Response of Multi-Incidence Angle Polarimetric RADARSAT-2 Data to Herbaceous Vegetation Features in the Lower Paraná River Floodplain, Argentina

Wetland ecosystems play a key role in hydrological and biogeochemical cycles. In emergent vegetation targets, the occurrence of double-bounce scatter is indicative of the presence of water and can be valuable for hydrological monitoring. Double-bounce scatter would lead to an increase of σ0HH over σ0VV and a non-zero co-polarized phase difference (CPD). In the Lower Paraná River floodplain, a total of 11 full polarimetric RADARSAT-2 scenes from a wide range of incidence angles were acquired during a month. Flooded targets dominated by two herbaceous species were sampled: Schoenoplectus californicus (four sites, Bulrush marshes) and Ludwigia peruviana (three sites, Broadleaf marshes). As a general trend, σ0HH was higher than σ0VV, especially at the steeper incidence angles. By modeling CPD with maximum likelihood estimations, we found results consistent with double-bounce scatter in two Ludwigia plots, at certain scene incidence angles. Incidence angle accounted for most of the variation on σ0HH, whereas emergent green biomass was the main feature influencing σ0HV. Multivariate models explaining backscattering variation included the incidence angle and at least two of these variables: emergent plant height, stem diameter, number of green stems, and emergent green biomass. This study provides an example of using CPD to decide on the contribution of double-bounce scatter and highlights the influence of vegetation biomass on radar response. Even with the presence of water below vegetation, the contribution of double-bounce scatter to C-band backscattering depends on scene incidence angles and may be negligible in dense herbaceous targets.


Introduction
Wetland ecosystems play a key role in hydrological and biogeochemical cycles and comprise a large part of the world's biodiversity and resources [1]. South America is the continent with the largest surface covered by wetlands (>20%, [1]), with the greatest extension being covered by fluvial wetlands associated with the Amazonas, the Orinoco, and the Paraguay-Paraná rivers [2]. Floodplain wetlands are complex macrosystems with mosaics of different wetland types dominating the landscape [3]. These ecosystems' dynamics are mainly controlled by flood pulses, which determine fluxes of materials of double-bounce scatter [22]. In targets with no significant symmetry rotation, crosspolarized (HH-HV or VV-HV) phase difference distributions can also be informative of scattering mechanisms (cross-polarized phase difference, hereafter named XPD) [26,30].
This study addressed the interaction between C-band SAR signal and herbaceous targets in a temperate-humid fluvial wetland, the Lower Paraná River floodplain (also known as Paraná River Delta). These wetlands have previously been classified with C-band and X-band data [31,32], but the phase difference response was not explicitly addressed, nor explicit models between SAR signal and vegetation features. Our aims were: (a) to assess the relation between backscattering power and phase differences, and to study how they vary with incidence angles; and (b) to evaluate the effect of vegetation features on backscattering power. RADARSAT-2 scenes from a wide range of incidence angles (beams FQ-2 to FQ-29, mean angles 20.7 • to 47.4 • ) were acquired over one month. In February 2018 we sampled plots from two dominant herbaceous targets with different architectures, Schoenoplectus californicus and Ludwigia peruviana. These two species dominate extensive Bulrush marshes and Broadleaf marshes, respectively, in the Lower Paraná River floodplain [33]. We analyzed whether double-bounce scatter occurred and discussed the backscatter dependence on SAR incidence angle and vegetation features.

Study Area
The study area is a sector of the Lower portion of the Paraná River floodplain, which runs 400 km South-Southeast along Argentina's main populated and industrial area ( Figure 1). In this zone, the floodplain reaches 10 to 30 km wide and emergent macrophytes dominate. The climate is temperate humid; mean annual temperature is 17.1 • C. January is the hottest month and July the coldest (24. Natural forests occur in reduced areas covering up to 6% of the Lower Paraná River floodplain, and are mainly located at high elevations such as levees or river banks [34]. Emergent macrophytes plant communities cover more than 90% of the wetland area, dotted by shallow lakes and secondary rivers and streams, and are usually dominated by one or very few species [33,35,36]. Macrophytes have high productivity, are an input of organic carbon, provide habitats for wildlife and fish, and are essential for flood regulation. Several herbaceous plant communities differing in their structure and functions were described, including marshes, grasslands, salt marshes, broadleaf marshes, bulrush marshes, floating meadows, and scrublands [33]. Bulrush marshes dominated by Schoenoplectus californicus (C.A. Mey.) Soják (Cyperaceae) and Broadleaf marshes dominated by Ludwigia peruviana (L.) H. Hara (Onagraceae) are two of the typical plant communities in the Lower Paraná River floodplain (especially in the Middle Delta) [33]. Although these marshes have a relatively low taxonomic diversity [36], they cover large areas with generally high plant biomass, having a significant effect on the ecosystem functioning of the floodplain. Preserving a mosaic of these and other marshes promotes biodiversity at a landscape scale [36]. Bulrush and Broadleaf marshes also contribute to sustaining the regional economy by providing nursery areas for commercial fishing and forage for cattle grazing [37]; and Ludwigia species are usually part of the bee flora [38].

