Radio Propagation and Remote Sensing of the Environment - Chapter 15 (end) pot

We will use the following classification of theland covers when we discuss radio methods for remote sensing: • Bare terrain and geological structures • Hydrology structures • Vegetation

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of statistically homogeneous areas, such as forest tracts, steppes and deserts, andsome tundra regions The situation can be improved by carrying out joint processing

of data provided by instruments with different degrees of resolution Some studycould verify the effectiveness of several processing procedures, but this technologyhas still not found wide application We will use the following classification of theland covers when we discuss radio methods for remote sensing:

• Bare terrain and geological structures

• Hydrology structures

• Vegetation canopy

• Internal basins

• Snow cover and ice

15.2 ACTIVE RADIO METHODS

Active radio methods are synonymous with radar technology, which is widelyemployed now due to the development of spaceborne radar techniques SAR systemshave become instrumental for systematic monitoring of the surface of Earth Radarimages reflect many peculiarities of the researched area, such as landscape elements,hydrology network, vegetable canopy, and artificial construction Gathering thiscomplicated information allows us to assemble special thematic maps: topographic,geologic, hydrologic, forestry, etc One of the main requirements for radar images

is an accurate tie-in to the terrain which is based partly on navigation data and partlyTF1710_book.fm Page 405 Thursday, September 30, 2004 1:43 PM

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406 Radio Propagation and Remote Sensing of the Environment

on position data of the fixed points Certainly, knowledge of the appropriate antennaorientation is included on a list of information required for correct radar datainterpretation

In fact, the radar image is a map of the backscattering coefficient, which dependsnot only on surface scattering of the radiowaves by soil but also on volumetricscattering by elements of a vegetable canopy To begin, we will address scattering

by bare soil and primarily consider the inclined incidence of radiowaves typical forSAR and scatterometer systems In this case, the separation of large- and small-scale roughness is not as clear as for the ocean; therefore, it is difficult to distinguishbetween specular and resonant scattering This is one reason why empirical or semi-empirical models have found wide application for the interpretation of experimentaldata Theoretical models and experimental data show the distinct dependence of soilscattering intensity on surface roughness parameters and on soil permittivity, which,

in turn, is strongly dependent on soil moisture The simplest model of soil tivity can be described by the so-called refractive formula:43,116

Here, εw is the water permittivity, described by Equations (14.1) and (14.2); εg isthe dry ground dielectric constant; and ξ is the water volumetric content (i.e., thevolume part occupied by water in mixture) Numerically, this value coincides withvolumetric soil moisture mv (g/cm3) The absence of a numerical difference indicatesthat we should not separate these terms We must be careful when comparing ourmoisture definition to moisture determined by the gravimetric method with ovendrying The full water content determined by the gravimetric method includes bothfree water and bound moisture, while electromagnetic waves react only to freemoisture The quantity of bound moisture depends on soil type; it is about 2 to 3%

in sandy soils and can reach values of 30 to 40% of dry soil mass in clay and loessgrounds The soil permittivity depends weakly on the soil moisture at small concen-tration Equation (15.1) has no theoretical background and is a suitable approxima-tion only in the microwave region;116 other approximations can be found in Ulaby

et al.90 The permittivity of dry soil depends only on its density in the first approach.This dependence can be expressed in the form:118

where ρg is the ground density (g/cm3)

For our discussion here, we will use the following values for the various ical calculations: ρg = 2 g/cm3; t = 20°C; S = 2‰; εg = 4, εw≅ 80, and σ≅ 2.4 · 109

numer-CGSE For many practical applications, however, ρ = 1.5 g/cm3 is more realistic.These values indicate that the behavior of various types of ground is our primarypractical independence of soil permittivity at the C- and L-bands is apparent This

is understandable, as the water permittivity real part is practically constant at these

