Location of the study area

The study area is located in the municipality of San José del Rincón, northwest of the State of Mexico, in the plot named La Sabaneta (Figure 1), between the coordinates 19°29’ and 19°47’ N, and 100°01’ and 100°16’ W. It comprises a surface area of 16 826 has. Its climate is predominantly sub-humid, semi-cold, with rains in the summer, when it becomes more humid, and with a mean annual temperature of 10 to 14 °C. The annual minimum precipitation is 800 mm, and the maximum is 1 000 mm. The plot is under forest management; two species are commercially exploited: Abies religiosa (Kunth) Schltdl. et Cham. and Pinus pseudostrobus Lindl. Other species such as Cupressus lindleyi Klotzsch ex Endl., Quercus rugosa Née and Prunus sp. have also been cited (^{Probosque, 2010}).

Figure 1 Localization of the study area. 

Inventory data

Dasometric variables were estimated at sixty-four 1 000m² sampling sites systematically distributed in 12 stands (Figure 2). The following characteristics were registered for each sampling unit: vegetation type, condition, slope (%), cover (%), exposure, altitude (masl), central coordinate, number of trees per site, species, diameter at breast height (cm), total height (m) and age (years). The design used was based on a network of sampling sites at equal distances of 400 m² (Figure 2).

Figure 2 Distribution of the sampling sites. 

In the estimation of the biomass/carbon per sampling site, allometric equations of the occurring species were applied (Table 1). The individual carbon values were added to obtain the totals per sampling unit.

Table 1 Allometric equations utilized in this study. 

DBH= Diamater at breast height; H= Total height.

Satellite images and pre-processing

A SPOT 5 HRG image was obtained from the Mexico Receiving Station through the collaboration agreement with the National Institute for Forestry, Agriculture and Livestock Research (INIFAP) and Mexico Receiving Station (ERMEX). The date when the SPOT image was taken is April 1, 2009, with a 2A processing level. The Quickbird image was donated by Merrick^® Mexico and was taken on March 6, 2009. Both images were georreferenced to UTM zone 14 N, using Datum WGS84 (Figure 3).

Figure 3 False color SPOT (left) y Quickbird (right) satellite images; red and green near infrared bands. 

The satellite images were pre-processed before being utilized to extract spectral information. The SPOT image was corregistered to the Quickbird image to ensure spatial correspondence. Both images were transformed into radiance values (^{Krause, 2005}; ^{Soudani et al., 2006}) and exoatmospheric reflectance (^{Thenkabail et al., 2004}). Furthermore, they were atmospherically corrected using the Cost model proposed by ^{Chávez (1996)} to obtain the surface reflectance.

Spectral vegetation indices and extraction of spectral values

The vegetation indices (VIs) are combinations of reflectance measurements that are sensitive to the combined effects of the concentration of chlorophyll in the foliage, foliar areas and canopy architecture. VIs are designed to provide a measure of the status of the vegetation, and although some have certain limitations (^{Romero-Sánchez et al., 2009}), they have been used in many applications, even for purposes of estimating biomass/ aboveground carbon (^{Avitabile et al., 2012}).

After reviewing the literature, documented vegetation indices were selected to estimate forest parameters (Table 2) and were applied in the present study.

Table 2 Spectral information utilized in the present study. 

The vegetation indices indicated in each image were calculated to highlight traits of interest and, subsequently, use these as dependent variables in regression models.

For both images, the spectral values were extracted in two different ways: a) central spectral values of each site, and b) average spectral values for each sampling site. Also, spectral values of 30 sites without cover were extracted for each image and added to the database.

Supervised classification

To determine the forest cover of the area, a supervised classification was carried out with the Quickbird image. Classification was divided into three categories -forest, non- forest and shades-, using the ERDAS software 2010, version 10.1, by Imagine^®. A total of 30 spectral signatures were defined: 10 for the forest, 10 for non-forest, and 10 for shades. The classification of the forest part was adjusted to the area comprising the 64 sampling sites.

