tut_ccrs_polarim.pdf

Radar Polarimetry

Advanced Radar Polarimetry Tutorial

Introduction This tutorial will introduce the reader to the principles, technology and practical applications of radar polarimetry. Note that this tutorial makes extensive reference to items in the "Remote Sensing Glossary" of the Canada Centre for Remote Sensing. While a printable version is also offered, the fully interactive version with several animated illustrations is only offered on-line.

For a simpler and much shorter approach to this topic, the reader is invited to read the "Radar Polarimety" chapter of the "Fundamentals of Remote Sensing" tutorial, also on the CCRS Web site.

1 Basics of SAR Polarimetry

1.1 Introduction to EM Waves and their Properties

An electromagnetic (EM) plane wave has time-varying Electric and Magnetic Field components in a plane perpendicular to the direction of travel . Ttwo fields are orthogonal to one another, and are described by Maxwell's equations. The fields propagate at the speed of light in "free space", which includes most realistic atmospheric conditions. Three parameters are necessary and sufficient to describe tpropagation of EM waves in a given medium: dielectric constant (or permittivity), permeability and conductivity.

he

he

nd

g

In general, when an EM wave is emitted from a source, such as a radar antenna, it propagates in all available directions, (with a specific field strength aphase in each direction). At a long distance from the antenna, we can assume that the wavefront lies on a plane, rather than on the surface of a sphere. Since weare only interested in what happens to the wave alonone specific direction, the "plane wave" assumption is appropriate.

A propagating, polarized, electromagnetic wave. The red arrow represents the total electric field, which traces an elliptical locus during one cycle.

Canada Centre for Remote Sensing

Radar Polarimetry 2

Polarization is an important property of a plane EM wave. Polarization refers to the alignment and regularity of the Electric and Magnetic Field components of the wave, in a plane perpendicular to the direction of propagation. By convention, we direct our attention to the Electric Field component of the wave, as the orthogonal Magnetic Field component "follows" it according to Maxwell's equations (the Magnetic Field is directly related to the Electric Field, and can always be calculated from it). For this reason, the EM wave can be characterized by the behaviour of the Electric Field vector as a function of time. The propagation of an electromagnetic wave is illustrated in Figure 1-1.

Did you Know? The predictable component of the EM wave has a characteristic geometric structure, which defines its polarization properties. When viewed along its direction of propagation, and assuming horizontal and vertical axes with respect to a specific coordinate system (e.g. axes defined parallel to the long and short sides of the radar antenna), the tip of the Electric Field vector traces out a regular pattern. The length of the vector represents the amplitude of the wave, and the rotation rate of the vector represents the frequency of the wave. Polarization refers to the orientation and shape of the pattern traced by the tip of the vector, as discussed in the next section.

Figure 1-1 Illustrating the propagation of an electromagnetic plane wave. The Electric Field vector has horizontal (green) and vertical (blue) components, which combine to


Radar Polarimetry 3

yield the net Electric Field vector (red). The locus of the tip of the Electric Field vector is shown in brown, tracing one cycle of the waveform on a plane perpendicular to the propagation direction.

The waveform of the Electric Field vector can be predictable or random, or a combination of both. A random component is like pure noise, with neither a recognizable frequency nor a pattern to its amplitude. An example of a predictable component is a monochromatic sine wave, with a constant, single frequency and a constant amplitude. An EM wave that has no random component is called fully polarized.

1.2 The Polarization Ellipse

The Electric Field of a plane wave can be described as the vector sum of two orthogonal components, typically horizontal and vertical components. The two components are characterized by their amplitudes and the relative phase between them. When viewed along its direction of propagation, the tip of the Electric Field vector of a fully polarized wave traces out a regular pattern. In its most general form, the pattern is an ellipse, as shown in Figure 1-2.

Figure 1-2: Polarization ellipse showing the orientation angle and ellipticity , which are a function of the semi-major and semi-minor axes, a and b

The ellipse has a semi-major axis of length a, and a semi-minor axis of length b. The angle of the semi-major axis, measured counter-clockwise from the positive horizontal axis, is the "orientation", , of the EM wave, and can take on values between 0° and 180°. The degree to which the ellipse is oval is described by a shape parameter called eccentricity or "ellipticity", defined as = arctan(b/a), which can take values between -45° and +45°.


Radar Polarimetry 4

The shape of the ellipse is governed by the magnitudes and relative phase between the horizontal and vertical components of the Electric Field vector. Figure 1-3 illustrates the effect of relative phase between the components, when the magnitudes of the components are equal. When the components are in phase, the polarization is linear (ellipticity = 0), with an orientation of 45°. As the relative phase angle increases to /2 radians, the orientation remains at 45°, but the ellipticity increases to 45°, representing circular polarization. This sequence is shown in the top row of Figure 1-3 (plus the first entry in the second row), where the phase in increased in steps of /8.

Then as the relative phase increases from /2 to 3 /2 radians, the orientation flips to 135°, and the ellipticity goes from 45° to zero then to -45°. This sequence is shown in rows 2 and 3 of the figure (plus the first entry in the fourth row). Finally in row 4, the relative phase goes from 3 /2 to 15 /8, the orientation flips to +45°, and the ellipticity tends to zero again.

Figure 1-3: The shape of the polarization ellipse as the relative phase between the horizontal and vertical components of the Electric Field vector is varied from 0 to 15 /8 radians in steps of /8

Figure 1-3 illustrates how a circle and a straight line are limiting cases of the ellipse. If the phase angle between the horizontal and vertical components is zero or radians, the


Radar Polarimetry 5

ellipse becomes a straight line. In this case, the ellipticity is zero and the polarization is referred to as "linear".

Figure 1-3 assumes that the magnitudes of the horizontal and vertical components are equal, but if they are not equal, the orientation can take on any value between 0 and 180°. If the ellipticity is zero and the orientation is = 0 (180° is equivalent), the polarization is horizontal linear (the vertical component is zero), and if = 90°, the polarization is vertical linear (the horizontal component is zero). These are the two linear polarizations in common use.

If the phase angle between the horizontal and vertical components is 90°, and the horizontal and vertical components are equal, the ellipse becomes a circle. In this case, the ellipticity has a magnitude of 45°, and the orientation is not defined. An ellipticity of = +45° corresponds to a left circular polarization and = -45° corresponds to a right circular polarization. If the wave is observed along the direction of propagation, the polarization is left-handed if the rotation of the Electric Field vector is counter-clockwise.

Did you Know?Did you know that a fully polarized wave could be made up of sine waves of many frequencies? However, in SAR system analysis, we usually assume a single frequency or "monochromatic sine wave". This is a valid assumption, as SAR systems usually have a very narrow bandwidth (compared to the carrier frequency) so that the transmitted wave can be approximated by a sine wave.

Examples of linear, elliptical and circular polarizations athe rotation of the Electric Field vector is also shown.

re shown in the figures, where

Figure 1-4: The Electric Field vector (red) and the locus traced by the tip (blue) perpendicular to the direction of propagation - case of linear polarization.

Figure 1-5: The Electric Field vector (red) and the locus traced by the tip (blue) perpendicular to the direction of propagation - case of elliptical polarization.

Figure 1-6: The Electric Field vector (red) and the locus traced by the tip (blue) perpendicular to the direction of propagation - case of circular polarization.


Radar Polarimetry 6

1.2 Whiz Quiz Question: Why are the horizontal and vertical components sufficient to describe the polarization of an EM wave? Answer: The polarization of a plane EM wave is described by the locus of its Electric Field vector in a plane perpendicular to the direction of propagation. Two orthogonal components are required to describe the location of the vector in the plane, and horizontal and vertical components, Ex and Ey (or Eh and Ev) are the most convenient ones to use.

1.3 Polarization in Radar Systems

How does a radar system create polarized waves? It uses an antenna that is designed to transmit and receive EM waves of a specific polarization. Antennas come in many forms, including horns, waveguides, dipoles and patches. In each case, the electric and mechanical properties of the antenna are such that the transmitted wave is almost purely polarized with a specific design polarization. In a simple radar system, the same antenna is often configured so that it is matched to the same polarization on reception (when an EM wave is incident upon it) .

Signals with components in two orthogonal or basis polarizations are needed to create a wave with an arbitrary polarization. The two most common basis polarizations are horizontal linear or H, and vertical linear or V. Circular polarizations are also in use for some applications, e.g. weather radars. Their basis components are denoted by R for Right Hand Circular and L for Left Hand Circular.

In more complex radar systems, the antenna may be designed to transmit and receive waves at more than one polarization. On transmit, waves of different polarizations can be transmitted separately, using a switch to direct energy to the different parts of the antenna in sequence (e.g. the H and V parts). In some cases the two parts can be used together, for example, a circular polarized signal can be transmitted by feeding the H and V parts of the antenna simultaneously, with signals of equal strength and a 90° phase difference (recall Figure 1-3).

Because the scatterer can change the polarization of the scattered wave to be different from the polarization of the incident wave, the radar antenna is often designed to receive the different polarization components of the EM wave simultaneously. For example, the H and V parts of an antenna can receive the two orthogonal components of the incoming wave, and the system electronics keep these two signals separate.


Radar Polarimetry 7

Denoting the transmit and receive polarizations by a pair of symbols, a radar system using H and V linear polarizations can thus have the following channels:

HH - for horizontal transmit and horizontal receive, (HH) VV - for vertical transmit and vertical receive, (VV) HV - for horizontal transmit and vertical receive (HV), and VH - for vertical transmit and horizontal receive (VH).

The first two of these polarization combinations are referred to as like-polarized, because the transmit and receive polarizations are the same. The last two combinations are referred to as cross-polarized because the transmit and receive polarizations are orthogonal to one another.

A radar system can have different levels of polarization complexity:

single polarized - HH or VV or HV or VH dual polarized - HH and HV, VV and VH, or HH and VV four polarizations - HH, VV, HV, and VH

A quadrature polarized (i.e. polarimetric) radar uses these four polarizations, and measures the phase difference between the channels as well as the magnitudes. Some dual polarized radars also measure the phase difference between channels, as this phase plays an important role in polarimetric information extraction.

1.4 The Polarization State

The polarization state of a plane wave can be described by orientation and ellipticity, plus a parameter S0 that is proportional to the total intensity of the wave. Writing the horizontal and vertical components of the Electric Field vector as Eh and Ev, the British physicist, Gabriel Stokes, described the polarization state of the EM wave by a 4-element vector, [ S0, Q, U V ] T, now known as the Stokes vector:

(1)

where | . | is the absolute value and * is the complex conjugate. An electromagnetic plane wave can be completely polarized, partially polarized or completely unpolarized. In the completely polarized case, only 3 of the Stokes parameters are independent, because of the total power relation:


Radar Polarimetry 8

(2)

For a completely polarized wave, the polarization state can be described by a point on the Poincaré sphere, as shown in Figure 1-8. The radius of the sphere is S0, the intensity of the wave. The latitude of a point on the sphere corresponds to 2 , i.e. two times the ellipticity of the wave.

The longitude of a point on the sphere corresponds to 2 , i.e. two times the orientation of the wave. Did

you Know? The British physicist, George Gabriel Stokes, was

born on August 13, 1819 in Skreen, County Sligo, Ireland, and became a professor at Cambridge in 1849, a position he held until his death on February 1, 1903 (the centennial is soon). In addition to his work with polarimetry and the theory of light, he is also known for his research in fluid mechanics, spectrum analysis, geodesy, and the theory of sound and vector calculus. He was elected as a member of the Royal Society in 1851, and was its president from 1885 to 1890. He was also a member of the British Parliament from 1887 to 1892, noted for supporting educational issues.

We can see from this notation that linear polarizations lie on the equator, with horizontal and vertical polarizations opposite each other. Left-hand circular and right-hand circular polarizations lie on the north and south poles respectively. All other points on the sphere represent elliptical polarizations of various ellipticities ( ) and orientations ( ). Points on the sphere that are directly opposite one another represent polarizations that are orthogonal to one another, and are referred to as cross polarizations.

If the electromagnetic wave is partially polarized, it can be expressed as the sum of a completely polarized wave and a completely unpolarized or noise-like wave. The degree of polarization is the ratio of the polarized power to the total power, and in terms of the Stokes parameters, the degree of polarization is given by

(3)

so that for partially polarized waves, the total power is greater than the polarized power:

(4)


Radar Polarimetry 9

Figure 1-8: Orientation and ellipticity of a fully polarized wave represented on the Poincaré sphere.

1.4 Whiz Quiz Question: If an EM wave is horizontally polarized, what is the corresponding orthogonal polarization? Answer: The orthogonal or cross polarization to linear horizontal is linear vertical polarization. Two orthogonal polarizations can form a basis set, used to describe the polarization of an EM wave. Linear horizontal and linear vertical are two orthogonal polarizations that are commonly used as the basis set, but left-hand circular and right-hand circular are another set that is sometimes used.

1.5 Polarimetric Scattering

Having defined how to represent a polarized wave, we now describe how an EM wave of a certain polarization is scattered by a target. In this regard, we will use "target" to mean either a discrete reflector or a distributed surface.

The scattering properties of a target can be measured by a polarimetric radar, as depicted in Figure 1-10. The radar system illuminates the target with an incident wave (A), and the wave is scattered in all directions by the target (C). The radar system records the part of the scattered wave that is directed back towards the receiving antenna (B). Often the receiving antenna is in the same location as the antenna that transmitted the wave - this is called the monostatic case, and the received energy is referred to as backscatter. By controlling the polarization of the incident wave and measuring the full polarization


Radar Polarimetry 10

properties of the backscattered wave, the radar system can be used to learn more about the target than by using a single polarization.

Fig 1-10a: Illustrating the monostatic case.

Figure 1-10b: Illustrating backscatter - only a small part of the scattered energy (C) is received back at the radar antenna (B)

A polarimetric or quadrature polarization radar transmits with two orthogonal polarizations, often linear horizontal (H) and linear vertical (V), and receives the backscattered wave on the same two polarizations. This results in four received channels, i.e. HH, HV, VV and VH, where both the amplitude and relative phase are measured. The measured signals in these four channels represent all the information needed to measure the polarimetric scattering properties of the target - hence the quadrature polarization radar is also called a fully polarimetric radar. In the case of dual polarized radars, some but not the entire target scattering properties can be obtained from the two channels.

