Characterization of the Amazon Rainforest Backscatter at X-Band Using TanDEM-X Data

The radiometric calibration of spaceborne SAR products plays a key role for ensuring a good performance of the whole end-to-end system and requires a precise knowledge of both the radar system and the illuminated target on ground. The shape of the antenna pattern in elevation can be directly estimated by analyzing SAR detected images in presence of a homogeneous and flat backscatter profile in the slant range dimension. To this aim, tropical rainforests have been established by the SAR community as well-known calibration sites for performing such an activity. Here, according to the hypothesis of isotropic scattering, the backscattering coefficient in terms of unit area perpendicular to the antenna, called gamma nought, is assumed to remain constant with respect to the incidence angle. Nevertheless, several studies using X- and C-band sensors have shown a slight dependency of the backscatter on the incidence angle, as well as on ground target properties and meteorological conditions. In this work, we present a detailed statistical characterization of radar backscatter at X-band over the Amazon rainforest using TanDEM-X data and we provide insights on how to best utilize radar backscatter data in this region for SAR calibration and modeling purposes. In particular, we concentrate on the dependency of the Amazon rainforest backscatter on the day-time of acquisition, which is directly related to the orbit direction of TanDEM-X. Furthermore, we analyze the seasonal variation of the radar backscatter, as well as possible radiation variations over different locations in the Amazon, characterized by different climate conditions and biomes. Finally, we provide a series of backscatter models for different scenarios, which can be used, e.g., for X-band spaceborne SAR system design and theoretical modeling.

Characterization of the Amazon Rainforest Backscatter at X-Band Using TanDEM-X Data Luca Dell'Amore , José-Luis Bueso-Bello , Patrick Klenk , Jens Reimann , and Paola Rizzoli Abstract-The radiometric calibration of spaceborne SAR products plays a key role for ensuring a good performance of the whole end-to-end system and requires a precise knowledge of both the radar system and the illuminated target on ground.The shape of the antenna pattern in elevation can be directly estimated by analyzing SAR detected images in presence of a homogeneous and flat backscatter profile in the slant range dimension.To this aim, tropical rainforests have been established by the SAR community as well-known calibration sites for performing such an activity.Here, according to the hypothesis of isotropic scattering, the backscattering coefficient in terms of unit area perpendicular to the antenna, called gamma nought, is assumed to remain constant with respect to the incidence angle.Nevertheless, several studies using X-and C-band sensors have shown a slight dependency of the backscatter on the incidence angle, as well as on ground target properties and meteorological conditions.In this work, we present a detailed statistical characterization of radar backscatter at X-band over the Amazon rainforest using TanDEM-X data and we provide insights on how to best utilize radar backscatter data in this region for SAR calibration and modeling purposes.In particular, we concentrate on the dependency of the Amazon rainforest backscatter on the day-time of acquisition, which is directly related to the orbit direction of TanDEM-X.Furthermore, we analyze the seasonal variation of the radar backscatter, as well as possible radiation variations over different locations in the Amazon, characterized by different climate conditions and biomes.Finally, we provide a series of backscatter models for different scenarios, which can be used, e.g., for X-band spaceborne SAR system design and theoretical modeling.

I. INTRODUCTION
S YNTHETIC aperture radar (SAR) systems represent nowa- days a well-recognized technique in the field of remote sensing, thanks to their capability to operate in presence of clouds and independently of day-light and weather conditions.They are able to acquire high-resolution images of the Earth's surface and to provide useful data for a large variety of scientific applications, ranging from the assessment of physical phenomena to the monitoring of Earth's surface dynamics.
One of the key components for ensuring a high quality of the derived SAR images is an accurate absolute calibration The authors are with the Microwaves and Radar Institute, German Aerospace Center, 82234 Wessling, Germany (e-mail: luca.dellamore@dlr.de;Jose-Luis.Bueso-Bello@dlr.de;patrick.klenk@dlr.de;jens.reimann@dlr.de;paola.rizzoli@dlr.de).
In this article we present a detailed statistical characterization of X-band radar backscatter over the Amazon rainforest using TDX data at large scale.The rest of this article is organized as follows.Section II and III present the utilized backscatter mapping quantities and the considered data sets, respectively.In Section IV, we concentrate on the equatorial Amazon rainforest; specific considerations are drawn regarding the backscatter dependency on the day-time of acquisition and orbit direction, whereby descending and ascending orbit acquisitions are generally acquired in the morning and in the evening, respectively.Section V investigates the seasonal variations of the radar backscatter over the equatorial Amazon rainforest by comparing data acquired during dry and wet seasons.In Section VI we analyze different locations in order to characterize the Amazon rainforest depending on latitude positions and, therefore, on different climate conditions and biomes at large scale.Moreover, a temporal stability analysis on the rainforest radiation is also provided by considering data sets collected over the same area but spread over a time span of several years.In Section VII, we characterize the radar backscatter over few test sites in the Amazon rainforest for other polarization channels as well.In Section VIII we provide a series of backscatter models for different scenarios.Some considerations about the well-known and widely used Ulaby and Dobson models in [56] are also drawn.A discussion on the results follows in Section IX.Finally, Section X concludes this article.A summary of all evaluated backscatter statistical parameters is reported in the Appendix.

