remote sensing Article
Multifrequency and Full-Polarimetric SAR Assessment for Estimating Above Ground Biomass and Leaf Area Index in the Amazon Várzea Wetlands Luciana O. Pereira 1,2, *, Luiz F. A. Furtado 2,3 , Evlyn M. L. M. Novo 2 Veraldo Liesenberg 4 ID and Thiago S. F. Silva 5 ID 1 2 3 4 5
*
ID
, Sidnei J. S. Sant’Anna 2 ,
University of Exeter, Exeter, Devon EX4 4QJ, UK Brazilian National Institute for Space Research-INPE, São José dos Campos SP 12245, Brazil;
[email protected] (L.F.A.F.);
[email protected] (E.M.L.M.N.);
[email protected] (S.J.S.S.) Department of Geography, Federal University of Rio de Janeiro, Rio de Janeiro RJ 21941-916, Brazil Department of Forest Engineering, Santa Catarina State University (UDESC), Lages SC 88520-000, Brazil;
[email protected] Ecosystem Dynamics Observatory, Institute of Geosciences and Exact Sciences, São Paulo State University (UNESP), Rio Claro SP 13506-900, Brazil;
[email protected] Correspondence:
[email protected]; Tel.: +44-7846-711911
Received: 4 July 2018; Accepted: 21 August 2018; Published: 25 August 2018
Abstract: The aim of this study is to evaluate the potential of multifrequency and Full-polarimetric Synthetic Aperture Radar (SAR) data for retrieving both Above Ground Biomass (AGB) and Leaf Area Index (LAI) in the Amazon floodplain forest environment. Two specific questions were proposed: (a) Does multifrequency SAR data perform more efficiently than single-frequency data in estimating LAI and AGB of várzea forests?; and (b) Are quad-pol SAR data more efficient than single- and dual-pol SAR data in estimating LAI and AGB of várzea forest? To answer these questions, data from different sources (TerraSAR-X Multi Look Ground Range Detected (MGD), Radarsat-2 Standard Qual-Pol, advanced land observing satellite (ALOS)/ phased-arrayed L-band SAR (PALSAR-1). Fine-beam dual (FDB) and quad Polarimetric mode) were combined in 10 different scenarios to model both LAI and AGB. A R-platform routine was implemented to automatize the selection of the best regression models. Results indicated that ALOS/PALSAR variables provided the best estimates for both LAI and AGB. Single-frequency L-band data was more efficient than multifrequency SAR. PALSAR-FDB HV-dB provided the best LAI estimates during low-water season. The best AGB estimates at high-water season were obtained by PALSAR-1 quad-polarimetric data. The top three features for estimating AGB were proportion of volumetric scattering and both the first and second dominant phase difference between trihedral and dihedral scattering, extracted from Van Zyl and Touzi decomposition, respectively. The models selected for both AGB and LAI were parsimonious. The Root Mean Squared Error (RMSEcv), relative overall RMSEcv (%) and R2 value for LAI were 0.61%, 0.55% and 13%, respectively, and for AGB, they were 74.6 t·ha−1 , 0.88% and 46%, respectively. These results indicate that L-band (ALOS/PALSAR-1) has a high potential to provide quantitative and spatial information about structural forest attributes in floodplain forest environments. This potential may be extended not only with PALSAR-2 data but also to forthcoming missions (e.g., NISAR, Global Ecosystems Dynamics Investigation Lidar (GEDI), BIOMASS, Tandem-L) for promoting wall-to-wall AGB mapping with a high level of accuracy in dense tropical forest regions worldwide. Keywords: SAR data; Above Ground Biomass (AGB); Leaf Area Index (LAI); Wetlands Amazon
1. Introduction The estimation and monitoring of Above Ground Biomass (AGB) and Leaf Area Index (LAI) in tropical forests is of great relevance for understanding biogeochemical cycles and the effects of climate Remote Sens. 2018, 10, 1355; doi:10.3390/rs10091355
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change on forest resources. Such measurements also support international protocols such as the United Nations Reducing Emissions from Deforestation and Forest Degradation (REDD+) [1]. AGB is regarded as an important indicator in ecological studies and management of vegetation, whereas LAI is a key parameter in plant ecology. Due to frequent cloud coverage [2], Synthetic Aperture Radar (SAR) remote sensing has been shown to be an important tool for the assessment of both LAI and AGB in tropical regions [3–5]. This is due to the capacity of SAR systems to both penetrate clouds and interact with vegetation canopies, with the volumetric backscattering component being a function of canopy structure. Although SAR systems are not able to retrieve the vertical structure of vegetation as easily as airborne Light Detection and Ranging (LiDAR) systems, the wide swath orbital coverage capability of SAR systems is useful for assessing large wetland ecosystems such as the floodplains along Amazonian rivers, known for their biodiversity, complexity and difficult access [6]. The applicability of SAR data to determine forest biophysical parameters depends on the number of polarizations and the frequency or wavelength used [6,7]. Most orbital SAR platforms acquire data in only single- and dual-polarization modes, thus having limited potential for discriminating subtle structural differences in the vegetation [7–10]. Quad-pol, or full-polarimetric mode, provide the complete scattering matrix of the backscattered wave, allowing the calculation of polarimetric decomposition and other polarimetric descriptors, which can potentially better describe canopy structural properties [11,12]. This has already been shown by several studies [12–20]. Multi-frequency SAR data can also be used as an alternative to single-frequency single- or dual-pol data. Its synergy enables discrimination of subtle vegetation types and assessment of structural properties, albeit with different degrees of success, as different frequencies interact with distinct sections of the plant canopy [15,21–23]. To date, provision of orbital quad-pol SAR data has been limited to experimental mode, with limited swath coverage, and/or the data are more expensive than single- and dual-pol images. Multi-frequency analysis entails acquisition of data from different orbital sensors provided by different space agencies, therefore raising project costs and computational demands and complexity. However, it is still important to assess the efficacy and feasibility of applying both multi-polarimetric and multi-frequency methods to estimate forest structural attributes. SAR literature indicates that both X- and C-band backscattering coefficient images (σ0 ) saturate at relatively low AGB levels (i.e., up to 50 and 250 t/ha, respectively [21,24–29]). L-band saturates at 88 to 900 t/ha [30–36], depending on vegetation structural complexity. In general, SAR signal saturation thresholds tend to decrease with vegetation structural complexity, especially for tropical forests. Therefore, exploring the saturation threshold and investigating the potential of polarimetric features in such environments is still necessary. Várzeas are eutrophic river floodplains associated with large high-sediment load (“white water”) rivers in the Amazon. They occupy approximately 200,000 km2 within the Amazon basin [37], providing important ecosystem services to human populations and hosting endemic fauna and flora species, such as the Amazonian manatee (Trichechus inunguis) [38] and the Pirarucu fish (Arapaima gigas) [39]. They also have an important role in regional biogeochemical cycles, although estimates are still quite uncertain as they are one of the most under-sampled Amazon ecosystems [40,41]. Várzeas are currently threatened by anthropogenic land-use/land-cover changes [42]; approximately 54% of the original forest cover in lower Amazon várzeas was lost between 1984 and 2009 [43,44]. Therefore, developing efficient remote sensing methods for assessing structural forest attributes such as Leaf Area Index (LAI) and Above Ground Biomass (AGB) is of major importance to further ecological and biogeochemical studies in várzeas, because these attributes have noticeable relationships with ecophysiological processes such as evapotranspiration, photosynthetic activity, carbon assimilation and biomass stocks [45]. Such information may also serve as more accurate proxies for habitat structure in biodiversity studies. Quantitative data about várzea forests can also assist decision-makers, public governance and environmental policies regarding planning and conservation.
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proxies for habitat structure in biodiversity studies. Quantitative data about várzea forests can also of 23 public governance and environmental policies regarding planning 3and conservation. Therefore, this paper answers two questions: (a) Does multifrequency SAR data perform more Therefore, this paper answers two questions: (a) Does multifrequency SAR data perform more efficiently than single-frequency data in estimating LAI and AGB of várzea forests?; and (b) Are efficiently than single-frequency data in estimating LAI and AGB of várzea forests?; and (b) Are quad-pol SAR data more efficient than single- and dual-pol SAR data in estimating LAI and AGB of quad-pol SAR data more efficient than single- and dual-pol SAR data in estimating LAI and AGB of várzea forest? várzea forest? Remote 2018, 10, 1355 assistSens. decision-makers,
Materials and and Methods Methods 2.2.Materials 2.1.Study Study Area Area and and Field Field Inventories Inventories 2.1. The study study area area is is located located within within Pará Pará State State (Brazil) The (Brazil) and and encompasses encompassesan an~88 ~88ha hasection sectionofofthe the Lago Grande de Curuai (Figure 1). This floodplain lake has an annual and monomodal Lago Grande de Curuai (Figure 1). This floodplain lake has an annual and monomodalflooding flooding regime,with with high-water high-water season season occurring occurring between regime, between May May and and June, June, and and low-water low-waterseason seasonoccurring occurring from November to December [46]. from November to December [46].
Figure 1. 1. (a) state (dark gray) within Brazil (light gray); (b) detailed view of the Lago Figure (a) Location LocationofofPará Pará state (dark gray) within Brazil (light gray); (b) detailed view of the Grande de Curuai; (c) classes and field plots location; (d) Radarsat-2 HV image in low-water season; Lago Grande de Curuai; (c) classes and field plots location; (d) Radarsat-2 HV image in low-water (e) advanced land observing satellitesatellite (ALOS)/ phased-arrayed L-band L-band Synthetic ApertureAperture Radar season; (e) advanced land observing (ALOS)/ phased-arrayed Synthetic (PALSAR-1) HV image in high-water season. Radar (PALSAR-1) HV image in high-water season.