1.6 The Scattering Matrix

When a horizontally polarized wave is incident upon a target, the backscattered wave can have contributions in both horizontal and vertical polarizations. The same applies to a vertically polarized incident wave. As the horizontal and vertical components form a complete basis set to describe the electromagnetic wave, the backscattering properties of the target can be completely described by a scattering matrix, S,

(5)

which describes the transformation of the Electric Field of the incident wave to the Electric Field of the scattered wave (in (1-5), the superscript i refers to the incident wave, and s refers to the scattered wave). Having measured this matrix, the strength and polarization of the scattered wave for an arbitrary polarization of the incident wave can be computed, as any incident wave can be expressed in the [ Eh

i , Evi ] basis set.



The four elements of the scattering matrix are complex, and can be obtained from the magnitudes and phases measured by the four channels of a polarimetric radar. A precise calibration procedure is needed to get the elements, but if the calibration were not necessary, the four scattering matrix elements would be directly measured by the corresponding channels of the radar system. The measured scattering properties of the target apply only at that frequency and radar beam angle used in the mission. However, the scattering properties can vary significantly with radar frequency and beam direction (or rotation of the target), so care should be taken to choose these parameters to be representative of the desired operating scenario.

In monostatic radars, the reciprocity property holds for most targets. This property means that Shv = Svh, i.e. the scattering matrix is symmetrical and has only 3 independent elements. Note that as the elements of the scattering matrix are complex, a phase change that may occur during the scattering process can be represented.

Coordinate conventions: The propagation of a plane EM wave is described in a three-dimensional space with the coordinates given by the three axes x, y and z. The z-axis is in the direction of propagation, while the x- and y-axes lie in a plane perpendicular to the direction of propagation, with the (x, y, z) forming a right-hand orthogonal set. In scattering situations, the coordinate space has to be defined for both the incident wave and the scattered wave.

Two conventions have arisen in the literature; the forward scatter alignment (FSA) and the back scatter alignment (BSA). For the FSA, the positive z-axis is in the same direction as the travel of the wave (for both the incident and scattered wave), while in the BSA, the positive z-axis points towards the target for both the incident and scattered wave. Comparing these two cases, the z-axis points in the same direction for the incident wave, but in opposite directions for the scattered wave. For the monostatic radar case, the coordinate systems are the same for the incident and scattered wave in the BSA convention, so the BSA is more commonly used for imaging radars.

Because of the differing convention rules, the scattering matrix takes on a different form in the BSA and FSA conventions. In the BSA convention, the scattering matrix is called the Sinclair matrix , while in the FSA convention, the scattering matrix is called the Jones matrix , page 278.



1.6 Whiz Quiz Question: How does the polarization of a scattered EM wave differ between the FSA and BSA conventions? Answer: The BSA convention can be viewed as seeing the EM wave from the opposite direction as in the FSA convention. This has the effect of reversing the apparent direction of rotation of the wave and results in a change of sign of the ellipticity of the wave.

2 Polarimetric Data Expressed in the Power Domain There are many different ways of representing the scattering properties of a target, and they are often expressed in the power domain. Several of the most widely used power representations are introduced in this section.

2.1 The Covariance and Coherency Matrices

The scattering vector or covariance vector kC is a vectorized version of the scattering matrix. Assuming reciprocity, whereby Svh = Shv , this vector is

(2-1)

It is convenient to construct a power-domain representation of the scattering properties, which is done by forming the product of this vector with itself. This results in the covariance matrix, which also fully describes the scattering properties of the target [ ,

Section 5-4.10]:

(2-2)

where + denotes conjugate transpose and * the conjugate. The covariance matrix has conjugate symmetry.



The coherency matrix is closely related to the covariance matrix, and is preferred by some analysts . To obtain the coherency matrix, the scattering matrix is vectorized in a different way using the Pauli spin elements (again assuming reciprocity):

(2-3)

This vector is sometimes preferred because its elements have a physical interpretation (odd-bounce, even-bounce, diffuse, etc.). Note that some authors use (Svv - Shh) for the second element of this vector , obtaining an equivalent analysis. Again, the information in (2-3) is expressed in the power domain by forming the "product" of this vector with itself, resulting in the coherency matrix:

(2-4)

The eigenvalues of the covariance matrix and the coherency matrix are real and are the same. The sum of the diagonal elements (the trace) of both matrices is also the same, and represents the total power of the scattered wave if the incident wave has unit power. Note that most authors use the BSA convention for these definitions.

2.2 The Stokes and Mueller Matrices

When the polarization of the incident wave is described by a Stokes vector Si and that of the backscattered wave by a Stokes vector Ss, then the backscattered power from a scatterer is defined by

(2-5)

where M is the Stokes matrix, which is a 4x4 array of real numbers page 291, . In other words, the Stokes matrix is another way of transforming the incident EM wave into the backscattered wave.

Assuming reciprocity, the Stokes matrix is symmetric, containing 10 different numbers, of which 9 are independent. Each element can be computed from the scattering matrix.

The Mueller matrix is a close relative of the Stokes matrix, except that reciprocity is not assumed and so it contains more independent elements. The Mueller matrix is used in the



FSA convention. There is an equivalent form of the power equation (2-5) for the Mueller matrix, and for the covariance and coherency matrices as well.

The Kennaugh matrix K is the version of the Stokes matrix used in the BSA convention. They are related by M = diag[1 1 1 -1] K. The trace of the Kennaugh matrix equals the total power, but the trace of the Mueller matrix does not. The elements of the Kennaugh matrix are defined in .

Remark: Unfortunately, there is inconsistency in the literature about the naming of the matrix M in (2-5). The convention used here comes from page 119 of Raney's chapter in the Manual of Remote Sensing . The matrix M is called the Stokes scattering operator on page 29 of the Ulaby & Elachi book . We assume the conventions used in the Manual of Remote Sensing in this tutorial.

2.3 Averaging the Power Forms

Averaging of adjacent samples is very useful in polarimetric radar data analysis. It has a similar effect as look summation in single-polarization SAR processing. It reduces the "noisy" effects of speckle, but at the expense of degrading the resolution of the image

, . When values in the neighbourhood of a sample are averaged, scatterers that were once represented by distinct samples become consolidated in the image.



The resulting reduction of speckle and noise, and the grouping of scatterers, makes the image easier to interpret and can make automatic classifiers work more reliably

.

Averaging is performed in the power domain, because the energy of individual components is preserved in power representations (energy is not preserved when averaging in the "voltage" domain). Usually the Stokes, covariance or coherency matrix representations are used for the averaging. The averaging is usually performed as a post-processing operation, by averaging the power matrix values of adjacent samples. Averaging has the additional advantages of reducing the data volume, and can be used to create equal pixel spacing in ground range and in azimuth.

2.4 Data Compression and Storage Formats

and SIR-C polarimetric radars, ta

Did you Know?When the scattering matrix of a single pixel is measured by the radar system, there are not enough degrees of freedom to represent noise as well as the target's scattering properties, even though noise is present in the observation. For this reason, a single scatterer is assumed even though there may be multiple scattering mechanisms and noise present in the pixel. However, when converted to a power representation and neighbouring samples are averaged, a composite pixel is obtained in which the noise and different scattering mechanisms can be explicitly represented.

In order to deal efficiently with data from the AIRSARscientists at the Jet Propulsion Lab (JPL) sought a way of storing and distributing the dathat was simple, compact and contained all the essential information for data interpretation and classification. Rather than storing the four complex elements of the scattering matrix, possibly using 32 bytes per pixel, they chose the Stokes



(Kennaugh) matrix for the AIRSAR data, and compressed each sample (or group of averaged samples) into a 10-byte word. Other radar systems have used the covariance matrix for data compression , page 292.

In the JPL scheme, the total power of each sample is computed and stored in 2 bytes, one for the mantissa and one for the exponent. The remaining 8 unique elements of the Stokes matrix are normalized by the top left element, M11, and stored in 1 byte each. The four smallest of these, related to the cross-products of the co-pol and cross-pol channels, are square rooted as well. The original elements of the Stokes matrix are easily recovered from the stored values .

With higher storage capacities becoming available, it is possible to store the full scattering (Sinclair) matrix for each sample, without averaging to reduce the data volume. More sophisticated methods of compressing radar image data have been developed for single channel data, e.g. based upon the DCT or wavelets, but these methods have not been fully tested on polarimetric data yet.

2.4 Whiz Quiz Question 1: What is meant by a "scattering mechanism"? Answer 1: Every feature or structure on the ground scatters radar energy in a certain way. Examples are water, a cornfield, a farmhouse, or a car. Most of these features scatter energy in a different way from the others. The term "scattering mechanism" is an attempt to characterize the scattering from a given feature in terms of simple elements for which we know or can model the scattering behaviour. Examples of scattering mechanisms are a sphere, a dihedral, a helix, and composite scatterers such as a random distribution of dipoles.

Question 2: How is a "scattering mechanism" defined? Answer 2: There are two basic ways of defining a "scattering mechanism". The first is to create a physical model of a scatterer, such as a dipole or a trihedral corner reflector. Then mathematical and physical principles (such as Maxwell's equations) are used to derive how the EM waves scatter off the surface. The scattering is then expressed as a scattering matrix, or its derivatives such as the Stokes or covariance matrix. The term "mechanism" refers to the elemental scatterer or model, plus its associated mathematical definition of scattering behaviour. The second method is to make an explicit measurement of the scattering, either in the

Did you Know?Did you know that the Stokes and covariance matrices contain phase information, even though they are power representations? This is because the cross terms such as the expected value of (Ehh Evv*) are complex numbers, and the angle of the complex number depends upon the phase angle between the HH and VV channels.



field or under laboratory conditions (e.g. in an anechoic chamber). In this case, the measured echo is usually made up of a number of elemental mechanisms, and mathematical procedures have been developed to separate the signal into its constituent components (e.g. eigenvalue decomposition of the coherency matrix). Each component is then referred to as a scattering mechanism, and hopefully can be related to a physical model mentioned in the previous paragraph.

Question 3: Why is the covariance matrix considered to be a "power" representation? Answer 3: Because the scattering matrix elements relate the "voltage" of the scattered EM wave (the Electric Field strength) to the "voltage" of the incident wave, and the covariance matrix is formed from "products" of these elements. In other words, the covariance matrix relates the power of the scattered EM wave to the power of the incident wave.

3 Polarization Synthesis As described above, a polarimetric radar can be used to determine the target response or scattering matrix using two orthogonal polarizations, typically linear horizontal and linear vertical on both transmit and receive. If the scattering matrix is known, the response of the target to any combination of incident and received polarizations can be computed. This operation is referred to as polarization synthesis, and illustrates the power and flexibility of a polarimetric radar.



If a scattering matrix is measured by a polarimetric radar, then all the information is available about the backscattering properties of the target at each sample, for that frequency and angle with which the radar beam strikes the target. While the radar measures the response at four polarization combinations, the information obtained can be used to synthesize an image for any combination of transmit and receive polarizations. For example, a quadrature polarization radar may measure the responses at HH, HV, VV and VH, and with this information, an image can be constructed that would be received from a radar with right-hand circular polarization on both transmit and receive.

The polarization synthesis can be performed by converting the scattering matrix to the Stokes matrix, then pre-multiplying and post-multiplying the matrix by the unit Stokes vector representing the desired polarizations of the receive and transmit antennas respectively. One common use of polarization synthesis is to construct the polarization signatures for a selected class of targets, and use these geometric representations to help interpret the scattering mechanisms present in a scene (see Section 5).

Did you Know?Through polarization synthesis, an image can be created to improve the detectability of selected features. As an example, consider the detection of ships in sea clutter. To find the best polarization to use, the polarization signature of a typical ship is calculated, as is the signature of representative ocean areas (Bragg scattering). Then the ratio of these signatures can be determined. The transmit-receive polarization combination that maximizes the ratio of backscattered strength should improve the detectability of ships. This procedure is called "polarimetric contrast enhancement" , . A related procedure is called a "polarimetric matched filter"

.

4 Polarimetric Parameters When polarimetric radar data is analyzed, there are a number of parameters that can be computed that have a useful physical interpretation . They can be computed for every sample in a polarimetric radar image, but are often averaged over groups of samples to reduce the effe of noise.

Total Power

A quantity giving the total power received by the four channels of a polarimetric radar

The power received by a polarimetric radar can be expressed by the covariance, onal to

Co-pol Correlation Coefficient

The correlation between the two co-polarized channels in a multi-polarized or polarimetric radar.

ct

system. In terms of the Sinclair (scattering) matrix, the total power equals |Shh|2 + |Shv|2 + |Svh|2 + |Svv|2

coherence or Kennaugh matrices. The total power in the four channels is proportithe sum of the diagonal elements or trace of these matrices.



The co-pol channels are often HH and VV. The correlation coefficient is compcomputed as the ave

lex and is rage of the product between the complex amplitude of the HH

channel and the conjugate of the complex amplitude of the VV channel. It is normalized by the square root of the product of the powers in the HH and VV channels

(equation 4-1)

If the magnitude of the correlation coefficient is unity, the received signals from the two channels are linearly related (i.e. one can be comp er). An example is the backscatter received from an ideal trihedral corner reflector. If the magnitude of the

uted from the oth

correlation coefficient is less than one, it means that the backscattering at HH and VV arenot directly related. It also may mean that noise is present on one or both of the channels or the received EM waves are partially polarized. It is possible to compensate the coefficient for the receiver noise in the radar system , page 294.

Co-pol Phase Difference

The phase difference between the two co-polarized channels in a multi-polarized or se angle of the co-pol correlation coefficient. Note that

when averaging is performed, the coherent scattering matrix elements are averaged, and

or group of pixels) in

the HH and the VV channels. The co-pol phase difference is often helpful in classifying a

oughness (i.e. not too rough such that multi-bounce scattering would occur) will backscatter with a co-pol phase

a co-

upon

er, the little correlation

between the scattering phase centres of the HH and HV channels (for example). If a

polarimetric radar. It is the pha

then the co-pol phase difference is calculated from the average.

Often the co-pol channels are HH and VV, and the co-pol phase difference is the averagedifference between the phase angles of the corresponding pixels (

pixel, as it is characteristic of the number of bounces that the EM wave experiences during reflection. An ideal single-bounce (or odd-bounce) scatterer will have a co-pol phase difference of 180° in the BSA convention, while an ideal double-bounce (or even-bounce) scatterer will have a co-pol phase difference of 0°.

