Accurate measurement of tree parameters in forested environments is of great value for forest resource inventory and protection in response to environmental and climate changes. Synthetic aperture radar (SAR) has irreplaceable advantages in forest parameter estimating. Studies have shown that a long wavelength SAR signal saturates at a high level of forest parameters (e.g., stand density and tree size) [1,2] and is more suitable for forest parameter retrieval. It is especially true for the P-band (with a wavelength, λ, of ~70 cm) SAR [3]. Moreover, a polarimetric SAR (PolSAR) system fully uses the polarization characteristics of electromagnetic waves backscattered from a tree or a radar target, obtaining more forest information than a single-pol SAR sensor. Thus, the P-band PolSAR is widely considered and used for forest parameter retrieval [4–6]. Additionally, the study of the decomposed scattering power from ponderosa pine forests shows that as the stand density changed from sparse to dense, the dynamic range of the P-band total power increased by 5 dB [7]. The enlarged dynamic range is substantial and provides better potential in forest parameter retrieval because the SAR backscatter’s saturation level is elevated.

Several airborne PolSAR P-band sensors were developed, including the United States (US) National Aeronautics and Space Administration/Jet Propulsion Laboratory (NASA/JPL) airborne SAR (AIRSAR) (https://airsar.jpl.nasa.gov) and the NASA/JPL UAVSAR-P (https://airmoss.jpl.nasa.gov). With the to-be-launched P-band SAR in 2024 (https://www.esa.int/Applications/Observing_the_Earth/Biomass) by the European Space Agency, the acquired SAR data are publicly available through the Internet. Thus, it is of great value to investigate P-band PolSAR forest electromagnetic scattering characteristics further in theory and application. One is ready to embrace the upcoming launch and its significance in PolSAR studies in forested environments.

Researchers develop backscatter models to understand the radar backscatter in forested environments. The models primarily include simulation or forward ones [8–11], scattering feature delineation models [12,13], and vertical structure ones [14,15]. They advance the understanding of the radar backscatter in forests. Although the forest floor is usually assumed to be rough, the influence of complex terrain on the forest backscatter is not fully revealed yet. It is of significant concern when a P-band PolSAR sensor is considered because of its strong penetration ability (through tree canopies). The ground surface-related backscatter can play a significant role. Also, electromagnetic scattering from complex terrain can adversely influence the radar backscatter in forested areas, introducing uncertainty and errors in the forest parameter inversion [16,17]. To ensure accurate forest parameter retrieval from P-band PolSAR data, one must fully understand and quantify the impact of complex terrain scattering on the forest backscatter and compensate for the impact as much as possible. Therefore, we aim to analyze the topographic impact on P-band PolSAR data from forested areas based on the polarimetric decomposition technique and achieve the objective of decreasing or mitigating the topographic effect on the PolSAR data. The algorithm’s theoretical novelty is i) to separate radar backscatter components related to the ground surface from the non-ground surface and ii) to use backscatter components of the ground surface to compensate for the topographic effect. The innovative aspects in applications include quantifying the impact of radar look directions, large and small radar incidence angles, and soil moisture on the topographic compensation.

Azimuthal symmetry is one important scattering feature of trees in forests in PolSAR data. A tree is typically considered azimuthally symmetric due to the shapes of a trunk and crown being geometrically symmetrical or near-symmetrical. An azimuthally symmetric radar target should have an azimuth orientation angle (θ₀) of zero, and then the azimuth angle effect is 0. On the contrary, rough terrain typically has a facet feature or is azimuthally asymmetric [18]. The θ₀ value deviates from 0. With the significant penetration ability through tree canopies and reaching the ground at the P-band, the radar backscatter from the complex terrain is, unfortunately, influenced by θ₀ that can deviate from 0 considerably.

Using the P-band PolSAR data collected by the NASA/JPL AIRSAR sensor (https://airsar.jpl.nasa.gov), we created the S_HH intensity image near Mt. Shasta, California, US. Fig. 1 (a) shows the image in black (low value) and white (high value). The acquisition date was 1 May 1991. The image size is 1000 rows by 600 columns and covers an area of about 3.8 km (width) by 5.3 km (height). The area was mainly covered by ponderosa pine (Pinus ponderosa) trees [1,10]. The topographic features are rolling hills and are evident in Fig. 1 (a). Fig. 1 (b) is the θ₀ image generated from P-band PolSAR data, where colors from blue to red represent the low to high values. The θ₀ image indicates significant derivation from 0. One should consider forest targets azimuthally asymmetric. The asymmetric characteristics are consistent with the revealed topographic features in Fig. 1 (a).

