Spatial resolution is an important consideration when using remote sensing for forest characterization [9]. Currently the spatial resolution of systems frequently used for vegetation characterization range from coarse (e.g., 1 km of the Advanced Very High Resolution Radiometer) to very high (e.g., 0.4 m of the GeoEye-1 sensor). The adequacy of remotely sensed data for a specific purpose (e.g., attribute level: tree, stand, landscape, region) is conditioned by its spatial resolution, which is also inversely related to the extent covered by the image [10], also known as the image footprint.

Medium spatial resolution data with pixels sized 10–100 m (e.g., Landsat Thematic Mapper (30 m), ASTER (15 m)) are appropriate for characterization of forest condition [11] and monitoring of conditions and change at the forest stand level [12]. Certainly a key to the applications and monitoring success of Landsat is the ability to capture conditions and dynamics that relate human interaction with terrestrial ecosystems. However, more detailed spatial data available since the launch of various commercial satellites (e.g., IKONOS in 1999, Orbview-3 in 2003) provide the opportunity for more precise depiction of forest parameters and are poised to reduce estimation errors of forest attributes to an acceptable level for operational applications [13]. HSR imagery facilitates, for instance, the detection of individual tree characteristics [14], providing improved estimates of forest structural attributes [7]. Panchromatic imagery, with fine spatial resolution (< 1 m) is particularly well suited for analysis of spatial relations through image texture measures [15,16]. Texture measures enable the combination of spatial detail of panchromatic imagery with unique spectral information conferred by multispectral imagery serving to leverage complementary information [17] that can be employed separately or with a pan-sharpening approach [18,19]. Spectral measures may be understood to inform on vegetation status, type, and condition with textural measures informing on vegetation structure.

Still, the dearth of established methods for image processing and the complex interactions between sun-sensor-surface geometry and forest structural characteristics [20], particularly in complex topographies, persist in making the use of HSR data challenging [6]. HSR imagery acquired using space-borne platforms allows for data collection over remote areas, with predictable georadiometic qualities, and information content analogous to mid-scale aerial photography—commonly used for forest inventory purposes. Lidar (Light detection and ranging) technology has a demonstrated capacity to characterize forest structure [21–24] albeit with high costs persisting to limit operational, wide-area applications [25]. Although lidar, with a capacity to collect highly detailed information regarding forest attributes, shows promise as a means to collect plot-like data for training attribute estimation algorithms applied to HSR imagery.

The research literature is replete with studies relating forest structural parameters estimated from HSR satellite data (Table 1). Frequent techniques to obtain information from HSR images include crown isolation [26,27], shadow analysis [18,28], texture analysis [13,29,30], and geostatistical approaches [31–33]. The capacity to characterize forest structural attributes typically decreases as crown closure increases [6], with an asymptotic relationship predictably emerging for vertically distributed attributes of forest structure [34].

The Spanish Plan Nacional de Teledetección (PNT) is committed to acquiring complete national coverages of HSR satellite imagery annually [41] and to make data available for research at no cost. The acquisition phase started in 2008 [42], capitalizing upon archival data to backdate the database to 2005 coverage. Initial coverage consist of SPOT5-HRG XS+P (2.5 m) data, with other sensors being considered for future acquisitions [43]. Access to this data represents a unique opportunity to incorporate HSR into Spanish forest inventories as an operational and low cost data source to meet a range of information needs. The data is to be collected with a primary focus on land-use land-cover change assessment [42], but capacity to generate information for forest monitoring and reporting can also be generated.

Encouraged by a readily available source of data there has recently been an increased interest by the Spanish research community in relation to remote sensing technologies and the potential application to forest environments, in particular the characterization of forest structure. Vázquez de la Cueva [44] explored relationships between forest structural attributes at the plot level (e.g., height, basal area, and crown canopy closure) and spectral information derived from Landsat Enhanced Thematic Mapper Plus (ETM+; 30 m pixel size) imagery combined with topographic data. The study considered three types of forest in Central Spain and applied a multivariate canonical ordination method. The author found a strong influence of vegetation type on the results, with a low percentage of variance explained precluding development of robust empirical models. Pascual et al. [45] used lidar data and a two stage object based methodology to characterize the structure of Pinus sylvestris L. stands in forests of Central Spain. Five structure types were defined based on height and density parameters. The median and standard deviation of height were found to be the most valuable for definition of structure types, with the approach developed being proposed for operational application suitable for inclusion in forest inventory procedures in support of forest management plans. Merino de Miguel et al. [33] investigated the strength of relations between dasometric parameters and textural variables in Pinus pinaster Ait. stands in Central Spain. The authors used geostatistical tools (i.e., variograms), calculated with orthophotography and IKONOS-2 imagery with original and degraded spatial resolutions. The authors found the strongest correlations when the variogram was calculated for spatial resolutions of 1 m and 2 m. As such, opportunities to further explore the capacity of HSR imagery to estimate a range of forest structural parameters remain.