In practical situations, there will be a fair amount of variation in the co-pol phase difference measurements. A surface with a small amount of r

difference near 180°, and an open upright structure like a telephone pole will havepol phase difference near zero. However, backscatter from an agricultural field could have a variety of co-pol phase difference values between -180° and 180°, depending the size, spacing and type of vegetation. For example, backscatter from a cornfield with well-defined vertical stalks is expected to have a significantly lower co-pol phase difference than a field of peas (depending upon the radar frequency).

There is also a "cross-pol phase difference", with the analogous definition. Howevcross-pol phase difference is usually very random, as there is generally



scene-dependent pattern is observed in the cross-pol phase difference, it is likely due to channel cross-talk that has not been corrected in the processing.

Degree of Polarization

The degree of polarization is given by the ratio of the power in the polarized part of an total power in the electromagnetic wave.

ch of the two parts. The total power in the wave is given by the Stokes parameter S0, while

electromagnetic wave to the

An electromagnetic wave can have a polarized and a non-polarized component, and the Stokes parameters are a convenient way of expressing the powers in ea

gives the total power in the polarized part. Accordingly, the degree of polarization can be expressed in terms of the Stokes parameters:

( equation 4-2)

Coefficient of Variation

The normalized ratio between the maximum and minimum power in a polarization

signal is fully polarized. When the coefficient equals zero, the polarization signature is flat and the received signal is unpolarized (e.g. all noise).

signature (Pmax - Pmin) / Pmax.

When the coefficient of variation equals one, the signature has a null at some polarization, and the received

The coefficient of variation is also called the fractional polarization .

5 Polarization Signatures Because the incident wave can take on so consists of 4 complex numbers, it is helpfu

many polarizations, and the scattering matrix l to have a graphical method of visualizing the

response of a target as a function of the incident and backscattered polarizations. One such visualization is provided by the polarization signature of the target .

The scattering power can be determined as a function of the four wave polarization variables, the incident and and backscattered and angles, but thes nse co titute too many independent variables to observe conveniently. To simplify the visualization, the

d

backscattered polarizations are restricted to be either the same polarization or the orthogonal polarization as the incident wave. This choice of polarization combinations leads to the calculation of the co-polarized and cross-polarized responses for each incident polarization, which are portrayed in two surface plots called the co-pol ancross-pol signatures. These two signatures do not represent every possible transmit-receive polarization combination, but do form a useful visualization of the target's



backscattering properties , . The BSA convention is usually used for the signatures.

An incident electromagnetic wave can be selected to have an Electric Field vector with an ellipticity between -45° and +45°, and an orientation between 0° and 180°. These

tter g

is

rization plots have peaks at polarizations that give rise to maximum received power, and valleys where the received power is smallest, in agreement with the concept

tures of the simplest class of targets - a large conducting sphere, a flat plate or a trihedral corner reflector. The wave is backscattered

of

variables are mapped along the x- and y-axes of a 3-D plot portraying the polarization signature. For each of these possible incident polarizations, the strength of the backscacan be computed for the polarization that is the same as the incident polarization (givinthe co-pol signature plot) and for the polarization that is orthogonal to the incident polarization (giving the cross-pol signature plot). For an incident wave of unit amplitude, the power of the co-polarized (or cross-polarized) component of the scattered wavepresented as the z value on the plots. Often the plots are normalized to have a peak value of one.

The pola

of Huynen's polarization fork in the Poincaré sphere. Polarization signatures and the Poincaré sphere can be conveniently drawn on polarimetric analysis workstations. One example is the PWS software for PCs.

Figure 5-1 shows the polarization signa

with the same polarization, except for a change of sign of the ellipticity (or in the caselinear polarization, a change of the phase angle between Eh and Ev of 180°). The sign changes once for every reflection - the sphere represents a single reflection, and the trihedral gives three reflections, so each behaves as an "odd-bounce" reflector.

Figure 5-1: Polarization signatures of a large conducting sphere or trihedral corner reflector

complicated targets, the polarization signature takes on different characteristic shapes. Interesting signatures are obtained from a dihedral corner reflector and from For more

Bragg scattering off the sea surface. In the case of the dihedral reflector, when its corner (the intersection of its sides) is aligned horizontally, parallel to the horizontal axis of the EM wave, the co-pol response is a maximum for linear or elliptical horizontal, linear or elliptical vertical and circular polarizations (Figure 5-2). Because the two reflecting surfaces of the dihedral sides negate the sign of the ellipticity a second time, this results in a typical "double-bounce" or "even-bounce" signature.



However, if the reflector is rotated by 45° around the radar line of sight, the linear horizontal co-pol response is zero and the linear horizontal cross-pol response is a maximum. This property means that the dihedral can be used as a simple way of creating a cross-pol response in an HH radar system.

Figure 5-2: Polarization signatures of a dihedral or double-bounce reflector

In the case of Bragg scattering, the response has a ridged shape similar to the single-r than that

of the horizontal polarization (see Figure 5-3). The co-pol response has a peak at bounce sphere, except that the backscatter of the vertical polarization is highe

orientation angle = 90° and at ellipticity angle = 0°.

Figure 5-3: Polarimetric signatures of Bragg scattering from the sea surface (Syy = 1.2*Sxx)

. The pedestal height is the minimum value of intensity found on the signature, when the maximum response is normalized to unity. The height of the pedestal is an

signal,

d

The pedestal height is a useful parameter that can be obtained from polarization signatures

indicator of the presence of an unpolarized scattering component in the received and thus is related to the degree of polarization of a scattered wave. If a single target is scattering and the backscattered wave is fully polarized, or if the signature is calculatefrom a single unaveraged measurement, the pedestal height is zero. But if the signature iscalculated from an average of several samples, and there are multiple, dissimilar scatterers present or there is noise in the received signal, the pedestal height will be non-zero. Thus the pedestal height is also a measure of the number of different types of scattering mechanism found in the averaged samples.



Figure 5-4: Polarization signature of a target having a pedestal height of about 0.2




5.0 Whiz Quiz Question 1: Why does the polarization signature of a simple reflector such as a sphere have a ridge-like appearance? Answer 1: You might expect the co-polarized response to be unity for all incident polarizations, and the cross-polarized response to be zero, but the change of sign of the ellipticity causes the signatures to have the "ridge" and "valley" shapes shown. The co-pol response is unity and the cross-pol response is zero for all linear polarizations (where the change of sign has no effect). But for circular polarizations such as RR, the co-pol response is zero and the cross-pol response of the target is unity. This "change of sign" property is a function of the coordinate frame convention used, and applies to the BSA convention .

Question 2: The polarization signature can have a "pedestal". What does this mean? Answer 2: A polarization signature computed from a single observation (i.e. a single sample of a polarimetric radar system) represents a fully polarized wave, even though multiple scattering types and noise are present in the measurement. This is because a single observation does not have enough degrees of freedom to represent more than a single pure scattering mechanism. As the scattered wave is assumed to be fully polarized, the signature will be zero for at least one combination of transmit and receive polarization. However, when the Stokes matrices of adjacent pixels are averaged, the net response will contain components from more than one type of scatterer and noise as well, assuming that the individual Stokes matrices are not identical . In this case, the minimum of the polarization signature will not be zero, but a certain positive value. This gives the polarization signature the appearance of "sitting on a pedestal". The height of the pedestal depends upon how different the various scattering mechanisms are present in the averaged pixels, or how much noise is present in the observations.

Question 3: What is the main use of polarization signatures? Answer 3: Polarization signatures are one way of visualizing the backscatter behaviour of a target. The polarization signature of a pixel in an image can be related to the signatures of known elemental targets, making it possible to infer the type of scattering that is taking place. When pixels in an image are averaged, the net response will contain components from more than one type of scatterer and noise as well. When analyzed in the power domain, these scattering components are additive. If we are lucky, we can relate the composite signature to known elemental signatures, and deduce the types of terrain in the image

.


6 Polarimetric Image Interpretation One of the main objectives of remote sensing is to make a thematic map of the Earth's surface, indicating the type of material at each location imaged by the radar. The type of material can be estimated from the polarimetric radar data, using a computer-based classification algorithm. Pixels or groups of pixels are assigned to terrain classes that have a meaningful geoscientific interpretation.

In the case of polarimetric radar, a larger number of parameters can be measured compared to a single-channel radar. This should make it possible to achieve a more accurate image classification. However, measurement noise, system calibration difficulties, the understanding of scattering mechanisms and the mixing of many different scattering mechanisms in one pixel or group of pixels are obstacles that must be overcome to obtain an accurate classification. The issues of calibration and image interpretation are addressed in this section. Details of classification algorithms are given in Section 7.

6.1 Data Calibration

One of the critical requirements of polarimetric radar systems is the need for calibration. This is because much of the information lies in the ratios of amplitudes and the differences in phase angle between the backscattering in the four received polarization combinations. If the calibration is not sufficiently accurate, the scattering mechanisms will be misinterpreted and the advantages of using multiple polarizations will be lost.

Calibration is achieved by a combination of radar system design and analysis of the received data. Consider the response to a trihedral corner reflector shown in Figure 5-1. This ideal response is represented by the identity scattering matrix:

and is only obtained if the four channels all have the same gain, the phase differences between channels are corrected to zero, there is no energy leakage from one channel to another (crosstalk), and there is no receiver noise. Even if the radar system does not have these ideal properties, if the imbalances can be measured, they can be largely corrected by calibration procedures.

In terms of the radar design, the channel gains and phases should be as carefully matched as possible. In the case of the phase balance, this means that the signal path lengths should be effectively the same in all channels. Calibration signals are usually built into the system design to measure the channel balances.

In terms of data analysis, channel balances (amplitude and phase), crosstalk and noise can be measured and corrected by analyzing the data received from specific targets. In addition to analyzing the response of internal calibration signals, the signals from known targets such as corner reflectors, active transponders, uniform clutter and radar shadow can be used to calibrate some of the parameters.



Many different calibration procedures have been developed, some sensor-specific , , , , , , , . One of the common difficulties is that the

calibration parameters tend to vary with beam elevation angle (because of antenna properties) and with incidence angle (because of scattering properties), which means that the calibration procedure has to account for range variations in the scene.

In addition to compensating for system imbalances, there are the calibration issues of interpreting absolute gain values, and the geometric location of the processed samples. Traditionally, corner reflectors and active radar calibrators (ARCs) are deployed on the ground for these purposes. For geometric location, a simple, economical wire mesh reflector can be used (see Figure 6-1). But for precise gain measurement, a corner reflector with close structural tolerances or an ARC are generally used (see Figure 6-2).

Figure 6-1: A wire mesh 1.4 meter corner reflector used for geometric calibration. The internal surfaces meet at 90°, and are covered by a conducting mesh to create a strong backscatter. CCRS calibration specialist, Bob Hawkins is the proud father.



Figure 6-2: Small (40 cm) and large (140 cm) trihedral corner reflectors used by CCRS for radar calibration. Larger reflectors are needed at lower frequencies, as the reflector gain is proportional to the square of the radar frequency. (source: CCRS)

6.2 Visual Interpretation

The simplest classification method is performed by visual interpretation. An interpreter learns how surface features are portrayed in the image, and his/her mind fills in missing details based upon local knowledge and experience.

To aid visual interpretation, the multiple channels of polarimetric data can be used to present the data in a colour image, in which certain image features are recognizable by a trained interpreter. As a simple example, a colour image can be made using an HH=red, HV=green and VV=blue channel assignment (see Figure 6-3). This tends to "look realistic" as water reflections have a higher VV component than HH, and vegetation has a higher than average HV backscatter.

Figure 6-3: SIR-C L-band colour composite image of Nipawin Provincial Park, north of Prince Albert, Saskatchewan (HH - red, HV - green and VV - blue)

As an example of the interpretation that can be obtained from such an image, the following description is from the NASA web site: http://visibleearth.nasa.gov/. Search: Space Radar Image of Prince Albert, Canada

"This is a false-color composite of Prince Albert, Canada, centered at 53.91 north latitude and 104.69 west longitude. This image was acquired by the Spaceborne Imaging Radar C/X-Band Synthetic Aperture Radar (SIR-C/X-SAR) aboard space shuttle Endeavor on its 20th orbit. The area is located 40 kilometers (25 miles) north and 30 kilometers (20 miles) east of the town of Prince Albert in the Saskatchewan province of Canada. The image covers the area east of the Candle Lake, between gravel surface highways 120 and 106 and west of 106. The area in the middle of the image covers the entire Nipawin (Narrow Hills) provincial park. The look angle of the radar is 30 degrees and the size of the image is approximately 20 kilometers by 50 kilometers.



The image was produced by using only the L-band. The three polarization channels HH, HV and VV are illustrated by red, green and blue respectively. The changes in the intensity of each color are related to various surface conditions such as variations in forest stands, frozen or thawed condition of the surface, disturbances (fire and deforestation), and areas of regrowth. Most of the dark areas in the image are the ice-covered lakes in the region. The dark area on the top left corner of the image is the White Gull Lake north of the intersection of highway 120 and 913. The right middle part of the image shows Lake Ispuchaw and Lower Fishing Lake. The deforested areas are also shown by dark areas in the image. Since most of the logging practice at the Prince Albert area is around the major highways, the deforested areas can be easily detected as small geometrically shaped dark regions along the roads.

At the time of the SIR-C/X-SAR overpass a major part of the forest is either frozen or undergoing the spring thaw. The L-band HH shows a high return in the jack pine forest. The reddish areas in the image are old jack pine forest, 12 to 17 meters in height and 60 to 75 years old. The orange-greenish areas are young jack pine trees, 3 to 5 meters (10 to 16 feet) in height and 11 to 16 years old. The green areas are due to the relative high intensity of the HV channel, which is strongly correlated with the amount of biomass. The L-band HV channel shows the biomass variations over the entire region. Most of the green areas, when compared to the forest cover maps are identified as black spruce trees. The dark blue and dark purple colors show recently harvested or regrowth areas respectively."

6.3 Interpretation Based on Scattering Models

The next higher level of complexity involves an understanding of the scattering mechanisms present. Van Zyl introduced an unsupervised classifier in which image pixels are assigned to classes of "odd bounce", "even bounce" and "diffuse" scattering mechanisms . This is based upon the principle that scatterers of simple geometrical structure have primarily a co-pol response, but the number of bounces or reflections that the radar signal experiences creates a recognizable phase difference between the HH and the VV channels (the relative phase changes by 180° for every bounce). Van Zyl developed a simple mathematical test to separate each pixel into these three classes .