ε ξ ε= w+ −( )1 ξ εg

εg = +1 0 5 ρg TF1710_book.fm Page 406 Thursday, September 30, 2004 1:43 PM

focus The soil permittivity dependence on moisture is plotted in Figure 15.1 The

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Researching Land Cover by Radio Methods 407

frequencies and the imaginary part is small The frequency dependence occurs closer

to millimeter-wavelength bands which is reflected by the 37.5-GHz curve Moredetailed analysis can be found, for example, in Ulaby et al.90 and Shutko.116

The predominance of specular or diffuse scattering mechanisms is primarilydetermined by the radio-wave frequency The analysis of experimental data provided

by Shi et al.120 gives the values cm for roughness amplitude and

l = 20 to 30 cm for correlation length The data of Dierking121 provided values of 1

to 7 cm for field roughness amplitude and 2 to 37 cm for correlation length.Profilometer measurements allow us to conclude that the exponential autocorrelationfunction is the best approximation of experimental data Shi et

al.120 tested the autocorrelation function in the form , wherethe most probable value of index ν is again unity More exactly, about 76% of themeasured profiles of roughness could be described by the correlation function with

ν 1.4 The index difference produces a difference in the spatial spectrum which isproportional to the function:

on the index ν value; therefore, it would be enough to be confined by the case ν = 1.This means that we are dealing with fractal surfaces of Brownian type, and thespectrum given by Equation (14.40) is suitable for our purposes

The data reported by Dierking121 suggest that many natural surfaces havestationary random processes with a power-law spatial spectrum of the form

, where 3 α 3.7, which indicates the fractal character of surfaces

FIGURE 15.1 Average values of soil permittivity dependence on moisture: (1) 1.3 GHz; (2) 5.3 GHz; (3) 37.5 GHz.

0 6 12 18 24

TF1710_book.fm Page 407 Thursday, September 30, 2004 1:43 PM

The curves of Figure 15.2 demonstrate the weak dependence of the spatial spectrum

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bounded by natural media The available analytical approximation of these spectrawith conservation of roughness magnitude and correlation length can be written as:

Brownian type of spectrum is from this family

Now, we are ready to analyze the processes of scattering by the terrain First,

we will consider the P-band waves scattered by bare soil The parameters specifiedabove allow us to employ the perturbation method approximation; that is, we willangular dependence of backscattering coefficients for horizontally and verticallypolarized waves of the P-band It was assumed for our computations that ξ = 0.2,

of soil surfaces For this reason, we cannot apply any modern asymptotic approaches

of scattering theory One of the best alternatives is to use semi-empirical modelsthat approximate the experimental data One of these models is the Oh, Sarabandi,and Ulaby (OSU) model,122 which provides an expression for the cross-polarizedratio :

FIGURE 15.2 Graphics demonstrate the weak dependence of spatial spectrum on the index value: ——, v = 1; ···, v = 1.2; – – – –, v = 1.4.

wave parameter 0

0.2 0.4 0.6 0.8 H

base all of our computations on Equations (6.48) and (6.49) Figure 15.3 shows thewhich is similar to the spectra used to describe turbulence (see Chapter 7) The

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(15.5)

We must use a two-term subscript now in order to emphasize the fact we are dealingwith matched and cross-polarized components of the scattered signal An equationthat applies to the copolarized ratio p = is:

where the incident angle θi is expressed in radians The backscattering coefficient

of vertical polarization is approximated by the formula:

(15.7)

incident angle at the L- and C-bands The volumetric moisture value is chosen to

be equal to 0.2 The “m” added to the subscript reflects the fact that this model wasdeveloped at the University of Michigan We can see that the backscattering coef-ficients of horizontal and vertical polarizations differ slightly at the C-band Thisweak difference takes place at the chosen parameter of roughness Obviously, this difference will be bigger for a smoother surface This smalldifference is emphasized by the Kirchhoff (or geometrical optics) approximation

FIGURE 15.3 Angular dependence of backscattering: (1) σvv; (2) σhh.

