1 Spatial Modelling of the Terrestrial Environment - Georeferencial

Coupled Land Surface and Microwave Emission Models 63
temperature calculated by a land surface model and the Wilheit (1978) microwave emission
model (Lee et al., 2002a). The sharp decrease in brightness temperatures on DOY 210 and
252 is caused by irrigation while the decrease on DOY 253 results from rainfall. The nearsurface
water content ranges from 40% to 10% for both drying periods. Diurnal variation
in the near-surface soil water content and temperature are also reflected in the modelled
microwave brightness temperatures.
4.2.2 Effect of Vegetation on Microwave Emission from the Soil
The presence of vegetation has a significant impact on the relationship between near-surface
soil moisture and microwave brightness temperature. For a bare soil, the dynamic range
in brightness temperature is approximately 180 K, whereas for a crop with canopy water
content of only 3.3 kg m −2 , the dynamic range is significantly reduced, to approximately
60 K. In general, the effects of the vegetation on the microwave emission from the soil can
be described using radiative transfer equations. These can be solved either numerically or
after applying simplifying assumptions. The following sections describe radiative transfer
theory, and its application to describing the effect of vegetation on microwave emission
from the soil.
Radiative transfer theory. A vegetation canopy will scatter and absorb microwave emission
from the soil. It will also contribute with its own emission, which will be scattered
and absorbed by the canopy through which it passes. Within an infinitesimal volume of the
canopy, the energy balance for upward radiative transfer with horizontal polarization is:
µ dT Bh(θ,z)
= K a T can (z) − K e (θ)T Bh (θ,z)
dz
∫ 1
+ ((h, h ′ )T Bh (θ ′ , z) + (h,v ′ )T Bv (θ ′ , z)) dµ ′ . (2)
−1
The energy balance for downward radiative transfer with horizontal polarization is:
−µ dT Bh(π − θ,z)
= K a T can (z) − K e (π − θ)T Bh (π − θ,z)
dz
∫ 1
+ ((h(π − θ), h ′ )T Bh (θ ′ , z) + (h(π − θ),v ′ )T Bv (θ ′ , z)) dµ ′ (3)
−1
where T Bh is the horizontally polarized microwave brightness temperature (K), T can is the
physical temperature of the canopy (K), z is the depth within the canopy (m), K a is the
absorption coefficient, K s is the scattering coefficient, K e (= K a + K s ) is the extinction
coefficient, θ and θ ′ are incidence angles, with µ = cos θ and µ ′ = cos θ ′ , and (h,h ′ ) and
(h,v ′ ) are scattering phase functions, where (p, q ′ ) represents the scattering probability of
p polarized radiation being scattered into q polarized radiation. (Note: p and q represent
horizontally (h) and vertically (v) polarized radiation interchangeably.) The first term on
the right-hand side in equations (2) and (3) describes the thermal emission from the canopy,
the second term represents the energy absorbed and scattered by the canopy, and the final
term represents the redistribution of scattered energy among different look angles.
There are no analytical solutions to equations (1) and (2). However, they can be solved
numerically as they are, for example, in the complex ‘discrete’ model of Wigneron et al.