II. BACKSCATTER MAPPING QUANTITIES
Typically, the quantity used for measuring and analyzing backscatter levels in SAR data over rainforests is the backscattering coefficient gamma nought γ 0 (θ l ), which can be expressed as where β 0 (θ) is the radar brightness, θ the slant range-dependent incidence angle, which monotonically increases from near to far range, and θ l the local incidence angle, which depends on the observed topography, as depicted in Fig. 1.In particular, γ 0 (θ l ) describes the reflectivity of distributed targets per unit area of the incident wave front.Unlike the more popular scattering projection σ 0 (θ l ), i.e., radar reflectivity per unit area on ground, γ 0 decreases the sensitivity of the cross section to the incidence angle and it has the property of maintaining a relatively flat backscatter profile over a wide range of incidence angles for very dense and homogeneous volumetric targets [57], [58].This is the case of the Amazonas, where the γ 0 profile over the local incidence angle can be considered as an isotropic scattering measure.The radar brightness β 0 (θ) in (1), i.e., radar reflectivity per unit pixel area, is directly derived through the absolute calibration of the focused SAR data as with DN being the recorded digital number and K the absolute calibration constant.Its computation does not require the knowledge of local incidence angle.
In order to avoid confusion, in the following sections the backscatter characterization will rely on the local incidence angle θ l as independent variable.Therefore, a precise knowledge of the underlying topography is required in order to precisely estimate the local incidence angle as θ l = θ − α, with α being the local terrain slope in the slant range direction.

III. AMAZON RAINFOREST DATA SET
The vast majority of TDX acquisitions was acquired using horizontal polarization in transmit as well as in receive, i.e., (HH) polarization.Overall, we processed 3723 SAR images acquired over the Amazon rainforest in stripmap mode in HH polarization, at almost-full resolution, i.e., 6 m ×6 m, using the experimental TDX interferometric processor [59].Unlike previous works concerning TDX backscatter analysis [23], [34], which relied on quicklook images at 50 m resolution in order to limit the computational burden when considering large data sets [60], the use of almost-full resolution data allows for a reliable estimation of the complete signal dynamics as explained in [23].First, we absolutely calibrated each image in order to retrieve β 0 .As exhaustively described in [1], [2], [3], [4], [5], and [6], the TSX and TDX systems were absolutely calibrated with an outstanding accuracy of 0.39 dB and 0.48 dB, respectively; in-orbit calibration and dedicated activities were performed during the commissioning phase by exploiting reference point targets on ground (transponders and corner reflectors).Then, we generated the corresponding local incidence angle map θ l using the annotated satellite orbit position and the TDX global edited DEM [61], which is currently the most accurate DEM available at global scale.Note that the use of a precise external DEM allows for properly dealing with local terrain depressions/valleys and, more in general, with local higher relief terrain.Some considerations can be formulated regarding the reliability of the reference DEM: Given the interpolation from the original 30 m to the current 6 m resolution, it is reasonable to assume that DEM measurements are somehow smoothed, thus, mitigating possible local height errors.Also, the TDX global DEM provides an estimation of the topographic height corresponding to the location of the mean phase center within a resolution cell and is the result of the mosaicking of multiple acquisitions.This procedure also mitigates the impact of possible outliers.Moreover, it is worth noting that both the current analysis and the reference DEM are based on data from the same sensor, i.e., TDX, so that we can assume the consistency of the measurements between the considered backscatter data and the underlying DEM product.In particular, given the same radar central frequency and system parameters and assuming the Amazon rainforest to be composed of dense vegetation, we rely on the assumption that the measured radiation in both cases mostly comes from the upper layers of the canopy [62], [63].Finally, possible residual errors in the estimation of the local terrain slope α and, consequently, of the local incidence angle θ l , are not expected to significantly bias  the final results, given the predominant low-relief topography characterizing the Amazon rainforest.As a final step, we computed γ 0 by applying (1).Both γ 0 and θ l are, then, geocoded and interpolated on a common latitude/longitude grid in order to generate large-scale mosaics.
Fig. 2 shows γ 0 (left) and θ l (right) mosaics over the whole Amazon rainforest, which were composed using TDX images acquired between 2012 and 2013 with shallow/large incidence angles.Given the low-relief topography of the Amazon rainforest basin, it can be seen that the local incidence angle map reasonably approximates the slant-range dependent incidence angle.Moreover, the two orbit direction geometries are clearly visible, where data in the Northern Hemisphere were mostly acquired in ascending orbit direction, whereas data in the Southern Hemisphere in descending one [29], [64].Moreover, given the sun-synchronous, dawn-to-dusk orbit of the TDM, descending and ascending orbit acquisitions are typically acquired in the morning and in the evening, respectively.
The analyses in the following sections are spread over different locations of the Amazon rainforest.As first investigation, we considered the equatorial rainforest between  ] latitude, which comprises images acquired using all twenty nominal TDX beams, i.e., all TDX ascending/descending geometries, used for the generation of the global DEM [35], [36].Here, we utilized the complete data set acquired from December 2010 to September 2014 (consisting of 1998 acquisitions) for characterizing the backscatter dependency with respect to orbit direction and seasonality.The area is depicted in Fig. 3. Afterward, we considered different regions of the Amazon rainforest, characterized by different climate conditions and biomes [65], [66], [67], [68], [69], [70].We concentrated on three different test sites, which differ in latitude, comprised between  4. Note that each data set is within a 2 • latitude span and does not overlap with the others, which is a reasonable setting in order to properly separate the different test sites depending on local conditions at large scale.In particular, this is a compromise between the number of available data and the large-scale diversity between the observed