incident angle, degrees

σhh σ

0 vv 0

θ

hh vv

i 0

The plots of Figure 15.4 show the dependence of backscattering coefficients on the

(see Chapter 6), which reflects its qualitative correctness Figure 15.5 shows the

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dependence of values of the cross-polarization coefficient on the incident angles forthe L- and C-bands The fact that backscattering coefficients are determined relative

to only one parameter is an advantage of the OSU model Recall that, in geometricaloptics approximations, the backscattering coefficient depends on only one parameter:the slope

Large elements of the terrain caused by changes in slope and variations in theroughness parameters are distinguished on radar images by varying brightness Radarimages provide a good representation of the peculiarities of a landscape This is one

of the reasons why radar mapping has found application in geology The specificmethod of observation at normal viewing angles from the Earth’s surface allows us

to detect faintly marked relief elements of slightly rugged terrain such as hills,valleys, etc Radar maps often have more contrast compared to aerial photographsdue to their employment of polarization methods It is important to note that the use

of radar mapping overcomes the screening effect of vegetation to reveal variousfeatures of geological structures, including lineaments and circular structures

FIGURE 15.4 Dependence m of backscattering coefficients at the L-band (——) and C-band (– – –) on the incident angle: (1) and (3) σvv; (2) and (4) σhh.

FIGURE 15.5 Cross-polarization coefficient dependence on the incident angle for the (1) band and (2) C-band.

4

1 2

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Interferometry technology is very effective

for mapping landscape details A brief

explana-tion of this technology is as follows Imagine that

similar radar scenes are obtained by subsequent

flights over a neighboring orbit separated by

dis-tance d, as shown in Figure 15.6 Assume that the

satellite orbits lie at planes parallel to the x-axis

and that base d is oriented along the y-axis Then,

let us also assume summation of the signals

reflected by any pixel of the surface which is

possible due to the high coherency of the radar

system itself The intensity of the summarized

signals will depend on their phase difference,

which occurs because of the different radar positions Each reflected signal is like, but, in the case of small distances between the two satellite passes, a high level

noise-of coherency between the signals reflected by the same pixel is maintained, and thephase difference has a definite value More correctly, the discussed phase difference

is stochastic but its mean value is not zero.9 The latter depends on the pixel positionand the base size If the investigated surface is flat, on average, then the lines ofconstant phase difference will be straight along the flight direction The values ofthe x-coordinate are assumed to be much less than platform height H and horizontaldistance y from the flight trace and observation point (point O in Figure 15.6) Whenobserving some hill elements above a flat terrain, the equiphase will differ from astraight line and its curvature will depend on the hill topography It is possible toshow (neglecting small values) that equiphase lines are described by the equation:

Here, h is the hill height, and f(x,y) is the function describing the hill shape.The case h = 0 corresponds to a flat surface Having subtracted the first termfrom the experimental data, we can obtain the equiphase lines related directly to thehill topography An example of equiphase counters is given by Figure 15.6 Thetwo-pass positions of the radar antenna can be compared to the two-antenna inter-ferometer system, and we can talk about a synthetic interferometer The real onewas realized during the shuttle radar topography mission (SRTM) when the secondantennae of the C- and X-band radars were situated at the end of a 60-m boom Thismission provided interferograms within Earth latitudes ±60°

The processing of interferogram data permits retrieval of a terrain topographywith high accuracy This accuracy is due to the high interferometry sensitivity,particularly when the interferometer lobe angular width is much greater than theangular size of the investigated pixel; that is, , where θis the incidentangle This inequality can be rearranged into , where D is the synthesislength of the SAR

z d

y

Hill o x

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Now, we will turn our attention to the problem of surface parameter measurement

by means of radar systems As backscattering coefficients depend only on surfaceroughness and on the permittivity of the sounded medium, our discussion will focus

on measurement of the roughness parameters and the permittivity value Definingsurface roughness parameters is a very important problem for many reasons Forexample, pedology is an area where information about the roughness properties isimportant for our understanding of many processes, such as flooding, infiltration,erosion, etc Surface roughness is connected with the properties of some materialsand this information is of value in geology

