SPECTROSCOPIC EFFECTS AND EDDY COVARIANCE CALCULATIONS OF METHANE FLUX
G. Burba*, T. Anderson, D. McDermitt, A. Komissarov, L. Xu, B. Riensche, D. Allyn, and K. Ediger
LI-COR Biosciences, Lincoln, N E, USA,*[email protected]
INTRODUCTION
•
DENSITY EFFECTS
•
Eddy Covariance (EC) is one of the most accurate and direct
methods to measure fluxes of H2O, CO2 and CH4 [1,2,3]
•
•
Fluxes of CO2 and H2O are typically measured by EC using
NDIR technology with compact low-power gas analyzers
•
CH4 flux studies cannot utilize NDIR, so CH4 gas analyzers use
single-line or narrow-band laser spectroscopy
•
•
Like CO2 and H2O, the CH4 density changes due to the flux
itself, but also due to the air density changes related to
temperature (T), water vapor (Q) and pressure (P)
•
•
CH4, however, is measured by single-line or narrow-band
lasers, and is also influenced by T, Q, and P, affecting
spectroscopic properties of the absorption line
•
RELATING DENSITY & SPECTROSCOPIC EFFECTS
Depending on the absorption line probed, spectroscopic effects may
add or subtract from density effects, or may differ for T, Q, and P
•
CH4 density, μmol m-33
Examples below are for T and Q effects for the specific case of LI-7700
for CH4 density of 176 umol m-3 at initial conditions of 0oC and dry air
constant volume: actual density does not change
with T
200
190
Initial
density
170
160
150
-40
-20
0
20
Temperature T, 0C
40
CH4 density, μmol m-3
180
DERIVATION OF TOTAL EFFECTS
one can correct both effects by multiplying thermal expansion term in WPL by 1.3
• Or, if it is known that spectroscopic effect of Q is 40% of the density effect of Q, one
can correct for both effects by multiplying dilution term in WPL by 1.4
• Over wide range of conditions, the relationships between spectroscopic and density
10
20
30
Water Vapor Q, ppT
40
effects for T and Q are complex, because at each point they depend on P
(i) express actual mass density of gas qc in terms of measured density qcm
(ii) express Q in terms of equivalent pressure Pe and water vapor line broadening
(iii) construct 3D surface κ describing the relationships for wide range of T and P
(iv) re-compute new WPL equation using qcm, Pe, and κ [4, 5, 9]
κ
Raw flux covariance,
for
density
Flux corrected for both density
and spectroscopic effects [4,5,9]
Maximum of chamber flux range
Minimum of chamber flux range
-2
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
3
Summer: maize field
15<T<38 °C
0
-3
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Hour of the Day
Effects are individual for each specific absorption line, highly dependent
on measurement technique, and known from spectroscopy laws and
HITRAN [7]
•
Spectroscopic effects influence measured gas density depending on
fluctuations in T, Q and P
KEY CONCEPT
Fluxes corrected for
both spectroscopic and
density
effects, as
proposed above, did
not significantly differ
from zero or chambers
in late fall (-0.11+/-0.19
mg m-2h-1) and summer
(0.13+/-0.29 mg m-2h-1)
Fast changes in T, Q, or P lead to:
(i) gas density effects as per Ideal Gas Law and Partial Pressures Law
(ii) spectroscopic effects as per spectroscopy laws and HITRAN
So, if one can establish relationships between density effects and
spectroscopic effects of T, Q and P respectively, one can incorporate
the spectroscopic effects into WPL terms [4,5,9].
