5.1.1.1 Clutter Measurements

The results of Chapter 5 are based on Phase One five-frequency land clutter measurements at 42 different sites as described in Chapter 3. At each Phase One site, all of the discernible land clutter within the field-of-view was measured at each of five frequencies, VHF, UHF, L-, S-, and X-bands, and at both vertical and horizontal polarization and at low and high range resolution. These raw Phase One data were calibrated, pulse-by-pulse and cell-by-cell, into absolute units of clutter strength. The resultant large 475-Gbyte five-frequency land clutter measurement database comprises a unique resource that is planned to be maintained indefinitely at Lincoln Laboratory. These data were provided to government authorities in Canada and the United Kingdom, and coordinated analyses took place in these countries as well as in the United States [6–9]. The results of Chapter 5 are based on the spatially comprehensive 360° survey data from all 42 Phase One sites. Previous Phase One results discussed in Chapters 3 and 4 were based on the relatively narrow (e.g., 20°) azimuth sector of repeated measurement concentration at each site called the repeat sector. Clutter experiments acquired in survey mode, as opposed to repeat sector mode, are further described in Chapter 3, Section 3.2.2.

5.1.1.2 PARAMETRIC EFFECTS

The following review of parametric clutter dependencies summarizes earlier discussions in this book. As developed in Chapter 2, a fundamental parametric dependence in low-angle clutter amplitude statistics is that of depression angle as it affects microshadowing among dominant discrete clutter sources, such that mean clutter strengths increase and cell-to-cell fluctuations decrease with increasing angle. At very low angles, clutter is to a very great extent caused by isolated discrete sources. Numerous low-reflectivity or shadowed cells occur between cells containing discrete clutter sources, even though the overall region from which the clutter amplitude distribution is formed is under general illumination by the radar. The combination of many shadowed or low-reflectivity weak cells together with many discrete-dominated strong cells causes extensive spread in the resultant low-angle clutter amplitude distribution.

As depression angle increases, the low reflectivity areas between discrete vertical features become more strongly illuminated, resulting in less shadowing and a rapid decrease in the spread of the distribution. As a result, measures of spread in the amplitude statistics such as ratio of standard deviation-to-mean and mean-to-median ratio decrease rapidly with increasing angle as the shadowed and weak samples at the low end of the distribution rise toward the stronger values that dominate the mean. However, the upper tail of the clutter distribution and mean level that is largely determined by the upper tail are still primarily caused by discrete sources and increase more slowly with increasing depression angle. These general effects of depression angle are important at all frequencies in the Phase One measurements.

Because of the heterogeneous process involved, wherein groups of cells providing strong returns are often separated by cells providing weak or noise-level returns, the spatial resolution of the radar fundamentally affects the amount of spread in clutter amplitude distributions from spatial macroregions. Increasing resolution results in less averaging within a cell, more cell-to-cell variability, and hence increased spread in the distributions. This general effect of resolution is also important at all frequencies in the Phase One measurements.

Within the context of the above mechanisms, radar frequency does not generally play as fundamental a role as do depression angle and resolution. However, as discussed in Chapter 3, two strong trends with frequency occur in particular circumstances. One of these is directly the result of the intrinsic backscattering coefficient σ° having an inherent frequency-dependent characteristic. Thus, at high depression angles in forested terrain, propagation measurements show that forward reflections are minimal (i.e., F ≈1)In such terrain, intrinsic σ° decreases strongly with increasing frequency due to the absorption characteristic of forest increasing with frequency.

The other trend with frequency is the result of a general propagation effect entering clutter strength σ°F⁴ through the pattern propagation factor F. At low depression angles in level open terrain, strong forward reflections cause multipath lobing on the free-space antenna pattern. At low frequencies such as VHF, these lobes tend to be broad so that returns from most clutter sources are received well on the underside of the first multipath lobe, and clutter strengths are much reduced. As frequency increases, the multipath lobes become narrower; typical clutter sources such as buildings or trees tend to extend over multiple lobes, with the result that at higher frequencies the overall multipath effect on illumination has less influence on the clutter strength. Thus, at low angles on level open terrain, there exists a characteristic of strongly increasing mean clutter strength with increasing frequency introduced through the pattern propagation factor. In inclined or rolling open terrain of increased relief, multipath is as likely to reinforce as to cancel clutter returns even at low radar frequencies.

Polarization has little general effect on ground clutter amplitude statistics. On the average, mean ground clutter strength is often 1 or 2 dB stronger at vertical polarization than at horizontal. The reason may be associated with the preferred vertical orientation of many discrete clutter sources. As discussed in Chapter 3, occasional specific measurements can show more significant variation with polarization but almost always less than 6 or 7 dB.

5.2.2.1 MEAN STRENGTH

A key attribute of the first moment or mean strength in a low-angle clutter amplitude distribution is that it is independent of radar spatial resolution. This fact and its importance are often unrecognized. It is both theoretically true in power-additive spatial ensemble processes and observed to be empirically true in the Phase One measurements. That it is theoretically true was discussed in Chapter 3, Section 3.5.3, and in Chapter 4, Section 4.5.4. In the Phase One measurement data, differences in mean strength between high (15 m or 36 m) and low (150 m) range resolution across the complete matrix of repeat sector patches were often less than one decibel (i.e., in the distribution of differences of mean strength with resolution, the mean difference was 0.8 dB and the median difference was 0.9 dB; see Figure 3.43).

The fact that the mean is independent of resolution in the modeling construct being utilized here has the important benefit of reducing the parametric dimensionality in this construct. Looking ahead to the tabularized modeling information of Chapter 5, if in these tables had to be further partitioned in several categories of resolution, the number of measurements in any given category would become too small to allow the development of useful general trends, and the modeling information would begin to degenerate to trendless tabularization of data.

The mean is the only attribute of low-angle clutter amplitude distributions that is independent of resolution. A number of early investigations emphasized the median rather than the mean in such distributions, since means usually occur high in the distributions, often near the 90-percentile level, driven there by occasional strong returns from discrete sources. It was thought that the median might be a better central measure of a discrete-free area-extensive clutter background. However, attempts to characterize the changing shapes of low-angle clutter amplitude distributions using the median instead of the mean as the central measure of each distribution required unwieldy normalization procedures and did not lead to useful general results, since the median central measure of each distribution as well as its shape were strongly dependent on resolution [12]. Because the mean occurs high in a distribution is not a reason to discard standard statistical techniques of using the first two moments of any distribution as the best way to begin to bring it under general description.

5.2.2.2 SHAPE PARAMETER a_w

The shapes of low-angle clutter spatial amplitude distributions are strongly and fundamentally dependent on spatial resolution. However, as with the mean strengths, there is a similar savings in model dimensionality with the shape parameter. With a_w, this savings is in the fact that the shapes of distributions, as observed in the clutter data, are not very sensitive to the remaining radar parameters of radar frequency and polarization. This key fact is an empirical observation here that apparently has not been advanced elsewhere. The reason why shapes of clutter amplitude distributions are largely insensitive to frequency and polarization is that essentially the same set of discrete sources on the landscape cause the dominant clutter returns, whatever the radar frequency or polarization. This is observed in PPI clutter plots showing the spatial texture of clutter. Insensitivity of distribution shape to radar frequency allows bringing to bear the varying Phase One azimuth beamwidths with frequency, from 13° at VHF to 1° at X-band, to help provide a combined broad range of spatial resolutions across which to establish trends.

It can be seen in the modeling information of Chapter 5 that, in working across frequency in this manner to establish trends of spread vs spatial resolution, radar frequency is essentially undetectable in the trends observed. That is, looking ahead to Figure 5.9 and the following 18 similar figures showing measured results of sd/mean vs A, it is evident that the different colored plot symbols in each such figure which correspond to different frequency bands contribute much more towards establishing one overall scatter plot through which it is most sensible to define one overall regression line, as opposed to five individual scatter plots with five different regression lines. If it were necessary to separate a_w with radar frequency and/or polarization, there would not be enough available range in resolution in the Phase One data to properly establish a trend, nor would there be enough data to properly fill the matrix.

Thus two important factors upon which the success of the modeling construct employed herein is based are that is dependent on frequency and polarization but is independent of resolution; whereas a_w is independent of frequency and polarization but is dependent on resolution—that is, that the important radar parameters decouple in their effects on low-angle clutter spatial amplitude distributions, much reducing the required parametric dimensionality of the model.

