard for turbulence. All we can do is compare instruments or CFD

Transducer-Shadow Effects After Horst (2015)

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Transducer-Shadow Effects After Huq et al. (2017)

Gas Analyzer Measurement Principles

1

4

23

3

5

5

6

1 Temperature controlled detector

2

2 Precision optical components

3 Scratch resistant windows

4 Brushless chopper motor

5 CO2 and H2O scrubbers

6 Infrared source

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CO2 and H2O Infrared Gas Analyzer Measurement Principles

Mid-infrared

Electromagnetic excitation of inter-atomic vibrationElectromagnetic energy is absorbed and converted to heat


Different Vibration modes of some GHG with strong absorption coefficients

CO2: asymmetrical stretching at 4.3 µm

H2O: asymmetrical stretching at 2.7 µm

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CO2 Absorption Bands in the Infrared

4 Positions Filter WheelDispersive Non-dispersive

CO2 active (absorbing) CO2 reference (non-absorbing) H2O: active (absorbing) H2O: reference (non-absorbing)


400 ppm

600 ppm

800 ppm

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𝐴𝑁Δν

1 exp𝑆 α cL

𝜋 𝜈 𝜈 𝛼𝑑𝜈

A = Absorbed light energy in the spectral intervalN = Number of absorption lines in the spectral intervalν = Wave number of the individual spectral linec = Density of the absorbing gasL = Path lengthSi = Strength of the individual lineαi = Half-width of the individual line

Si = f(T,P) αi = f(T,P)

T = Air temperature, P = barometric pressure

IRGA optical design schemes

Single path dual wavelength

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Gas Analyzer Measurement PrinciplesInfrared spectroscopymeasures density in mol m-3, not the required mixing ratios

Eddy Covariance Measurement PrinciplesNeed to convert from density to mixing ratio. Instantaneous pressure and temperature of the mixture in the sensing path are required, but are not available for traditional open-path sensors.

Point-by-point conversion of high frequency time series

For open-path sensors density terms (WPL) on 30 min fluxes. Pressure is neglected

Closed-path analyzers IRGASON due to the co-location of the sonic

Correction of sonic temperature for humidity effects

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Point-by-point conversion of high frequency CO2 density time series

All variables must be measured simultaneously

Must consider time lag and hi-frequency attenuation in the intake tubing

This approach can be used with the IRGASON due to the co-location of the sonic

Closed-path sensors: the air-temperature fluctuations are attenuated in the intake tubing. Temperature and pressure are measured in the sample cell


Point-by-point conversion of high frequency CO2 density time series

Open-path sensors with co-located sonic anemometer: the air-temperature fluctuations in the sample volume can be measured correctly

u, v, wTs

H2OCO2P

Static Pressure

probe

Common Electronics

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d

Instrument array filters high frequencies (low-pass filter)

Line-averaging along the instrument path causes loss of variance

Spatial separation between instruments causes loss of covariance

Minimum eddy size > ~2d

800 850 900 950 1000 1050 1100 1150 1200

Seconds

31

32

33

34

35

36

37

38

39

deg_

C

800 850 900 950 1000 1050 1100 1150 1200

-1.5

-1

-0.5

0

0.5

1


d1

800 850 900 950 1000 1050 1100 1150 1200

Seconds

31

32

33

34

35

36

37

38

39

deg_

C

800 850 900 950 1000 1050 1100 1150 1200

-1.5

-1

-0.5

0

0.5

1

d2

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In the same sampling volume and well synchronized

Open-path sensors: subjected to the air-temperature fluctuations of the atmosphere. Fast-response air temperature is required: sonic BUT at a distance d

Separated by distance dLow-pass filteredNeed spectral correction

Eddy Covariance Sensor Separation: Case Study

CSAT3

IRGASON

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Eddy Covariance Sensor Separation

01/16 03/07 04/26 06/15 08/04 09/23 11/12 01/01

-700

-600

-500

-400

-300

-200

-100

0

100

Cumulative CO2 flux

Date

Cu

mu

lativ

e C

O2 f

lux

[g C

O2 m

-2]