TABLE I DATA SETS USED FOR THE CURRENT INVESTIGATIONS USING IMAGES IN HH POLARIZATION
areas, due to potential differences in climate conditions and biomes.Moreover, we assume that the transition between different locations in the Amazon rainforest is smooth, so that γ 0 backscatter estimations over missing latitudes could be reasonably interpolated.Of course, local phenomena could occur and play a role, but are anyway expected to be averaged given the large-scale nature of the investigation.The last two data sets, acquired in the Southern Hemisphere, consist of data acquired in descending and ascending orbit directions in 2011-2012 and 2018-2019, respectively.Here, ascending orbit acquisitions were made possible, thanks to a swap of the TSX and TDX satellites, which took place in September 2017 [64].However, given the sun-synchronous and dawn-to-dusk orbit of TDX, descending/ascending orbit acquisitions were still performed during morning/evening, respectively.Therefore, we always combined data depending on the day-time of acquisition.As far as the test site between [0 • , 2 • ] latitude is concerned, ascending orbit acquisitions were retrieved from the investigated data set depicted in Fig. 3, whereas descending orbit data were acquired after the satellites swap, in 2018-2019.Table I summarizes all data sets used for the current investigations.In particular, the table reports the latitude/longitude locations of each test site, together with the acquisition time interval.By considering the three latitude intervals, a temporal stability analysis on the γ 0 backscatter was performed in order to ensure the comparability between the results from ascending/descending orbit acquisitions, as data acquisition times are very different.To this aim, the long-term temporal radiation stability was analyzed over a small test site used for long-term system monitoring (LTSM) tasks during the TDM.The area is depicted within the white box in Fig. 5.In particular, a time-series of 178 data takes was collected between 2011 and 2019, with all data acquired in the morning (in descending orbit configuration) and in HH polarization.Since all nominal TDX acquisitions are acquired in HH polarization, the core of the present analysis concentrates on data acquired in this polarization.Further considerations on other polarization channels are presented in Section VII.Very few images were collected using the other channels, i.e., vertical polarization in transmit as well as in receive (VV) and horizontal polarization in transmit and vertical in receive (HV), resulting in limited data sets.These are depicted in Fig. 5, where data takes were repeatedly performed for LTSM purposes over selected test sites, identified by the cyan (VV) and green (HV) boxes.Overall, 156 single polarization stripmap SAR images, among which 146 in VV and 10 in HV polarization, were collected between November 2010 and September 2014.Note that the orange box identifies test site (c) in Table I, which is used as reference HH data set for comparison purposes between different polarization channels.

