© 2005 by CRC Press 275 10 General Problems of Remote Sensing The second part of this book is dedicated to the background of remote sensing by radio methods. The notion of remote sensing of the environment is usually understood as the determination of characteristics of a medium by devices that are far from the object being studied. The concept of environment includes all objects (both natural and of anthropogenic origin) that form man’s habitat. These are the natural objects (soil, vegetation, atmosphere, etc.) around us on Earth, as well as near Earth and in outer space. These objects also include people themselves and animals. Some ele- The goal of measurements carried out for remote sensing is to define various environmental parameters that can be used to obtain a deeper understanding of natural processes, to improve economic activities through the realization of the preventive actions necessary to protect the environment, and to discover and monitor extraordinary natural and anthropogenic situations. 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 a global 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 in the studied medium during measurements. This is achieved by electromagnetic application 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 waves with the environment, defined by the electrophysical and geometrical parameters of the 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. The devices for research, as well as the development of processing technology for experimental data, are created on this basis. In the following chapters, we consider devices 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 remote sensing, some problems of environmental remote sensing are covered from the position 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 is ments of the environment are represented schematically in Figure 10.1. © 2005 by CRC Press 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 various kinds 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 and natural 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 coherent waves, while incoherent waves are typical for passive methods. The high frequency power gathered by an antenna at the receiver input is amplified (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 linearly related to the field strength entered the measuring system input. Sometimes this relation has a functional character. Also, the receiving–amplifying part of a device contributes the complementary noise, the power of which is defined by the receiver noise 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 processing device, 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 TF1710_book.fm Page 276 Thursday, September 30, 2004 1:43 PM © 2005 by CRC Press General Problems of Remote Sensing 277 a result, the instrument can be mathematically represented as a set of operators ( A 1 , A 2 , …, A i ) converting the characteristics of input strengths E in at the antenna into the voltages V i at the output. Thus, this relation has a statistical character: , (10.1 ) where ∆ V i is the errors generated by the noises of i -th channel of the measuring instrument or the measuring system. We will now provide simple examples of the relations of output voltages with measured quantities of parameters for some instruments. In order to do this, we will the most frequently used instruments of remote sensing. 10.1.1 R ADAR At least two operators, , and , correspond with this instrument. They are associated with output voltages and , corresponding to two characteristics of received radiation. One of them is proportional to the time delay between radiated and received signals and the second one to the received signal power: (10.2) where is the power of the j -th polarization of the wave in the receiving antenna input, is the effective area of the receiving antenna at the j- th polarization, is the transmitter power at the i- th polarization, is the gain of the transmitting antenna at the i -th polarization, σ ij is the radar cross-polarization section of the target backward scattering, R is the distance from the target to the radar, and c ( R ) is the radiowave velocity. Signal processing may be more varied. In particular, the oper- ators of polarization and spectral analyses would be added to the two mentioned above, which are most commonly used. 10.1.2 S CATTEROMETER The scatterometer is a variant of a radar where the power of the received signal is the only object of measurement. The operator A sct 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 corresponding polarization): , (10.3) Vt A E t V ii i () ()= {} + in ∆ A rl 1 A rl 2 V rl 1 V rl 2 Vt A Et t dR cR V rl rl R ij 11 0 2() () ~() () , {} = ∫ in ι 222 rl rl j ii tAEt P PG ij () () ~ {} = in rec rad rad σ iij j A R rec 16 24 π , P j rec A j rec P i rad G i rad V ij sct P j rec P i rad Vt A Et P PR dl ij J i sct sct in rec rad () () ~= {} ⇒ 1 16 22 π ∫∫ () ( ) () ∫ DlAd ijij rad rec ΩΩΩΩσ π , 2 TF1710_book.fm Page 277 Thursday, September 30, 2004 1:43 PM briefly describe the main points of operators (discussed further in Chapter 11) for © 2005 by CRC Press 278 Radio Propagation and Remote Sensing of the Environment 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, sea- surface irregularities). Therefore, in the considered case, is the cross section per volume unit. It is supposed