Radio Propagation and Remote Sensing of the Environment - Chapter 10 pptx

In this chapter, which may be considered as an introduction to remotesensing, some problems of environmental remote sensing are covered from theposition of radio methods: • Formulation o

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The time and spatial scales of observed characteristics have a very wide range(from part of a second to centuries for time and from units of meters to units of aglobal scale for space) The measurers can be mounted on ground and air platforms,

on rockets, and on space craft Some of these platforms are also shown in Figure 10.1.Environmental remote sensing assumes the practical absence of disturbance inthe studied medium during measurements This is achieved by electromagneticapplication or remote sensing acoustic waves The wide application includes elec-tromagnetic, microwave, and ultrahigh-frequency waves, all of which interact effec-tively with natural media It is supposed that the interaction of electromagnetic waveswith the environment, defined by the electrophysical and geometrical parameters ofthe researched objects, is closely connected with the structure, thermal regime,geophysical characteristics, and other parameters of these objects Radiowave inter-

the physical background of radio methods for remote sensing of natural media Thedevices for research, as well as the development of processing technology forexperimental data, are created on this basis In the following chapters, we considerdevices that are used for remote sensing and some methods for processing experi-mental data In this chapter, which may be considered as an introduction to remotesensing, some problems of environmental remote sensing are covered from theposition of radio methods:

• Formulation of the remote sensing problem

• Radiowave bands applied to remote sensing

• Main principles of processing remote sensing experimental data

TF1710_book.fm Page 275 Thursday, September 30, 2004 1:43 PM

action with natural media was described in the first part of this book (Chapters 1 to

9), which was devoted to radio propagation theory in various media This theory isments of the environment are represented schematically in Figure 10.1

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276 Radio Propagation and Remote Sensing of the Environment

10.1 FORMULATION OF MAIN PROBLEM

The main goal of remote sensing is, as was already mentioned, to obtain variouskinds of data about the environment In this book, we will consider only radiowaves

as the source of such information Radiowaves are generated from both artificial andnatural sources The methods applied to artificially generate waves are often called

active as opposed to passive approaches based on using naturally generated waves

It is necessary to point out that active methods are generally connected with coherentwaves, while incoherent waves are typical for passive methods

The high frequency power gathered by an antenna at the receiver input isamplified (often with a frequency decrease due to heterodyning) As a result, one

or several voltages are formatted at the receiver output Each of them is linearlyrelated to the field strength entered the measuring system input Sometimes thisrelation has a functional character Also, the receiving–amplifying part of a devicecontributes the complementary noise, the power of which is defined by the receivernoise temperature (T n) The sources of interference may have another origin, partic-ularly with regard to extraneous waves at the antenna input As a rule, interference

is supposed to be additive, although this does not hold in all cases

The signal from the receiving/amplifying component enters the processingdevice, where the required measurement parameters (e.g., amplitude, phase, fre-quency, delay time) are separated The processing operation is optionally linear As

FIGURE 10.1 Schematic representation of the environment.

Environment and platforms with measurers

1 Outer space

2 Ionosphere

3 Atmosphere

4 Earth OZONE

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General Problems of Remote Sensing 277

a result, the instrument can be mathematically represented as a set of operators (A1,

A2, …, A i) converting the characteristics of input strengths Ein at the antenna intothe voltages V i at the output Thus, this relation has a statistical character:

The scatterometer is a variant of a radar where the power of the received signal isthe only object of measurement The operator Asct associates the output voltage with a quantity equal to the ratio of the power at the receiving antenna input

to the power at the transmitting antenna output (i and j are the correspondingpolarization):

ij

02

rec

16π2 4 ,

P jrec

A j rec

briefly describe the main points of operators (discussed further in Chapter 11) for

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where is the transmitting antenna directional coefficient at the i-th polarization

On the right side is the integral with respect to depth l and over the solid angle as

a distributed object of our research (e.g., cloud drops, ionospheric electrons, surface irregularities) Therefore, in the considered case, is the cross sectionper volume unit It is supposed that the target is distributed in some volume; thus,

sea-we have an integral with respect to l It is assumed further that the layer thickness

is much less than the distance to the radar, and the integration over Ω is mainlyconcentrated within the major lobe of a pencil-beam antenna This gives us theopportunity to put distance R outside the integral sign If we deal with a surface

t a rg e t ( s e a r i p p l e s , f o r ex a m p l e ) , i t i s n e c e s s a r y t o a s s u m e t h a t

