Study area

It is located on the Western Sierra Madre (WSM), in the southwest of the state of Durango, Mexico. It includes parts of the municipalities of Pueblo Nuevo, Durango and San Dimas within UMAFOR 1008, between the extreme coordinates 106°00'0.668" W, 23°03'2.2" N and 105°11'12.2" W, 24°11' 57.8" N (Figure 1).

Figure 1 Location of the study area. 

The study area measures 853 255.98 ha and is located in the great province known as the Western Sierra Madre. Its topoform systems are Great Plateau with Ravines, High Mountain Range with Ravines and Typical Cannyon. The mean altitude is 1 784 masl; the maximum altitude is 3 321 masl, and the minimum, 242 masl. The slopes range between 0 % and 100 %, with an average of 19.2 %. The climates registered in the region are subhumid temperate, with a warm summer (C(w₂)a,) (97 %) and semiwarm subhumid, within the group of temperate climates ((A)C(w₂)(w) (3 %), according to Köppen’s climate classification modified by ^{García (1988}). Figure 2 shows the nine sub-watersheds that make up the study area.

Figure 2 Sub-watersheds of the study area. 

The vegetal cover of the area consists of pine, pine-oak and oak forests (85 %), low deciduous and sub-deciduous forests (6 %), induced grasslands (6 %) and rainfed agriculture, medium deciduous and sub-deciduous forests, human settlements and chaparral (the remaining 3 %). The prevailing soil types are Regosol (38 %), Lithosol (34 %) and Cambisol (17 %), and, in a lesser proportion: Acrisol (5 %), Ranker (4 %) and Vertisol (2 %).

The present research used data from 51 polygons of forest plots managed by staff of Forest Services Provision Unit (UPSE) No. 6. The first database consisted of the stands generated using photogrammetric techniques with digital orthophotograps (^{Inegi, 2013}). The stands were digitalized by members of the technical staff of UPSE No. 6, based on the photointerpretation criteria using the ArcGis 10.0 software (^{ESRI, 2011}), and corresponds with their most recent delimitation (2017-2027 felling cycle). For comparative purposes, the polygons of the plots were united, and a single identifier was assigned to each stand.

The second database consisted in the generation of stand with semi-automated procedures, based on geospatial processes using GIS software with the digital input of three Digital Elevation Models (DEMs). The following DEMs were considered: (i) Inegi, Continuum of Mexican Elevations (CEM 3.0) of the National Institute of Statistics and Geography (Instituto Nacional de Estadística y Geografía) (^{Ávalos, 2004}; ^{Inegi, 2015}); (ii) ASTER (Advanced Spaceborne Thermal Emission and Reflection Radiometer), from the Terra satellite (^{Abrams, 2000}; ^{NASA 2015}); and (iii) SRTM, of the Shuttle Radar Topography Mission (^{Rabus et al., 2003}; ^{USGS, 2015}). The DEMs have a 30 m x 30 m pixel size and are georeferenced to projected UTM coordinates, Zone 13, using WGS84 datum.

The delimitation of the stands or micro watersheds was based on the ^{SIATL (2015)} Information GeoPortal of INEGI, consisting of vector information from the hydrographic Network at a 1:50 000 scale, which models the superficial drainage of a watershed.

Stand delimitation using the DEM’s geomorphometric land surface analysis

Debugging of DEMs. The DEMs utilized for stand delimitation exhibit various sources of error: (i) positional, deficient geographical location of the marked points or of the contour line trajectory; (ii) altitude values; or (iii) related to the interpolation process. The most common refer to the existence of depressions, areas surrounded by cells with a higher altitude, and peaks surrounded by areas or cells with lower altitudes (^{Pérez and Mas, 2009}).

In order to avoid the effect of depressions on DEMs, direction flow geoprocessing was applied (^{Neteler, 2005}), using the GRASS GIS^TM software (^{GRASS, 2012}). Subsequently, a mean (student t) test was carried out to verify the existence of significant differences in the altitude variable between the various analyzed DEMs.

Stand delimitation

The stands were semi-automatically delimited based on the DEMs in the GRASS GIS^TM software (^{Jasiewicz and Metz, 2011}; ^{GRASS, 2012}). The minimum desired size was specified, according to the mean surface area of the stand estimated using the photogrammetric database, with 115 has and a minimum size of 10 ha. The pixel size of the models --30 m x 30 m (900 m² per cell)-- was considered for one hectare (10 000 m²), and a size of 11.11 cells per hectare was determined; thus, a value of 111.11 cells was used to delimit watersheds with a minimum size of 10 ha.