that the target is distributed in some volume; thus, 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 mainly concentrated within the major lobe of a pencil-beam antenna. This gives us the opportunity to put distance R outside the integral sign. If we deal with a surface target (sea ripples, for example), it is necessary to assume that , where is a dimensionless value (cross section per area unit or backscattering reflectivity). When the backscattering reflectivity is a constant, Equation (10.3) is quite simplified and, at the matched polarization: (10.4) 10.1.3 R ADIO ALTIMETER The radio altimeter is also a functionally simplified radar. The main interest here is the arriving time of the signal; the operator A alt relates output voltage to the time interval ( τ ) between the radiated and received radio pulses: , (10.5) where h is the altimeter altitude above a reflecting surface, and c ( h ) is the radiowave velocity depending on altitude. 10.1.4 M ICROWAVE RADIOMETER The operator A rm associates the output voltage with a quantity that is proportional to the brightness temperature of an object: . (10.6) The operators mentioned above will be refined later when we describe specific techniques for calibration will also be given in Chapter 11. This calibration allows us to estimate the coefficients of proportionality and permanent biases that are negligible in Equations (10.2) to (10.6). D i rad σ ij l(, )Ω σσδ ij llR ij (, ) ( ) ( )ΩΩ= − 0 σ ij 0 ()Ω AEt P P A R j j j sct in rec rad rec () ~ () . {} ⇒ σ π 0 2 0 4 V alt Vt A Et t dh ch h alt alt in () () () () = {} ⇒ = ∫ τ 2 0 Vt A Et P T ii j rm in rec rm () () ~= {} ⇒ TF1710_book.fm Page 278 Thursday, September 30, 2004 1:43 PM instruments used for remote sensing (Chapter 11). Information about the primary © 2005 by CRC Press General Problems of Remote Sensing 279 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 using this spectral part of the region as opposed to the optical or infrared is connected with the depth of penetration that can be achieved in a medium which allows us to detect variation in medium parameters related to the depth of the structure. Using vehicle-borne instruments, radiowaves are absorbed weakly in the atmosphere and clouds. This creates the conditions for all weather observations of Earth’s surface. In addition, the application of radio instruments, as opposed to optical ones, does not require illumination of the area being studied by solar light, which allows us to carry out investigations regardless of the time of day. Also, some spectral intervals in this region interact effectively with the ionosphere, atmosphere, and atmospheric formations, as well as with elements of ground and sea surfaces. This gives us the opportunity 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 and achieve spatial resolution comparable with optical and infrared devices (see FIGURE 10.2 Electromagnetic waves, which can be used for remote sensing of the environment. UV OPT 0.28−0.38 µ 0.38−0.78 µ 0.78−3 µ 3−8 µ 8−1000 µ 3·10 −7 3·10 −6 3·10 −5 3·10 −4 3·10 −3 3·10 −2 3·10 −1 10 8 10 9 10 10 10 11 10 12 10 13 10 14 10 15 3 λm λ cm fHz 0.1 0.1 0.3 3 30 100 100 10 1 fΓHz PLSCXK u K a Kmm IR TF1710_book.fm Page 279 Thursday, September 30, 2004 1:43 PM Chapter 11). electromagnetic waves — from ultraviolet to radio (see Figure 10.2). Each section © 2005 by CRC Press 280 Radio Propagation and Remote Sensing of the Environment Effective application of radiowaves to investigate natural objects depends on the required spatial resolution and specific peculiarities of radio propagation in the experimental conditions. The problem of various objects interacting with electro- In the case of sounding from space through the ionosphere, the lower limit of the frequency region ( f min ) is determined by the maximum of the ionospheric plasma frequency ( f p ) connected with the maximum of electron concentration N max (see p concentration maximum is on the order of 10 MHz. The limitations connected with wave propagation in the ionosphere are naturally no longer relevant to the use of airborne instruments; however, they appear again if, for example, we are dealing The upper frequency border of the sounding region from space is defined by the atmospheric absorption of electromagnetic waves. The main absorbing components are water vapor and oxygen. In the radio band, oxygen has a series of absorption lines 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 at frequency 3 ·10 11 Hz is of the order at 10 db this frequency is assumed to be the upper border frequency region for the radio sensing of Earth from space. Hence, the electromagnetic region of sounding waves from space is determined by the inequality . The transparency windows of the millimetric wave region lie at the wave bands of One 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 radiowave scattering and absorption by hydrometeors (clouds, rains, snow). In underground sounding, an important consideration is the depth of penetration into the researched layers, and UHF is the band used in this case. A similar band is Frequencies 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, centime- tric, and decimetric bands, depending on the requirements for the sounding depth and spatial resolution, are also preferable for the study of biological objects. Remote sensing with radiowave help is based, as indicated earlier, on changes in the wave characteristic as a result of interaction with the environment. The change in radiowave characteristics is detected by the receiving systems. The output signals then allow us to obtain the position, form, and geophysical parameters of natural formations. 