5.2.3.1 DERIVATION OF RESULTS

Like-classified groups of measured clutter histograms were formed in which the classifiers were: terrain type, relief, depression angle, radar frequency band (VHF, UHF, L-, S-, or X-band), and radar polarization (HH or VV). For each like-classified group, the mean clutter strengths of all the measured clutter histograms within the group were collected, one value of mean strength per histogram. The median or 50-percentile value from this set of mean strengths was selected as the representative value of mean strength by which to characterize that particular like-classified group of measurements. This 50-percentile value of mean clutter strength for each like-classified group of measurements was tabulated as the Weibull mean clutter strength coefficient in Sections 5.3 and 5.4 of Chapter 5. The number of measurements in each like-classified group was also tabulated in Sections 5.3 and 5.4, as an indication of the degree of generality of each coefficient presented. Color plots of vs frequency by depression angle regime and polarization are provided for each terrain type/relief category in Sections 5.3 and 5.4. The like-classified sets of mean clutter strength, upon which the modeling information of Chapter 5 is based, number 864.

Information Underlying . As an example of the derivation of each value of provided as modeling information in what follows, Table 5.2 illustrates the like-classified groups of measured clutter histograms for one terrain type—namely, low-relief forest with depression angle from 0.25° to 0.75°. The data in Table 5.2 are separated by frequency band (VHF, UHF, L-, S-, X-bands), range resolution (F = fat = 150 m; T = thin = 36 m for VHF and UHF bands, = 15 m for L-, S-, X-bands), and polarization (V = vertical, H = horizontal).

Each line in the table corresponds to one group of like classified histograms. In each line, the following information is provided: the number of histograms in the group (Npts) which is also the number of available like-classified values of clutter patch mean strength in dB; the median of these dB values (which is what is selected for ); the mean of these dB values; the standard deviation of these dB values (i.e., the 1-σ variability of ); the maximum of these dB values (the strongest like-classified patch measured); and the minimum of these dB values (the weakest like-classified patch measured). Looking ahead to Table 5.27 in Section 5.4.3.1, the values shown in the 0.25° to 0.75° lines in the upper and lower subtables of Table 5.27 come from Table 5.2. For example, lines 5 and 6 in Table 5.2 provide Npts = 113, 113 (4th column) and (5th column) for vertical and horizontal polarization, respectively, at VHF. Corresponding information to that shown in Table 5.2 lies behind all terrain type/depression angle categories for which values are provided in following Sections 5.3 and 5.4.

5.2.3.2 DERIVATION OF a_w RESULTS

The spread in a clutter spatial amplitude distribution as given, for example, by the ratio of standard deviation-to-mean or by the mean-to-median ratio, is fundamentally dependent on radar spatial resolution. Radar spatial resolution A (see Section 2.3.1.1) is given by

(5.5)

where

r = range,

Δr = range resolution, and

Δθ = one-way 3-dB azimuth beamwidth.

Like-classified groups of measured clutter histograms were formed in which the classifiers were: terrain type, relief, depression angle, range interval, range resolution, and azimuth beamwidth. Three range intervals were utilized, as: interval 1, 1 to 11.3 km; interval 2, 11.3 to 35.7 km; interval 3, range > 35.7 km. The measured clutter histograms are approximately equally distributed within these three intervals. Two range resolutions are available, wide pulse (i.e., 150 m) or narrow pulse (i.e., 36 m at VHF and UHF, 15 m at L-, S-, and X-bands). Five azimuth beamwidths are available, one per frequency band, as: 13° at VHF, 5° at UHF, 3° at L-band, 1° at S- and X-bands. Although S- and X-bands both have ≈1° azimuth beamwidth, they are kept separate in spread analysis classification grouping to keep the frequency bands separate in the scatter plots (but not in the regression).

For each like-classified group of measured clutter histograms, three parameters were collected from each of the measured clutter histograms within the group. These three parameters are: (1) the ratio of standard deviation-to-mean, (2) the mean-to-median ratio, and (3) the value of spatial resolution A applicable for the measurement. The median values of each of these three parameters were selected as representative values to characterize the spread in that particular like-classified group of measurements. Spread characterization utilizing these three parameters proceeded as follows. For each terrain type/relief/depression angle category, two scatter plots were formed. The first scatter plot shows the ratio of standard deviation-to-mean vs log₁₀ A. The second scatter plot shows the mean-to-median ratio vs log₁₀ A.

Each plotted point in the first of these scatter plots shows the median value of ratio of standard deviation-to-mean vs the median value of log₁₀ A for a particular like-classified group of measured clutter histograms. A number of these scatter plots of standard deviation-to-mean vs log₁₀ A are shown in Sections 5.3 and 5.4, one scatter plot for a selected depression angle regime in each terrain type/relief category. Similar to the first scatter plot, each plotted point in the second scatter plot shows the median value of mean-to-median ratio vs the median value of log₁₀ A for a particular like-classified group of measured clutter histograms. The maximum number of points in a scatter plot is 30 (five azimuth beamwidths, two pulse lengths, three range intervals), but little narrow pulse data is generally available in the third range interval.

Regression analysis was performed in each scatter plot. These regression analyses generally show significantly decreasing spread with decreasing resolution (i.e., increasing A) for each terrain type/relief/depression angle category. The regression line for each scatter plot is provided as modeling information for spread in clutter amplitude distributions in Chapter 5. The regression line is generally characterized by its values at A = 10³ m² and A = 10⁶ m², with a few noted exceptions.

Modeling information characterizing spread in clutter spatial amplitude distributions based on regression analysis in the scatter plots is provided two ways: (1) based on measured ratios of standard deviation-to-mean and (2) based on measured mean-to-median ratios. For both ways, the regression line values at A = 10³ m² and A = 10⁶ m² are converted to the corresponding two values of Weibull shape parameter a_w at A = 10³ m² and A = 10⁶ m² by Equations (5.3) and (5.4). These pairs of values of a_w are tabulated by terrain type/relief/depression angle category in Sections 5.3 and 5.4. In addition to the paired values of a_w, the underlying paired values of ratios of standard deviation-to-mean and mean-to-median ratio are also tabulated. The number of clutter patches and number of measured clutter histograms that each scatter plot (i.e., regression analysis) is based on is also tabulated.

This tabulated modeling information for Weibull shape parameter a_w is used as follows. First, the spatial resolution A of the radar under study is calculated at the terrain point under consideration. Then linear interpolation on log₁₀ A between the values of a_w at A = 10³ m² and A = 10⁶ m² for the appropriate terrain type/relief/depression angle category is performed to obtain the value of a_w at the radar spatial resolution A in question. Preference is given to the tabulated values of a_w based on measured ratios of standard deviation-to-mean. The additional provision of tabulated values of a_w based on measured mean-to-median ratios provides a first indication of the degree of validity of modeling the underlying measured data with Weibull statistics, based on how closely a_w computed from measured ratios of standard deviation-to-mean approximates a_w computed from measured mean-to-median ratios. The like-classified sets of measured clutter histograms, upon which the a_w modeling information of Chapter 5 is based, number 1,510. Note that these are different sets than those upon which the modeling information is based.

Information Underlying a_w. As described above, the a_w values provided as modeling information in what follows come from regression in scatter plots. Two scatter plots were formed: one of sd/mean (dB) vs log₁₀ A; the other of mean/median (dB) vs log₁₀ A. Each scatter plot comes from like-classified groups of measured clutter histograms. As an example of the information underlying the two scatter plots for low-relief forest with depression angle from 0.25° to 0.75°, Table 5.3 is shown here in three parallel parts. Parts (a), (b), and (c) show results for sd/mean (dB), mean/median (dB), and patch mid-range (km), respectively.

Consider first Table 5.3(a) for sd/mean (dB). The data in Table 5.3(a) are separated by frequency band (VHF, UHF, L, S, X), range resolution (Fat or Thin), and range interval (1, 2, or 3, as described previously). Each line in the table corresponds to one group of like-classified histograms and one point in the corresponding scatter plot—note that the groups are different from those of Table 5.2. In each line of Table 5.3(a), the following information is provided: the median value of mid-range cell size A for the group (shown under X as X = log₁₀ A and A = r Δr Δθ in m²); the number of histograms in the group (Npts), which is also the number of available like-classified values of ratio of sd/mean (dB), one from each clutter patch histogram; the median of these dB values of sd/mean (which forms the ordinate of the point in the scatter plot corresponding to this line); the mean of the dB values of sd/mean; the standard deviation of the dB values of sd/mean (i.e., the vertical 1-σ variability of this point in the scatter plot); the maximum of these dB values of sd/mean (i.e., the maximum patch value of sd/mean in this group); and the minimum of these dB values of mean/median. Thus, each line in Table 5.3(a) corresponds to the ordinate of a given point in a given scatter plot. For example, the scatter plot for low-relief forest, 0.0° to 0.25° depression angle is shown as Figure 5.27 in Section 5.4.3.2 (note: the plot corresponding to the 0.25° to 0.75° depression angle regime of Table 5.3 is not shown).

Table 5.3(b) is similar to Table 5.3(a) except Table 5.3(b) provides underlying information for the ordinate of the plotted points in the scatter plots of mean/median (dB) vs log₁₀ A. Examples of the mean/median scatter plots are not shown in this book; they appear similar to the sd/mean scatter plots, except that they employ a different y-scale.