Another set of scattering models based on physical principles was introduced by Freeman and Durden . Taking a tree on rough ground as a generic scatterer, the radar energy backscattered by the canopy, the trunk and the ground are modelled and used to categorize naturally occurring scatterers. A mathematical procedure was developed that computed the percentage of each type of scatterer in each pixel. The method is similar to that of van Zyl, except that a physical model is used to separate scattering mechanisms in the data, rather than a purely mathematical rule.

When faced with a large number of measured parameters, classifiers work better if the parameter set can be transformed into an orthogonal set, and the dimensionality of the set reduced to those parameters containing meaningful information (i.e. removing noisy parameters). Eigenvalue methods can be used to advantage, and it is helpful to use



scattering models that are independent of the scene content. One of the latest methods of parameter selection is based on an eigenvalue decomposition of the coherency matrix developed by Cloude and Pottier Cloude decomposition), where the parameters of polarimetric entropy, polarimetric anisotropy and alpha angle are calculated from the eigenvalues and eigenvectors of the matrix.

Entropy (H) represents the randomness of the scattering, with H = 0 indicating a single scattering mechanism and H = 1 representing a random mixture of scattering mechanisms, i.e. a depolarizing target. Values in between indicate the degree of dominance of one particular scatterer. The angle is based upon the eigenvectors and is a number indicative of the average or dominant scattering mechanism. The lower limit of = 0° indicates surface scattering, = 45° indicates dipole or volume scattering, while theupper limit of

= 90° represents a dihedral reflector or multiple scattering. Another

parameter that provides useful scattering information is anisotropy, a parameter based upon the ratio of eigenvalues, which indicates multiple scatterers.

7 Classification Algorithms Classification algorithms are generally grouped into supervised and unsupervised methods, although some algorithms combine features from each group. In the supervised case, a specialist identifies terrain classes in a scene, and class means and/or boundaries are identified in parameter space that serve to separate the classes. This is called "training", and the training data can be chosen from the scene itself, or from previously acquired scenes that possess similar characteristics. After the training, the algorithm automatically assigns classes to each pixel based on the predetermined class means or boundaries.

In a basic unsupervised classifier, the algorithm has no prior information of the scene content or of the terrain classes present. The algorithm examines the parameter space for each scene, and assigns classes and boundaries based on the clustering of pixels. Sometimes, the classes and boundaries can be based upon physical models, e.g. . In either case, the operator must identify each class manually after the class assignments.

The supervised classifiers have the disadvantage of requiring operator input, and the classes obtained tend to be scene specific. The unsupervised classifiers sometimes yield classes whose physical meaning is uncertain. In the next few subsections, an example of an unsupervised and a supervised classifier are given, which have been applied to polarimetric radar data. Finally, a promising new classifier is outlined, which combines the best features of the two previous types.

7.1 Unsupervised Classification Based on H / A / Parameters

In any classifier, the choice of parameters is important, and in the case of polarimetric radar data, content-independent scattering models can be used to get parameters that provide reasonable class separation. A current example is the H / A / set of parameters derived from an eigenvalue decomposition of the coherency matrix. The H / A /



algorithm was developed by Cloude and Pottier, who showed that terrain classes sometimes produced distinct clustering in the H / plane .

The H / plane is drawn in Figure 7-1. The observable alpha values for a given entropy are bounded between curves I and II (i.e. the shaded areas are not valid). This because the averaging of the different scattering mechanisms (i.e. averaging of the different eigenvectors) restricts the range of the possible a values as the entropy increases. As H and are both invariant to the type of polarization basis used, the H / plane provides a useful representation of the information in the coherency matrix .

Figure 7-1: The H / plane showing the model-based classes and their partitioning. A

description of the classes (Z1 - Z9) is given in the text.

The bounds shown in Figure 7-1 (Curve I and Curve II) show that when the entropy is high, the ability to classify different scattering mechanisms is very limited. An initial partition into nine classes (eight usable) has been suggested by Cloude and Pottier , and is shown in Figure 7-1. Classes are chosen based on general properties of the scattering mechanism and do not depend up on a particular data set. This allows an unsupervised classification based on physical properties of the signal. The class interpretations suggested by Cloude and Pottier are as follows (see for more details):

Class Z1: Double bounce scattering in a high entropy environment Class Z2: Multiple scattering in a high entropy environment (e.g. forest canopy) Class Z3: Surface scattering in a high entropy environment (not a feasible region

in H / space) Class Z4: Medium entropy multiple scattering Class Z5: Medium entropy vegetation (dipole) scattering Class Z6: Medium entropy surface scattering



Class Z7: Low entropy multiple scattering (double or even bounce scattering) Class Z8: Low entropy dipole scattering (strongly correlated mechanisms with a

large imbalance in amplitude between HH and VV) Class Z9: Low entropy surface scattering (e.g. Bragg scatter and rough surfaces)

It is important to note, however, that the boundaries are somewhat arbitrary and do depend upon the radar calibration, the measurement noise floor and the variance of the parameter estimates. Nevertheless, this classification method is linked to physical scattering properties, making it independent of training data sets. The number of classes needed as well as the usability of the method depends upon the application. Additional interpretation of the classes is given in , where a small change in the class boundaries is proposed.

The third variable of polarimetric anisotropy has been used to distinguish different types of surface scattering. The H / A-plane representation for surface scattering is given in Figure 7-2, where the shaded region is not feasible. The line delineating the feasible region can be calculated using a diagonal coherency matrix with small minor eigenvalues

2 and 3, with 3 varying from 0 to 2.

Figure 7-2 Types of surface scattering in the Entropy/Anisotropy plane.

Introduction of the anisotropy to the feature set represents a third parameter that can be used in the classification. One approach is to simply divide the space into two H / planes using the green plane shown in the 3-D space of Figure 7-3, one side for A 0.5 the other side for A > 0.5. This introduces 16 classes if the H / planes are divided according to Figure 7-1. Note that the upper limit of H is restricted when A > 0, as shown in Figure 7-2.



The H / A / -classification space, given in Figure 7-3, now provides additional ability to distinguish between different scattering mechanisms. For example, high entropy and low anisotropy ( 2 3) correspond to random scattering whereas high entropy and hanisotropy (

igh 2 >> 3) indicate the existence of two scattering mechanisms with equal

probability.

Figure 7-3: Illustration of how an A = 0.5 plane (green) creates 16 classes from the

original 8 H / classes shown in Figure 7-1. This gives 16 regions in the Entropy / Anisotropy / space for use in an unsupervised classifier.

The three parameters H, A and are based on eigenvectors and eigenvalues of a local estimate for the 3x3 Hermitian coherency matrix ("Hermitian" means a square matrix that has conjugate symmetry - it has real eigenvalues). The basis invariance of the target decomposition makes these three parameters roll invariant, i.e. the parameters are independent of rotation of the target about the radar line of sight. It also means that the parameters can be computed independent of the polarization basis.

Estimation of the three parameters H, A and allows a classification of the scene according to the type of scattering process within the sample (H, A) and the corresponding physical scattering mechanism ( ). The data need to be averaged in order to allow an estimation of H, A and (without averaging, the coherency matrix has rank 1), which has the benefit of reducing speckle noise .

An example of the clustering of pixels from a sea ice SIR-C scene is shown in Figure 7-4a . The H/A plane shows evidence of clustering into two and possibly three classes. Figure 7-4b shows the distribution of H/ values for a white spruce field; the target shows a dominant dipole scattering ( about 45°), with a high value of entropy H of



about 0.8, indicating rather heterogeneous scattering. Figure 7-4b was produced on CCRS's Polarimetric Workstation (PWS).

Figure 7-4a Scatter plots showing distribution of SIR-C ice data over the H / A /

classification space (Scheuchl)

Figure 7-4b Scatter plots showing distribution of SIR-C ice data over the H / A /

classification space.

7.2 Supervised Bayes Maximum Likelihood Classification

An alternative to the model-based approach is to define classes from the statistics of the image itself. The classes are defined by an operator, who chooses representative areas of the scene to define the mean values of parameters for each recognizable class (hence it is a "supervised" method). A probabilistic approach is useful when there is a fair amount of randomness under which the data are generated. Knowledge of the data statistics (i.e. the theoretical statistical distribution) allows the use of the Bayes maximum likelihood classification approach that is optimal in the sense that, on average, its use yields the lowest probability of misclassification .



After the class statistics are defined, the image samples are classified according to their distance to the class means. Each sample is assigned to the class to which it has the minimum distance. The distance itself is scaled according to the Bayes maximum likelihood rule.

Bayes classification for polarimetric SAR data was first presented in 1988 . The authors showed that the use of the full polarimetric data set gives optimum classification results. The algorithm was only developed for single-look polarimetric data, though. For most applications in radar remote sensing, multi-looking is applied to the data to reduce the effects of speckle noise. The number of looks is an important parameter for the development of a probabilistic model.

The full polarimetric information content is available in the scattering matrix S, the covariance matrix C, as well as the coherency matrix T. It has been shown that T and C are both distributed according to the complex Wishart distribution . The probability density function (pdf) of the averaged samples of T for a given number of looks, n, is

(7.1)

where:

<T> is the sample average of the coherency matrix over n looks, q represents the dimensionality of the data (3 for reciprocal case, else 4), Trace is the sum of the elements along the diagonal of a matrix, V is the expected value of the averaged coherency matrix, E{<T>}, and K(n,q) is a normalization factor.

To set up the classifier statistics, the mean value of the coherency matrix for each class Vm must be computed

(7.2)

where m is the set of pixels belonging to class m in the training set.

According to Bayes maximum likelihood classification a distance measure, d, can be derived :

(7.3)



where the last term takes the a priori probabilities P( m) into account. Increasing the number of looks, n, decreases the contribution of the a priori probability. Also, if no information on the class probabilities is available for a given scene, the a priori probability can be assumed to be equal for all classes. An appropriate distance measure can then be written as :

(7.4)

which leads to a look-independent minimum distance classifier:

(7.5)

Applying this rule, a sample in the image is assigned to a certain class if the distance between the parameter values at this sample and the class mean is minimum. The look-independence of this scheme allows its application to multi-looked as well as speckle-filtered data . This classification scheme can also be generalized for multi-frequency fully polarimetric data provided that the frequencies are sufficiently separated to ensure statistical independence between frequency bands .

The classification depends on a training set and must therefore be applied under supervision. It is not based on the physics of the scattering mechanisms, which might well be considered a disadvantage of the scheme. However, it does utilize the full polarimetric information and allows a look-independent image classification.

Note that the covariance matrix can also be used for this type of Bayes classification. The coherency matrix was chosen for the simple reason of compliance with the H / A / -classifier described in the previous section.

7.3 A Combined Classification Algorithm

Both unsupervised and supervised methods described above have their weaknesses. For the H / A / -classification, the thresholds are somewhat arbitrary and not the entire polarimetric information can be used due to the inability to determine all four angles that parameterize the eigenvalues. The Bayes minimum relies on a training set or initial clustering of the data. However, each algorithm overcomes some of the shortcomings of the other.

Therefore, a combination of the two algorithms seems attractive . An improved classification can be obtained by first applying the H / A / unsupervised classifier to set up and cluster 16 initial classes, followed by the minimum distance classifier based upon the distribution of clustered parameters. The distribution can be taken from the complex Wishart distribution, and iterations can be used to optimize the class separation boundaries , , .



Figure 7-5: Combined Entropy / Anisotropy / - minimum distance classifier

The combined algorithm is outlined in Figure 7-5. It can be viewed as an unsupervised algorithm, as the initial classification is unsupervised. However, as the iterations refine the cluster means and boundaries, the final classes should be scrutinized and assigned labels based upon a physical interpretation. Note that while the initial clustering is made in the H / A / domain, the minimum distance classification is performed using the coherency matrix directly. After the Bayes classification, the clusters may overlap in the H / A / domain. The classifier results do depend upon the number and diversity of classes input to the Bayes classifier, so it is always useful to experiment with different initial classes.

An example of the results of the combined H / A/ Bayes classification algorithm is given in Figure 7-6. Four sea ice types, three water classes and four land classes have been extracted from an April 1994 SIR-C image off the west coast of newfoundland . The level of detail of the extracted ice types is an indication of the power of computer classification of polarimetric radar data.

Classification algorithms can include a segmentation algorithm in which neighbouring pixels that have common characteristics are grouped together prior to the assignment of classes. If done properly, segmentation can significantly improve the classification results

.



Figure 7-6: Classification of land, ocean and ice types from a SIR-C polarimetric C-band scene off the West coast of newfoundland .

Did you Know?that many classification algorithms are in use and more are still being developed, because the success of the algorithms are very dependent upon the sensor characteristics, and even upon the scene content? Some of the common tools developed include the method of principal components, maximum likelihood estimation (MLE), optimal Bayesian methods, maximum a posteriori estimation (MAP), clustering methods, neural networks, minimum distance and parallelepiped methods and Markov random fields.

8 Polarimetric Interferometry SAR interferometry has been successfully used to make a topographic map of the surface of the Earth. However, there is uncertainty as to whether the radar returns come from the actual ground surface, or from a higher point such as the canopy of a forest. By investigating the interferometric properties of the polarimetric data, some information can be gained on where the scattering is coming from, as the polarization signatures of the



vegetated canopy and the ground are quite different and can be separated using polarimetric data analysis. In the ideal case, information can be obtained on both the height of the surface and on the height of the trees, as well as parameters of the scattering volumes in between .

When two polarimetric images are obtained that satisfy the usual interferometric conditions of baseline and time lapse, the complete polarimetric/interferometric information is stored in three 3x3 complex matrices, the coherency matrix of each image, and the analogous matrix formed from the scattering vector of Image 1 times the scattering vector Image 2 . Cloude and Papathanassiou develop a phase-preserving polarimetric basis transformation that allows them to form interferograms between all possible elliptical polarization states. Then they develop an optimization procedure based on singular value decomposition, which is used to find the polarization of Image 1 and the polarization of Image 2 that maximizes the interferometric coherence between the images. Most likely, the maximum coherence is obtained when the polarization of the two images is the same. The optimization finds polarizations that reduce the effect of baseline and temporal decorrelation, although if the temporal decorrelation is high, the procedure does not help significantly, as the coherence will remain low independent of polarization.