01 10 3 , <<λ cm TF1710_book.fm Page 280 Thursday, September 30, 2004 1:43 PM 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. © 2005 by CRC Press General Problems of Remote Sensing 281 Listed below are the main radiowave characteristics determined by remote sensing: • 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 inverse problem 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 its interaction with the electromagnetic field. 10.3 BASIC PRINCIPLES OF EXPERIMENTAL DATA PROCESSING The main goal for thematic processing of experimental data obtained through envi- ronmental remote sensing is to define the characteristics of a medium in space and time. As a rule, such characteristics are the values related to its physico-chemical properties, structure, etc. In order to reach this goal, we must solve a wide range of problems that are referred to as inverse ones from the point of view of causal and investigatory connections. However, it is an inverse problem in only some cases — FIGURE 10.3 Microwave absorption due to atmospheric gases: 1, normal humidity (7.0 g/m 3 ); 2, humidity (4 g/m 3 ). 0 50 100 150 200 250 300 0.01 0.1 1 10 100 1000 1 2 frequency (GHz) TF1710_book.fm Page 281 Thursday, September 30, 2004 1:43 PM © 2005 by CRC Press 282 Radio Propagation and Remote Sensing of the Environment namely, those having a great number of unknown parameters (where the state of an object is described by some coordinate function); we will discuss those problems further toward the end of this chapter. The other inverse problems have been given such labels as problems of classification, factorization, parameter estimation, model discrimination. 83,84 We have divided these problems into three groups according to the requirements for remote sensing data processing: • Classification problems are related to defining the type of object being observed and its qualitative characteristics (e.g., space observation of land areas where it is difficult to distinguish forest tracts from open soil or ice plots 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 of continuous profile distributions for various parameters of the researched objects (e.g., height profiles of tropospheric temperature, height profiles of ionospheric electron concentration). The problems of classification deal with the selection of object groups having approximately similar parameters with regard to interaction with electromagnetic waves and, consequently, as one may expect, comparable physico-chemical and structural characteristics. One can subdivide a body of mathematics for classification based on different directions of cluster (grouping close results of multidimensional measurements) and structure (grouping of spatio-temporary areas with structures of close multidimensional measurements) analyses, as well as multidimensional scaling (limitation by magnitude). 84 The classification problem is generally solved by multichannel methods; how- ever, before turning to them, let us say a few words about some of the possible single-channel methods. The simplest one is associated with the establishment of boundaries for the functional quantities of instrument output voltages (parameters of interaction) within limits, where the investigated objects may be related to a particular 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 defined elements of the sounding environment and with the contours of two-dimensional images. The technique of multidimensional scaling is seldom applied for multichannel measurements (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 TF1710_book.fm Page 282 Thursday, September 30, 2004 1:43 PM situ methods) (see Figure 10.4a). The characteristics of the distribution function and © 2005 by CRC Press General Problems of Remote Sensing 283 analyses. As a rule, three types of information are taken into consideration: multi- 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 obtained from different measurement channels. The closeness criterion here is defined by the parameters of discrepancy or similarity for the separated sets (clusters) of the exper- imental data, such as intercorrelation data in different measurement channels, the intersection of data, or other similar parameters (e.g., the Euclidean distance between two similar objects or some other functional closeness). For classification purposes, the ensemble of experimental points (comparable according to some feature) is intercepted in the measurement space. This process is known as clusterization . The set boundaries are defined by the expected credibility value of the obtained results. From this point of view, the intuition of the researcher plays 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. 