Table 5.3(c) is similar to Table 5.3(a) except Table 5.3(c) provides underlying information for the abscissas of the plotted points in both kinds of scatter plots. The abscissa is 10log A where A is cell area in m². As discussed above, A = r·Δr·Δθ where Δr (range resolution) and Δθ (azimuth beamwidth) are fixed within any like-classified group (i.e., any line in the table), but r is the range in km to the center (i.e., mid-range) of each clutter patch in the group. Thus each line in Table 5.3(c) applies to the like-classified set of patch mid-range values, and the median value of mid-range is selected as r in the computation of A and hence the value of X = log₁₀ A shown in each line of Table 5.3(c).

Thus a given point in the scatter plot of sd/mean (dB) vs log₁₀ A for forest/low-relief/depression angle from 0.25° to 0.75° is obtained by selecting the appropriate value of “Median” in Table 5.3(a) as the ordinate, and the corresponding value of X that comes from the corresponding value of “Median” in Table 5.3(c). Scatter plots of sd/mean vs log₁₀ A and mean/median vs log₁₀A were generated for all terrain type/depression angle categories. Each pair of scatter plots came from corresponding information similar to the three parts of Table 5.3. Shape parameter a_w data obtained from regression in these scatter plots is provided in Sections 5.3 and 5.4.

5.2.3.3 STATISTICAL CONFIDENCE

In Chapter 5, some clutter modeling results are obtained from many similar measurements leading to high statistical confidence, whereas other results are obtained from fewer measurements leading to less confidence. The rationale followed in Chapter 5 is to present all of the results obtained regardless of the degree of trust, confidence coefficient, or generality associated with each. This is in contrast to the interim clutter model of Chapter 4, Section 4.2, where some smoothing of thinner data was employed. In Chapter 5, information specifying the number of like-classified measurements involved for each or a_w number is included as a means of allowing assessment of statistical validity or generality of the result. Statistical sampling populations and associated confidence levels are usually large in the depression angle regimes near grazing incidence. The sampling populations decrease as depression angle moves to outlying positive or negative depression angle regimes. In the color plots of mean clutter strength vs frequency, open symbols are occasionally used to indicate numbers judged likely to be relatively measurement specific and non-representative of the general mean clutter strength applicable to that situation, on the basis of relatively few measurements and clutter strength values far removed from the general trends otherwise observed.

5.2.3.4 USE OF MODELING INFORMATION

The Weibull coefficient modeling information may be employed to generate a σ°F⁴ clutter strength number (i.e., realization) for a given spatial cell. First, it is determined if the cell is geometrically visible from the antenna position or if the cell is masked or shadowed by intervening terrain of higher elevation. If masked, as a first approximation, zero clutter power is assigned to the cell (the information of this book is not directly applicable to shadowed cells; but see Appendix 4.D). If visible, the depression angle from the antenna position to the cell is computed, the terrain type and relief for the cell is determined, and the radar spatial resolution A at the cell is calculated. This determination of terrain type/relief/depression angle/spatial resolution for the cell leads to the pair of Weibull coefficients, , a_w, which specify the clutter amplitude distribution for that combination of terrain type, relief, depression angle, and resolution. A single random variate from this clutter amplitude distribution is assigned as clutter strength to the cell under examination. The modeler then proceeds to the next cell and repeats the process. In this manner, all visible cells at the site are assigned Weibull random variates as clutter strength, each appropriate to the radar parameters, geometry, and terrain type for the cell under consideration. The cell-to-cell spatial correlation that occurs in this process is that provided by the underlying land cover and DTED information; otherwise, the random variates of clutter strength occur independently from cell to cell, as indeed for the most part do the measured data (see Chapter 4, Section 4.6.3). Further explanation of this terrain-specific modeling rationale is provided in Chapter 4. Techniques for validating and improving this approach to clutter modeling are briefly described in Section 5.5.

For those interested in general clutter levels (e.g., means, medians) exclusive of cell-to-cell variability, use of the modeling information provided in Chapter 5 is more direct. Mean clutter strength is σ_w^odirectly tabulated. Median clutter strength σ°₅₀ and other percentile levels and moments are dependent on radar spatial resolution A. Median clutter strength σ°₅₀ is simply calculated from and the mean-to-median ratio; the mean-to-median ratio may be obtained for the radar resolution A under consideration by linear interpolation on log₁₀ A between tabulated values at A = 10³ m² and A = 10⁶ m². The standard deviation may be obtained in a manner directly parallel to that by which the median is obtained. Other percentile levels may be simply calculated from the Weibull cumulative distribution function [Eq. (5.2)].

5.2.3.5 PRESENTATION OF MATERIAL

Sections 5.3 and 5.4 provide extensive modeling information for low-angle land clutter spatial amplitude statistics within a standard presentation format. The format utilized follows that of the interim clutter model presented in Chapter 4, Section 4.2, and illustrated in Figure 4.3. The format of presentation of mean clutter strength is reviewed here as an aid to the presentation of the extensive modeling information that directly follows.

The clutter modeling information that follows is based on depression angle. Figure 5.6 shows depression angle to be the angle below the horizontal from the radar to the backscattering terrain point. A precise mathematical definition of depression angle is given by Equation (5.1); see also Appendix 2.C of Chapter 2. As shown in Figure 5.6, terrain can occasionally rise to elevations higher than the radar which leads to negative depression angle. Approximately 30% of the clutter modeling information to follow applies to clutter measurements obtained at negative depression angle.

The clutter modeling information that follows is presented within bins (i.e., narrow angular regimes) of depression angle. The depression angle bins utilized are shown in Table 5.4. As is apparent in Table 5.4, different binning is utilized in low-relief terrain (terrain slopes < sin 2°) than in high-relief terrain (terrain slopes > 2°). In low-relief terrain, five positive and three negative depression angle bins are used; in high-relief terrain, five positive and two negative bins are used. The bins are very narrow, particularly at low depression angle, and more so for low-relief than high-relief terrain. Each bin typically contains hundreds of clutter measurements. What is plotted is the median value of clutter patch mean strength within each bin.

It will be seen in the clutter modeling information to follow that, as a result of medianizing over many measurements, the small differences in depression angle shown in Table 5.4 can account for systematic differences in mean clutter strength that in total can cover wide ranges. The bins are shown color-coded in Table 5.4; the same color coding is used in plotting mean clutter strength σ_w^o in color figures to follow, with different shaped symbols used to plot at VV-polarization (circles) and HH-polarization (squares). The color codes are as follows: for increasing positive depression angle, cyan, dark blue, purple, magenta, red for bins 1 to 5, respectively; for increasing negative depression angle, dark green, intermediate green, light green for bins −1, −2, and −3 in low-relief terrain, and dark green, intermediate green for bins −1, −2 in high-relief terrain, respectively. The category of long-range mountains requires a specialized negative depression angle category. Complete data are not always available for all terrain types at outlying depression angles.

In the clutter modeling information that follows, for each terrain type mean clutter strength is plotted vs radar frequency against a log-frequency x-axis in order to show results for all five frequency bands together. The plotting methodology is shown representationally in the diagram of Figure 5.7. Within each frequency band, results separated by depression angle bin are plotted by slightly displacing the plot symbols horizontally from bin to bin to avoid symbol overlap. This plot methodology, covering eight depression angle bins, is shown for X-band in an exaggerated way in the diagram of Figure 5.7. The sequential horizontal displacements shown in Figure 5.7 do not imply an in-band frequency shift; the cluster of sixteen plotted values of shown in Figure 5.7 all apply for a single X-band frequency. Similar bin-to-bin horizontal offsetting of plot symbols is also employed in the lower four bands.

Mean clutter strength generally increases both with increasing positive depression angle and with increasing negative depression angle. As a result, the in-band clusters of plotted data in multiple depression angle bins often take on the v-shape shown representatively by the X-band cluster in Figure 5.7. Thus, as a point of departure in interpreting the results, it is suggested that the reader first look for v-shapes indicating whether or not consistent depression angle effects on clutter strength occur for the particular frequency band and terrain type of interest.

5.3.1.1 High-Relief General Mixed Rural Terrain

Table 5.5 shows the number of patches and measured clutter histograms by depression angle regime and terrain relief for general mixed rural terrain. Table 5.6 presents Weibull mean clutter strength for general mixed rural terrain of high relief, by depression angle, frequency band, and polarization. The number of measured clutter histograms upon which each value of in Table 5.6 is based is also presented in the lower of the two subtables comprising Table 5.6. High-relief terrain has terrain slopes > 2°. The data of Table 5.6 are plotted in Figure 5.8. To avoid obscuring results with overlapping plot symbols, within each frequency band in Figure 5.8 the colored plot symbols are plotted with small increasing horizontal displacements to the right as depression angle decreases from its highest positive regime through zero to its highest negative regime (i.e., top to bottom in Table 5.6). These small artificial displacements do not indicate an in-band frequency shift.