Object-oriented classification

The same image was processed with a multiresolution segmentation application, which broke it up into homogeneous multipixel regions based on user-defined parameters. This process may influence the result of the segmentation process through specification and weighting of the input data (^{Blaschke, 2010}).

The segmentation algorithm is described as a technique for the fusion of those regions in which the individual pixels cluster into small objects (Figure 4), followed by successive iterations in which small objects gradually fuse into larger objects, so that the heterogeneity among the objects of the resulting image is minimized (^{Chubey et al., 2006}).

Figure 4 Object-oriented classification process. 

The values of the cover per site were also entered in the database. The accuracy of the classifications in both cases was validated by estimating the kappa index and the overal accuracy matrix (^{Congalton and Kass, 2009}), with field data independent from the forest inventory described above.

Correlation between the forest and spectral variables

Correlation tests. A Pearson’s analysis (r;_α=005) of the correlation between the forest density parameters and the spectral response captured in the pixels of the image was carried out using the vegetation indexes to determine the degree of association between the evaluated variables.

(Parametric) Regression analysis. The type of relationship existing between the spectral data from the satellite image and the response variables of interest was determined. The dependent variables included forest density parameters: total carbon (Mg/ site); mean diameter at breast height (cm) and total height (m). The independent variables were the spectral values per band and their mathematical transformations (vegetation indices), and the response variable was the parameter of interest, as suggested by ^{Zheng et al. (2004)} and ^{Aguirre-Salado et al. (2009)}.

The stepwise regression procedure was utilized to identify the variables that best predict the variables of interest. The model was as follows:

y = β₀ + β₁ X₁ + β₂ X₂ +... + β_n X_n +ɛ;

Where:

y = Forest parameter to be estimated

X_n= Spectral bands, Vegetation indices, Crown cover

β_n = Regression coefficients

ε = Random error

The construction of the regression model took 85 % of the inventory database, while the remaining 15 % was used to validate the models. The adjustment indicators were the determination coefficients (R²). Furthermore, the predictive capacity of the models was assessed by calculating the root mean square error (RMSE) and the relative root mean square error (RRMSE). 95 % confidence intervals were estimated for all the parameters (^{Kutner et al., 2004}).

The forest variables in the study area were estimated by multiplying the weightings or coefficients calculated based on the equations of each spectral band or VI, to obtain the spatially explicit estimate of the variable of interest.

Correlation tests

Tables 3 and 4 summarize the estimated values of the correlations for the SPOT and Quickbird images, respectively. In the case of the SPOT image, the spectral indices to be associated with the infrared region (B3) were observed to show relatively high correlations (>0.50, α=0.05) with the aboveground carbon values, consistently with the existing records for the temperate forests (^{Aguirre-Salado et al., 2009}). However, in the case of SPOT, some of the highest correlations occurred in the green region (B₁). The diameter at breast height and height had high correlations in most of the values extracted from the image, for both the central and mean values of the plot.

Table 3 Correlation coefficients in the spot SPOT image. 

C = Total carbon; DBH = Diameter at breast height; H = Total height; Bn = Reflectances of each band; NDVI, GARI, TVI, NDVI₂₃, NDVI₄₁, NDVI₄₂; IK_R, IK_IRC= Vegetation indices; CC = Crown cover.

In the Quickbird image (Table 4), the parameters with high correlation coefficients (> 0.6) were the blue, green and red bands, and most spectral indices associated with the infrared region of the electromagnetic spectrum.

Table 4 Correlation coefficients in the Quickbird image. 

C = Total carbon; DBH = Diameter at breast height; H = Total height; Bn = Reflectances of each band; NDVI, GARI, TVI, NDVI₂₃, NDVI₄₁, NDVI₄₂; IK_R, IK_IRC= Vegetation indices; CC = Crown cover.

The negative correlation for the forest parameters against the reflectances and certain vegetation indices of this work agree with the findings of ^{Hall et al. (2006)} and ^{Aguirre-Salado et al. (2009)}, who explain this correlation by the reduction of the albedo in areas with dense, closed vegetation. This negative correlation was increased in band 4 (Infrared) of the SPOT 5 HRG image (-0.60 to -0.75), and in band 3 (Red) of the Quickbird image (-0.58 to -0.80).

