The objective of this research is to develop theoretical models that are useful and practical in the remote sensing of the Earth environment including the Earth terrain, the lower and the upper atmospheres. Various models applicable to the microwave remote sensing of vegetation, snow-ice, and atmospheric precipitation have been developed. Such studies shall be extended to the higher frequency range to unify the optical band and the microwave theoretical foundations. The study, which had an emphasis on vegetation canopy to include all terrain media, and the whole Earth environment will be extended. A data base will be developed to generate scene radiation characteristics which will benefit the studies of global inhabitability, meteorological applications, and crop yield

Kong, J. A.

English

NASA Technical Reports Server

REMOTE SENSING OF EARTH TERRAIN 
Jin Au Kong 
Massachusette Institute of Technology 
1. Objective 
The objective of this research is to develop theoretical models that are useful and 
practical in the remdte sensing of the earth environmect including the earth terrain, the 
lower and the upper atmospheres. We have been very successful in developing various mod- 
els applicable to the microwave remote sensing of vegetation, snow-ice, m d  atmospheric 
precipitation. We shall extend such studies to the higher frequency range to unify the 
optical band and the microwave theoretical foundations. We shall also extend our study, 
which had an emphasis on vegetation canopy to include all terrain media, <and the whole 
earth environment. A data base will be developed to generate scene radiation characteris- 
tics which will benefit the studies of global inhabitability, meteorological applications, and 
crop yield. 
2. Technical A~proach 
The radiative transfer theory has been fully developed to treat the volume and rough 
surface scattering effects. The combined random rough surface and volunle scattering ef- 
fects have been studied by employing a Gaussian random surface and applying the slnall 
perturbation methods which are modified with the use of cumulant techniques. The rough 
surface effects are incorporated into the radiative transfer equations by modifying the 
boundary conditions for the intensities. The T-matrix method, which utilizes vector spher- 
ical wave functions for the expansion of incident, scattered, and surface fields is used to 
derive the extinction niatrix and the phase matrix for the radiative transfer equations. 
Densely distributed spherical dielectric scatterers is studied with the qlxmtum mechanical 
potential approach. The quasi-crystalline approximation is applied to truncate the hier- 
archy of multiple scattering equations and the Percus-Yevick result is used to represent 
the pair distribution function. The modified radiative transfer theory is studied with the 
Feynman diagrammatic representation. Atmospheric precipitation is also studied with the 
vector radiative transfer equations by making use of the Mie scattering phase functions and 
incorporating the rain-drop size distributions. To study scattering by anisotropic medium 
modelling sea ice arid vegetation field with row structures, the dyadic Green's function is 
first derived and used in conjunction with the first-order Born approxilnation to calculate 
the backscattering coefficients. 
https://ntrs.nasa.gov/search.jsp?R=19860004339 2020-03-20T16:37:20+00:00Z
3. Research Results 
In active n~icrowave remote sensing, a two-layer anisotropic random mcdium model 
has becn developed to investigate the anisotropic effect of sea ice in which, due to the 
flow of sea water, the brine ilclusions are tilted 'and to study the aziniuthally anisotropic 
behavior of vegetation canopy which is attributed to the orientations of the vegetation 
stalks. In this scheme, the dyadic Green's function for a two-layer anisotropic medium is 
developed 'md used in conjunction with the first order Born approximation to calculate the 
backscattering coefficients. I t  is shown that strong cross-polarization occurs in the single 
scattering process and is indispensablc in the interpretation of radar measurements of sea 
ice at  different frequencies, polarizations, and viewing angles. The effects of anisotropy on 
angle responses of backscattering coefficients are also illustrated. For passive microwave 
remote sensing of a two-layer anisotropic random niedi:lm, the principle of reciprocity is 
invoked to compute the brightness temperatures. The bistatic scattering coelficients are 
first calculated with Born approxilnation and then integrated over the upper hemisphere 
to be subtracted from unity, in order to obtain the ernissivity for the random medium 
layer. The theoretical results are illustrated by plotting the emissivities as functions of 
viewing angles and polarizations. They are used to interpret remote sensing data obtained 
from vegetation canopy where the aniostropic random mediunl model applies. Field mea- 
surements with corn stalks arranged in various configurations with preferred azimuthal 
directions arc successfully interpreted with this model. 
The problem of microwave scattering from periodic surfaces is solved by using a rig- 
orous niodal technique which conserves energy, obeys reciprocity, and takes into account 
the multiple scattering and shadowing effects. The theorctical results have been applied 
to the calculation of the radar backscattering cross sections in active remote sensing and 
the brightness temperatures in passive rernote sensing, and used to match field data from 
soil moisture measurements. The angular behavior of the brightness temperatures has 
becn cxplaincd with the threshold phenomenon 'oy considering the appearance and dis- 
appearance of the various Floquet modes. The Kirchhoff approximation is used to study 
the scattering of electuronlagnetic waves from randomly perturbed quasi-periodic plowed 
fields. The narrow-band Gaussian random variation around the spatial frequency of the 
sinusoidal variation is used to introduce the quasiperiodicity. The physical optics integral 
is evaluated to obtain closed form solutions for coherent and incoherent bistatic scatter- 
ing cocficiex~ts. In the geometrical optics limit, it is shown that the bistatic scattering 