IV. γ 0 DEPENDENCY ON THE LOCAL INCIDENCE ANGLE
In this section, we concentrate on the equatorial Amazon rainforest corresponding to test site (a) in Table I, and we present a large-scale analysis for the characterization of γ 0 at X-band with respect to the local incidence angle θ l .The corresponding γ 0 mosaic is depicted in Fig. 3.The whole range of nominal local incidence angles θ l , which extends from about 25 • to about 51 • , was sampled with angular intervals of 1 • .γ 0 samples, which belong to each single interval were then grouped together, allowing for the derivation of distribution statistics, such as mean and median γ 0 , its standard deviation (SD) and percentiles.Moreover, we applied the TDX Forest/NonForest (FNF) map [50] in order to select forested pixels only.Given the very different resolution of the FNF map (50 m × 50 m) compared with the considered γ 0 backscatter data, we eroded forested areas with a square kernel of 5 × 5 pixels in order to avoid misclassification at the borders.For each incidence angle interval, possible outliers were removed by taking only the backscatter distribution between the 1st and 99th percentiles.
The obtained results are presented in Fig. 6 for both data acquired in the morning, i.e., descending orbit acquisitions, and in the evening, i.e., ascending orbit ones. 1 In particular, the figure shows the γ 0 backscatter distributions with respect to each interval of local incidence angles.The boxes extend from the lower to upper quartile values of the data distribution, i.e., from the 25th to 75th percentiles, with whiskers reaching the 5th and 95th percentiles.The solid line within each box  I.Moreover, the white box identifies the LTSM region used for the long-term temporal stability analysis on the γ 0 radiation.Fig. 6. γ 0 backscatter distributions with respect to each interval of local incidence angles.Data distributions are shown for both data acquired in the morning, i.e., descending orbit acquisitions, and in the evening, i.e., ascending orbit ones.Each box extends from the lower to upper quartile values of the data distribution, i.e., from the 25th to 75th percentiles, with whiskers reaching the 5th and 95th percentiles.The solid line within each box indicates the mean value of the distribution, with triangles identifying the SD confidence interval of each data group, i.e., from mean −SD to mean +SD.The histograms depicting the number of samples used for the derivation of the backscatter statistical parameters are reported as well in the background.
indicates the distribution mean value, with triangles identifying the SD confidence interval of each data group, i.e., from mean −SD to mean +SD.Note that all the statistics were computed in linear scale and only afterward were converted to dB.The corresponding histograms depicting the number of samples used for the derivation of the backscatter statistical parameters are shown in the background.The figure demonstrates the nonperfectly-isotropic nature of the Amazon rainforest, as the backscatter profiles are not completely flat over the full range of incidence angles.Moreover, ascending and descending orbit acquisitions show a different behavior: Acquisitions performed in the morning present higher backscatter values, with a bias of about 0.5 dB, when compared with the ones acquired in the evening.Also, it can be seen that the backscatter variability increases when considering larger incidence angles.
Finally, all statistical parameters derived in this analysis as well as in the following sections are provided in the Appendix.
V. γ 0 SEASONAL VARIABILITY This section investigates the seasonal variability of the radar backscatter over the equatorial Amazon rainforest presented in Fig. 3, by comparing dry and wet seasons.The statistical analysis relies on the same procedure described in Section IV and was performed for ascending and descending orbit acquisitions separately.For this investigation, the dataset (a) in Table I was first split between ascending and descending orbit data.Second, the two derived data sets were subsampled by considering data acquired during dry and wet seasons only.For this scope, we assumed as dry the months between June and September, whereas wet acquisitions were collected starting from December until March [71], [72], [73], [74].Fig. 7 shows the resulting γ 0 distributions with respect to local incidence angles.Unlike the previous investigation in Section IV, where distributions of γ 0 were derived from a quite balanced number of samples between ascending and descending orbit acquisitions, the radar backscatter from dry and wet seasons is characterized by unbalanced data sets.Nevertheless, this aspect is not expected to bias the estimation, given the large amount of available data for each case, even for the worst-case local incidence angles interval, consisting of around 30 million samples.This could be verified by looking at the standard error of the mean (SEM) in the corresponding table in the Appendix (Table III).Clearly, a more precise estimation of the sample mean is achieved in presence of larger data sets.Nevertheless, as suggested by the SEM values in the tables, the estimated mean values are derived with great precision in all cases, so that small differences between different data groups are not expected to significantly impact the final results.The analysis shows that no significant difference between the two seasons is Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
detectable.Whereas, it is worth noting that the main driver of the γ 0 radar backscatter variation over the Amazon rainforest remains the day-time of acquisition, as an overall offset of about 0.5 dB can still be seen between descending (morning) and ascending (evening) orbit data.As already mentioned in the previous section, a larger backscatter variability can be observed as moving toward larger incidence angles.VI. γ 0 ANALYSIS OF DIFFERENT AMAZON LOCATIONS In the following, we focus on three different locations in the Amazon rainforest, characterized by different latitude positions and, therefore, by different climate conditions and biomes at large scale [65], [66], [67], [68], [69], [70].In order to do so, we consider the three test sites, i.e., (b), (c), and (d) in Table I, which correspond to the green, orange, and red boxes in Fig. 4, respectively.As previously done in Section V, the investigation was performed for ascending and descending orbit acquisitions separately.
The obtained results are presented in Fig. 8 for both data acquired in the evening/ascending orbit (top) and in the morning/descending orbit (bottom).The γ 0 backscatter distributions are shown with respect to each interval of local incidence angles and for the three different test sites, confirming the nonperfectlyisotropic nature of the Amazon rainforest.Even though a different amount of data is available for each test site, statistics were derived from a large amount of samples, as proven by the order of magnitude of the corresponding histograms and, therefore, are not expected to be significantly biased.Different behaviors can be observed for the different test sites by comparing ascending and descending orbit images.The γ 0 backscatter distributions look similar to each other, when considering data acquired in the evening, i.e., acquired in ascending orbit direction; a small bias can be detected in case of smaller incidence angles, with test site (d) showing slightly lower backscatter values on average, whereas the three backscatter distributions converge as moving toward far-range geometries.On the other hand, test sites (c) and (d) appear less stable compared with (b) [near-and far-range log-backscatter difference around 0.65 dB (b), 1.59 dB (c), and 1.15 dB (d)] when considering data takes acquired in the morning, i.e., with a descending orbit configuration.Here, despite remaining quite stable up to middle-range incidence angles, the backscatter mean value significantly drops as moving toward larger angles.There, the backscatter variability increases and the two distributions converge to similar values.Moreover, a higher backscatter variability can be detected on average during night/morning, i.e., from descending orbit acquisitions.In order to ensure the comparability between ascending/descending orbit results, as they correspond to very different data acquisition times, a long-term temporal radiation stability analysis was also performed over the small test site depicted in the white box in Fig. 5.In particular, data were grouped together depending on seasonality and, consequently, considering similar local conditions.Moreover, as exhaustively discussed in [16], [17], [18], and [19], no significant trends or radiometric degradation have been observed in TSX and TDX systems since launch.LTSM measurements and extended analyses have shown a stable performance of all parameters, confirming the outstanding radiometric stability of the instrument.As a consequence, eventual and significant γ 0 radiation variations are assumed to be related to the nonstationary behavior of the Amazon rainforest itself.The obtained results are presented in Fig. 9.Note that no data were acquired between 2015 and 2016.The plot confirms a substantial backscatter stability over time for both seasons, with a log-backscatter deviation of 0.2 dB and 0.11 dB for dry and wet periods, respectively.Furthermore, as already discussed in Section V, no significant difference between the two seasons behavior is detectable, with dry and wet periods showing an almost-equal backscatter average over time of -6.81 dB and -6.83 dB, respectively.An analysis on the dependency of the γ 0 backscatter on the seasonal acquisition period, not shown here for the sake of brevity, was performed as well for the three considered locations.As outcome, similar conclusions as in Section V can be formulated, where no significant difference between the two seasons behavior is detectable.Nevertheless, special attention has to be paid on test sites (c) and (d), in case of morning/descending orbit data takes.As discussed above for the general case depicted in Fig. 8, the two test sites seem to be less stable during night/morning with respect to local incidence angles.Similar instabilities can then be observed as well in the corresponding backscatter angular profiles, depending on the considered season.

