9 Soil Moisture
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VOLUMETRIC SOIL MOISTURE. Mv
Fig. 9.1. The real and imaginary parts of the dielectric constant as a function of volumetric soil
moisture for a loam soil measured at four frequencies (after Ulaby et al. 1986)
where e = (I-r) is the emissivity and is dependent upon dielectric constant of the
soil and the surface roughness. Thus over the nonnal rage of soil moisture, a decrease in the emissivity from about 0.95 to 0.60 or lower can be expected. This
translates to a change in brightness temperature on the order of 80 degrees K.
Though the relationship between emissivity and brightness temperature is linear
(see Eq. 9.5), the soil moisture has a non-linear dependence on reflectivity because
the reflection coefficient R of the ground is related in a non-linear way to the dielectric constant of the soil (£). For horizontal polarization, the reflection coefficient is given by
R=cosq-b
cosq + b
(9.6)
where b = ~ £ - sin 2 q and q is the angle of incidence. The expression for vertical
polarization can be written in a similar way. The dielectric constant, £, is a complex quantity and the empirical relationships between dielectric constant and soil
moisture derived by Dobson et al. (1985) show that dielectric constant has a nonlinear dependence on soil moisture. However, even though the brightness temperature -soil moisture relation has a strong theoretical basis, most algorithms are
empirical in that they depend upon ground data for the relationship.