coefficients are proportional to  the probdbility of the occurrence of the slopes which will 
specularly reflect the incident wave into the observation direction. The theoretical results 
are illustrated for the various cases by plotting backscattering cross sections as a func- 
tion of the incident angle. It is shown that there is a large difference between the cases 
where the incident wave vector is parallel or perpendicular to the row direction. When 
the incident wave vector is perpendicular to the row direction, the nlaximunr value of the 
backscattering cross section does nut necessarily occur at  normal incidence. The scattering 
coefficients can be interpreted as a convolution of the scattering patterns for the sinusoidal 
and for the random rough surfaces. For the backscattering cross sectiolis we observe the 
occurrence of peaks the re'iative magaitudes and locations of which are explained in terms 
of the scattering patterns for sinusoidal surfaces. The combined random rough sc~face 
and volun~e scattering eifects have been studied by en~ploying a Gaussian random surface 
and applying the small perturbation methods which are modified with the use of cumulant 
techniques. The rough surface effects are incorporated into the radiative transfer equations 
by modifying the boundary conditions for the intensities. The radiative transler equations 
are then solved nunlerically using the Gaussian quadrature method and the results are 
illustrated and compared with experimental data. 
The radiative transfer theory is applied to calculate the scattering by a layer of ran- 
domly positioned and oriented nonspherical particles. The scattering amplitude functions 
of each individual particle are calculated with M'at,erman's T-matrix method, which uti- 
lizes vector spherical wave functions for the expansion of Incident, scattered, and surface 
fields. The orientation of the particles is described by a probability density fu~lction of the 
Eulerian angles of rotation and a rotation matrix is used to relate the T-matrix of the prin- 
cipal frame to that of the natural frame of the particle. The extinction and phase matrices 
for the radiative transfer equations are expressed in. terr~ls of the T-matrix elements. The 
extinction matrix for nonspherical particles is generally nondiagonal. I t  is shown that; there 
are only two attenuation rates in a specified direction of propagation. The scattering of a 
plane wave obliquely incident on a half space of densely distributed spherical dielectric scat- 
terers is studied with the quantur~l ~nechanical potential approach. Tlre quasi-crystalline 
approximation is applied to truncate the hierarchy of multiple scattering equations and 
Pertus-Yevick result is used to represent the pair distribution function. While results a t  
high frequencies are calculated numerically, closed form solutions are obtained in the low 
frequency limit for the effective propagation constants, the coherent reflected wave and the 
bistatic scattering coefficients. 
In the strong fluctuation theory for 2 bounded layer of random discrete scatterers, the 
second liloments of the fields in the second order distorted Born a,pproximation me obtained 
for co-polarized fields. The backscattering cross sections per unit area are czlculated 
by including the mutual coherence of the fields due to the coincident ray paths, and 
those due to the opposite ray paths, corresponding to  the ladder and cross terms in the 
F e y n m a ~ ~  diagrammatic representation. It  is proved that the contributio~~s fro111 laclder 
and cross t e r m  for the co-polarized backscattering cross sections are the same, while the 
contributions for the cross-polarized backscattering cross sections are of the same order. 
The bistatic scattering coefficients in the second order approximation for both the ladder 
and cross terms are also obtained. The contributions from the cross terms explain the 
enhancelnent in the backscattering direction. 
Both passive and active remote sensing of atmospheric precipitation are studied with 
the vector radiative transfer equations by making use of the Mie scattering phase fucctions 
and incorporating the rain drop size distributions. For passive remote sensing we enlploy 
the Gaussiali quadrature method to solve for the brightness temperatures, 'and for active 
renlote sensing an iterative approach carryied out to second order in albedo is used to 
calculate the bistatic scattering coefficients and the backscattering cross sections per unit 
volume. 
4. Significance of Results 
The anisotropic medium model that has been developed is now able to account for 
the like as well as cross polarization measurements of the backscattering cross sections in 
active remote sensing of sea ice. The same model applies to the interpretation of data  
from the passive remote sensing of vegetaiion field. Extending this two-layer medium 
model to multilayered configuration will facilitate the interpretation for more complicated 
scene radiation characteristics. 
The strong fluctuation theory has been successfully developed to account for the 
volume scattering effects, not only for earth terrain media such as vegetation and snow-ice 
fields, but also for the remote sensing of atmospheric precipitation. The periodic rough 
surface theory provides a rigorous approach that satisfies both the principle of reciprocity 
and the principle of energy conservation. 
5. Next Maior Steps 
There are three major steps: 1) To extend our study to include the effects of the upper 
atmosphere such as the troposphere, the ionosphere, and the magnetosi>here. Our initial 
snccess with the usage of the random medium model applied to atmospheric precipitation 
serves as a solid starting point. 2) To extend our study to other earth terrain medium 
co~figurations such as canopy-covered soil moisture investigation, snow-covered fields, and 
layered-medium model including both volume scattering and rough surface scattering ef- 
fects. 3) To extend our study to unify the theoretical foundation for the microwave and 
the optical spectra. The starting point is the application of the radiative transfer theory, 
which has been developed in both frequency ranges rather independently. 


Remote Sensing of Earth Terrain

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