VII. γ 0 BEHAVIOR FOR OTHER POLARIZATIONS
A comparison of the radar backscatter between HH, VV, and HV polarizations, with respect to the local incidence angle and the orbit direction, is shown in Fig. 10.The corresponding histograms, depicting the number of samples used for deriving the backscatter statistical parameters, are depicted in Fig. 11.It is worth noting that VV and HV samples are not uniformly distributed over the full range of incidence angles, given the limited number of available acquisitions.The analysis shows an almost constant offset of about 0.5 dB between HH and VV channels over data takes acquired with an ascending orbit geometry, i.e., evening acquisitions, with the VV polarization showing lower backscatter values.On the other hand, this offset gets smaller for descending orbit data takes, i.e., morning acquisitions, as moving toward middle-and far-range geometries.In this case, an almost negligible difference between HH and VV polarizations is observed.Given the considerable polarimetric calibration accuracy between the two copolarized channels, performed using reference targets [4], no polarimetric amplitude imbalance is expected to affect the final results by introducing a systematic bias.Therefore, possible differences between polarizations are expected to be simply related to different scattering mechanisms within the canopy and/or to external local conditions.Regarding the HV cross-polarization channel, the radar backscatter significantly drops compared with the HH and VV copolarizations, with differences up to 7 dB for all the investigated scenarios.It is worth noting that acquisitions performed in the evening and in HV polarization show a very stable radar backscatter, with negligible variations over the entire range of illuminated incidence angles.

VIII. γ 0 EMPIRICAL MODELING
In this section, we derive a series of empirical X-band backscatter models over the Amazon rainforest, based on the analyzed TDX data.In particular, we concentrate on the test sites described in Table I, focusing on the γ 0 dependency on the day-time of acquisition and on seasonal variability, as reported in Sections IV, V, and VI.Backscatter models for VV and HV polarizations are derived as well.For this scope, the angular dependency of the γ 0 mean value (dB), i.e., γ0 mean (dB), is determined by an iterative least-squares, nonlinear curvefitting approach.Given the wide utilization in the literature of the models provided by Ulaby and Dobson in [56] and since the radar radiation principles on which they were built still stand, we decided to rely on the same curve-fitting formulation.
Accordingly, the nonlinear fitting function consists of the sum of an exponential and a cosine term, which allows for a precise representation of the nonlinear fluctuations of the radar backscatter, while maintaining its overall decreasing behavior over incidence angles.The underlying model formulation is given by f (θ l ) = P 1 + P 2 e −P 3 θ l + P 4 cos(P 5 θ l + P 6 ) (3) Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.where P = [P 1 , P 2 , P 3 , P 4 , P 5 , P 6 ] is a vector of fitting coefficients, which is estimated through a least-squares optimization as with γ0 mean being the derived backscatter model and γ 0 mean the computed sample mean of the data distribution.It is important to mention that the local incidence angle θ l is given to the model in radians.
The resulting fitting parameters (P 1 to P 6 ) are provided in Table II and refer to the backscatter distributions shown in Figs. 6, 7, 8, and 10.Besides the fitting coefficients and the considered angular range, Table II reports latitude/longitude locations of the considered TDX data for fitting the models as well as the orbit direction of acquisition and seasonal information.If no seasonal description is provided, the models refer to the yearly data sets, where no filtering was performed depending on the acquisition period.Although the resulting coefficients for dry/wet months appear quite different compared with the results without distinguishing between seasons, the corresponding models do not significantly differ, as already shown in Sections IV and V. Actually, the observed differences in the fitting parameters are simply caused by the least-squares minimization procedure.
A fitting example is presented in Fig. 12 over test site (a) and for HH polarization.The measured γ 0 mean (dB) values are reported as green/blue point markers for morning/descending orbit and evening/ascending orbit acquisitions, respectively, and are Fig. 10.Comparison of the γ 0 radar backscatter dependency on incidence angle between HH, VV, and HV polarization channels.Data distributions are shown for both data takes acquired in the evening/ascending orbit (top) and in the morning/descending orbit (bottom).Boxes extend from the 25th to 75th percentiles of the data distributions, with whiskers reaching the 5th and 95th percentiles.Solid horizontal lines indicate the mean values of the total distributions, with triangles identifying the corresponding SD confidence intervals, i.e., from mean −SD to mean +SD.
then fitted according to (3) and (4) (green/blue lines).It is worth noting that the assumed nonlinear fitting function precisely estimates the true derived measurements.Moreover, the 50th occurrence intervals of the γ 0 distributions, comprised between 25th and 75th percentiles, are shown as well with respect to local incidence angles.The model provided in [56] and corresponding to forests and orchards (trees) is also depicted (black solid line) for comparison purposes.To this aim, it is important to remind that all the models presented in [56] were derived in dB for the σ 0 backscatter mapping quantity and, therefore, they have to be converted to γ 0 in order to be consistent with the present analysis.The estimated γ0 mean (dB) is derived from the σ0 mean (dB) Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
Moreover, the reported 5th (dotted) and 95th (dashed) occurrence levels are derived as in [56], by simply adding ±1.645 • s(θ l ), where s(θ l ) is the SD model.Even though the Ulaby and Dobson models have been used worldwide for a large variety of applications, it can be seen that they do not always precisely represent the radar backscatter when investigating specific test sites, specially when dealing with vegetated areas.This is shown in Fig. 12, where different types of forests are modeled, as suggested by the discrepancy between green/blue and black curves.This is reasonable, as our models refer to the tropical Amazon rainforest, whereas the Ulaby and Dobson one was derived from terrestrial scatterometric measurements over temperate forests in Pennsylvania, USA.Moreover, it is worth noting that the 50th confidence intervals of γ 0 backscatter derived in this work lie within the 90th occurrence range provided by Ulaby and Dobson.As exhaustively discussed in [56], the large variability of the Ulaby and Dobson backscatter model is explained by the wide variations in the magnitude of the radar backscatter among different measurement programs.In particular, this could be explained by a variety of systems and platforms used for in-situ campaigns, as well as by the presence of different on-ground conditions mixed within the same land cover class.