Field Sampling
Field sampling was conducted in February 2018, in flooded sites dominated by the herbaceous species Schoenoplectus californicus (hereafter named Schoenoplectus) or Ludwigia peruviana (hereafter named Ludwigia) ( Figure 1). These species show contrasting architectures ( Figure 2). Schoenoplectus is a bulrush, with no leaves and cylindrical stems distributed almost vertically. Ludwigia is a broadleaf herb, and usually has a main stem with branches and leaves.
Seven almost monospecific sites were selected: four dominated by Schoenoplectus and three by Ludwigia. These sites were georeferenced. In each site, two plots were sampled. Vegetation censuses were conducted in 1 m 2 plots by means of a Braun-Blanquet scale, to estimate plant abundance-coverage and address the potential accompanying species [39]. To illustrate plant sizes and stem angles, photographs were taken with a grid behind the vegetation (see Figure 2). In each plot, three records of the photosynthetically active radiation (PAR) above and below vegetation were obtained with a 1 m linear quantum sensor (Cavadevices BAR-RAD 100); and the average PAR intercepted fraction was computed (fPAR). Water level and vegetation features were measured in a 25 cm × 25 cm area: number of stems, stem diameters, emergent plant height, plant moisture content, and emergent biomass. To estimate biomass and moisture, vegetation was harvested, and the fresh weight was recorded with a field scale. In the laboratory, harvests were separated per species and green/dry portions. Samples were dried at 60 °C for 72 h and dry weight was

Field Sampling
Field sampling was conducted in February 2018, in flooded sites dominated by the herbaceous species Schoenoplectus californicus (hereafter named Schoenoplectus) or Ludwigia peruviana (hereafter named Ludwigia) (Figure 1). These species show contrasting architectures ( Figure 2). Schoenoplectus is a bulrush, with no leaves and cylindrical stems distributed almost vertically. Ludwigia is a broadleaf herb, and usually has a main stem with branches and leaves.
Seven almost monospecific sites were selected: four dominated by Schoenoplectus and three by Ludwigia. These sites were georeferenced. In each site, two plots were sampled. Vegetation censuses were conducted in 1 m 2 plots by means of a Braun-Blanquet scale, to estimate plant abundance-coverage and address the potential accompanying species [39]. To illustrate plant sizes and stem angles, photographs were taken with a grid behind the vegetation (see Figure 2). In each plot, three records of the photosynthetically active radiation (PAR) above and below vegetation were obtained with a 1 m linear quantum sensor (Cavadevices BAR-RAD 100); and the average PAR intercepted fraction was computed (fPAR). Water level and vegetation features were measured in a 25 cm × 25 cm area: number of stems, stem diameters, emergent plant height, plant moisture content, and emergent biomass. To estimate biomass and moisture, vegetation was harvested, and the fresh weight was recorded with a field scale. In the laboratory, harvests were separated per species and green/dry portions. Samples were dried at 60 • C for 72 h and dry weight was measured. Emergent green biomass (g·m −2 ) and gravimetric moisture content (%) were estimated for Schoenoplectus and Ludwigia. Vegetation variables were averaged on the two plots of each site.