•
•
To compute correct CH4 flux, the raw flux covariance should be
corrected for both density effects and spectroscopic effects
Using physical relationships described before, the standard WPL
equation correcting for just density effects becomes the modified
equation correcting for both density effects and spectroscopic effects:
Fc =
B
C
)
• Please
note that the only difference between the standard WPL
equation and the modified equation correcting for both density effects
and spectroscopic effects are the three multipliers: A, B and C [4, 5, 9]
• At normal
where
•
•
•
2
0
•
Fc = A(
These derivations are made from the first principles and do not rely on empiricism:
detailed description and step-by-step derivation is provided in [5, 9]
SUMMARY AND CONCLUSIONS
The proposed concept was tested at the field experimental site of the
University of Nebraska-Lincoln, with multi-year history of chamberbased CH4 fluxes ranging from -0.12 to 0.13 mg m-2 h-1 [10]
Flux corrected
effects only [6]
Spectroscopic effects are related to the changes in shape of the
absorption line due to the changes in gas T, Q, and P [7,8]
qc=qcmκ
Effects of changing Q
FIELD VALIDATION
Late Fall: partially frozen bare soil
2<T<7 °C
•
• However, one can derive a single relatively simple equation for actual flux Fc :
Effects of changing T
constant pressure: measured density is reduced due
to spectroscopic effects of Q on the absorption line,
as expected from the spectroscopy and HITRAN
Measured
density
When gas density is measured by laser spectroscopy, there are also
spectroscopic effects affecting measured values, in addition to the
density effects
FULL EQUATION
• In simple terms, if it is known that spectroscopic effect of T is 30% of the density effect,
constant pressure: actual density is reduced due to
water vapour dilution, as expected from the Law of
Partial Pressures
Initial
density
170
0
Ensemble Averaged Hourly CH4 Flux, mg CH4 m-2 h-1
Thermal Expansion Term:
computed from any fast air T measured
nearby, at the same time as CH4 (this term is
small in closed-path analyzers)
constant volume: actual density does not change
with Q
160
•
Water DilutionTerm:
computed from any fast
H2O measured nearby, at
the same time as CH4
Fc – final corrected flux; w - vertical wind speed; qc – gas density; μ− ratio of mol. masses of air to water; qd – dry air
density; qv – H2O vapor density;
; T– air temperature in K;
constant pressure: measured density is reduced due
to spectroscopic effects of T on the absorption line, as
expected from the spectroscopy and HITRAN
Measured
density
The gas flux is usually corrected for the density effects using widelyused Webb-Pearman-Leuning terms [6]:
Raw Flux Covariance:
computed from vertical
wind speed and CH4 density,
or other gas of interest
constant pressure: actual density is reduced due to
temperature expansion, as expected from the Ideal
Gas Law
180
These processes are described by the Ideal Gas Law and by the Law of
Partial Pressures, and often are called density effects
Fc =
The proposed concept is tested on a low-power open-path high-speed
gas analyzer, the LI-7700 (LI-COR, Lincoln, NE, USA [4,5,7])
•
Measured changes in gas density happen due to gas flux itself, due to
thermal expansion and contraction of the air, water vapor dilution, and
pressure-related expansion and contraction
•
LI-7700
Here we propose a new concept to account for spectroscopic effects in
the same way as Webb et al. (1980) accounted for respective density
effects
•
SPECTROSCOPIC EFFECTS
When EC flux is computed, the fast changes in gas density are
correlated with the fast changes in vertical wind speed
•
•
Reliable relationships were established between density effects and
spectroscopic effects based on the first principles of Ideal Gas Law,
Partial Pressures Law, spectroscopy laws and HITRAN
Spectr0scopic effects were incorporated into WPL density terms,
originally developed to compensate for the density effects
Results were field-validated for cold and warm periods versus chamber
measurements over a “zero-flux” experimental site
The proposed approach allows the use of cost-effective low-power
single-gas analyzers in EC flux measurements without the need for fast T,
H2O, and P measurements inside the sampling cell
conditions for LI-7700, the A ranges from 0.96 to 0.99, B
ranges from 1.41 to 1.43, and C ranges from 1.32 to 1.34
• Multipliers A, B, C can be permanently programmed into flux processing
code - please contact [email protected] for the detailed algorithm
REFERENCES AND RESOURCES
[1] Foken T., 2008. Micrometeorology. Springer-Verlag: 306 pp.
[2] Lee X., W. Massman, and B. Law (Eds.), 2004. Handbook of Micrometeorology: A Guide
for Surface Flux Measurement and Analysis. Kluwer Academic Publishers: 250 pp.
[3] Burba G., and D. Anderson. 2010. A Brief Practical Guide to Eddy Covariance Flux
Measurements: Principles and Workflow Examples for Scientific and Industrial
Applications. LI-COR Biosciences: 211 pp.
[4] McDermitt D., G. Burba, L. Xu, T. Anderson, A. Komissarov, J. Schedlbauer, D. Zona , W.
Oechel, S. Oberbauer, G. Starr, and S. Hastings, 2011. A new low-power, open path
instrument for measuring methane flux by Eddy Covariance. Applied Physics B: Lasers
and Optics, 102(2): 391-405
[5] Miller T., and LI-7700 Team, 2010. LI-7700 Open-path CH4 Analyzer Instruction Manual.
LI-COR Biosciences Publication No.984-10751, 170 pp.
[6] Webb E.K., G. Pearman, and R. Leuning, 1980. Correction of flux measurements for
density effects due to heat and water vapor transfer, Quarterly Journal of the Royal
Meteorological Society, 106: 85-100
[7] Rothman L.S., I. E. Gordon, A. Barbe, D. C. Benner, P. F. Bernath, et al., 2009. The
HITRAN 2008 molecular spectroscopic database. Journal of Quantitative Spectroscopy
& Radiative Transfer, 110: 533-572
[8] Gharavi, M., and S. G. Buckley, 2005. Diode laser absorption spectroscopy
measurement of linestregths and pressure broadening coefficients of the methane 2v3
band at elevated temperatures. Journal of Molecular Spectroscopy, 229: 78-88
[9] Burba G., D. McDermitt, A. Komissarov, L. Xu, B. Rienche, 2009. Method and Apparatus
for Determining Gas Flux. Patent AU 2009292601
[10]Arkebauer, T. 2007-2010. Personal Communications.
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