The bare soil backscattering coefficient is determined by both roughness andmoisture One problem with the radar data processing procedure is separation ofthese effects, but this can be accomplished by polarization measurements One way

to select the roughness effect is to define the correlation coefficient between thesignals of orthogonal polarizations.120 If U p is the complex amplitude of the receivedsignal of matched p polarization, then the unknown correlation coefficient is definedas:

where U q is the signal of the other orthogonal matched polarization Shi et al.120

used ρpq for their calculations, although the value 1/2Reρpq is more logical for suchapplications Their reason for using ρpq was that the magnitude of the copolarizedcorrelation coefficient is weakly affected by calibration errors Analysis of experi-mental data and theory120 suggest that the coefficient of correlation between rightand left circularly polarized signals depends on the roughness amplitude and weaklyreacts to changes in soil moisture This assumption allows us to consider the corre-lation coefficient mentioned as being representative of bare soil roughness

Another parameter frequently under discussion is soil moisture It is a veryimportant value that plays an essential role in the various phenomena of hydrology,meteorology, climatology, agronomy, etc Such areas as meteorology and climatol-ogy require moisture data on a large spatial scale (even global) Moreover, the soilmoisture content is a changeable parameter that must be monitored periodically.These data cannot be obtained by onsite measurements; therefore, remote sensingtechnology becomes particularly significant The multiplicity of different terrainareas in the landscape requires relatively high spatial resolution for the soundingtools Among microwave devices, only SAR, as we noted earlier, satisfies thiscondition, especially in the case of observation from space This explains the greatinterest in soil moisture estimation on the basis of SAR data The complexity of theradar signal returning from a rough surface makes this a difficult estimation problem

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at the L-band for both polarizations as a function of the incident angle The

men-tioned sensitivity is expressed in decibels and corresponds to the point ξ = 0 This

sensitivity is sufficient, especially in the case of vertical polarization At vertical

polarization, a weak maximum of the sensitivity occurs at an incident angle of 40°

Such dependence is the basis for development of soil moisture measurement by

radar technology; however, it cannot be the basis for an algorithm to solve the inverse

problem (i.e., soil moisture retrieval) because the backscattering coefficient depends

on both soil electrophysical properties and the roughness parameters It is difficult

to state the cause of changes in the backscattering coefficient, as they can be the

result of a change in roughness or variations in moisture

It is necessary to know in advance the terrain roughness characteristics in order

to evaluate the radar data against the soil moisture value It is impossible to have

such preliminary information on a large scale, so such methods can hardly be

considered successful An investigation conducted at test areas to determine

rough-ness parameters is more likely to help determine the correctrough-ness of various scattering

models than develop a retrieval algorithm It is important, then, to have an algorithm

of radar data processing that does not take into account the roughness parameters

This is a reason why algorithms based on polarimetric analysis of radar data are

more effective

It is easy to see that, within the framework of the perturbation method, the ratio

of the backscattering coefficient does not depend on the roughness spectrum (see

Equations (6.48) and (6.49)); that is, the ratio depends only on soil permittivity and

angle of incidence:

(15.11)

This means that P-band radar, for which the perturbation method can be valid, can

of volumetric soil moisture at the P-band for incident angles of 30° and 50°

FIGURE 15.7 Angular soil moisture sensitivity: (1) ηv; (2) ηh.

incident angle, degrees

2

1 2TF1710_book.fm Page 413 Thursday, September 30, 2004 1:43 PM

be used for this kind of measurement This ratio is shown in Figure 15.8 as a function