Scene Acquisition and Processing
A total of 11 full polarimetric RADARSAT-2 C-band scenes were acquired in February 2018, differing in their orbit direction and beams (FQ5 to FQ29, mean incidence angles between 20.7° and 47.4°) ( Table 1). RADARSAT-2 is a SAR satellite mission of the Canadian Space Agency and MacDonald, Dettwiler and Associates, operating at a 5.405 GHz frequency. In the Fine Resolution Quad-polarization beam (FQ), scenes have a nominal swath of nominal swath width of 25 km and a resolution of 5.2 m (range) × 7.6 m (azimuth). The system repeat pass is of 24 days (same sensor mode and geometry); but our acquisition plan covered 11 scenes in 24 days-varying incidence angles, see Table 1.
Scenes were acquired in Single Look Complex (SLC) processing type and were calibrated to the coherence matrix (slant range geometry). Additionally, multilooking was applied (6 pixels in azimuth × 3 pixels in range) and coherence matrices were geocoded to a 12.5 m × 12.5 m pixel by means of linear resampling (ground range geometry). Based on the sampling sites' georeferenced position, regions of interest (ROIs) were drawn on ground-range geocoded SAR imagery, aided with optical imagery from close acquisition dates (Sentinel-2 and SPOT-6). The components of the complex covariance matrix (C3) were extracted for each ROI, and single polarization backscattering coefficients (σ 0 HH, σ 0 HV, σ 0 VV), CPD and XPD were derived (with XPD defined as HH-HV phase difference). Multilooking substantially decreased the number of pixels per ROI, hindering the analysis of CPD and XPD distributions. To circumvent this issue, we projected back the ROIs onto the C3 matrices on slant range geometry (reverse geolocation, see [40,41]), and CPD and

Scene Acquisition and Processing
A total of 11 full polarimetric RADARSAT-2 C-band scenes were acquired in February 2018, differing in their orbit direction and beams (FQ5 to FQ29, mean incidence angles between 20.7 • and 47.4 • ) ( Table 1). RADARSAT-2 is a SAR satellite mission of the Canadian Space Agency and MacDonald, Dettwiler and Associates, operating at a 5.405 GHz frequency. In the Fine Resolution Quad-polarization beam (FQ), scenes have a nominal swath of nominal swath width of 25 km and a resolution of 5.2 m (range) × 7.6 m (azimuth). The system repeat pass is of 24 days (same sensor mode and geometry); but our acquisition plan covered 11 scenes in 24 days-varying incidence angles, see Table 1.
Scenes were acquired in Single Look Complex (SLC) processing type and were calibrated to the coherence matrix (slant range geometry). Additionally, multilooking was applied (6 pixels in azimuth × 3 pixels in range) and coherence matrices were geocoded to a 12.5 m × 12.5 m pixel by means of linear resampling (ground range geometry). Based on the sampling sites' georeferenced position, regions of interest (ROIs) were drawn on ground-range geocoded SAR imagery, aided with optical imagery from close acquisition dates (Sentinel-2 and SPOT-6). The components of the complex covariance matrix (C3) were extracted for each ROI, and single polarization backscattering coefficients (σ 0 HH , σ 0 HV, σ 0 VV ), CPD and XPD were derived (with XPD defined as HH-HV phase difference). Multilooking substantially decreased the number of pixels per ROI, hindering the analysis of CPD and XPD distributions. To circumvent this issue, we projected back the ROIs onto the C3 matrices on slant range geometry (reverse geolocation, see [40,41]), and CPD and XPD were re-extracted. After checking that median values and histogram shapes were conserved in both geometries, we decided to use CPD and XPD extracted on slant range data (with a higher number of pixels than ground range data) for fitting purposes. Software PolSARpro [42] and SNAP [43] were used to process the scenes and extract data on the ROIs. During the acquisition period, the hydrometric level measured at a water gauge on the Paraná River was similar and relatively low, and precipitation was not substantial ( Figure 3). Wind speed at the time of the acquisitions ranged between 0 and 11 km·h −1 , i.e., wind conditions were "calm" to "gentle breeze". Based on this information, and provided that vegetation growth was negligible during February 2018, we assumed that backscattering changes between scenes were mostly related to incidence angles. XPD were re-extracted. After checking that median values and histogram shapes were conserved in both geometries, we decided to use CPD and XPD extracted on slant range data (with a higher number of pixels than ground range data) for fitting purposes. Software PolSARpro [42] and SNAP [43] were used to process the scenes and extract data on the ROIs. During the acquisition period, the hydrometric level measured at a water gauge on the Paraná River was similar and relatively low, and precipitation was not substantial ( Figure 3). Wind speed at the time of the acquisitions ranged between 0 and 11 km·h −1 , i.e., wind conditions were "calm" to "gentle breeze". Based on this information, and provided that vegetation growth was negligible during February 2018, we assumed that backscattering changes between scenes were mostly related to incidence angles.   Table 1).

Single Polarization and Phase Difference Analyses
The backscattering coefficients at single polarizations (HH, HV, and VV) were explored with boxplots and scatter plots, and further assessed using generalized linear models [44]. Analyses were performed on a species-basis (Schoenoplectus and Ludwigia). Since no significant differences were observed between ascending and descending orbit directions, data was analyzed and discussed together.
Estimations of the CPD and XPD two-parameter distribution were computed as follows. With fully polarimetric SAR data acquired with phase-calibrated images, such as  Table 1).