The vegetation comprises a mosaic of vegetation types, including grasslands, shrubs and forests, whose distribution, species composition, canopy structure and phenology are strongly linked to the
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The vegetation comprises a mosaic of vegetation types, including grasslands, shrubs and forests, whose distribution, species composition, canopy structure and phenology are strongly linked to the seasonal comprises six seasonal flooding flooding dynamics dynamics [40,47,48]. [40,47,48]. Specifically, Specifically, the the land land cover cover in in the the study study area area comprises six major defined and and mapped mapped using using dual-season dual-season PolSAR PolSAR Radarsat-2 Radarsat-2 data data [8]. [8]. major classes, classes, previously previously defined The class corresponds corresponds to to the the water water surface surface previously previously mapped mapped using using C-band C-band SAR SAR The Open Open Water Water class imagery during the the low-water low-water season. season. The imagery (Figure (Figure 1d) 1d) acquired acquired during The water water surface surface during during the the high-water high-water season as Open Open season was was mapped mapped using using the the L-band L-band SAR SAR image image (Figure (Figure 1e) 1e) and and will will be be referenced referenced here here as Water High Season class. Therefore, the class Várzea Fields was mapped as the difference in water Water High Season class. Therefore, the class Várzea Fields was mapped as the difference in water surface between the the two two periods. periods. surface between In this study, floating (Figure 1d)1d) were merged because theythey are not In this study, floatingand andemergent emergentmacrophytes macrophytes (Figure were merged because are distinguishable from each other in L-band SAR scenes [21]. As the Várzea fields correspond to the not distinguishable from each other in L-band SAR scenes [21]. As the Várzea fields correspond to regions colonized by grasses during the low-water season, we decided to group all these classes into the regions colonized by grasses during the low-water season, we decided to group all these classes ainto new classclass named Non-forested. Therefore, the following classes werewere examined in this study: (1) a new named Non-forested. Therefore, the following classes examined in this study: Floodable Forests: forest growing on high floodplains subject to shorter seasonal flooding periods; (1) Floodable Forests: forest growing on high floodplains subject to shorter seasonal flooding periods; (2) Shrubs: Shrubs: shrubs (2) shrubs and/or and/or early early succession succession tree tree vegetation vegetation with with sparse sparse canopies canopies and and low low height, height, subject to longer seasonal flooding; and (3) Non-forested: emergent and floating herbaceous plant subject to longer seasonal flooding; and (3) Non-forested: emergent and floating herbaceous plant communities and subject subject to to communities dominated dominated by by palustrine palustrine grasses, grasses, with with high high biomass biomass and and density density levels levels and longer seasonal flooding periods, and floodplain regions that are colonized by terrestrial herbaceous longer seasonal flooding periods, and floodplain regions that are colonized by terrestrial herbaceous plants during during low-water low-water season. season. plants The (Figure 2) 2) summarizes summarizes the the main main steps steps described described in in the the following following sections. sections. The flowchart flowchart (Figure
Figure 2. Flowchart Flowchart for for estimating estimatingabove-ground above-groundbiomass biomassand andleaf leaf area index from SAR dataset Figure 2. area index from thethe SAR dataset on on Amazon floodplain forests. Amazon floodplain forests.
Forest inventories were carried out from 18 October 2013 to 29 October 2013, during the lowForest inventories were carried out from 18 October 2013 to 29 October 2013, during the low-water water season, by establishing eighteen 25 × 25 m (0.0625 ha) sample plots, distributed between season, by establishing eighteen 25 × 25 m (0.0625 ha) sample plots, distributed between Flooded Flooded Forest areas (Figure 1c). LAI was measured using an LAI-2200 Plant Canopy Analyzer (LiForest areas (Figure 1c). LAI was measured using an LAI-2200 Plant Canopy Analyzer (Li-Cor Inc., Cor Inc., Lincoln, NE, USA). Eight measurements were taken within each sample plot beneath the Lincoln, NE, USA). Eight measurements were taken within each sample plot beneath the canopy canopy (two rows of four measurements), using a 270-degree lens cap with the closure turned (two rows of four measurements), using a 270-degree lens cap with the closure turned towards the towards the holder. All measurements were taken with the sun at low elevation angles, always located holder. All measurements were taken with the sun at low elevation angles, always located behind behind the operator, avoiding the incidence of direct light on the sensor. Clear sky reference the operator, avoiding the incidence of direct light on the sensor. Clear sky reference measurements measurements were taken before and after plot sampling, no earlier or later than 10 min from the were taken before and after plot sampling, no earlier or later than 10 min from the observations, observations, at nearby clearings. at nearby clearings. At each sample plot, we measured the total height (h, in m) and the diameter at the breast height At each sample plot, we measured the total height (h, in m) and the diameter at the breast (DBH > 10 cm) (d, in cm) for all living tree individuals. Each single tree species was identified in the height (DBH > 10 cm) (d, in cm) for all living tree individuals. Each single tree species was field by a trained parabotanist. Based on this identification, we compiled measurements of wood identified in the field by a trained parabotanist. Based on this identification, we compiled density (p, in g cm3) from Wittmann, et al. [49] and from the Global Wood Density Database—GWDD; measurements of wood density (p, in g cm3 ) from Wittmann, et al. [49] and from the Global http://datadryad.org/handle/10255/dryad.235). Wood density of similar species within the Wood Density Database—GWDD; (http://datadryad.org/handle/10255/dryad.235). Wood density family/genera was used whenever the species were not found in the database. of similar species within the family/genera was used whenever the species were not found in the database.
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The AGB of each single tree was computed as the average AGB o according to Schöngart and Wittmann [50] for Amazonian flooded fo 𝐴𝐺𝐵 = 𝐹 ∗5 of 𝑃 23 ∗ ℎ𝐴𝐺𝐵 ∗ 𝜋(𝑑/2)
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𝐴𝐺𝐵 = 0.112 ∗ (𝑝 ∗ ℎ ∗ 𝑑 ) . The AGB of each single tree was computed as the average AGB obtained from Equations (1)–(3), 𝐴𝐺𝐵 = 0.0509 ∗ 𝑝 ∗ ℎ ∗ 𝑑 according to Schöngart and Wittmann [50] for Amazonian flooded forests.
In (2), F is a fixed form factor of 0.6 [51]. The AGB of individu AGB1 = F ∗ P ∗ hAGB1 ∗ π (d/2)2 (1) summed, and their values scaled to t/ha. Boxplots for both AGB an outliers that 0.916 could impact model fitting [52]. AGB2 = 0.112 ∗ ( p ∗ h ∗ d2 ) (2) 2.2.∗SAR AGB3 = 0.0509 p ∗ hImage ∗ d2 Acquisition
(3)
SARofsatellite datatrees fromof three platforms In (2), F is a fixed form factor of 0.6 [51]. The AGB individual eachsensor plot were then were acquired: ad (ALOS)-phased-arrayed L-band (i.e., 1.27-GHz center frequency, ~ summed, and their values scaled to t/ha. Boxplots for both AGB and LAI helped identify possible Radarsat-2 at the C-band frequency [54], and TerraSAR-X at the X-b outliers that could impact model fitting [52]. and TerraSAR-X images were provided through the Science and Op 2.2. SAR Image Acquisition (SOAR) program of the Canadian Space Agency (CSA), and PALSAR ALOS & Carbon Initiative and the satellite ALOS PI program of th SAR satellite data from three sensor platforms were Kyoto acquired: advanced land observing Agency (Table 1). (ALOS)-phased-arrayed L-band (i.e., 1.27-GHz center frequency, ~23 cm) SAR (PALSAR-1) [53], Radarsat-2 at the C-band frequency [54], and TerraSAR-X at the X-band frequency [55]. Radarsat-2 Table 1. Characteristics of SAR data. and TerraSAR-X images were provided through the Science and Operational Applications Research (SOAR) program of the Canadian Space Agency (CSA), and PALSAR-1 scenes were provided by Wavelength Sensor Band Operation Mode Polarization the ALOS Kyoto & Carbon Initiative and the ALOS PI program of theband Japan Aerospace Exploration (cm) Agency (Table 1). Multi Look Ground TerraSAR-X Band-X ~3.1
Table 1. Characteristics of SARBand-C data. Radarsat-2 ~5.6
Range Detected (MGD)
Standard Qual-Pol (SQ) Full-polarimetri
PALSAR-1
Fine-beam dual (FBD) Observation Spatial Band-L ~23.6 Polarization PALSAR-1 Fine-beam dual(m) (FBD) Date resolution
Sensor
Band
Wavelength band (cm)
Operation Mode
TerraSAR-X
Band-X
~3.1
Multi Look Ground PALSAR-1 Polarimetric HH Oct. 19st 2011 20 × 20 (PLR) Band-L ~23.6 Range Detected (MGD)
Radarsat-2
Band-C
~5.6
Band-L
~23.6
Band-L
~23.6
PALSAR-1 PALSAR-1 PALSAR-1 PALSAR-1
PALSAR-1
Standard Qual-Pol (SQ) Full-polarimetric Fine-beam dual (FBD) Field HH campaign: and HV Fine-beam dual (FBD) HH and HV Polarimetric (PLR) Full-polarimetric Polarimetric (PLR) Full-polarimetric
Field campaign: Oct. 18st to 29st 2013
HH
Polarimetric (PLR)
Oct. 20st 2011 st Oct. 29st Oct.18 25stto 2010 Oct. 08st 2010 Mar. 30st 2009 May. 15st 2009
20 × 20
2013
19 (in range) × 10 (in azimuth)
HH and HV HH and HV
Full-polarimetri
Full-polarimetri
Mosaicked im
23 × 23
Mosaicked images.
All SAR images werefor acquired in October (low-water season), e All SAR images were acquired in October (low-water season), except the ALOS/PALSAR-1 PLR scene, which was obtained during theinfluence high-water season. This s PLR scene, which was obtained during the high-water season. This seasonal variation may forest backscattering signals according vegetation forest backscattering signals according to vegetation structure, affecting the estimates of LAItoand AGB. structure, affe AGB. It must be noted that forest inventory It must be noted that forest inventory was not concurrent with satellite overpasses. Nevertheless, most was not concurr Nevertheless, Floodplain Forest regions Floodplain Forest regions have remained unchanged for the pastmost seventeen years, according to have [56]. remained unchang according to [56]. 2.3. Image Processing 2.3. Image Processing The full polarimetric image processing is summarized in Figure 3. The Radarsat-2 SQ image was The full polarimetric image processing is summarized in Figure multilooked using four looks in azimuth and one look in range, resulting in approximately 20 × 20 m multilooked using four looks in azimuth and one look in range, resul ground-range spatial resolution. The ALOS/PALSAR-1 PLR image was multilooked using six looks ground-range spatial 23 resolution. The ALOS/PALSAR-1 PLR image w in azimuth and one look in range, which resulted in approximately × 23 m spatial resolution. in azimuth and one look in range, which resulted in approximately 2 Both Radarsat-2 and ALOS/PALSAR-1 PLR scenes were used to compute the Covariance (C) and Radarsat-2 ALOS/PALSAR-1 PLR resolution scenes were used to com Coherence (T) matrices. In order to minimize speckle noise and and preserve image spatial (T)5 matrices. order minimize speckle and information, the Refined Lee adaptive filterCoherence with a 5 × window In size wastoapplied over the noise and prese full-polarimetric scenes. For consistent results, filtering with similar window sizes was applied to both ALOS/PALSAR-1 FBD and TerraSAR-X images. Table 2 shows the polarimetric decomposition and incoherent SAR features (including sigma-nought (σ0 )) extracted from the full-polarimetric data.