Once the dasocratic division was created, the stands were converted to a vector format in order to soften the border line, eliminating those polygons that were under 10 ha using routines developed in the open-source PYTHON programming language code (^{van Rossum and Drake, 2011}) in order to estimate the micro watersheds or stands.

Figure 3 shows the first modeling of the terrain for semi-automatic stand delimitation based on a DEM in a process flow in which the polygons were defined according to the micro watersheds and to the drainage network, using the Strahler method of classification, in which the first-order drainage sections receive the water directly from the mountain sides (^{Zambrano et al., 2011}).

Figure 3 Block I: First phase of the semi-automatic stand delimitation processes. 

The second process block (Figure 4) shows a cycle with each of the polygons generated in the previous block; these intersect with the drainage network within them in order to carry out a subdivision of the same and to form the study area stands.

Figure 4 Bloch II: Second phase of processes for the semi-automatic stand delimitation. 

The slope intervals (in percentages) were derived using spatial analysis geoprocessing, and reclassified and coded as shown in Table 1.

Table 1 Classification of slope ranges. 

Subsequently, the exposure data were classified according to Table 2.

Table 2 Classification of exposure ranges. 

Zonal statistics

The values of the altitude, slope variables and mean exposure derived from the various DEMs were calculated using zonal statistics geoprocessing (^{QGIS, 2014}). This procedure allows estimating the statistics by defining the raster layer pixels (DEM) through the superimposition of a vector layer of polygons that correspond to the generated stands.

Statistical analysis

The statistical comparison between the mean values of the altitude, slope and exposure variables of the stands generated in the process by using photointerpretation of the images viewed in the computer and those generated semi-automatically for this study using the ^{Kruskal-Wallis non-parametric method (Kruskal and Wallis, 1952}), which does not assume the normality of the data or homogeneity of variance as a hypotheses. The significance of the differences was determined considering a confidence interval of 95 % ( = 0.05). The analysis was carried out using the NPAR1WAY of the SAS/STAT^TM statistical system (^{SAS, 2008}). In addition, kite and box plot diagrams were developed for each variable in order to facilitate the interpretation of the results.

Debugging of the DEMs

Table 3 shows the results of the statistical comparison of the mean altitude of the stands between the original and the corrected DEMs. No statistical differences were observed between any of the mean altitude values (p>0.05). There were no differences in the DEM developed by INEGI, while those of NASA (ASTER and SRTM) exhibited minimal differences.

Table 3 Statistics describing the DEMs before and after correction. 

O= Original model; C = Corrected model.

Comparison between stand delimitation techniques

Table 4 shows the statistics describing the altitude, slope and exposure variables for the stands or micro watersheds generated with each of the assessed stand delimitation techniques. The photogrammetric technique produces a higher number of stands than the semi-automated method.

Table 4 Statistics describing the stands obtained with the semi-automated method and the photointerpretation technique, based on the 51 polygons of the plots used in this research. 

The analysis of the mean altitude of the stands using the semi-automated method registers a variation of 18 to 93 masl between the ASTER and SRTM models, with respect to that of Inegi. The slope intervals of the stands varied in the first model, describing a steep terrain. No significant variations were found for the exposure variable; the result was a prevalent southward exposure.

Figure 5 shows continuity and homogeneity in the outline of the stands corresponding to the three DEMs generated with the semi-automated method based on the geomorphometric land surface analysis of the various DEMs analyzed.

Figure 5 Stands generated using the ASTER, SRTM and INEGI DEMs with the semi-automated method. 

The results of the Kruskal-Wallis non-parametric test carried out in order to assess significant differences in the generation of stands using the photogrammetric technique and the semi-automated method, in the geomorphometric analysis of the various DEMs are shown on Table 5. Highly significant differences (p<0.01) were determined between the DEMs for the altitude and slope variables, while there were no significant differences (p>0.05) for the exposure.

Table 5 Results of the Kruskal-Wallis test for the assessment of differences in the considered variables between the stands generated through photogrammetric techniques and through the semi-automated method for the geomorphometric land surface analysis, by DEM. 

