20
Bias of CO2 Surface Fluxes Estimated by Eddy
Covariance due to “Adjustment Fluxes”.
Gerhard Peters
Meteorological Institute
University Hamburg
Bundesstrasse 55, 20146 Hamburg, Germany
[email protected]
Abstract The advection of horizontal inhomogeneous CO2 concentrations by a
wind field with vertical gradient causes a height dependent vertical CO2 flux. It
is shown that the corresponding bias between the flux at few meters above the
surface and the flux through the surface is in the order of the natural CO2 flux
variability through the air–sea interface, if horizontal CO2 gradients are assumed
that are typical for land conditions or epicontinental seas. Although this bias
is a zero mean effect on the long term, it is suspected that it may contribute
significantly to the estimation uncertainty of air–sea CO2 transfer velocities based
on eddy correlation flux measurements. A simple model is suggested to retrieve
the surface flux from extrapolation of flux measurements at two height levels.
20.1 Introduction
A standard procedure to estimate fluxes of a passive air ingredient through
the air-surface interface is the eddy covariance method (ECM) which calculates F = w 0 c 0 in the air close to the surface. w 0 and c 0 are turbulent
fluctuations of the vertical wind component w and of the concentration c
of the air ingredient respectively. The overline indicates temporal averaging over typically 10 to 60 min. After application of several standard corrections the flux F measured at few meters above the surface is identified
with the flux through the surface. Fluxes of some air ingredients including
CO2 through the air/sea interface are limited by the surface transfer resistance and show relatively small flux velocities k = F /c, where F is the flux
density and c is the mass density of the substance. Although Jones and
Smith [2] demonstrated already 1977 that ECM copes also with the small
flux amplitudes of CO2 , and although relatively good agreement with geochemical methods was found recently by McGillis et al. [6], there is still
controversy about the general validity of air-sea CO2 flux estimates based
on ECM.
C.S. Garbe, R.A. Handler, B. Jähne (eds.): Transport at the Air Sea Interface
pp. 289-296, 2007, © Springer-Verlag Berlin, Heidelberg 2007
290
G. Peters
Here only the most important sensor siting conditions and environmental conditions required for ECM are recalled, which are well known
for being precarious.
• Measuring ”close” to the surface means that the measuring height z1
is small compared to the height of the atmospheric reservoir zi , i.e. of
the atmospheric boundary layer. At the top zi of the boundary layer
the flux assumes the entrainment flux, which may be of opposite sign
as the surface flux.
• If there are horizontal gradients of the surface flux, the method does
not represent the local flux density underneath the measuring point
rather than a weighted average over some upwind-area, which is usually called the ”footprint” [5]. As the footprint increases with increasing measuring height the weighting function changes with height and
thus the measured flux as well. Transfer velocities based on locally
measured CO2 concentrations on one hand and area averaged fluxes
on the other hand can be seriously biased, if the surface conditions are
inhomogeneous on the footprint scale. A first approximation for the
bias at measuring height z was provided by Wesely [11] as a function
of the corresponding horizontal concentration gradient δc/δx:
∆F = z
δc
u
δx
(20.1)
where u is the horizontal velocity.
In addition, standard ECM signal processing includes various first-order
corrections which are applied to the ”raw”-fluxes:
• Although there should be no mean vertical wind component w over
flat terrain, there is usually some component observed in the measured
data due to artificial reasons. To minimize its impact on the estimated
surface-flux the coordinate system is rotated until w = 0 [12].
• Only concentration fluctuations c 0 , which are solely due to fluctuations
of the mixing ratio of the considered ingredient, may be attributed to
the surface flux. Dilution effects contributing to c 0 may give rise to differences between the measured flux and the surface flux. Such mechanisms include fluctuations of air temperature or of air constituents as
for example water vapour. The correction of such effects is known as
Webb-correction [9].
• Spectral corrections are related to sensor characteristics as finite frequency response, path averaging and the separation of sensors for w
and c respectively [7].