Furthermore, they develop a modified coherent target decomposition method, so that when combined with the coherence optimization procedure, the optimum scattering mechanisms can be found that lead to the best differential phase measurements (i.e. the highest coherence). The interferometric phase difference leads to the height difference between the physical scatterers possessing these mechanisms. The decomposition helps to understand the structure of the canopy of forests, by separating the return that comes from the upper and lower parts of the trees, or from the ground.

Looking at some quantitative aspects of the technology, Papathanassiou and Cloude use a forest model involving a random volume of scatterers situated over a ground scattering model. Their model involves 6 parameters: the vegetation height, the topographic phase at the ground level, the mean volume extinction coefficient (attenuation in dB/m that is related to canopy density) and three ground to volume scattering ratios (at 3 analyzed polarizations). When six measurements of coherence magnitude and angle (at the three polarizations) are obtained, the model can be "inverted", i.e. solved for the model coefficients given the radar observations. This is done using a non-linear optimization procedure, which finds the model parameters that fit the data best in the mean squared sense. The quality of the results and their physical interpretation are monitored by viewing the complex coherence of the interferogram as a function of polarization (which affects mainly the ground to volume scattering ratio). Ideally, the complex coherence forms a straight line in the complex plane as polarization is varied, and the intercept with the unit circle gives the topographic phase angle (i.e. bald-Earth terrain height - see Figure 6 of ). They analyze data from an L-band airborne radar, and find that the rms difference between measured and radar-estimated tree heights to be 2.5 m. They show that longer radar wavelengths give a longer, more accurate coherence line in the complex plane (see Figure 2 in ), and that the use of multi-baselines adds additional



information to solve for the model coefficients . In this way, a more accurate estimate of the forest height, canopy density (biomass), stem biomass and ground height may be obtained.

Although the analysis techniques are still being developed, there is some promise that the technology can be used to improve quantitative remote sensing applications such as

crop monitoring, mapping of clear-cut areas, deforestation and burn zones, land surface structure for geological analysis, damage assessment and land use, hydrology (soil moisture, flood assessment), land mine detection , and ocean and coastal monitoring (sea ice, oil spills).

A recent snapshot of progress in the field can be found in the five papers on the topic presented at IGARSS in 2002:

1. T. Mette, K. P. Papathanassiou, I. Hajnsek and R. Zimmermann, Forest Biomass Estimation using Polarimetric SAR Interferometry, pp. 817-819.

2. D. Kasilingam, M. Nomula and S. Cloude, A Technique for Removing Vegetation Bias from Polarimetric SAR Interferometry, pp. 1017-1019.

3. H. Woodhouse, S. Cloude, K. Papathanassiou, J. Hope, J. Suarez, P. Osborne and G. Wright, Polarimetric Interferometry in the Glen Affric Project: Results and Conclusions, pp. 820-822.

4. S. R. Cloude, Robust Parameter Estimation Using Dual Baseline Polarimetric SAR Interferometry, pp. 838-840.

5. M. Tabb, T. Flynn and R. Carande, An Extended Model for Characterizing Vegetation Canopies Using Polarimetric SAR Interferometry, pp. 1020-1022.

as well as the January 2003 Frascati Workshop on Applications of SAR Polarimetry and Polarimetric Interferometry .

9 Applications of SAR Polarimetry Apart from the SIR-C Mission, radar polarimetry has been limited to a number of experimental airborne systems. Thus the data sets available for analyses are limited and those with sufficient ground truth data to support significant research efforts are even more rare. A number of geoscience applications have been studied by remote sensing specialists and the results are promising, especially for terrain classification. The number of these airborne data sets available for distribution and analyses is increasing and ENVISAT with its multi-polarization capability is also providing more data for analysis. RADARSAT-2 and other spaceborne systems with it's multi-polarization and polarimetric modes will be supplying more data in the near future and thus the future for polarimetric applications development looks bright.



We discussed in the sections above how the polarimetric data can be used to generate multi-polarization products, such as HH, HV, and VV intensity images as well as making use of the full capabilities of the polarimetric data.

For some applications the availability of multi-polarization data may be enough to solve the problem, such as discriminating water from land and ice for mapping applications. In other cases, the use of the full capabilities of the polarimetric data to produce polarimetric parameters will be necessary. We are just beginning to exploit and understand SAR polarimetry for geoscience applications and the ongoing research and development efforts are expected to increase our knowledge and therefore use of polarimetric SAR data.

The following are some examples of the use of multi-polarization and polarimetry for SAR applications. The material selected was chosen on the basis of availability and suitability as an example for that particular application. In general the material was chosen from published work with the references provided. The material is not meant to necessarily be the best or most recent example as new results continue to be published.

9.1 Agriculture Applications

9.1.1 Introduction

The use of SAR imagery for agricultural applications has been studied extensively in particular because it is possible to acquire data at various times during the growing season. Single channel SAR data have been found to provide less information than multi-spectral optical data. This can be often overcome with a temporal series of SAR observations. As the crops grow and mature the backscatter characteristics change and these variations which depend on the crop can be used as the basis of crop discrimination.

The backscatter from agricultural targets is composed of surface scattering from the soil, volume scattering from the plants, and a soil-vegetation interaction term. The relative contribution of each component is a function of system and target parameters. In general, at C-band, the return is composed of a combination of these components with the soil surface term dominating early in the growing season and the vegetation volume term dominating during the peak growth period. At the end of the growing season, a mixture of the component returns is generally present with surface and soil-vegetation interaction terms being the dominant ones. This makes information extraction difficult as the soil or the crop may be the target of interest and other components produce "noise" which adds significant error to the estimation process. Once again multi-temporal observations help, but difficulties persist.

Research to date has demonstrated that the additional information in polarimetric data (both magnitude and phase) can help to increase the information content for agricultural applications thereby decreasing the need for multi-temporal imagery.

Two examples of such work are given on the following pages:



• Soil conservation: Soil tillage and crop residue • Crop productivity / Within field variation

9.1.2 Soil Conservation: Soil Tillage and Crop Residue

Soil conservation is a major concern in agriculture. Tillage practices have direct bearing on the potential for wind and water erosion, and soil quality, especially as it relates to the maintenance of soil organic matter. The ability to monitor the type of tillage, and amount of residue is important for soil conservation. Tillage affects surface roughness (as a function of implements used and number of passes) and the amount of residue , ,

. Due to the sensitivity of radar backscatter to field characteristics including surface roughness, polarimetric data may prove very useful for monitoring soil tillage and crop residue.

There are a number of polarimetric parameters found to be useful for discriminating soil tillage/residue. Highlighted here are the use of Co-polarization Signatures and Co-polarization Phase Difference.

9.1.2.1 Polarimetric Signatures

Polarization signatures are a graphical method of visualizing the backscatter response of a target as a function of incident and backscattered polarizations. Polarization signatures can be used to give a graphical presentation of the backscattering characteristics and can therefore be useful in differentiating target characteristics. In this example, this is shown in relation to variations in tillage and residue cover.

Co-polarization plots were obtained from SIR-C imagery for fields with varying tillage and amounts and types of residue in a study by McNairn et al.

A) Tilled Field with Little or No Residue

The following co-polarization plots were obtained from C-band (Figure 9-1) and L-band (Figure 9-2) imagery for tilled fields with varying amounts and types of residue. Incidence angles were between approximately 42 and 50 degrees .



A) Pea Residue (25% residue cover)

B) Lentil Residue(25% residue cover)

C) Canola Residue (40% residue cover)

D) Wheat/Barley Residue (20% residue cover)

E) Sunflower Residue (40% residue cover)

Figure 9-1. C -Band co-polarization signatures, tilled field with little or no residue (from ).

The smoothest fields, those with the finest residue have a maximum response at VV polarization (Orientation Angle of 90°). Backscatter was approximately equal at all linear polarizations for the canola, wheat/barley and sunflower residue fields, suggesting that these fields appear rougher.

A) Pea Residue (25% residue cover)

B) Lentil Residue(25% residue cover)

C) Canola Residue (40% residue cover)

D) Wheat/Barley Residue (20% residue cover)

E) Sunflower Residue (40% residue cover)

Figure 9-2. L-Band co-polarization signatures, tilled field with little or no residue. (from ).

In the L-Band example, fields that had been tilled or had very fine residue cover exhibited responses typical of surface scattering. For these targets, maximum response is at an Orientation Angle of 90° and the target appears flat relative to the wavelength. For these fields, the low pedestal heights(0.18-0.24) indicate minimal depolarisation, hence confirm that surface scattering is dominant. These surfaces are not rough enough and do not have enough vegetative material to cause significant multiple or volume scattering. The difference between VV and HH backscatter is much more pronounced at L-Band than at C-Band, since at this longer wavelength, these surfaces appear much smoother.

B. No-Till Residue Fields with Multiple Scattering

The following co-polarization plots were obtained from C-band (Figure 9-3) and L-band (Figure 9-4) imagery for no-till fields with varying amounts and types of residue. (from

)



Plots for C-Band (Figure 9-3) with the exception of (a) exhibit a saddle type shape typical of double bounce scattering. The pedestal height in these co-polarization plots was larger and thus indicates that greater depolarization was occurring on the no-till fields as compared to the tilled fields with low residue cover. The pea residue field (Figure 9-3a) shows a response similar to that for the field with pea residue that had been tilled (Figure 9-1a). Comparison of these two figures suggests that very fine residue has little effect on radar response as this target appears "smooth" at C-Band.

A) Pea Residue B) Lentil Residue C) Canola

Residue

D) Wheat/Barley Residue

E) Sunflower Residue

Figure 9-3. C-Band co-polarization signatures, no till fields with multiple scattering. (from ).

The co-polarization plots for L-Band imagery are significantly different when compared to those at C-Band. Relative to C-band the double bounce scattering is substantially reduced with a VV peak often present, indicating significant surface scattering for wheat/barley, and sunflower residues.

A) Pea Residue B) Lentil Residue C) Canola

Residue

D) Wheat/Barley Residue

E) Sunflower Residue

Figure 9.4. L-Band co-polarization signatures, no till fields with multiple scattering (from ).

A full discussion of polarimetric plots and other polarimetric parameters related to differentiating tillage and field residue is given in McNairn et al (PDF format).

9.1.2.2 Co-Pol Phase Difference (PPD)

The Co-polarization Phase Difference is a polarimetric parameter that may be useful for characterizing backscattering mechanisms. For instance, a single bounce (or odd bounce) scatterer will have a relative phase difference between HH and VV of 0° in the FSA For a double bounce (or even bounce) scatterer, the phase difference will be 180°. If the basis convention is changed to the BSA there is a further sign change, which adds 180° to the phase difference. As an example, bare soils are surface scatterers, and generally have a mean Co-polarized Phase Difference equal to 0° with a small standard deviation.



Ulaby et al. suggested that much of the information content provided by the Co-polarized Phase Differences lies in the distribution of these differences (as expressed by the standard deviation) e.g., a rough plowed field has a phase distribution that is broad when compared to that for a smoother disked field.

As shown in the study by McNairn et al. , the Mean Co-polarized Phase Difference was found to be close to zero for most fields with residue and so provided little useful information . Standing senesced crops did show phase differences significantly greater than 0° with the mean phase differences varying between the fields where multiple scattering is believed to occur. In terms of tillage practices, mean phase differences for fields could not be used to distinguish between the presence or absence of tillage and residue types, although differences were found between standing senesced crops and harvested fields. For example, the standing senesced corn and sunflower fields tended to have much higher mean phase differences varying between -30° and -130° for C-Band and -30° and -90° for L-Band. The field based phase distribution data can be used to differentiate tilled low residue fields from no-till (high residue) fields. The standard deviation of the phase differences for fields with low residue cover was less than 30o; the standard deviation for no-till fields exceeded 45°. These results are consistent with those reported by Ulaby et al. . An example figure showing the distribution of fields with various Mean Phase Differences is given as Figure 9.5 (modified from ).

Figure 9-5. C-Band field based co-polarized phase distribution does vary as a function of residue characteristics (modified from McNairn et al. ).

9.1.2 Whiz Quiz Question: How would the polarization phase difference (PPD) compare for a bare field and a standing corn field?



Answer: The PPD would have a mean close to zero with a small standard deviation for the bare field. The corn field would have a mean PPD different from zero with a larger standard deviation.

9.1.3 Crop Productivity/Within Field Variation

eristics, climatic

is a

Crop productivity depends on numerous factors including soil charactvariables and crop management practices. Crop biomass, green leaf area and green leaf duration are indicators of crop condition and potential yield.. The extent to which biomass and Leaf Area Index (LAI), can be effectively monitored using microwave imagery is an ongoing area of research. The sensitivity of SAR data to crop conditionfunction of imaging parameters such as wavelength, incidence angles and polarization, as well as parameters such as crop type and phenological stage (e.g. size, distribution, orientation and dielectric properties of component parts of the canopy).

In the following, two examples of the use of polarimetric data for crop condition monitoring are presented (from the work of McNairn et al. ):

1. the use of imagery in multiple polarizations to separate regions in a field with variations in crop condition.

2. the ability to discern scattering mechanisms associated with zones of crop condition variability using the H/A/ algorithm developed by Cloude and Pottier

.

9.1.3.1 Within Field Variation as related to Polarization

etric C-SAR The ability to determine variations within a field is illustrated using polarimdata acquired over Southen Ontario on June 30, 1999 as described by McNairn et al. . Imaging polarization combinations examined included the four linear transmit-receive polarizations (HH, VV, HV, and VH), as well as two circular transmit-receive polarizations (RR and LR).

A winter wheat field is used to illustrate the mapping of in-field variations(Figure 9-6a). A simple RGB image (R=VV, G=HV, B=HH) shows regions of low backscatter. Yield monitor data obtained two weeks following the SAR acquisition showed that these low backscatter areas corresponded to yields less than 70 bushels per acre (BPA).



Figure 9-6. a) C-band image of winter wheat image (R=VV, G=HV, B=HH ); b)

classified yield monitor data, bushels per acre (BPA), c) classified SAR data differentiating low and high yield zones (Noetix Research Inc., 2001)

It is noted that imagery at C-Band in HH alone could not have been used to separate the zones of different productivity. (Figure 9-7). Imagery in the linear cross-polarization (HV) was found to show the greatest contrast between the higher and lower productivity zones (4.1 dB), and this was followed by imagery in VV, RR, and LR polarizations showing differences of approximately 2 dB.

Figure 9-7. Backscatter at linear and circular polarizations for lower and higher producing zones of white winter wheat (from ).

The areas of low yield within the wheat field identified using the three linear polarizations agreed reasonably (77%) with the low yield areas identified by the yield monitor data.