In each frequency band of Figure 5.8, the resultant set of colored plot symbols has a v-shape. The consistent v-shape indicates consistent depression angle effects in each band, where increases with both increasing positive (left side of v-shape, cyan through magenta) and increasing negative (right side of v-shape, dark green through intermediate green) depression angle. In what follows in Chapter 5, the data for each terrain type are plotted in a figure in which the manner of data presentation is similar to that employed in Figure 5.8.

The cyan (i.e., light blue) colored symbols in Figure 5.8 represent the lowest positive depression angle regime (0° to 1°) in high-relief terrain. These results are based on a significantly larger number of measurements than the other depression angle regimes in

Table 5.6 and hence may be regarded as the most reliable data shown in Figure 5.8. In moving from cyan through the higher positive depression angles in Figure 5.8, there is a monotonic rise up the left side of the v-shaped cluster from cyan to dark blue (1° to 2°) to purple (2° to 4°) to magenta (4° to 6°). Thus in each frequency band Figure 5.8 shows a strong monotonic increase in with increasing positive depression angle. The number of measurements falls off with increasing positive or negative depression angle (see Table 5.5). No data are available for depression angle > 6° (red) in any band in Figure 5.8, and no data are available from 4° to 6° (magenta) at S- and X-bands in Figure 5.8 due to the limited Phase One elevation beamwidths in those bands (see Appendix 3.A).

Values of for negative depression angle are plotted in shades of green. Negative depression angle occurs when steep terrain is observed by the radar at elevations above the antenna. The darkest shade of green shows results in the lowest negative depression angle regime, which is 0° to −1° in high-relief terrain. These dark green (0° to −1°) results in Figure 5.8 are generally close to and usually slightly higher than the cyan (0° to 1°) results, as intuitively would be expected. The shade of green becomes lighter with increasing negative depression angle. In high-relief terrain, only one additional negative depression angle regime is utilized, for depression angle < −1° (intermediate green in Figure 5.8). In every band, the intermediate green values of in Figure 5.8 are significantly stronger than the dark green values, thus providing the right sides of the v-shaped clusters.

There is a general trend of decreasing with increasing radar carrier frequency in Figure 5.8. At the lowest (positive or negative) depression angles, this trend is slight (e.g., for cyan, 0° to 1°, UHF, L-, and X-band results are all remarkably close in the −29 dB vicinity, with VHF slightly stronger and S-band slighter weaker). At higher (positive or negative) depression angles, the trend is stronger. This trend is largely due to increasing absorption of radio frequency (RF) power from the incident radar wave by tree foliage, VHF to S-band (see Chapter 3). Mixed rural terrain of high relief has a larger component of trees than at low relief. At the highest positive depression angles (magenta and purple) in Figure 5.8, the variation of with radar frequency f VHF to S-band is approximately . In the historical literature, what little information is available on the subject usually suggests a slight trend of increasing clutter strength with increasing radar frequency, for example, or . Thus the trend of decreasing clutter strength with increasing radar frequency seen in many of the Phase One high-angle forest measurements is relatively unexpected. Note that at all positive depression angles in Figure 5.8, the trend of decreasing with increasing radar frequency from VHF to S-band reverses from S-band to X-band. That is, at all positive depression angles there is an S-band dip between L-band and X-band in Figure 5.8, indicating that over the range of frequencies shown, maximum RF absorption occurs at S-band. It is probably not entirely coincidental that S-band is also the frequency band in which the common household microwave oven operates (at 2.45 GHz). In Figure 5.8, the differences with polarization are generally small, on the order of several dB or less, with vertical polarization (VV) almost always stronger than horizontal (HH).

Table 5.7 presents the Weibull shape parameter a_w and ratios of standard deviation-to-mean and mean-to-median for general mixed rural terrain of high relief, by depression angle and radar spatial resolution. Whereas the information of Table 5.6 specifies the mean or first moment of the clutter spatial amplitude distribution, the information of Table 5.7 specifies the spread or variability in the distribution as determined by the second moment or other derivative quantities. Table 5.5 shows the number of terrain patches and number of measured clutter histograms for general mixed rural terrain of high relief, broken down by depression angle in a parallel manner to that of Table 5.7; that is, the statistical populations underlying the data of Table 5.7 are available in Table 5.5. The numbers of measured clutter histograms in Table 5.5 are further broken down by frequency band and polarization in Table 5.6. Table 5.5 shows no data available for depression angle > 6° for general mixed rural terrain of high relief. Generally, there is little Phase One data available at such a high depression angle, although Section 5.4 shows that there is one high-relief forest clutter patch and six mountain clutter patches at depression angles > 6°.

In Table 5.7, a_w is calculated two ways: (1) from the ratio of standard deviation-to-mean and (2) from the mean-to-median ratio. In Table 5.7, and in general throughout Chapter 5, no major systematic difference results between these two methods of calculation of a_w, or, including as a third alternative, in the a_w that comes from the least-mean-squares best-fitting true Weibull distribution that is matched to the measured distribution over a large central part (i.e., noise level to 0.999 cumulative probability) of the measured distribution. However, a_w results by two different methods of calculation are shown in Table 5.7 and in all similar tables throughout Chapter 5 as a first indication of the degree to which Weibull statistics approximate the characteristics of the measured distributions; if the measured distributions were exactly Weibull, the two different methods of calculation of a_w would yield identical results.

Each pair of a_w numbers in Table 5.7 comes from a scatter plot in which each individual point plotted shows the median value of spread vs the median value of spatial resolution in a group of like-classified measured clutter histograms. For example, for Table 5.7 the standard deviation-to-mean scatter plot for the 2° to 4° depression angle regime is shown in

Figure 5.9. This scatter plot is based on 51 terrain patches and 987 measured clutter histograms, as indicated in Table 5.5. Twelve similar scatter plots underlie the 12 pairs of a_w numbers in Table 5.7.

The major parametric variation of a_w in Table 5.7 is with radar spatial resolution. In every case, a_w is much greater at 10³ m² resolution than at 10⁶ m² resolution. There is also a weaker trend in Table 5.7 whereby a_w decreases as depression angle increases from the 0° to 1° regime (more so with increasing positive depression angle than with increasing negative depression angle). For cell-by-cell Weibull random clutter strength numbers, a_w for the radar spatial resolution at the cell under consideration is required. The value of a_w applicable at resolution A is obtained by linear interpolation on log₁₀A between the tabulated values of a_w at A = 10³ m² and A = 10⁶ m² shown in Table 5.7. For example, in general mixed rural terrain of high relief in the depression angle regime from 1° to 2°, the applicable value of a_w at A = 10⁴ m² based on: (1) measured ratios of standard deviation-to-mean is a_w = 2.53, (2) measured mean-to-median ratios is a_w = 2.77, and (3) equal weighting of ratios of standard deviation-to-mean and mean-to-median is a_w = 2.65.

The lower subtable of Table 5.7 shows the ratios of standard deviation-to-mean and mean-to-median from which the a_w numbers in the upper subtable come. The large spreads in low-angle land clutter spatial amplitude distributions at high spatial resolution are perhaps more dramatically evidenced by these lower numbers (e.g., mean-to-median ratio = 18.9 dB at 10³ m², compared to 6.3 dB at 10⁶ m², Table 5.7, depression angle regime from 1° to 2°). Figure 5.5 allows quick conversion between the numbers in the upper and lower subtables of Table 5.7, and similar tables throughout Chapter 5. Interpolation in these lower numbers directly yields general second moment or median values at the spatial resolution under consideration. For example, at A = 10⁴ m², for general mixed rural terrain of high relief in the 1° to 2° depression angle regime, the ratio of standard deviation-to-mean is 5.0 dB and the mean-to-median ratio is 11.7 dB. The applicable mean level is obtained from Table 5.6. If L-band and vertical polarization happen to be the frequency and polarization of the radar in question, then, continuing the example, in general mixed rural terrain of high relief in the 1° to 2° depression angle regime at spatial resolution of 10⁴ m², the applicable low-angle land clutter spatial amplitude distribution has , , and standard deviation equal to −21.0 dB.

5.3.1.2 LOW-RELIEF GENERAL MIXED RURAL TERRAIN

Table 5.8 presents Weibull mean clutter strength for general mixed rural terrain of low relief by depression angle, frequency band, and polarization. The lower of the two subtables comprising Table 5.8 shows the number of measurements upon which each value in the upper subtable is based. Low-relief terrain has terrain slopes < 2°. Table 5.5 indicates that, within the Phase One general mixed rural clutter data, low relief occurs somewhat more frequently (viz., 56%) than high relief (viz., 44%).