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Figure 3. Full polarimetric image processing. Figure 3. Full polarimetric image processing. Table 2. Polarimetric Features extracted from the full-polarimetric SAR data (quad-pol). Table 2. Polarimetric Features extracted from the full-polarimetric SAR data (quad-pol). Polarimetric
Polarimetric Decomposition Decomposition
α angle α angle Entropy Entropy Anisotropy Anisotropy Volumetric scattering Volumetric scattering Double-bounce Double-bouncescattering scattering Odd scatering Odd scatering Scattering type magnitude
Scattering type magnitude
Symbol
Symbol
Description
Description
Cloude-Pottier [57] Cloude-Pottier [57] α α Dominant scattering type. Dominant scattering type. H H Proportional importance of the dominant scattering Proportional importance of the dominant scatteringtype. type. A A Proportional importance of secondary and Proportional importance of secondary andtertiary tertiaryscattering scattering types. types. Freeman–Durden (Freeman & Durden 1998) Freeman–Durden (Freeman & Durden 1998) FDVFD Proportion of volumetric scattering. Proportion of volumetric scattering. V FDDFDD of double-bounce ProportionProportion of double-bounce scattering. scattering. FDS FDS Proportion of odd (surface) scattering. Proportion of odd (surface) scattering. Touzi[58] [58] Touzi Angle of the symmetric scattering vector direction in the trihedralAngle of the symmetric scattering vector direction in the αS1; αS2; αS3; αSm; αS1 ; αS2 ; αS3 ; αSm ; dihedral basis. Similarbasis. to Cloude-Pottier’s α angle. trihedral-dihedral Similar to Cloude-Pottier’s α angle.
Scattering phase Phase difference between trihedral and dihedralscattering. scattering. Scattering typetype phase difference ΦαS1Φ, αS1 ,Φ ,Φ , ΦαSm αS2 ΦαS2 ,Φ αS3 , ΦαS3 αSm Phase difference between trihedral and dihedral difference Symmetric nature of target scattering. If τ = 0, target is isotropic. Helicity τ1 ; τ2 ; τ3 ; τm Helicity angle τ1; ψ τ2;; τψ3; ;τψ m Symmetric nature Orientation Target tilt angle.of target scattering. If τ = 0, target is isotropic. 1 2 3 ; ψm Orientation angle
Volumetric scattering
Volumetric scattering Double-bounce scattering Double-bounce scattering Odd scattering Odd scattering
ψ1; ψ2; ψ3; ψm Y
YV V YD YD Y S YS
Target tilt angle. Yamaguchi [59] Yamaguchi [59] Proportion of volumetric scattering. Proportion of volumetric scattering. Proportion of double-bounce scattering. Proportion of double-bounce Proportion of odd (surface)scattering. scattering. Proportion of odd (surface) scattering. Van Zyl [60] Van Zyl [60] Proportion of volumetric scattering. Proportion of volumetric scattering. Proportion of double-bounce scattering. Proportion of double-bounce scattering. Proportion of odd (surface) scattering. Proportion of odd (surface) scattering. Description of Features Description of Features Backscatter coefficient (dB) Backscatter coefficient (dB) Backscatter coefficient (dB) Backscatter coefficient (dB) Backscatter coefficient (dB) Backscatter coefficient (dB) Linear units Linear units Linear units Linear units Linear units Linear units Linear units Linear units Linear units Linear units Linear units Linear units SPAN = |S |2 + 2|Shv |2 + |Svv |2 [11] (Linear units) 𝑆𝑃𝐴𝑁 = |𝑆 | hh + 2|𝑆 | + |𝑆 | [11] (Linear units) (HH + VV)/2-magnitude images [61] (Linear units) (HHRV + VV)/2-magnitude [61] (Linear units) I = 8σ /(σ +images σ + 2σ ) [62] (dB)
Volumetricscattering scattering Volumetric VZVVZV Double-bounce scattering VZ Double-bounce scattering VZD D Odd scattering VZS Odd scattering VZS Incoherent SAR Features Acronyms Incoherent SAR Features Acronyms * HH-dB (σ◦ ) HH band (σ°) ◦HH band * HH-dB (σ ) HV band * HV-dB (σ°) ◦HV band * HV-dB * VV-dB (σ ) VV band (σ°) VV band * VV-dB * (HV/VV) Ratio (HV/VV) Ratio (HV/VV) * (HV/VV) Ratio (HV/HH) * (HV/HH) Ratio (HV/HH) * (HV/HH) * (VV/HH) Ratio (VV/HH) Ratio (VV/HH) * (VV/HH) * (HV-VV) Difference (HV/VV) Difference (HV/VV) * (HV-VV) * (HV-HH) Difference (HV/HH) Difference (HV/HH) * (HV-HH) * (VV-HH) Difference (VV/HH) Difference (VV/HH) * (VV-HH) SPAN SPAN SPAN SPAN Biomass index BMI index index BMI RVI The Biomass radar vegetation HV HH VV HV The radar vegetation RVI the ALOS-PALSAR-1 𝑅𝑉𝐼 = 8𝜎 /(𝜎 + 𝜎FBD, + 2𝜎 ) [62] (dB) To identify the features extracted from PLR and TerraSAR-X and, Radarsat-2 SQ the index symbol * was replaced by the acronyms PL-PLR, PL-FDB, TX and RC2, respectively.
To identify the features extracted from the ALOS-PALSAR-1 PLR and FBD, TerraSAR-X and, Radarsat-2 SQ the symbol * was replaced by the acronyms PL-PLR, PL-FDB, TX and RC2, respectively.
Range-doppler terrain correction and georeferencing were applied using the digital elevation modelRange-doppler (DEM) extracted from correction the Shuttleand Radar Topography Mission (SRTM), withthe a spatial terrain georeferencing were applied using digitalresolution elevation of 3 arc-seconds (90 m) and approximately 5 m of vertical resolution [63]. All processing steps were model (DEM) extracted from the Shuttle Radar Topography Mission (SRTM), with a spatial performed the polarimetric SAR Processing and Tool (PolSARPRO) software, resolution with of 3 arc-seconds (90 m) andData approximately 5 m Educational of vertical resolution [63]. All processing steps were performed with the polarimetric SAR Data Processing and Educational Tool (PolSARPRO)
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version 5.0 [64], with exception of the range-doppler correction, which was carried out with the Sentinel-1 Toolbox version 4.0 [65]. TerraSAR-X and PALSAR-1 FBD images were converted to sigma-nought (σ0 ) intensity backscattering coefficients (dB) using the Equation (4) [66,67]. σ0 = 10 ∗ log10 h DN 2 i + CF
(4)
where DN is Digital Number (amplitude) and CF is the calibration factor in dB for the channels. For PALSAR-1 FBD and TerraSAR-X MGD the CF is equal to −83 and −46.7, respectively. 2.4. Assembly of SAR Modeling Sets In order to answer the proposed scientific questions, the SAR data were grouped as follows: (i) single/dual pol: TerraSAR-X band, ALOS PALSAR-1 FDB, and the features (HH and HV) extracted from Radarsat-2 SQ and PALSAR-1 PLR (acquired in the high-water season); (ii) multifrequency group: combination of the features extracted from TerraSAR-X, Radarsat-2 and ALOS/PALSAR-1 FBD images acquired during the low-water season; (iii) full-polarimetric data (Table 3). Table 3. Definition, acronyms and description of SAR predictor sets. The description and acronyms of features composing the single and dual-pol groups (Table 2) are highlighted in gray. The original datasets identified by the symbol * in the Table 2 are replaced by their acronyms shown in the third column of this table. Dataset description (Features)
j = numbers of features
TX RC2 PL-FBD PL-PLR
TX(HH-dB) R2C(HH-dB), R2C(HV-dB), R2C(HV/HH), R2C(HV-HH) PL(HH-dB), PL(HV-dB), PL(HV/HH), PL(HV-HH) PLR(HH-dB), PLR(HV-dB), PLR(HV-HH), PLR(HV-HH)
1 4 4 4
PL-FBD+TX PL-FBD+RC2 TX+RC2 PL-FBD+RC2+TX
PL-FBD+TX PL-FBD+RC2 TX+RC2 MULT
Same acronyms of features PL-FBD+TX dataset Same acronyms of featuresPL-FBD+RC2 dataset Same acronyms of features TX+RC2dataset Same acronyms of features TX+RC2+PL-FBD dataset
5 8 5 9
Radarsat-2 ALOS/PALSAR-1 PLR
RC2(POL) PL-PLR(POL)
Table 2 Table 2
40 40
Data type
Data source
SAR single and dual-pol
TerraSAR-X Radarsat-2 ALOS/PALSAR-1 FBD ALOS/PALSAR-1 PLR
Multifrequecy
Full-polarimetric
Acronyms of dataset
2.5. Above Ground Biomass and Leaf Area Index Modeling Univariate and multivariate Generalized Linear Models (GLMs) were estimated for predicting both AGB and LAI, using SAR datasets as predictor (Table 3). Two different link functions were tested for GLM specification, the identity function (i.e., Multivariate Linear Regression, Equation (5)), and the log link function (Equation (6)), since AGB and LAI variables R+ [68]. The predicted quantities will hereafter be referred as E(Yi) and lnE(Yi), respectively. E(Yi ) = µi , Yi ∼ N (µi , σ2 ) µi = b0 + b p x p , p = 1, 2, . . . , j
(5)
ln E(Yi ) = µi , Yi ∼ N (µi , σ2 ) µi = b0 + b p x p , p = 1, 2, . . . , j
(6)
where b0 , bρ , xp , ln are the intercept, regression coefficients, the predictor variables (features) and natural logarithm, respectively. Mean SAR responses (Table 2) correspond to a homogenous region around each 0.0625 ha plot, encompassing a minimum of four pixels. A routine was implemented in the R scripting language [69] for automatic model calibration, selection and assessment, as well as for outputting AGB and LAI maps (Supplementary Material). The core package of the routine is the “glmult” package [70], which allows model fitting using all predictor variable combinations. A two-level routine (Figure 4) applies
maps (Supplementary Material). The core package of the routine is the “glmult” package [70], which allows model fitting using all predictor variable combinations. A two-level routine (Figure 4) applies different numerical criteria for defining the best models. Thus, for j independent predictor (Table 3), the number of calibrated models is 2j + 1. Remote Sens. 2018, 10, selection 1355 8 of 23 In the first level, the small-sample-size corrected version of the Akaike information criterion (AICc) was applied, following the recommendation that models with ΔAICc ≤ 2 units, relative to the lowest AICc value, should not be dismissed [71] (Figure 4). At the second level, models different numerical criteria for defining the best models. Thus, for j independent predictor (Table 3), were assessed based on statistical significance (α = 0.05), R-squared (R2) or pseudo R-squared (for the number of calibrated models is 2j + 1. lnE(Yi)), and leave-one-out cross-validation using the Root Mean Squared Error (RMSEcv). To In the first selection level, the small-sample-size corrected version of the Akaike information support model assessment, the relative overall RMSEcv (Rel. RMSE) in percentage, bias and average criterion (AICc) was applied, following the recommendation that models with ∆AICc ≤ 2 units, relative relative error (ARE) were also reported. Pixel level spatial prediction maps (output maps) were then togenerated the lowest AICc should not be dismissed [71] 4). At the second level, models were from all value, significant models and submitted to (Figure visual assessment. assessed based statistical significance (αfull-polarimetric = 0.05), R-squared (R2 ) models or pseudo R-squared (for lnE(Yi)), Given theon high computation cost of based (i.e., j = 40), polarimetric and leave-one-out cross-validation using the Root Mean Squared Error (RMSEcv). To support model features were split into three groups of analogous decompositions that could represent similar assessment, relative RMSEcv in percentage, bias average error informationthe (Figure 5). overall Then, each group(Rel. wasRMSE) submitted to the levels of and selection (seerelative gray box in (ARE) were also reported. Pixel level spatial prediction maps (output maps) were then generated from Figure 4). The predictors of the selected models were then regrouped into a new set of predictors (k’), all significant models and used submitted to visual assessment. which was subsequently as input to the “Levels of selection”, showed as step B in Figure 5.