Considering the digital elevation model (DEM) of the Shasta area, one notes that the rolling hills dominate. Referring to the flight or azimuth direction of Fig. 1 (a), Fig. 1 (c) is the slope angle image along the azimuth direction (short for the azimuth slope angle, θ), calculated from DEM. The image has 530 rows and 380 columns. Comparing Fig. 1 (c) with Fig. 1 (b), one may conclude that they are similar. The θ₀ and azimuth slope angle or slope (tan θ) are significantly correlated. Thus, the azimuth slope or topography should greatly affect the scattering characteristics of forest targets when imaged by the P-band PolSAR sensor. Additionally, the slope or inclined surface causes depolarization of the incoming polarized radar waves, producing cross-polarized scattering. It should be noted that due to the vegetation covering and rough surface [1], Fig. 1 (b) appears noisier than Fig. 1 (c).

The Bragg scattering model is widely used for the backscatter from rough surfaces [10,12,14]. Its Sinclair matrix is

$ {{\mathbf{S}}_{{\mathrm{Bragg}}}} = \left[ {\begin{array}{*{20}{c}} {{B_{{\mathrm{HH}}}}}&0 \\ 0&{{B_{{\mathrm{VV}}}}} \end{array}} \right] $ (1)

where B_HH and B_VV are the modeled horizontally transmitted and horizontally received (HH) backscatter and the modeled vertically transmitted and vertically received (VV) backscatter, respectively. They, determined by the radar local incidence angle (θ_i) and ground relative dielectric constant (ε_r), are

$ \left\{ {\begin{array}{*{20}{l}} {{B_{{\mathrm{HH}}}} = \dfrac{{\cos {\theta _i} - \sqrt {{\varepsilon _r} - {{\sin }^2}{\theta _i}} }}{{\cos {\theta _i} + \sqrt {{\varepsilon _r} - {{\sin }^2}{\theta _i}} }}} \\ {{B_{{\mathrm{VV}}}} = \dfrac{{\left( {{\varepsilon _r} - 1} \right)\left[ {{{\sin }^2}{\theta _i} - {\varepsilon _r}\left( {1 + {{\sin }^2}{\theta _i}} \right)} \right]}}{{{{\left( {{\varepsilon _r}\cos {\theta _i} + \sqrt {{\varepsilon _r} - {{\sin }^2}{\theta _i}} } \right)}^2}}}.} \end{array}} \right. $ (2)

The backscatter from a rough surface at the azimuth orientation angle (θ₀) is modeled by rotating the Bragg scattering model [18]

$ {{\mathbf{S}}_{{\mathrm{Bragg}}\_{\mathrm{rotated}}}} = \left[ {\begin{array}{*{20}{c}} {\cos {\theta _0}}&{ - \sin {\theta _0}} \\ {\sin {\theta _0}}&{\cos {\theta _0}} \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {{B_{\rm{HH}}}}&0 \\ 0&{{B_{{\mathrm{VV}}}}} \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {\cos {\theta _0}}&{\sin {\theta _0}} \\ { - \sin {\theta _0}}&{\cos {\theta _0}} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} {{S_{\rm{HH}}}}&{{S_{{\mathrm{HV}}}}} \\ {{S_{{\mathrm{VH}}}}}&{{S_{{\mathrm{VV}}}}} \end{array}} \right] $ (3)

where S_HH (horizontally transmitted and horizontally received) and S_VV (vertically transmitted and vertically received) are co-polarized scatterings, and S_HV (horizontally transmitted and vertically received) and S_VH (vertically transmitted and horizontally received) are cross-polarized scatterings. For the mono-state radar sensor, S_HV = S_VH when the reciprocity is applied.

In general, the radar backscatter is a function of ε_r, θ_i, and θ₀. ε_r is directly determined by soil moisture and its components/textures. θ_i and θ₀ relate to the terrain topography and radar imaging geometry, including the azimuth slope angle (θ), range slope angle (θ_s), and radar look angle (θ_l). Fig. 2 shows their relationships. When the slope faces the radar look direction (Fig. 2 (a) and Fig. 2 (b)), one has

$ {\theta _i} = \left| {{\theta _l} - {\theta _s}} \right| . $ (4)

θ_l ≥ θ_s in Fig. 2 (a), but θ_l < θ_s in Fig. 2 (b). If the slope faces away from the radar look direction, the viewable area is by the radar if θ_l + θ_s ≤ 90° (Fig. 2 (c)). Then,

$ {\theta _i} = {\theta _l} + {\theta _s} . $ (5)

If θ_l + θ_s > 90°, the area is not viewable and is a radar shadow. No radar return from the shadowed area exists.