While there is general consensus that the parameterization of the transfer
velocity with the wind speed u10 is too simplistic (see for example Jacobs
et al. [1] for a comprehensive discussion of further processes controlling the transfer velocity) the large scatter of transfer velocities, which is
20 Bias of CO2 Surface Fluxes due to “Adjustment Fluxes”
291
typically found in ECM field campaigns including a recent long term measurement Weiss et al. [10] calls for the search of further potential sources
of error affecting the standard ECM applicability.
In this note a mechanism is discussed, which - to the author’s knowledge - was not considered in previous studies, but which may give rise to
differences between the measured eddy flux and the surface flux . Their
magnitude is comparable to Equation (20.1), and they are particularly significant for ingredients like CO2 with high transfer resistance at the airsurface interface.
For simplicity homogeneous surface conditions are assumed on scales
far beyond the footprint size. Even in this case the atmospheric mean
concentration c of CO2 may show a ”cloud like” i.e. a horizontally heterogeneous distribution. If the wind field would be uniform, its only effect
would be the translation of these structures without changing their form.
But due to the non-slip condition at the surface the wind field close to the
ground exhibits a vertical gradient, and the differential advection related
to the height–dependent wind–speed together with a horizontal gradient
of c causes the evolution of a vertical gradient of c. Subsequent vertical
turbulent mixing will then reduce this gradient. As explained in the following, it is this mixing (called ”adjustment flux” henceforth), which causes
a potentially significant difference ∆F between the ECM flux at measuring
height z and the surface flux.
20.2 Vertical Flux Gradient due to Differential Advection
A simple conceptual model is considered where the local temporal change
˙ at the measuring height z is controlled only by two processes, namely
c(z)
horizontal advection by the mean wind and the vertical turbulent flux
gradient:
˙
˙
˙ = c(z)
c(z)
(20.2)
h + c(z)v
with
∂c(x, z)
˙
c(z)
(horizontal advection)
h = −u(z)
∂x
and
(20.3)
0 0
∂w c
˙
c(z)
(vertical flux–gradient),
(20.4)
v =−
∂z
where x and z are positive in downwind and upward direction respectively. The overlines indicating mean values will be omitted for shortness
in the following. In order to obtain the bias of the flux measured at the
height z versus the surface flux, Equation (20.2) is rewritten putting the
vertical flux–gradient on the left side:
∂w 0 c 0
∂c(x, z)
= −u(z)
− ċ(z)
∂z
∂x
(20.5)
292
G. Peters
The flux-bias ∆F at some height z is obtained by integrating Equation
(20.5) from the surface to z:
Zz
Zz
∂c(x, ζ)
ċ(ζ)dζ
(20.6)
u(ζ)
∆F (z) = −
dζ −
∂x
0
0
It is assumed that the vertical turbulent mixing is sufficiently efficient
to maintain well mixed conditions with respect to c against the height
dependent advection term ċ(z)h . This implies height-independence of ċ
and ∂c(x)/∂x respectively, which facilitates the integration over z:
Z
∂c(x) z
∆F (z) = −
u(ζ)dζ − zċ
(20.7)
∂x
0
That means, that stable stratification with suppressed mixing and corresponding errors – which can be severe – are not considered here. Likewise
any buoyancy effects on the wind profile are neglected here, as this would
probably overstrain this simple conceptual model.
A logarithmic height dependence of the wind speed, applicable in neutral conditions, yields
u∗
z
∂c
∆F (z) = z
1 − ln
− ċ
(20.8)
k
z0
∂x
with u∗ , k and z0 are the friction velocity, von Kármán constant and z0
roughness length respectively.
An alternative convenient form of Equation (20.8) is
∂c
u∗
∆F (z) = z
− u(z)
− ċ
(20.9)
k
∂x
which contains the wind speed u(z) instead of z0 .
The variables ċ, u(z) and u∗ can be derived from local measurements.
