Biomass prediction in tropical forests : the canopy grain approach

radar-based studies can provide new insights on this problem


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The challenging task of biomass prediction in dense and heterogeneous tropical forest 11 requires a multi-parameter and multi-scale characterization of forest canopies. Completely 12 different forest structures may indeed present similar above ground biomass (AGB) values. 13 This is probably one of the reasons explaining why tropical AGB still resists accurate 14 mapping through remote sensing techniques. There is a clear need to combine optical and 15 radar remote sensing to benefit from their complementary responses to forest 16 characteristics. Radar and Lidar signals are rightly considered to provide adequate 17 measurements of forest structure because of their capability of penetrating and interacting 18 with all the vegetation strata. 19 However, signal saturation at the lowest radar frequencies is observed at the midlevel of 20 biomass range in tropical forests (Mougin et al. 1999;Imhoff, 1995). Polarimetric 21 Interferometric (PolInsar) data could improve the inversion algorithm by injecting forest 22 interferometric height into the inversion of P-band HV polarization signal. Within this 23 framework, the TROPISAR mission, supported by the Centre National d'Etudes Spatiales 24 (CNES) for the preparation of the European Space Agency (ESA) BIOMASS program is 25 illustrative of both the importance of interdisciplinary research associating forest ecologists 26 and physicists and the importance of combined measurements of forest properties. 27 Lidar data is a useful technique to characterize the vertical profile of the vegetation cover 28 (e.g. Zhao et al. 2009) which in combination with radar (Englhart et al. 2011) or optical (e.g. 29 Baccini et al. 2008; Asner et al. 2011) and field plot data may allow vegetation carbon stocks 30 to be mapped over large areas of tropical forest at different resolution scales ranging from 1 31 hectare to 1 km². However, small-footprint Lidar data are not yet accessible over sufficient 32 extents and with sufficient revisiting time because its operational use for tropical studies 33 remains expensive. 34 At the opposite, very-high (VHR) resolution imagery, i.e. approximately 1-m resolution, 35 provided by recent satellite like Geoeye, Ikonos, Orbview or Quickbird as well as the 36 forthcoming Pleiades becomes widely available at affordable costs, or even for free in certain 37 regions of the world through Google Earth®. Compared to coarser resolution imagery with 38 pixel size greater than 4 meters, VHR imagery greatly improves thematic information on forest 1 canopies. Indeed, the contrast between sunlit and shadowed trees crowns as visible on such 2 images (Fig. 1) is potentially informative on the structure of the forest canopy while new 3 promising methods now exist for analyzing these fine scale satellite observations (e.g. 4 Bruniquel Besides, we believe that there is also a great potential in similarly using historical series of 6 digitized aerial photographs that proved to be useful in the past for mapping large extents of 7 unexplored forest (Le Touzey, 1968; Richards, 1996) for quantifying AGB changes through time. 8 This book chapter presents the advancement of a research program undertaken by our team 9 for estimating high biomass mangrove and terra firme forests of Amazonia using canopy 10 grain from VHR images (Couteron et as soon as the contrast between sunlit and shadowed tree crowns becomes perceptible. This 1 property increases with the fineness of image spatial resolution ( Fig. 1) that explains why, in 2 VHR images, the tropical forest no longer appears as a continuous homogenous layer, or 3 'red carpet', as it is the case on medium resolution images with pixel size greater than 5 4 meters (Fig. 1). Intuitively, the canopy grain depends on both the spatial distribution of trees 5 within a scene and the shapes and dimensions of their crowns. The question is then how to 6 derive quantitative measurements of such canopy grain texture. Following Rao and Lohse 7 (1993), who explained that repetitiveness is the most important dimension of human 8 perception for structural textures, our idea is to measure the degree of repetitiveness 9 expressed in canopy grain within a forest scene. Two dimensional (2D) Fourier or wavelet 10 transforms proved to be well adapted for this purpose (e.g. Couteron, 2002;Ouma et al., 11 2006) because they allow shifting canopy grain properties from the spatial domain to the 12 frequency domain. Though of potential larger application, we focus in this paper on the 2D 13 Fourier-based frequency spectra as a mean for relating tropical forest canopy grain to above-14 ground biomass (AGB A prerequisite of the method is to mask non-forest areas, such as clouds and their shadows, 25 water bodies, savannas, crops and civil infrastructures areas (Fig. 2, step 1). The method 26 then proceeds with the specification of a square window size in which 2D-Fourier spectra 27 are computed (Fig. 2, step 2). To be clear, the window size WS is expressed in meters as: 28 where N is the number of pixels in the X or Y direction of the image and S is the pixel size 30 in meters. WS may influence the FOTO results as discussed in the following sub-section. 31 Using large WS also means that spatial resolution of the FOTO outputs and subsequent 32 biomass maps will be N times coarser than the spatial resolution of the source image(s). 33 Although the use of a sliding window is computationally intensive, it can attenuate the 34 effects of both spatial resolution degradation and study areas fringe erosion. 35 After windowing the forest images, Fourier radial spectra (or r-spectra) are computed and 36 give for each window, the frequency vs. amplitude of a sinusoidal signal that fits the spatial 37 arrangement of pixels grey levels (Fig. 2, step 3) as described in the next paragraph. The r-38 spectra may be then stacked into a common matrix in which each row corresponds to the r-39 spectrum of a given window, whereas each column contains amplitude values. This table is  40 then submitted to multivariate analysis techniques (ordinations/classifications). With this 41 approach, the study can concern as many images as necessary, providing they have the 42 same spatial resolution.