IRGASON approach: w',T',

v',

c' all co-located 27%41%

Grelle 2007 approach:T',

v',

c' co-located

but w' is separated

Traditional approach: w',T' measured by CSAT3are separated from

v',

c' measured by IRGA

Eddy Covariance Experimental VerificationA case study- zero CO2 flux over asphalt . Kondo & Tsukamoto (2008)

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Measurements of heat, water vapor and CO2 fluxes must have the same spectral and co-spectral response

It is challenging when the corrections are large

Eddy Covariance Experimental Verification

Example: Instrument surface heating causing apparent CO2 uptake

Eddy Covariance Instrumentation Biases

After Burba (2008)

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Grelle and Burba (2007) installed a fine wire PRT in the sensing volume of the open-path analyzer to measure the extra heat generated by the lower cylinder


Grelle and Burba (2007)


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Ma, J. et al. (2014). A downward CO2 flux seems to have nowhere to go. Biogeosciences, 11: 6251-6262.


Ma, J. et al. (2014). A downward CO2 flux seems to have nowhere to go. Biogeosciences, 11: 6251-6262. The desert is a carbon sink

Eddy Covariance Instrumentation Biases?

Schlesinger, W. (2016). An evaluation of abiotic carbon sinks in deserts. Global Change Biol., doi: 10.1111/gcb.13336 We can’t find the carbon?

Where is the carbon?

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Eddy Covariance Instrumentation BiasesA parking lot experiment: Where is the carbon?

80 80.5 81 81.5 82 82.5-0.05

0

0.05

0.1

Half-Hourly CO2 Flux

DOY

Fc

[mg

m-2

s-1

]

IRGASON EC155 IRGASON corr

Ham et al. (2003)0.032 mg m-2 s-1

Eddy Covariance Instrumentation BiasesOpen-path and closed-path comparison

-0.6 -0.4 -0.2 0 0.2 0.4

-0.6

-0.4

-0.2

0

0.2

0.4

Hourly CO2 Flux

EC155 Fc [mg m-2 s-1]

IRG

AS

ON

Fc

[mg

m-2

s-1

]

1:1

Hs[W]

-50

0

50

100

150

200

-50 0 50 100 150 200 250

-5

0

5

FcOP

- FcCP

Hs [W m-2]

Fc O

P -

Fc C

P [

mo

l m-2

s-1]

=-0.014257*Hs+0.066828

=-0.0035314*Hs+0.06371

Slow Temp fitFast Tempfit

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Eddy Covariance Instrumentation BiasesSpectroscopic bias in IRGASON

-50 0 50 100 150 200 250

-5

0

5

FcOP

- FcCP

Hs [W m-2]

Fc O

P -

Fc C

P [

mol

m-2

s-1]

=-0.014257*Hs+0.066828

=-0.0035314*Hs+0.06371

Slow Temp fitFast Tempfit

2280 2300 2320 2340 2360 2380 24000

0.2

0.4

0.6

0.8

1

CO2 Absorption

Wave Number

Abso

rptio

n

T: 240 KT: 330 K

Fast-response Slow-response 10

-210

0

10-4

10-2

100

Power Spectrum of Air Temperature

Frequency [Hz]

S [d

eg C

]2

-5/3

IRGASONCSAT3ATemp Probe


A parking lot is not a carbon sink

80 80.5 81 81.5 82 82.5-0.05

0

0.05

0.1

Half-Hourly CO2 Flux

DOY

Fc

[mg

m-2

s-1

]

IRGASON EC155 IRGASON corr

Ham et al. (2003)0.032 mg m-2 s-1

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Example: Flow distortion causing artificial cross correlations between u’ and v’


Example: Flow distortion errors


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Instrument Requirements

Perfect instruments should:

Be invisible (or very small) so that it does not affect the flow (create or destroy

eddies) and not average small eddies in the sensing path

Be fast-response to capture the rapid changes in the measured quantities

Be sensitive to small changes in measured quantities

Be highly accurate, stable, linear and unaffected by environmental factors

(temperature, precipitation , dust, etc.)