The only unknown on the right hand side of Equation (20.9) is the horizontal concentration gradient ∂c/∂x. Basically two approaches are imaginable
to account for ∂c/∂x:
1. Direct measurement by a horizontally distributed array of sensors.
2. Indirect determination by measuring the flux at two or more levels.
Here only the second option is considered. The total vertical turbulent
flux, measured at two heights z1 and z2 , is
F (z1,2 ) = Fs + ∆F (z1,2 )
(20.10)
Solving these equations for Fs and elimination of ∂c/∂x yields:
Fs =
F (z2 )U(z1 ) − F (z1 )U (z2 ) − (∂c/∂t) (z2 U (z1 ) − z1 U (z2 ))
U (z1 ) − U (z2 )
with U(z) = z (u(z) − u∗ /k)
(20.11)
20 Bias of CO2 Surface Fluxes due to “Adjustment Fluxes”
293
20.3 Significance of ∆F
As a general rule surface fluxes should be deduced from measurements
as close to the surface as possible. In reality trade–offs between various
constraints have to be made leading sometimes to measuring heights up
to 10 m over ground – or even higher. Here typical conditions over sea are
considered where the lower limit should be around 5 meter to protect the
instruments from swell.
In order to estimate realistic figures for the flux bias as function of
height, Equation (20.8) is rewritten in a slightly modified form:
z
∂c 1 u∗
+ u(zc )
(20.12)
1 − ln
∆F (z)/c = z
∂x c
k
z0
with u(zc ) = −(∂c/∂t)(∂c/∂x)−1 , which is obviously the velocity, that is
required to explain the observed temporal variation of c solely by advection. Likewise zc can be interpreted as that height, where u(z) assumes
the "mean" drift velocity. It should be located somewhere in the midst of
the boundary layer.
As an example zc = 100 m, z0 = 2 · 10−4 m, u∗ = 0.2 ms−1 is chosen, and u(zc ) ≈ 6.5 m/s is assumed, which would fit to the logarithmic
wind profile extending up to zc . For the choice of the horizontal gradient
∂c/∂x spatial scales must be considered, which fit to the aforementioned
averaging times of 10 to 60 min and to the drift velocity u(zc ).
Simulations of atmospheric CO2 concentrations, provided by Karstens
et al. [4], show that the spatial variability is area–dependent: Continental
conditions are characterized by strong heterogeneous and time–dependent
sources and sinks, which lead to enhanced small– and meso–scale concentration variability, while more homogeneous CO2 distributions prevail
over the open oceans. The variability of CO2 fields over epicontinental
seas like the Baltic Sea resemble more the inhomogeneous continental
conditions rather than ocean conditions. This becomes apparent from
the inspection of modeled CO2 fields as shown in Figure 20.1. It represents a snapshot of the horizontal field of CO2 concentration at 300 m
height provided by the regional model REMO with 0.5◦ and 1 hour resolution [3]. One recognizes strong meso–scale textures over the continents,
which cover also the Mediterranean and Baltic Sea, but which are absent
over the North Atlantic. CO2 surface flux estimates by ECM over coastal
waters are therefore faced with large, land dominated inhomogeneities
on one hand and with marine surface fluxes on the other hand, which are
typically small compared to fluxes over vegetation.
Based on these model results a typical gradient of |(∂c/∂x)/c| =
10−6 m−1 is assumed for continental conditions. The bias corresponding to these exemplary parameters is shown in Fig. 20.2 as a function
of z. Its significance becomes obvious by comparison with the transfer velocity k of CO2 , which is an upper bound for actually occurring
294
G. Peters
Figure 20.1. Snapshot (1 h) of the REMO-modeled horizontal CO2 concentration
pattern at 300 m height, (from [3]).
flux velocities. Common parameterizations (e.g. Wanninkhof and McGillis
[8]) yield k ≈ 10 cm/h for the chosen conditions (which correspond to
u10 = 5.7 ms−1 ).
The dominating error of ECM measurements is the sampling error,
which limits the relative accuracy of flux estimates to about ±20 % (depending on wind speed, stability, measuring height and sampling period).