2-D FFT spectrum
Average over all directions Average over all directions axes are used as texture indices (the so-called FOTO indices) that are mapped by composing 1 red-green-blue (RGB) images expressing window scores values against first, second and 2 third axes, respectively. Such FOTO maps have a spatial resolution equal to the window size 3 WS. The final step (Fig. 2, step 5) is to relate ground truth forest plot biomass to FOTO 4 indices using a linear model of the form: where a 0 and a c are the coefficients of the multiple regression of AGB onto the texture indices 7 T obtained from the first three PCA axes. 8

Computing radial spectra of forest plots 9
The computation of radial spectra has to be detailed because such frequency signatures are 10 essential components of the canopy grain analysis. It is to note that the calculation of r-11 spectra is also possible for any single image extract centered on one forest plot as illustrated 12 in the numerous examples provided hereafter. 13 Each image extract is subjected to the two dimensional discrete fast Fourier transform 14 algorithm implemented in most of the technical computing software. Image intensity 15 expressed in spatial XY Cartesian referential domain is transposed to the frequency domain. 16 Power spectrum decomposing the image variance into frequency bins along the two Cartesian 17 axes is then obtained for each square window (

Principal component analysis for regional analysis 26
Standardized principal component analysis of the spectra table created by the stacking of all  27 r-spectra is a mean to perform regional analysis of canopy grain variations through one or 28 several image scenes. For illustration, a 0.5-m panchromatic Geoeye image covering (after 29 masking non-forest areas) 11271 hectares of mangroves is analyzed (Fig. 3). The three first 30 factorial axes of the PCA accounted for more than 81% of the total variability. The first PCA 31 axis opposes coarse and fine canopy grain that correspond to spatial frequencies of less than 32 100 cycles/km (=10 m) and more than 250 cycles/km (=4 m), respectively. Intermediate 33 spatial frequencies are found with high negative loadings on the second axis. 34 From this analysis, we coded window scores on the three main PCA axes as RGB real values 35 (Fig. 4). Pioneer and young stages of mangroves are characterized by red-i.e. high scores on 36 PC1 only-whereas intergrades between blue and cyan corresponded to areas with adult 37 trees (low positive scores on PC1 and negative scores on PC2). Green color maps mature and 38 decaying stages of mangrove with high PC2 and very low PC1 scores. Hence, 39 coarseness/fineness gradients of thousands of unexplored hectares of mangrove can be 40 mapped and allow to capture, at a glance, the overall spatial organization presented in the 41 image. An equivalent result was also obtained using a 1-m panchromatic Ikonos image 1 (Proisy et al. 2007). The FOTO analysis is confirmed of prime interest for mangrove 2 monitoring studies and for highlighting coastal processes in French Guiana (Fromard et al. 3 2004) through the mapping of forest growth stages. 4