A) Area of Agreement (Higher Yield) 77% B) Area of Agreement (Lower Yield) 77% C) "Error" (omission/comission) 23% Figure 9-8. Percent agreement between SAR classification and yield monitor data .

9.1.3.2 Scattering Mechanisms and Within-Field Variation

Relating backscatter values to crop condition is not always straight forward. An area of high biomass within a wheat field for example, may have lower backscatter or a higher backscatter relative to an area of lower biomass depending on the phenological stage of a crop and/or environmental conditions (including background soil moisture) at the time of image acquisition. For example, in a wheat field with high volumetric soil moisture, low biomass areas will have higher backscatter than the high biomass area. The opposite can be true given low volumetric soil moisture.

Polarimetric classification algorithms such as those based on Cloude and Pottier's H/A/ can be used to identify the scattering mechanism and thus help in the interpretation of the observed backscatter.

Polarimetric C-SAR data were collected near Indianhead, SK using the CV-580 platform. Several polarizations were synthesized from the complex data. The polarizations used in the unsupervised classification including HH, VV, HV, RR, RL and linear polarizations with 45° and 135° orientations. The resulting map created 6 productivity zones over three crop types (Figure 9-9).

In one study performed by McNairn et al. polarimetric C-SAR data were collected near Indian Head, SK in June 2000. Several polarizations were synthesized from the complex data, including two circular polarizations (RR and RL). Linear polarizations were synthesized by choosing an ellipticity angle ( ) of zero and by varying the orientation angle ( ) at 45° increments from 0° to 180°. Incidence angles over the test site were between 42° and 46°. The SAR image was classified into sixteen clusters using seven of these polarizations as input and a K-Means algorithm (Figure 9.9). The



polarizations used in the unsupervised classification included HH, VV, HV, RR, RL and linear polarizations with = 45° and = 135°. These seven images were used as input to classify the wheat crops into six classes representing three growth zones: very healthy growth (zone 1); average growth (zone 2); poor growth (zone 3).

Figure 9-9. Productivity zones generated from an unsupervised classification of images for HH, VV, HV, RR, RL and linear polarizations with = 45° and = 135° for wheat (1), canola (2) and peas (3), June 28, 2000 .

The three growth zones representing high to low biomass for the wheat fields were used as a mask to extract the H/ parameters of Cloude and Pottier. The H/ plane for a high biomass site is presented in Figure 9-10. In general, regions 1, 4, and 7 identify regions dominated by multiple scattering, regions 2, 5,and 8 dominated by volume scattering, and regions 3, 6, and 9 by surface scattering.

Figure 9-10 suggests that the backscatter from high biomass wheat is dominated by volume scattering. Figure 9-11 was derived from the zone of average growth and again, volume scattering by the canopy is the dominant mechanism. In Figure 9-12 the zone of poor growth, where crop biomass is low, is dominated by surface scattering [McNairn, Personal Communication].

Area 24: wheat Line 0 Pass 0 0 Cloude Alpha ( ) vs Entropy (H) - Density Histogram



A = Multiple Scattering B = Volume Scattering C = Surface Scattering

D = Low Entropy E = Medium Entropy F = High Entropy

Entropy Anisotropy

Average 0.81 0.43 42.04 17.51

Standard Deviation 0.03 0.07 2.65 2.89

Figure 9-10. H / plane with bounds and partitioning showing a high biomass area within the wheat field






Entropy Anisotropy

Average 0.75 0.53 41.34 16.39


Figure 9-11. Scattering as shown in the H/ plane for a medium biomass area within the spring wheat field.






Entropy Anisotropy

Average 0.74 0.44 35.52 15.27


Figure 9-12. Scattering as shown in the H/ plane for a low biomass area within the spring wheat field.

9.2 Sea Ice Applications

9.2.1 Introduction

Synthetic Aperture Radar imagery is well suited to Sea Ice mapping and monitoring applications. This was a significant driver for the development of RADARSAT-1. RADARSAT-1 is used operationally by Canada as well as several other countries for the mapping and monitoring of sea-ice.

However, data from single-channel SARs, such as the one on RADARSAT-1, are limited in their application to sea ice monitoring especially outside of cold winter conditions and



in marginal ice zones. Interpretation and analysis difficulties include the ambiguity between water and ice at low incidence angles and/or in high wind conditions, confusion between water and thin ice, masking of ice signatures under wet (spring) conditions, and ice type identification. The following sections illustrate how polarimetric SARs can provide additional information for addressing these difficulties in interpretation and analysis.

9.2.2 Polarimetric Analyses for Sea-Ice

Polarimetric SAR data can be used to create a variety of output products including multi-polarization intensity images as well as polarimetric parameters. Images acquired with the various combinations of polarizations on transmit and receive can be displayed on single channels or in various combinations including ratios and false colour composites. Figure 9-14 shows images acquired in each of the three linear polarizations as single channel intensity images and combined into a false colour composite. The imaged areas is in the Labrador Sea off the coast of Newfoundland with ice and open water.

Figure 9-14. C-band false colour composite and single channel intensity images from SIR-C for an ice infested region of the Labrador Sea off the coast of newfoundland. The data were acquired on April 18, 1994 with incidence angles ranging from 26 to 31 degrees. (from )



The complex data can also be used to generate polarimetric signatures as well as polarimetric parameters which can be used to aid in interpretation and understanding of the scattering mechanisms. Polarimetric discriminants can also be generated and used for classification purposes. The following material illustrates these approaches for sea ice applications.

9.2.3 Ice-Water Ambiguity

At steep incidence angles, especially under high wind conditions, confusion can often occur between open water and sea ice in imagery acquired by single channel SARs such as RADARSAT-1 or ERS1/2. Imagery from multi-polarization SARs can be used to greatly reduce this confusion in two different ways: Due to the minimal backscatter from the water in the cross-polarization (HV or VH), imagery acquired at these polarizations can be used to improve discrimination between the water/ice/land classes: The land and to some degree the ice both experience volume scattering giving rise to a cross-polarized return Figure 9-15 illustrates this for the same area of the Labrador Sea as shown in Figure 9-14.

Figure 9-15. Single channel intensity C-band images from SIR-C of the Labrador Sea illustrating the improved contrast of the first-year ice/water boundary of the HV channel due to a lack of multiple scattering from the water surface (from ).



Figure 9-16 demonstrates how a ratio of HH /VV can be used to achieve similar results as the different scattering characteristics of the two targets at HH and VV can be used to improve the contrast compared to any single channel.

Figure 9-16. Ratios between images of Labrador Sea acquired by SIR-C show the advantages of the co-polarization ratio for improving the contrast of the first-year ice/water boundary (from ).

Polarimetric decomposition techniques can be used to generate polarimetric discriminators that can be used to aid interpretation or to use for classification. Figures 9-17 and 9-18 show examples of the contrast between ice and water that is visible in C- and L-band images with particular improvements visible in the use of anisotropy at C-band and the entropy at L-band.



Figure 9-17. C-band entropy (H), anisotropy (A), and alpha-angle ( ) images for the Labrador Sea demonstrating the improved contrast of ice/water using the anisotropy parameter (from ).



Figure 9-18. L-band entropy (H), anisotropy (A), and alpha-angle ( ) images for the Labrador Sea demonstrating the improved contrast of ice/water using the entropy parameter (from ).

9.2.4 Ice Structure and Type

Polarization signatures generated from the scattering matrix can be used to interpret the scattering properties of the target helping to understand the roughness, polarization dependence, and scattering mechanisms for that ice type. Figure 9-20 shows C-band co-polarization signatures for smooth first year ice with varying snow cover and for young and ridged ice. Note, there is less of a peak at VV for the ridged ice due to roughness effects and the reduced polarization dependence in the ice. This is partly due to plates of thin ice layers in the snow giving rise to differential HH and VV responses.



Figure 9-20. C-band Co-polarization signatures for a) young and ridged ice and b) for smooth first year ice with different snow cover properties (from ).

The use of polarization signatures for ice type interpretation can also be demonstrated by comparing signatures for new, grey, rough grey, and desalinated sea ice types which represent a time series in terms of evolution and development. Figure 9-21 shows these polarization signatures and demonstrates the migration of the peak response from HH to VV which is related to the reduction in the dielectric constant of the ice surface over this time period. It is noted that the polarization response changes once again towards an HH peak as the ice further evolves, becomes rougher and desalinated.

Figure 9-21. Co-polarization C-band signatures of new, grey, rough grey, and desalinated sea ice types from scatterometer measurements. Note the change in the peak polarization response as the ice ages from new to desalinated ice types (from ).



9.2.5 Sea Ice Classification

The ability to perform robust and unambiguous ice type classification is critically important for operational applications and is one of the limitations of single channel SARs. Polarimetric SARs offer the potential of improved classification accuracy due to the increased information content of the additional polarizations and the phase data. Sea-ice classification methodologies for polarimetric SAR's are being developed and the results are demonstrating improved separability with the polarimetric response at both C- and L-bands. An example for C-band data acquired by the CV-580 off PEI in March 2001, is provided in Figure 22. It was found that while the multi-polarization data provided better class separability than single polarization data the fully polarimetric data provided enough information to provide an effective classification of the ice types.

Colour Assignment

Colours Description

blue Smooth, thin Fast Ice

red Fast Ice with rough surface

magenta Rough RYI

cyan Rough, thicker FYI

white Rough, thicker FYI / Land

green Land

dark green Land

black Land

grey Classes not used for comparison in



the scatterplots (white dark green and black)

Figure 9-22. Classified image of the north shore of PEI using CV-580 polarimetric C-band SAR data using a complex Wishart classifier with 8 initial classes and 12 iterations (from ).

Polarimetric decomposition was used to illustrate the extra information content of the polarimetric data. Figure 9-23 shows the Entropy (H), Anisotropy (A), and Alpha( )-Angle for these data. The bottom image shows land, while fast ice is highlighted in the central image and rough first-year ice in the top image. Smooth ice shows the lowest entropy due to homogenous scattering whereas land has higher entropy. The anisotropy is lower for land and higher for ice providing the best contrast for land/ice and between ice types. The alpha-angle is low for smooth ice, which along with low entropy demonstrates surface scattering dominates. For rougher first year ice both the alpha angle and entropy are higher which, as demonstrated in the cross-polarization channel, indicates that more volume scattering is occurring.



Figure 9-23. Entropy (H), Anisotropy (A), and Alpha ( )-Angle for images from C-band data acquired with the CV-580 off the North shore area of PEI in March, 2001. The bottom image shows land, while fast ice is highlighted in the centre image and rough first-year ice in the top image (from ).

The use of fully polarimetric multi-frequency SAR such as the JPL AIRSAR is very



attractive because the additional frequencies allow more target information to be extracted. For example the varying penetration characteristics allow further separability between ice types especially among multi-year ice types and first-year ice types. This can be illustrated by the use of multi-frequency polarimetric decomposition techniques to identify surface versus volume scattering target characteristics. Figure 9-24 shows the classification of surface versus volume scattering using this technique while Figure 9-25 provides the classification results. Future spaceborne SAR systems are planned at both C- and L-band which are expected to make multi-frequency polarimetric SAR imagery available in the not too distant future.

Did you Know?Arctic sea ice data for 1953-1998 indicate that 6 of the 10 years of smallest ice extent have occurred since 1990, with increased regional variability in recent years. Summer 1998 was particularly unusual:. Open water formed earlier than in prior years, and the ice extent in September was 25 percent smaller than during the previous record minimum. For more information: CRYSYS


http://www.msc.ec.gc.ca/crysys/


Figure 9-24. Total power images of the Freeman-Durden decomposition of C-L, and P-band AIRSAR data showing surface versus volume scattering (from ).



Class Assignment To Ice Types

Class Colours Description

ThI / SFYI blue new forming thin ice / Smooth first year ice

RFYI / R orange green black

Ridged first year ice / Rubble

CFYI pink pastell green Compressed First Year Ice

MYI white grey Multi Year Ice

Figure 9-25. Ice type classification results using data acquired by the JLP AIRSAR. An entropy based polarimetric decomposition using eight classes and 12 iterations (from

).

9.2.5 Whiz Quiz Question: What is the difference in scattering mechanism between new ice and multi-year ice? How would you use polarimetry to determine this? Answer: New ice is dominated by surface scattering whereas multi-year ice has a large volume scattering component. The pedestal height would indicate the degree of roughness, the HV would help identify volume scattering and the polarimetric



classification of scattering mechanisms could be used to determine areas of volume scattering.

9.3 Forestry There is an ongoing need to understand and quantify the state and dynamics of forests both regionally and globally. Required information includes forest type mapping, identification of clear cuts, and recent burns, and the extraction of a variety of biophysical parameters such as total biomass and tree age.

Use of polarimetric data is anticipated to improve the detection of structural differences between forest canopies and thus to help in forest type mapping and provision of additional information for other forest management applications. Figure 9-26, a multi-polarization false color composite of an area east of Ottawa, illustrates the increased information content for forest identification.

Figure 9-26. . False colour composite image of the Mer Bleue study site near Ottawa , showing six forest areas with different species composition (C-SAR data, Red: HH, Green: HV and Blue: VV).Courtesy of CCRS.

9.3.1 Frequency Dependence

The usefulness of SAR data for the extraction of biophysical parameters is most dependent on frequency. Microwaves at lower frequencies such as L-band (2.0-1.0 GHz)



and P-band (1.0-0.3 GHz) are better able to penetrate the canopy and interact more extensively with its structural components (leaves, branches, trunks). Microwaves at higher frequencies (C-band, 3.8 - 7.5GHz) tend to interact primarily with the upper portion of the canopy. The sensors at higher frequency therefore have a more limited potential use in the discrimination of variations in dry biomass whereas it is expected that L-band data and P-Band data can be used to discriminate increasing biomass variations.

9.3.2 Polarization Dependence

Le Toan et al., 1992 showed that the dynamic range of backscatter over uniform pine stands had a strong variation with polarization e.g., the dynamic range for such data obtained at P-band for the HV polarization was approximately 15 dB, at HH approximately 11 dB, and at VV approximately 4.8 dB. At L-band, the dynamic range was reduced , with a dynamic range of approximately 8.6 dB at HV, approximately 5.3 dB at HH and approximately 4.6 dB at VV. At C-band the dynamic range was significantly lower, with data for the HV polarization showing the greatest range (approximately 4 dB) and those in HH and VV polarizations showing a dynamic range of only 2dB.