Fot = DEM of the stands generated using photogrammetric techniques; Mod = DEM of the stands generated with the semi-automated method for the geomorphometric land surface analysis.

Figure 6 shows the mean values for each variable and DEM using kite and box plot charts.

Figure 6 Kite and box plot chart for the variables estimated for the photogrammetric stands (InegiFot) and for the stands generated with the semi-automated method for the geomorphometric land surface analysis of the three DEMs. 

Notably, there are no significant differences in the exposure variable between the stands generated using the photointerpretation technique and those obtained with the proposed semi-automated method, since in every case the hydrological network is considered as the main feature for stand delimitation. However, ^{González et al. (2004)} report a strong influence of exposure, which is relatively easy to photointerpret directly on the computer, and therefore becomes the main trait of the terrain for supporting the stand delimitation.

The semi-automated method yields a precise definition of the set of exposure values and a zone delimitation that are similar to those obtained using traditional methods. Figure 7 illustrates a visual comparison between the stand delimitations resulting from photointerpretation and from the semi-automated method for the geomorphometric land surface analysis based on INEGI’s DEM, considering exposure as the main input variable of the models. Figure 7 shows no significant differences in the exposure-based stand delimitation between the two assessed stand delimitation techniques.

Figure 7 Superimposition of stand layers generated in relation to the exposure variable upon a Google Earth image using photogrammetric techniques (fuchsia) and the semi-automated method for the geomorphometric land surface analysis based on INEGI’s DEM (red). 

The zonal statistics for the slope and altitude variables estimated using the semi-automated method differed significantly from the values calculated with the photointerpretation technique. Under the assumption that the layer of stands generated through the latter represents the desired situation, we might say that the proposed semi-automated method generates statistically different zonal statistics from those produced in stand delimitations using the traditional method.

These differences may be accounted for by the fact that the use of photointerpretation does not allow the forest technician to capture the whole range of slopes and altitudes in the study area (^{Ancira-Sánchez and Treviño, 2015}). However, we must consider other important aspects that take place during the stand delimitation process and are the cause of differences --including the subjectivity of the photointerpreter, poor outlining or discrepancies in the borders of the stands with respect to the contour lines or to the field grade elevations, use of aerial photograps or orthophotographs with a low spatial resolution (^{Aguirre, 2013}; ^{Ancira-Sánchez and Treviño, 2015}). A viable alternative to improve the technique for the photointerpretation of the stands would consist in the use of aerial or satellite images with a very high spatial resolution favoring the identification of objects located on the surface; however, this entails high investment costs (^{Ancira-Sánchez and Treviño, 2015}; ^{Valdez et al., 2006}).

On the other hand, the semi-automated method has the advantage of producing zonal statistics for the slope and altitude variables based on the same criteria and in a significantly shorter time than the photogrammetric technique and is therefore regarded as a useful tool with potential to support and monitor the cartography for forest management programs. Its use also makes it possible to attain standardized polygon delimitation in order to ensure the continuity of the outer boundaries of the plots.

The differences in the outline and delimitation of the stands between the methods described above are shown in Figure 8, which was obtained by exporting the delimitation of both layers to the KML format of Google Earth and, subsequently adding an altitude factor in order to view it in 3D. The stands generated using the semi-automated method based on the DEMs show a better outlining of the higher parts of the plots, as well as of the streams, wherever the slope is pronounced, although they do not clearly outline the valleys or the relatively flat areas. On the other hand, the stand delimitation using photogrammetric techniques shows differences in the continuity of the boundaries of adjacent plots; this can be corrected by utilizing the proposed methodology.

Figure 8 Comparative detail of the stand delimitation on a Google Earth image using photogrammetric techniques (red) and the semi-automated method for the geomorphometric land surface analysis based on Inegi’s DEM (white); the border of the plot is marked in yellow. 

Based on the findings of this research, we recommend using the DEMs, regardless of their source (ASTER, STRM or Inegi), as basic input for the generation of micro watersheds, since they all showed similar results, are open-source and have a national or global coverage. Debugging with the method presented herein is relatively simple, in contrast with the generation of the model based on contour lines (^{González et al., 2004}). There are various comparative studies (^{Szabó et al. 2015}; ^{Forkuor and Maathuis, 2012}; ^{Huggel et al. 2008}) on the DEMs of ASTER and SRTM which conclude that both can be used in geomorphological applications.