σ ◦ Generating Function Land Clutter Model

Often backscatter coefficient models are developed that are described by a set of equations which yields a constant given a fixed set of measurement conditions. Due to the nature of these models, they therefore lack randomness of trueσ◦observations. Mediavalli and Connor [18], realised that in order to develop a land clutter model that produces backs- catter values that reflect the randomness of trueσ◦observations, it should be based upon real world backscatter characteristics. There are two possibilities to develop such a model, firstly a complicated electromagnetic model could be used that calculates the scattering of various terrain types in a Monte Carlo fashion, or to develop a generating function model

that returns values similar to those of measured terrain reflection coefficients. They argued that all the previous models would be generally unacceptable to use for model validation as they were deterministic in nature and repeatedly produced identical backscatter values, for a given category [64].

The data that they decided to base their model on was the Ulaby and Dobson set of radar scattering statistics for terrain. The data presented by Ulaby and Dobson does not rep- resent the actual backscatter numbers, but rather data of the statistical properties of the backscatter numbers and their frequency of occurrence in histogram form. The data re- flects the reality in which σ◦ _{from different terrain types is determined by the actual}

properties of the terrain.

The requirements for the generator were that the attributes of the coefficients in this gen- erator need to behave in a certain way. The mean and standard deviation of the generated distributions ofσ◦ need to approach those of the measured data, and the frequency of occurrence must be similar to the original data. The generator was thus designed such that it returns values that are similar to the observed measurement terrain scattering data found in [17]. The generator should output values for all terrain types, polarisations, and radar bands associated with the Ulaby and Dobson datasets.

They developed a probabilistic land clutter model (i.e. a model that does not repeatedly produce identical backscatter values for a given category setup, but produces results of varying values that conform to the statistical nature of real world measurements for a given category setup), that returns theσ◦for any combination of terrain type, frequency band, polarisation and grazing angle that would be similar to, and have similar statistical properties as the observed data by Ulaby and Dobson. Thus instead of using Ulaby and Dobson’s empirical model that only provides a deterministic answer, use the statistical data gathered by Ulaby and Dobson to develop a probabilisticσ◦generating land clutter model. Thus being able to obtain any percentile statistic and statistical properties rather than only the mean values.

The generating function is defined by Equation 3.10 [18].

where β is the amplitude term, α is the skewness parameter and γ is the distribution adjustment term. These model parameters are chosen in such a way that they produce backscatter values that form a set of combinations that yield the required mean and stand- ard deviation values for each category. An optimisation algorithm is used to correctly choose values for α and β for a fixed γ value, such that it generates the desired mean and standard deviation values with minimum error (i.e. the aim is to minimise the error between the generated standard deviation and mean values and those from the measured data determined by Ulaby and Dobson). If the algorithm rejects the distribution, theγ term either increases or decreases until the output of mean and standard deviation is ac- ceptable [18].

As with the Ulaby and Dobson land clutter model, this generator is limited to the cat- egories of data sets where sufficient data exists. The categories with insufficient data thus corresponds with the null areas shown in Table 3.6. For conditions of low grazing angle, an adapted version of the GTRI sea clutter model was used. The use of the GTRI sea clut- ter model for determining reflectivity from low angle land clutter is discussed in section 3.1.8.

Figure 3.6 shows the mean reflected energyσ◦ in dBs for the various terrain types at 10 GHz, polarisation HH, using the generating function developed by Mediavalli and Conner. The number of samples used to generate the below plot was N= 1000000.

Figure 3.6: Mean reflected energy σ0 in dBs for the various terrain types at 10 GHz, polarisation HH, using the generating function developed by Mediavalli and Connor.

Due to the fact that this model is based upon datasets by Ulaby and Dobson, it repres- ents the same advantages as well as disadvantages and limitations. However the gamma generating function generates a probabilistic output instead of deterministic at a better an- gular resolution than the standard Ulaby and Dobson model [18]. The probabilistic nature makes it suitable for validation purposes. This is an excellent model to use to simulate any percentile statistic and backscatter characteristics that behaves in a similar way to real world observed data. The model does however use more computing resources than the Ulaby and Dobson model due to its probabilistic nature. Theσ◦generating function land clutter model would in general be classified as an excellent model to use for site specific radar land clutter modelling for grazing angles ranging in the plateau region.