Figure Flowchart:Models Modelsselection selectionprocess process for for SAR SAR Single/dual-pol Single/dual-pol and Figure 4.4.Flowchart: andMultifrequency Multifrequencydata datatype. type.
Given the high computation cost of full-polarimetric based models (i.e., j = 40), polarimetric features were split into three groups of analogous decompositions that could represent similar information (Figure 5). Then, each group was submitted to the levels of selection (see gray box in Figure 4). The predictors of the selected models were then regrouped into a new set of predictors (k’), which was subsequently used as input to the “Levels of selection”, showed as step B in Figure 5.
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Figure 5. Flowchart: Model selection process for the quad-pol SAR data type. Figure 5. Flowchart: Model selection process for the quad-pol SAR data type.
2.6. Visual Assessment of Maps LAI and AGB Maps
2.6. Visual Assessment of Maps LAI and AGB Maps
Finally, the LAI and AGB output maps from selected models for both polarimetric and nonFinally, the LAI and AGB outputtomaps selected models and polarimetric SAR data were submitted visualfrom analyses (Figures 4 and for 5) inboth orderpolarimetric to assess their non-polarimetric data submitted to visual analyses (Figures 4 and in order to assess their suitability withSAR respect towere the reference map, land-cover classes (Figure 1c–e;5)Table 1), and ground suitability withregarding respect toland-use the reference map, land-cover classes2011) (Figure and ground information and land-cover classes (April and1c–e; fromTable field 1), observations provided by Arnesen, land-use et al. [72], and Furtado, et al. [73]classes and Furtado, Novo [8].field The observations best model information regarding land-cover (April Silva 2011)and and from was that the minimum the[73] highest agreement with theNovo spatial of provided bywith Arnesen, et al. [72],RMSEcv Furtado,and et al. and Furtado, Silva and [8].distribution The best model woody vegetation cover classes (Figure inspecting thethe output maps. To facilitate this was that with the minimum RMSEcv and 1), theassessed highest by agreement with spatial distribution of woody inspection, the classes maps were generated automatically in ascending order of RMSEcv. vegetation cover (Figure 1), assessed by inspecting the output maps. To facilitate this inspection, All final predictions were cut considering the lower and upper thresholds observed in the LAI the maps were generated automatically in ascending order of RMSEcv. and (Figure 6). Thus, lower and the upper bounds AGBthresholds were 0 and 600 t/ha,in and AllAGB finaldata predictions were cutthe considering lower and for upper observed thefor LAI LAI, 2 and 6. Values outside this range were clipped to the nearest threshold. and AGB data (Figure 6). Thus, the lower and upper bounds for AGB were 0 and 600 t/ha, and for
LAI, 2 and 6. Values outside this range were clipped to the nearest threshold. 3. Results
3. Results
3.1. Exploratory Analysis of LAI and AGB Data
3.1. Exploratory Analysis of LAI andAGB AGB(the Data Both boxplots contain two largest-Figure 6a) and LAI (the smallest-Figure 6b) values that mayboxplots be outliers. To better the impact of these possible outliers on model calibration Both contain two understand AGB (the largest-Figure 6a) and LAI (the smallest-Figure 6b) values and/or map accuracy, the selection process was carried out by including and excluding them.calibration To refer that may be outliers. To better understand the impact of these possible outliers on model to the number of LAI or AGB samples used in the model calibration, subscribed numbers (16 or 18) and/or map accuracy, the selection process was carried out by including and excluding them. To refer were added to the dataset acronyms henceforth (Table 3). To compare the results of equivalent to the number of LAI or AGB samples used in the model calibration, subscribed numbers (16 or models calibrated with either 18 or 16 samples for both LAI and AGB, their observed versus predicted 18) were added to the dataset acronyms henceforth (Table 3). To compare the results of equivalent scatterplots (OBS vs. PREDs) were joined.
models calibrated with either 18 or 16 samples for both LAI and AGB, their observed versus predicted scatterplots (OBS vs. PREDs) were joined.
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Figure (a) Above Above Ground Ground Biomass Figure 6. 6. Boxplot Boxplot graphic: graphic: (a) Biomass (AGB) (AGB) ee (b) (b) Leaf Leaf Area Area Index Index (LAI). (LAI).
3.2. 3.2. LAI LAI Models Models In biases were low,low, however the LAI obtained from the lnE(Yi) In general, general,all allmodel model biases were however the estimates LAI estimates obtained from the models lnE(Yi) had better spatial correspondence with land-cover classes (Figure 1), supported by the empirical models had better spatial correspondence with land-cover classes (Figure 1), supported by the knowledge of study area (Tablearea 4). (Table Models4).selected RC2(POL) and PL-PLR(POL) empirical knowledge of study Modelsfrom selected from RC2(POL) and PL-PLR(POL) 16 16 did not provide reliable reliable maps and were therefore not considered further.further. Among the models selected from did not provide maps and were therefore not considered Among the models selected 2 and SAR dataset, PL-FBD the highest R2 andRthe lowest RMSEcv and Rel.and RMSE fromsingle/dual-pol SAR single/dual-pol dataset, PL-FBD 18 showed the highest the lowest RMSEcv Rel. 18 showed with as predictor (Table 4). The same feature alsowas ranked the model OBS vs. RMSEHV-dB with HV-dB as predictor (Table 4). The same was feature also in ranked in thePL-FBD model16PL-FBD 16 PREDs (Figure 1). The best output map resulted from the 18 LAI samples model OBS vs.distribution PREDs distribution (Figure 1). The best LAI output LAI map resulted from the 18 LAI samples (Figure 7a). model (Figure 7a). 2 and Regarding best model (highest R2 R and thethe lowest RMSEcv and and Rel. Regardingthe themultifrequency multifrequencydataset, dataset,the the best model (highest lowest RMSEcv 2 2and the RMSEcv RMSE was provided by PL-FBD+TX (Figure 7b). Despite the similarity in the R Rel. RMSE was provided by PL-FBD+TX 18 18 (Figure 7b). Despite the similarity in the R and the RMSEcv and RMSE statistics statistics of of both and PL-FBD PL-FBD1818, ,their theiroutput outputmaps maps are are quite quite different. different. and Rel. Rel. RMSE both PL-FBD+TX PL-FBD+TX1818 and This regions with high andand lowlow LAILAI values (i.e.,(i.e., green and and red This isisclearly clearlyobserved observedwhen whencomparing comparingthe the regions with high values green regions, respectively) because there are not coincident. PL-FBD was selected as best model, because red regions, respectively) because there are not coincident. PL-FBD 18 was selected as best model, 18 it presented coherent coherent results based onbased visualon analyses and consists a singleofpredictor (HV-dB) (thus because it presented results visual analyses andof consists a single predictor (HVhaving operational advantages). dB) (thus having operational advantages). Visual LAI map (Figure 7a) indicated that the in redin (i.e., values Visual analysis analysisofofthe thebest best LAI map (Figure 7a) indicated thatregions the regions redlowest (i.e., lowest set for the LAIthe maps) locations of the Non-forested class (Figure 1). This a clear values set for LAI match maps) with matchthe with the locations of the Non-forested class (Figure 1).isThis is a indication that L-band dual-pol SARSAR images are are lessless sensitive to to lower LAI clear indication that L-band dual-pol images sensitive lower LAIvalues values(i.e., (i.e.,22 or or less), less), likely likely due due to to the the longer longer wavelength. wavelength. The The LAI LAI map map also also shows shows that that the the Flooded Flooded Forest Forest class class is is clearly clearly discriminated discriminated from from the the Non-forested Non-forested class, class, because because most most of of the the regions regions with with the the highest highest LAI LAI values values are located within it, except for some of the Shrub areas. are located within it, except for some of the Shrub areas. 3.3. 3.3. AGB AGB Regression Regression Models Models The AGB models models fitted fitted with withlnE(Yi) lnE(Yi)presented presentedlower lowerRMSEcv RMSEcvand and Rel. RMSE values and, The AGB Rel. RMSE values and, in in general, showed betterspatial spatialcorrespondence correspondencewith withland-cover land-coverclasses classes (Figure (Figure 1) 1) than than those general, showed better those estimated estimated with with E(Yi) E(Yi) models models (Table (Table5). 5).The Themodels modelsestimated estimatedusing usingsingle/dual-pol single/dual-pol SAR SAR data data did did not not 22 values, nor for map visual provide satisfactory results, neither in terms of RMSEcv, Rel. RMSE and R provide satisfactory results, neither in terms of RMSEcv, Rel. RMSE and R values, nor for map visual analysis. analysis. Thus, Thus, these these models models were were not not considered considered further. further. As can be observed in the graphic OBS vs. PRED in Figure 8, the absence of possible outliers in the estimated models did not positively impact their accuracy. Thus, the further analyses considered only the models calibrated with 18 samples of AGB. The models PL-FBD+RC218 and MULT18 presented satisfactory accuracy (i.e., the lowest RMSEcv, Rel. RMSE and highest R2). However, the last one displayed better results in the map visual analyses (Figure 8a). Therefore, considering multifrequency data, the best result was achieved by MULT18 (Figure 8a).
