Modeling Tools

Inverse Soil Moisture Retrieval Model

Research since the mid 1970's has established and verified the physical basis for passive microwave emission from land surfaces. Jackson (1993) assembled relevant components into an algorithm to solve the inverse problem of soil moisture retrieval from microwave brightness temperatures using a single frequency at horizontal polarization. A summary of the algorithm can be found below with modifications for vertical polarization. We developed code for this algorithm and have used it extensively in a number of experiments to verify accuracy of retrieved moisture and examine the sensitivity of results to various components and parameterizations.

Theory

The theory behind microwave remote sensing of soil moisture is based on the large contrast between the dielectric properties of liquid water (~80) and dry soil (<4). The dielectric properties of wet soil were studied by several investigators (e.g., Wang and Schmugge, 1980; Dobson et al., 1985; Ulaby et al., 1986). As the moisture increases, the dielectric constant of the soil-water mixture increases and this change is detectable by microwave sensors (Njoku and Kong, 1977). The emission of microwave energy is proportional to the product of the surface temperature and the surface emissivity, which is commonly referred to as the microwave brightness temperature (T_B). For typical soil moisture applications using longer microwave wavelengths at low altitude, temperature contributions from the atmosphere and the sky can be neglected.  Thus, the brightness temperature of an emitter of microwave radiation is related to the physical temperature of the source through the emissivity such that

where R is the hemispherical-directional reflectivity from the surface, T_eff is the effective radiating temperature of the surface, and e = (1-R) is the effective emissivity, which depends on the dielectric constant of the medium (Schmugge, 1990).  Although the relationship between emissivity and T_B is linear, the relationship between emissivity and dielectric constant is nonlinear because the water content of the media has a nonlinear effect on the dielectric constant.  Reflectivity is described by the Fresnel equation that defines the behavior of electromagnetic waves at a smooth dielectric boundary.  For horizontal and vertical polarized waves (H, V) at non-nadir incidence (θ), the Fresnel reflectivity may be derived from electromagnetic theory (Kong, 1990) as:

	,	(2)
	,	(3)

where ε_p is the polarization-dependent complex dielectric constant of the emitter.  Because the contribution of the imaginary part of ε_p is relatively small, inversion of eqns. (2) and (3) can be simplified if we consider only the real part of the complex dielectric constant, or permittivity.  Application of the Fresnel equation requires remote observations of reflectivity and assumptions that the dielectric and temperature properties of the soil are uniform throughout the emitting layer, that emissivity is related principally to the permittivity, and that the soil depth emitting the energy being measured is known.  Through inversion of the Fresnel equation, we obtain an estimate of the effective permittivity of the emitting layer.  For H-pol we obtain from eqn. (2):

and for V-pol from eqn. (3):

Where a = R_V^1/2 + 1 and b = R_V^1/2 – 1. 

Volumetric soil moisture content is determined from ε_eff by inverting the soil dielectric mixing model of Dobson et al. (1985) using known dielectric properties of soil, water and air.

Assumptions

Although it is desirable to use complete and physically based models to estimate soil moisture from microwave remote sensing instruments, it is rarely possible to obtain the ancillary data these models require (Jackson, 1993).  Consequently, application of the Fresnel equation requires assumptions that the dielectric and temperature properties of the soil are uniform throughout the emitting layer, that emissivity is related principally to the real part of the complex dielectric constant, and that one has knowledge of the soil depth emitting the energy being measured.  There are several additional considerations that also should be incorporated in a retrieval algorithm.  Jackson et al. (1997) provides a comprehensive review of many of these issues. 

Correction Procedures

From Eq. (1), it is clear that observed microwave emission depends on both soil moisture and temperature.  Because soil moisture and temperature are not independent, we must normalize the observed brightness temperature by the effective radiating temperature of the soil if we are to relate T_B to soil moisture.  As described by Choudhury et al. (1982), effective temperature, T_eff, may be defined as

where T_d is the deep (e.g. 10-15 cm) soil temperature, T_s is the surface temperature, and C is an empirical parameter weighting the relative contribution of surface and deep soil to the microwave emission at the soil surface.  Although C in principle depends on soil moisture, it is impractical to consider this dependence in the algorithm.  Normalizing T_B with respect to T_eff helps to reduce the diurnal hysteresis in the T_B-soil moisture relationship.