300 200 100 13 57 9 1311 15 17 19 21 23 25 27 29 3331 35 Coordinate point number I I I III III II II II T b T b (a) (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 © 2005 by CRC Press 284 Radio Propagation and Remote Sensing of the Environment 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 is carried out for unknown objects by measuring various elements of the known environment and subsequently comparing these measurement results with the out- come of the cluster processing. The results of theoretical and experimental research can be also used for the identification. Many standard computer programs are available 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 in Livingstone et al. 136 The texture methods, as compared to cluster methods, are associated with another type 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 usually considered, but it is also possible to examine noncontinuous fields. The body of mathematics regarding this area is extensive, it is well algorithmized, and numerous computer 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 for remote sensing. It is necessary to point out once more that the need to address these methods is conditioned by the complicated structure of many natural objects and the practical impossibility of computing exactly the results of their interaction with electromagnetic waves. Therefore, these methods do not assume knowledge of the relations between some parameters of the environment and the characteristics of their 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. (a) (c) (b) 6 3 2 1 TF1710_book.fm Page 284 Thursday, September 30, 2004 1:43 PM [...]... to be constant), and research of the remainders on the normality Along with analysis of the remainders, stepped regression is applied based on a sequence of including and excluding some variables and determining their influence and significance Other, more complicated methods are also available.83 10. 3.1 INVERSE PROBLEMS OF REMOTE SENSING The procedure of thematic processing of remote sensing data is... = TF1 710_ book.fm Page 290 Thursday, September 30, 2004 1:43 PM 290 Radio Propagation and Remote Sensing of the Environment or I = AX The solution will have the form: X = A −1 I (10. 13) where the matrix A −1 is the inverse one The inverse matrix appears when the matrix determinant differs from zero; however, if the matrix elements are given approximately, then the question about the determinant of matrix... influence grade of the j-th common factor; p1 j p rj are factor scores (the numerical value of influencing characteristics) at the j-th sample; and ζ i 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... General Problems of Remote Sensing 295 The following procedure is applied for selecting the best model All models, after assessment of the physical foundation (the third criterion), can be arranged by complexity (first and second criteria), then the parameters of these models can be estimated After that, the correctness of the models is analyzed The correctness means that the variance of the experimental... the case of uncorrelated factors, R = AA ' , © 2005 by CRC Press (10. 10a) TF1 710_ book.fm Page 287 Thursday, September 30, 2004 1:43 PM General Problems of Remote Sensing 287 where A′ is the transposed matrix of the factorial loads, and R = ACA ' (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... 2 j j Fj , (10. 20) σ 2 is the errors dispersion in j-th channel, and Fi = a i1 , a i 2 , , a in Thus, the j dispersion matrix equals M–1 This estimation minimizes the sum of the squares of the weighted deviations on the right and left sides of the equations If the measurements in channels are uniformly precise and their dispersion is unknown, we can substitute unity for the dispersion The estimation,... number of equations On the other hand, we can neglect the measurement errors by assuming them to be equal to zero In this case, the number of equations is usually more than the number of unknown parameters and the system becomes contradictory The solution of Equation (10. 11) is divided into two steps:140 (1) definition of unknown parameters using the minimum of data, and (2) definition of unknown parameters... given segment of processing and estimate the quantity and the intensity of the factors impacting the output signal change Factorial analysis is especially useful for the preliminary simultaneous processing 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 natural object being... September 30, 2004 1:43 PM 300 Radio Propagation and Remote Sensing of the Environment P, mbar h, km 400 7 500 600 700 6 5 4 3 800 2 900 1 100 0 1 2 3 4 5 6 7 8 9 q, g/Kg FIGURE 10. 8 Matching of the recovered profiles of dampness at simulation of radiometric measurements in a 1.35-cm wave band (dotted line) with profiles obtained by measurement by probes (full curve) and by interpolation of ground values (triangles)... 286 Radio Propagation and Remote Sensing of the Environment To solve more complicated problems related to unknown causes, different variants 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 . remote sensing of the environment. UV OPT 0.28−0.38 µ 0.38−0.78 µ 0.78−3 µ 3−8 µ 8 100 0 µ 3 10 −7 3 10 −6 3 10 −5 3 10 −4 3 10 −3 3 10 −2 3 10 −1 10 8 10 9 10 10 10 11 10 12 10 13 10 14 10 15 3 λm λ. Press 275 10 General Problems of Remote Sensing The second part of this book is dedicated to the background of remote sensing by radio methods. The notion of remote sensing of the environment. to remote sensing, some problems of environmental remote sensing are covered from the position of radio methods: •Formulation of the remote sensing problem • Radiowave bands applied to remote sensing •