800 850 900 950 1000 1050 1100 1150 1200

Seconds

31

32

33

34

35

36

37

38

39

deg_

C

800 850 900 950 1000 1050 1100 1150 1200

-1.5

-1

-0.5

0

0.5

1

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Instrument Requirements

Perfect instruments should:

Make all measurements simultaneously and in the same point in space

(preserve covariance)

Consume no power

Operate forever with no maintenance or calibration under all conditions

Easy to operate

800 850 900 950 1000 1050 1100 1150 1200

Seconds

31

32

33

34

35

36

37

38

39

deg_

C

800 850 900 950 1000 1050 1100 1150 1200

-1.5

-1

-0.5

0

0.5

1

Instrument Selection Guide and Tradeoffs

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‘Know Thy Site’

Ray Leuning

Most Flux Instruments are Very Good; Pick the Instrument System that is Most Appropriate to Your Weather and Climate

‘Know Thy Sensor’

And thy methods, tools, model assumptions and experiments!

Some instruments are better than others. Pick the instrument that is right for You.Consider:• Site conditions (rain, Hs, CO2

flux, canopy…) • Power budget• Scientific objectives

(uncertainties)• Cost of operation,

maintenance, calibration

Open- or Closed-Path System?

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Open-path Systems

Sonic and gas analyzer separateOr co-located

Open-path systems

Advantages:• Excellent spectral response• Low power consumption• Less complex (no pumps,

tubing and filters)• Lower cost • Low maintenance• No tube delays and

minimal time lag (scales with wind)

Disadvantages:• Data loss due to

precipitation, dust, birds, inscts (data spikes and drift)

• Larger density corrections• No possibility for

automated field calibrations

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Closed-path Systems with Short Intake Tube

Advantages:• Not affected by precipitation, dust, birds

(less data spikes) But the sonic might be!• Temperature fluctuations are attenuated in

the intake tube - smaller density corrections• Calculate mixing ratio in real time• Possibility for automated field calibrations


High-frequency attenuation and time lag depend on flow rate, tube diameter and length, tube material, RH (becomes worse as dirt accumulates on the filter!)

Different attenuation and lags for CO2 and H2O especially in at high RH regimes

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Disadvantages:• Loss of frequency response due to tube attenuation and

accumulation of particulates on the face of the filter (worse for water)

• Changing lag due to changes in flow• Higher power requirements due to the pump• Loss of synchronicity due to time variable lags• Higher cost and increased maintenance (filters, pump,

tubing)

Closed-path Gas Analyzer Vortex Intake

Particle separation based on size and massNo accumulation of particulate mater Constant flow conditions

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Flux Time Series

Math Tools and Concepts

• Variance and Covariance

• Spectral Decomposition: changing from time

to frequency domain to identify instrumentation

issues

• Aliasing errors due to discrete sampling:

signals not measured at the correct frequency

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Calculate Variation of a Signal or a Co-Variation Between Two Signals

• Variance: A measure of how a signal varies about its mean

• Covariance: A measure of how two signals vary together

about their means

N

kxkx

NxVar

1

21)(

ykyxkxN

yxCoVarN

k

)()(1

,1

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Seconds

-1.5

-1

-0.5

0

0.5

1

1.5

No U

nits

w1;overplot(w15,lred);setx(0,2)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Seconds

-2

-1

0

1

2

3

4

No

Uni

ts

Covariance=0.50

Covariance - Amplitude Attenuation

Double the variation of one signal

Covariance = 1.00

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Seconds

-2

-1

0

1

2

3

4

No

Uni

ts

Covariance=0.50

Covariance = 0.50

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Seconds

-2

-1

0

1

2

3

4

5

No

Uni

ts

Covariance=1.00

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Covariance - Signal Time Delay

Two signals perfectly synchronized

Covariance = 1.00

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Seconds

-2

-1

0

1

2

3

4

5

No

Uni

ts

Covariance=1.00

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Seconds

-2

-1

0

1

2

3

4

5

No U

nits

Covariance=0.71

Time shift one signal by 1/8 of the period

Covariance = 0.71

Covariance - Signal Time Delay

Time delay by 1/4 of a period

Covariance = 0.00

Time shift one signal by 1/2 of a period

Covariance = -1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Seconds

-2

-1

0

1

2

3

4

5

No

Uni

ts

Covariance=0.00

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Seconds

-2

-1

0

1

2

3

4

5

No

Uni

ts

Covariance=-1.00

Spatial separation is equivalent to a time delay

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Spectral Decomposition of a Time Series

