## Physical Fundamentals

The interaction of radar energy with agricultural targets is different from that with visible-infrared energy. Interpretation of radar data requires an understanding of the physical processes involved in the scattering of electromagnetic waves by objects that are smaller, comparable to, and larger than the wavelength. Therefore modeling these processes is relatively difficult because simplifying mathematical assumptions often results in a lack of correspondence with physical reality. In an agricultural context, the radar signal can interact with vegetation or soil only, but more likely there is scattering within the canopy and the return signal is from multiple sources.

The attenuation of the radar signal and the interaction with vegetation and soil depends on a number of system and target parameters. The frequency (or wavelength), polarization, incidence angle, look direction, and resolution of the sensor all influence the sensor capabilities; important target parameters are surface roughness, complex dielectric constant, structural geometry, slope angle, and orientation of the target. The distinction between system and target parameters is convenient for understanding radar interactions. However, all parameters interact to influence each other. For example, the roughness of the target as seen by the sensor is dependent on the wavelength, the local angle of the sensor, which is a function of both the look angle of the sensor and the slope angle of the target, and the look direction, which affects the geometry of the target in question.

### System Parameters

Polarization Radar instruments distinguish the polarization of the transmitted and the received electromagnetic waves. In microwave remote sensing, "horizontal" polarization (H) means that the electric field vector of the electromagnetic wave is oriented parallel to the earth's surface, while "vertical" polarization (V) means that a wave arrives at the interface with a vertical component (but a horizontal component also exists). When the polarization of the transmitting antenna is the same as for reception of the signal, one speaks of like-polarization (HH or VV), and otherwise of cross-polarization (HV or VH). Until the launch of ENVISAT, all satellite systems used linear combinations in either the horizontal (HH in the case of RadarSat and JERS-1) or vertical directions (VV in the case of ERS-1 and ERS-2).

Crop structure has a strong effect on the polarization of the backscat-tered waves. Generally, if the target has a strong vertical structure (e.g., grain crops), scattering is dominated by the returns from the underlying ground surface. Modified by vegetation density and radar frequency, HH polarization tends to interact to a lesser extent with the crop than VV and penetrates more effectively to the underlying soil. Cross-polarized signals (HV or VH) depend on multiple reflections between the canopy and the soil to depolarize the transmitted signal. Experimental and modeling studies suggest that the ability to estimate soil and vegetation parameters will be enhanced significantly with the launch of fully-polarized SAR systems such as RadarSat-2 and ALOS (Bindlish and Barros, 2000).

Frequency The effect of radar frequency on backscatter is largely a function of the size and dielectric properties of the target. The dielectric constant of water, which constitutes 80-90% of plant matter and is present in the soil, differs markedly depending on radar frequency. As frequency decreases and wavelength increases, the size of the target components become smaller relative to the sensor, and the scattering surfaces appear "smoother," making scattering by vegetation elements less efficient.

In the presence of dense vegetation, at high frequencies or smaller wavelengths, radar backscatter is primarily a function of canopy scattering, and the soil has a minor impact. At lower frequencies or longer wavelengths, the impact of soil becomes greater as the radar signal penetrates farther into the canopy. It is usually believed that radars operating in X or K band (table 8.1) are not sensitive to soil moisture when crops are fully established, whereas L- and P-band radars penetrate crop and grass canopies even at the height of the growing season.

As a result of differential backscatter from cotton and alfalfa in Ku and C band, Moran et al. (1998) suggested that dual frequency would be useful in estimating vegetation status and soil moisture. Unfortunately, no spaceborne SAR system has yet been approved that would allow instantaneous measurements at two different frequencies.

