Mathematical and Physical Modelling of Microwave Scattering and Polarimetric Remote Sensing

Monitoring the environment is most urgent and is receiving more attention from scientists worldwide. Various means can be used; a main role, however, is played by radar. Efficient use of radar for receiving authentic volumetric information of investigated objects is one of the major issues for radar experts, previously involved in the field of radio location. The scope of the subject in this monograph is to provide a review of available polarimetric radar techniques for solving practical inverse problems in remote sensing of various types of scatterers on the earth’s surface (vegetation, ocean, terrain, etc.)

The research program includes the following topics:

An introduction to mathematical and physical modelling of microwave scattering for remote sensing with use of polarimetry is provided in Part II of the Monograph. This part is composed of four chapters (1-4).

Presently, ecological problems attract great attention. That is why the decision to institute ecological monitoring is of current interest and a search for the best methods of radar monitoring is being carried out in many countries. The main problem with ecological monitoring is the interpretation of radar measurements. The method of measurements consists of transmitting an electromagnetic signal of a given form through a medium under investigation and picking-up at the receiver the signal scattered after the interaction with the medium. The received signal is distorted by the scattering medium. The interpretation of the modifications on the received signal are made at the receiver by a signal processor.

Our goal in this chapter is to analyze the process of radar monitoring based on polarimetric data. This analysis is made in two steps. First, by looking into the physical process of how data can be generated by a scattering object (source/encoder) and extracted by a polarimetric radar (receiver/decoder) for the interpretation and classification of the remote-sensed object. Secondly, by investigating the procedures of implementing solutions to inverse scattering problems using polarimetric radar techniques within the framework of specific applications.

The general physical problem in remote sensing is to measure the scattering of electromagnetic waves from (random) media. The design of remote sensing radars requires knowledge of radio-wave scattering processes for various types of media.

In Chapter 3, we provided a descriptive introduction to the physics of scattering (physical modelling) and the statistics of scattered signals (mathematical modelling). In the last part of that chapter we also discussed the problem of using different approximations in the scattering model with regard to the accuracy of the prediction of scattering. In this chapter, we present an overview of the available scattering methods used to calculate the scattering cross section in random media. We consider two types of scattering: (a) surface scattering and (b) volume scattering. The major difference between the two is the depth of penetration into the medium. For surfaces of lossy media (such as wet soil), the scattering originates at the surfaces and the volume effects are usually ignored. For volume scattering media, such as vegetation and snow cover, the penetration may be significant and scattering within the volume may become the dominant scatter contribution.

Basic mathematical modelling for random media is provided in this chapter. This background information is needed for the calculation of the fields scattered by vegetation-covered ground surfaces, with specific applications to radar remote sensing.

Many papers have been devoted to the problem of radio wave reflection from vegetation. The investigations have been pursued over a wide range of wavelengths (meterwave, microwave, millimeterwave, optical wave) using active methods (radar, scatterometers) and passive methods (radiometry, photography) as well. Ground-based, aircraft and satellite-based measurements and theoretical analyses have been performed. The results have been published in a number of reviews [Potapov, 1992; Yakovlev, 1994; Chuhlantzev, 1980] and monographs [Shutko, 1986; Ratchkulik, 1981; Kondratiev, 1984].

In this chapter, the interrelations between electrodynamic and physical characteristics of earth surfaces are considered. The electrodynamics characteristics are measured by the permittivity that reflects the polarizability of the medium under the perturbation of an external electromagnetic field. The physical characteristics are measured by the thermodynamic (e.g., temperature, pressure) or chemical parameters (e.g., moisture, salinity) of the medium. The electrodynamic characteristics depend on the frequency of the external electromagnetic field, the natural frequencies of the medium, as well as the physical properties indicated above. Since the reflectivity properties of the medium depend on its electrodynamic properties (permittivity), we see how important it is to derive the electrodynamic properties from the physical characteristics of the medium.