Considering the above discussion, one can link the four angles with

$ {\mathrm{tan}} {\theta _0} = \frac{{{\mathrm{tan}} \theta }}{{ - {\mathrm{tan}} {\theta _s}\cos {\theta _l} + {\mathrm{sin}} {\theta _l}}} {\mathrm{.}} $ (6)

Since θ_l is a radar system parameter, θ₀ topographically relates primarily to the azimuth slope angle [18]. The relevance is evident in Figs. 1 (b) and (c).

Similarly, one can derive the θ_i, θ_s, θ_l, and θ relationship as

$ \mathrm{cos}\theta_i=\frac{\mathrm{tan}\theta_s\mathrm{sin}\theta_l+\cos\theta_l}{\sqrt{1+\mathrm{tan}^2\theta_s+\mathrm{tan}^2\theta}}. $ (7)

Considering the relative importance of the numerator and denominator, θ_i is mainly determined by θ_s.

The PolSAR backscatter from the complex terrain is determined by various factors such as the azimuth slope, range slope, and ground relative dielectric constant. The complicated backscatter can be solved if the inputs are available. However, θ₀, θ_i, and ε_r are usually unavailable. Since the azimuth orientation angle is a function of the azimuth and range slope angles and radar imaging geometry, an alternative relationship among them exists. With (6) and (7), one has

$ \mathrm{tan}\theta_0=\frac{\mathrm{tan}\theta}{\sqrt{\mathrm{tan}^2\theta-\mathrm{sin}^2\theta_i\left(1+\mathrm{tan}^2\theta+\mathrm{tan}^2\theta_s\right)}}\mathrm{.} $ (8)

θ₀ can be considered the surrogate for the effects of θ, θ_i, and θ_s collectively in the topographic compensation. Unfortunately, the presence of trees in forested environments introduces additional interactions between the terrain and trees, including trunk-ground and canopy-ground interactions. Quantifying scattering components related to the ground and non-ground surfaces is necessary, removing the influence of the ground scattering-related component and then finding θ₀. Thus, one can compensate for effects related to the ground-related interactions and better remove the topographic influence.

A mono-state and linearly-polarized PolSAR sensor alternatively transmits an H-polarized signal and receives H- and V-polarized backscatters and then transmits a V-polarized signal and receives H- and V-polarized backscatters. One typically uses S_pq to present the scattering component of the backscatter, with q being the polarization transmitted and p being the polarization received. p or q represents the H or V polarization. The data type of S_pq is complex. In the PolSAR data analysis and with the reciprocal rule (S_HV = S_VH), one presents S_pq as a vector, k, or

$ {\bf{k}} = [{S_{{\text{HH}}}}{\text{ }}\sqrt 2 {S_{{\text{HV}}}}{\text{ }}{S_{{\text{VV}}}}] {\mathrm{.}} $ (9)

The covariance matrix of PolSAR data C₃ is

$ {{\bf{C}}_3} = {{\mathbf{k}}^{\mathrm{T}}} \times {{\mathbf{k}}^*} = \left[ {\begin{array}{*{20}{c}} {{S_{{\text{HH}}}}S_{{\text{HH}}}^*}&{\sqrt 2 {S_{{\text{HH}}}}S_{{\text{HV}}}^*}&{{S_{{\text{HH}}}}S_{{\text{VV}}}^*} \\ {\sqrt 2 {S_{{\text{HV}}}}S_{{\text{HH}}}^*}&{2{S_{{\text{HV}}}}S_{{\text{HV}}}^*}&{\sqrt 2 {S_{{\text{HV}}}}S_{{\text{VV}}}^*} \\ {{S_{{\text{VV}}}}S_{{\text{HH}}}^*}&{\sqrt 2 {S_{{\text{VV}}}}S_{{\text{HV}}}^*}&{{S_{{\text{VV}}}}S_{{\text{VV}}}^*} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} {{C_{11}}}&{{C_{12}}}&{{C_{13}}} \\ {{C_{21}}}&{{C_{22}}}&{{C_{23}}} \\ {{C_{31}}}&{{C_{32}}}&{{C_{33}}} \end{array}} \right] $ (10)

where T is the transpose operator and * is the conjugate operator for a complex variable/value.