Single Polarization and Phase Difference Analyses
The backscattering coefficients at single polarizations (HH, HV, and VV) were explored with boxplots and scatter plots, and further assessed using generalized linear models [44]. Analyses were performed on a species-basis (Schoenoplectus and Ludwigia). Since no significant differences were observed between ascending and descending orbit directions, data was analyzed and discussed together.
Estimations of the CPD and XPD two-parameter distribution were computed as follows. With fully polarimetric SAR data acquired with phase-calibrated images, such as that from RADARSAT-2, the derivation of an absolute co-polarized phase difference ψ is given by: where S HH and S VV are the HH and VV complex amplitudes and * denotes complex conjugate. In terms of the C3 matrix, S HH S * VV is the element C 13 . The statistical distribution of ψ for a 1-look speckled image is known and its closed-form expression is [45]: The phase difference distribution p ψ is unimodal, symmetric and modulus 2π about its mode, which occurs at ψ 0 . As Equations (2) and (3) show, the phase difference distribution depends on the coherence |ρ c |. For a coherence close to 1, the distribution resembles a delta function located at ψ 0 ; whereas for a coherence close to zero, the distribution is very close to a uniform distribution [45].
In Equations (2) and (3), the parameters ψ 0 and |ρ c | will be estimated from the 1-look histogram from measured ψ by means of a Maximum Likelihood Estimation (MLE) [46] using Equation (2) as the likelihood function to be maximized. Thus, the co-polarized phase difference estimator ψ 0 is estimated for each sampling site on each acquisition day.
Analogously to CPD, XPD is given by: where S HH S * HV is the element C 23 of the C3 matrix.

Effects of Vegetation Features on Backscattering Coefficients
To assess the relation between in situ obtained vegetation measures and SAR variables, generalized linear models (GLM) were conducted [44]. The median values of the backscattering coefficients at HH, HV, and VV were computed for each ROI and scene, as well as the mean scene incidence angle. Explanatory variables (vegetation features) were averaged per each of the plots, and then centered by subtracting the variable mean and scaled by their standard deviations. All the univariate models were addressed for each species and polarization (HH, HV, or VV). Next, multiple models were fitted, and the best models were selected with a manual upward stepwise multiple regression procedure. Each term addition was evaluated based on a significant reduction (>2) in the Akaike's information criterion (AIC) [44]; provided that all terms were significant, with a p-value lower than 0.05. A bootstrap procedure with 1000 permutations was performed on the regression coefficients: those coefficients for which the 95% confidence interval included the zero were removed [47]. To avoid collinearity, models were restricted to have variance inflation factors <3 for all the variables [48]. To discard overdispersion, we checked the ratios between residual deviance and degrees of freedom were lower than 1.5. The residual to null deviance ratio was used as an estimator of the model's explanatory power. The distribution of the model residuals was tested to assess normality and homoscedasticity assumptions.

Results
Target features are summarized in Table 2. The seven sites were characterized by a dominance of Schoenoplectus californicus (Sch-1 to Sch-4) or Ludwigia peruviana (Ludw-1 to Ludw-3). To facilitate the interpretation of further results, sites dominated by the same species were numbered by increasing emergent green biomass ( Table 2). The emergent green biomass of the dominant species represented 56 to 100% of the total biomass (green + dry portions) (mean 78%); whereas the total biomass of the dominant species accounted for 64 to 100% of the total biomass of the vegetation stand (mean 95%). Based on this high dominance, each of the sampling sites can be regarded as a homogeneous target. For the three polarizations, median backscattering coefficients were higher at Ludwigia targets than at Schoenoplectus targets (p < 0.0001). The overall trend for median backscattering coefficients was a decrease with incidence angles, both at Schoenoplectus and Ludwigia plots (Figure 4). Regarding co-polarizations, σ 0 HH was higher than σ 0 VV, especially at steep incidence angles (FQ_02), obtaining σ 0 HH-σ 0 VV differences of a maximum of 3.6 dB (minimum −1.74 dB, mean 0.53 dB) for Schoenoplectus and of a maximum of 4.4 dB (minimum −0.69 dB, mean 1.5 dB) for Ludwigia. Cross-polarization σ 0 HV was always lower than co-polarization, with maximum σ 0 HH-σ 0 HV differences of 17.2 dB (Schoenoplectus at FQ_08 scenes) and 14.6 dB (Ludwigia plots at FQ_08 and FQ_10).  Table 2 for detailed target descriptions. Data extracted from geocoded ground-range scenes.