, where is a dimensionless value (cross section perarea unit or backscattering reflectivity) When the backscattering reflectivity is aconstant, Equation (10.3) is quite simplified and, at the matched polarization:

(10.4)

The radio altimeter is also a functionally simplified radar The main interest here isthe arriving time of the signal; the operator Aalt relates output voltage to thetime interval (τ) between the radiated and received radio pulses:

where h is the altimeter altitude above a reflecting surface, and c(h) is the radiowavevelocity depending on altitude

The operator Arm associates the output voltage with a quantity that is proportional

to the brightness temperature of an object:

j

sct in

instruments used for remote sensing (Chapter 11) Information about the primary

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10.2 ELECTROMAGNETIC WAVES USED FOR REMOTE

SENSING OF ENVIRONMENT

Remote sensing of the natural environment is realized within a wide range of

of the range has its own merits and demerits; therefore, the most effective approach

is the application of different areas of the electromagnetic spectrum as appropriate

We consider in this book only part of the radio region: millimetric, centimetric,decimetric, and, particularly, ultrahigh frequency (UHF) The advantage of usingthis spectral part of the region as opposed to the optical or infrared is connectedwith the depth of penetration that can be achieved in a medium which allows us todetect variation in medium parameters related to the depth of the structure Usingvehicle-borne instruments, radiowaves are absorbed weakly in the atmosphere andclouds This creates the conditions for all weather observations of Earth’s surface

In addition, the application of radio instruments, as opposed to optical ones, doesnot require illumination of the area being studied by solar light, which allows us tocarry out investigations regardless of the time of day Also, some spectral intervals

in this region interact effectively with the ionosphere, atmosphere, and atmosphericformations, as well as with elements of ground and sea surfaces This gives us theopportunity to use them to investigate these media

The main drawback of using the radio region is the rather low (in comparison

to the optical and infrared regions) spatial resolution, especially by passive sounding(see Equation (1.120)) Only synthetic aperture radars overcome this difficulty andachieve spatial resolution comparable with optical and infrared devices (see

FIGURE 10.2 Electromagnetic waves, which can be used for remote sensing of the environment.

S C X

Ku

Ka K mm

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Effective application of radiowaves to investigate natural objects depends on therequired spatial resolution and specific peculiarities of radio propagation in theexperimental conditions The problem of various objects interacting with electro-

In the case of sounding from space through the ionosphere, the lower limit ofthe frequency region (fmin) is determined by the maximum of the ionospheric plasmafrequency (f p) connected with the maximum of electron concentration Nmax (see

p

concentration maximum is on the order of 10 MHz The limitations connected withwave propagation in the ionosphere are naturally no longer relevant to the use ofairborne instruments; however, they appear again if, for example, we are dealingThe upper frequency border of the sounding region from space is defined by theatmospheric absorption of electromagnetic waves The main absorbing componentsare water vapor and oxygen In the radio band, oxygen has a series of absorptionlines at a wavelength of 0.5 cm and a separate line at a wavelength of 0.25 cm.Water vapor has absorbtion lines corresponding to wavelengths 1.35 and 0.163 cm,and also a series of absorption lines at waves shorter then 1 mm As absorption atfrequency 3 ·1011 Hz is of the order at 10 db this frequency is assumed to be theupper border frequency region for the radio sensing of Earth from space Hence, theelectromagnetic region of sounding waves from space is determined by the inequality

.The transparency windows of the millimetric wave region lie at the wave bands ofOne has to take into account when planning experiments the help of both aerospace-borne instruments and devices mounted on the ground Meteorology radar, in par-ticular, is a common example It is fitted to take into consideration radiowavescattering and absorption by hydrometeors (clouds, rains, snow)

In underground sounding, an important consideration is the depth of penetrationinto the researched layers, and UHF is the band used in this case A similar band isFrequencies lying at the transparency windows and at regions of selective atmos-pheric absorption, depending on the problem being studied, are applied for the study

of the atmosphere and atmospheric formations The waves of millimetric, tric, and decimetric bands, depending on the requirements for the sounding depthand spatial resolution, are also preferable for the study of biological objects.Remote sensing with radiowave help is based, as indicated earlier, on changes

centime-in the wave characteristic as a result of centime-interaction with the environment The change

in radiowave characteristics is detected by the receiving systems The output signalsthen allow us to obtain the position, form, and geophysical parameters of naturalformations