The study focuses on pines in the Central Range of Spain (Figure 2), an area mainly dominated by P. sylvestris L., P. pinaster Ait., and P. nigra Arn. species. Two sites representing different forest conditions were chosen for availability of field data. Pinar de Valsaín (hereafter Valsaín) is a 7,627 ha forest of Pinus sylvestris L. on the North facing slopes of Sierra de Guadarrama (Segovia). It is a multifunctional forest (timber production, recreation, and protection) with an established management plan since 1889 that has evolved from a rigid to a more flexible scheme over the subsequent decades. Management actions and recreational activities have had an impact on the forest structure [46]. Valle de Iruelas (hereafter Iruelas) is a 5,483 ha forest of P. pinaster Ait., P. sylvestris L., and P. nigra Arn. in Sierra de Gredos (Ávila). It is also a multifunctional forest (wood, resin, and pasture production, recreation, and wildlife habitat). Although the first management plan was approved in 1886, historical circumstances prevented its implementation. The production of resin during the twentieth century favoured old growth development and a complex history of fires has also conditioned the forest structure.

Systematic surveys based on ground sample plots are conducted periodically over the study sites measuring attributes including density, diameter at breast height (dbh), and height. For this study, data is from 2005 for Iruelas and 1999 for Valsaín, with the latter updated to 2004 conditions using a locally appropriate growth model following procedures recommended by the Spanish National Forest Inventory. The quadratic mean diameter (QMD) and basal area (BA) were calculated at each inventory plot (Equations (1–2)) where the total number of trees per unit area (N) was also available; expansion factors were used to scale values to a given area [47]. BA and QMD are adequate attributes for volume modeling at the stand level. QMD was preferred over the arithmetic mean diameter as it has a stronger correlation to stand volume [48]. (1) QMD = ∑ i d i 2 N (2) B A = Π 4 * ∑ i d i 2

Geostatistics provides a means for extrapolation of measured values to unmeasured points and areas, and facilitates the derivation of thematic layers for integration with other data [49]. Kriging is a spatial interpolation method that yields the best possible estimation of the spatial variable of interest at every unmeasured point [50] and the error committed in the estimation is minimized and known at each point [51]. In this study we mapped the forest variables of interest (QMD, BA, and N) measured in ground plots located over grids sided 150 m in Iruelas and 200 m in Valsaín into raster layers through a process of ordinary kriging. The relative standard error (i.e., the standard error of the kriged surface relative to the mean attribute value at the polygon level) was on average 15% for the QMD kriged layer and 25% for the BA and N layers, similar to the variability found for multiple plots found within the same polygon. More accurate averaging is facilitated, as sampling is complete and spatial correlation of plot values is accounted for.

QuickBird-2 is an Earth Observation satellite launched by Digital Globe in 2001, providing data in five spectral bands (Table 2). It has the capacity to be oriented and to capture images off nadir enabling a temporal revisit of 2–6 days depending on latitude [52]. The pixel size of QuickBird-2 images is 2.4 m for the multispectral bands and 0.68 m for the panchromatic band (Table 2).

Two QuickBird-2 images, supplied in a georeferenced form by the data provider were used in this study, each covering one of the study sites (Figure 2, Table 2). Images were orthorectified with a Digital Elevation Model (DEM) derived from a contour vector map 1:10,000 (www.sitcyl.jcyl.es) and registered to aerial photography with 0.25 m pixels (www.sitcyl.jcyl.es). The multispectral and panchromatic bands were orthorectified separately with root mean square errors (RMSE) of 0.69–0.72 m (multispectral bands) and 0.66–0.81 m (panchromatic band). Images were resampled with cubic convolution to 2.0 m (multispectral bands) and 0.6 m (panchromatic band) for alignment with the regionally appropriate coordinate grid (UTM 30N) and to facilitate integration with rasterized attributes. Atmospheric correction of the multispectral images was performed with the COST model [53] using water bodies as dark objects and the atmosphere-scattered path radiance L_λ^p estimated with a relative spectral scattering DOS model (λ⁻⁴) under very clear atmospheric conditions [54].

Image segmentation is the partitioning of images into uniform continuous spatial units [55]. Through the application of automated algorithms the criteria for homogeneity can be defined by the user, based on parameters such as tone or spatial pattern. Image objects or segments composed of various pixels provide supplementary features for image analysis, not available in pixel based analysis, such as local statistical relations of digital numbers [37], shape, size or context. That is, once segments are produced, objects (i.e., trees or groups of trees) or spatially constrained summaries of the digital numbers within the segment may be used to provide representative segment-level information [39]. In forest environments, the segments can often be considered as analogous to the manually delineated stands found in forest inventories [56].