A PolSAR decomposition algorithm can identify the ground and non-ground components in the PolSAR data. After the identification, one separates the ground backscatter from the non-ground backscatter. The eigenvector-eigenvalue-based decomposition algorithm extracts the PolSAR backscatter of forest targets without complicated physical scattering models [7,19,20]. With the criteria [7], we decompose C₃ as

$ \begin{split} {{\mathbf{C}}_3} = {\lambda _{\rm{single}}}{{{\boldsymbol{\mathbm{μ}}}}_{\rm{single}}}{{\boldsymbol{\mathbm{μ}}}}_{\rm{single}}^* + {\lambda _{\rm{double}}}{{{\boldsymbol{\mathbm{μ}}}}_{\rm{double}}}{{\boldsymbol{\mathbm{μ}}}}_{\rm{double}}^* + {\lambda _{\rm{volume}}}{{{\boldsymbol{\mathbm{μ}}}}_{\rm{volume}}}{{\boldsymbol{\mathbm{μ}}}}_{\rm{volume}}^* = {\lambda _{\rm{single}}}{{\mathbf{C}}_3}_{\rm{single}} + {\lambda _{\rm{double}}}{{\mathbf{C}}_3}_{\rm{double}} + {\lambda _{\rm{volume}}}{{\mathbf{C}}_3}_{\rm{volume}} \end{split} $ (11)

where ${\lambda _{\rm{single}}}$, ${\lambda _{\rm{double}}}$, and ${\lambda _{\rm{volume}}}$ are eigenvalues of the single, double, and volume scattering components, respectively. ${{{\boldsymbol{\mathbm{μ}}}}_{\rm{single}}}$, ${{{\boldsymbol{\mathbm{μ}}}}_{\rm{double}}}$, and ${{{\boldsymbol{\mathbm{μ}}}}_{\rm{volume}}}$ are eigenvectors corresponding to the three scattering mechanisms. ${{\mathbf{C}}_3}_{\rm{single}}$, ${{\mathbf{C}}_3}_{\rm{double}}$, and ${{\mathbf{C}}_3}_{\rm{volume}}$ are corresponding covariance matrices of the three scattering components and calculated using the eigenvectors.

The radar backscatter in forested areas mainly comes from the tree canopy, ground surface, interactions between the ground surface and tree trunks, and interactions between the ground surface and canopy (e.g., [8―11]). The canopy volume scattering does not relate to the ground surface or topography. The P-band single scattering is mainly from the ground surface, and the double-bounced interactions of the surface and trunk primarily produce the double scattering. Therefore, both components relate to the ground. The ground component ${{\mathbf{C}}_3}_{\rm{ground}}$ is

$ {{\mathbf{C}}_3}_{\rm{ground}} = {\lambda _{\rm{single}}}{{\mathbf{C}}_3}_{\rm{single}} + {\lambda _{\rm{double}}}{{\mathbf{C}}_3}_{\rm{double}}{\mathrm{.}} $ (12)

It is known that trees growing on the flat ground remain largely azimuthally symmetric as radar targets in the PolSAR data. The deorientation method restores the radar backscatter from the non-flat terrain to the flat one, using the polarimetric orientation angle derived from the PolSAR data [21], i.e.,

$ {{\mathbf{C}}_3}_{f{\mathrm{lat}}{\text{ }}{\mathrm{ground}}} = {\mathbf{U}}\left( {{\theta _0}} \right){{\mathbf{C}}_3}_{\rm{ground}}{\mathbf{U}}{\left( {{\theta _0}} \right)^{\mathrm{T}}} $ (13)

where $ {\mathbf{U}}\left( {{\theta _0}} \right) $ is a rotation matrix. θ₀ is estimated from the PolSAR data. With (13), $ {{\mathbf{C}}_3} $ in (11) is updated as

$ \mathbf{C}_3^{\mathrm{updated}}=\mathbf{C}_{3\mathrm{flat}\text{ }\mathrm{ground}}^{ }+\lambda_{\rm{volume}}\mathbf{C}_{3\mathrm{volume}}^{ }\mathrm{ } $ (14)

where considering $ {\mathbf{C}}_3^{{\mathrm{updated}}} $, one can interpret that the influence of the non-flat topography on the PolSAR backscatter in forested environments is considered removed.

