X ¼ ðD=c þ 1Þ=ðD=c þ 1 þ ðr c =r a ÞÞ
ð4:27Þ
Equation (4.27) shows the preponderant role of canopy resistance in determining X, for forest-type canopies, characterized by high r c and low r a values.
The X factor is associated with the analysis of the relative change of canopy
resistance with the relative variation of water vapor flux (Jarvis and McNoughton
1986). This factor is about one in smooth and well-watered surfaces, with evapotranspiration rates of about LE eq . The X factor has a value close to zero for surfaces
with greater aerodynamic roughness, where the evapotranspiration rates are coupled
to the atmospheric vapor pressure deficit.
Typical values for X are 0.1 and 0.2 for forests (strong coupling) and 0.8 and 0.9
for lower canopies (Monteith and Unsworth 1991). In the absence of precipitation
and surface dryness, the lower canopies with higher aerodynamic resistance are
weakly coupled to atmospheric dynamics. Thus, the respective evaporation regimes
will be more dependent on either available energy or net radiation, rather than the
vapor pressure deficit. In contrast, high canopies are strongly coupled to thick
atmospheric layers, so that the latent heat flux will be more closely associated with
changes in atmospheric vapor pressure deficit.
The mean annual X, obtained by the inverse Penman–Monteith equation for
eucalypt stands in Portugal, was about 0.26 to 0.11. These values obtained between
2004 and 2005 correspond to conditions of extreme drought when there was about a
50% reduction in precipitation relative to the long-term average of 709 mm
(Rodrigues et al. 2011). Initially, in 2004, the evapotranspiration of about 723 mm
was more dependent on net radiation, whereas, during the second phase in 2005, the
evapotranspiration decreased dramatically to 392 mm due to stronger stomatal
control, under conditions of extreme water stress, and imposed evapotranspiration .
Values for the decoupling factor were about 0.18 for cork oak stands in Portugal
(Rodrigues 2002).
If E c and E f are the evapotranspiration for the lower canopy and forest, and T c and
T are the temperatures of the canopy and the air, the evapotranspiration regimes of
the two cover types can be given by the following simplified equations (Oke 1992):
E c ¼ e s T c
ð Þ À e T
ð Þ
ð
Þ = r c þ r a
ð
Þ
ð4:28Þ
E f ¼ e s T c
ð Þ À e T
ð Þ
ð
Þ = r c þ r a
ð
Þ% e s T
ð Þ À e T
ð Þ
ð
Þ =r c
ð4:29Þ
In Eq. (4.29), the term for aerodynamic resistance is negligible and the
assumption is made that the leaves are small and with rough surfaces, so that T c % T.
During active daytime transpiration, the surface temperature of lower canopies is
higher than the air temperature, thus the numerator of Eq. (4.28) will be greater than
that of Eq. (4.29). Moreover, the total resistance of lower canopies is smaller than
that of the forest canopies with higher canopy resistance, r c , (Oke 1992). Thus, the
denominator of Eq. (4.28) is lower than for Eq. (4.29) and under dry conditions,
E c > E f . Equation (4.28) shows that the evaporative potential of the lower canopies
120
4 Exchange of Energy and Mass Over Forest Canopies
ð4:27Þ
Equation (4.27) shows the preponderant role of canopy resistance in determining X, for forest-type canopies, characterized by high r c and low r a values.
The X factor is associated with the analysis of the relative change of canopy
resistance with the relative variation of water vapor flux (Jarvis and McNoughton
1986). This factor is about one in smooth and well-watered surfaces, with evapotranspiration rates of about LE eq . The X factor has a value close to zero for surfaces
with greater aerodynamic roughness, where the evapotranspiration rates are coupled
to the atmospheric vapor pressure deficit.
Typical values for X are 0.1 and 0.2 for forests (strong coupling) and 0.8 and 0.9
for lower canopies (Monteith and Unsworth 1991). In the absence of precipitation
and surface dryness, the lower canopies with higher aerodynamic resistance are
weakly coupled to atmospheric dynamics. Thus, the respective evaporation regimes
will be more dependent on either available energy or net radiation, rather than the
vapor pressure deficit. In contrast, high canopies are strongly coupled to thick
atmospheric layers, so that the latent heat flux will be more closely associated with
changes in atmospheric vapor pressure deficit.
The mean annual X, obtained by the inverse Penman–Monteith equation for
eucalypt stands in Portugal, was about 0.26 to 0.11. These values obtained between
2004 and 2005 correspond to conditions of extreme drought when there was about a
50% reduction in precipitation relative to the long-term average of 709 mm
(Rodrigues et al. 2011). Initially, in 2004, the evapotranspiration of about 723 mm
was more dependent on net radiation, whereas, during the second phase in 2005, the
evapotranspiration decreased dramatically to 392 mm due to stronger stomatal
control, under conditions of extreme water stress, and imposed evapotranspiration .
Values for the decoupling factor were about 0.18 for cork oak stands in Portugal
(Rodrigues 2002).
If E c and E f are the evapotranspiration for the lower canopy and forest, and T c and
T are the temperatures of the canopy and the air, the evapotranspiration regimes of
the two cover types can be given by the following simplified equations (Oke 1992):
E c ¼ e s T c
ð Þ À e T
ð Þ
ð
Þ = r c þ r a
ð
Þ
ð4:28Þ
E f ¼ e s T c
ð Þ À e T
ð Þ
ð
Þ = r c þ r a
ð
Þ% e s T
ð Þ À e T
ð Þ
ð
Þ =r c
ð4:29Þ
In Eq. (4.29), the term for aerodynamic resistance is negligible and the
assumption is made that the leaves are small and with rough surfaces, so that T c % T.
During active daytime transpiration, the surface temperature of lower canopies is
higher than the air temperature, thus the numerator of Eq. (4.28) will be greater than
that of Eq. (4.29). Moreover, the total resistance of lower canopies is smaller than
that of the forest canopies with higher canopy resistance, r c , (Oke 1992). Thus, the
denominator of Eq. (4.28) is lower than for Eq. (4.29) and under dry conditions,
E c > E f . Equation (4.28) shows that the evaporative potential of the lower canopies
120
4 Exchange of Energy and Mass Over Forest Canopies