A Microwave Scattering Model For Wetland Environments

K. Clint Slatton¹, Melba M. Crawford¹, James C. Gibeaut², and Roberto Gutierrez²
(1): Center for Space Research, University of Texas at Austin
3925 W. Braker Ln., Suite 200, Austin, TX 78759-5321
(2): Bureau of Economic Geology, University of Texas at Austin
E-mail: slatton@csr.utexas.edu; Ph: (512) 471-5509; Fax: (512) 471-3570

1.0 Introduction
2.0 Scattering Model
3.0 Site Description
4.0 Data Characterization
5.0 Simulation Results
6.0 Conclusions and Future Work

1.0 Introduction

In the absence of significant vegetation cover, the surface-air boundary dominates the scattering of the incident SAR energy, but if vegetation is present it will attenuate the energy and introduce additional scattering. The model must therefore account for surface scatter, attenuation due to vegetation, and scattering (direct and multiple) from the vegetation. The most common methods for describing surface-only scatter are:

1. Small Perturbation Model (SPM),
   
2. Kirchhoff models - scalar approximation (KSA) and stationary phase (KSP) [Ulaby, Moore, and Fung 1986b],
   
3. Integral Equation Method (IEM) [Fung 1994], and
   
4. Semi-empirical Methods [Oh et al. 1992].

The SPM and Kirchhoff models apply to surfaces with specific roughness characteristics. The IEM model is a more complex model, but has the advantage of applying to a wider range of surfacesconfirm this statement. The semi-empirical model also applies to a wide range of surfaces, but requires extensive in situ surface measurements.

Models accounting for volume scatter and attenuation due to vegetation fall into two categories:

1. radiative transfer models and
   
2. wave approach models [Ulaby, Moore, and Fung 1986c].

The radiative transfer models can, in some formulations, account for higher-order scattering, but because they work with scattering intensity instead of EM field quantities, they cannot account for coherent enhancement of multiple scattering. The wave approach derives directly from Maxwell's equations and treats the vegetation as layered equivalent medium above the surface with scattering contributions from discrete elements and attenuation due to the dielectric of the equivalent medium.

These volume-scatter models have applied extensively to forested terrain, and in some cases the roughness of the surface has been incorporated using one of the mentioned surface-scatter models [Sun et al. 1991] and [Ferrazzoli and Guerriero 1995]. To date, the ability of these models to simulate SAR returns from wetlands has not been extensively studied.

For this work, we formulated a single, integrated scattering model to account for both rough-surface and volume scatter. Various in situ measurements were taken of the surface and vegetation characteristics in the study area. Based on those measurements, the surface fell within the range of validity of the KSA model (see Figure 1). A volume-scatter model based on the wave approach and distorted Born approximation was used to describe the scattering from the vegetation layer. The approach was closely based on the model proposed in [Saatchi, et al. 1994]. The surface-scatter model was integrated with a volume-scatter model by introducing extra scattering and attenuation terms [Chauhan et al. 1991].

The study area consisted of a region of wetlands along the Texas coast. The salinity variations produce fresh, brackish, and saline marshes[1]. Polarimetric SAR data were collected by the NASA/JPL AIRSAR sensor in 1995 and 1996 over Galveston Island and Bolivar Peninsula (see Figure 2). The marshes on these barrier structures are predominantly saline. Wetlands constitute a critical environment. They are valuable for their ability to act as a water catchment absorbing excess water and reducing the risk of flood to highlands.

2.0 Scattering Model

To accurately simulate the scattering of microwave energy from natural terrain, an integrated model that accounts for volume scattering, surface scattering, and interactions between the volume and surface scatterers is necessary. The basic volume-scatter models compute ground reflections assuming a perfectly smooth surface. Even in the presense of dense vegetation, surface scatter will be significant at small incidence angles and long SAR wavelengths, thus it is important to simulate it accurately by accounting for surface roughness.

For this work, a KSA surface scatter model was incorporated into a volume scatter model based on the wave approach by introducing a surface-only scattering term and roughness effects into the Fresnel reflection factors. In the random media portion of the model the mean electric field in the vegetation layer is computed using the Foldy approximation and a perturbation technique that is valid for sparsely distributed scatterers. The distorted Born approximation is then used to calculate the backscattering coefficients [Lang 1981], [Seker 1982], and [Lang and Sidhu 1983]. The vegetation layer is comprised of uniformly distributed scattering elements. Elliptical disks with specified dimensions and orientation statistics are used as scattering elements. Because the wetland study site contains very few trees, a single uniform layer of scatterers is sufficient for simulation. The disks can be adjusted to simulate a range of herbaceous vegetation by adjusting the semi-major and -minor axes as well as the thickness and orientation. The scatterers are assumed to occupy a small fraction of the total volume of the vegetation layer and have a small albedo (lossy).