An expression for the bare rough soil surface reflectance, R_br, can be derived from eqn. (1) in Jackson and Schmugge (1991) in terms of the transmissivity and the single scattering albedo (α):

Correction for the amount of scattering that takes place due to roughness of the soil surface uses the simple statistical model of Choudhury et al. (1979), which treats the soil surface height as having a Gaussian distribution with variance σ².  The microwave reflectance of a bare smooth surface is thus given by:

where:

and λ = wavelength.  This single-parameter roughness correction is very simple and is certainly not adequate under all conditions.  More elaborate models incorporate information on the correlation length scale for surface roughness and even allow roughness to vary as a function of soil moisture Wigneron et al. (2004).

Compensation for energy attenuation by vegetation is based on the relationship between the vegetation transmissivity (γ) and optical depth (τ) Jackson and Schmugge (1991):

and the optical depth is parameterized in terms of the vegetation water content (W_c) and an empirical parameter B:

According to Wigneron et al. (2004), the B parameter depends on frequency, polarization and incidence angle.  This correlation is very conducive to remote sensing applications because proxies for vegetation water content can be obtained by other remote sensing methods.

References Cited

Choudhury, B. J., Schmugge, T. J., and Mo, T. (1982),  A parameterization of effective soil temperature for microwave emission. J. Geophys. Res., 87, 1301-1304.

Choudhury, B. J., Schmugge, T. J., Newton, R. W., and Chang, A. T. C. (1979), Effect of surface roughness on microwave emission of soils. J. Geophys. Res., 84, 5699-5706.

Dobson, M. C., Ulaby, F. T., Hallikainen, M. T., and El-Rayes, M. A. (1985),  Microwave dielectric behavior of wet soil - part II: dielectric mixing models. IEEE Trans. Geosci. Remote Sens.,GE-23, 35-46.

Jackson, T. J. (1993), Measuring surface soil moisture using passive microwave remote sensing. Hydrol. Proc., 7, 139-152.

Jackson, T. J., and O'Neill, P. E. (1990), Attenuation of soil microwave emission by corn and soybeans at 1.4 and 5 GHz. IEEE Trans. Geosci. Remote Sens., 28, 978-980.

Jackson, T. J., O'Neill, P. E., and Swift, C. T. (1997), Passive microwave observation of diurnal surface soil moisture. IEEE Trans. Geosci. Remote Sens., 35, 1210-1222.

Jackson, T. J. and Schmugge, T. J. (1991), Vegetation effects on the microwave emission of soils. Remote Sens. Environ., 36, 203-212.

Kirdiashev, K. P., Chukhlantsev, A. A., and Shutko, A. M. (1979), Microwave radiation of the Earth's surface in the presence of vegetation. Radio Eng. and Elec., 24, 256-264.

Kong, J. A. (1990) Electromagnetic Wave Theory, 2^nd ed., Wiley-Interscience, New York.

Njoku, E. G. and Kong, J. A. (1977), Theory for passive microwave remote sensing of near-surface soil moisture. J. Geophys. Res., 82, 3108-3118.

Schmugge, T. (1990), Measurements of surface soil moisture and temperature, In Remote Sensing of Biosphere Functioning (R.J. Hobbs, and H.A. Mooney, Eds.). Springer-Verlag, New York. 

Shutko, A. M. (1986), Remote sensing of the waters and lands via microwave radiometry (the principles of method, problems feasible for solving, economic use).  Pontificiae Academiae Scientiarvm Scripta Varia, 68, 413-440.

Wang, J. R. and Schmugge, T. J. (1980), An empirical model for the complex dielectric permittivity of soils as a function of water content. IEEE Trans. Geosci. Remote Sens., GE-18, 288-295.

Wigneron, J.-P., Parde, M., Waldteufel, P., Chanzy, A., Kerr, Y., Schmidl, S. and Skou, N. (2004) Characterizing the dependence of vegetation model parameters on crop structure, incidence angle, and polarization at L-band, IEEE Trans. Geosci. Remote Sensing, 42, 416-425.

Ulaby, F. T., Moore, R. K., and Fung, A. K. (1986), Microwave Remote Sensing, Active and Passive, vol.III: From Theory to Applications, Artech House, Massachusettes.