**2.3.2 3D forest templates**

A first step within this modeling framework is to reproduce biologically realistic 3D templates of forests. Depending on the level of detail and biological realism one is to obtain, different approaches can be considered to build 3D forest mock-ups. For instance, the Stretch model (Vincent & Arja, 2008) allows accounting for dynamic crown deformations through various mechanisms and levels of plant plasticity. However, for our present purpose, we focus on variations in size-frequency distributions of trees, without entering too much into architectural (i.e. structural and dynamic) details. For this reason, we developed the Allostand model (Barbier et al. in press), a simple Matlab® algorithm using a DBH distribution, established DBH-Crown-height allometric relationships, and an iterative hard-core point process generator, to reproduce 'lollipop stands', that is a 3D arrangement of trunk cylinders bearing ellipsoid crowns. This forest template matches the DART maket requirements, e.g. a list of trees with parameters of their 3D geometry. Such simulation framework is particularly well adapted to the study of mangroves forest in which few species grow rapidly over areas with no relief (Fig. 5).

Fig. 5. Examples of 110 x 110m mockups obtained for a young Avicennia mangrove of 159 tDM.ha-1 (top left) and a mixed adult mangrove of 360 tDM.ha-1 (top right). Associated 1-m pixel DART images simulated at 0.75 µm are shown below.

#### **2.3.3 Virtual canopy images**

66 Remote Sensing of Biomass – Principles and Applications

A first step within this modeling framework is to reproduce biologically realistic 3D templates of forests. Depending on the level of detail and biological realism one is to obtain, different approaches can be considered to build 3D forest mock-ups. For instance, the Stretch model (Vincent & Arja, 2008) allows accounting for dynamic crown deformations through various mechanisms and levels of plant plasticity. However, for our present purpose, we focus on variations in size-frequency distributions of trees, without entering too much into architectural (i.e. structural and dynamic) details. For this reason, we developed the Allostand model (Barbier et al. in press), a simple Matlab® algorithm using a DBH distribution, established DBH-Crown-height allometric relationships, and an iterative hard-core point process generator, to reproduce 'lollipop stands', that is a 3D arrangement of trunk cylinders bearing ellipsoid crowns. This forest template matches the DART maket requirements, e.g. a list of trees with parameters of their 3D geometry. Such simulation framework is particularly well adapted to the study of mangroves forest in which few

Fig. 5. Examples of 110 x 110m mockups obtained for a young Avicennia mangrove of 159 tDM.ha-1 (top left) and a mixed adult mangrove of 360 tDM.ha-1 (top right). Associated 1-m

pixel DART images simulated at 0.75 µm are shown below.

**2.3.2 3D forest templates** 

species grow rapidly over areas with no relief (Fig. 5).

In this work, we only simulated mono-spectral images in the visible domain on flat topography without taking into account atmospheric effects (Fig. 5). Standard optical profiles of reflectance for soil, trunks and leaves are selected from the DART database using, for instance, '2D soil-vegetation', '2D bark\_spruce' and '3D leaf\_decidous' files. Such oversimplified images of virtual forest stands composed of trees with 'lollipop-shaped' crowns produce homogeneous texture dominated by few frequencies. The FOTO analysis of 330 DART images however demonstrated their potential for benchmarking textural gradient of real forest canopies throughout the Amazon basin (cf. Fig. 3 in Barbier et al. 2010).

#### **2.4 Influence of instrumental characteristics 2.4.1 Window size and spatial resolution**

Large windows may include features characterizing landforms such as relief variations rather than canopy grain (Couteron et al., 2006) whereas small windows may be unable to adequately capture large canopy features observable in mature growth stages. However, whatever the window size taken within a reasonable range of variations, i.e. 75 to 150 m for tropical forest, spatial frequencies should display more or less the same patterns of contribution to PCA axes (Couteron et al. 2006). The influence of spatial resolution on the sensitivity of r-spectra to capture canopy grain of different forest types was highlighted using 1-m panchromatic and 4-m near infrared (NIR) Ikonos images in Proisy et al. (2007).

Fig. 6. Radial spectra of 2 different mangrove growth stages using 0.5-m and 2-m panchromatic and near infrared Geoeye channels.

Biomass Prediction in Tropical Forests: The Canopy Grain Approach 69

Fig. 8. Example of discrete sampling of θv and s-v acquisition angles with θs =59° (left) to generate the Bidirectional Texture Function (BTF). The BTF diagram (right) is computed from the mean PC1 scores resulting from the FOTO analysis of numerous DART images and 3D forest templates. Brighter intensities values imply finer perceived canopy textures.