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Obviously, the ratio under discussion is more sensitive to moisture change at large

incident angles

Another way to estimate soil moisture is to determine the cross-polarization

ratio (see Equation (15.5)) This ratio vs volumetric soil moisture is represented in

Figure 15.9 for the C- and L-bands It does not depend on the incident angle in the

approximation given by the OSU model At the C-band, this ratio is more sensitive

to moisture content change compared to the L-band However, this advantage is the

seeming one, in the general case, taking into account the scattering and screen effects

of vegetation Before investigating this problem further, we should note that the

procedures of polarization data processing presented here reflect only basic

approaches to the problem solution; other procedures can be found in the

litera-ture.90,120,124

For our discussion of soil covered by vegetation, we will first consider grassland

The backscattered signal, in this case, consists of at least five components The first

of them is directly scattered by the soil roughness component (the ground-bounce

term) and is attenuated by extinction due to vegetation elements (absorption and

spatial scattering) This component can be represented in a very simplified form:

FIGURE 15.8 Soil moisture sensitivity at the L-band for both polarizations as a function of

incident angle: (1) 30°; (2) 50°.

FIGURE 15.9 Volumetric soil moisture ratio for the (1) L-band and (2) C-band.

2 1

0 0.1 0.2 0.3 0.4 ξ

volumetric soil moisture 1

1.5 2 2.5

0.4 2 1 q

ξ

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Here, is the soil backscattering coefficient, γ is the amplitude extinction

coef-ficient, and h is the vegetation height Two-pass attenuation is taken into account in

Equation (15.12)

The next term describes the direct backscattering by vegetation elements In

order to simplify the problem, let us assume similarity of the cross sections of all

elements Based on this assumption:

where is the backscattering cross section of vegetation per volume unit

The third term represents ground/grass scattering when the wave reflected by

the soil is scattered by vegetation canopy elements (the ground-bounce term) The

formula for this term is:

where is the differential cross section of scattering outward by unit volume of

vegetation

A similar fourth summand corresponds to grass/ground scattering when the

waves, initially scattered by the canopy elements, are then reflected by the soil In

this case:

where is the cross section of scattering inward; generally,

Finally, the fifth component describes the ground/grass/ground process of

scat-tering (the double-bounce term) The corresponding formula can be represented in

the form:

(15.16)

Here, the cross section reflects inward vegetation backscattering In each

case, only single scattering by the vegetation elements was considered, and the

i

expcos

2 0

h

i

σvg( )−ei TF1710_book.fm Page 415 Thursday, September 30, 2004 1:43 PM

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contribution of multiscattering effects was omitted It is practically assumed that a

lack of soil surface roughness leads to a coherent process of scattering, as reflected

by the use of the Fresnel reflection coefficient to describe soil effects

Forestry areas are characterized by similar terms of radio-wave scattering;

how-ever, it is necessary to distinguish more clearly the scattering cross sections of the

elements of crown, brushwood, and trunks Sometimes this is not done, and

gener-alized parameters have to be introduced (e.g., for the cloud model)

The dielectric properties of canopy constituents depend on the water content in

the vegetation elements: leaves, stalks, trunks, and branches It is difficult to justify,

theoretically, the development of a procedure to calculate the electromagnetic

param-eters of complicated elements such as canopy constituents; therefore, we have to

resort to experimental data interpolation Ulaby et al.125 proposed such an

interpo-lation formula:

Here, εw is the water complex permittivity defined by Equations (14.1) and (14.2),

where it is necessary to let S = 0 and assume that σ = 1.137 · 1010 CGSE The

coefficients A, B, and C are governed by volumetric moisture content mv:

(15.18)

In this considered case, both free water and bound water assume a role The

volu-metric moisture content is related to gravivolu-metric moisture content mg by the equation:

where ρ is the bulk density of the vegetation material The volumetric moisture

content varies from 0.5 to 0.8.116

In principle, knowledge of the canopy element permittivities allows computation

of their cross sections of scattering and absorption, as well as determination of

radio-wave attenuation in a vegetation canopy and the intensity of the backscattered radio-waves