The DART modelling method 5
Large-scale validation of the FOTO method is highly desirable, to study both the method's 6 sensitivity to complex variations in forest structure and to instrumental perturbations. 7 However, it is notoriously difficult to obtain both detailed forest structure information in 8 inaccessible tropical environments and cloudless imagery over field plots. It was therefore 9 necessary to develop a modeling framework for testing FOTO sensitivity, in simplified but 10 controlled conditions (Barbier et al. 2010;in press DBH distribution, established DBH-Crown-height allometric relationships, and an iterative 10 hard-core point process generator, to reproduce 'lollipop stands', that is a 3D arrangement 11 of trunk cylinders bearing ellipsoid crowns. This forest template matches the DART maket 12 requirements, e.g. a list of trees with parameters of their 3D geometry. Such simulation 13 framework is particularly well adapted to the study of mangroves forest in which few 14 species grow rapidly over areas with no relief (Fig. 5

Virtual canopy images 1
In this work, we only simulated mono-spectral images in the visible domain on flat 2 topography without taking into account atmospheric effects (Fig. 5). Standard optical 3 profiles of reflectance for soil, trunks and leaves are selected from the DART database using, 4 for instance, '2D soil-vegetation', '2D bark_spruce' and '3D leaf_decidous' files. Such 5 oversimplified images of virtual forest stands composed of trees with 'lollipop-shaped' 6 crowns produce homogeneous texture dominated by few frequencies. The FOTO analysis of 7 330 DART images however demonstrated their potential for benchmarking textural gradient 8 of real forest canopies throughout the Amazon basin (cf. Fig. 3 The loss of sensitivity to the finest textures was also observed using 2-m NIR channel of 1 Geoeye image (Fig. 6). Whereas r-spectra of 0.5-m and 2-m image extracts displayed the 2 same behaviour with an identical dominant frequency, they did not exhibit the same 3 profiles for the pioneer stage consisting of a very high density of trees with 2-3 m crown 4 diameters. This limitation was also observed for the same forest growth stages after 5 comparison of 1-m and 4-m Ikonos channels (see Fig. 4 in Proisy et al. 2007). As the 6 limitation with regard to the youngest stages appeared using 2-m channels, it was 7 recommended to privilege the use of panchromatic satellite images with metric and sub-8 metric pixels. 9

Sun and viewing angles: the BTF 10
Parameters of VHR image acquisitions such as sun elevation angle θ s , viewing angle from 11 nadir θ v and azimuth angle Φ s-v between sun and camera can vary significantly as illustrated 12 in Fig. 7. We introduced the bidirectional texture function (BTF; Barbier et al. 2011) diagrams 13 to map the influence of different acquisitions conditions in terms of texture perception (Fig.  14  8). The finest textures are perceived in the sun-backward configuration whereas the coarsest 15 are observed when sun is facing the camera (the forward configuration) due to the loss of 16 perception in shadowed areas. These findings show that to ensure a coherent comparison 17 between scenes, one must either use images with similar acquisition conditions, or use a BTF 18 trained on similar forest areas or derived from a sufficiently realistic physical simulations to 19 allow minimizing these effects (Barbier et al. 2011  The canopy grain approach must be calibrated at the forest plot scale i.e. by conducting 8

