Ulaby and Dobson Land Clutter Model

Ulaby and Dobson [17] present a comprehensive set of land clutter models that have been derived from a number of measurement campaigns conducted by amongst others, Ohio State University, the US Naval Research Laboratory, NASA, University of Kansas and the University of Michigan. The set of models present average σ◦ data versus terrain type and incidence angle with respect to nadir, polarisation and carrier frequency. Their

Figure 3.4: Backscatter coefficient at 10 GHz using the GTRI land clutter model. model covers a range of terrain types, frequencies and angles in the plateau and high grazing angle region (10◦to 90◦). The Ulaby and Dobson set of models include tabulated data and graphs on the mean, standard deviation, median, 5th, 25th,75th, 95th and most extreme percentile values of the distribution as a function of terrain type, incidence angle, polarisation and carrier frequency. In addition it also provides probabilities of occurrence of averageσ◦[17].

The model takes into account nine terrain types that are characterised as follows:

1. Barren and sparsely vegetated land. Classified in the model as “Soil and rock sur- faces”.

2. Forests and orchids. Classified in the model as “Trees”. 3. Grasses. Classified in the model as “Grasses”.

4. Shrubs, bushy plants, and other crops. Classified in the model as “Shrubs”. 5. Grass, shrubs and wetlands. Classified in the model as “Short vegetation”. 6. Man-made surface. Classified in the model as “Road surfaces”.

7. Residential, commercial and industrial areas. Classified in the model as “Urban”. 8. Dry snow. Classified in the model as “Dry snow”.

9. Wet snow. Classified in the model as “Wet snow”.

The data for the nine terrain types are grouped to their corresponding frequency bands. The range of frequencies included in this model are L, S, C, X, Ku, Kaand W bands. Then

for each terrain category and frequency band, the data are arranged by polarisation and valid incidence angles. Three polarisation types are included, namely HH, VV , and HV [10]. The data for each category can be found in the appendix section of [17]. It should be noted that the validity of the data provided is not the same for all categories. They differ by the valid incidence angle ranges and number of observations taken. Some categories can be classified as having insufficient data due to the low number of observations taken. An overview of the source data in terms of number of observations and the range of valid incidence angles is given in Tables 6.6 through to 6.8, from [17].

From the datasets provided, Ulaby and Dobson derived an empirical model for the mean value as a function of incidence angle, for each terrain category, frequency band and polarisation. The model takes the form shown in Equation 3.6. This relationship between the mean value of σ◦ was calculated by a least squares curve fitting process for each terrain type [10].

σ_mean◦ (dB) = P1+ P2exp(−P3θ) + P4cos(P5θ+ P6) (3.6)

whereθ is the incidence angle expressed in radians and P1through to P6are empirically

derived constants which differ for each category type. This model is only valid for the categories with sufficient data. Expressions to compute the standard deviation SD is also given, as shown in equation 3.7.

SD(dB) = M1+ M2exp(−M3θ) (3.7)

where M1through to M3are resultant coefficients used for the standard deviation function.

For instances where the sample space is small, (i.e. N<6), the values for M are statistically insignificant and are therefore not included [17]. From computed values for theσ◦

meanand

SD, the 5th and 95th percentile values are then given as shown in Equation 3.8 and 3.9. These are based upon the assumption of Gaussian distributions.

σ_5%◦ (dB) = σ_mean◦ _{+ 1.645 × SD} (3.8) and

σ_95%◦ (dB) = σmean◦ − 1.645 × SD (3.9)

By taking the compliment of the incidence angle, the above models can easily be ex- pressed in terms of the grazing angle instead. The values for P and M can be found in the appendix section of [17] for each category. Table 3.6 provides a summary of the valid grazing angle ranges of each terrain type category, for the various frequency bands and polarisations. The categories with a null, indicates insufficient data where equations 3.6 to 3.9 can not be used. Ulaby and Dobson do however provide mean values for a limited range of discrete grazing angles for categories that are classified as having insufficient data. These values should be used with caution. As shown in Table 3.6, the urban terrain type has no sufficient data for all frequency ranges and polarisations.

Figure 3.5 shows the backscatter coefficient in dBs for the various terrain types at 10 GHz using the Ulaby and Dobson land clutter model for polarisations HH, HV and VV . These plots agree with the valid grazing angle ranges and terrain types as shown in Table 3.6. Snow terrain types were purposefully excluded from the plot as snow rarely falls within the SADC region. It is assumed that a Log-normal distribution is generally accep- ted to provide a good fit to the measured data [17].

The Ulaby and Dobson land clutter model provides valid data for a range of terrain types, frequencies and polarisations at grazing angles in the plateau and high region. Caution should be taken when using the Ulaby and Dobson model for categories which has in- sufficient data, especially for urban terrain which has no sufficient data for all categories. Caution should also be taken when using the model for certain grazing angle ranges, as many of the categories valid range differs from the assumed 10◦to 90◦as shown in Table 3.6. Due to the many advantages and extra information given for the Ulaby and Dobson model as compared to others, this model would in general be classified as an excellent model to use for site specific radar land clutter modelling for grazing angles ranging in

(a)

(b)

(c)

Figure 3.5: Backscatter coefficient in dBs for the various terrain types at 10 GHz using the Ulaby and Dobson land clutter model for polarisations (a) HH, (b) HV and (c) VV.

Table 3.6: Valid grazing angle ranges of each terrain type category, for the various fre- quency bands and polarisations: (a) HH polarisation, (b) HV polarisation, (c) VV polar- isation.

(a)

Polarisation HH Valid Grazing Angle Ranges [degrees]

Terrain Types

Radar Bands Soil & Rock Trees Grasses Shrubs Short Veg Road Surfaces Urban Dry Snow Wet Snow

L 40-90 - 10-90 10-90 10-90 - - 20-90 20-90 S 40-90 - 10-90 10-90 10-90 - - 20-90 20-90 C 40-90 - 10-90 10-90 10-90 - - 20-90 20-90 X 10-90 10-90 10-90 10-90 10-90 20-80 - 15-90 20-90 Ku 10-30 10-90 10-90 10-90 10-90 20-80 - 15-90 15-90 Ka - - 20-80 20-70 10-90 20-80 - 15-90 20-90 W - - - - (b)

Polarisation HV Valid Grazing Angle Ranges [degrees]

Terrain Types

Radar Bands Soil & Rock Trees Grasses Shrubs Short Veg Road Surfaces Urban Dry Snow Wet Snow

L 40-90 10-90 10-90 10-90 - - 20-90 20-90 S 50-90 10-90 10-90 10-90 - - 20-90 20-90 C 40-90 10-90 10-90 10-90 - - 20-90 20-90 X 20-90 10-90 20-70 20-70 20-80 - - 15-70 15-90 Ku 30-80 10-90 20-50 20-50 20-90 - - 15-90 15-90 Ka - - - - W - - - - (c)

Polarisation VV Valid Grazing Angle Ranges [degrees]

Terrain Types

Radar Bands Soil & Rock Trees Grasses Shrubs Short Veg Road Surfaces Urban Dry Snow Wet Snow

L 40-90 - 10-90 10-90 10-90 - - 20-90 20-90 S 50-90 - 10-90 10-90 10-90 - - 20-90 20-90 C 40-90 - 10-90 10-90 10-90 - - 20-90 20-90 X 20-80 10-90 10-90 10-90 10-90 20-80 - 20-90 20-90 Ku 30-90 10-90 10-90 10-90 10-90 20-80 - 20-90 20-90 Ka - - 20-80 20-70 10-80 20-80 - 20-90 20-90 W - - - 15-90 15-50

the plateau region.