11. Canopy Fluxes
surface is approached, however, the spectrum of
turbulence includes a larger proportion of smaller
eddies that actively exchange mass and momentum
between the surface and the atmosphere. The instrumentation must therefore be capable of sampling high-frequency eddies, typically up to 10 Hz.
In principle, one could use an eddy covariance system well above the canopy in order to avoid the
problem of frequency response of analyzers. However, as we move up in height, the area of flux integration becomes larger and the requirements of
surface homogeneity become more and more stringent. In fact, if the instruments are placed too high
above the surface it is possible that they could extend out of the boundary layer representative of the
nearby vegetation and be measuring some component of fluxes from a different type of vegetation
further upwind. A convenient rule-of-thumb suggests a fetchlheight ratio of about 100: 1; thus a
fetch of 500 m would allow instruments to be
placed up to a height of about 5 m above the surface. The fetchlheight ratio depends on atmospheric
stability and surface roughness insofar as they influence the degree of mixing of internal boundary
layers as they are advected over different types of
surface (Mulhearn 1977; Gash 1986; Grelle and
Lindroth 1996).
One promising approach is to define a "footprint" or source region that is a measure of the relative importance of sources upwind that contribute
to the measured flux. This area can be regarded as
contributing most of the flux measured, and its areal
extent and position can be calculated from a knowledge of surface roughness, atmospheric stability,
wind speed and direction (e.g., Schuepp et al. 1990,
Schmid and Oke 1990). The approach is based on
the same theory as underlies dispersion modeling
of pollutants using the familiar Gaussian plume approach. A number of models are available concerning footprint calculation based either on lagrangian
or particle trajectory models (Schuepp et al. 1990;
Finn et al. 1996; Flesch 1995) or analytical dispersion models (Horst and Weil 1994; Schmid 1994).
At present, however, most are of limited application
in the roughness sublayer.
Ideally, the measurement site should be extensive, flat, and horizontally uniform to ensure that
fluxes are measured in the constant flux layer. To a
first order approximation, the error F z - F o , fol165
lowing a change in surface with a flux of F] to one
with flux F 0 may be estimated using
lOz/x In(z/zo)
In(x/lOzo)
(11.1)
where x is the upwind distance from the change in
surface and Zo is the roughness length of the downwind surface (obtained from wind profiles) (Moncrieff et al. 1996). From this expression, it is clear
that the error in the flux measurement, F z - F o ,
is proportional to the difference in fluxes of the
upwind and downwind surfaces, F] - Fo. The error also diminishes as zJx decreases, and is < 5%
of F[ - Fo for z/x < 0.01, in conformity with the
micrometeorological rule-of-thumb that the measurement height should be < x/IOO to ensure accurate measurements. This ratio needs to be increased for stable conditions and may be relaxed
under unstable stratification (Kaimal and Finnigan
1994). According to (Schuepp et al. 1990) the
relative contribution to the vertical flux
[(l/Qo)(dQ/dx)] at height z, coming from an infinite crosswind source of unit width at an upwind
distance x, in neutral conditions is given by:
1 dQ
Qo dx
u(z - d) e~u(z~cI)/(ku*x)
u*kx?
(11.2)
and the upwind position (xmax) of the peak of the
cumulative flux of the source area is:
Xmax =
u(z - d)
u*2k
(11.3)
where u is the mean wind velocity at height z, d
the zero-plane displacement (obtained from wind
profiles), u* the friction velocity, and k the von
Karman constant (0.41). Figure 11.4 is an example
of the distribution of the relative contribution to
the vertical flux as a function of height of measurement. Increasing the height of measurements,
the peak of the flux footprint becomes more and
more distant from the point of measurement. Similarly, the peak contribution moves closer to the
point of measurement as the atmosphere becomes
more unstable. With increasing stability, the peak
contribution moves further from the point of
measurement.
surface is approached, however, the spectrum of
turbulence includes a larger proportion of smaller
eddies that actively exchange mass and momentum
between the surface and the atmosphere. The instrumentation must therefore be capable of sampling high-frequency eddies, typically up to 10 Hz.
In principle, one could use an eddy covariance system well above the canopy in order to avoid the
problem of frequency response of analyzers. However, as we move up in height, the area of flux integration becomes larger and the requirements of
surface homogeneity become more and more stringent. In fact, if the instruments are placed too high
above the surface it is possible that they could extend out of the boundary layer representative of the
nearby vegetation and be measuring some component of fluxes from a different type of vegetation
further upwind. A convenient rule-of-thumb suggests a fetchlheight ratio of about 100: 1; thus a
fetch of 500 m would allow instruments to be
placed up to a height of about 5 m above the surface. The fetchlheight ratio depends on atmospheric
stability and surface roughness insofar as they influence the degree of mixing of internal boundary
layers as they are advected over different types of
surface (Mulhearn 1977; Gash 1986; Grelle and
Lindroth 1996).
One promising approach is to define a "footprint" or source region that is a measure of the relative importance of sources upwind that contribute
to the measured flux. This area can be regarded as
contributing most of the flux measured, and its areal
extent and position can be calculated from a knowledge of surface roughness, atmospheric stability,
wind speed and direction (e.g., Schuepp et al. 1990,
Schmid and Oke 1990). The approach is based on
the same theory as underlies dispersion modeling
of pollutants using the familiar Gaussian plume approach. A number of models are available concerning footprint calculation based either on lagrangian
or particle trajectory models (Schuepp et al. 1990;
Finn et al. 1996; Flesch 1995) or analytical dispersion models (Horst and Weil 1994; Schmid 1994).
At present, however, most are of limited application
in the roughness sublayer.
Ideally, the measurement site should be extensive, flat, and horizontally uniform to ensure that
fluxes are measured in the constant flux layer. To a
first order approximation, the error F z - F o , fol165
lowing a change in surface with a flux of F] to one
with flux F 0 may be estimated using
lOz/x In(z/zo)
In(x/lOzo)
(11.1)
where x is the upwind distance from the change in
surface and Zo is the roughness length of the downwind surface (obtained from wind profiles) (Moncrieff et al. 1996). From this expression, it is clear
that the error in the flux measurement, F z - F o ,
is proportional to the difference in fluxes of the
upwind and downwind surfaces, F] - Fo. The error also diminishes as zJx decreases, and is < 5%
of F[ - Fo for z/x < 0.01, in conformity with the
micrometeorological rule-of-thumb that the measurement height should be < x/IOO to ensure accurate measurements. This ratio needs to be increased for stable conditions and may be relaxed
under unstable stratification (Kaimal and Finnigan
1994). According to (Schuepp et al. 1990) the
relative contribution to the vertical flux
[(l/Qo)(dQ/dx)] at height z, coming from an infinite crosswind source of unit width at an upwind
distance x, in neutral conditions is given by:
1 dQ
Qo dx
u(z - d) e~u(z~cI)/(ku*x)
u*kx?
(11.2)
and the upwind position (xmax) of the peak of the
cumulative flux of the source area is:
Xmax =
u(z - d)
u*2k
(11.3)
where u is the mean wind velocity at height z, d
the zero-plane displacement (obtained from wind
profiles), u* the friction velocity, and k the von
Karman constant (0.41). Figure 11.4 is an example
of the distribution of the relative contribution to
the vertical flux as a function of height of measurement. Increasing the height of measurements,
the peak of the flux footprint becomes more and
more distant from the point of measurement. Similarly, the peak contribution moves closer to the
point of measurement as the atmosphere becomes
more unstable. With increasing stability, the peak
contribution moves further from the point of
measurement.