Several publications have reported attempts to do so The canopy elements are

considered as bodies of simplified shapes (e.g., cylinders of bonded length, thin

plates), which allows us to calculate their cross sections in analytical or very

31 4

1 59 5

2 2

m

v

g g

=

− −( )ρρ

1 1TF1710_book.fm Page 416 Thursday, September 30, 2004 1:43 PM

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simplified numerical forms It is necessary to include in these calculations the effects

of coherency that can occur, especially in the case of a grass canopy,127,128 whenthese effects arise during synchronized movement of leaves on the same stalk and

on neighboring stalks This coherency amplifies the effect of scattering Anothercoherency effect takes place in a cultivated grass canopy when tillage forms relativelystraight, periodic rows that act as a diffraction grating

Taking into account all of these circumstances leads to a very complex vegetationcanopy scattering model This model often contains many unknown parameters, thedetermination of which is realized only when the calculated results fit the experi-mental data It is difficult to avoid the impression that each such model would have

an individual character according to the vegetation species This is the reason why

we do not provide all of the details of such models here, restricting ourselves instead

to a rough estimation of radiowave extinction in the vegetation canopy and scattering processes

back-With regard to extinction, we can model a vegetation canopy as a layer of amedium that is a mixture of green mass and air Then, we can use Equation (15.1)

to calculate an approximation of the complex refractive index of this mixture:

The imaginary part of this index defines the coefficient of radiowave attenuation

a green mass concentration of ξg = 0.02 (relatively dense canopy) and two values

of volumetric moisture m v: 0.6 and 0.8 It is easy to see that attenuation in a grasscanopy can be considerable and can mask radiowave scattering by the soil, especially

in the cases of C- and X-bands Thus, we can conclude that P- and L-band radar ispreferable for soil moisture measurement; with regard to monitoring a grass canopy,the C- and X-band radar is more effective As a rule, the grass backscatteringcoefficient is correlated with canopy biomass, and the biomass value is the mainproduct of radar data interpretation Polarimetric analysis provides an opportunity

to distinguish various grass species Reflections by both ground and vegetation aredetected by radar, so, ideally, a multifrequency and fully polarized system that issensitive to all Stokes components would be best for remote sensing of soil Such

a system can be realized relatively easily on an aircraft platform (for example, theAIRSAR system of JPL) but requires a large satellite platform for monitoring fromspace Currently, this has occurred only for a SAR–C/X system during several Shuttlemissions

The application of radar technology for monitoring the state of forests and theirdynamic parameters is acquiring greater significance The complexity of the forestcanopy architecture has led, as noted earlier, to attempts to construct very compli-cated models to describe the radiowave scattering One of these is the MichiganMicrowave Canopy Scattering (MIMICS) model,125 which divides the canopy intothree regions: the crown region, the trunk region, and the underlying ground region.Each region is characterized by its own scattering and absorbing properties and

nvg= −1 ξg( εΦ −1)

(see Equation (2.8)) The results of our computations are plotted in Figure 15.10 for

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parameters The result of radiowave scattering is described in terms of a 4 × 4 like transformation matrix that provides corresponding expressions for backscatter-ing coefficients of matched and cross-polarizations The effect of forest structureand the biomass on remote sensing is analyzed, for example, in Imhoff128 for tropicalforests

Stokes-Kurvonen et al.129 studied a simpler model for boreal forests, based essentially

on the cloud model together with experimental data Let us introduce the parameters:

where V is the stem value (biomass; m3/ha) Then, all of the scattering summandsare concentrated into two groups:

The first component here represents the direct forest canopy backscattering and the

second one is related mostly to ground effects We can connect the coefficients C1and C2 to the vegetation moisture by the relations:

10 20 30 40 50

γ

1 2

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