The region above the scattering layer is treated as a vacuum with relative permittivity =1. The particles in the scattering layer have uniform dimensions and orientations. Each element has a volume and relative complex permittivity . The effective relative permittivity of the scattering medium (particles plus empty space in between) is . The lower half space represents the ground, or a water surface in the case of inundation, and has relative permittivity . The wave propagation vector denotes the direction of the incident wave, and polarization vectors and denote the orientation of the linearly polarized waves. Three scattering mechanisms are considered: (1) direct scatter from the vegetation, (2) direct-reflected scattering between the ground and scatterers, and (3) surface-only scattering. The model allows the formulation of a double ground reflection term, but its effect is neglibally small and is typically omitted [Saatchi et al. 1994].
The expressions for the polarized backscattering coefficients are
, (1)

where
, (2)

, (3)

. (4)

, and (5a)

. (5b)

The scattering amplitude relates the size, shape, and orientation of a scatterer to the scattered field. The scattering amplitude for thin elliptical disks is
, (6)

where
, (7)

, (8)

, (9)

, (10)

. (11)

Here,
= scattering amplitude
= low frequency, or dipole, approximation for a thin disk
= Fourier transform of the cross-sectional shape function of the disk
= relative complex dielectric constant of the scattering disk
= scattering disk's effective area (area relative to incident and scattered waves)
= Bessel function of the first kind with argument of
= component of
= component of
= semi-major axis of elliptical scattering disk (prior to any rotation of the disk through the elevation and azimuth angles, lies along the axis)
= semi-minor axis of elliptical scattering disk (prior to any rotation of the disk through the elevation and azimuth angles, lies along the axis)
= thickness of elliptical scattering disk
= unit normal vector to the surface of the scattering disk

3.0 Site Description

For this study, the vegetation classification used by the University of Texas' Bureau of Economic Geology (BEG) is adapted with minor modifications. The BEG classification map was derived from a combination of 1:66,000-scale color-infrared aerial photography flown in 1979 and field verification. A section of a BEG-classified map that corresponds to a portion of the study area is shown in Figure 4.

4.0 Data Characterization

1996 AIRSAR of saline marsh on Bolivar Peninsula: C-HH, L-HH, and L-VV

Many of the plants in the study area have annual growth cycles. They are typically senescent during the winter months and reach full maturity in late summer or early fall. There had been no recent precipitation at the time of acquisition, and the annual marsh plants had not reached their fully-mature heights or densities. In 1996, both 20 MHz chirp and 40 MHz bandwidth data were acquired. The 40 MHz chirp resulted in pixel spacings of 4 m in azimuth and 3 m in range, but only C- and L-band were collected get exact number of pixel spacings. Heavy precipitation occurred throughout the study area immediately prior to and during the acquisition. The annual plants were slightly more mature than in the April 1995 period. For both years, the L-band data broke out the meaningful environments better than C- and P-bands. The distribution of homogeneous areas in the 1995 L-band data was very similar to that of the wetland maps. The 1996 L-band data were also quite similar, but because the precipitation increased the extent of inundation beyond the proximal marsh.

The C-band data were strongly scattered by all environmental units and were sensitive to subtle, small-scale variations due to varying plant-species mixtures. The P-band data differentiate the environmental units well, but the data suffered from RF interference and uncompensated motion. The L-band data provided a compromise. Only L-band data were simulated because of their close correspondence to the wetland maps. Figures 5 and 6 show the L-band data that correspond to Figure 4.

Before the SAR data were used to characterize the four environmental units, the variability of was investigated. The data variation among the images (inter-image variation ) was examined by sampling values using 31 x 31-pixel windows over nearly homogeneous areas of open water in several images. Small differences in the mean values (~± 1 dB) are expected, even from perfectly calibrated images, due to slight differences in the water surfaces that are sampled in the various images. The values fell within a ± 1 dB range for L-band. Therefore, values for the environmental units were sampled from various images over the study area without the need for a bias correction.

5.0 Simulation Results

While the model was fit to the data, care was taken to ensure that the assumptions of the surface scatter and volume scatter models were not violated, and that all input values were consistent with values measured in the field or reported by other investigators [Saatchi et al. 1994], [Dobson et al. 1985], [El-Rayes and Ulaby 1987]. Although no data were available for <15°, the simulated curves for that range of incidence angle are consistent with measured L-band values over grass lands reported by other investigators [Ulaby and Dobson 1989].