The canopy grain approach must be calibrated at the forest plot scale i.e. by conducting forest inventories from which above ground biomass will be estimated. Areas of about one hectare are necessary to take into account structural diversity within the forest plot. This area of inventory can possibly be reduced for simpler forest stands and plantations, but this is basically dependent on the size of the canopy trees since the computation of FOTO indices should be meaningful at plot scale (Couteron et al. 2005). AGB estimation for each plot will be taken as the AGB of reference to correlate with FOTO indices. Since very labor-intensive destructive measures are necessary to acquire biomass values, reference field AGB values are generally computed indirectly using pre-established allometric functions predicting tree AGB from the measure of the tree diameter at breast height (DBH) as explained, for example, by Chave et al. (2005). On this basis prediction of stand AGB in reference field plots can be computed by measuring DBH>5cm in young forest and DBH>10cm in adult forest. Allometric equation between DBH and tree biomass are established from few cut trees that are weighed on site (e.g. Fromard et al. 1998 for mangroves and Brown et al, 1989 for tropical moist forest). Due to the extreme difficulty of achieving this kind of field work, relationships are often limited to trees with DBH<40cm whereas DBH histograms in tropical forest show values above 150 cm.

**3. From canopy grain to AGB 3.1 Requirements for forest data** 

The loss of sensitivity to the finest textures was also observed using 2-m NIR channel of Geoeye image (Fig. 6). Whereas r-spectra of 0.5-m and 2-m image extracts displayed the same behaviour with an identical dominant frequency, they did not exhibit the same profiles for the pioneer stage consisting of a very high density of trees with 2-3 m crown diameters. This limitation was also observed for the same forest growth stages after comparison of 1-m and 4-m Ikonos channels (see Fig. 4 in Proisy et al. 2007). As the limitation with regard to the youngest stages appeared using 2-m channels, it was recommended to privilege the use of panchromatic satellite images with metric and submetric pixels.

#### **2.4.2 Sun and viewing angles: The BTF**

Parameters of VHR image acquisitions such as sun elevation angle θs, viewing angle from nadir θv and azimuth angle Φs-v between sun and camera can vary significantly as illustrated in Fig. 7. We introduced the bidirectional texture function (BTF; Barbier et al. 2011) diagrams to map the influence of different acquisitions conditions in terms of texture perception (Fig. 8). The finest textures are perceived in the sun-backward configuration whereas the coarsest are observed when sun is facing the camera (the forward configuration) due to the loss of perception in shadowed areas. These findings show that to ensure a coherent comparison between scenes, one must either use images with similar acquisition conditions, or use a BTF trained on similar forest areas or derived from a sufficiently realistic physical simulations to allow minimizing these effects (Barbier et al. 2011).

Fig. 7. Variation of acquisition parameters through a dataset of 292 images. The dataset includes 270 Quickbird, 8 Geoeye, 9 Ikonos and 5 Orbview images acquired over tropical forest of Bangladesh, Brazil, Cameroun, Central African Republic, French Guiana, India, Indonesia, Democratic Republic of Congo.

The loss of sensitivity to the finest textures was also observed using 2-m NIR channel of Geoeye image (Fig. 6). Whereas r-spectra of 0.5-m and 2-m image extracts displayed the same behaviour with an identical dominant frequency, they did not exhibit the same profiles for the pioneer stage consisting of a very high density of trees with 2-3 m crown diameters. This limitation was also observed for the same forest growth stages after comparison of 1-m and 4-m Ikonos channels (see Fig. 4 in Proisy et al. 2007). As the limitation with regard to the youngest stages appeared using 2-m channels, it was recommended to privilege the use of panchromatic satellite images with metric and sub-

Parameters of VHR image acquisitions such as sun elevation angle θs, viewing angle from nadir θv and azimuth angle Φs-v between sun and camera can vary significantly as illustrated in Fig. 7. We introduced the bidirectional texture function (BTF; Barbier et al. 2011) diagrams to map the influence of different acquisitions conditions in terms of texture perception (Fig. 8). The finest textures are perceived in the sun-backward configuration whereas the coarsest are observed when sun is facing the camera (the forward configuration) due to the loss of perception in shadowed areas. These findings show that to ensure a coherent comparison between scenes, one must either use images with similar acquisition conditions, or use a BTF trained on similar forest areas or derived from a sufficiently realistic physical simulations to

Fig. 7. Variation of acquisition parameters through a dataset of 292 images. The dataset includes 270 Quickbird, 8 Geoeye, 9 Ikonos and 5 Orbview images acquired over tropical forest of Bangladesh, Brazil, Cameroun, Central African Republic, French Guiana, India,

metric pixels.

**2.4.2 Sun and viewing angles: The BTF** 

allow minimizing these effects (Barbier et al. 2011).

Indonesia, Democratic Republic of Congo.

Fig. 8. Example of discrete sampling of θv and s-v acquisition angles with θs =59° (left) to generate the Bidirectional Texture Function (BTF). The BTF diagram (right) is computed from the mean PC1 scores resulting from the FOTO analysis of numerous DART images and 3D forest templates. Brighter intensities values imply finer perceived canopy textures.
