11. Canopy Fluxes
turbulent mixing is low. This is particularly relevant
to flux measurements over forests, as discussed
later.
Equation 11.13 sho,,:s that we must have instrumentation that can sample vertical wind speeds and
scalar concentrations and be able either to perform
real-time analysis in which means are subtracted
from raw data to yield the fluctuating components
from which cross-products are formed or to store
all the raw data for later processing in the
laboratory.
In principle, then, Equation 11.13 defines the
eddy covariance method but, in reality, there are a
number of corrections that have to be applied to
allow for instrumental and software effects on the
final flux. Of more concern however, is the acceptance, based on recent field studies, that large-scale
subsidence in the ABL and nocturnal (katabatic)
drainage can induce a non-zero mean vertical velocity and thus a mass flux that has to be taken into
account in any study using eddy covariance. If, in
expansion of the conservation equation (Equation
11.11) we omit the molecular terms and concentrate
on the x-z plane for clarity (x being aligned with
the mean wind direction and z is perpendicular to
the local ground surface) and we use e for scalar
concentration then
ae a(ue) a(we)
- + - - + - - = s
at
ax
az
(11.16)
After Reynold's decomposition as before, we get:
ae
au' e'
ae
aa
+
+a-+e~
~
~
~
aw'e'
a(vve)
+ - - + - - = S (11.17)
az
az
Given the not unreasonable assumption that air is
incompressible over the small heights involved,
Lee (1998) writes:
aa
ax
(11.18)
and a more complete equation for a flux by eddy
covariance becomes (Equation 11.19)
Fo = rz' ae dz + (w' e')r
Jo at
+ vvrCer - (e»)
(11.19)
(overbars represent means over a specified averaging period, subscript r represents parameters at
169
the reference level) where Zr is the reference or measurement height, (e) is the mean scalar concentration between the ground and the reference level, Wr
is the vertical velocity at the reference height. Thus
the simple Equation 11.13 has been modified to acknowledge that canopy storage below the level of
measurement has to be measured (the first term on
the right-hand side of Equation 11.19), together
with the eddy flux itself (second term), plus a mass
flow term (third term) to allow for horizontal flow
convergence/divergence or a non-zero mean vertical velocity.
Mention has been made already of the relatively
small size of the storage correction during the day,
but at night it can be substantial. The correction
term for non-zero mean velocity or convergence
arises at even seemingly ideal field sites for micrometeorology. Atmospheric subsidence is common
in highly convective conditions and in synopticscale subsidence; local circulations, such as lake
breezes (Sun et al. 1998) and katabatic drainage
even on slopes as little as 1: 1000, can induce a nonzero mean vertical velocity, as drainage flow on a
slope is compensated by a descending motion. According to Lee (1998) a mean vertical velocity of
3 cm sec - 1 could be generated on a slope of only
1°. The implications for long-term flux measurement over a forest site of a trace gas such as CO 2
are important. Lee (1998) showed that the mass
flow mechanism may contribute as much as 12
/lmol m - 2 sec - 1 with a mean vertical velocity of
only 0.5 cm sec - 1. He also gives the example of a
typical flux site with a slope of 1°, which induced
a mean vertical velocity at night of 1 cm sec - 1,
sufficient to induce a mass flux that was twice the
size of the measured eddy flux. As Lindroth et al.
(1998) point out, for their long-term flux site in an
old-growth spruce plantation in Sweden, a 1
/lmol m- 2 sec- 1 bias averaged over 12 hours per
day for 365 days would be equivalent to 200
g C m - 2 yr - 1 and large enough to change the sign
of the net carbon flux over this period. Since the
size of the correction term is proportional to height,
the problem is not so large over short canopies,
such as cereals.
Correction Terms in Eddy Covariance
Although the eddy covariance technique is widely
considered to carry with it the least amount of empirical baggage of any micrometeorological tech-
turbulent mixing is low. This is particularly relevant
to flux measurements over forests, as discussed
later.
Equation 11.13 sho,,:s that we must have instrumentation that can sample vertical wind speeds and
scalar concentrations and be able either to perform
real-time analysis in which means are subtracted
from raw data to yield the fluctuating components
from which cross-products are formed or to store
all the raw data for later processing in the
laboratory.
In principle, then, Equation 11.13 defines the
eddy covariance method but, in reality, there are a
number of corrections that have to be applied to
allow for instrumental and software effects on the
final flux. Of more concern however, is the acceptance, based on recent field studies, that large-scale
subsidence in the ABL and nocturnal (katabatic)
drainage can induce a non-zero mean vertical velocity and thus a mass flux that has to be taken into
account in any study using eddy covariance. If, in
expansion of the conservation equation (Equation
11.11) we omit the molecular terms and concentrate
on the x-z plane for clarity (x being aligned with
the mean wind direction and z is perpendicular to
the local ground surface) and we use e for scalar
concentration then
ae a(ue) a(we)
- + - - + - - = s
at
ax
az
(11.16)
After Reynold's decomposition as before, we get:
ae
au' e'
ae
aa
+
+a-+e~
~
~
~
aw'e'
a(vve)
+ - - + - - = S (11.17)
az
az
Given the not unreasonable assumption that air is
incompressible over the small heights involved,
Lee (1998) writes:
aa
ax
(11.18)
and a more complete equation for a flux by eddy
covariance becomes (Equation 11.19)
Fo = rz' ae dz + (w' e')r
Jo at
+ vvrCer - (e»)
(11.19)
(overbars represent means over a specified averaging period, subscript r represents parameters at
169
the reference level) where Zr is the reference or measurement height, (e) is the mean scalar concentration between the ground and the reference level, Wr
is the vertical velocity at the reference height. Thus
the simple Equation 11.13 has been modified to acknowledge that canopy storage below the level of
measurement has to be measured (the first term on
the right-hand side of Equation 11.19), together
with the eddy flux itself (second term), plus a mass
flow term (third term) to allow for horizontal flow
convergence/divergence or a non-zero mean vertical velocity.
Mention has been made already of the relatively
small size of the storage correction during the day,
but at night it can be substantial. The correction
term for non-zero mean velocity or convergence
arises at even seemingly ideal field sites for micrometeorology. Atmospheric subsidence is common
in highly convective conditions and in synopticscale subsidence; local circulations, such as lake
breezes (Sun et al. 1998) and katabatic drainage
even on slopes as little as 1: 1000, can induce a nonzero mean vertical velocity, as drainage flow on a
slope is compensated by a descending motion. According to Lee (1998) a mean vertical velocity of
3 cm sec - 1 could be generated on a slope of only
1°. The implications for long-term flux measurement over a forest site of a trace gas such as CO 2
are important. Lee (1998) showed that the mass
flow mechanism may contribute as much as 12
/lmol m - 2 sec - 1 with a mean vertical velocity of
only 0.5 cm sec - 1. He also gives the example of a
typical flux site with a slope of 1°, which induced
a mean vertical velocity at night of 1 cm sec - 1,
sufficient to induce a mass flux that was twice the
size of the measured eddy flux. As Lindroth et al.
(1998) point out, for their long-term flux site in an
old-growth spruce plantation in Sweden, a 1
/lmol m- 2 sec- 1 bias averaged over 12 hours per
day for 365 days would be equivalent to 200
g C m - 2 yr - 1 and large enough to change the sign
of the net carbon flux over this period. Since the
size of the correction term is proportional to height,
the problem is not so large over short canopies,
such as cereals.
Correction Terms in Eddy Covariance
Although the eddy covariance technique is widely
considered to carry with it the least amount of empirical baggage of any micrometeorological tech-