The low-relief data of Table 5.8 are plotted in Figure 5.10 in a manner similar to that employed with the high-relief data in Figure 5.8. As in Figure 5.8, in each frequency band of Figure 5.10 the set of colored plot symbols continues to have a consistent v-shape indicating consistent depression angle effects in each band. The v-shapes of the low-relief data in Figure 5.10 are, however, considerably more pronounced than those of the high-relief data in Figure 5.8. That is, depression angle effects are stronger at low relief than at high relief.

The cyan colored symbols in Figure 5.10 represent the lowest positive depression angle regime (0° to 0.25°) in low-relief terrain and are based on a large number of measurements (see Table 5.8). In moving from cyan through the higher positive depression angles in Figure 5.10, in general there is a monotonic rise (with a few minor exceptions) up the left side of the v-shaped cluster from cyan to dark blue (0.25° to 0.75°) to purple (0.75° to 1.5°) to magenta (1.5° to 4°) to red (depression angle > 4°). Thus in each frequency band Figure 5.10 shows a strong increase in with increasing positive depression angle. The number of measurements falls off at outlying positive and negative depression angles (see Tables 5.5 and 5.8). No data are available for depression angle > 4° (red) at S- and X-bands in Figure 5.10 due to the limited Phase One elevation beamwidths in those bands.

Values of for negative depression angle are plotted in shades of green. The darkest shade of green shows results in the lowest negative depression angle regime, which is 0° to −0.25° in low-relief terrain. These dark green (0° to −0.25°) results in Figure 5.10 are generally close to and usually slightly higher than the cyan (0° to 0.25°) results. The shade of green becomes lighter with increasing negative depression angle. In low-relief terrain, two additional negative depression angle regimes are utilized for depression angles from −0.25° to −0.75° (intermediate green) and for depression angles < −0.75° (light green). In moving from cyan through the three green negative depression angle regimes in Figure 5.10, in general there is a strong monotonic rise (with two minor exceptions) up the right side of each v-shaped cluster.

At VHF in Figure 5.10, at low depression angles (e.g., cyan, 0° to 0.25°) clutter strengths are low due to multipath loss over the open components of the low-relief mixed rural terrain—this effect is not at work in the high-relief data of Figure 5.8. Remaining with VHF in Figure 5.10, at high depression angles (e.g., red, > 4°) clutter strengths are high because of the low RF absorption at VHF by the forested components of the low-relief mixed rural terrain—this effect is at work in the high-relief data of Figure 5.8. As a result of these two effects, the amplitude of the v-shaped cluster of plot symbols at VHF in Figure 5.10 is wide, viz., 24 dB, compared to 13 dB in Figure 5.8. These are the ranges over which small changes in depression angle affect the mean strength of land clutter at VHF in general mixed rural terrain of low and high relief, respectively. In Figure 5.10, as radar carrier frequency f rises from VHF into the microwave regime, at low depression angle (cyan) rises from VHF to L-band due to decreasing multipath loss with approximate dependence , whereas at high depression angle (red and magenta) _w^o (f) falls from VHF to S-band due to increasing RF absorption by tree foliage with approximate dependence . At intermediate depression angles, the variation with radar frequency is intermediate between these extremes. As a result of these two opposite trends with radar frequency, the data points plotted in Figure 5.10 take on a funnel shape. As in the high-relief data of Figure 5.8, there is an S-band dip between L-band and X-band in the low-relief data of Figure 5.10, with the dip more pronounced at high depression angle (magenta) than at low depression angle (cyan). This dip occurs at all positive depression angles in Figure 5.10. As in Figure 5.8 at high relief, in Figure 5.10 at low relief the differences with polarization are generally small, on the order of several dB or less, with vertical polarization (VV) almost always stronger than horizontal (HH).

Comparison of Figures 5.8 and 5.10 indicates that there exist considerable differences in mean clutter strength between general mixed rural terrain of high relief (terrain slopes > 2°) and low relief (terrain slopes < 2°), respectively. A major reason for this is that low-relief mixed rural terrain allows multipath propagation to occur, which drives down clutter strengths at low depression angle in the lower bands. Multipath propagation does not occur to any significant degree in high-relief terrain or at high depression angles in low-relief terrain. At high depression angles in the lower bands and at all depression angles in the upper bands, mean clutter strengths in high-relief terrain are somewhat greater than in low-relief terrain, within similar depression angle regimes. Such differences are due directly to the effect of terrain relief on intrinsic σ°; they are less than the low depression angle differences in the lower bands caused by multipath. A contributing factor to all the differences in mean clutter strength with terrain relief indicated in Figures 5.8 and 5.10 is that high-relief mixed rural terrain tends to be somewhat more forested whereas low-relief mixed rural terrain tends to be somewhat more open. Classification by terrain relief in two major regimes as shown in Figures 5.8 and 5.10 is a simple and practicable approach for sorting out the complex phenomenological influences at work in low-angle land clutter.

Table 5.9 presents the Weibull shape parameter a_w and ratios of standard deviation-to-mean and mean-to-median for clutter amplitude distributions in general mixed rural terrain of low relief, by depression angle and radar spatial resolution. The statistical populations underlying the data of Table 5.9 are available in Table 5.5. In Table 5.9, a_w is calculated two ways: (1) from the ratio of standard deviation-to-mean and (2) from the mean-to-median ratio. Many of the corresponding a_w numbers resulting from these two methods of calculation are remarkably close in Table 5.9. Each pair of a_w numbers in Table 5.9 comes from a scatter plot in which each individual point plotted shows the median value of spread vs the median value of spatial resolution in a group of like-classified measured clutter histograms. The standard deviation-to-mean scatter plot for the 0.25° to 0.75° depression angle regime in Table 5.9 is shown in Figure 5.11. The major parametric variation of a_w in Table 5.9 is with radar spatial resolution. In every case, a_w is much greater at 10³ m² resolution than at 10⁶ m² resolution. There is a weak trend in Table 5.9 whereby a_w decreases as depression angle increases from the 0° to 0.25° regime. There is little indication for a_w in terrain of high relief as shown in Table 5.7 to be lower than in terrain of low relief as shown in Table 5.9, as might be expected in these results. The lower subtable of Table 5.9 shows the ratios of standard deviation-to-mean and mean-to-median from which the a_w numbers in the upper subtable come. The large spreads in low-angle land clutter spatial amplitude distributions at high spatial resolution continue to be dramatically evidenced by these lower numbers.

5.4.2.1 HIGH-RELIEF AGRICULTURAL TERRAIN

Trends in . Table 5.17 presents mean clutter strength for high-relief agricultural terrain by frequency band, polarization, and depression angle and includes the number of measurements upon which each value of is based. Relatively little Phase One measurement data exists for high-relief agricultural terrain—just 250 measured clutter histograms from 20 clutter patches at eight measurement sites. The primary reason for this sparsity of data is that little high-relief farmland exists; farm machinery cannot easily access high-relief terrain.

The data of Table 5.17 are plotted in Figure 5.18. Except for the uncertain outliers plotted as open symbols, the data of Figure 5.18 lie largely in the −29- to −36-dB range without major trends with frequency or depression angle. At first consideration, the cluster of L-band results appears 3 or 4 dB stronger than the other bands; however, the more reliable cyan (0° to 1°) results do not show stronger at L-band. In these results, at vertical polarization is usually several decibels stronger than at horizontal polarization.

Uncertain Outliers. Now consider the uncertain outliers in the results for high-relief agricultural terrain of Table 5.17. These uncertain results are plotted as open plot symbols in Figure 5.18. Within these uncertain outlier results in high-relief agricultural terrain, three particular clutter patch measurements are discussed. Two of these patch measurements involve borderline-high incidences of trees occurring within patches classified as pure farmland terrain causing stronger than expected outlier values of ; and one patch measurement involves a terrain inclination away from the radar causing a weaker than expected outlier value of .

First consider the very strong, green (0° to −1°) results at VHF in Figure 5.18. These results are dominated by one strong clutter patch, viz., patch 37 at the Penhold measurement site in Alberta. This patch is classified as pure farmland, although with ∼10% tree cover. These patch 37 results agree very closely with corresponding results (not shown here) at VHF for high-relief mixed terrain classified as open/forest, these latter results being based on a large number of measurements. Thus it would appear that patch 37 at Penhold may have been more appropriately classified as mixed terrain with a secondary component of forest. Misclassification of occasional single patches is usually of little consequence in the general (i.e., medianized) results of Chapter 5 that are more typically based on measurements from many patches.

