Passive Microwave Remote Sensing of Soil Moisture and Regional Drought Monitoring - Monitoring and Predicting Agricultural Drought: A Global Study - page 91

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Soil Moisture and Reflectivity Assuming that the earth is a plane surface
with surface geometric variations and volume discontinuities much less
than the wavelength, only refraction and absorption of the media need
to be considered. This situation permits the use of the Fresnel reflection
equations as a model of the system (Ulaby et al., 1986). These equations
predict the surface reflectivity as a function of dielectric constant ( k ) and the
viewing angle ( θ ) based on the polarization of the sensor (H

= horizontal

or V = vertical).

k

2

sin 2 θ

cos θ − −

r H

= k [7.1]

sin 2 θ

cos θ + −

k

2

sin 2 θ k cos θ − −

r V = k [7.2]

[91],

sin 2 θ

k cos θ + −

Polarization refers to the orientation of the electromagnetic waves with
respect to the surface. The dielectric constant of soil is a composite of
the values of its components (air, soil, and water). The basic reason that
microwave remote sensing can provide soil moisture information is that
there is a large difference between the dielectric constants of water (

Line
——
-2.3
——
Norm
PgEn

∼ 80)

and the other components ( < 5).
Based on an estimate of the mixture dielectric constant derived from the
Fresnel equations and soil texture information, volumetric soil moisture
can be estimated using an inversion of the dielectric mixing model (i.e.,
Hallikainen et al., 1985). The depth of soil contributing to the measure-
ment is about one-quarter the wavelength (based on a wavelength range
of 2-21 cm). As noted above, it is desirable to use low frequencies because
the measurement at these frequencies provides more information on the
soil column.

[91],

So il Moisture and Brightness Temperature Passive microwave remote
se nsing uses radiometers that measure the natural thermal microwave emis-
sio n within a narrow band centered on a particular frequency. The mea-
su rement provided is the brightness temperature in degrees Kelvin, T B ,
w hich includes contributions from the atmosphere, reflected sky radiation,
an d the land surface. Atmospheric contributions are negligible at frequen-
ci es < 10 GHz, and the cosmic radiation contribution to sky radiation has
kn own values that vary only slightly in the frequency range used for obser-
va tions of soil water content.
The brightness temperature of a surface is equal to its emissivity ( e )
m ultiplied by its physical temperature ( T ).

T B = eT [7.3]

The emissivity is equal to 1 minus the reflectivity, which provides the link
to the Fresnel equations and soil moisture for passive microwave remote
sensing. Figure 7.1 illustrates the relationships between emissivity and soil