Incident Angle The incident angle is defined as the angle between the incident radar beam and the vertical to the intercepting surface. In early studies using single-channel C-band radar, steeper incident angles (15-25°) were generally found to be more useful in estimating soil moisture in presence or absence of vegetation. In absence of vegetation and at steeper angles, the radar backscatter is affected to a lesser extent by surface roughness, but in presence of vegetation, the path length through and attenuation by the

 Band Frequency (GHz) Wavelength (cm) Ka 27-40 0.8-1.1 K 18-27 1.1-1.7 Ku 12-18 1.7-2.4 X 8-12.5 2.4-3.8 C 4-8 3.8-7.5 L 1-2 15-30 P 0.3-1 30-100

vegetation decrease. Conversely, at shallow angles (40-45°) the path length through the canopy increases, and so does the vegetation response. Consequently, backscatter measurements at different incident angles provide useful information about the relative contributions of soil and vegetation to total backscatter. Although SAR sensors have only one antenna that looks at the earth's surface from one direction, the scatterometers onboard ERS-1/2 and METOP have three and six antennas, respectively, that acquire instantaneous measurements at different incidence angles. This multiangle capability of scatterometers enables soil moisture and vegetation effects to be separated quite efficiently (Wagner et al., 1999a).

### Target Parameters

The important target characteristics influencing radar backscatter are geometry and dielectric properties. The dielectric constant, which is a measure of the relative effectiveness of a substance as an electrical insulator, ranges from as high as 80 for liquid water at low microwave frequencies to <4 for dry matter. Thus, in an agricultural environment, radar backscatter is a function of soil surface roughness and moisture content and, where vegetation exists, of crop type, phenological state, and vegetation water content.

Soil Radar measurements of bare soil surfaces are very sensitive to the water content in the soil surface layer due to the pronounced increase in the soil dielectric constant with increasing water content. For longer wavelengths, the backscatter coefficient may increase up to about 10-fold from dry to wet soil conditions. Although there is a very strong relationship between the backscatter measurements and the soil moisture content, the retrieval of soil moisture is a challenging task due to the confounding influence of surface roughness.

There are several empirical and theoretical models that describe back-scatter from bare soil in terms of the soil moisture and surface roughness (Fung, 1994; Dubois et al., 1995). Unfortunately, many studies found relatively poor agreement between modeled and experimentally observed radar responses. It has been suggested that the inadequate representation of surface roughness variations of real surfaces may be one of the reasons for this failure. Surface roughness is usually expressed in terms of the root mean square (r.m.s.) of height or, in the case of the more complex models, in terms of the autocorrelation function of the surface height variations. It appears that agricultural and other natural soil surfaces are relatively complex and often have a multiscale structure. That is why simple parameters such as the r.m.s. of height fail to adequately describe radar backscatter (Davidson et al., 2000). One way of working around this problem is to use change detection techniques that only interpret changes in soil moisture under stable surface roughness conditions.

Vegetation Crop type, crop phenology, and crop condition influence the architecture and dielectric constant of the canopy and thus radar backscat-ter. There are numerous studies related to crop discrimination using radar (Bouman and Uenk, 1992; Brisco et al., 1992; Ban and Howarth, 1999; Treitz et al., 2000). The ability to discriminate crop type and phenological stage with radars may be attributed to changes in both canopy geometry and plant biophysical parameters. The radar frequency and incident angle influence the relationship.

Radar backscatter from an agricultural field is normally not influenced just by the plants, but also by the underlying soil and by soil-plant interactions. As indicated in figure 8.1, there are three main contributions from a vegetation canopy: direct backscatter from the vegetation elements, multiple scattering from plants and soil, and the contribution from the soil surface. Accordingly, total canopy backscatter, a0, is formulated as the sum of three parts:

Figure 8.1 The interaction of radar with an agricultural target results in backscatter (1) directly from the crop, (2) from a combination of crop and soil, and (3) directly from the soil [from Brisco and Brown, 1998].

where a 0veg is the backscatter attributable to vegetation, a 0soil is the direct backscatter from the underlying soil surface, at is the one-way attenuation factor, and a 0int represents multiple scattering in soil and vegetation.

In many models the interaction term a 0int is neglected because multiple scattering by vegetation and soil is generally smaller than the direct contributions from the canopy and the soil. One such model is the Cloud Model proposed by Attema and Ulaby (1978), which assumes that the vegetation volume can be represented by a cloud of water droplets that are uniformly distributed throughout the volume. Although the Cloud Model does not take structural effects into account, it has been used with some success to empirically relate ground measurements of vegetation water content, vegetation height, and other crop parameters to backscatter measurements acquired with ground-based, airborne, or spaceborne radar sensors (Bouman, 1991; Taconet et al., 1994; Xu et al., 1996).

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