Reflection of electromagnetic waves from layered structures under different polarization conditions is studied. The main medium electrodynamic characteristic property taken into account is the electric permittivity. The analysis is performed using either a deterministic or a probabilistic (stochastic) approach. Various permittivity profiles are chosen: linear, exponential and polynomial. In the case that the permittivity has a random fluctuating part, a stochastic approach leading to an integral equation is used to determine the ensemble-averaged reflection coefficient and the average power.

In some radar remote sensing problems connected with investigations of the earth’s surface, it is necessary to investigate reflections from structures with internal ruptures (e.g., fractures in ice ravines), or with all kinds of hollow spaces. Application of electrodynamic models of ruptures (fractures) in the form of an endless deep pit with vertical walls and with a reflection coefficient equal to zero, turns out to be ill-defined. Experimental data shows that the reflection coefficient may have quite a significant magnitude. A slight deviation of the pit walls parallel orientation can also cause this effect. Analysis based on models therefore must always be extended very carefully.

In this chapter, the analysis of electromagnetic scattering from a surface layer with rough borders is carried out. It is well known that the degree of roughness essentially influences the process of interaction of the radio wave with the surface. It is assumed that the surface roughness is described by some random function of the space coordinates. Appropriate equations for the scattered fields and their solutions are discussed. These are illustrated by examples using the first and the second-order approximations discussed in Chapter 5. Algorithms for higher-order approximations are constructed carefully. Strategies for construction of scattering diagrams are considered and some particular results are indicated.

A principally new method for determining the complex dielectric permittivity of layered media arising in remote sensing problems is considered. It is shown that a relative comparison of the voltages and the phases of the signals in the orthogonal channels of receiving devices allows us to determine the desired complex dielectric permittivity for a wide class of layered media. This method permits us to construct a special sphere (referred to as KLL-sphere), each point of which displays a certain type of an earth surface. The distinction of the different types of earth surfaces depends on the complex dielectric permittivities that are involved. The KLL-sphere properties are investigated in detail. In particular, a rule is established for changing the earth surface “images” on the KLL-sphere as the real earth surface physical and chemical characteristics vary.

We have seen that polarization measurements provide information on characteristics of a medium, e.g. surface roughness, morphology, permittivity, etc. Measurements of time of arrival and spectral contents of the scattered-echo signal allow the determination of the position and speed of a reflecting object. The solution to the inverse problem is to find from the measurements of polarization responses these characteristics of a medium or a scatterer. To this purpose, various types of polarimetric radar are used. Scatterometers are used to measure the surface reflectivity as a function of frequency, polarization and illumination direction. They are used to characterize quantitatively surface roughness. Altimeters are used for topographic mapping applications. Synthetic aperture radars (SAR) are used to produce high resolution images. Applications are for earth remote sensing, e.g., monitoring of vegetation, weather-atmospheric conditions, ocean profiles, terrain roughness, etc. The remote sensing data can also be used to improve adaptive radar techniques (e.g. adaptive clutter suppression).

The problem of polarization diagnostics and ecological monitoring of the environment is complex. It has been shown that any remote sensing system contributes to the solution of inverse problems leading to the determination of the physical, geophysical, and mechanical characteristics of surface and atmosphere.

Research on the polarization properties of electromagnetic waves (EMW) began in the USSR during the 1940-50 decade. The first stage of that work was completed in the mid 60’s and was summarized in two monographs [Kanarejkin et al., 1966; Kanarejkin et al., 1968 ]. The monographs generalized results obtained by Soviet scientists until that period. Especially it is worth to mention contributions from Central Aerological Observatory (CAO) and Voejkov’s Main Geophysical Observatory (GGO) in the field of meteorology. Their publications stimulated the interest of Soviet scientists to work on theoretical and practical problems connected with the use of the polarization properties of EMWs for extending the information-seeking capability of various types of radar systems.