IX. DISCUSSION
Despite appearing to be a quite stable and isotropic target, the Amazon rainforest shows a nonperfectly-isotropic behavior when illuminated using X-band radar waves.
The X-band γ 0 backscatter profile appears to be mostly influenced by the day-time of acquisition, as presented in Section IV.Overall, images acquired in the morning, i.e., with a descending orbit direction, present higher backscatter values, with a bias of about 0.5 dB, when compared with the ones acquired in the evening, i.e., with an ascending orbit geometry.Some considerations could then be formulated, based on the findings in [25] and [75].First, X-band radar backscatter is probably attenuated during the day-light hours by the high humidity in the air.Then, during night/morning hours, an increase of the radar backscatter could be explained by higher levels of rainwater storage on the tree leaves, due to condensation and cooler air.Moreover, this discrepancy could also be associated to a different amount of rainfall in the afternoon compared with night/morning.In this case, the increase of the radar backscatter caused by rainwater storage on the tree leaves surface could be lower than the backscatter attenuation due to the rainfall itself, resulting in an overall lower scattering.It is worth noting that this overall bias between morning/evening acquisitions is consistent with [11], [12], and [13], where a systematic offset of about 0.3 dB was observed between descending and ascending passes of the RADARSAT-1/2 satellites.In particular, the higher difference observed in X-band compared with C-band is reasonable, as an increased atmospheric attenuation is expected in presence of high humidity, due to the shorter wavelength.
Similar hypotheses could be formulated regarding the γ 0 backscatter dependency on seasonality, presented in Section V.In this case, we did not observe significant differences between dry (June-September) and wet (December-March) seasons.This could be explained by the fact that no predominant scattering effects occur depending on the considered season.Also, it is important to mention that although precipitations reduce during the driest months, the Amazon gets a significant amount of rain throughout the year [74].
Different locations in the Amazon rainforest, characterized by different climate conditions and biomes at large scale [65], [66], [67], [68], [69], [70], are also analyzed in Section VI.The three investigated test sites [see Table I show radar backscatter profiles over local incidence angles in agreement with each other, when considering acquisitions performed in the evening, i.e., with an ascending orbit direction.This could be explained by high and uniform levels of humidity during day-light hours, which could result in a more uniform γ 0 backscatter distribution over incidence angles.Moreover, as explained in [25], more attenuation is expected in presence of humid air and for larger incidence angles, as the radar wave propagation path is longer.As a consequence, backscatter profiles tend to converge as moving toward far-range geometries.A different behavior is observed when considering acquisitions performed in the morning, i.e., with a descending orbit configuration.The analysis revealed a more stable backscatter profile over local incidence angles when considering the equatorial rainforest, with a log-backscatter bias around 0.78 dB [test site (a)] and 0.65 dB [test site (b)] between near and far range.When considering the southern test areas, i.e., (c) and (d), the γ 0 backscatter appears less stable along the entire range of illuminated incidence angles,  [56], corresponding to forests and orchards (trees), is reported in black together with the corresponding occurrence levels.with log-backscatter variations higher than 1 dB.This could be explained by different local conditions over these regions, related to, e.g., forest properties themselves (e.g., canopy density and structure) [65], [69], [70] and/or deforestation effects [66], [67], [68], [72], [73].The presence of rainwater on the tree leaves surface, due to condensation and cooler morning air, could then contribute in different manners to the backscatter: In presence of a lower canopy density, for example, the radar backscatter over larger/shallower incidence angles could be less affected by rainwater, due to a less direct interaction with the canopy leaves, and could be further attenuated by the longer wave propagation path through the vegetation itself [25].Moreover, changing climate conditions could also contribute to some extent to these instabilities: A different amount of precipitations on a more irregular basis and/or different local humidity levels and temperatures in the air during night/morning hours might then play a nonnegligible role.As a further consideration, it is worth noting that different types of vegetation might also contribute to the different backscatter behaviors and could be mixed in the analysis, due to the large-scale nature of the investigation.Anyhow, the future challenge will be to find reliable reference measurements in order to investigate all these aspects and to better characterize the impact of different climate conditions and biomes on SAR data.
A statistical characterization of the radar backscatter is then presented for VV and HV polarizations in Section VII, using the small amount of available TDX data.An accurate calibration of the copolarized channels, i.e., HH and VV, was ensured over reference calibration point targets, such as corner reflectors and transponders, leading to an overall almost-equal performance [4].The analysis confirmed the backscatter investigations done during the TDX bistatic commissioning phase, regarding HH and VV polarizations [33].Indeed, slightly lower backscatter levels are observed from images acquired in vertical copolarization (VV) compared with the horizontal copolarization (HH) channel.This bias appears small and almost negligible for acquisitions performed in the morning; a possible reason for the observed instabilities over the entire range of illuminated incidence angles could be found in the general comments on test site (c) discussed above.On the other hand, a higher bias of about 0.5 dB is observed from acquisitions performed in the evening: This discrepancy is probably caused by the combination of particular scattering mechanisms within the canopy volume and the extremely humid climate of the Amazon rainforest during day-light hours.According to theoretical considerations about randomlydistributed targets, negligible differences between the two copolarizations should be expected after the polarimetric calibration.Nevertheless, the noncompletely-randomly-distributed nature of the scattering mechanisms within the upper layers of the canopy could impact the backscatter in a different way depending on the considered polarization; reflections from the canopy itself could then be more dominant than the radiation coming from the trunk and branches, or vice versa.From the obtained results, all these effects could then be emphasized by the higher humidity in the air and/or by an increased water content on the tree leaves surface due to a larger amount of precipitations during the day-light time compared with night.As far as the HV cross-polarization is concerned, a backscatter drop up to 7 dB is observed.The reason can be found in the intrinsic properties of HV-polarized images, which record the part of the transmitted horizontal-polarized waves, which are redirected back vertically-polarized to the sensor after the interaction with the target on ground.As well documented in the literature, the HV contribution is lower than that of HH and VV in most cases [76].
Overall, it is important to mention that a higher backscatter variability (wider backscatter confidence intervals) is detected as moving toward larger incidence angles, i.e., far-range geometries.A possible reason could be found in the scattering mechanisms dependency on the incidence angle [75]: Smaller/steeper angles allow the incident wave to penetrate more in the canopy and more likely to reach the ground, resulting in higher branches and trunks contributions.On the other hand, in presence of larger/shallower incidence angles the incident wave has to travel longer through vegetation before reaching the ground, and is more likely affected by specular reflection mechanisms, thus, resulting in higher backscatter variability.
Finally, based on the findings in [25] and [75], a future investigation of other potential and hidden variables could further improve the accuracy of the statistical models provided in this work, e.g., by including precipitation information data or humidity measurements from ground-based radar data.However, the inclusion of additional variables, describing more specific local geophysical processes, will face the lack of ground-truth data over several regions, thus, limiting large-scale studies in favor of smaller and more stationary test sites.