Multivariate Models on the Effect of Vegetation Features
Generalized linear models (GLMs) show an effect of incidence angle on co-polarized backscattering, especially for σ 0 HH (p < 0.0001): incidence angles accounted for 64.3% and 72.2% of variation of the HH backscattered power for Schoenoplectus and Ludwigia, respectively (Table 3). For σ 0 HV, emergent green biomass was the vegetation feature with higher explanatory power, accounting for 39.3% and 75.6% of the total variation in Schoenoplectus and Ludwigia targets, respectively. Table 3. Univariate generalized linear models fitted for SAR outputs and vegetation features. For each significant model, the positive (+) or negative (−) sign of the coefficient estimate is indicated, along with the p-value of the coefficient and its explanatory power (%, ratio of explained deviance to null deviance). The best univariate models for each species and polarization are highlighted in bold characters. See Table 4 for multivariate models.   Table 2 for detailed target descriptions. Data extracted from geocoded ground-range scenes.

Multivariate Models on the Effect of Vegetation Features
Generalized linear models (GLMs) show an effect of incidence angle on co-polarized backscattering, especially for σ 0 HH (p < 0.0001): incidence angles accounted for 64.3% and 72.2% of variation of the HH backscattered power for Schoenoplectus and Ludwigia, respectively (Table 3). For σ 0 HV , emergent green biomass was the vegetation feature with higher explanatory power, accounting for 39.3% and 75.6% of the total variation in Schoenoplectus and Ludwigia targets, respectively. Table 3. Univariate generalized linear models fitted for SAR outputs and vegetation features. For each significant model, the positive (+) or negative (−) sign of the coefficient estimate is indicated, along with the p-value of the coefficient and its explanatory power (%, ratio of explained deviance to null deviance). The best univariate models for each species and polarization are highlighted in bold characters. See Table 4 for multivariate models. Multivariate GLMs that included scene incidence angle and vegetation features show high explanatory power for most single polarization backscattering coefficients (Table 4), except for Ludwigia-σ 0 VV for which no multivariate model was fitted. Besides the aforementioned effect of incidence angle, co-polarized backscattering of Schoenoplectus targets increases with emergent plant height and decreases with stem diameter; whereas crosspolarized backscattering increases with the number of green stems and stem diameters. In Ludwigia targets, σ 0 HH increases with stem diameters, and cross-polarized backscattering increases with emergent green biomass.

Phase Difference Analyses
A total of 75 CPD and XPD distributions were analyzed, each corresponding to a target site on a given scene (with scenes differing on their incidence angles). Figure 5 shows the ψ 0 value of the CPD distribution of the four Schoenoplectus and three Ludwigia targets, extracted using the MLE technique (Equation (2)).
Remote Sens. 2021, 13, x FOR PEER REVIEW 10 of 17 except for Ludwigia-σ 0 VV for which no multivariate model was fitted. Besides the aforementioned effect of incidence angle, co-polarized backscattering of Schoenoplectus targets increases with emergent plant height and decreases with stem diameter; whereas crosspolarized backscattering increases with the number of green stems and stem diameters.
In Ludwigia targets, σ 0 HH increases with stem diameters, and cross-polarized backscattering increases with emergent green biomass.