It is believed that the backscatter for the HV polarization at longer wavelengths can be more effectively used to characterize forest biomass as shown in the work of Dobson et al. (e.g. Figure 9-27.)

C-Band L-Band

Figure 9-27. Calibrated C-band and L-band backscatter as a function of total above ground biomass (tons/ha) of maritime pine and loblolly pine plotted on a logarithmic scale (from ).



9.3.3 Polarimetric Parameters

9.3.3.1 Co-polarization Signatures

Polarimetric data may provide unique information on forest canopies related in particular to canopy architecture and the consequent scattering mechanisms. Backscatter mechanisms include direct backscatter from branches (single bounce/volume scattering), backscatter from trunks (single bounce), scattering from branch-ground interaction (double bounce), scattering from trunk-ground interaction (double bounce), and direct backscatter from the ground (surface scattering). The relative contribution of each of these depend on the nature of the canopy and imaging parameters such as incidence angle and frequency. Components within the canopy (leaves and twigs) may play a significant role in the scattering and attenuation interactions depending on frequency. It is expected that use of polarimetric data analysis will help understand the nature of scattering within a canopy.

An example modelled co-polarization signature representative of a hardwood forest at L-band shows that backscatter from a heavy forest cover at HH and VV polarizations is similar with that at VV being slightly lower, suggesting the dominance of multiple branch scattering combined with a weak double bounce component (Figure 9-28a). The pedestal height indicates a large unpolarized component in the backscatter return indicative of multiple scattering .

Modelling of the same canopy with a branch density that is an order of magnitude lower results in a polarization signature that is characteristic of a dihedral corner reflector (double bounce) (Figure 9-28b), suggesting the dominance of trunk-ground scattering mechanisms for this forest with fewer branches. The lower branch density also results in a significantly lower pedestal height due to a lower unpolarized component, indicating a smaller amount of volume scattering

P = Normalized Power

Figure 9-28. Co-polarization signature at L-band of, a) a hardwood forest and b) a hardwood forest with a branch density that is of an order of magnitude less than (a) (from

).

Figure 9-29 shows the modelled co-polarization signatures for a forested area and a clear cut area. The clear cut area has a lower pedestal height indicative of a lower unpolarized



component due to greater direct return from the ground surface and a smaller amount of volume scattering. The stronger return in the VV case compared to that at HH is indicative of surface scattering.

P = Normalized Power

Figure 9-29. Co-polarization signature for, a) forested area and b) clear cut (from ).

9.3.3.2 Polarization Phase Difference

The Co-polarization Phase Difference can be useful in understanding the scattering mechanisms for a particular target. Single bounce scatterers generally result in a phase difference close to 0o whereas ideal double bounce scatterers have a phase difference of

180°. In the example from the work of LeToan et al. for a forest canopy the Co-polarization Phase Difference has been correlated with stand age (Figure 9-30), and to a lesser extent with forest stand height, and trunk biomass In this case, the mean Co-polarization Phase Difference obtained for the clear cut area ( = 6.8°) indicates that the backscatter is largely a function of surface scattering from the ground. The mean value for the mature forest stand is much higher (approximately 66°) and has a larger standard deviation (90°) than that obtained for the clear cut area (70°). This is indicative of volume scattering.



F = Frequency of occurence (%), D = Polarization phase difference (Deg)

Figure 9-30. Histograms of P-band Copolarization Phase Differences between HH and VV polarizations ( ) for (I) a clear cut area and (II) a 46 year old pine forest plantation ( ).

9.4 Hydrology The use of SAR for hydrology applications has a long history and has been extensively investigated for soil moisture estimation, snow mapping, and flood/wetland mapping. These applications have not realized operational or commercial success as of yet partly due to limitations of single channel SAR systems such as RADARSAT-1. Polarimetry has a potential to improve the use of SAR data for these applications helping to operationalize these applications. Some examples of this are provided in the following sections.

9.4.1 Soil Moisture Mapping

9.4.1.1 Introduction

Soil moisture is an important parameter for many natural resource applications such as hydrological modeling, stream flow forecasting, and flood forecasting. SAR data are well suited for estimating soil moisture due to the dependence of the dielectric constant on moisture at these frequencies. As described in the work of Dobson et al. , for a given



soil condition (roughness or texture) radar backscatter was found to be linearly dependent on volumetric moisture (mv ) in the upper 2 to 5 cm of soil with a correlation r 0.8 to 0.9 ( = A+Bmv) .

The presence of vegetative cover introduces another level of complexity to soil moisture mapping due to the interaction of the microwaves with the vegetation and soil. Depending on the amount of vegetation present, its dielectric properties, height and geometry (size, shape and orientation of its component parts) the sensitivity of microwave backscatter to volumetric soil moisture may be significantly reduced. The ability to effectively map soil moisture can be improved by judicious selection of imaging parameters such as incidence angle, wavelength and polarization.

Imaging at steep incidence angles is often chosen to minimize the contributions to backscatter of soil roughness and attenuation associated with above ground biomass. Backscatter is significantly affected by surface roughness at incidence angles beyond about 40°. Hence, imaging at lower incidence angles is recommended for soil moisture estimation.

C- Band in the HH polarization was found to be most sensitive to soil moisture and least sensitive to surface roughness in the presence of low biomass. In agricultural fields, as the vegetative component over the soil increases, longer wavelengths (e.g., L-band ) are needed to permit continued monitoring of soil moisture during the growing season

. For shrubby or forest covered areas only longer wavelengths such as L-band or better yet P-band provide the penetration necessary for soil moisture estimation. Polarimetric data may help by reducing and/or accounting for the effects of roughness and/or vegetation on the soil moisture estimate.

9.4.1.2 Polarization Dependence

The ability to estimate surface soil moisture (for depths from 0 to 2.5 cm) using various polarizations and polarimetric parameters of SIR-C data was reported in . The data were collected over bare soil surfaces in Southern Manitoba during April and October 1994. Evaluation of the polarimetric data was confined to data at incidence angles from 33 o to 38o. Polarimetric parameters examined included synthesized linear and circular polarizations, total power, Co- and Cross-polarization ratios, pedestal height, and Co-polarization Phase Differences (Table 9-1)

Data acquired in both the HH and VV polarizations were highly correlated with soil moisture (r = 0.86 - 0.87), whereas those at HV were more poorly correlated (r =0.71). Multiple regression analysis using various combinations of linear polarizations showed no significant improvement in soil moisture estimation.

The co- and cross polarization ratios were not as effective for soil moisture estimation as the data in HH or VV polarizations, although they have been used successfully elsewhere to help reduce the impacts of soil roughness and vegetation for data acquired at shallower incidence angles .



The mean Co-polarized Phase Difference (r = -0.35) was not significantly correlated to soil moisture. This parameter is often used to differentiate between scattering mechanisms, which in this case were relatively invariant and indicative of surface scattering (single bounce). Therefore, the low correlation was not unexpected.

The SIR-C data obtained in southern Manitoba show that information in the images at various polarizations and polarimetric parameters are highly inter-correlated (Table 9-2). Backscatter in HH, VV, and RL showed highest correlation with soil moisture.

Table 9-1. Correlation between radar backscatter and surface (0-2.5 cm) soil moisture (from ).

C-Band Polarimetric Parameter

Correlation Coefficient

(r)

Simple Linear Correlation Results

HH Backscatter 0.86*

VV Backscatter 0.87*

HV Backscatter 0.71*

Total Power 0.87*

Co-Pol Ratio (HH/VV) 0.53*

Cross-Pol Ratio (VV/HV) -0.79*

Cross-Pol Ratio (HH/HV) -0.74*

Co-Pol Pedestal Height 0.82*

RL Backscatter 0.88*

RR Backscatter 0.68*

Co-Pol Phase Difference -0.35

Multiple Linear Correlation Results

HH + VV 0.87*

HH + HV 0.86*

VV + HV 0.87*



HH + VV + HV 0.79*

* statistically significant at p < 0.05

Table 9-2. Correlations between field averaged backscatter recorded for each linear and circular polarization on bare fields (from ).

HH VV HV Pedestal Height RL

VV 0.99*

HV 0.86 0.86

Pedestal Height 0.94 0.92 0.94

RL 0.98 0.98 0.85 0.91

RR 0.73 0.77 0.90 0.76 0.78

* correlation (r) coefficients

Examples of Co-polarization Signatures for backscatter from wet and dry soils are shown in Figure 9-13. It was found that for wet soils, where little penetration into the soil occurs, the intensity is highest in VV and the pedestal height is low (0.2) indicating a smooth surface with surface scattering predominating. For drier soils the maximum at VV is no longer present although the pedestal height is still 0.2 indicating a smooth surface. The increased microwave penetration of the soil under dry conditions accounts for the similarity of the responses in the HH and VV polarizations.

Figure 9-31. Co-polarization signatures from SIR-C data for, a) wet soils (30.5% moisture, surface roughness (rms) 17.4 mm) and, b) dry soil (17.7% moisture, surface roughness (rms) 13.2 mm (from ).



9.4.2 Snow Mapping


Estimation of snow cover and snow properties is important for input to hydrological applications such as modeling and forecasting runoff from snow melt as well as understanding changes in local, and regional climatic regimes. Typical snow parameters derived from radar data include, snow extent, snow water equivalence (SWE), and snow state (wet/dry).

The backscatter response from a snow covered surface is a function of numerous interrelated factors including the dielectric properties of snow, snow temperature, density, age, and snow structure. The backscatter received from a snow covered surface includes contributions from surface scattering at the air/snow interface, volume scattering from the snow layer, and scattering from the snow/ground interface. The extent to which backscatter is a function of surface scattering or volume scattering is governed by the properties of the snow. When a snow pack is dry (at a temperature less than 0°C) microwaves easily penetrate the snow (Figure 9-32) and the backscatter is largely a function of snow depth and snow density.

= Penetration Depth (m) mv = Volumetric Liquid Water Content (percent)



Figure 9-32. Snow penetration depth as a function of liquid water content and microwave frequency (from ).

Depending on the microwave frequency and snow depth, backscatter from a dry snow pack may largely be a function of the ground surface characteristics underlying the snow pack due to the relative transparency of dry snow at microwave frequencies.

At C-band, wet snow is an absorber and dry snow is transparent making the estimation of SWE difficult. Polarimetry may help by providing additional information about the snow pack helping to improve the SWE estimate.

9.4.2.2 Polarimetric Signatures

One study [ ] used the C-SAR on the Environment Canada CV-580 to investigate the polarimetric properties of a snow pack. Figure 9-33 shows snow pit profiles for 4 dates during the winters of 1997-1998 and 1998-1999. Figure 9-34 shows Co-polarization Signatures derived from the C-SAR data for these sites on these 4 dates. It can be seen that on the wet snow date, March 6, the signature is indicative of a smooth surface (pedestal height = 0.2) with little polarization dependence.

Figure 9-33. Snow pit profiles for 4 dates (From ).

The polarization signature for the Dry Snow (December 1, 1997) shows a polarization signature with a higher pedestal (0.4) due to the penetration to the ground surface, which is rougher. In this case, the peak at the VV polarization is indicative of surface scattering. As the snow pack develops and horizontal ice layers form within it, the polarization



signature changes (as seen on March 12, 1998). The surface appears rougher with a pedestal height of 0.6. Significant backscatter is seen to occur at the HH and VV polarizations. The polarization signature is significantly different on March 9, 1999 where significant backscatter is seen in the HH polarization with much less at VV.

These examples show that the polarimetric signatures make it possible to extract more information from imagery of the snow-pack. It is not yet clear how this might improve SWE estimation.

December 1, 1997 (Dry Snow) March 6, 1998 (Wet Snow)

March 12, 1998 (Dry Snow) March 9, 1999 (Dry Snow) = Normalized V = Orientation Angle X = Ellipticity Angle

Figure 9-34. C-Band Co-polarization plots for selected snow packs derived from data acquired by the C-SAR on the Environment Canada CV-580 (from ).

9.4.3 Flood/Wetland Mapping


SAR imagery has proven to be very useful for flood mapping and for wetland vegetation classification. The dark returns from water contrast with the brighter ones from land and flooded vegetation thus making it possible to identify open flooded areas. This makes possible the determination of the extent of the flood although problems can occur when attempting to map flooded vegetation. Wetland vegetation also has a variety of shapes, sizes, and distributions, which can be used for discrimination between vegetation types.



The use of multi-temporal SAR data has been shown to be useful for wetland classification due to the seasonal changes in vegetation and water levels which affect the microwave backscatter. Polarimetric SAR data can be used to improve extraction of information for these applications.

9.4.3.2 Flooded Areas Figures 9-35 to 9-37 show various C-band images acquired by SIR-C of the Red River flood in 1994. There is a significant improvement in the mapping of the flooded regions using the HV image on April 11 compared to the HH image where most of the flooded area is delineated and the VV image where identification of the flooded region is difficult. On April 12, there is little such difference between images in the different polarizations. On April 16, the HH and HV images are very similar. These relative changes between images in the different linear polarizations show the value in the use of imagery in the various polarizations for flood mapping.

Figure 9-35. Linearly Polarized SIR-C C-Band images acquired on April 11, 1994 of the

Red River, Manitoba (from .

Did you Know?Wetlands are a key part of the ecosystem for maintaining both water quality and quantity. They are also prime breeding locations and thus are critical components for maintaining ecosystem health.


Red River, Manitoba. (from ).


Radar Polarimetry


76


Red River, Manitoba (from .

9.4.3.3 Wetlands

The use of imagery in multiple polarizations has been found to improve wetland classification when compared to the use of single channel data alone. Two classes may be confused in imagery of a particular polarization but separable in imagery at other polarizations. This is especially true for wetlands which have a mix of vertically oriented plants such as sedges, rushes, and grasses interspersed with shrubs and trees, which have a more random distribution of vegetative components.

An example C-SAR image of an area in the valley of the St. Lawrence River showing several classified wetlands is shown in Figure 9-38.


A = Marsh

B = Woody Marsh C = Shrubby / Herbaceous swamp

D = Marsh / shrubby Swamp E = Wooded Bog

Figure 9-38. False colour composite of C-SAR imagery acquired September 1, 1997

showing several wetland classes along the St. Lawrence River, Ontario: Red: HH; Green:HV Blue: VV. Courtesy of CCRS.