...coscoscos 333222111 aaaaaaaaaaa tAtAtAkts

Spectral Decomposition of a Sine Wave

0 2 4 6 8 10 12 14 16 18

Seconds

-1.5

-1

-0.5

0

0.5

1

1.5

Volts

0 2 4 6 8 10 12 14 16 18 20 22 24

Hertz

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

Volts

spectrum(w10);setcolor(green)

1-Hz Sine Wave as a function of time

1-Hz Sine Wave as a function of frequency

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Spectral Decomposition of a Sine Wave

0 2 4 6 8 10 12 14 16 18

Seconds

-1.5

-1

-0.5

0

0.5

1

1.5

Volts

gsin(1000,1/50,5);setvu("V")

0 2 4 6 8 10 12 14 16 18 20 22 24

Hertz

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

Volts

spectrum(w10);setcolor(green)

5-Hz Sine Wave as a function of time

5-Hz Sine Wave as a function of frequency

Spectral Decomposition of a Periodic Signal

0 0.5 1 1.5 2 2.5 3 3.5

Seconds

-1.5

-1

-0.5

0

0.5

1

1.5

No

Uni

ts

Gsin(4*1024,1/1024,1)/1;sety(-1.5,1.5)

0 0.5 1 1.5 2 2.5 3 3.5

Seconds

-1.5

-1

-0.5

0

0.5

1

1.5

No

Uni

ts

Gsin(4*1024,1/1024,3)/3;sety(-1.5,1.5)

0 0.5 1 1.5 2 2.5 3 3.5

Seconds

-1.5

-1

-0.5

0

0.5

1

1.5

No

Uni

ts

Gsin(4096,1/1024,5)/5;sety(-1.5,1.5)

+

+

+ …

=

0 0.5 1 1.5 2 2.5 3 3.5

Seconds

-1

-0.5

0

0.5

1

No

Uni

ts

W1+W2+W3+W4+W5+W6+W7+W8+W9+W10+W11+W12

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Spectral Decomposition of a Periodic Signal

0 5 10 15 20 25 30 35 40 45 50

Hertz

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

No U

nits

spectrum(w1);setx(0,50);sety(-.2,1.2);setcolor(2)

0 5 10 15 20 25 30 35 40 45 50

Hertz

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

No U

nits


0 5 10 15 20 25 30 35 40 45 50

Hertz

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

No U

nits


+

+

+ …

=

0 5 10 15 20 25 30 35 40 45 50

Hertz

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

No U

nits


Vertical Wind

As a function of time

As a function of frequency(phase not shown)

0 50 100 150 200 250 300 350 400 450 500 550 600

Seconds

-2

-1

0

1

2

m/s

[Uz:Ts_data_2006_07_30_0000.dat] Start time=2006/07/30 16:40:00.000.

0.01 0.1 10.002 4

Hertz

1e-005

0.0001

0.001

0.01

0.1

1

10

(m/s

)^2 H

z^-1

psd(W6-mean(W6));setylab("(m/s)^2 Hz^-1")

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Spectral Resolution

Length of the time series T determines the spectral resolution Δf and the sampling period Δt determines the maximum frequency

Spectral Smoothing of a “Raw” Spectrum

Scatter is reduced by averaging a frequency window that expands in width with frequency (log scales)

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Spectral Smoothing of a “Raw” w Spectrum

S(f) Spectral density A2/Δf (units of variance per Δf)

Area under the curve = variance

Sometimes frequency weighted spectrum is used fS(f) (units of variance)

0.01 0.1 10.002 4

Hertz

0.01

0.1

11

(m/s

)^2

Hz^

-1

PSD (W)

Universal spectral shape:

Kaimal Spectrum -5/3

Frequency Weighted Spectrum

Frequency weighted spectrum is shows the spectral gap at the low frequency range

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Spectral Similarity

Normalized spectra have similar shape for different variables (but not exactly the same)

10-2

100

10-2

100

102

Normalized Spectra of IRGASON Variables

Frequency [Hz]

S/

2

-5/3

Uz

Tair

CO2

H2O

Patm

High-frequency Distortion due to Instrumental Effects

Noise spikes in sonic w measurement (bug or precipitation)

Noise floor of PRT temperature measurement

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Spectral Decomposition - Co-spectra

We can compute covariance in the time domain or the frequency domain.

