**3. Estimation of biomass in Chilean forests**

274 Remote Sensing of Biomass – Principles and Applications

data. The method can estimate the spatial variation of AGB at a stand or sub-stand level, and measure the uncertainty attached to the estimation, depending on local conditions. These results are promising and demonstrate the feasibility of using this approach in the evaluation and monitoring of stock biomass or communal farm scale. They are applicable to the actual landscape configuration of the country, open a series of new interest in research and development, and constitute a novel way to solve the problem of assessing biomass

Some remote sensing studies using LANDSAT TM/ETM + imagery have focused on estimating the forest attributes through correlation or regression analysis with the spectral response obtained from the images. The estimated attributes may include basal area, AGB, canopy closure, diameter at breast height (DBH), tree height, stand density, and leaf area index (LAI) (Franklin, 1986; Horler and Ahern, 1986; Peterson et al., 1986 and 1987; Lathrop and Pierce, 1991; Ardo, 1992; Curran et al., 1992; Cohen and Spies, 1992; Gemmell, 1995; Kimes et al., 1996; Trotter et al., 1997; Turner et al., 1999; Eklundh et al., 2001; Lu et al., 2004; Hall et al., 2006). One of the methods used to estimate attributes of forests from LANDSAT imagery is the direct correlation with radiometric values where regression relationships can be calculated between spectral bands, band ratios or vegetation indices (Franklin, 1986; Roy and Ravan, 1996; Jakubauskas and Price, 1997; Foody et al., 2003; Labrecque et al., 2006). The most used way to perform this kind of method is by applying stepwise forward variable

selection. Table 1 summarizes some studies using this method in several countries.

this problem is to include further co-variables independent to reflectance values.

Tomppo and Halme, 2004).

The k-NN method has become popular for forest inventory mapping and applications of estimation over the last years (McRoberts et al., 2007; McRoberts and Tomppo, 2007; Bafetta et al., 2009; Tomppo et al., 2009; Maselli et al., 2005; Tomppo and Halme, 2004; Thessler et al., 2008). The basic idea of this method is to estimate a target attribute of an object, i.e. AGB, using its similarity to objects with known attributes. Its application has focused on estimating continuous variables such as size, age, height, basal area, mean DBH, standing volume, and leaf area (Tomppo et al., 2009; McRoberts et al., 2007; Bertini et al, 2007;

Some of the advantages of using remotely sensed data are through the provision of a synoptic view of the study zone, capturing the spatial variability in the attributes of interest such as biomass, dominant height or crown closure (Zhen et al., 2007). Remotely sensed data can also be used to fill spatial and temporal gaps in forest inventory attributional data, improving estimates of forest biomass and carbon stocks, which can done for large areas as they are not limited by the extend of forest inventories (Birdsay, 2004; Fournier et al., 2003). However, the complicated vegetation stand structures in mature forest and in advanced successional forests often make the results less accurate given similar TM reflectance even if the above ground biomass varies significantly. This disadvantage is often called data saturation. For instance, in Manaus (Brazil) the canopy reflectance of tropical secondary successional forests saturated when AGB approached about 15 kg m-2 or vegetation age reached over 15 years (Steininger, 2000). Nelson et al. (2000) analyzed secondary forest age and AGB estimation using Landsat TM data and found that AGB cannot be reliably estimated without the inclusion of secondary forest age. The main approach to overcome

**2. Multispectral data for forest biomass estimation** 

stocks.

Estimation studies of forest biomass in Chile began to appear in the late 80's, primary for plantation of *Pinus radiata* (Caldentey, 1989) and, subsequently, for some local native species (Caldentey, 1995; Garfias, 1994; Herrera and Waisberg, 2002; Schlegel, 2001; Schmidt et al., 2009). In native forest, the background data is limited. The estimation method to be applied depends to the forest composition, structure and site variability. Natural forests are highly variable in the these attributes (Donoso, 1993; Gajardo, 1994; Luebert and Pliscoff, 2006) while plantations have less variation because they are monospecific and grow under intensive management regimes, designed to standardize the size and the quality of all trees (Lewis and Ferguson, 1993; Lavery, 1986; Gerding, 1991; Toro and Gessel, 1999). Secondary native forests, especially those dominated by the genus *Nothofagus*, have an intermediate degree of variation and heterogeneity (Donoso, 1981; Donoso, 1993; FIA, 2001). Traditionally, AGB estimation methods are based on sampling methods designed to assess standing timber (Husch et al., 1993; Anuchin, 1960; Bitterlich, 1984, Avery and Burkhart, 1994; Loetsch et al., 1973; Prodan et al., 1997). There is no reason for a different design because the volume/biomass ratio is relatively constant mainly depending on wood density. For the same reason, existing inventory plots can be used to estimate AGB directly. The AGB estimation method, which is usually performed for trees larger than 5 cm in diameter at breast height (DBH) and the understory is not included, should be done taking the following steps:

a. Estimate AGB at individual tree level. Given the high cost of measuring the biomass into its components (stem, bark, branches and leaves) it is preferable to use existing allometric equations for biomass by species and component. These equations depend on easy-to-measure state variables (i.e. DBH and height (H) ) and allow estimating AGB in similar trees within the stand (Keith et al., 2000; Wang, 2006; Baker et al., 1984; Ares and Braener, 2005; Zewdie et al., 2009; Ketterings et al., 2001). The biomass components are estimated based on basic density samples (dry weight / green volume) multiplied by the total volume of the component (Keith et al., 2000; Steininger, 2000; Ishii and Tatedo, 2004; Hall et al., 2006). All these functions have the following generic form:

<sup>c</sup> B f(DBH ,H ,S ) i i ii i 

where:

<sup>c</sup> Bi is the biomass of component *c* in the *ith* tree

DBHi is the diameter at breast height of the *ith* tree

(1)

Geostatistical Estimation of Biomass Stock in Chilean Native Forests and Plantations 277

According to the available data one can use different methods to estimate AGB (Figure 1).If data are traditional forest inventory plots, estimates should be made by using traditional statistical parameters for total and average quantities, which don´t give any explicit information about the spatial variability of forest attributes. If data are georeferenced, distributed in such a way that they represent the whole territory of interest, then a spatial interpolation method, such as inverse distance interpolation or kriging, can be applied. The former approach has the advantage of being an unbiased probabilistic method where the degree of confidence (accuracy) can be calculated. The basic assumption behind kriging interpolation is that the spatial dependence models described in variograms assume the behavior of a regionalized variable, which is not necessarily true in reality and should be proved. On the other hand, if it is possible to have other variables (covariates), which besides being cheaper to obtained, are spatially well correlated to the variable of interest (AGB), then they can used to somehow correct the weakness of kriging by accounting for spatial discontinuities or irregularities found in

Kriging Local estimators (sub-stands)

Survey data + Georefence (*x,y*)

> Cokriging *Local estimators (sub-stand)*

Survey data + Georefence (*x,y*) + Co-variates *(TM/ETM+DEM)* 

Chilean forests cover an area of 15.6 million hectares (20.7% of the national territory), of which 13.4 million hectares are natural forests (85.9% of the forested area). Currently 3.6 million hectares of forest are secondary forests (CONAF et al., 1999). Mixed forest of *Nothofagus obliqua*, *Nothofagus alpina* and *Nothofagus dombeyi* are one of the most important forest types in the country and cover 1.5 million hectares (12.2% of the total native forest). The genus *Nothofagus* has ten species that have a high economic value because of the quality of their wood. These *Nothofagus* forests area concentrated between 36° 30' S and 40° 30' S and between 100 and 1,000 m a.m.s.l. in Central Chile. They are present in both mountain ranges, costal and the Andes, where *N. obliqua* occupies the lowest areas (between 100 and 600 m, approximately), *N. alpina* intermediate ones (between 600 and 900 m) and *N. dombeyi* the highest (between 900 and 1,000 m), resulting in overlap ecotones with pure and mixed formations (CONAF et al., 1999; Donoso, 1981; Gajardo 1994). The main secondary species in these mixed *Nothogafus* second growth forest are *Aextoxicon punctatum*, *Genuine avellana*, *Laurelia sempervirens*, *Persea lingue* and *Eucryphia cordifolia* (Donoso, 1981). Today, a major part of these forests exhibit some state of degradation or have some form of human perturbation (Donoso, 1981; Gajardo, 1994). Nevertheless, they have a high productive potential and they need to be managed to improve their current condition. Usually, the quantification of these resources is done by applying volume tables or biomass functions, but these biomass functions rarely exist for native species and have only local applications

Fig. 1. Alternative AGB estimation based on the type of the available data.

nature (Coulston, 2008).

**3.1 Native forest description** 

Survey data

Traditional statistics *Global estimators (mean for each stand)*

Hi is the total height for the *ith* tree

<sup>i</sup> S is an estimator of the sound/dead biomass proportion of the *ith* tree


The estimated AGB at plot level has the following generic form:

$$\mathbf{B}\_{\mathbf{j}}^{\mathbf{c}} = \sum\_{\mathbf{i}=1}^{n\_{\mathbf{j}}} \mathbf{B}\_{\mathbf{i}\mathbf{j}}^{\mathbf{c}} \times \mathbf{F}\_{\mathbf{j}}$$

where:

<sup>c</sup> B is the biomass of the component j *c* for the *jth* plot (ton/ha)

(2)

n is the number of trees in the j *jth* plot

F is the hectare expansion factor for the j *jth* plot

c. Estimation of biomass at the stand, local, regional or national levels. The scales of interest for estimating AGB ranges from stand up to national levels according to the scale of the project. From stand level estimations the other aggregation levels can easily be archived by simply adding other stands estimation into the calculation. The biomass estimate at stand level has the following generic form:

$$\mathbf{B}\_{\mathbf{r}}^{c} = \mathbf{a} \sum\_{\mathbf{k}=1}^{m} \mathbf{B}\_{\mathbf{k}}^{c} \times \frac{1}{m}$$

where:

<sup>c</sup> B is the biomass of the component r *c* for the *rth* stand (ton)

(3)


The use of optical satellite and topography data as auxiliary variables (covariables) allow the accuracy of AGB estimations to improve because they are based on their spatial covariation to field data by applying geostatistical interpolation. Using topographic data, the AGB variation is scaled to the actual values for that area, and then, AGB can be obtained by overlaying any available administrative division (stands, sites or districts).

Fig. 1. Alternative AGB estimation based on the type of the available data.

According to the available data one can use different methods to estimate AGB (Figure 1).If data are traditional forest inventory plots, estimates should be made by using traditional statistical parameters for total and average quantities, which don´t give any explicit information about the spatial variability of forest attributes. If data are georeferenced, distributed in such a way that they represent the whole territory of interest, then a spatial interpolation method, such as inverse distance interpolation or kriging, can be applied. The former approach has the advantage of being an unbiased probabilistic method where the degree of confidence (accuracy) can be calculated. The basic assumption behind kriging interpolation is that the spatial dependence models described in variograms assume the behavior of a regionalized variable, which is not necessarily true in reality and should be proved. On the other hand, if it is possible to have other variables (covariates), which besides being cheaper to obtained, are spatially well correlated to the variable of interest (AGB), then they can used to somehow correct the weakness of kriging by accounting for spatial discontinuities or irregularities found in nature (Coulston, 2008).