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Table 4. Generalized Linear Model (GLM) specifications and model evaluation for predicting Leaf Area Index from synthetic aperture radar data in floodplain forests Remote Sens.Amazon 2018, 10, x FOR PEER REVIEW 11 of 24 of the basin. Table 4. Generalized ModelLinear (GLM)Model specifications and model evaluation forevaluation predictingfor Leaf Area Index aperture radar data inradar floodplain Table 4. Linear Generalized (GLM) specifications and model predicting Leaffrom Areasynthetic Index from synthetic aperture data in floodplain forests of the forests Amazon of basin. the Amazon basin. TX Table 4. Generalized Linear Model (GLM) specifications and model evaluation for predicting Leaf Area TX TX Index from synthetic aperture radar data in floodplain forests of the Amazon basin. TXTX 18 18 TX16 TX18 TX16
TX16
Rel. Rel. AICc R² RMSEcv Fp-value 5% Bias Model AICc RMSEcv Fp-value Model AICc R² RMSEcv Fp-value 5% ARE R2ARE
Rel. GLM Bias RMSE
Model GLM Bias GLM RMSE RMSE TX16 0.36 0.78 ❶ sig 13.613.6❶ 17sig 17 0.002 lnE(Yi) ❷ intercept NA 0.61 NA NANA NA NA NANA 45.1 8.7E-03 0.36 0.78 13.6 17 0.002 lnE(Yi) ❷ intercept lnE(Yi) 45.1 0.36 45.10.78 8.7E-03 sig8.7E-03 0.002 lnE(Yi) intercept32.3 NA 0.6132.3 NA 32.3 NANANA0.61 Rel. Rel. GLM TX(HH-dB) E(Yi) Model AICc R² RMSEcv ARE Bias5.6E-03 GLM Model AICc R² intercept RMSEcv Fp-value 5% ARE E(Yi) 44.2 0.39Fp-value 5.6E-03 sig 13.0 17 0.000 E(Yi) intercept 32.3 NANANA0.61 TX(HH-dB) 44.20.76 0.395% 0.76 sig 13.0 0.000 E(Yi) intercept 32.3 NA 0.6132.3 NA Bias NA NANA NA NA NANA E(Yi) TX(HH-dB) 44.2 5.6E-03 0.39 sig 17 13.0 17 0.000 E(Yi) NA 0.61 RMSE0.76 RMSE
GLM
GLMModel GLM Model TX18 lnE(Yi) TX(HH-dB) TX(HH-dB) lnE(Yi) TX(HH-dB)
Rel. Rel. TX R² RMSEcv 5% AREARE 5% ARE Bias AICc RMSEcv Fp-value 5% Fp-value ModelR2 AICc AICcFp-value R² RMSEcv
lnE(Yi) TX(HH-dB)
RMSE RMSE
45.1 0.36
0.78
8.7E-03 ❶ sig 13.6
18 RC218 44.2 0.39 RC2 0.76 RC2 18 5.6E-03 sig
E(Yi) TX(HH-dB)
13.0
17
RC2 RC2RC2 0.002 lnE(Yi) ❷ intercept
32.3 NA
0.61
17
0.000 E(Yi) intercept
32.3 NA
16 0.61 RC2NA
NA
NA NA
NA
NA
NA RC2 NA 16
NA
NA
PL-FBD PL-FBDsig 18 46.2 0.43 0.8018 1.4E-02
PL-FBD18
PL-FBD
13.4
17
0.000 E(Yi) intercept
32.3 NA
16 0.61PL-FBD NA
PL-FBD NA NA 16 NA
NA
ARE
NA NA NA NA
NA NA
Bias
5%
NA
NA NA NA
Model GLM Model PL-FBD18 lnE(Yi) PL(HV-dB) lnE(Yi) PL(HV-dB)
E(Yi) PL(HV-dB) + PL(HV-HH)
Model
PL-FBD+TX PL-FBD+TX 35.9 0.69 0.63 18 1.9E-04 sig 18 9.2
14
PL-FBD+TX
-0.004 E(Yi) PL(HV-dB)
26.2 0.44
PL-FBD+TX 16 PL-FBD+TX 16 0.49 5.3E-03 sig 7.8 10
Bias NA NA
ARE NA NA
Rel. RMSE NA NA
Bias NA NA
PL-FBD16
Rel. Rel. Rel. Rel. PL-FBD AICc R² RMSEcv 5% Fp-value ARE Bias GLM Bias GLM Model AICc R² RMSEcv Fp-value 5% ARE Bias AICcFp-value R² RMSEcv 5% ARE Model AICc R² RMSEcv Fp-value 5% ARE Bias RMSE Rel. RMSE RMSE RMSE Bias PL-FBD GLM AICc RMSEcv Fp-value 5% ARE GLM Model AICc RMSEcv Fp-value 5% R2 R2 16 RMSE 38.7 0.55 0.61 sig 4.3E-04 10.3 13 0.002 lnE(Yi) PL(HV-dB) sig 7.9 38.7 4.3E-04 0.55 0.61 sig 10.3 13 0.002 lnE(Yi) PL(HV-dB) 26.8 0.42 0.4926.8 7.0E-03 0.42 0.49 7.0E-0310sig 0.001 7.9 10 0.001 Rel. Rel. lnE(Yi) PL(HV-dB) 38.7 0.55 0.61 4.3E-04 sig 10.3 13 0.002 lnE(Yi) PL(HV-dB) 26.8 0.42 0.49 7.0E-03 sig GLM Model AICc+ PL(HV-HH) R² RMSEcv Fp-value ARE Bias1.9E-04 GLM 14 Model AICc R² PL(HV-dB) RMSEcv Fp-value 5% ARE E(Yi) PL(HV-dB) + PL(HV-HH) 35.9 0.695% 0.63 sig 9.2 -0.004 E(Yi) PL(HV-dB) 26.2 0.44 0.4926.2 5.3E-03 sig 7.8 E(Yi) PL(HV-dB) 35.9 1.9E-04 0.69 sig 9.2 14 -0.004 E(Yi) 0.44 Bias 0.49 5.3E-0310sig 0.000 7.8 10 0.000 RMSE0.63 RMSE E(Yi) PL(HV-dB) + PL(HV-HH) 35.9 0.69 0.63 1.9E-04 sig 9.2 14 −0.004 E(Yi) PL(HV-dB) 26.2 0.44 0.49 5.3E-03 sig PL-FBD+TX PL-FBD+TX lnE(Yi) PL(HV-dB) 38.7 0.55 0.61 4.3E-04 sig 10.3 13 0.002 lnE(Yi) PL(HV-dB) 26.8 0.42 0.49 7.0E-03 sig 7.9 10 0.001 GLM
Rel. RMSE NA NA
RC216
Rel. Rel. Rel. Rel. RC2 Model 5% Fp-value ARE Bias GLM Bias GLM Model AICc R² RMSEcv Fp-value 5% 2ARE Bias GLM Model 2 AICc R² RMSEcv AICcFp-value R² RMSEcv 5% Rel. ARE Model AICc R² RMSEcv Fp-value 5% ARE GLM Model AICc RMSEcv Fp-value 5% ARE GLM Model AICc RMSEcv Fp-value Bias R R RMSE RMSE RMSE RMSE RMSE RC218 RC216 lnE(Yi) R2C(HH-dB) R2C(HV-HH)+ R2C(HV-HH)47.0 0.41 0.8147.0 2.0E-02 sig 2.0E-02 13.9 18 0.002 lnE(Yi) intercept NA 0.61 NA NANA NANA NA NA NA lnE(Yi)+R2C(HH-dB) 0.41 0.81 sig 13.9 18 0.002 lnE(Yi) intercept 32.3 NA 0.6132.3 NA lnE(Yi) R2C(HH-dB) + R2C(HV-HH) 47.0 0.41 0.81 2.0E-02Rel. sig 13.9 18 0.002 lnE(Yi) intercept 32.3 NA 0.61 NA Rel. GLM Model AICc +R²R2C(HV-HH) RMSEcv Fp-value 5% 0.80 ARE Bias1.4E-02 GLM 17 Model AICc R² intercept RMSEcv Fp-value 5% ARE E(Yi) R2C(HH-dB) + R2C(HV-HH) 46.2 0.43 1.4E-02 sig 13.4 0.000 E(Yi) intercept NA Bias NA NANA NA NA NANA E(Yi) R2C(HH-dB) 46.2 0.43 0.80 sig 13.4 17 E(Yi) NA 0.61 E(Yi) R2C(HH-dB) + R2C(HV-HH) 46.2 0.43 0.80 1.4E-02 13.4 17 0.000 0.000 E(Yi) intercept 32.3 NA 0.6132.3 32.3 NANANA0.61 RMSE sig RMSE PL-FBD PL-FBD lnE(Yi) R2C(HH-dB) + R2C(HV-HH) 47.0 0.41 0.81 2.0E-02 sig 13.9 18 0.002 lnE(Yi) intercept 32.3 NA 0.61 NA NA NA NA NA GLM
E(Yi) R2C(HH-dB) + R2C(HV-HH)
5% Bias
ARE 7.9 7.8
Rel. RMSE 10 10
Bias 0.001 0.000
0.000
PL-FBD+TX Rel. Rel. Rel. Rel. 16 GLM Model AICc R²PL-FBD+TX RMSEcv 5% Fp-value ARE Bias GLM Bias GLM Model AICc R² RMSEcv Fp-value 5% ARE Bias GLM Model AICcFp-value R² RMSEcv 5% ARE Model AICc R² RMSEcv Fp-value 5% ARE Bias RMSE Rel. RMSE RMSE RMSE PL-FBD+TX18 PL-FBD+TX16 2 2 lnE(Yi) PL(HV-dB) + TX(HH-dB) 36.2 0.69 0.56 2.2E-04 sig 8.9 12 -0.005 lnE(Yi) MSEq PL-FBD 16 26.8 0.42 0.49 7.0E-03 sig 7.9 10 0.001 lnE(Yi) PL(HV-dB) + TX(HH-dB) 36.2 0.69 0.56 2.2E-04 sig 8.9 12 -0.005 lnE(Yi) MSEq PL-FBD 16 26.8 0.42 0.49 7.0E-03 sig 7.9 10 0.001 GLM Model AICc RMSEcv Fp-value 5% ARE RMSE Bias GLM Model AICc RMSEcv Fp-value 5% R R Rel. Rel. GLM Model AICc+ TX(HH-dB) R² RMSEcv Fp-value ARE Bias1.5E-04 GLM 13 Model AICc R² 16MSEq RMSEcv Fp-value 5% ARE E(Yi) PL(HV-dB) + TX(HH-dB) 35.3 0.695% 0.59 sig 8.9 0.000 E(Yi) MSEq PL-FBD 26.2 0.4926.2 5.3E-03 sig 7.8 E(Yi) PL(HV-dB) 35.3 1.5E-04 0.69 sig 8.9 13 0.000 E(Yi) PL-FBD 16 0.44 0.44 Bias 0.49 5.3E-0310sig 0.000 7.8 10 0.000 RMSE0.59 RMSE lnE(Yi) PL(HV-dB) + TX(HH-dB) 36.2 0.69 0.56 2.2E-04 sig 8.9 PL-FBD+RC2 12 −0.005 lnE(Yi) MSEq PL-FBD16 26.8 0.42 0.49 7.0E-03 sig PL-FBD+RC2 lnE(Yi) PL(HV-dB) + TX(HH-dB) 36.2 0.69 0.56 2.2E-04 sig 8.9 12 -0.005 lnE(Yi) MSEq PL-FBD16 26.8 0.42 0.49 7.0E-03 sig 7.9 10 0.001 PL-FBD+TX18
E(Yi)
PL(HV-dB) + TX(HH-dB)
E(Yi) PL(HV-dB) + TX(HH-dB)
35.3
0.69
0.59
1.5E-04
PL-FBD+RC2 35.3 PL-FBD+RC2 0.69 0.59 181.5E-04 sig 18 8.9
13
sig
8.9
13
0.000
0.000 E(Yi) MSEq PL-FBD16
E(Yi)