Next, consider the relatively strong, purple (2° to 4°) results at UHF in Figure 5.18. These results are based on measurements from one clutter patch, viz., patch 30 at the Polonia measurement site in Manitoba. Again, this patch is classified as pure farmland with ∼10% tree cover. Comparison with other results indicates that the clutter from patch 30 at Polonia was also very likely dominated by trees. That is, patch 30 at Polonia may also have been more appropriately classified as mixed open/forest. Most farmland has some small incidence of occurrence of trees. The percentage incidence at which trees begin to dominate the backscatter from farmland landscapes can be quite low. The results from these two patches show the importance in clutter prediction of accurately depicting the relative proportion of trees on generally open landscapes.

Finally, consider the relatively weak, dark blue (1° to 2°) results at VHF, S-, and X-band in Figure 5.18. These results are based almost entirely on three clutter patches, and, at S- and X-bands, on just two clutter patches. One of these patches, viz., patch 12 at the Magrath measurement site in Alberta, was relatively weak in all bands. Patch 12 was at close range (1.2 to 2.2 km) on the side of the slope at the top of which the Phase One radar was situated, and as a result may be weak due to its outward inclination and/or due to it being borderline-shadowed by intervening higher terrain (brow-of-hill effect; see Appendix 4.B). More measurements were made from patch 12 than the other contributing patches in the dark blue (1° to 2°) results in Figure 5.18 at VHF, S-, and X-band—hence the median result from the set is low in these bands. In contrast, more measurements were made from the other two contributing patches than from patch 12 at UHF and L-band—hence the median results from these sets are higher and in line with the data from the other depression angle regimes in Figure 5.18. It is evident from such considerations that caution must be exercised in using any Chapter 5 open-symbol results based on sparse data.

Shape Parameter a_w. Table 5.18 presents the Weibull shape parameter a_w and ratios of standard deviation-to-mean and mean-to-median for clutter amplitude distributions in high-relief agricultural terrain by depression angle and radar spatial resolution. The statistical populations underlying the data of Table 5.18 are shown in Table 5.16. Table 5.18 shows that very large values of spread occur in spatial clutter amplitude distributions at low angles and high resolution in high-relief agricultural terrain. In every case, a_w is greater at 10³ m² resolution than at 10⁶ (or 10⁵) m² resolution. At the higher resolution of 10³ m², a_w also strongly depends on depression angle. In high-relief agricultural terrain, a_w at high resolution decreases strongly from large values at grazing incidence (i.e., 0° to 1°) to much smaller values at higher angles (e.g., 2° to 4°). Therefore, modeling of clutter from high-relief agricultural terrain must be done in narrow regimes of depression angle to accommodate this strong trend of decreasing spread in clutter amplitude distributions with increasing angle of illumination, even though mean clutter strengths in high-relief agricultural terrain are relatively insensitive to angle of illumination.

Each pair of a_w numbers in Table 5.18 comes from a scatter plot of spread vs spatial resolution. The standard deviation-to-mean scatter plot for the 1° to 2° depression angle regime in Table 5.18 is shown in Figure 5.19. The data in Figure 5.19 show a strong trend of decreasing spread with decreasing resolution (i.e., increasing A). Note that all of the results in Figure 5.19 happen to come from the first range interval, 1 to 11.3 km. As a result, it is easier to follow the variations with frequency and pulse length in this figure than in many of the similar scatter plots in Chapter 5. Further note that although the measured data extend only to A ≅ 10⁵ m ² in Figure 5.19, it is reasonable to extend the regression line to A = 10⁶ m²; indeed, this was done to provide the sd/mean based results at A = 10⁶ m² for the 1° to 2° depression angle interval in Table 5.18. However, for the corresponding mean/median scatter plot, it was not reasonable to extend the regression line to A = 10⁶ m²; hence the mean/median based results are shown at A = 10⁵ m², not A = 10⁶ m², for the 1° to 2° depression angle regime in Table 5.18.

5.4.2.2 LOW-RELIEF AGRICULTURAL TERRAIN

Trends in . Table 5.19 presents mean clutter strength for low-relief agricultural terrain by frequency band, polarization, and depression angle and includes the number of measurements upon which each value of is based. These results are based on a very large amount of Phase One measurement data—10,107 measured clutter histograms from 505 clutter patches; see Table 5.16. These measurements come from 30 sites.

The data of Table 5.19 are plotted in Figure 5.20. The main parametric trend observed in Figure 5.20 is that increases significantly—by about 10 dB—with increasing frequency, VHF through L-band, then levels off, L-band through X-band. Weaker values of at VHF and UHF are due to multipath loss from forward reflections on generally open, low-relief, agricultural terrain. At the lower frequencies, the multipath lobes on the elevation pattern are broad, and returns from clutter sources are typically received at reduced gain well on the underside of the first multipath lobe. At the higher frequencies, the multipath lobes are narrower and clutter sources tend to be more fully illuminated. The details of the multipath depend on the terrain between the clutter patch and the radar. Some patches will experience more multipath loss and some less (see Section 3.4.1.4). Figure 5.20 shows medianized results from many measurements in generally low-relief agricultural terrain.

The results of Figure 5.20 show little variation with depression angle. The results at X-band form a very tight cluster. The results from L-band through X-band are remarkably invariant with both frequency and depression angle, all largely in the −29 dB to −33 dB range. At first consideration, the results at UHF appear to show increasing with increasing positive depression angle. However, further consideration of these UHF data reveals that, in the cyan, 0° to 0.25° results, large multipath loss exists, as large as that which exists in the cyan results at VHF, but in the dark blue, purple, and magenta, higher depression angle UHF results, the multipath loss is less and little or no variation of occurs with depression angle in these higher angle results. Note that in the dark blue, 0.25° to 0.75° results in Figure 5.20, at S-band is approximately equal to at L-band and X-band, but with increasing depression angle, purple, 0.75° to 1.5°, through magenta, 1.5° to 4°, at S-band increasingly dips below at L-band and X-band. A more significant S-band dip at high depression angle was discussed in the low-relief general mixed rural results of Figure 5.10.

At X-band in Figure 5.20, is one or two dB stronger than in every depression angle regime. This slight polarization bias continues to be largely true at S-band but is less evident at the lower frequencies, and at VHF is reversed such that is generally slightly stronger than .

Uncertain Outliers. Now consider the uncertain outliers in results for low-relief agricultural terrain which are plotted as open plot symbols in Figure 5.20. First consider the light green, −0.25° to −0.75° results. Table 5.19 shows that these results are based on significantly fewer measurements than the other depression angle regimes. At VHF these light green results show a very significant difference with polarization, with stronger than by 13 dB. At horizontal polarization, the light green result at VHF comes from five measurements, four from the Altona site and one from a very weak clutter patch at the Neepawa site. Thus at horizontal polarization, the median measurement is an Altona measurement. At vertical polarization, however, the light green result at VHF comes from only two measurements, both from the weak Neepawa patch. Thus at vertical polarization, the median measurement is an atypically weak Neepawa measurement. At UHF the light green, −0.25° to −0.75° results in Figure 5.20 no longer show a polarization difference, but remain dependent on relatively few samples, and are significantly weaker than the dark green, 0° to −0.25° results. One reason that the light green, −0.25° to −0.75° results are relatively weak at UHF and, indeed, also relatively weak at S-band and X-band is that among the 15 clutter patches contributing to these results are three clutter patches that exist at long ranges, from 35 to 65 km. For these three patches, effective radar height is negative, on the order of several hundred feet. Even so, these three patches are at ranges nearly as great as (i.e., one patch) or significantly greater than (i.e., two patches) the quantity (see Appendix 2.C). Therefore, much of the negative depression angle to these three patches is caused by geometry on the spherical earth. These patches are weak because of diffraction loss due to propagation over the long ranges of intervening terrain at near grazing incidence. Similarly weak clutter occurring for long-range urban patches is discussed in Section 5.4.1.

Now consider the magenta, 1.5° to 4° results in Figure 5.20. At S-band these magenta results show a significant dip of 5 to 6 dB below the magenta results at L-band and X-band. These magenta results also are based on fewer measurements than in the lower depression angle regimes in Figure 5.20. Among these measurements are those from one relatively weak clutter patch, viz., patch 31, at the Beiseker measurement site. Patch 31 was at close range (1.0 to 2.2 km) on the side of the long hill upon which the Phase One radar was situated at Beiseker and, therefore, may have been borderline-shadowed (brow-of-hill effect). Deleting the patch 31 measurements would significantly raise the magenta S-band results in Figure 5.20 but would have less effect at X-band. Thus the exaggerated S-band dip in the magenta results in Figure 5.20 may partially reflect a real effect, but in addition may be partially due to atypically weak S-band clutter from patch 31 at Beiseker.

Shape Parameter a_w. Table 5.20 presents the Weibull shape parameter a_w and ratios of standard deviation-to-mean and mean-to-median for clutter amplitude distributions in low-relief agricultural terrain by depression angle and radar spatial resolution. The statistical populations underlying the data of Table 5.20 are shown in Table 5.16. Table 5.20 shows that very large values of spread occur in spatial clutter amplitude distributions at low angles and high resolution in low-relief agricultural terrain. For example, at near grazing incidence (i.e., 0° to 0.25° depression angle) and at high resolution (i.e., A = 10³ m²), ratios of mean-to-median and standard deviation-to-mean of 29.5 dB and 13.7 dB, respectively, indicate a very highly skewed distribution.