A valid topographic compensation algorithm removes the adverse influence caused by the complex topography on the radar backscatter from trees. However, it should not affect the scattering characteristics of trees on the gentle or flat terrain. Thus, we used PolSAR data covering the Howland Forest, Maine, US, to investigate the validity. The forest (45°12′N, 68°44′W) is situated within expansive and lowland areas, 7.5 km west of the town of Howland. Established in 1986, it is a forest ecosystem research site with mature evergreen forests where the conifer/northern hardwood transition characterizes forests. The dominant species are spruce (e.g., black spruce, Picea mariana) and hemlock (e.g., eastern hemlock, Tsuga canadensis (L.) Carr.), with an average age of 140 years old (https://crsf.umaine.edu/forest-research/howland-research-forest/). The terrain varies from flat to gently rolling hills (https://www.nrs.fs.fed.us/ef/locations/me/howland_cef/). The NASA/JPL UAVSAR P-band PolSAR data was acquired on 26 August 2014, with a 167° azimuth direction. The ground-range data has a pixel size of 15.4 m by 15.4 m. Fig. 3 (a) is an S_HH intensity image of the PolSAR data. The image size is 570 rows and 570 columns. The brightness of the entire image is relatively uniform, indicating a lack of topographic variation, or the terrain is flat or gentle in slope.

Figs. 3 (b) and (c) are θ₀ values computed from the PolSAR data before and after the topographic compensation algorithm. Both images are mainly cyan. The estimated orientation angle values are low and close to 0°. Thus, the compensation has not affected the scattering characteristics of trees in the PolSAR data, and the similar colors in both images show that the algorithm has little influence on the scattering characteristics of the forests. Quantitatively, in the sampling site (the green box in Fig. 3 (a)), the mean and standard deviation values of θ₀ are 0.36° and 2.57° before the compensation, and they become –0.33° and 1.40° after the compensation. The changes are small. The algorithm does not affect the PolSAR data. Thus, the compensation is unnecessary when the terrain is flat or gentle. The results support the algorithm’s validity.

Fig. 4 shows the azimuth orientation angle (θ₀) after the topographic compensation. The figure was mainly green, indicating that the θ₀ values are close to 0. Compared to Fig. 1 (b), θ₀ values decrease, and features related to terrain topography may disappear. The topographic compensation is effective. Quantitatively (as shown in Table 1), before the compensation, θ₀ values are mostly dispersed between –20° and 20°, with about 45.2% of values (in absolute) > 5°. After the compensation, θ₀ values may be centered from –10° to 10°. About 4.2% of values (in absolute) are > 5°. Thus, the compensation effectively improves the azimuthal symmetry of radar targets at P-band PolSAR.

Next, whether the topographic compensation algorithm creates unwanted compensation or negative consequences in the PolSAR backscatter is of further interest. After performing 3×3 Boxcar filtering to reduce the noise and speckle effect, we extracted |S_HH|², |S_HV|², and |S_VV|² values before and after the compensation. Fig. 5 shows their scatterplots. The X-axis and the Y-axis represent the values before and after the compensation, respectively. For the |S_HH|² and |S_VV|² plots (Figs. 5 (a) and (b)), the points are clustered with a linear feature. After the linear regression analyses, the regression line slopes are near 1.0, and the intercepts are close to 0. The R² values are ≥ 0.98. Therefore, the compensation does not alter their values, which is expected for an effective topographic compensation algorithm.

In contrast, |S_HV|² values before and after the compensation are not well clustered near a line (Fig. 5 (c)). Instead, they spread. The regression line slope is 0.80, deviating from 1.0. Although the intercept of 0.002 is small, the overall |S_HV|² values are generally small. Thus, the intercept value can be relatively and proportionally large. Again, the considerable variation in the cross-polarized backscatter is expected since the topographic effect depolarizes the incoming radar wave. However, with a slope value of 0.80 (less than one), the depolarization value (i.e., effect) caused by topography decreases after the compensation. Thus, the algorithm performs as intended.

Then, all types of backscatter values used in the PolSAR decomposition and for the entire Mt. Shasta area were compared before and after the topographic compensation. The mean (μ) and one standard deviation (σ) of the backscatter are shown in Table 2. Δ=(mean after compensation minus mean before compensation)/(mean after compensation). The compensation has little influence on the co-polarized backscatter. The relative change rates are about 5%. However, the compensation significantly impacts the cross-polarized backscatter. The relative change rates are about –11% to –25% after the compensation. Thus, the proposed algorithm performs well.

