AM #1
AM #2
AM #3
+4.59 -3.46
-9.78 +10.45
+4.18 -4.24
119
+118.52
-89.64
+50.52
+0.02
-0.03
+0.05
-5.12
+41.93
-3.81
AM #1: 56% tree, 44% crop. AM #2: 39% tgrass, 28% dtree, 22%
crop, 11% tree. AM #3: 36% etree, 36% tree, 17% bog, 11% tgrass.
Table 1 Difference in annualy averaged and seasonally averaged (for idealized experiment)
simulated surface fluxes of latent heat, sensible heat, and momentum and in soil moisture and
runoff between dominant vegetation type (CONTROL) and distributed vegetation type
(SUBVEG) experiments (see text).
4.2.2. Intra-patch heterogeneity
As already mentioned, intra-patch heterogeneity requires a continuous rather than a
discrete representation. The conceptual framework of this representation is presented for
example by Avissar (1992) and is referred to as statistical-dynamical approach. Basically,
this approach consists of defining the spatial variability of a given variable ¢ with an
analytical probability density function (PDF) f pdf ( ¢ )dr/!. It is useful to select the function
such that it is normalized, i.e.
J fpdf(¢)d¢ = 1
(61)
with the additional constraint that
(62)
where ¢ is the grid point average of ¢. In principle, then the procedure is to multiply all
terms in the equations of an ESEMs by fpdf(¢ )d¢ and integrate over the whole distribution.
As illustrative example, Avissar (1992) applies this procedure to describe the effect
of intra-patch variations in stomatal resistance, r s, on a simplified canopy model. The
energy budget equation for this canopy model can be written as
(63)
where the terms in Eq. (63) have been defined in the previous sections. After a number
of manipulations and simplifications, the energy balance equation for a given r s reduces
to
(64)
AM #2
AM #3
+4.59 -3.46
-9.78 +10.45
+4.18 -4.24
119
+118.52
-89.64
+50.52
+0.02
-0.03
+0.05
-5.12
+41.93
-3.81
AM #1: 56% tree, 44% crop. AM #2: 39% tgrass, 28% dtree, 22%
crop, 11% tree. AM #3: 36% etree, 36% tree, 17% bog, 11% tgrass.
Table 1 Difference in annualy averaged and seasonally averaged (for idealized experiment)
simulated surface fluxes of latent heat, sensible heat, and momentum and in soil moisture and
runoff between dominant vegetation type (CONTROL) and distributed vegetation type
(SUBVEG) experiments (see text).
4.2.2. Intra-patch heterogeneity
As already mentioned, intra-patch heterogeneity requires a continuous rather than a
discrete representation. The conceptual framework of this representation is presented for
example by Avissar (1992) and is referred to as statistical-dynamical approach. Basically,
this approach consists of defining the spatial variability of a given variable ¢ with an
analytical probability density function (PDF) f pdf ( ¢ )dr/!. It is useful to select the function
such that it is normalized, i.e.
J fpdf(¢)d¢ = 1
(61)
with the additional constraint that
(62)
where ¢ is the grid point average of ¢. In principle, then the procedure is to multiply all
terms in the equations of an ESEMs by fpdf(¢ )d¢ and integrate over the whole distribution.
As illustrative example, Avissar (1992) applies this procedure to describe the effect
of intra-patch variations in stomatal resistance, r s, on a simplified canopy model. The
energy budget equation for this canopy model can be written as
(63)
where the terms in Eq. (63) have been defined in the previous sections. After a number
of manipulations and simplifications, the energy balance equation for a given r s reduces
to
(64)