The main parametric trend of a_w in Table 5.20 is with radar spatial resolution. In every case, a_w is greater at 10³ m² resolution that at 10⁶ m² resolution. However, at the higher resolution of 10³ m², a_w also strongly depends on depression angle. That is, in low-relief agricultural terrain, although is largely invariant with depression angle, a_w at high resolution decreases strongly from large values at grazing incidence (i.e., 0° to 0.25°) to much smaller values at higher angles. Consideration of Table 5.16 and comparison of Table 5.20 with Table 5.18 indicates that this trend in low-relief agricultural terrain is supported by a much larger population of measurements separated into more finely graduated depression angle regimes than the corresponding trend in high-relief agricultural terrain. Therefore, as in high-relief agricultural terrain, modeling of clutter in low-relief agricultural terrain must still be done in narrow regimes of depression angle to accommodate this strong trend of decreasing spread in clutter amplitude distributions with increasing angle of illumination, even though mean clutter strengths in low-relief agricultural terrain are relatively insensitive to angle of illumination.

The reasons that depression angle affects spread (see Table 5.20) but not mean strength (see Figure 5.20 and Table 5.19) in clutter spatial amplitude distributions in low-relief farmland are as follows. In low-relief farmland, dominant clutter sources are large, discrete, vertical objects. At low angles strong returns are received from these discrete sources, but much (e.g., 75%) of the intervening terrain is either shadowed or provides very weak returns due to the illumination being at grazing incidence. As a result, in low-relief farmland at low depression angle clutter amplitude distributions have very large spread. As depression angle increases, the intervening terrain between strong discrete sources comes under stronger illumination. The weak returns from these regions rapidly increase, and as a result spreads in amplitude distributions rapidly decrease, as shown in Table 5.20. However, the strong returns from the discrete objects at the high ends of the distributions tend to be relatively independent of depression angle and continue to dominate their mean strengths, with the result that the mean strengths in low-relief farmland as shown in Table 5.19 and Figure 5.20 are largely independent of depression angle (cf. Chapter 2, Figure 2.47).

Each pair of a_w numbers in Table 5.20 comes from a scatter plot of spread vs spatial resolution. The standard deviation-to-mean scatter plot for the 0° to 0.25° depression angle regime in Table 5.20 is shown in Figure 5.21. The data in Figure 5.21 show a very strong trend of decreasing spread with decreasing resolution (i.e., increasing A). There is a very large amount of measurement data underlying the scatter plot of Figure 5.21; see Table 5.16. In terms of plot symbols, Figure 5.21 is more highly populated than most similar scatter plots in Chapter 5, only missing three plot symbols, i.e., only missing narrow pulse data in the third range interval in the three high bands. Not only does the regression line in Figure 5.21 show a very strong trend whereby the ratio of standard deviation-to-mean rapidly drops from very high values—among the highest of any presented in Chapter 5—to very low values with increasing A, but in addition the plot symbols are for the most part tightly correlated to the regression line and show relatively little scatter away from this line.

Underlying Variability. In low-angle land clutter there is considerable patch-to-patch variability for any given specification of terrain type, relief, depression angle, and radar parameters. This is particularly true in low-relief agricultural terrain where specific influences of discrete sources and propagation prevail. For example, consider the results in the dark blue, 0.25° to 0.75° depression angle regime in Figure 5.20 and Table 5.19, which is the depression angle regime containing the largest number of measurements in low-relief agricultural terrain. In Figure 5.20, these dark blue results show a smooth trend of increasing with frequency, VHF to L-band, which levels off from L-band through X-band. Underlying this smooth general trend is considerable patch-to-patch variability. Within these dark blue data, the maximum and minimum values of mean clutter strength within the set of contributing like-classified measurements²⁶ in each frequency band are as follows: at VHF, −6.1 and −72.2 dB; at UHF, −10.7 and −74.4 dB; at L-band, −7.8 and −75.7 dB; at S-band, −10.9 and −73.5 dB; and at X-band, −15.1 and −50.0 dB. The standard deviation of the decibel values of mean clutter strength as a measure of spread in each frequency band is: at VHF, 12.7 dB; at UHF, 11.0 dB; at L-band, 8.8 dB; at S-band, 7.2 dB; and at X-band, 4.8 dB. Thus significantly decreasing patch-to-patch variability in mean clutter strength occurs with increasing frequency VHF through X-band in low-relief agricultural terrain (cf. corresponding discussion based on repeat sector data in Chapter 3 at the end of Section 3.7.3). The principal reason for this decreasing variability with increasing frequency is that propagation influences diminish with increasing frequency. Such underlying patch-to-patch variability makes clear why selected individual measurements historically did not lead to a very clear overall picture of the general characteristics of low-angle land clutter. As indicated here, a large amount of measurement data is required to find general trends.

5.4.2.3 LEVEL AGRICULTURAL TERRAIN

The previous section showed that at lower frequencies (viz., VHF and UHF) in open low-relief agricultural terrain, mean clutter strengths are reduced due to multipath loss entering effective clutter strength σ°F⁴ through the propagation factor F. In such situations, the direct ray tends to be canceled by the multipath ray that reflects from terrain with 180° phase reversal. The interference between the direct ray and multipath ray causes lobing on the antenna elevation pattern as from a two-element interferometer, resulting in a null in the horizon plane which is the general direction of clutter sources.

The details of the multipath loss depend on the terrain between the clutter patch and the radar. For the Phase One 60-ft antenna mast height, the elevation angle to the peak of the first multipath lobe above a level surface is 1.5° at VHF, 0.6° at UHF, and 0.2° at L-band. Depending on the particular undulations and inclinations of the terrain between the radar and the clutter patch, differing amounts of multipath loss or even gain can occur depending upon where on the lobing pattern the clutter patch is illuminated. Since terrain slopes in low-relief terrain are less than 2°, these undulations and inclinations are seldom extreme enough to raise VHF illumination completely out of the horizon plane null. Differing amounts of VHF multipath loss will occur depending from where on the underside of the first multipath lobe (i.e., how deeply into the null) the patch is illuminated (see Section 3.4.1.4 for specific examples).

From these considerations, it is clear that maximum multipath loss occurs in very level open terrain such that clutter sources are constrained to lie deep in the horizon plane null. What is the frequency characteristic of land clutter—how much multipath loss occurs and how high in frequency is the effect seen—in very level agricultural terrain, in contrast to the generally low-relief agricultural terrain of the preceding section? If the terrain is level enough (no terrain is perfectly level), the only factor involved in raising clutter sources into illumination is the heights of the clutter producing objects on the terrain surface.

To provide empirical information on this matter, results are provided in Section 5.4.2.3 from the Phase One measurement site situated at Corinne on the Regina Plain in southcentral Saskatchewan. Corinne is selected because it is a canonically level farmland site with only farmland discretes rising as clutter sources above level fields. Repeat sector clutter measurements at Corinne were discussed in Chapter 3, e.g., Sections 3.3.2.1 and 3.4.1.4.3; see also Figure 3.7.

Corinne was one of the 30 measurement sites contributing to the low-relief agricultural land clutter results of Section 5.4.2.2. Table 5.21 indicates that the Corinne database for level agricultural terrain consists of 345 measured clutter histograms from 14 different clutter patches. Of these 14 pure level farmland clutter patches, five occurred at ranges from 1 to 2 km, seven occurred at ranges from 2 to 12 km, one extended from 12 to 24 km, and one extended from 24 to 28 km. Within 12 km, terrain elevations over contributing patches varied by no more than 15 ft from site center. Terrain elevations of the two clutter patches beyond 12 km were about 100 ft higher than site center. Of the 14 contributing clutter patches at Corinne, three were classified with 0% incidence of trees, and the remaining 11 were classified with 1 to 3% incidence of trees. A significant portion of the

Corinne terrain was mixed farmland/herbaceous rangeland; this mixed open terrain was not included in the Corinne level farmland results presented here. By “level” at Corinne is meant terrain with slopes < 1°; that is, terrain that is of landform class 1 or 3; see Table 2.2. Corinne patches of landform classes other than 1 or 3 are also excluded in the results presented here. An aerial photo of the Corinne terrain is provided in Figure 3.35.

Phase One measurements were conducted at Corinne with three different antenna heights, nominally, 30, 45, and 60 ft. All of the results presented here are for the 60-ft antenna height. Results are presented in Figure 3.36 and Table 3.5 for all three antenna heights at Corinne.