As illustrated in Fig. 2, the same inclined surfaces change from facing the radar to facing away from the radar when the radar images the area from opposite directions. In this case, topographic effects on the PolSAR data differ. A valid algorithm should reduce the topographic effect regardless and output similar θ₀ values of radar targets at the same ground location. The θ₀ after an adequate compensation should be small and vary less spatially as a function of local topography (i.e., slope and aspect) and radar imaging geometry (i.e., the radar azimuth angle and look angle). Then, we studied another forested area near the Eno River State Park, North Carolina, US (https://www.ncparks.gov/eno-river-state-park/home). The park is about 175000 km²., mixed primarily with beech (Fagus Grandifolia), dogwood (Cornus), maple (Acernis), oak (Quercus), poplar (Populus), and loblolly pine (Pinea Taeda). The altitude of the study area is from 119.8 m to 227.2 m. The terrain is piedmont.

Two NASA/JPL UAVSAR P-band PolSAR data acquired on 5 September 2015 were downloaded. The data identifications are DukeFr_22529_15130_006_150905_PL09043020_05_XX_01 (short for DukeFr_225 in the following) and DukeFr_04534_15130_005_150905_PL09043020_05_XX_01 (DukeFr_045 short for). DukeFr_225 was acquired with the aircraft flying at an azimuthal heading of 225° in aspect (North being 0° in aspect), and the azimuthal heading angle was 45° in aspect for DukeFr_045. Thus, the P-band SAR imaged the study area from opposite directions, which is excellent in evaluating the influence of the terrain on the radar backscatter from the forested areas. The spatial resolution of the PolSAR datasets is ~15.4 m in azimuth and ~15.4 m in the ground range.

Figs. 6 (a) and (b) are the S_HH intensity images of DukeFr_225 and DukeFr_045, respectively. The UAVSAR is a left-side-looking imaging system. The image brightness varies with the undulation of the terrain and the radar-looking direction. The area, pointed by the red arrow, faces the radar-looking direction in DukeFr_225 data, but it faces away from the radar in DukeFr_045 data. Thus, the area is brighter in the former than that in the latter. Figs. 6 (c) and (d) show the azimuth slope angles calculated from the DEM data with the 225° and 45° aspect angles (i.e., the flight headings of DukeFr_225 and DukeFr_045), respectively. The slopes (i.e., inclined surfaces) are reversed as indicated by colors. The azimuth slope data (Fig. 6 (c)) have a mean value of 0.16° and one standard deviation of 4.43°. A mean value of –0.16° and one standard deviation of 4.43° are for the azimuth slope data in Fig. 6 (d). According to previous analyses (Fig. 2 and (4) and (5)), the local radar incidence angle (θ_i) decreases when a slope faces SAR. In contrast, θ_i increases when the slope faces away from SAR if the inclined surface is viewable by the radar. With the available DukeFr_225 and DukeFr_045 θ_i data, we co-registered each with the corresponding PolSAR data. The SAR and θ_i data have the exact spatial resolution. Figs. 6 (e) and (f) are the θ_i images, in greyscale, of DukeFr_225 and DukeFr_045, respectively. The reverse of the topographic features (e.g., convex becoming concave and vice versa) at the same location is evident.

The θ_i values were extracted at two sample sites, pointed by white letters A₁ and A₂ in Figs. 6 (e) and (f). Each rectangle has a 5×5 size. A₁ is on the slope facing away from the SAR look direction in DukeFr_225, but it faces the look direction in DukeFr_045. The mean value of θ_i is 60.0° in Fig. 6 (e) but becomes 40.0° in Fig. 6 (f). A₂ is just the opposite topographically, with a mean θ_i value of 42.2° in DukeFr_225 and a mean θ_i value of 62.2° in DukeFr_045. Therefore, different radar look directions in the non-flat ground produce variable azimuthal slopes and range slopes, creating different degrees of topographic effects on PolSAR data.

Figs. 7 (a) and (b) are the θ₀ images before the topographic compensation. The θ₀ values change significantly over the study area. They are nearly opposite (or reverse) in positive and negative values (Fig. 7 (a) c.f. Fig. 7 (b)). The reverse in values in sing (plus or minus) corresponds to the opposite radar look directions, suggesting the validity using the θ₀ values to component for the topographic effects. Incidentally, spatial patterns in Fig. 7 (a) and Fig. 6 (a) may be similar, and so are the patterns in Fig. 7 (b) and Fig. 6 (b). The topography influences P-band PolSAR data from forests in piedmont.