For any meaningful comparison between fluxes measured at two levels,
the relative difference must by larger than the sampling error. Therefore
the upper measuring height should be as high as possible. On the other
hand it should not exceed the 10 m level too much, as the error of extrapolation according to Equation (20.11) becomes increasingly sensitive
to the actual wind profile, which may deviate from the logarithmic model
- particularly in shallow marine boundary layers. In Fig. 20.2 measuring
heights at z1 = 5 m and z2 = 10 m are indicated. One recognizes that
|∆F (z1 ) − ∆F (z2 )| is sufficiently large compared with |∆F (z1 )|, which
20 Bias of CO2 Surface Fluxes due to “Adjustment Fluxes”
295
Measuring height m
20
15
10
5
0
0
2
4
6
8
Δ F/c cm/h
10
Figure 20.2. Normalized flux bias as a function of measuring height according to
Equation (20.12) with zc = 100 m, z0 = 2 · 10−4 m, u∗ = 0.2 ms−1 , ∂c/∂x = 10−6
m−1 .
means that this set of measuring heights would be a feasible choice for
reducing the estimation-error of Fs .
20.4 Summary
It has been shown that even for horizontal homogeneous conditions with
respect to the surface fluxes the ECM flux, measured at few meters above
the surface, does not necessarily represent the surface flux. Flux samples
may be biased by height dependent adjustment fluxes induced by differential advection. Although this is a zero-mean error in the long term, it may
contribute significantly to the uncertainty of measurement results. This
effect is expected to be particularly significant for CO2 -fluxes in a coastal
marine environment, where the horizontal atmospheric distribution of
CO2 is determined by heterogeneous and instationary sources and sinks
over the land, but where the local surface fluxes - being controlled by the
296
G. Peters
air-sea transfer resistance - are small compared to land conditions. The
bias considered here is reaching many hundred kilometers into the open
sea until the continentally generated CO2 cloud structures are diluted (see
Fig. 20.1). It should not be mistaken for the well–known footprint effect
related to internal boundary layers close to surface inhomogeneities as for
example coastal lines. Measurement of the turbulent fluxes at more than
one height is suggested in order to mitigate the effects on the estimation
of the surface flux.
References
[1] Jacobs C., Kohsiek W., Oost W.A. (2002), Air-sea flux and transfer
velocity of CO2 over the North Sea: results from ASGA/AGE, Tellus.
Series B, Chemical and Physical Meteorology 51: 629-641.
[2] Jones E.P., Smith S.D. (1977) A fgirst measurement of sea-air CO2
flux by eddy correlation, J. Geophys. Res., 82: 5990-5992.
[3] Karstens U. (2006), Max-Planck-Institute for Biogeochemistry, Jena,
Personal Communication.
[4] Karstens U., Gloor M., Heimann M., Rödenbeck C. (2006) Insights
from simulations with high-resolution transport and process models
on sampling of the atmosphere for constraining midlatitude carbon
sinks. J. Geophys. Res. 111:D12301
[5] Kljun N., Calanca P., Rotach M.W., Schmid H.P. (2004) A Simple Parameterisation for Flux Footprint Predictions. Boundary-Layer Meteorology 112:503-523
[6] McGillis, W.R., Edson J.B., Hare J.E., Fairall C.W. (2001) Direct covariance air-sea CO2 fluxes, J. Geophys. Res., 106, 16: 729-16,745
[7] Moore C.J. (1986) Frequency response corrections for eddy correlation systems. Boundary-Layer Meteorol. 37: 17 - 35.
[8] Wanninkhof R., McGillis W. (2001) A cubic relationship between airsea CO2 exchange and wind speed, Geophys. Res. Lett., 26(13):18891892
[9] Webb E, Pearman G, Leuning R (1980) Correction of the flux measurements for density effects due to heat and water vapor transfer,
Quart. J. Roy. Meteorol. Soc. 106:85-100.
[10] Weiss A., Kuss J., Peters G., Schneider B. (2006) Evaluating transfer
velocity-wind speed relationship using a long-term series of direct
eddy correlation CO2 flux measurements, Journal of Marine Systems,
In Press, Corrected Proof, Available online 20 September 2006,
[11] Wesely, M. (1986), Response to ”Isotopic Versus Micrometeorologic
Ocean CO2 Fluxes: A Serious Conflict” by W. Broecker et al., J. Geophys. Res., 91, C9: 10,533 - 10,535.
[12] Wilczak J.M., Oncley S.P., Stage S.A. (2004) Sonic Anemometer Tilt
Correction Algorithms. Boundary-Layer Meteorology 99: 127-150