X. CONCLUSION
In this article, we presented a detailed statistical characterization of γ 0 radar backscatter at X-band over the Amazon rainforest using almost-full resolution TDX data.
Although the Amazon rainforest appears to be a quite stable and isotropic target, analyses over different test sites demonstrated its nonperfectly-isotropic nature, as backscatter profiles slightly decrease with respect to local incidence angles.Overall, morning acquisitions appear brighter than evening ones, confirming that the X-band γ 0 backscatter of the Amazon rainforest is mostly influenced by the day-time of acquisition.
We also provided a statistical characterization of γ 0 backscatter depending on seasonality, by comparing dry and wet seasons.In this case, we did not observe significant differences between the two seasons.Moreover, we analyzed different regions of interest in the Amazon rainforest, characterized by different climate conditions and biomes at large scale.In particular, the analysis revealed more stable local conditions on average over the equatorial rainforest.
Furthermore, a statistical characterization of the radar backscatter was presented for VV and HV polarizations as well.
Here, since all nominal TDX data takes are performed in HH polarization, only small data sets were acquired in VV and HV channels for LTSM purposes over selected test sites.Nevertheless, the analysis revealed slightly lower backscatter levels at VV polarization if compared with HH polarization.On the other hand, HV cross-polarized images showed higher backscatter differences compared with copolarized data, i.e., acquired in HH/VV channels, with backscatter values up to 7 dB lower.
In addition, we derived a series of empirical X-band backscatter models over the Amazon rainforest for all the investigated scenarios, based on the analyzed TDX data.To this aim, we relied on the same formulation introduced by Ulaby and Dobson in [56], showing that such models do not precisely represent the radar backscatter when considering tropical vegetated areas, since they were derived from temperate forests.
Never before has a similar investigation at X-band been performed at large scale and in such a detailed manner.Therefore, we are convinced that the derived insights presented in this work can guide users for a proper exploitation of the Amazon basin at X-band in order to define more suitable regions for SAR calibration purposes and to enhance the estimation accuracy of the antenna pattern shape in elevation.Moreover, the proposed analysis could be considered as reference groundwork for future investigations, aiming not only at including additional local geophysical variables but also at extending the study to the characterization of regional climate conditions and biomes from SAR data.The presented results could also motivate a deeper and more accurate investigation of the temporal stability of the Amazon rainforest radiation over stationary test sites in order to monitor the radiometric degradation of current X-band missions over time.Finally, we believe that the models derived in the present analysis represent an extremely valuable input for radar system design and physical modeling purposes, as scientists can utilize them to obtain a very accurate statistical estimation of the γ 0 backscatter over the Amazon rainforest.