The integrated model has eleven input parameters that pertain to terrain and vegetation. The effect of any one of those parameters on is a dependent on the other values. As a result, several iterations could be required to achieve and acceptable match to the data in general. However, it was possible to reduce the number of trials using qualitative sensitivity analysis to determine which parameters dominated. It was found that as long as surface roughness and dielectric constants were within a range of reasonable values, their effect on was small. Small changes in elevation angles of the scatterers also made little difference. Parameters involving the size and shape of the scatterers were by far the most dominant.

5.1 Uplands
Figure 7 shows the simulated and measured backscatter data for the uplands environment. The upland simulation required the largest scattering disks. These larger disks represent the dense woody branches that form the center of shrubs found in this unit. The long axes of the disks were allowed to take on values uniformly in the range of ± 30° from vertical. This orientation represented the Spartina spartinea grasses and tall shrubs. Many of the shrubs were well over 1 m tall, but the scatterer-layer thickness was only 1 m. This is because the shrubs do not form a uniform cover, but rather a distribution of discrete plants. Therefore, their effective height over the ~ 8 m pixel posting is less than the average heights of the plants. The rms surface roughness in this unit was the second largest, and the surface correlation length was by far the shortest, indicating steep surface slopes. This is consistent with the observed terrain which was cattle roughened and pimpled with the dense bases of the Spartina spartinea plants. The scatterer density was relatively small because this unit is characterized by individual shrubs and clumps of grasses.

The simulation curves in Figure 7 show the uplands to be dominated by surface scattering for 0° <= <= 20°, and by the scattering elements for >= 20°. In the far range, becomes a weak function of because the effective cross section of the tall vegetation is nearly constant.

5.2 Transition zone
Moving from the uplands to the transition zone, the rms surface roughness and correlation length that were measured at the test site both increased, indicating a rougher, but more slowly varying surface (see Figure 8). As a result, the transition-zone simulation used a larger rms surface roughness and a larger correlation length. The small surface slopes indicated that this unit was very smooth. The scatterer density increased because individual shrubs gave way to a uniform layer of marsh grasses and succulents.

The SAR returns in the near range of the transition zone are stronger than in any of the other environmental units. The component terms from the simulation showed that this strong near-range return was almost entirely due to surface-only scatter. These simulated near-range values were compared with measured L-band over grasslands reported by Ulaby and Dobson [1989] and found to be roughly 5 dB stronger. The most probable explanation is that the transition zone surface is smoother than most inland grasslands. The low-energy tidal processes that supply the sediment to these marshes create extremely smooth surfaces. It is reasonable to assume that, despite some surface roughening by livestock, the transition zone is still very smooth at the L-band wavelength. For > 20°, the simulated curves become flatter because scattering is dominated by the scattering particles in that incidence range.

The simulated and values are less than they were in the uplands for > 20°. This occurs because both the semi-major and semi-minor axes of the disks are smaller. In addition, the disks are more vertically aligned in the transition zone because the elevation angles occupy only a ± 10° range. This is consistent with the short, straight marsh grasses observed in the transition zone. The simulation also captures the flat trend and the positive trend in the data, but it slightly overestimates the return .

5.3 Continuous marsh
The soil in this unit is continuously saturated, loosely-packed mud that leads to a very smooth surface. This fact was represented in the model by decreasing the rms surface roughness and increasing the correlation length relative to the transition zone. The scatterer density is less than in the transition zone, but the thickness of the scattering layer is much larger. The decrease in scatterer density and increase in scatterer-layer thickness are consistent with the distribution of biomass observed in these two environments[3]. The transition zone contained short marsh grasses and rhizomatous succulents; thus, a relatively large biomass was contained within a thin layer close to the ground. The continuous marsh contained taller marsh grasses, but without the understory succulents. In effect, the continuous marsh had less biomass per unit volume of vegetation than the transition zone.

Surface scatter dominates the simulated returns in the continuous marsh for <= 10°, but the returns are dominated by the scattering particles for > 10° (see Figure 9). Beyond the surface-dominated scattering, > for 10° < < 25°, and < for > 25°. Even though the vegetation in this unit is dominated by tall Spartina alterniflora plants, the best fit to the data was obtained using disks that had a wide range of elevation angles (± 30°), and whose long axes were aligned in a horizontal direction. This surprising result is probably a response to an increase in the horizontal cross section of the plants relative to their heights, as mentioned in section 4.2.3.3. Even though the vegetation had an increased horizontal component, the plants still appeared to be predominantly vertical. Although it is possible that an adequate fit to the data could have been obtained using vertically aligned scatterers, none was found.