From canopy grain to AGB
forest inventories from which above ground biomass will be estimated. Areas of about 9 one hectare are necessary to take into account structural diversity within the for est plot. 10 This area of inventory can possibly be reduced for simpler forest stands and plantations, 11 but this is basically dependent on the size of the canopy trees since the computation of 12 FOTO indices should be meaningful at plot scale (Couteron et al. 2005 Additionally, for a given species varying tree heights and crowns dimensions may yield 1 important mass differences that the parsimonious relationships cannot take into account. 2 Selecting an appropriate allometric model is then crucial and the sampling uncertainty 3 relative to the size of the study plot should also be addressed carefully (e.g. Chave et al. 4 2004). 5 Tree location, crown shape, tree height and wood specific gravity also constitute useful 6 information that will contribute to the characterization of the forest structure typology. 7 Although it remains unrealistic in heterogeneous forests without the help of skilled 8 botanists, identification of tree species is advisable in low-diversified situations, since the 9 inclusion of a specific wood gravity parameter into allometric equations proved to improve 10 significantly the model (Chave et al. 2005). Such additional data will also be valuable for 11 initializing 3D forest templates. It is important to note that, in tropical forest, tree height 12 measurements from the ground are problematic and cumbersome explaining the 13 enthusiasm aroused by Lidar data (e.g. Gillespie et al. 2004). Another important point to 14 improve AGB prediction would be to conduct forest inventories simultaneously to image 15 acquisitions. 16

Sensitivity to forest structure and AGB 17
Assuming that the constituted forest plots dataset is well distributed within the acquired 18 scene(s), Fourier r-spectra can be computed for windows centred on each plot. For 19 example, when applied to 1-m Ikonos (Proisy et al. 2007) or 0.5-m Geoeye panchromatic 20 images (Fig. 9) r-spectra permit good discrimination of a wide array of canopy structures 21 of mangroves (Fig. 9). Furthermore pre-adult, mature and decaying mangrove forests 22 show contrasted signatures with dominant frequencies around 180, 80, 50 and 30 cycles 23 per kilometre. 24 Inverting FOTO indices (the three first PCA axes) into AGB of forest plots distributed 25 over two different sites (i.e. two different images) yielded good correlations and low 26 errors, as presented in Fig. 10. Compared to estimations provided by the P-band HV 27 polarisation channel, FOTO-derived AGB did not show saturations over the whole range 28 of mangrove biomass (Fig. 9), i.e. up to 500 tDM.ha -1 and rmse error remains acceptable 29 (33 tDM.ha -1 ). This result suggests that, in the case of closed canopies with sub-strata of 30 low biomass (e.g. the mangrove ecosystem in French Guiana), the canopy grain approach 31 is suitable to map AGB because crown size and spatial distribution are directly 32 correlated to standing biomass of the dominant trees. However, one do not forget tha t 33 the remote sensing-based model of AGB is assessed with respect to allometric 34 predictions of "true" AGB, i.e. the aboveground dry mass of trees, from dendrometric 35 data, so that the quality of the allometric model is potentially a additional source of bias 36 (Chave et al. 2004;. 37 Assuming the constituted forest dataset is well distributed within the acquired scene(s) 38 r-spectra can be computed for Fourier windows centred on each plot. For example, when 39 applied to 1-m Ikonos (Proisy et al. 2007) or 0.5-m Geoeye panchromatic images, r-40 spectra permit good discrimination of a wide array of forest structures of mangroves 41 (Fig. 9 However, forest heterogeneity and presence of relief makes the canopy approach to be 3 used carefully, that is one must analyze visually whether the relief influences or not some 4 of the PCA axes (e.g. Ploton, 2010). Only axes immune to relief influence should be used 5 for biomass prediction otherwise the result may be biased or highly context-dependent. 6 Moreover, due to the diversity of forest stand structures in tropical terra firme forests, a 7 sufficient number of studies in diversified locations and contexts are still needed before 8 general conclusions can be reached about the robustness of such correlations. 9 Independent ongoing studies suggest that the correlation with density is highly context -10 specific while the correlation with the mean quadratic diameter may be a more robust 11 feature. this plot is available in Fig. 11