The covariance computed in the time domain equals the area under the curve of a Co-Power Spectral Density function (CoPSD).

...coscoscos 333222111 aaaaaaaaaaa tAtAtAkts

...coscoscos 333222111 bbbbbbbbbbb tAtAtAkts

...cos

cos

cos,cov

33033

33

22022

22

11011

11

2

2

2

baif

baba

baif

baba

baif

baba

ba

AA

AA

AAss

Co-Spectral Analysis

10-2

100

10-2

100

Cospectrum of CO2 and w

Frequency [Hz]

Co

CO

2 [pp

m m

s-1

]

IRGASONEC155-7/3

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Frequency Weighted Co-Spectra

After Leuning

Aliasing – Discrete Time-Sampled Signal

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Seconds

-1.5

-1

-0.5

0

0.5

1

1.5

No

Uni

ts

decimate(w1,64);points;setsym(1);setcolor(lred);setx(0,2)

What is the shape of the measured signal ?

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0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Seconds

-1.5

-1

-0.5

0

0.5

1

1.5

No

Uni

ts


What is the true shape of the original signal?

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Seconds

-1.5

-1

-0.5

0

0.5

1

1.5

No U

nits



0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Seconds

-1.5

-1

-0.5

0

0.5

1

1.5

No

Uni

ts


What is the true shape of the original signal?

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Seconds

-1.5

-1

-0.5

0

0.5

1

1.5

No

Uni

ts

-Gsin(4*1024,1/1024,15)/1;sety(-1.5,1.5);overplot(w15,lred);setx(0,2)

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Folding of Spectral Energy

Misrepresentation of the high frequency components

fo –Nyquist frequency

fo=fsample/2

For proper frequency representation

fsample=2fmax

Folding of Spectral Energy

Misrepresentation of the high frequency components

The variation of the signal is preserved, so aliasing is not a problem for calculating fluxes

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Folding of Spectral Energy Misrepresentation of the rate at which the signals are changing

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Seconds

-1.5

-1

-0.5

0

0.5

1

1.5

No

Uni

ts

-Gsin(4*1024,1/1024,15)/1;sety(-1.5,1.5);overplot(w15,lred);setx(0,2)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Seconds

-1.5

-1

-0.5

0

0.5

1

1.5

No

Uni

ts


Variance = ???

Variance = ???

Variances and covariances are correct

Eddy Covariance System RequirementsAdequate frequency response of the sensors (small d, high flow)

Preserve temporal and spatial correlation of vertical wind and scalar

800 850 900 950 1000 1050 1100 1150 1200

Seconds

31

32

33

34

35

36

37

38

39

deg_

C

800 850 900 950 1000 1050 1100 1150 1200

-1.5

-1

-0.5

0

0.5

1

Sonic Temperature

(deg C)

Vertical Wind

(m/s)

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Eddy Covariance System Requirements

Flux vs. Measurement Synchronicity(60 Hz Samples)

40

50

60

70

80

90

100

110

-0.250 -0.200 -0.150 -0.100 -0.050 0.000 0.050 0.100 0.150 0.200 0.250

Seconds

% o

f m

axim

um

284.0 W m-2

334.6 W m-2LE; Thick Grassh = 0.6 mz = 2.6 m

U = 8.55 m s-1

T = 9 min60 Hz Samples

Two sensors, each running at 20 Hz, but not synchronized to one another, will be

asynchronous to one another by at least 50 msec

18 percent loss of flux


Flux vs. Covariance Cutoff Frequency(60 Hz Samples)

-10

10

30

50

70

90

110

0.001 0.010 0.100 1.000 10.000 100.000

Hertz

% o

f m

axim

um

td 0.00 s 0.05 s 0.10 s 0.20 s

LEmax = 334.6 W m-2

U = 8.55 m s-1

z = 2.6 m

Note decrease in covariance

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Flux vs. Measurement Synchronicity(60 Hz Samples)