0 1, < <λ 103cm

magnetic waves is discussed in Chapters 12 to 15

Equation (2.31)) It was pointed out in Chapter 2 that the value of f in the electron

with upper ionosphere observations (see Chapter 3)

also applied for ionospheric research for other reasons (see Chapters 3, 13, and 15).0.2, 0.3, 0.8, and 1.25 cm (Figure 10.3) in the absence of clouds, snow, rain, etc

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Listed below are the main radiowave characteristics determined by remotesensing:

• Amplitude, intensity, and power flow of the electromagnetic field

• Time of propagation

• Direction of the radiowave propagation

• Phase properties of radiowaves

• Frequency and frequency spectrum of receiving signal

• Polarization characteristics of received signal

• Change of the pulse shape

In order to obtain information about the geometry, physico-chemical properties,structure, state, and dynamics of a natural formation, we must formulate an inverseproblem to study the change of these values in space and time and use a priori

information about the investigated object itself and about the characteristics of itsinteraction with the electromagnetic field

10.3 BASIC PRINCIPLES OF EXPERIMENTAL DATA

PROCESSING

The main goal for thematic processing of experimental data obtained through ronmental remote sensing is to define the characteristics of a medium in space andtime As a rule, such characteristics are the values related to its physico-chemicalproperties, structure, etc In order to reach this goal, we must solve a wide range ofproblems that are referred to as inverse ones from the point of view of causal andinvestigatory connections However, it is an inverse problem in only some cases —

envi-FIGURE 10.3 Microwave absorption due to atmospheric gases: 1, normal humidity (7.0 g/m 3 ); 2, humidity (4 g/m 3 ).

frequency (GHz)

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namely, those having a great number of unknown parameters (where the state of anobject is described by some coordinate function); we will discuss those problemsfurther toward the end of this chapter The other inverse problems have been givensuch labels as problems of classification, factorization, parameter estimation, modeldiscrimination.83,84 We have divided these problems into three groups according tothe requirements for remote sensing data processing:

• Classification problems are related to defining the type of object beingobserved and its qualitative characteristics (e.g., space observation of landareas where it is difficult to distinguish forest tracts from open soil or iceplots from open water)

• Parameterization problems are connected with the numerical estimation

of parameters of studied objects (e.g., not a question of what we see during

a flight above the ocean, but rather determining the surface temperature

of the water or the seawave intensity)

• Inverse problems of remote sensing are associated with the creation ofcontinuous profile distributions for various parameters of the researchedobjects (e.g., height profiles of tropospheric temperature, height profiles

of ionospheric electron concentration)

The problems of classification deal with the selection of object groups havingapproximately similar parameters with regard to interaction with electromagneticwaves and, consequently, as one may expect, comparable physico-chemical andstructural characteristics One can subdivide a body of mathematics for classificationbased on different directions of cluster (grouping close results of multidimensionalmeasurements) and structure (grouping of spatio-temporary areas with structures ofclose multidimensional measurements) analyses, as well as multidimensional scaling(limitation by magnitude).84

The classification problem is generally solved by multichannel methods; ever, before turning to them, let us say a few words about some of the possiblesingle-channel methods The simplest one is associated with the establishment ofboundaries for the functional quantities of instrument output voltages (parameters

how-of interaction) within limits, where the investigated objects may be related to aparticular class The simplest kind of such functionals can be maximum and mini-mum values, medians, dispersion, correlation coefficients of experimental, a priori

data, etc Obviously, the boundaries themselves are established on the basis of a priori information (from theory or previous experimental data often obtained by in

especially its having multiple modes can be used for classification (Figure 10.4b).The elements of the textured analyses can be applied in the case of sufficient a priori

information These elements may relate to the specific form of signal from definedelements of the sounding environment and with the contours of two-dimensionalimages

The technique of multidimensional scaling is seldom applied for multichannelmeasurements (thresholds are established from a priori data similarly to the one-channel case) More often, in this case, we resort to different methods of cluster

situ methods) (see Figure 10.4a) The characteristics of the distribution function and