APPENDIX
A summary of all statistical parameters from the investigations performed in Sections IV, V, VI, and VII is presented in this appendix in Table III .In particular, statistical distribution tables over the Amazon rainforest are reported for HH, VV, and HV polarization acquisitions at X-band.As already mentioned, all statistics are computed in linear scale and are here expressed in dB.The γ 0 backscatter distributions are characterized with respect to each interval of local incidence angles θ l , ranging from near, i.e., 25 • , to far range, i.e., 51 • .At each incidence angle, the following information is provided: 1) minimum/maximum values, denoted as γ 0 min and γ 0 max , respectively; 2) 5th, 25th, 50th (median value), 75th, and 95th percentiles, denoted as γ 0 x , x being the corresponding percentile; 3) mean value; 4) SD of the distribution; and 5) SEM.Moreover, it is important to comment about the different statistical meaning of SD and SEM [77], [78], [79].SD measures the amount of variability, or dispersion, from the individual data values of a distribution to the mean value.Differently, SEM measures how far the sample mean (average) of the data set is likely to be from the true population mean.Thus, SEM describes how precise the mean of the sample is as an estimate of the true mean of the population.The SEM is computed as with N being the size of the sample data.It is worth noting that SEM decreases as the data set size increases, meaning that the sample mean estimates the true mean of the population with greater precision.Finally, all reported values in the table can be directly downloaded in csv format at the web link in [80].

Fig. 1 .
Fig. 1.Reference geometry for the incidence angle θ and for the local incidence angle θ l .

Fig. 2 .
Fig. 2. γ 0 (left) and θ l (right) mosaics over the whole Amazon rainforest visualized on GoogleEarth.They are composed using TDX stripmap data in HH polarization and acquired in 2012/2013 with steep/shallow incidence angles.

Fig. 3 .
Fig. 3. γ 0 mosaic over the equatorial Amazon rainforest, corresponding to test site (a) in Table I, visualized on GoogleEarth.It is composed by the complete TDX data set of stripmap, HH polarization data acquired between December 2010 and September 2014.

Fig. 4 .
Fig. 4. γ 0 mosaic over test sites (b) and (c), and (d) in Table I, visualized on GoogleEarth.It is composed by the corresponding complete TDX data sets of stripmap, HH polarization data reported in the table.The three test sites are identified by colored boxes, i.e., (b) green, (c) orange, and (d) red.

Fig. 5 .
Fig. 5. γ 0 mosaic over LTSM test sites in the Amazon rainforest, visualized on GoogleEarth.It is composed by TDX data takes acquired in stripmap mode in VV (cyan boxes) and HV (green boxes) single polarizations, between November 2010 and September 2014.Orange box identifies test site (c) in TableI.Moreover, the white box identifies the LTSM region used for the long-term temporal stability analysis on the γ 0 radiation.

Fig. 7 .
Fig. 7. Seasonal variability of the γ 0 radar backscatter with respect to local incidence angles, by comparing dry and wet seasons.Dry season is defined as the period between June and September, whereas the wet season is comprised between December and March.Data distributions are shown for both evening/ascending orbit (top) and morning/descending orbit (bottom) acquisitions.Each box extends from the 25th to 75th percentiles of the data distribution.For each interval, the solid line represents the γ 0 mean value, with triangles identifying the SD confidence interval between mean −SD and mean +SD; whiskers indicate the 5th and 95th percentiles.The histograms depicting the number of samples used for the derivation of the backscatter statistical parameters are reported as well in the background.

Fig. 8 .
Fig. 8. γ 0 backscatter characterization of different Amazon locations with respect to local incidence angles.Data distributions are shown for both evening/ascending orbit (top) and morning/descending orbit (bottom) acquisitions.Each box identifies the confidence interval between the 25th and 75th percentiles of the backscatter distribution, with the solid line being the mean value of the total set of samples.Triangles indicate the SD confidence interval between mean −SD and mean +SD, whereas whiskers correspond to the 5th and 95th percentiles.Histograms depicting the number of samples used for the derivation of the backscatter statistical parameters are presented as well in the background.

Fig. 9 .
Fig. 9.Long-term temporal stability analysis of γ 0 radiation.Data distributions are shown for morning/descending orbit acquisitions only.Each box extends from the 25th to the 75th percentiles of data distribution, with whiskers reaching the 5th and 95th percentiles.Solid line within each box indicates the estimated mean value of the population, with triangles showing the SD confidence interval between mean −SD and mean +SD.Two almost-fully-overlapping dashed horizontal lines report the estimated mean values average over time, computed in linear scale, and then converted to dB.Histograms depicting the corresponding number of samples are reported as well in the background.

Fig. 11 .
Fig. 11.Histograms in logarithmic scale corresponding to γ 0 distributions in Fig. 10 and depicting the number of samples used for the derivation of the backscatter statistical parameters.

Fig. 12 .
Fig. 12. Nonlinear curve fitting of the γ 0 radar backscatter over test site (a) in Table I and for HH polarization.It refers to morning/descending orbit (green) and evening/ascending orbit (blue) acquisitions.Model-based backscatter estimations are shown with solid lines.Dotted and dashed lines represent confidence levels.γ0 Ulaby and Dobson model[56], corresponding to forests and orchards (trees), is reported in black together with the corresponding occurrence levels.

TABLE II RESULTING
FITTING PARAMETERS CORRESPONDING TO THE γ 0 DISTRIBUTIONS IN FIGS.6, 7, 8, AND 10

TABLE III STATISTICS
OF γ 0 BACKSCATTER AT X-BAND OVER THE AMAZON RAINFOREST (VALUES ARE IN DB) licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.

TABLE III (
CONTINUED.)Authorizedlicensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.