40

50

60

70

80

90

100

110

-0.250 -0.200 -0.150 -0.100 -0.050 0.000 0.050 0.100 0.150 0.200 0.250

Seconds

% o

f m

axim

um

297.4 W m-2

309.7 W m-2

LE; Thick Grassh = 0.6 mz = 2.6 m

U = 2.37 m s-1

T = 9 min60 Hz Samples

4 percent loss of flux


Flux vs. Covariance Cutoff Frequency(60 Hz Samples)

-10

10

30

50

70

90

110

0.001 0.010 0.100 1.000 10.000 100.000

Hertz

% o

f m

axi

mu

m

td 0.00 s 0.05 s 0.10 s 0.20 s

LEmax = 309.7 W m-2

U = 2.37 m s-1

z = 2.6 m

Check rule of thumb f_req = n u/zf_req10 = 10*2.4/2.6 = 9.2 Hz

f_req4 = 4*2.4/2.6 = 3.7 Hz

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Summary

• Know the limitations and the assumptions of the method

• Know thy site (heterogeneity, advection, storage)

• Select instruments appropriate for your conditions and

research goals (adequate frequency response, temporal

and spatial synchronization)

• Know your instruments (test in lab conditions,

intercompare, calibrate and maintain)

• QC your data (spectra, co-spectra, stationarity, advection,

instrument effects)

Outlook after T. Foken:

• Energy balance closure (not always an instrument

problem)

• Night-time fluxes (sweeps systematic bias)

• Heterogeneous terrain (larger scales and

secondary circulations)

• Accuracy of the method

Four Problems of the Eddy-covariance Technique

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Trace Gas Analyzer (TGA) for CH4, N2O and 13C Isotope Measurements

What is a TGA?CSI has been manufacturing TGA’s since 1993TGA is a tunable diode laser absorption spectrometer (TDLAS), and new lasers are TE cooledThey are rugged, portable, and designed for use in the lab or out in the fieldUses a small sample cell volume for good frequency response no mater the application

System Components for CH4, N2O and 13C Isotope Measurements

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System Components for CH4, N2O and 13C Isotope Measurements from Multiple Inputs

SampleDeliveryPump

P

FFP TGA

Sample Flow

Bypass Flow

Manifold

ExcessFlow Sample

Bypass

AnalyzerPump

PD1TDryer

TGA pressure control

Cal Tanks

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Infrared Spectrum of CH4, N2O

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Example Configurations & Applications

Argentina (N2O/CO2, Eddy Covariance)

Australia (CO2 Isotopes, Leaf Chamber)

Minnesota (Methane, Eddy Covariance)

Brazil (N2O/CO2, Multi-Site Gradient)

Example Pump Shelters


LOCATION: NORTHEAST ARGENTINARESEARCH: UNDERSTAND NITROGEN AND CARBON CYCLES FOR CORN AND SOYBEAN ROTATIONS AND VARIOUS TILLAGE/FERTILIZER PRACTICESMAJOR SYSTEM COMPONENTS: TGA200 ANALYZER, CSAT3 3D SONIC ANEMOMETER, FW05 FINEWIRE THERMOCOUPLE, LI-7500A, TIPPING RAIN BUCKET, NET RADIOMETER, SOIL MOISTURE PROBES, SOIL HEAT FLUX PLATES, SOIL TEMPERATURE PROBES

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LOCATION: NORTHEAST ARGENTINARESEARCH: UNDERSTAND NITROGEN AND CARBON CYCLES FOR CORN AND SOYBEAN ROTATIONS AND VARIOUS TILLAGE/FERTILIZER PRACTICESMAJOR SYSTEM COMPONENTS: TGA200 ANALYZER, CSAT3 3D SONIC ANEMOMETER, FW05 FINEWIRE THERMOCOUPLE, TIPPING RAIN BUCKET, NET RADIOMETER, SOIL MOISTURE PROBES, SOIL HEAT FLUX PLATES, SOIL TEMPERATURE PROBES

China Flux 2019 Eddy Covariance Instrumentation 2.1 3.2... · 2019. 8. 15. · Eddy Covariance...

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