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analyses As a rule, three types of information are taken into consideration: dimensional data of measurements, data about closeness after processing the exper-imental materials, and data about classes obtained as a result of experimental and a priori data processing multidimensional data chosen from the train of data obtainedfrom different measurement channels The closeness criterion here is defined by theparameters of discrepancy or similarity for the separated sets (clusters) of the exper-imental data, such as intercorrelation data in different measurement channels, theintersection of data, or other similar parameters (e.g., the Euclidean distance betweentwo similar objects or some other functional closeness)

multi-For classification purposes, the ensemble of experimental points (comparableaccording to some feature) is intercepted in the measurement space This process isknown as clusterization The set boundaries are defined by the expected credibilityvalue of the obtained results From this point of view, the intuition of the researcherplays no small role here These boundaries may be ascertained in the process of

FIGURE 10.4 (a) Schematic image brightness temperature around Antarctica; (b) histogram

of this temperature I, sea; II, sea ice; III, continental ice.

(b) 120.0 140.0 160.0 180.0 200.0 220.0 240.0 260.0

12 10 8 6 4 2 0 N TF1710_book.fm Page 283 Thursday, September 30, 2004 1:43 PM

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establishing the relations of these sets with the elements of the studied environment.This process, known as cluster identification, is usually realized by teaching and iscarried out for unknown objects by measuring various elements of the knownenvironment and subsequently comparing these measurement results with the out-come of the cluster processing The results of theoretical and experimental researchcan be also used for the identification Many standard computer programs areavailable for cluster analysis of experimental data The example of ice field cluster-ization on the basis of remote sensing at three microwave channels is discussed inLivingstone et al.136

The texture methods, as compared to cluster methods, are associated with anothertype of classification If the cluster techniques classify objects by single elements

of the spatial resolution of an instrument, then the texture methods do so according

to the structure of the fields of the observed objects Continuous fields are usuallyconsidered, but it is also possible to examine noncontinuous fields The body ofmathematics regarding this area is extensive, it is well algorithmized, and numerouscomputer programs are available for texture analyses Figure 10.5 shows the results

of the texture procedure for the selection of forest tracts.137,138

Certainly, other more complicated methods of pattern recognition are available,but the techniques described briefly above have gained the widest application forremote sensing It is necessary to point out once more that the need to address thesemethods is conditioned by the complicated structure of many natural objects andthe practical impossibility of computing exactly the results of their interaction withelectromagnetic waves Therefore, these methods do not assume knowledge of therelations between some parameters of the environment and the characteristics oftheir interaction with electromagnetic fields; however, knowledge of interaction

FIGURE 10.5 (a) Application of two classification stages of forest types with a usage texture parameter; (b) application for classification of a trizonal artificial neural network; (c) image of a fir forest obtained as a result of processing synthetic aperture radar (SAR) data.

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models facilitates both the clusterization and identification of separated clusters and

cluster spatial structures

Before turning to the second group of problems (problems of parameterization),

let us consider briefly the factorial approach to remote sensing problems This

approach is associated with both the classification and the parameterization of natural

formations Parameters such as atmospheric humidity, water content and temperature

of clouds, temperature of the sea surface, soil moisture, vegetation biomass, and

factors The simplest factorial problems (e.g., assessing the influence of a small

number of known causes) are solved, as a rule, by regressive analysis technique.139

In regressive analyses, we graph the regressive curves reflecting the statistical

rela-tion between numerical values of factors (e.g., soil moisture, biomass of vegetarela-tion)

and parameters of the radiowave interaction with the medium being researched, such

as brightness temperature or the scattering cross section An example of a

one-dimensional linear regression of two variables, x and y,is provided in Figure 10.6

The regressive line is plotted by the experimental points y j based on

the condition

dependence on the subsoil water level) give an example of the regressive line use

in remote sensing The regressive lines inclination angles may be used in some cases

for the identification (classification) of factors

FIGURE 10.6 (a) Straight line of regression y on x and straight line of regression x on y; (b)

regression for the same field of a correlation, where and are average values of the

−

many other characteristics (described in Chapters 12 to 16) can be considered as the