Phase Difference Analyses
A total of 75 CPD and XPD distributions were analyzed, each corresponding to a target site on a given scene (with scenes differing on their incidence angles). Figure 5 shows the value of the CPD distribution of the four Schoenoplectus and three Ludwigia targets, extracted using the MLE technique (Equation (2)).  Table 2. Data extracted on SLC scenes.
The CPD values observed in the histograms we analyzed can result from singlebounce, double-bounce, or multiple-scattering [17]. Single-bounce backscatter always produces CPD values near zero degrees, but with a probability distribution given by Equation (2). Double-bounce backscatter can produce high, intermediate, or low CPD values degrees [14,17,26], depending on the moisture content, size, and geometry of the vegetation. Multiple scattering produces a random distribution of CPD, forming a "pedestal" in the histogram, above which one or two peaks are often found [26].
In Figure 5 we observe that the peaks for Schoenoplectus are always centered near zero degrees, independent of incidence angle: CPD ranged between −15.32° and 29.04° and the coherence ranged between 0.11 and 0.70. The high values of moisture content (Table 2),  Table 2. Data extracted on SLC scenes.
The CPD values observed in the histograms we analyzed can result from singlebounce, double-bounce, or multiple-scattering [17]. Single-bounce backscatter always produces CPD values near zero degrees, but with a probability distribution given by Equation (2). Double-bounce backscatter can produce high, intermediate, or low CPD values degrees [14,17,26], depending on the moisture content, size, and geometry of the vegetation.
Multiple scattering produces a random distribution of CPD, forming a "pedestal" in the histogram, above which one or two peaks are often found [26].
In Figure 5 we observe that the peaks for Schoenoplectus are always centered near zero degrees, independent of incidence angle: CPD ranged between −15.32 • and 29.04 • and the coherence ranged between 0.11 and 0.70. The high values of moisture content (Table 2), together with recent modelling work [17], rule out the possibility of doublebounce backscatter from these stands. The histograms used to extract the mode CPD values indicate that the signal is dominated by single-bounce backscatter, with a small amount of multiple scattering. At steep incidence angles the single-bounce backscatter could come from a combination of backscatter from the plants and backscatter from the water and floating vegetation. At shallower incidence angles, most of the backscatter is expected to come from the plants.
The CPD values observed for Ludwigia (Figures 5 and 6) show evidence of doublebounce backscatter, especially at larger incidence angles. CPD ranged between −120.57 • and 7.65 • and the coherence ranged between 0.08 and 0.46. The histograms also show evidence of single-bounce backscatter and multiple scattering. In Figure 6, the maximum likelihood estimations of the CPD distribution are shown for the four samples with CPD values significantly lower than zero. As can be seen in the photographs (Figure 2), vegetation targets have rotational symmetry, i.e., vertical stems have random orientation angles and not a dominant orientation. Consistently, none of the cross-polarization phase distributions showed fitted XPD values significantly different from zero. together with recent modelling work [17], rule out the possibility of double-bounce backscatter from these stands. The histograms used to extract the mode CPD values indicate that the signal is dominated by single-bounce backscatter, with a small amount of multiple scattering. At steep incidence angles the single-bounce backscatter could come from a combination of backscatter from the plants and backscatter from the water and floating vegetation. At shallower incidence angles, most of the backscatter is expected to come from the plants.
The CPD values observed for Ludwigia (Figures 5 and 6) show evidence of doublebounce backscatter, especially at larger incidence angles. CPD ranged between −120.57° and 7.65° and the coherence ranged between 0.08 and 0.46. The histograms also show evidence of single-bounce backscatter and multiple scattering. In Figure 6, the maximum likelihood estimations of the CPD distribution are shown for the four samples with CPD values significantly lower than zero. As can be seen in the photographs (Figure 2), vegetation targets have rotational symmetry, i.e., vertical stems have random orientation angles and not a dominant orientation. Consistently, none of the cross-polarization phase distributions showed fitted XPD values significantly different from zero. , for CPD values significantly lower than zero. The estimations were obtained with Equation (2). Coherence is notated | |. Each subfigure shows a sampling site (see Table 2 for target description) and scene beam ordered by increasing incidence angle (see Table 1

Discussion
The use of SAR data in wetlands provides valuable information to assess flooding and monitor vegetation changes [8,9]. Here, we studied two of the typical marsh communities of the Lower Paraná River floodplain, dominated by Bulrush marshes and Broadleaf marshes. In the presence of water below vegetation, the contribution of double-bounce scatter can enhance the backscattered return, be responsible for σ 0 HH greater than σ 0 VV, and produce high co-polarized phase differences (CPD) [22]. However, this response depends on the signal frequency, on the scene incidence angle and on vegetation features: our re- Figure 6. Maximum likelihood estimations of co-polarized phase difference (CPD) ψ 0 , for CPD values significantly lower than zero. The ψ 0 estimations were obtained with Equation (2). Coherence is notated |ρ c |. Each subfigure shows a sampling site (see Table 2 for target description) and scene beam ordered by increasing incidence angle (see Table 1