Regression analysis

Table 5 shows the different models of regression obtained by means of the stepwise regression analysis, based on the spectral values of the SPOT 5 HRG image and the covers.

Table 5 Regression models obtained through stepwise regression, for the SPOT 5 HRG image. 

C = Total carbon; DBH = Diameter at breast height; H = Total height; B_n =Reflectances.

The most common predictive variables for most forest parameters were the crown cover, certain NDVIs and the K indices. The models with the highest determination coefficient corresponded to the diameter at breast height and height, for both the mean and central values of the plot.

Table 6 shows the regression models obtained for the Quickbird image, in which the most common predictive values were, similarly: object-oriented classification, reflectances, certain NDVIs and the K indices. The models of diameter at breast height and total height had the highest determination coefficients.

Table 6 Regression models obtained using the Stepwise regression, for the Quickbird image. 

C = Total carbon; DBH = Diameter at breast height; H = Total height.

Table 7 lists the estimates of aboveground carbon, diameter at breast height and total height for each of the images in which the mean values of the plot were used. The values for the aboveground carbon and total height variables are visibly consistent in both images.

Table 7 Forest parameter estimations by sensor type. 

* = MgC; ** = Centimeters, *** = Meters.

Error estimation and validation

The root mean square error estimated for each of the utilized models is shown in Table 8. In the case of the aboveground carbon, the root of both the absolute (Mg) and relative (%) error were below 0.79 and 26 %, respectively, for both images. The results of this study proved that it is possible to estimate forest parameters (total height, diameter at breast height, aboveground carbon) with multiple linear regression models. According to the generation of the various equations, using the stepwise procedures, the determination coefficients were observed to be acceptable (R²> 0.55) for both images and treatments (the mean and central values of the plot).

Table 8 Error estimation for each variable. 

The error associated to the aboveground carbon estimations was located within the interval documented by other authors. For example, ^{Aguirre-Salado et al. (2012b)} reported a RRSME of 36.81 % for the aboveground biomass in linear models in the forests of the state of San Luis Potosí. In another case, in which information from SPOT images was used to estimate aboveground carbon in pine forests, the RRSME was 30.16 % (^{Aguirre-Salado et al., 2009}).

The strong relationships occurring between the vegetation indices and the assessed forest parameters agree with the findings of other authors (^{Franklin, 2001}; ^{Mora et al., 2013}; ^{Ji et al., 2015}), especially, the NDVI, and therefore, the spectral bands (R and IR). The NDVI is considered to be an indicator of the status of the vegetation, as it is characterized by representing a clear contrast between the regions that correspond to the visible red and the near infrared (^{Franklin, 2001}).

Another common variable for most models was the K index (^{Luévano et al., 2006}); the value of K is defined as the spectral value of the density of the components in the pixel; besides, it also takes into account the digital value of the pixels, the total number of the species present, and the total number of individuals in a specific area, which, for the purposes of this study was 1 000 m².

The models for estimating the diameter at breast height and total height had high determination coefficients, for diameters (R²=0.86 y 0.84) and heights (R²=0.93 y 0.86) (p<0.01) for the SPOT and Quickbird sensors, respectively. The results suggest that, when reliable estimates of the diameters and heights are available, these can be applied to allometric equations, which would substantially simplify the evaluations of carbon or volume in temperate forests. It is important to point out that the conditions of the site (age, diversity, etc.) were key for obtaining the models and results described above; it is, therefore, necessary to evaluate the viability of this type of studies under different conditions from those that were presented in this study.

Although regarding spatial resolution Quickbird is better than SPOT 5 HRG, the results show that contrary to the expectations, SPOT 5 HRG had the best adjustment models in most evaluated forest parameters, especially diameters and heights. The evaluated forest parameters, mainly carbon, were linked to the spectral response of the image (primarily mean values), and the type of sensor did not play a major role in the results