26.2 0.44
MSEq PL-FBD16
26.2
PL-FBD+RC2 16 0.49 5.3E-0316PL-FBD+RC2 sig 7.8 10
0.44
0.000
0.49
5.3E-03
sig
Rel. PL-FBD+RC2 Rel. Rel. Rel. Model AICc R²PL-FBD+RC2 RMSEcv 5% Fp-value ARE Bias GLM Bias GLM Model AICc R² RMSEcv Fp-value 5% ARE Bias GLM Model AICcFp-value R² RMSEcv 5% ARE Model AICc R² RMSEcv Fp-value 5% ARE Bias RMSE RMSE RMSE RMSE PL-FBD+RC2 PL-FBD+RC2 18 16 PL-FBD+RC218 PL-FBD+RC216 lnE(Yi) ❸ MSEq PL-FBD 38.7 0.55 0.61 sig 4.3E-04 10.3 13 0.002 lnE(Yi) MSEq 26.8 0.4926.8 7.0E-03 sig 7.9 lnE(Yi) ❸ 18MSEq PL-FBD18 38.7 4.3E-04 0.55 0.61 sig 10.3 13 0.002PL-FBD lnE(Yi)16MSEq PL-FBD 16 0.42 0.42 0.49 7.0E-0310sig 0.001 7.9 10 0.001 Rel. Rel. Rel. Bias MSEq Model AICc RMSEcv Fp-value 5% ARE14 GLM Model AICc Bias RMSEcv Fp-value 5% Model AICc R² RMSEcv ARE Bias1.9E-04 GLM Model AICc R² 16MSEq RMSEcv Fp-value 5% ARE R2Fp-value R2 7.8 E(Yi) MSEq PL-FBD 35.9 0.695% 0.63 sig 9.2 -0.004 E(Yi) PL-FBD 26.2 0.4926.2 5.3E-03 sig 10sig 0.000 E(Yi) 18MSEq PL-FBD 18 35.9 1.9E-04 0.69 sigRMSE 9.2 14 -0.004 E(Yi) PL-FBD 16 0.44 0.44 0.49 5.3E-03 7.8 10 0.000 RMSE0.63 RMSE
ARE
Rel. RMSE
Bias
7.9 7.8
10 10
0.001 0.000
GLM
GLM GLM
lnE(Yi) MSEqPL-FBD PL-FBD lnE(Yi) ❸ MSEq 18 18 E(Yi) MSEqPL-FBD PL-FBD E(Yi) MSEq 18 18
38.7 0.610.554.3E-04 0.61sig 38.7 0.55
4.3E-0413 10.3
sig lnE(Yi) 10.3MSEq13 0.002 PL-FBD160.002
35.9 0.630.691.9E-04 0.63sig 35.9 0.69
1.9E-0414 9.2
sig E(Yi) 9.2 MSEq 14 -0.004 PL-FBD− 16 0.004
lnE(Yi) 26.8 0.42 MSEq 0.49 PL-FBD 7.0E-0316 sig 7.9 E(Yi) 26.2 0.44 MSEq 0.49 PL-FBD 5.3E-0316 sig 7.8
0.42 1026.8 0.001 0.44 1026.2 0.000
0.49 0.49
7.0E-03 5.3E-03
sig sig
ARE 7.9 7.8
Rel. RMSE 10 10
Bias 0.001 0.000
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Table 4. Generalized Linear Model (GLM) specifications and model evaluation for pred forests of the Amazon basin.
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TX TX18
Table 4. Cont. GLM
Model
Rel. RMSE
Bias
17
0.002
17
0.000
Rel. RMSE
Bias
13.9
18
0.002
13.4
17
0.000
ARE
Rel. RMSE
Bias
AICc R² RMSEcv Fp-value 5% ARE
TX+RC2
lnE(Yi) TX(HH-dB)
TX+RC218 GLM lnE(Yi) E(Yi)
Model MSEq TX18 MSEq to TX18
AICc
R2
45.1 44.2
0.36 0.39
RMSEcv Fp-value 0.78 0.76
8.7E-03 5.6E-03
5%
ARE
sig sig
13.6 13.0
Rel. RMSE 17 17
45.1 0.36
TX+RC216
Bias
E(Yi) TX(HH-dB) GLM Model
AICc
R2
0.002 0.000
lnE(Yi) E(Yi)
32.3 32.3
NA NA
intercept intercept
0.78
8.7E-03 ❶ sig 13.6
Rel. 44.2 0.395% 0.76 5.6E-03 sig RMSEcv Fp-value ARE Bias RMSE 0.61 0.61 RC2 18
NA NA
NA NA
NA NA
NA NA
NA NA
13.0 RC2
MULT
GLM
MULT18 GLM lnE(Yi) E(Yi)
Model MSEq PL-FBD+TX18 MSEq PL-FBD+TX18
AICc
R2
36.2 35.3
0.69 0.69
RMSEcv Fp-value 0.56 0.59
2.2E-04 1.5E-04
5%
ARE
sig sig
8.9 8.9
Rel. RMSE 12 13
Model
Bias
GLM Model + lnE(Yi) R2C(HH-dB)
AICc R2 R2C(HV-HH)
−0.005 0.000
lnE(Yi) PL-FBD16 + E(Yi)MSEq R2C(HH-dB) E(Yi) MSEq PL-FBD16
26.8 0.42 R2C(HV-HH) 26.2 0.44
RC2(POL)
lnE(Yi) E(Yi)
Model R2C(HV-dB) + R2C(VV-dB) + R2C(SPAN) + R2C(BMI) + R2C(HV-VV) + ΦαS2 + ψ2 R2C(HV-dB) + R2C(VV-dB) + R2C(SPAN) + R2C(BMI)+ R2C(HV-VV) + ΦαS2 + ψ2
AICc
R2
34.4
0.94
0.50
31.3
0.95
0.43
Rel. RMSEcv Fp-value ARE 2.0E-02 Bias 47.0 0.415% 0.81 sig RMSE 0.49 7.0E-03 sig 7.9 10 0.001 46.2 0.43 0.80 1.4E-02 sig 0.000 0.49 5.3E-03 sig 7.8 10
PL-FBD
PL-FBD18 RC2(POL) 16
RC2(POL)18 GLM
AICc R² RMSEcv Fp-value 5% ARE
MULT16
5%
ARE
Rel. RMSE
Bias
GLM GLM
Model
AICc Model
1.9E-05
sig
3.9
11
0.002
lnE(Yi) R2C(HV-VV) lnE(Yi) PL(HV-dB)
29.7
0.30
0.56
2.9E-02 38.7 0.55sig
12 0.000 0.618.0 4.3E-04 sig
10.3
13
0.002
8.2E-06
sig
3.7
9
0.000
E(Yi)R2C(HV-VV) PL(HV-dB) E(Yi)
+ PL(HV-HH) 30.0
0.29
0.57
35.9 0.69sig 3.2E-02
0.638.2 1.9E-04 sig 12 0.000
9.2
14
-0.004
ARE
Rel. RMSE
Bias
8.9
12
-0.005
8.9
13
0.000
Rel. RMSE
Bias
RMSEcv Fp-value
R2
Rel. RMSEcv Fp-value ARE Fp-value Bias AICc R² 5% RMSEcv 5% RMSE
PL-FBD+TX
PL-PLR
2018, x FOR PEER REVIEW PEER10, REVIEW
of1824 11 of 24 PL-FBD+TX PL-PLR11 16
PL-PLR18
Rel. Rel. Bias GLM Model AICc RMSEcv Fp-value 5% ARE Bias R2 RMSE RMSE GLM Model AICc R² RMSEcv Fp-value 5% lnE(Yi) PL(HV-dB) + PL(HV-HH) 49.0 0.34 0.85 4.6E-02 sig 12.6 19 0.000 lnE(Yi) PL(HV-dB) + PL(HV-HH) 24.2 0.60 0.41 2.5E-03 sig 5.7 8 0.000 Generalized Model (GLM) specifications and model predicting Leaffrom Area Index from synthetic aperture radar data 24.1 in floodplain Linear ModelLinear (GLM) specifications and model evaluation forevaluation predicting Leaf Area Index aperture radar data in floodplain E(Yi) PL(HV-dB) + PL(HV-HH) 49.0 0.34 0.87for 4.6E-02 sig 12.6 synthetic 19 0.000 E(Yi) PL(HV-dB) + PL(HV-HH) 0.61 0.41 2.4E-03 8 0.000 lnE(Yi) PL(HV-dB) + TX(HH-dB) 36.2 0.69sig 0.565.7 2.2E-04 sig GLM
Model
R2
AICc
RMSEcv Fp-value
5%
ARE
4. zed son ofbasin. the Amazon basin.
odel
PL-PLR(POL)
TX TX18 Model
GLM TX18
Model
E(Yi) PL(HV-dB) + TX(HH-dB)
PL-PLR(POL)18 R2
RMSEcv Fp-value
Rel.49.0 0.34 Rel. lnE(Yi) MSEq PL-PLR18 0.85 AICc R² RMSEcv 5% ARE AICc R² RMSEcv Fp-value 5% Fp-value ARE Bias GLM RMSE E(Yi) MSEq PL-PLR18 49.0 0.34 RMSE 0.87
0.59
1.5E-04
PL-PLR(POL)16
TX
AICc
35.3 0.69
5%
4.6E-02 sig Bias GLM Model 4.6E-02
sig
Rel. ARETXRMSE 16 12.6 12.6
Bias TX16GLM
Model
AICc
RMSEcv 18Fp-value R2 PL-FBD+RC2
sig
PL-FBD+RC2 5%
ARE
Rel. RMSE
Bias
Rel. 24.2 0.60Rel. 0.41 19 lnE(Yi) MSEq PL-PLR16 5.7 8 0.000 Model AICc R² RMSEcv Fp-valueModel 5% ARE Bias 2.5E-03 AICc R²0.000 RMSEcv Fp-value 5% ARE Bias GLM AICc R² sig RMSEcv Fp-value 5% ARE 0.000 RMSE0.41 19 0.000 E(Yi) MSEq PL-PLR18 RMSE 24.1 0.61 2.4E-03 sig 5.7 8
HH-dB)
45.1 0.36
0.36 0.78 ❶ sig = 13.6 17 ❷0.002 lnE(Yi) ❷ intercept 32.3 NA NANA NA NAequal. NA 0.7845.1 8.7E-03 ❶ sig 8.7E-03 13.6 17 sig 0.002 lnE(Yi) intercept 32.3 NA NA❸0.61 NA NA significant/ intercept = any model selected was 0.61 significant/ MSEq =Model selected lnE(Yi) MSEq PL-FBD 18
NA 38.7 0.55
0.61
4.3E-04
sig
10.3
13
0.002
HH-dB)
44.2 0.39
0.39 0.76 0.7644.2 5.6E-03 sig 5.6E-03 13.0 17sig
NA 35.9 0.69
0.63
1.9E-04
sig
9.2
14
-0.004
odel
Model
32.3 NA
NA 0.61 0.6132.3 NAMSEq NAPL-FBD NA NA18NANA NA E(Yi)
NA
RC2
RC2 RC218
13.0 17 intercept 0.000 E(Yi) intercept 0.000 E(Yi)
RC218
RC216
Rel. Rel. AICc R² RMSEcv 5% ARE AICc R² RMSEcv Fp-value 5% Fp-value ARE Bias GLM RMSE RMSE
RC216
Rel. Rel. Model AICc R² RMSEcv Fp-value 5% ARE AICc R² RMSEcv Fp-value 5% ARE Bias RMSE RMSE
Bias GLM Model
Bias
HH-dB) HV-HH)+ R2C(HV-HH)47.0 0.41
0.41 0.81 0.8147.0 2.0E-02 sig 2.0E-02 13.9 18sig
13.9 18 intercept 0.002 lnE(Yi) intercept 0.002 lnE(Yi)
32.3 NA
0.6132.3 NA NA
0.61 NA NA NANANA NA
NA
NA
HH-dB) HV-HH)+ R2C(HV-HH)46.2 0.43
0.43 0.80 0.8046.2 1.4E-02 sig 1.4E-02 13.4 17sig
13.4 17 intercept 0.000 E(Yi) intercept 0.000 E(Yi)
32.3 NA
0.6132.3 NA NA
0.61 NA NA NANANA NA
NA
NA
PL-FBD
PL-FBD PL-FBD18
PL-FBD18
PL-FBD16 Rel.