Discussion
The use of SAR data in wetlands provides valuable information to assess flooding and monitor vegetation changes [8,9]. Here, we studied two of the typical marsh communities of the Lower Paraná River floodplain, dominated by Bulrush marshes and Broadleaf marshes. In the presence of water below vegetation, the contribution of double-bounce scatter can enhance the backscattered return, be responsible for σ 0 HH greater than σ 0 VV , and produce high co-polarized phase differences (CPD) [22]. However, this response depends on the signal frequency, on the scene incidence angle and on vegetation features: our results with RADARSAT-2 C-band data highlight that even in the presence of water, double-bounce can be negligible for dense herbaceous targets or may only be detected at certain incidence angles.
Differences between σ 0 HH and σ 0 VV , especially at steep incidence angles, were previously described for Schoenoplectus species in flooded temperate wetlands [15,56]. The differential behavior between polarizations in flooded vegetated areas at steeper incidence angles has been reported in other studies accounting for multi-incidence scenes (e.g., [56], which interpreted that double-bounce may be occurring but have not explored that hypothesis). Grings et al. 2005 have conducted electromagnetic simulation models for Schoenoplectus californicus based on radiative transfer theory [15], and predicted strong differences between simulated C-band σ 0 HH and σ 0 VV temporal trends. Our Schoenoplectus sites can be compared to the mature marshes in the cited model [15]: dense, partially dry, and with loss of vertical orientation (see Table 2 and photographs in Figure 2). The dominating processes in these flooded targets would be: 1) cylinder bistatic specular scattering, higher in H incident polarization than in V; and 2) shoot attenuation (extinction coefficient) higher at V than at H [15,16]. Our CPD results do not evidence the occurrence of double-bounce scatter in Schoenoplectus targets, and the observed σ 0 HH -σ 0 VV differences are relatively low in comparison with results obtained when the double Brewster angle effect was reported and modeled [25]. Efforts in model improvements for Schoenoplectus californicus should aim at better modeling the stem structure by considering its non-cylindrical shape and the dielectric properties of aerenchyma tissues (see photograph in Figure 2d).
To our knowledge, no radiative transfer models have been conducted for Ludwigia peruviana or for a similar broadleaf emergent macrophyte. Ludwigia spp. models (or similar broad-leaf herbaceous species) are not available at the moment. We suggest that radiative transfer models for this species include cylinders (stems) and disks (leaves), and should contemplate that a portion of the plant individuals have hollow stems, as was reported for the Lower Paraná River floodplain [57]. For both Ludwigia and Schoenoplectus, accounting for stem tilting would help to simulate co-polarized phase differences accurately [17]. These model improvements may contribute to better-estimating phase differences and/or backscattering powers. Additionally, future models need to include full polarimetric analyses and predict phase difference changes.
Scene incidence angles had the most significant effect on σ 0 HH and explained a portion of the variations on σ 0 HV and σ 0 VV . This result is in accordance with the literature: signal attenuation increases with incidence angle [11], because of a higher wave-vegetation interaction and less penetration that leads to changes in the backscatter mechanism [58,59]. Based on this SAR signal behavior, several studies recommend using steep incidence angle scenes for flood monitoring and shallow incidence angles for better discrimination of herbaceous vegetation types [9,31]. Using multi-incidence angle scenes close in time provides optimum flood monitoring and vegetation type discrimination [56,60]. Our results also demonstrate that integrating different scene configurations including incidence angle benefits target discrimination, but also enhance the detection of double-bounce scatter, especially in dense herbaceous targets. The combined use of polarimetric data and interferometry (in search of phase change "fringes") would improve flood detection [22,23].
Volume scatter seems to be the main interaction mechanism contributing to the backscattered return in the dense herbaceous targets of the Lower Paraná River floodplain. The general pattern was similar at sites dominated by the two addressed species: a strong effect of scene incidence angles and vegetation features. However, backscattering coefficients were higher for Ludwigia than for Schoenoplectus targets, suggesting that their different architectures and vegetation distribution within the plot affect C-band SAR-target interaction [31]. The effect of incidence angle on co-polarized backscattering coefficients was higher in Ludwigia targets, and steep angles maximized the differences between these two vegetation types. The fitted generalized linear models highlight the effect of vegetation features for all polarizations. The response of C-band co-polarized signal to vegetation features of herbaceous vegetation has been widely reported in previous studies [9,16,61]. Here, emergent green biomass was strongly related to σ 0 HV in Ludwigia sites, whereas the best model for σ 0 HV in Schoenoplectus sites included the number of green stems and stem diameters.
Evidence consistent with double-bounce scatter was found on two of the Ludwigia sites, based on the CPD maximum likelihood estimations. These flooded Ludwigia targets were dense and showed high moisture content (75-80%), but their emergent green biomass was lower than in Schoenoplectus targets ( Table 2). Most notably, Ludwigia targets differed both in plant architecture and in the absence of dry stems, typical of mature Schoenoplectus targets [15]. Double-bounce scatter was expected to vary as a function of the incidence angle [22] because of changes in the Fresnel reflection coefficients [14,21,25,26]. However, our results are not conclusive in support of this hypothesis, probably because of the targets' high biomass: a trade-off between increasing contribution of double-bounce scatter and signal attenuation by the biomass has been reported [62].
