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Different approaches have been undertaken for the modeling of radar interaction with vegetation canopies. Some have relied on the experimental data to find the best fit for the assumed relationship (empirical/semi-empirical models). Others have sought to explain the phenomena which best represent the important scattering mechanisms during such interaction (phenomenological models). While the phenomenological models are based merely on an intuitive understanding of which scattering mechanisms should be important and therefore taken into account, another set of approaches have tried to model the full interaction between the microwave signal and whole vegetation layers (physical/analytical models).

i) Empirical/semi-empirical models.

Early attempts to model radar backscatter from vegetation canopies can mainly be classified into empirical and semi-empirical models. Empirical models use a regression analysis of experimental data to relate radar backscatter to vegetation parameters'such as plant moisture, plant height, and the underlying soil moisture content (Bush and Ulaby, 1976). Later improvements to these models led to the development of so-called semi- empirical models. In these, the effectiveness of previous empirical models is improved by combining experimental data with a hypothesis of the physical process involved. An example of such a model is that of Attema and Ulaby (1978). This is based on the assumption that volume scattering is the predominant mechanism responsible for backscatter from crops. It is therefore considered appropriate for modelling vegetation canopies as “water clouds” whose droplets are held in place by vegetative matter. Using this assumption, an expression is derived for the backscattering coefficient as a function of vegetation and soil parameters (Attema and Ulaby, 1978):

_ _ exp(2/dz^, sec0] + Aexp(5.m^, - sec6) (3.1)

where 0 is the local incidence angle, is the effective depth of the canopy, rj is the volume scattering coefficient, and /ris the canopy attenuation coefficient (values for rj and r a re found experimentally), mUs volumetric soil moisture content, A and B are constants at a given frequency, polarisation and incident angle.

The use of empirical/semi-empirical models provides the simplest description of the relationship between radar backscatter and vegetation parameters, thus making model inversion simpler. However, the validity of such models is limited to certain types of vegetation within strict environmental conditions under which the experimental data has been obtained. Furthermore, the use of such models for more complex vegetation structures such as crops with a large proportion of branches or for forest canopies may not be feasible. The assumption that volume scattering is the most predominant scattering

mechanisms at work can only hold for crops comprising no significant stalks or large branches. If they do comprise some stalks (such as in corn), the models can still be applicable, providing only a higher range of frequency (8-18 Ghz) is employed. The use of semi-empirical models is therefore very limited; only valid for certain crops and short- wavelength SAR. The extension of these models to longer wavelength SAR or for crops with more complex structures such as trees is difficult to achieve. These limitations have encouraged the development of later models, which are reviewed in the following sections.

ii) Phenomenological models.

Phenomenological models are based upon an intuitive understanding of the relative importance of different forest elements to the total backscatter. The scattering model is constructed through the summation of all backscattering contributions from these components. Examples of such models are those by Richard et al. (1987) and Durden et

a/. (1989).

Richard et al. (1987) have developed a two-layer phenomenological model for coniferous forest at L-band. In this model, the calculation of backscatter from forest is done by examining forest parameters thought to be important at L-band: foliage, trunk and ground surface. The calculation is simplified by treating the interaction of each of these components independently without electromagnetic coupling effects. This allows each scattering process to be modelled separately, using either empirical or analytical descriptions as appropriate. The foliage, for example, is represented by a cloud of water droplets, and the scattering from the crown layer is made by means of a water cloud model (Attema and Ulaby, 1978). Another process thought to be important at L-band is double-bounce scattering: 1) trunk-ground and 2) crown-ground scattering. To account for the former, trunks are modelled by dihedral corner reflectors (Ruck et al., 1970), while the latter is calculated using the model proposed by Engheta and Elachi (1982). The model of Richard et al. ( 1987) was one of the first radar backscatter models to attempt

forest canopy. The inclusion of this mechanism has been inspired by the experimental evidence shown by Ormsby et al. (1985) where they observed much higher backscatter from a flooded forest than from one with a dry undersurface. This significant difference was thought to be due to the strong occurrence of trunk-ground and crown-ground interaction in the flooded forest.