Present limitations of the methods and prerequisite 4
In tropical forest, both gaps and multi-strata organization are often observed. Gaps are due 5 to accidental tree falls or natural decaying of some canopy trees (Fig. 11, left). In presence of 6 gaps, r-spectra tend to be skewed towards low frequencies and this may be erroneously 7 interpreted as if the canopy contained large tree crowns (Fig. 9, r-spectrum of the decaying 8 stage). In fact, gap-influenced r-spectra cannot be automatically related to the same biomass 9 levels and must be removed from the PCA analysis to avoid biases in the AGB-FOTO 10 relationship. Identically, the method was so far tested principally on evergreen forests. 11 Further studies are needed regarding deciduous forests, not only because of the seasonal 12 changes of the canopy aspect, but also because biomass of understorey vegetation often 13 found in such forest type is not necessarily negligible. As spectral properties of the 14 understorey may influence the overall reflectance of the corresponding pixels, this may be 15 all more confusing if there is no intermediate stratum beneath the highest deciduous trees. 16 An example of this is provided by the so-called Maranthaceae forest in Africa (Fig. 11, analyzed after separating deciduous and evergreen forests than may be simultaneously 1 present in a given region. Appropriate regional pre-stratification using multispectral 2 satellite data and/or L-or P-band polarized signatures (Proisy et al. 2002) may help towards 3 this purpose. 4 5 6 Fig. 11. Two examples of specific forest structures for which canopy grain and total AGB 7 relationships cannot be safely derived without prior-stratification of the main forest types. 8 Left: Decaying mangrove, with both large surviving trees and large canopy gaps, French 9 Guiana © C. Proisy. Right: Maranthaceae understorey, overtopped by a fairly continuous 10 albeit deciduous forest canopy referred to as "Maranthaceae forests" in Cameroun, Africa, 11 note the absence of any intermediate tree strata © N. Barbier. 12

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The canopy grain approach is largely original. It combines common techniques, i.e. Fourier 14 transform and principal component analysis to characterize tropical canopy aspect and 15 beyond forest structure from images of metric resolution. It can be implemented without 16 prior radiometric correction, such as reflectance calibration or histogram range concordance. 17 Regarding the increasing availability of metric to sub-metric optical images, the FOTO 18 canopy grain analysis demonstrated its potential to capture gradients of forest structural 19 characteristics in tropical regions. Within this context, the possible contribution of the 20 canopy grain approach to the challenging task of estimating tropical above-ground biomass 21 is worth being assessed at very broad scale. Such aim requires conducting simultaneously 22 observational and simulation studies aiming at better understanding how canopy grain is 23 sensitive to forest structure or biomass in various types of forests under various conditions 24 of image acquisitions. There is particularly an important field of research in simulating 25 multi-spectral and metric reflectance images from realistic forest 3D templates to identify, 26 for instance, the range of conditions for which inversing above ground biomass of tropical 27 forests appears possible. Considering the extreme complexity of most the tropical forests, it 28 would be illusory to believe that only one remote sensing technique can provide all the 29 information required to the AGB inversion. We thus believe that combining canopy grain 30 analysis with low frequencies radar-based studies can provide new insights on this problem. 31

Acknowledgment
1 This work is supported by the Centre National d'Etudes Spatiales (CNES) for the 2 preparation of the 'Pleiades' mission and joins the Infolittoral-1 project funded by the French 3 "Unique Inter-ministerial Fund" and certified by the "Aerospace Valley competitiveness 4 cluster" (http://infolittoral.spotimage.com/). Nicolas Barbier has a Marie Curie 5 (UE/IEF/FP7) grant. Research in central Africa is supported by the Programme Pilote 6 Régional (PPR FTH-AC) of IRD. We thank J-L. Smock and Michel Tarcy for their strong 7 motivation in mangrove field measurements. We also thank Bruno Roux and Michel 8 Assenbaum for their kind support in providing us for free several Avion Jaune© images 9 (http://www.lavionjaune.fr