Trends in . Table 5.22 presents mean clutter strength for level agricultural terrain by frequency band, polarization, and depression angle and includes the number of measurements upon which each value of is based. The data of Table 5.22 are plotted in Figure 5.22. The mean strength results of Figure 5.22 may be compared with the Corinne repeat sector mean strength results shown in Figure 3.7 of Chapter 3. The main parametric trend observed in Figure 5.22 is that in level farmland increases strongly with increasing frequency, VHF through X-band. The amount of the increase in from VHF to X-band is 25 to 30 dB. No leveling off of this level farmland characteristic occurs in the microwave bands, in contrast to the corresponding characteristic for general low-relief farmland—see Figure 5.20. The strong trend of increasing with increasing frequency in level farmland is entirely due to multipath loss entering clutter strength through the propagation factor. There appears to be no multipath loss in at X-band on level farmland (compare Table 5.22 with Tables 5.19 and 5.17), but multipath loss occurs on level farmland for all bands below X-band. By frequency band, the approximate amount of multipath loss in on level farmland in Table 5.22 and Figure 5.22 is: several dB at S-band, 10 dB at L-band, 20 dB at UHF, and 25 to 30 dB at VHF. The resulting, very weak, −50 to −60 dB levels of at VHF in level farmland are approximately equal to corresponding clutter strengths in level desert and low-relief grassland, and somewhat stronger than corresponding clutter strengths in wetland. At X-band, the level farmland clutter strengths in the −30 to −35 dB range are somewhat stronger—by 5 to 10 dB—than corresponding clutter strengths in level desert, low-relief grassland, and wetland.

The weak, level farmland values of at VHF—in the −50 to −60 dB range—remain accurate, even though they are so weak. Almost all of the Phase One measured clutter histograms contain some samples at radar noise level. Mean clutter strength in the histogram is always computed two ways—first, as an upper bound, where the noise samples retain their noise power values, and second, as a lower bound, where the noise samples are given received power values equal to zero. The true value of mean clutter strength that would be measured by an infinitely sensitive radar, such that no noise samples would occur, must lie between these bounding limits. Only those measured clutter histograms are retained for which the differences between the upper bound and lower bound to mean clutter strength are < 1.5 dB. Usually these bounding estimates of mean clutter strength are within a small fraction of a dB. In any case, all values of mean clutter strength upon which Chapter 5 is based, even very weak ones, cannot be in error by more than 1.5 dB, and usually the error is much less. Coherent integration is utilized in processing the Phase One data to increase sensitivity to weak clutter returns (see Appendix 3.C).

Now consider more closely what is happening in the level farmland data of Table 5.22 and Figure 5.22. First consider the dark blue, 0.25° to 0.75° results. On the level Corinne landscape, such relatively high depression angles occur only because of the effect of antenna mast height over very near-range clutter patches. Thus the dark blue, 0.25° to 0.75° results come from the five level clutter patches all in the 1- to 2-km range interval from the radar. Clutter returns from these near-range clutter patches are clearly discernible well above system noise level at all five Phase One frequencies. However, clutter patches at longer ranges rapidly become too weak for Phase One measurement at the lower frequencies due to multipath loss. Thus at VHF, of the seven patches in the 2- to 12-km range interval, only two provided clutter strong enough to be measured (given by the cyan, 0° to 0.25° results in Figure 5.22), and neither of the two longer range patches beyond 12 km were measurable above radar noise. At UHF, in addition to the five 1- to 2-km patches (dark blue, 0.25° to 0.75°), all seven patches between 2 and 12 km were measurable (cyan, 0° to 0.25°), but the two longer range patches continued to not provide measurable returns at UHF. At L-band, all 1- to 2-km patches (dark blue, 0° to 0.75°) and 2- to 12-km patches (cyan, 0° to 0.25°) remained measurable, and the single, 12- to 24-km patch at 100-ft higher elevation also became measurable (dark green, 0° to −0.25°). At S- and X-bands, all 14 patches provided valid measurements, including the longest range, 24- to 28-km patch; this last patch was also at 100-ft higher elevation and also contributes to the dark green, 0° to −0.25° results in these bands.

Thus in Figure 5.22, with increasing frequency the clutter results come from patches enclosed within a gradually enlarging terrain region centered at the radar. This region is bounded by 4 km at VHF, 12 km at UHF, 24 km at L-band, and 28 km at S- and X-bands. Consider that, at VHF, the height to the peak of the first (1.5°) multipath lobe at 4 km is 105 m; obviously few clutter sources (e.g., farm buildings, grain storage silos, trees) reach this high, which explains the lack of discernible clutter beyond 4 km at VHF. In contrast, at X-band, the height to the peak of the first (0.03°) multipath lobe is only 6.3 m at 12 km. Thus at X-band, most clutter sources within 12 km are high enough to be fully illuminated. The strength of the illumination decreases with decreasing frequency from X-band.

The only common terrain region to all frequency bands in the results of Figure 5.22 is the close-range, 1 to 2 km region. Results from this close-range region are given by the dark blue, 0.25° to 0.75° plot symbols in Figure 5.22. Although the dark blue results generally show increasing clutter strength, VHF to X-band, they also show an S-band dip between L- and X-bands. The cyan, 0° to 0.25° results come from patches within the 2- to 12-km region, with fewer patches from within this region contributing at VHF than in the higher bands. The somewhat higher terrain beyond 12 km provides the dark green, 0° to −0.25° results. At L-band, these dark green results are shown as open plot symbols because they are based on single measurements. However, although relatively weak, these single L-band, dark green measurements may not be atypical, since at UHF and VHF the clutter returns from the terrain beyond 12 km drop to such low levels that they could not be measured with the Phase One equipment.

The purple, 0.75° to 1.5° results at X-band in Figure 5.22 are also shown as open plot symbols because they also come from single measurements. These results arose as follows. One of the patches in the 1- to 2-km region was at somewhat closer range than the others and had a depression angle close to 0.75°. In these particular (purple) X-band measurements of this patch which are at high range resolution, the precise positions of the range gates on the ground together with the precise X-band antenna height (slightly higher than the other bands) were such as to cause the depression angle to just exceed 0.75° (viz., 0.78°). For the corresponding low resolution X-band measurements of this patch, the range gate positions were at somewhat greater distances, and the depression angle was less than 0.75° (viz., 0.71°). Thus the low resolution X-band measurements from this patch are included in the dark blue results in Figure 5.22, as are all other measurements of the patch.

Similar migration of particular patch measurements across depression angle regime boundaries occasionally happens elsewhere in the results of Chapter 5. Specific discussion of individual sites such as is given here for Corinne is not possible in most other results of Chapter 5, which are generally based upon numerous sites in each terrain category. However, specific discussion of repeat sector results by individual site is given for many sites (including Corinne) in Section 3.4.

Shape Parameter a_w. Table 5.23 presents the Weibull shape parameter a_w and ratios of standard deviation-to-mean and mean-to-median for clutter amplitude distributions in level agricultural terrain by depression angle and radar spatial resolution. The statistical populations underlying the data of Table 5.23 are shown in Table 5.21. Since the level farmland results of Chapter 5 come from just one site (viz., Corinne), the populations shown in Table 5.21 are much lower than for most other terrain types. Table 5.23 shows that very large values of spread occur in spatial clutter amplitude distributions at low angles and high resolution in level agricultural terrain. For example, at near grazing incidence (i.e., 0° to 0.25° depression angle) and at high resolution (i.e., A = 10³ m²), ratios of mean-to-median and standard deviation-to-mean of 36.4 and 13.4 dB, respectively, indicate a very highly skewed distribution.

The main parametric trend of a_w in Table 5.23 is with radar spatial resolution. In every case, a_w is greater at 10³ m² resolution that at 10⁶ m² resolution. However, at the higher resolution of 10³ m², a_w also strongly depends on depression angle. That is, in level agricultural terrain, although is largely invariant with depression angle, a_w at high resolution decreases strongly from large values at grazing incidence (i.e., 0° to 0.25°) to much smaller values at higher angles.

Each pair of a_w numbers in Table 5.23 comes from a scatter plot of spread vs spatial resolution. The standard deviation-to-mean scatter plot for the 0° to 0.25° depression angle regime in Table 5.23 is shown in Figure 5.23. The data in Figure 5.23 show a very strong trend of decreasing spread with decreasing resolution (i.e., increasing A). There is a relatively small amount of measurement data underlying the scatter plot of Figure 5.23; see Table 5.16. In terms of plot symbols, Figure 5.23 is less populated than most similar scatter plots in Chapter 5, with results coming only from the first range interval at Corinne. The five individual frequency bands and the two pulse lengths per frequency band are easy to follow in these results. There is very tight correlation of these data to the regression line. These Corinne data strongly make the case, upon which all the results in Chapter 5 are based, that spread is predominantly affected by resolution and that direct effects of radar frequency on spread are small.