While this model accounts well for the observed differences between flooded and dry forest backscatter at L-band, the applicability of the model to other frequencies, or for other forest stands is still very limited due to the assumptions which have been taken while modeling the scattering from the foliage and trunk. The use of a water cloud model to calculate foliage backscattering from the coniferous forests may not be appropriate, as it does not account for the size and orientation of the leaves. This is especially crucial when seeking to extend the model to shorter wavelengths such as X- and K-band where foliage scattering is generally the dominant mechanism (Durden et a l, 1989). Furthermore, the treatment of the trunks as dihedral corner reflectors is only appropriate under very strict forest conditions which conform to the following: 1) the trunk and ground surfaces have to be “smooth” to facilitate the oeeurrenee of surface reflection and 2) the angle between the trunk and the ground has to be exactly 90”, as Richard et al (1987) has observed from the measurement that the shift of just 1° can cause a drop of radar cross section by 5 dB. These conditions are not met by most real forest stands, where the ground surface may have a slight slope, and be covered by understory vegetation or forest litter. Another drawback to this model is the absence of branches within the forest crown, especially at L- band the where scattering from branches is indeed very important (Karam and Fung,

1989).

To overcome these limitations, improvement of this model has been undertaken by Durden et al. (1989). They have extended the applicability of the model into a wider range of forest types (coniferous and deciduous forest) through the inclusion of branches into crown backscattering and by replacing dihedral corner reflectors with finite-length dielectric cylinders to represent the trunks. This model, however, neglects the contribution of leaves and twigs as they are considered to have only a small effect on the polarisation signature at L-band. This results in a model whose applicability is still strictly

limited for L-band, and perhaps P-band, and whose utility for X- and C- band may not be appropriate.

iii) Physical models.

In a way, physical models can be considered to be an improvement to phenomenological models, which attempt to calculate the main backscattering mechanisms in the forest canopies using only intuitive understanding. While the treatment of separate scattering mechanisms may avoid issues of complexity and make later inversion efforts easier, an intuitive representation of important forest components may not be consistent with a real one as some scattering mechanisms are inevitably neglected or ignored. Examples of this include the exclusion of branch scattering in the model by Richard et a l (1987), and of the foliage scattering in the model by Durden et al{\9%9). For certain bands, this may be acceptable, but when the model is extended, it can cause a problem. Therefore, the use of phenomenological approaches is limited, and only applicable at particular bands for particular types of forest. To overcome this limitation, physical models have been proposed by a number of studies and have become the most widely used in the development of radar backscatter models for forest canopies (Karam aand Fung, 1988; Ulaby et al, 1990; Sun et a l, 1991; Karam et a l, 1992; Wang et a l, 1993a; Ulaby et a l,

1994; Sun and Ranson, 1995).

Early physical models have treated the tree canopies as a single continuous layer consisting of leaves, branches and trunk scatterers (Tsang and Kong, 1983), whereas later models have separated tree canopies into crown, trunk and ground layers (Ulaby et al,

1990; Sun et a l, 1991 ; Karam et a l, 1992). The latter of these tend to have modeled the forest with full canopy closure, and are suitable only for dense forests. To extend the models to more open forest canopies, more recent attempts have included the modelling of forests as discontinuous layers (Sun et a l, 1991; Wang et a l, 1993a; Ulaby et al,

1994). The distribution of trees within real forest stands, however, may have distinct spatial distributions due to clumping. To account for this clustering effect. Sun and

Ranson (1995) have developed a model which takes full account of the spatial distribution of trees within the forest stand.

This present study makes use of the model within the physical category based on the following considerations: 1) this approach formulates the interaction between radar and forest constituents more realistically as it calculates the full interaction of all possible scattering processes, thus more complete results can be expected; 2) the wider applicability of such models to both short and long wavelengths band is considered. The next section reviews this approach in greater detail.