After the topographic compensation, the DukeFr_225 and DukeFr_045 θ₀ images are shown in Figs. 7 (c) and (d), respectively. The θ₀ ranges decrease, showing the adequate compensation. Also, Figs. 7 (c) and (d) are similar, indicating the azimuthal symmetric characteristics of trees as radar targets regardless of the radar look directions. As another assessment, we created a binary mask using Fig. 7 (a) for DukeFr_225, calling DukeFr_225_mask. All pixels with θ₀ < 0° belong to one category, and the rest belong to the other. The mean and standard deviation values were calculated for each category. The values are shown in Table 3, and they are substantially away from zero. Similarly, we created another mask (called DukeFr_045_mask) using Fig. 7 (b) for DukeFr_045, categorizing pixels with θ₀ < 0° and θ₀ ≥ 0°. The mean and standard deviations were computed for each category, and the values are tabulated in Table 3. They are significantly away from zero. The topographic effects can be substantial on PolSAR data from forests in piedmont. In both cases, reducing the effects as much as possible in P-band PolSAR data is needed.

Then, we extracted pixels from Fig. 7 (c) categorized by DukeFr_225_mask. The overall moving non-zero θ₀ toward zero values makes decreasing the topographic effects apparent qualitatively. The mean and standard deviations are also given in Table 3, quantifying the decrease. Similarly, pixels classified by DukeFr_045_mask were extracted from Fig. 7 (d). The mean and standard deviation values are tabulated in Table 3 as well. Again, the mean values are near 0° with the reduction in one standard deviation. Decreasing the topographic effects is also apparent quantitatively. Thus, the algorithm can effectively decrease the adverse impact of the terrain on P-band PolSAR backscatter from forested areas.

Two issues related to the topographic compensation effectiveness are next discussed. First, increasing soilmoisture increases the relative dielectric constant of soil (ε_r). High ε_r produces more backscatters related to the ground surface than soil with low ε_r. When the ground soil is saturated, the surface-reflected specular scattering is high. The specular scattering reaches its highest when the forest floor is flooded because water has the highest ε_r of the non-metallic materials. The specular scattering can then hit a tree trunk, increasing the (strongest) double-bounced trunk-ground interactions as observed [22] and modeled PolSAR backscatter [23] in flooded forests. Thus, the relative importance of the ground surface-related backscatter within the total radar backscatter increases. Second, from the SAR imaging point of view and for the same canopy depth, the path length through the canopy increases as the radar local incidence angle increases. Less radar energy penetrates through the canopy at a far range than at a near range. The attenuation is significant when the depth is deep, as shown in modeling studies [24,25]. Thus, scattering components related to the ground surface may not be well characterized, and the algorithm performance can degrade as a possible negative consequence. To the extreme, ground surface-related scattering components may be low and near the radar system noise. The algorithm performance deteriorates at the low radar signal-to-noise ratio (SNR). Next, we analyze NASA/JPL AIRSAR P-band PolSAR data from flooded forests (i.e., the forest floor’s ε_r being the highest) to understand both issues.

The PolSAR data covers a forested area around the Altamaha Wildlife Management Area (AWMA), Georgia, US. Fig. 8 (a) is an S_HH intensity image with 1000 rows × 700 columns. It covers an area of ~10.5 km in the azimuth and about 4.8 km in the range directions. The image is centered at 81°28.57' W and 31°23.20' N. The PolSAR data were acquired on 5 October 1994. The area is on a floodplain. Areas around river channels are constantly flooded because AWMA is in a managed tidal freshwater and brackish water reservoir (https://www.ducks.org/georgia/georgia-conservation-projects/altamaha-wma). The swamps mainly include low-lying hardwood and cypress-tupelo trees (https://georgiawildlife.com/altamaha-wma). The soil moisture of the forest floors is usually high due to gentle local topography and pool-drained soil, typical floodplain characteristics. Thus, the flooded forests are bright white in Fig. 8 (a), while the upland forests are gray. The dark features are river channels or water ponts. Two sample sites were identified, one at the near range with a radar local incidence angle of ~36.25° and the other at the far range with an angle of ~54.14°. The path length increases about 1.4× for the same canopy depth as the incidence angle increases from 36.25° to 54.14°. The two-way canopy attenuation increases about 8.0 times based on radar backscatter modeling [1,13]. With the canopy attenuation and for the same amount of the surface-related radar backscatter, the radar receives much less backscatters from targets at the far range than targets at the near range. The proposed topographic algorithm should perform less well at the far than near ranges.