Segmentation routines were applied to the QuickBird-2 images using Definiens Cognition Network Technology® [57,58]. In the process of image segmentation the size of resulting objects is determined by the scale parameter and by the landscape characteristics; for instance a given scale value would produce larger objects in a homogeneous landscape and smaller objects in irregular areas. The scale parameter was 50 in Iruelas and 100 in Valsaín. Other settings guiding the segmentation routine include color-shape 0.8-0.2 and smoothness-compactness 0.5-0.5. The homogeneity criteria included the visible and NIR bands with similar weight, and an aspect layer derived from the DEM to incorporate topographic information as one of the possible structural driving factors [59] was weighted 0.1.

Image texture, defined by Haralick and Bryant [60] as “the pattern of spatial distributions of grey-tone”, describes the relationship between elements of surface cover [61] and is one of the most valuable criteria in visual interpretation. The estimation of forest stand parameters is sometimes improved with a combination of spectral and spatial information [62] such as texture. Consequently a host of texture measures have been utilized to predict structural parameters in various environments [13,29,55,63,64] and has shown particular utility in complex structures such as tropical forests for above ground biomass estimation [17,65].

We applied an approach for texture analysis based on measures derived from the Grey Level Coocurrence Matrix (GLCM) [66,67]. The GLCM is a tabulation of how often different combinations of pixel grey levels occur in an image [68] at a specific distance and orientation (within a particular processing kernel, or analysis window). Texture analysis is a multiscale phenomenon [69] and choosing the right window size to capture meaningful local variance without generalizing unrelated features [13] is one of its key challenges [70]. For selection of window sizes to calculate the GLCM texture measures we used the semivariogram approach [71,72]. Semivariograms were calculated for image subsets over five experimental structural plots in Valsaín [73] and ten structurally different areas in Iruelas, identified with a combined approach based on inventory data and visual interpretation to cover all distinctive structural conditions. The range in the variogram indicates the distance beyond which pixel values are no longer correlated [71] and is an indication of the elements forming the texture present within the scene. The range is frequently associated with the most dominant elements in the scene, be it single tree crowns in open forests, or the canopy of groups of trees in close environments. Once the variograms were calculated, the range values were manually identified at the lag distance, where the variograms first flattened, corresponding with window sizes on the QuickBird-2 panchromatic band of 7 × 7, 9 × 9, and 13 × 13 pixels in Valsaín and 7 × 7, 13 × 13, and 23 × 23 pixels in Iruelas. We considered three GLCM texture variables, that is, Homogeneity, Contrast, and Entropy for each size of window (Small, Medium, and Large) (Table 3) based on their high values of correlation with structural parameters observed and pre-analysis investigations (results not shown).

One option to identify relations between variables in multivariate data sets resulting from object analysis is the use of decision tree data analysis [37] also known as Classification and Regression Trees (CART). Regression trees identify relationships between a single continuous response (dependent variable) and multiple, continuous and/or discrete, explanatory (independent) variables, through a binary recursive partitioning process, where the data are split repeatedly into increasingly homogeneous groups (nodes), using combinations of variables (rules) that best distinguish the variation of the response variable. Tree models do not make assumptions regarding the distribution of the input data [74,75]; plus, they are able to capture non linear relationships between variables and are robust to errors in the input and results. Tree modeling is a nonparametric method which basic theory is reported in Breiman et al. [76].

CART approaches have frequently been used in the environmental remote sensing community for classification and mapping [77–79] for modeling [80–82] and for forest characterization [83]. In the estimation of forest structural parameters with HSR satellite imagery, decision trees have been applied in diverse environments: Chubey et al. [37] used CART for analysis of percent species composition, crown closure, stand height, and age with IKONOS imagery based on analysis of objects in Alberta, Canada, obtaining the best estimations for species composition and crown closure. Goetz et al. [84] used IKONOS and shadow analysis to model and derive classified maps of canopy cover, with 97.3% overall accuracy, in Maryland, USA. Mora et al. [40] estimated mean height of forest stands in boreal coniferous forests in Yukon, Canada, obtaining a prediction accuracy of 53% and an RMSE of 2.84 m on stand height. All of the abovementioned approaches suggest local models for estimation of forest structural parameters as an alternative tool for alleviation of often costly and time consuming field inventories.

For development of decision tree models each segment was characterized with the mean and standard deviation of the reflectance and texture variables described above (Table 3), and the mean values of the kriged forest structural parameters (QMD, BA, N) and topographic orientation. These sets of data were input for the CART analysis in Matlab®.

Samples were randomly split into calibration (two thirds) and validation (one third) sets. The representativeness of the subsamples was tested with a Multi Response Permutation Procedure (MRPP) [85,86]. This non-parametric method tests the hypothesis of no difference between two or more data sets for a range of parameters (i.e., the metrics used as inputs to the regression tree). To fit the model a cross validation process with ten iterations was performed; to avoid over-fitting we considered the establishment of a minimum number of cases in terminal nodes and pruning with the 1 SE rule [76].