The scenes which allowed double-bounce scatter to be detected had intermediate to shallow scene incidence angles (36.2 • to 45.1 • ) and not steep angles. Thus, our approach with CPD maximum likelihood estimations can be useful as an indicator of double-bounce scatter, but scenes from contrasting incidence angles should be assessed. Although Cband can detect water presence in marshes, this is hindered with increasing plant cover and LAI [63]. In these cases, L-band signals may still penetrate through vegetation and double-bounce may happen when interacting with water and stems [9]. Cross-polarized phase differences (XPD) were not informative of the presence of double-bounce in the addressed targets, which is consistent with the lack of a dominant orientation in the stems of Schoenoplectus and Ludwigia (cf. results reported for urban and forest targets [30,64]).
Modeling the phase would provide new insights on wave-vegetation interaction. A dedicated model was proposed by Ulaby et al. (1987) [21]. It computes the co-polarized phase difference by considering the vegetation as a collection of randomly distributed vertical lossy cylinders over a dielectric half-space. Besides plant structure parameters such as diameter and height, the model requires the dielectric constant of the stems. Since this is a parameter that is difficult to measure, models computing bulk vegetation dielectric properties from vegetation moisture are available, being the Mätzler 1994 model [65] suitable for large moisture contents such as those found in the Schoenoplectus and Ludwigia sites (ranging between 62% and 80% on a weight basis). Although the model proposed by Ulaby et al. (1987) [21] was first validated on corn fields imaged at L-band, we found this model is not sensitive to the co-polarized phase difference resulting from the dielectric features presented in the study site (results not shown). More research is needed to model CPD for these herbaceous targets.
The two studied species dominate Bulrush marshes and Broadleaf marshes in the Lower Paraná River floodplain (mainly in the Middle Delta) [33], and are relevant for the ecosystem functioning of the freshwater wetlands of the area and for the regional economy. Due to the high biomass and coverage of these species, using optical data usually does not allow the detection of water, as has been described for other dense herbaceous vegetation targets [6,7,13]. However, the use of optical data combined with SAR data may improve both the discrimination of the vegetation types and the detection of water. For example, a previous study in the Paraná floodplain used SAC-C optical data to derive a land cover map and C-band ENVISAT ASAR data to estimate marsh plant density in burnt areas [66]. Applications with hyperspectral data have been poorly addressed in South American wetlands because of the restricted availability and expensive acquisition of these imageries [3], but have been used to map the invasion of Ludwigia spp. into Schoenoplectus californicus marshes in California, United States [67]. Besides, passive microwave data has been used to assess floods in the Paraná River floodplain [68], but the low spatial resolution limits the use of these data to discriminate vegetation types or monitor flooding at a detailed scale.
In regard to SAR data, based on the results of this study we suggest involving multiincidence angle scenes, or at least using two contrasting incidence angles, one steep and one shallow. The combined use of C-band and L-band data may help to better account for dense herbaceous targets: C-band backscattering would depend on vegetation features-as is described here-, and the L-band signal may still penetrate through herbaceous vegetation and detect the presence of surface water [9]. These recommendations may be useful not only for the Lower Paraná River floodplain but also for other areas of the Paraná floodplain [69,70] or other South American wetlands where these macrophytes can cover large areas. Bulrush marshes dominated by Schoenoplectus californicus are also typical of temperate wetlands in North America [71]. Besides, Ludwigia spp. behaves as an invasive species in North America [67] and South-West Europe [71], with a great impact on the ecosystem functioning of the natural marshes. Monitoring the state of Schoenoplectus spp. and Ludwigia spp. marshes and their changes due to flooding, phenology, fires or other anthropic impacts (or invasive spreading in the Northern Hemisphere) can improve the understanding of the ecological dynamics of freshwater wetlands.

Conclusions
Here, we assessed flooded herbaceous targets from two species, which are expected to have significant double-bounce scatter, with RADARSAT-2 C-band fully polarimetric scenes acquired at several incidence angles. Incidence angles and vegetation features explain most of the variability in backscattered power. This study provides an example of using co-polarized phase differences to decide on the contribution of double-bounce scatter in a temperate freshwater wetland and with herbaceous targets. Our results emphasize the need to be cautious with flood monitoring conclusions, since obtaining no evidence of double-bounce scatter with a particular scene does not indicate the absence of water. Indeed, we suggest using multi-incidence angle scenes or at least comparing two different beams before deciding on the contribution of double-bounce scatter. Due to the high effect of vegetation features on backscattered power, studies conducted during a growing season need to address plant height, stem density, and biomass changes. The assessment of these dense marshes could also be improved with L-band full polarimetric data (such as those from ALOS-2/PALSAR-2 and SAOCOM-1A and 1B missions) because of the higher penetration and less signal attenuation.