1 Spatial Modelling of the Terrestrial Environment - Georeferencial

Coupled Land Surface and Microwave Emission Models 65
where θ veg is the vegetation water content and β is the opacity coefficient. One output
from the Wigneron et al. (1993) discrete model is the extinction coefficient (K e ). Burke
et al. (1999) showed that the optical depth calculated using the extinction coefficient (equation
(7)) could be used in the simple model to predict accurate time series of microwave
brightness temperatures.
Extended Wilheit (1978) Model. Unlike the previous two models, which assume the
canopy consists of one uniform layer; the extended Wilheit (1978) model assumes a multilayered
vegetation canopy. The energy balance of each layer is determined using simplified
radiative transfer theory. This model requires as input profiles of both the dielectric and
temperature within the vegetation. Currently, there is only limited information on the dielectric
permittivity of either the vegetation matter (El-Rayes and Ulaby, 1987; Ulaby and
Jedlicka, 1984; Chuah et al., 1997; Colpitts and Coleman, 1997; Franchois et al., 1998;
Ulaby et al., 1986) or the canopy as a whole (Ulaby et al., 1986; Ulaby and Jedlicka, 1984;
Brunfeldt and Ulaby, 1984; Schmugge and Jackson, 1992). In order to model the dielectric
properties of a vegetation canopy, two separate mixing effects must be recognized. The
first is the mixing between constituents of the vegetation, which determines the dielectric
of the vegetation matter itself. One plausible approach to modelling the dielectric of the
vegetation matter is analogous to a linear version of the Dobson et al. (1985) mixing model
for soils, i.e., to assume:
ε v = ε dry V dry + ε fw V fw + ε bw V bw (9)
where ε v is the dielectric permittivity for leaf material as a whole, ε dry , ε fw , and ε bw are the
dielectric permittivities, and V dry , V fw , and V bw are the volume fractions of dry matter, free
water and bound water, respectively. It is assumed that ε dry , ε fw , and ε bw are independent of
the vegetation water content. The second mixing model determines the dielectric permittivity
of the mixture of vegetation matter and air that make up the vegetation canopy (ε can ).
If non-linear mixing is assumed:
εcan α = εα v V V + εair α (1 − V V)
where ε air is the dielectric permittivity of air; V v is the fractional volume of vegetation
elements per unit volume canopy; and α is a so-called “shape factor”. [Note: in the case
of the Dobson et al. (1985) mixing model for soils, α = 0.65.] Schmugge and Jackson
(1992) suggested that the refractive model [α = 0.5] provides a better representation of
the dielectric properties of the canopy than a linear model [α = 1]. Lee et al. (2002a)
optimized time series of modelled brightness temperatures against measurements from the
field experiment evaluated by Burke et al. (1998) and retrieved values ranging between 1.1
and 2.2.
Equations (9) and (10) together calculate the dielectric constant for the canopy as a whole
and, in the extended Wilheit (1978) model, this amount of dielectric is then distributed
vertically among the plane parallel layers above the soil. The heights of the top and bottom
of the canopy are specified, but gradual changes in dielectric permittivity are simulated
around these levels by introducing broadening that follows a Gaussian distribution with
specified standard deviations. This broadening reflects the natural variability between the
individual plants that make up the canopy, and its presence is also critical to the reliable
operation of this coherent emission model because avoiding sharp transitions in dielectric at