Fig. 8 (b) shows the θ₀ image without the topographic compensation. The upland forests are primarily on the left, and the flooded forests are on the right. The non-zero θ₀ values are mainly on the left compared to the near-zero or zero θ₀ values on the right. Thus, the ground surface-related backscatter affects the PolSAR data more in the former than that in the latter. After the compensation, θ₀ values move to near zero or zero (Fig. 8 (c) c.f. Fig. 8 (b)). Consequently, although high ε_r increases the relative importance of the ground surface-related backscatter within the total PolSAR backscatter, the topographic compensation algorithm downplays the elevated relative importance, reducing the topographic effects on the PolSAR P-band data acquired on the vegetated floodplain. Thus, the compensation is effective, and the first issue or related concern is addressed.

To understand the second issue, we located one sample site at the near range and one at the far range for the flooded forests. The sites are shown in red squares in Fig. 8 (a). Each square is 50×50 in size. Then, the absolute θ₀ values of pixels at both sites were extracted. The results are shown in Table 4. By column, the topographic compensation algorithm reduces the θ₀ values with smaller mean and standard deviation values at the near and far ranges. Then, the reduction ratio (mean before the compensation divided by mean after the compensation) at the same range was computed. The reduction ratio is 6.29 at the near range and becomes 5.10 at the far range. Thus, the elevated canopy attenuation at the far range, compared to that at the near range, does affect the performance of the topographic compensation algorithm. Thus, caution should be exercised when applying it to forests with deep canopy depth and high canopy density or PolSAR data with a short wavelength (less than the P-band wavelength).

A P-band SAR sensor has two distinct advantages in earth observation for forested environments. One is its deep penetration ability into and through vegetation canopies, and the other is the radar backscatter saturated at high levels of forest stand parameters. Thus, the sensor has great potential to assess the parameters accurately. The potential is furthered with the polarimetric SAR (PolSAR) because of its additional polarization and relative phase information among polarization channels. Unfortunately, the complex terrain backscatter can adversely impact the radar backscatter from forests in the P-band PolSAR data. Forest parameters assessed can be erroneous. Reducing the impact is urgently needed. In this study, a topographic compensation algorithm has been studied. Methodologically, a Bragg scattering model is used to model the ground backscatter. The backscatter is determined by the relative dielectric constant (ε_r), azimuth orientation angle (θ₀) induced by the topography, and radar local incidence angle (θ_i). The topography is quantified by the azimuth slope angle (θ) and range slope angle (θ_s) for a given SAR data acquisition or imaging geometry. The backscatter from an inclined surface at θ₀ is modeled by rotating the Bragg scattering model. Considering the SAR imaging geometry, we next show θ₀ as the surrogate for the θ, θ_i, and θ_s effects collectively in the topography compensation. Then, without setting components C₁₂ = C₂₁ = C₂₃ = C₃₂ = 0 of a covariance matrix of the PolSAR data, an eigenvalue-eigenvector-based decomposition algorithm is studied for decomposing the data into the ground and non-ground components. Finally, we develop a topographic compensation algorithm using the separated ground and non-ground backscatter components.

To validate the algorithm’s effectiveness in the topographic compensation, we applied it to P-band PolSAR datasets near Howland, Maine; Mt. Shasta, California; Eno River State Park, North Carolina; and Altamaha Wildlife Management Area, Georgia. All are in the US. Forests in the areas are diverse in tree species, and the ground soil and topographic conditions differ. The significant topographic impact on the P-band PolSAR datasets exists. After the topographic compensation algorithm, the impact decreases noticeably qualitatively and quantitatively. Thus, the algorithm is valid and effective in reducing the influence on the PolSAR datasets and, in turn, offers a better chance of deriving accurate forest parameters. As a final note and due to the exponential increase in canopy attenuation to the incoming and backscattered radar waves through canopies, one should be cautious when applying the algorithm to forests with deep canopy depth and high canopy density. The caution should also be true when the PolSAR data are acquired by the SAR sensor with a wavelength less than the P-band wavelength or at a large local radar incidence angle.

The US National Aeronautics and Space Administration (NASA) / Jet Propulsion Laboratory (JPL) AIRSAR P-band data were downloaded from the Alaska Satellite Facility (ASF) website https://asf.alaska.edu/datasets/daac/airsar/. The NASA/JPL UAVSAR P-band data were downloaded from the website (https://uavsar.jpl.nasa.gov/). Data analyses were primarily conducted using the public domain PolSARPro and licensed MATLAB software.

The authors declare no conflicts of interest.