Rel.
PL-FBD16 Rel.
Rel.
Remote Sens. 2018, 10, 1355 Remote Sens. 2018, 10, x FOR PEER REVIEW
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Figure 7. Comparison of predicted and observed values of LAI and spatial prediction for the models:
Figure 7. Comparison of predicted and observed values of LAI and spatial prediction for the models: (a) PL-FBD+TX 18; (b) PL-FBD18. The yellow arrow indicates some high-density shrubby areas. Central (a) PL-FBD+TX 18 ; (b) PL-FBD Amazon Floodplain, Brazil.18 . The yellow arrow indicates some high-density shrubby areas. Central Amazon Floodplain, Brazil. The RMSEcv, Rel. RMSE and R2 values were similar, with a low bias for the models calibrated from full-polarimetric data (i.e., RC2(POL) and PL-PLR(POL) ); their8,output maps are in the in As can be observed in the graphic18 OBS vs. PRED in 18Figure the absence of displayed possible outliers Figure 8b,c, respectively. The best AGB map was estimated from PL-PLR(POL)18 model (Figure 8c). the estimated models did not positively impact their accuracy. Thus, the further analyses considered This map, unlike other AGB maps, shows the highest AGB value within the Flooded Forest class and only the models calibrated with 18 samples of AGB. in some high-density shrub areas (indicated by a yellow arrow in this Figure). This also allows us to The models PL-FBD+RC218 and MULT18 presented satisfactory accuracy (i.e., the lowest RMSEcv, discriminate the Flooded Forest class from the Non-forested class. Furthermore, most of the regions Rel. with RMSE and highest R2 ). (around However, onelocated displayed results in the map visualForest analyses −1) are highest AGB values 600the t/halast in thebetter interior regions of the Flooded (Figure 8a). Therefore, considering multifrequency data, the best result was achieved by MULT class, which agrees with the AGB spatial distribution patterning observed during field work. This 18 (Figure 8a).also presented the best accuracy, resulting in the lowest average relative error (46.4%). model The RMSEcv, Rel. RMSEthat andthe R2 best values similar, with a low Therefore, we can conclude AGBwere model is PL-PLR(POL) 18. bias for the models calibrated
from full-polarimetric data (i.e., RC2(POL)18 and PL-PLR(POL)18 ); their output maps are displayed in the Figure 8b,c, respectively. The best AGB map was estimated from PL-PLR(POL)18 model (Figure 8c). This map, unlike other AGB maps, shows the highest AGB value within the Flooded Forest class and in some high-density shrub areas (indicated by a yellow arrow in this Figure). This also allows us to discriminate the Flooded Forest class from the Non-forested class. Furthermore, most of the regions with highest AGB values (around 600 t/ha−1 ) are located in the interior regions of the Flooded Forest class, which agrees with the AGB spatial distribution patterning observed during field work. This model also presented the best accuracy, resulting in the lowest average relative error (46.4%). Therefore, we can conclude that the best AGB model is PL-PLR(POL)18 .
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Table 5. GLM model specifications and model evaluation for predicting aboveground biomass from synthetic aperture radar data in floodplain forests of the Amazon basin. TX TX18 GLM lnE(Yi) E(Yi)
Model TX(HH-dB) TX(HH-dB)
TX16
AICc
R2
RMSEcv
Fp-value
5%
ARE
232.8 235.0
0.34 0.25
149.56 150.04
1.2E-02 3.5E-02
sig sig
66.8 79.8
Rel. RMSE 92 92
Bias (t.ha) −4.1 0.0
GLM lnE(Yi) E(Yi)
Model TX(HH-dB) intercept
AICc
R2
RMSEcv
Fp-value
5%
ARE
175.4 177.0
0.24 NA
51.49 55.85
4.6E-02 NA
sig NA
49.5 NA
AICc
R2
RMSEcv
Fp-value
5%
ARE
177.0 177.0
NA NA
55.85 55.85
NA NA
NA NA
NA NA
AICc
R2
RMSEcv
Fp-value
5%
ARE
177.0 177.0
NA NA
55.85 55.85
NA NA
NA NA
NA NA
Rel. RMSE 46.2 NA
Bias (t.ha) −0.2 NA
Rel. RMSE NA NA
Bias (t.ha) NA NA
Rel. RMSE NA NA
Bias (t.ha) NA NA
Rel. RMSE 46.2 NA
Bias (t.ha) −0.2 NA
RC2 RC218
RC216
GLM
Model
AICc
R2
lnE(Yi) E(Yi)
R2C(HH-dB) + RC2(HV/HH) + R2C(HV-HH) RC2(HV/HH)
222.1 235.5
0.82 0.23
RMSEcv
Fp-value
5%
ARE
107.90 159.43
1.5E-04 4.5E-02
sig sig
48.9 91.3
Rel. RMSE 66 98
Bias (t.ha) −30.3 0.0
GLM lnE(Yi) E(Yi)
Model intercept intercept
PL-FBD PL-FBD18 GLM lnE(Yi) E(Yi)
Model intercept intercept
PL-FBD16
AICc
R2
RMSEcv
Fp-value
5%
ARE
237.2 237.2
NA NA
163.22 163.22
NA NA
NA NA
NA NA
Rel. RMSE NA NA
Bias (t.ha) NA NA
GLM lnE(Yi) E(Yi)
Model intercept intercept
PL-FBD+TX PL-FBD+TX18 GLM lnE(Yi) E(Yi)
Model MSEq TX18 MSEq TX18
PL-FBD+TX16
AICc
R2
RMSEcv
Fp-value
5%
ARE
232.8 235.0
0.34 0.25
149.56 150.04
1.2E-02 3.5E-02
sig sig
66.8 79.8
Rel. RMSE 92 92
Bias (t.ha) −4.1 0.0
GLM lnE(Yi) E(Yi)
Model MSEq TX16 intercept
AICc
R2
RMSEcv
Fp-value
5%
ARE
175.4 177.0
0.24 NA
51.49 55.85
4.6E-02 NA
sig NA
49.5 NA
PL-FBD+RC2 PL-FBD+RC218 GLM lnE(Yi) E(Yi)
Model PL(HV/HH) + R2C(HH-dB) + R2C(HV/HH) + R2C(HV-HH) PL(HV/HH) + R2C(HV-dB)
PL-FBD+RC216
AICc
R2
RMSEcv
Fp-value
5%
ARE
Rel. RMSE
Bias (t.ha)
GLM
218.9
0.86
107.95
4.0E-05
sig
37.7
66
50.3
lnE(Yi)
233.6
0.44
142.10
1.6E-02
sig
70.7
87
2.2
E(Yi)
AICc
R2
RMSEcv
Fp-value
5%
ARE
Rel. RMSE
Bias (t.ha)
intercept
177.0
NA
55.85
NA
NA
NA
NA
NA
intercept
177.0
NA
55.85
NA
NA
NA
NA
NA
Model
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Table 5. Cont. TX+RC2 TX+RC218 GLM lnE(Yi) E(Yi)
Model MSEq RC218 MSEq TX18
TX+RC216
AICc
R2
RMSEcv
Fp-value
5%
ARE
222.1 235.0
0.82 0.25
107.90 150.04
1.5E-04 3.5E-02
sig sig
48.9 79.8
Rel. RMSE 66 92
Bias (t.ha) −30.3 0.0
GLM lnE(Yi) E(Yi)
Model MSEq TX16 intercept
AICc
R2
RMSEcv
Fp-value
5%
ARE
175.4 177.0
0.26 NA
51.49 55.85
4.6E-02 NA
sig NA
49.5 NA
AICc
R2
RMSEcv
Fp-value
5%
ARE
175.4 177.0
0.26 NA
51.49 55.85
4.6E-02 NA
sig NA
49.5 NA
Rel. RMSE 46.2 NA
Bias (t.ha) −0.2 NA
Rel. RMSE 46.2 NA
Bias (t.ha) −0.2 NA
Bias (t.ha) 0.1
MULT MULT18 GLM lnE(Yi) E(Yi)
Model PL(HV/HH) + RC2(HV/HH) + TX(HH-dB) PL(HV/HH) + RC2(HV-HH) + TX(HH-dB)
MULT16
AICc
R2
RMSEcv
Fp-value
5%
ARE
211.0 232.8
0.88 0.57
107.32 130.47
2.1E-06 1.4E-02
sig sig
35.1 71.1
Rel. RMSE 66 80
Bias (t.ha) −11.4 1.4
GLM lnE(Yi) E(Yi)
Model MSEq TX16 intercept
RC2(POL) RC2(POL)18
RC2(POL)16
GLM
Model
AICc
R2
lnE(Yi)
RC2(HV/HH) + τ2 RC2(VV-dB) +RC2(HV/HH) + RC2(HV-dB) + RC2(HV/VV) + VZS +τ2 + αSm
210.3
0.85
74.60
9.8E-07
sig
51.9
Rel. RMSE 46
226.4
0.88
83.77
4.9E-05
sig
43.9
52
E(Yi)
RMSEcv
Fp-value
5%
ARE
Bias (t.ha) −8.2
lnE(Yi)
−2.5
E(Yi)
GLM
Model
AICc
R2
RMSEcv
Fp-value
5%
ARE
YD + αS2 + ΦαS1 + τm
173.4
0.71
40.50
5.1E-03
sig
28.4
Rel. RMSE 36.4
αS2 + ΦαS1 + τm
172.6
0.62
42.18
7.4E-03
sig
33.0
37.9
0.0
AICc
R2
RMSEcv
Fp-value
5%
ARE
177.0 177.0
NA NA
55.85 55.85
NA NA
NA NA
NA NA
Rel. RMSE NA NA
Bias (t.ha) NA NA
Rel. RMSE 50.0 42.7
Bias (t.ha) -0.3 0.0
PL-PLR PL-PLR18 GLM lnE(Yi) E(Yi)
Model intercept intercept
PL-PLR16
AICc
R2
RMSEcv
Fp-value
5%
237.2 237.2
NA NA
163.22 163.22
NA NA
NA NA
ARE
Rel. RMSE NA NA
Bias (t.ha) NA NA
GLM lnE(Yi) E(Yi)
Model intercept intercept
PL-PLR(POL) PL-PLR(POL)18 GLM lnE(Yi) E(Yi)
Model VZD + ΦαS1 + ΦαS2 VZD + ΦαS1 + ΦαS2
PL-PLR(POL)16
AICc
R2
RMSEcv
Fp-value
5%
ARE
208.9 224.8
0.88 0.72
74.59 109.92
9.2E-07 4.1E-04
sig sig
46.4 75.5
Rel. RMSE 46 68
Bias (t.ha) −4.9 0.0
GLM lnE(Yi) E(Yi)
Model VZD + ΦαS1 + ψ2 VZD +ΦαS2 + ψ2
AICc
R2
RMSEcv
Fp-value
5%
ARE
176.6 175.5
0.51 0.54
55.66 47.53
3.1E-02 2.1E-02
sig sig
36.9 36.5
Remote RemoteSens. Sens.2018, 2018,10, 10,1355 x FOR PEER REVIEW
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Figure 8. Comparison of predicted and observed values of AGB and spatial prediction for the models: Figure 8. Comparison of predicted and observed values of AGB and spatial prediction for the models: (a) MULT18, (b) RC2(POL)18, and (c) PL-PLR(POL)18. The yellow arrow indicates some high-density (a) MULT18 , (b) RC2(POL)18 , and (c) PL-PLR(POL)18 . The yellow arrow indicates some high-density shrub areas. Central Amazon floodplain, Brazil. shrub areas. Central Amazon floodplain, Brazil.
