11. Canopy Fluxes
our model of eddy transport, we can argue that the
total flux of any scalar will be carried by the eddies
with a range of sizes. Although eddies are continually undergoing change, it can help to describe
eddies either by their cross-sectional diameter or
wavelength, I, in the space domain, or by their frequency, n, in the time domain. Taylor's "frozen turbulence" model relates the two measures by the
horizontal windspeed (u)
n = u/l
(11.23)
a relationship that is adequate for eddies with a
wavelength under about 100 m, whereas larger eddies may not move at the local average wind speed.
The intensity of an eddy is proportional to its kinetic energy and the total flux density of any scalar
is carried by all the eddies in the spectrum, albeit
not all contributing equally to the transport.
In order to compare spectra at different heights
above the surface and in different wind speeds, we
can use a normalized frequency (f) where
f = n(z - d)/u
(11.24)
It has been established by experiment that almost
all of the flux is carried by eddies in the range 0.001
< f < 10 (McBean 1972; Anderson et al. 1986).
Such knowledge is important if fluxes are to be
correctly calculated. For example, Garratt (1975)
showed that CO 2 fluxes measured in a system using
a Gill propeller anemometer (whose response time
was about 0.5 sec) at a height of 1.5 m above the
vegetation were 40% in error. If the anemometer
had been placed at a height of about 5 m, the error
would have been reduced to about 14%. Thus, the
instrument frequency response time should be
lO(z - d)/u or, on the other hand, it implies that
the height of the instrument over the zero plane
should be at least equal to ncu/10 where nc is the
intrinsic cutoff frequency.
For closed-path analyzers, the intrinsic cutoff
frequency (nc) is in the order of 2.5 to 5 Hz, which
typically decreases to about 0.5 Hz because of the
damping effect induced by the sampling tube. Corrections for these effects are now well known and
a system can be designed at the outset to have particular characteristics of frequency response (Leuning and Moncrieff 1990; Leuning and Judd 1996).
Since signals of two sensors become increasingly
uncorrelated with increasing separation distance,
the correct separation distance between instruments
171
should be less than the length scale of the smallest
eddy to be detected. Kristensen and Fitzjarrald
(1984) indicated that the maximum separation distance (d) between two sensors measuring scalar
quantities (e.g., sensible heat, water vapor, CO2)
should be:
z - d
d ) < - -
-
5
(11.25)
Sensors appropriately installed are important to
minimize the effect of flow distortion. As recommended by Wyngaard (1988) the design of an eddy
covariance array must be vertically symmetrical
about its horizontal midplane to minimize the flow
distortion effect. It is also recommended to place
the inlet of the tube just below the sonic
anemometer head, in order to minimize effects on
w (Valentini et al1996).
Instrument noise affects the uncertainty of a flux
measurement for a given sampling period. The
eddy covariance technique is inherently a noise
rejection method since the flux contribution from
random noise tends to be zero (i.e., the random
noise of vertical wind speed and scalar measurements is not correlated). However, under certain
circumstances, this general principle does not hold,
especially when the statistics of turbulence are not
enough to reduce the correlated random noise.
Lumley and Panofsky (1964) derived the following
expression to estimate the sampling time (Ts) required to obtain a given level of accuracy (a) of
flux determination:
2ra~
(a~2)
(11.26)
where ~ and ~ are the mean and variance of a
turbulent quantity, and 't is an integral time scale
usually approximated as (z - d)/u.
The ratio cr~/~2 is often assumed to be equal to 5
(Auble and Meyers 1992), and thus a simple expression for the required sampling time (seconds)
in order to obtain an accuracy of 10% in the flux
estimate is:
z - d
Ts = 1000-u
(11.27)
To satisfy these error requirements, sampling periods of about two hours are often found. However,
such long sampling periods may invalidate the
our model of eddy transport, we can argue that the
total flux of any scalar will be carried by the eddies
with a range of sizes. Although eddies are continually undergoing change, it can help to describe
eddies either by their cross-sectional diameter or
wavelength, I, in the space domain, or by their frequency, n, in the time domain. Taylor's "frozen turbulence" model relates the two measures by the
horizontal windspeed (u)
n = u/l
(11.23)
a relationship that is adequate for eddies with a
wavelength under about 100 m, whereas larger eddies may not move at the local average wind speed.
The intensity of an eddy is proportional to its kinetic energy and the total flux density of any scalar
is carried by all the eddies in the spectrum, albeit
not all contributing equally to the transport.
In order to compare spectra at different heights
above the surface and in different wind speeds, we
can use a normalized frequency (f) where
f = n(z - d)/u
(11.24)
It has been established by experiment that almost
all of the flux is carried by eddies in the range 0.001
< f < 10 (McBean 1972; Anderson et al. 1986).
Such knowledge is important if fluxes are to be
correctly calculated. For example, Garratt (1975)
showed that CO 2 fluxes measured in a system using
a Gill propeller anemometer (whose response time
was about 0.5 sec) at a height of 1.5 m above the
vegetation were 40% in error. If the anemometer
had been placed at a height of about 5 m, the error
would have been reduced to about 14%. Thus, the
instrument frequency response time should be
lO(z - d)/u or, on the other hand, it implies that
the height of the instrument over the zero plane
should be at least equal to ncu/10 where nc is the
intrinsic cutoff frequency.
For closed-path analyzers, the intrinsic cutoff
frequency (nc) is in the order of 2.5 to 5 Hz, which
typically decreases to about 0.5 Hz because of the
damping effect induced by the sampling tube. Corrections for these effects are now well known and
a system can be designed at the outset to have particular characteristics of frequency response (Leuning and Moncrieff 1990; Leuning and Judd 1996).
Since signals of two sensors become increasingly
uncorrelated with increasing separation distance,
the correct separation distance between instruments
171
should be less than the length scale of the smallest
eddy to be detected. Kristensen and Fitzjarrald
(1984) indicated that the maximum separation distance (d) between two sensors measuring scalar
quantities (e.g., sensible heat, water vapor, CO2)
should be:
z - d
d ) < - -
-
5
(11.25)
Sensors appropriately installed are important to
minimize the effect of flow distortion. As recommended by Wyngaard (1988) the design of an eddy
covariance array must be vertically symmetrical
about its horizontal midplane to minimize the flow
distortion effect. It is also recommended to place
the inlet of the tube just below the sonic
anemometer head, in order to minimize effects on
w (Valentini et al1996).
Instrument noise affects the uncertainty of a flux
measurement for a given sampling period. The
eddy covariance technique is inherently a noise
rejection method since the flux contribution from
random noise tends to be zero (i.e., the random
noise of vertical wind speed and scalar measurements is not correlated). However, under certain
circumstances, this general principle does not hold,
especially when the statistics of turbulence are not
enough to reduce the correlated random noise.
Lumley and Panofsky (1964) derived the following
expression to estimate the sampling time (Ts) required to obtain a given level of accuracy (a) of
flux determination:
2ra~
(a~2)
(11.26)
where ~ and ~ are the mean and variance of a
turbulent quantity, and 't is an integral time scale
usually approximated as (z - d)/u.
The ratio cr~/~2 is often assumed to be equal to 5
(Auble and Meyers 1992), and thus a simple expression for the required sampling time (seconds)
in order to obtain an accuracy of 10% in the flux
estimate is:
z - d
Ts = 1000-u
(11.27)
To satisfy these error requirements, sampling periods of about two hours are often found. However,
such long sampling periods may invalidate the