Figure 15.12 (brightness temperature with regard to

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To solve more complicated problems related to unknown causes, different

vari-ants of the factorial analyses are applied In this case, the processing of experimental

data obtained by a large number of measurement channels (more than the number

of expected factors) takes place These data have to be associated with the terrain

coordinates and have similar spatial resolution The data are joined in the rectangular

matrix Y for the factorial processing The rows of this matrix determine the

mea-surement channels and columns — the results of meamea-surements along the definite

curve on the terrain This matrix is called a matrix of data Analysis of this matrix

allows us to obtain information about the primary factors influencing the variation

of experimental data corresponding to defined areas of the studied terrain

These factors are classified as common and specific ones by their effect on

experimental data The specific factors influence only one channel; the common

factors that affect all processed channels are also referred to as general The data

are normalized for the factorial analysis, and matrix Y is rearranged into the so-called

standardized matrix Z with the elements:

where is the main signal value in the i-th channel, and is the standard deviation

in the same channel

Factorial analysis is practically reduced to standardized data presentation as a

linear combination of hypothetical variables or factors:

(10.8)

Here, are coefficients (determined during factor analysis) that define the influence

grade of the j-th common factor; are factor scores (the numerical value of

influencing characteristics) at the j-th sample; and is the common effect of the

unique factors of i-th channel This equality expresses the basic model of factor

analysis Thus, it is supposed that the matrix of standardized data is defined only

by common factors, and by applying the matrix form of notation we obtain:

Matrix A is the factor pattern and its elements, , are factorial loadings Matrix

P represents by itself the matrix of numerical quantities (parameters) of the factors

The fundamental theorem of factorial analysis maintains that matrix A is related

to the correlation matrix R, the elements of which are the correlation coefficients

between rows (channels) of standardized matrix Z In the case of uncorrelated

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where is the transposed matrix of the factorial loads, and

(10.10b)

in the case of correlation of factors C is the correlative matrix reflecting the relations

between factors

Matrix C is computed on the basis of a priori information about the physical

connections between factors Matrix A is defined by solving Equation (10.10a) The

method of main components or the centroidal method is often applied for thesepurposes

Different models of factorial analysis are used depending on the accepted a priori assumptions We can separate these models into two groups For the first

group, we assume that the number of common factors is known Then, the factor

loads a ij and the numerical quantities of the factors p ij are determined from Equation(10.10a) In the process, the summarized dispersion added by the negligible factors

in the general data dispersion of each channel, is minimized

For models of the second group, we must first determine the number of commonparameters required to provide affinity of experimental and calculated correlation

matrixes To do so, we use the sequential approach technique, from one to n common

factors The computation is stopped when the differences between elements of theexperimental and calculated matrix reach the same order as the measurement andcomputation errors It is useful to point out that, in this case, computation of thecommon factors is performed by applying Equation (10.10a) where the reduced

matrix Rh is substituted for the correlation matrix R Matrix Rh differs from matrix

R by its diagonal terms, which are called the commonalities in this case The

commonalities give us an estimation of the contribution of the common factors tothe common data dispersion in the processed segment The commonalities estimation

is a separate problem of factorial analysis A rough estimation is sufficient in thecase of a great number of channels; for example, the maximal value of nondiagonalterms of the chosen row can be used for the diagonal term The qualitative side ofThe first group of factorial analysis models is more appropriate for problems ofparameter estimation; the second group, for classification problems The factorialmodels perform linearization of experimental data on the given segment of process-ing and estimate the quantity and the intensity of the factors impacting the outputsignal change Factorial analysis is especially useful for the preliminary simultaneousprocessing of a great number of channels

Parameterization problems belong to the main class of remote sensing problems.

They are connected with quantitative estimation of the parameters of the naturalobject being studied It is supposed in the process of problem solving that the modelfunction relates the instrument displays with the structure and physico-chemical

properties of the objects This relation depends upon the accuracy of the parameters;

a priori model functions may be refined and modified during specific studies Some

these functions were addressed in the first part of this book and will be examined

in following chapters with regard to significant objects of the environment Here,

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we will consider only some general problems of estimating the parameters of afunction

Suppose that model functions F i connect measured electromagnetic wave

param-eters I i of the i-th channel with the studied objects characteristics, x j Then, we canwrite the following system for calculating the parameters of the medium:

including in the consideration the measurement errors, , and the model tion uncertainties, Here, i is the measurement channel number, n is the number

concep-of parameters to be determined, and are summarized errors of the

FIGURE 10.7 (A) Three channels have one general factor; (B) three channels have two

general factors; (C) three channels have one common factor (o) and two general factors (a and b).

(B) (A)

Factor o Factor a Factor a

Factor b Factor b

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