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4. Discussion The RMSEcv, Rel. RMSE and relative error were comparatively low (0.65, 13% and 10.3%, respectively) for the LAI model adjusted with only one predictor, HV-dB. Thus, the model had satisfactory accuracy. These results indicate the importance of cross-polarized data in providing information about the structural complexity of vegetation canopy by means of volumetric scattering in wetland environments [74]. As the results (i.e., map visual analyses and statistic indexes) from model PL-PLR18 were less accurate than those provided by PL-FBD18 , we inferred that the hydrological seasonality of the region might impact the accuracy of the models and the estimated maps. Considering the AGB range analyzed in this work and the structural complexity of floodable forests, we can state that the selected model for AGB provided good results, with comparatively low RMSEcv (74.59 t/ha), Relative RMSEcv and average relative error (both around 46%). The predictors composed of the polarimetric models were coherent, that is, phase dependent. One of them is VZD , which provides information about the proportion of double-bounce scattering generated by Van Zyl decomposition [60]. The others two selected parameters are ΦαS1 and ΦαS2 , extracted by the Touzi decomposition [58]. These predictors provide information about the first and the second dominant phase difference between trihedral and dihedral scattering, respectively. Some works, such as Martins, et al. [75], identified that the proportion of double-bounce scattering is an important feature for estimating the AGB in the Amazon forest. A possible explanation is that this kind of scattering mechanism may be enhanced due to the clear floor of floodable forests and the reduced understory layer [74,76]. However, this may be detected only by L or longer SAR band systems [77]. In relation to the predictors ΦαS1 and ΦαS2 , some researchers, such as Li, et al. [78], Sartori, Imai, Mura, Novo and Silva [12], Storie, et al. [79] and Touzi [58], reported that ΦαS1 improves the classification accuracy and thus the discrimination between some wetland vegetation types, such as macrophyte, open bog and small shrubs. This predictor has also been reported as sensitive to the water under vegetation [80]. The analyses related to AGB, presented above, lead us to conclude that L-band full-polarimetric data is an important predictor of AGB in both Amazonian flooded forests and dense forest regions characterized by high AGB values; thus, it has the potential to overcome the current limitations of orbital SAR data in mapping AGB with reliable accuracy in dense forest regions [5]. Furthermore, vegetation structural parameters such as canopy height and crown diameter are important for the development of ecological studies related to dynamic and spatial characterization of vegetation [81], which can also be used indirectly for estimating AGB (i.e., as data input in the allometric equations) [82] or can be integrated with other methodologies such as presented in [83]. Since the SAR signal is sensitive to form and structure of targets—rather than tree species and wood density, which are important parameters for estimating ground AGB [84]—we expect that the L-band polarimetric will presented the same or even more potential to estimate and map vegetation structural parameters such as canopy height and crown diameter. Therefore, we encourage the development of studies with this aim and highlight that the routine presented in this work can assist in their development. These results endorse and reinforce the potential of the forthcoming SAR missions at L-band, such as TanDEM-L [85]. Although data policy will restrict public access to the data, TanDEM-L is expected to overcome the current SAR data limitation in both mapping and monitoring AGB on a global scale with satisfactory accuracy and spatial resolution [86]. This potential is amplified with Airborne Light Detection and Ranging (LiDAR) data, which can be used to calibrate and validate SAR-adjusted models through the upscale approach, reducing the dependency of field inventory data. This is especially true in regions with difficult access, such as several environments found in the Amazon forest biome. Furthermore, information such as crown diameter, canopy height and number of individuals (trees) can be extracted directly from this source of data and can potentially be used as input in the allometric equations and, indirectly, to improve AGB estimation [82]. Thus, the data generated by future missions such as Global Ecosystems Dynamics
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Investigation Lidar (GEDI) [87] can extend the applicability of the methodology presented in this work to other forest environments worldwide. In addition, we stress that the quad-polarimetric SAR images with larger wavelengths, such as P-band and S-band, provide results quite similar or even better than those achieved in this work [88]. This is especially true given that the SAR signal can penetrate deeper in the dense multi-layer of the tropical forests. Thus, missions such as BIOMASS, which will generate P-band SAR images [88], and NISAR, which will generate quad-polarimetric images in L-band and S-band frequencies, hold promise for mapping and monitoring AGB with relatively high accuracy on a global scale [89–92]. 5. Conclusions Our results show that the model approach lnE(Yi) generally presented better results than E(Yi), especially in the visual analyses of the AGB and LAI maps. Furthermore, the models selected for both AGB and LAI were parsimonious, and their output maps matched with the classes and empirical knowledge about the study area. For both LAI and AGB retrievals, the best results were achieved using the features extracted from ALOS-PALSAR-1 scenes. This result indicates that, for the estimation and mapping both LAI and AGB parameter in a Floodable Forest environment, single-frequency polarimetric L-band images are more efficient than multifrequency dual-pol or single-pol SAR. For the estimation of LAI, the cross-polarization data (HV-dB) was sufficient. For AGB, however, the features extracted from polarimetric decompositions seems to be essential. Thus, for mapping LAI, dual-pol SAR images performed best, as they have operational advantages when compared with quad-polarimetric SAR. For AGB mapping procedures, the full-polarimetric data is preferable. These results reinforce the potential of this kind of data in mapping AGB in Floodable Forest environments. We also believe that this result can be extended to other dense forest environments worldwide. Considering the wide range of AGB values contemplated in this work, we strongly believe that the results achieved by the best AGB model were satisfactory and that the methodology presented is suitable for estimating this parameter. We believe this can be extended to vegetation structure parameters such as canopy height and crown diameter. However, to confirm these findings, more tests must be performed in other regions and environments, with more samples of AGB if possible. To better understand the potential and limitations of this routine, we encourage the development of future works with other modeling methods such as random forest and genetic algorithms. Finally, the authors believe that the results and the feature selection process presented in this research may provide important information for the scientific community regarding the applicability of L-band quad-polarimetric SAR images. This is related to the estimation of AGB and its potential to overcome the current limitation in the context of wetlands and densely tropical forests environments. In this sense, we expect to collaborate on the construction of a background for analysis and assessment of current (PALSAR-1 and -2) and future missions (NISAR, GEDI, BIOMASS, Tandem-L), which we believe have enormous potential for mapping of AGB with high accuracy on a global scale in the near future. Such information can provide essential information for future generations to better understand the dynamics of our planet in the face of modern issues such as climate change and anthropogenic land-cover change. Supplementary Materials: The following are available online at http://www.mdpi.com/2072-4292/10/9/1355/s1. Author Contributions: L.O.P., L.F.A.F., T.S.F.S. and E.M.L.M.N. conceived the study questions and sampling design. L.O.P. and L.F.A.F. were responsible for image processing. L.P.O., T.S.F.S., S.J.S.S. and V.L. implemented, validated and interpreted models and results. L.O.P. led the writing of the manuscript with significant inputs from all authors. Funding: This research was funded by Graduate Program in Remote Sensing of the National Institute for Space Research (INPE), São Paulo Research Foundation (FAPESP) [#2011/23594-8] and Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) [454779/2015-1]. Acknowledgments: L.O. Pereira thanks INPE and CNPq for the granted PCI-DC fellowship (Grant #301118/2017-5) and University of Exeter for the PhD‘s degree fellowship. L.F.A. Furtado thanks INPE and CNPq for the granted PCI-DC fellowship, and CAPES for the master’s degree fellowship. Field data collection
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was funded by the Graduate Program in Remote Sensing of the National Institute for Space Research (INPE) and by grant #2011/23594-8, São Paulo Research Foundation (FAPESP). During the development of this work, TSF Silva received postdoctoral support from grant #2010/11269-2, São Paulo Research Foundation (FAPESP), grant #458038/2013-0 CNPq, and currently receives a CNPq Productivity Grant (#310144/2015-9). We thank the Canadian Space Agency (CSA) for the Radarsat-2 images granted to TSF Silva by the Science and Operational Applications Research (SOAR) program, project number 5052. Radarsat-2 data and products are licensed by MacDonald, Dettwiler and Associates, Ltd. This work has been undertaken within the framework of JAXA’s Kyoto & Carbon Initiative, with ALOS PALSAR data provided by JAXA EORC. VL is supported by FAPESC 1703/2017. Conflicts of Interest: The authors declare no conflict of interest. The funding sponsors had no role in the design of the study; in the collection, analysis, or interpretation of data; in the writing of the manuscript, and in the decision to publish the results.
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