The simulated and are both greater in the continuous marsh than in the transition zone for 10° < < 25°, if surface-only scatter is neglected. This is because both disk axes are larger in the continuous marsh simulation. The increased disk size represents the larger Spartina alterniflora plants. Once > 25°, the values diminish rapidly with increasing while the simulated values remain relatively flat. Typically, attenuation in thick scattering layers increases dramatically with due to the increasing path length through the layer [Lang and Sidhu 1983]. Because these scatterers are elliptical and have a predominant orientation, this attenuation rate is not the same for and . The values are considerably stronger than for > 25° as a result.

5.4 Undifferentiated marsh with tidal flats
This unit contains mostly Spartina alterniflora, but here it grows taller than in the continuous marsh and occurs in discontinuous patches among the inundated, barren mud flats. As a result, it was expected that in moving from the continuous marsh to the undifferentiated marsh, the scatterer size would increase slightly and the density would decrease. However, the scatterer size actually decreased, while the scatterer density and layer thickness both increased. This unexpected result may suggest that the 1995 SAR data, with its pixel spacing of approximately 8 m x 6 m, cannot resolve the individual patches of vegetation among the tidal flats.

The simulation curves for the undifferentiated marsh show a very strong near-range response followed by a steep decline that is typical for smooth surfaces and is similar to the transitional zone simulation (see Figure 10). In this unit, the scattering disks are aligned horizontally, and the measured is greater than the measured for 30° < < 45°, as in the continuous marsh. However, the disks in this unit are more circular and assume a wider range of elevation angles (± 40°), so the difference between and in this range of incidence angles is less than it is in the continuous marsh. As increases, the observed values increase slightly, with > for > 45°. This is probably due to a weak double-bounce effect between the smooth surface and the vegetation. The simulation fails to capture this rise in .

Neither polarization exhibited the steadily decreasing behavior that is typical for thick scattering layers, as seen in the curve for the continuous marsh simulation. Initially, this was surprising because the scatterer layer is thicker in the undifferentiated unit than it is in the continuous marsh. The reason for this was found to be a decrease in the volume occupied by the scatterers. In spite of the fact that the number density increased for the undifferentiated unit, the fractional volume that was occupied by the disks actually decreased because the volume of each disk was so much smaller ( ). As a result, a significant amount of the incident energy was able to penetrate the vegetation layer. This is why the simulation curves for this unit resemble scattering from a slightly rough effective surface instead of a medium or very rough surface.

The undifferentiated marsh was the most difficult unit to simulate. For most incidence angles, the two simulation curves fall within the spread of the data, but the simulated slightly underestimates the far-range data, and the simulated slightly overestimates the far-range data. The difficulty in fitting this unit is due to the switch in dominance between and in the incidence range containing the sampled data. It may be that the use of only one scatterer shape, uniformly and continuously distributed over a surface, cannot adequately simulate a terrain that is actually made up of patches of vegetation, which are discontinuous at scales comparable to the SAR pixel spacing.

6.0 Conclusions and Future Work

Scattering models which are physically-based on electromagnetic theory, such as the one developed for this study, are usually more difficult to implement than empirical models. However, they have some important advantages. Physically-based models formally relate scattering observations to physical scattering mechanisms. Compared to empirical models, physically-based models also allow a great deal to be learned about a study area's terrain and vegetation cover with relatively little field data.

There are some improvements that could be made to the current model. Computing the cross-polarization signal would more fully characterize the scattering behavior of the study areas, and using more than one layer of scattering particles would enable to model to account for vertical variations in the vegetation cover. Allowing for realistically-shaped scattering particles would make the model more accurate. Other researchers have obtained improved simulations using very complex shapes, that closely resemble actual plant components, by parameterizing the scattering particles with shape functions [Stiles et al. 1996]. This could also be done for the vegetation in the study area because many vegetation samples were collected from the test site during the 1996 SAR acquisition. Future flight lines should be oriented so that the wetland environmental units were imaged at a wider range of incidence angles. Those data, along with future in situ field measurements, will allow the model to be accurately fit for a wider range of incidence angles, thus better constraining the simulation. Also, a detailed sensitivity analysis would make it possible to explicitly relate certain model inputs to the observed patterns.

[1] The definitions for saline (>18 ppt dissolved salts), brackish (1-18 ppt dissolved salts), and fresh (<1 ppt dissolved salts) used in this research are based on the classification of the study area in the Bureau of Economic Geology (BEG)'s submerged lands report [White et al. 1985]. Values may differ slightly from more general-purpose sources
[2] Silt refers to average soil grain sizes between 0.0625 mm and 0.0039 mm.
[3] Actual biomass was not measured. This decrease in scatterer volume is simply consistent with field observations.

Last Modified: Wed Apr 14, 1999
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