Objects smaller than 0.5 ha produced in the process of segmentation were eliminated. Furthermore, screening outliers of reflectance and texture variables (i.e., segments which values were three or more standard deviations from the mean) enabled identification of objects that did not appear representative of known local forest conditions, typically corresponding with shepherding areas with buildings present in Valsaín and objects dominated by bare soil in Iruelas. Thirty nine such unusual objects were removed as outliers for subsequent analysis. Finally the number of objects preserved for modeling was 490, with an average area of 5.3 ha. Table 4 lists the statistical descriptors of the structural attributes (QMD, BA, N) and topographic parameter (aspect) at the stand-like level. Figure 3 illustrates the distribution of the structural parameters.

Information regarding the calibration and validation subsamples is presented in Table 5. The MRPP test, performed including all stand level predictors, confirmed there were no significant differences between the calibration and validation datasets (p-value 0.77).

Fitting all regression tree models was statistically significant (p-value < 0.001) and with high values of correlation (Table 6) between structural parameters and image predictors. To assess the performance of the models we applied them to the independent set of validation data, analyzing values of the Root Mean Square Error (RMSE) and correlation coefficient (R²) (Table 6) and evaluating discrepancies between values measured on the field and values predicted by the regression tree models with the help of graphic tools (Figures 4 and 5).

Applied to the validation sample the models show varying strength of the relation between the structural parameters and the image variables used as predictors. The QMD model correlation value is the highest, followed by the BA model and with the N model ranking last (Table 6). The RMSE values, a means to measure the precision of the models, are moderate for QMD and BA, and relatively higher for N when a prediction of the exact number of trees is expected (Table 6). As practical decisions in forest management are often based on classes of attributes rather than exact values of structural parameters, we evaluated the performance of the CART model to classify values of N. The measured number of trees per unit area (N) was classified into density categories ranging from open (N < 150) to closed (N > 500) categories. The CART model classified 70% of the stand-like segments in the correct group, with all other segments classified in an adjacent class. The average relative error of the models was also evaluated as the percentage of RMSE respect to the average measured parameter (Table 6).

Scatter plots in Figure 4 illustrate the relation of observed values of QMD (a), BA (b) and N (c) versus the corresponding estimated values of the validation subsample (n = 163). The QMD model performs with very good accuracy for the smaller diameters, with points close to the 1:1 line, and more randomly spread to both sides for larger diameters. The BA model depicts a similar but less accurate pattern, while the N model shows increasing disagreement of observed to modeled values at the more dense stands. Noteworthy is a tendency of underestimation for parameters at high values (QMD ≥ 1.2, BA ≥ 50, and N ≥ 600), likely as an expression of the well known saturation of optical sensors at increasingly high biophysical parameter values [34,87]. This kind of error is important to note with reference to volume and biomass estimation, since larger trees contribute more to these estimates [88], but it is of minor importance in this particular area where few stands are over the thresholds mentioned above (Figure 3; Table 4).

A closer look at the residuals confirms the relative precision of the QMD model (Figure 5(a)); an assessment of relative errors revealed that the relative error committed is below 20% in 76% of the validation sample (n = 123). A comparison of 5 cm diametric classes between the estimated and observed data indicated an agreement in 53% of the stand-like segments, with 19% falling in the adjacent class. Furthermore, the random distribution of residuals in the most frequent classes (0.30–0.40) leads to an almost complete compensation of the average error. This optimistic result should be carefully considered, as averaged values over areas of different sizes could lead to miscalculations. The residuals in the BA model look randomly distributed (Figure 5(b)), but there is a higher number of underestimates (57% of the validation sample) and in these cases the absolute value of residuals is higher. In the N model 55% of the validation segments are underestimated; a tendency to underestimate lower values and overestimate higher densities is observed.

To reduce over-fitting and to make the models practical and operationally viable we established a minimum number of cases in terminal nodes (n = 80). Furthermore, examining the terminal nodes average values and the improvement of intra-group variance they represent from father nodes (i.e., decreased variance) appropriate pruning levels were determined. With these premises the number of terminal nodes obtained was between seven (for the QMD and BA models) and eight (for the N model) (Figure 6; Table 7).

The most relevant predicting variables determining decisions in the regression tree models are shown in Table 7. Noteworthy is the primacy of stdev B1 (standard deviation of blue reflectance) which enters all models in first place. All other reflectance bands (green, red and near-infrared) did also determine some branch rules (Figure 6). Among textural variables, contrast and entropy of various window sizes were the more relevant; homogeneity was not included in decision rules. A total of five or six variables were included in each of the models.