9.4.3 Whiz Quiz Question: How does multi-polarization aid in wetland mapping? Answer: The wetlands typically have vertically structured plants like rushes and sedges which can be separated using a combination of VV and HH responses. The cross-polarization can also help in delineating water from vegetated targets, especially under windy conditions during data acquisition.

9.6 Applications: Coastal Zone The coastal zone is a physically dynamic and ecologically sensitive environment which is subject to a variety of anthropogenic pressures (urban growth, industrial development, tourism) and natural (climatic induced) events resulting in significant coastal erosion. It is often densely populated and is a region of commercial, industrial, and recreational activity. It is an important environment to be monitored and managed effectively for sustainable use. Coastal applications that may benefit from the use of polarimetric SAR data include shoreline mapping, (in support of coastal change mapping) and substrate mapping (environmental sensitivity mapping/habitat mapping). The following sections provide examples of how multi-polarization or polarimetric data might help with these applications.

Shoreline Detection Substrate Mapping

9.6.1 Shoreline Detection

The extraction of shoreline information from SAR imagery is possible due to the large contrast between backscatter from the water and from the land: If the water is relatively calm, it acts as a specular reflector (low backscatter) and this contrasts well with land that typically has higher backscatter. The delineation of shorelines can become more difficult



due to wind induced surface roughness on the water which reduces the contrast between the water and land at the interface between the two. At moderate to high wind conditions and at shallow incidence angles, the microwaves interact primarily with the surface capillary waves resulting in increased backscatter as the surface roughness increases. This is particularly true for imagery in the VV polarization where poor contrast occurs between wind roughened water and land. Imagery in the HH and HV polarizations shows less sensitivity to wind induced surface roughness. Figure 9.44 (imagery in VV) shows high backscatter due to wind induced sea surface roughness and a relatively low water-land contrast. In the HH image, the backscatter from the sea surface is lower than that in the VV image although the surf results in a zone of higher backscatter along the shoreline. The image in the HV polarization shows the best contrast between land and water. Polarimetric data can be used to produce imagery with maximal contrast [ ] between selected features. This is seen in the sharp boundary between land and water in Figure 9.44d.

Figure 9-44. Water and land contrast as a function of polarization a) HH, b) VV, c) HV,

d) maximum contrast image (Courtesy of CCRS).

9.6.2 Substrate Mapping

Thematic maps of tidal and near-shore terrestrial areas provide a basis for coastal zone sensitivity assessment and for other applications such as military reconnaissance



mapping. Imagery in a single polarization is generally inadequate for discriminating coastal zone features. Multi-polarization or polarimetric imagery can be used to effectively discriminate the structural differences of various coastal features. Figure 9.46 shows an inter-tidal flat in the Minas Basin of the Bay of Fundy. The tidal flat is gently sloping (1 to 2°) and consists of friable sandstone, mudflats and gravel and boulder deposits along the channel. In the multi-polarization colour composite, regions corresponding to various substrates can be separately identified. The green tone associated with the area of sandstone indicates the dominance of the cross-polarized return that is typically associated with volume or multiple scattering. The mud flats show a very low backscatter return in images in the HH and HV polarizations, while the gravel and boulder deposits (white) are indicative of high backscatter return seen in imagery at all three of the polarizations.

Figure 9-46. RGB composite (R-HH, G-HV, B-VV) of tidal flat at Evangeline Beach, NS from CV-580 C-SAR data. Note: backscatter contrasts in the dry land area and the

tidal plane were enhanced independently (Courtesy of CCRS).



Polarimetric signatures for regions of different substrates within the tidal zone are shown in Figure 9-47. Each signature shows that backscatter is maximal at the VV polarization The mud flats exhibit a very low pedestal height (0.03), and the higher pedestal heights for sandstone and gravel suggest an increase of the unpolarized component due to rough surface scattering. A more prominent backscatter return in the HH polarization is evident in the area of the gravel/boulder substrate indicating significant double bounce scattering.

= Normalized

Figure 9-47. Polarimetric signatures for tidal zone substrates (Courtesy of CCRS). Surface types are (a) mud (b)sandstone and (c) gravel.

9.6.2.1 Polarimetric Classification Polarimetric classification according to scattering mechanism may provide additional useful information regarding target characteristics within tidal zones. Figure 9-48 shows a simple classification of the tidal flat using the method outlined by van Zyl (1989) . It classifies the dominant scattering behaviour of each pixel into one of three scattering classes: Odd Bounce scattering, Even Bounce scattering, or diffuse scattering.

Did you Know?The type of substrate along a coastline is important for environmental reasons such as susceptibility to erosion, oil spill remediation and habitat evaluation, as well as for military applications such as suitability as a landing site with respect to trafficability.



A = Sandstone B = Mud C = Gravel Red = Even (double) Green = Diffuse Blue = Odd

Figure 9-48. Unsupervised classification of scattering mechanisms (Courtesy of CCRS).

The classification results show that mud flats within the tidal zone are predominantly surface scatterers (Odd Bounce) characteristic of a smooth to slightly rough surface, sandstone areas are predominantly characterized by Odd Bounce scattering with a mix of Even Bounce and diffuse scattering. The gravel areas tend to have a high portion of Even Bounce scattering due to the presence of small boulders that act as corner reflectors.

9.6.2 Whiz Quiz Question: Why is imagery in the cross polarization better than that in VV for identifying the land/water boundary? Answer: Water is a surface scattering target with a very low backscatter at HV compared to land thus resulting in better land-water contrast. Also the VV polarization is more sensitive to wind induced surface roughness resulting in lower contrast between land and water.



9.7 Oceans

9.7.1 Introduction

SAR images can be used to detect and monitor a range of physical processes and phenomena, both natural and man-made that modulate the ocean surface roughness. Surface winds are the most important factor affecting ocean surface roughness. Rough surfaces typically have higher backscatter compared to smoother surfaces. The ocean surface roughness can be related to a number of atmospheric phenomena such as convective cells, atmospheric fronts, rain cells (Figure 9-49) and atmospheric gravity waves to name a few; and oceanic phenomena associated with currents, e.g., oceanic eddies, internal waves, water mass boundaries, and surface gravity waves. Other ocean surface features are related to either biogenic and/or anthropogenic ocean surface films, which damp small scale surface waves leading to a lower backscatter than that from surrounding areas.

Figure 9-49. a) Schematic sketch of the downdraft of a rain cell, spreading over the sea and causing roughening of the sea surface , b) Rain cells imaged by ERS-1, showing gust fronts (high backscatter) and areas where bragg waves are damped (low backscatter) by the ocean surface layer turbulence generated by heavy rainfall, (Source : http://www.ifm.uni-hamburg.de/ers-sar/).

The following sections will illustrate how multi-polarization and polarimetric SAR data and analyses can help with ocean applications including:

Study of Marine Winds Oil Slick Detection Ship Detection

9.7.2 Marine Winds



SAR images of the ocean surface often show the impact of atmospheric phenomena due to the interaction of the near surface wind field and the ocean surface roughness. In general, the higher the near surface wind speed the rougher the ocean surface becomes, resulting in increased radar backscatter and brighter image tones. This relationship is key to deriving wind information from SAR data.

The microwave signatures for ocean surface roughness with scales on the order of the radar wavelength are due mainly to Bragg scattering. Due to the increased sensitivity of the backscatter to the surface capillary waves, VV polarization is preferred for wind speed estimation when compared to HH. However, imagery obtained with HH polarization may be more suitable for monitoring other oceanic phenomena such as internal waves, currents, and bathymetry (as illustrated in Figure 9-50).

Figure 9-50. An illustration of polarization sensitivity to atmospheric and oceanic phenomena from real aperture radar data acquired at 13.3 GHz. a) This VV polarization image is dominated by atmospheric signatures, in this case wind speed variability and convective cells; b) Meanwhile, this simultaneously acquired HH polarization image shows evidence of oceanic phenomena, in this case internal waves (from ).

In general, for estimating information on winds and waves, the signal obtained in cross-polarized imagery is very low. This may result in the signal being close to or below the noise floor for spaceborne SAR systems, thus making the cross-polarized channel of little use for observation of marine phenomena. However, the potential of using imagery at HH and VV synergistically for wind and wave estimation has been demonstrated using C-SAR data from the CV-580 (Figure 9-51), as well as for estimation of the C-band co-polarization ratio, (Figure 9-52). The differences in the structures of the wave number spectra from the VV and HH channels, especially along the range wavenumber axis, illustrates the potential for improving ocean information estimation using imagery acquired at two polarizations. These studies showed that the C-VV and C-HH model functions are in reasonable agreement over the RADARSAT-2 incident angle range and that the Kirchoff-based C-band co-polarization ratio agrees well with observations. Thus, the dual channel, like polarization RADARSAT-2 mode may be attractive for ocean surface observation.



Interlook cross-spectrum of HH image Interlook cross-spectrum of VV image

Figure 9-51. An example of a SAR image spectrum of the same ocean wave field imaged using HH and VV polarization, illustrating the opportunity to improve the retrieval of ocean wave spectra by using dual polarizations. (graphic from CCRS for IGARSS 02 polarimetry workshop)

CV580,L3P3,27June2000-16:31,Lake Superior,Polarization Ratio,AziLines 2049:4096

A = boresight - 20° B = Far Edge of Nominal Swath C = CV580 boresight

Figure 9-52. Plot of C-band co-polarization ratio from C-SAR data acquired by the CV-

580 over a NOAA buoy on Lake Superior in June 2000, along with a Kirchoff-based scattering C-band co-polarization ratio (courtesy CCRS).



9.7.3 Oil Slick Detection

The SAR signal is sensitive to the roughness of the sea surface, which is modulated by wind speed and direction; imagery acquired at VV polarization is the most sensitive to wind speed variability. The suppression of the capillary waves by oil from either anthropogenic sources, such as an oil spill, or from natural biological slicks, reduces the surface roughness resulting in less radar backscatter and darker image tones. The detection of oil slicks has been found to be best in moderate wind conditions in the range of 3 to 10 m/s. Oil spill images are available from both HH (Figure 9-53) and VV polarization systems (Figure 9-54); examples are provided below.

Figure 9-53. RADARSAT-1 C-HH image of an oil slick off the coast of Wales (United

Kingdom), from February 1996. Source


http://ceos.cnes.fr:8100/cdrom-00b2/ceos1/satellit/ers/ew/cont_oil.htm


Figure 9-54. ERS-1 C_VV image of the same oil slick off the coast of Wales (United

Kingdom) from February 1996. Source: CEOS 2000

Although imagery in both VV and HH polarizations can be used for slick detection, the VVimagery is preferred as, in general, it offers a better signal to clutter ratio than other polarization choices (i.e., HH, VH, or HV). This is summarized in Table 9-3. Although VV is more sensitive than HH for slick detection, there may not be any advantage to using the co-polarized or cross-polarized signatures as oil-free and oil-covered surfaces tend to have similar contrast and polarization ratios (Figure 9-55) in these two cases. Slick thickness and the inability to differentiate oil slicks from "look-alikes" such as areas of low-wind, grease ice, or biological surfactants remain problematic.

Polarization Water Oil-covered Water

SAR noise floor Contrast

VV -20 dB -28 dB -30 dB 8 dB

HH -24 dB -32 dB -30 dB 6 dB

HV -30 dB -38 dB -30 dB 0 dB


http://ceos.cnes.fr:8100/cdrom-00b2/ceos1/satellit/ers/ew/cont_oil.htm


Table 9-3. Hypothetical radar backscatter values for water, oil-covered water, and the SAR noise floor illustrating the improved contrast at VV polarization for oil slick detection. (CCRS, Polarimetry Tutorial, IGARSS'02).

Co-pol Response Cross-pol Response

Co-pol Response Cross-pol Response

= Normalized V = Orientation Angle = Ellipticity Angle

Figure 9-55. C-band co-and cross-polarization signatures from SIR-C data acquired over an oil spill off the coast of Japan on April 16, 1994 showing little difference in slick-covered water (bottom) and open water (top), as suggested from polarization sensitivity analyses (CCRS, Polarimetry Tutorial, IGARSS'02).

9.7.4 Ship Detection

It has been demonstrated that RADARSAT-1 data in combination with an automated target detection system can provide operational detection reliability (up to 95%) using those beams that are best suited to ship detection. Ship detection using SAR relies either on the detection of the ship itself or detection of the ship wake. C band imagery in HH polarization is preferred for detecting the ship because the ship-sea contrast is usually higher for HH polarizations due to the increased scatter at VV by the surface capillary waves. This results in lower background clutter at HH polarization. Conversely VV is preferred for wake detection as the lower backscatter at HH decreases rapidly with



increasing incidence angle, resulting in ship wakes rarely being seen in HH polarized images. Figure 9-56 illustrates this using RADARSAT-1 and ERS-1 SAR imagery.



Figure 9-56(a & b). a) RADARSAT-1 C-HH image and b) ERS-1 C-VV image showing enhance ship detection at HH and better wake detection at VV .

Multi-polarization and polarimetric data are expected to allow the user to exploit various polarization combinations to optimize ship detection applications. For example for ship surveillance a VV and VH combination would be optimal as the VH channel provides point target information against a very dark clutter background. At the same time the VV polarization will provide adequate ocean surface backscatter to allow for wake analyses. Since the interaction mechanism between ship and sea is double bounce scattering it is expected that RR, or right-right circular polarization will also be a good polarization for ship signature enhancement.

Polarimetric data are expected to improve ship target detection and possibly classification. However it will only be suitable for ship tracking or perhaps surveillance in certain regions limited in size and strategically or commercially important for ship traffic, due to limited swath coverage. Polarimetric decomposition and classification by scattering mechanism is an exciting application of polarimetric data for ship detection. Polarization entropy is particularly promising, especially for incidence angles less than 60° where ships are only weakly visible in HH polarization images. This is clearly illustrated in HH and Polarization entropy images that show the enhanced ship-sea contrast in Figure 9-57. Since the incidence angles for the RADARSAT-2 sensor are less than 60°, the polarization entropy followed by circular polarization (RR), cross polarization (HV/VH), and HH polarization will provide the best opportunities for ship detection (Figure 9-58).

Figure 9-57. a) C-HH image and b) corresponding polarization entropy image of an area off the coast of Nova Scotia showing improved ship detection using the polarization entropy. Data from C-SAR on Canadian CV-580



Figure 9-58. Ship-sea contrast as a function of incidence angle for all linear polarization, RR polarization and polarization entropy (van der Sanden and Ross, [61]).

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