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## Geostatistically estimation and mapping of forest stock in a natural unmanaged forest in the Caspian region of Iran | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

Caspian Journal of Environmental Sciences | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

مقاله 9، دوره 13، شماره 1، بهار 2015، صفحه 61-76
اصل مقاله (976 K)
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نوع مقاله: Research Paper | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

چکیده | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

Estimation and mapping of forest resources are preconditions for management, planning and research. In this study, we applied kriging interpolation of geostatistics for estimation and mapping of forest stock at-tributes in a natural, uneven-aged, unmanaged forest in the Caspian region of northern Iran. The site of the study has an area of 516 ha and an elevation that ranges from 1100 to 1450 m a.s.l. Field sampling was per-formed on a 75m × 200m systematic grid using 309 geo-referenced circular sample plots of 1000 m2 area. Experimental variograms were calculated and plotted for basal area (BA), volume (V) and stem density (N). Whereas the calculated variograms of BA and V exhibited spatial auto-correlation only after data stratification based on diameter size classes and tree species, the variogram of stem density displayed a moderate spatial structure that was fitted by a spherical model. Stem density was estimated by ordinary block kriging and the accuracy of estimation was validated by cross-validation result. We conclude that geostatistical approaches have the potential to more accurately capture and describe the spatial variability of forest stock, and thus reduce the uncertainty in estimates of stem density as well as produce more accurate stem density maps of forests in comparison with the spatially uninformed classic method. Geostatistical methods provide a very suitable tool to derive more accurate estimates of growing stock, particularly in structurally complex, unmanaged, uneven-aged forest such as this one from the Caspian region of northern Iran. | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

کلیدواژه ها | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

Geostatistics؛ mapping؛ forest stock؛ unmanaged forest؛ Caspian region؛ Iran | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

اصل مقاله | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

(Received: April. 07.2014 Accepted: July. 30.2014)
Estimation and mapping of forest resources are preconditions for management, planning and research. In this study, we applied kriging interpolation of geostatistics for estimation and mapping of forest stock at-tributes in a natural, uneven-aged, unmanaged forest in the Caspian region of northern Iran. The site of the study has an area of 516 ha and an elevation that ranges from 1100 to 1450 m a.s.l. Field sampling was per-formed on a 75m × 200m systematic grid using 309 geo-referenced circular sample plots of 1000 m2 area. Experimental variograms were calculated and plotted for basal area (BA), volume (V) and stem density (N). Whereas the calculated variograms of BA and V exhibited spatial auto-correlation only after data stratification based on diameter size classes and tree species, the variogram of stem density displayed a moderate spatial structure that was fitted by a spherical model. Stem density was estimated by ordinary block kriging and the accuracy of estimation was validated by cross-validation result. We conclude that geostatistical approaches have the potential to more accurately capture and describe the spatial variability of forest stock, and thus reduce the uncertainty in estimates of stem density as well as produce more accurate stem density maps of forests in comparison with the spatially uninformed classic method. Geostatistical methods provide a very suitable tool to derive more accurate estimates of growing stock, particularly in structurally complex, unmanaged, uneven-aged forest such as this one from the Caspian region of northern Iran.
The implementation of close-to-nature silvi-culture that aimed at conserving and restor-ing unique, important and ecologically and economically endangered (due to human dis-turbances and illegal exploitation) Caspian forests of Iran (Abdollahpour & Assadi Atui, 2005) that resemble natural forests, requires a thorough understanding of ecological pro-cesses that have created the structures and composition of these natural archetypes. For-tunately, natural mixed uneven-aged hard-wood deciduous forests that encompass all three major development stages (i.e., the de-cay, initial, and optimal stages; Leibundgut, 1993, Korpel, 1995) still exist along the southern part of the Caspian Sea and the north-facing aspects of Elborz Mountain in northern Iran (Sagheb-Talebi
Caspian forests along the southern part of the Caspian Sea, span the elevational gradient of north-facing aspects of Elborz Mountain in northern Iran, occur in five main vegetation types (i.e.,
A network with 75 m (N-S) × 200 m (W-E) systematic rectangular grid was used for sapling. At each grid point, we established a circular sample plot of 1000 m2 surface area where we recorded the UTM coordinates of the plot center (Fig.1) and the diameter at breast height (d.b.h. in 1.3 m above the ground) of each tree with a d.b.h. that exceeded 7.5 cm. Further, the height of the closest tree to its respective plot center point and the largest tree in each plot were measured for volume estimation. The inventory was accomplished in the summer of 2011. Stand-level attributes of interest, i.e., basal area (BA), volume stock (V) and stem density (N) were computed for all trees as well as for trees in different size classes (i.e., small size [d.b.h. ≤ 32.5 cm, S], medium size [32.5< d.b.h. ≤ 52.5, M], large size [52.5 < d.b.h. ≤72.5 , L], and extra large size [d.b.h. > 72.5 cm, EL]; after Sagheb-Talebi
To identify and describe the spatial depend-ency (i.e., spatial auto-correlation) of BA, V and N of all trees and the diameter size clas-ses of the two dominant tree species, we used variogram (semi-variance) analysis as our geostatistical approach. Three parameters are commonly used to describe and model the behavior of variogram: range, sill and nugget effect. The range is the distance where the spatial correlation disappears and the variogram levels off, the sill corresponds to the height of the variogram after leveling off, and the nugget effect is represented by the intercept of variogram on the ordinate axis. The ratio of the nugget effect to the sill is known as the relative nugget effect. This is a measure of the percentage of the variability in the data from sources other than spatial auto-correlation. A low relative nugget effect (≤ 25%) is a sign of strong spatial auto-correlation where the application of geostatistical techniques is particularly beneficial. Nugget effects between 25% and 75% indicate moderate spatial auto-correlation and high relative nugget effect (≥75%) can indicate either weak spatial autocorrelation in the population or spatial patterns at scales smaller than the sampling distance (Cambardella 2000): for for Where h, c0, c, and a represent a particular lag vector, nugget effect, structural variance, and range, respectively. After normalization of the data, only omnidirectional (isotropic) variograms were calculated, because experi-mental variogram surfaces showed no vario-gram anisotropy. By common convention, the analysis was restricted to distances of half of the study area dimension (i.e., 2200 m). We further used the Kriging interpolation method as our geostatistical approach for possible interpolating values among sample plots and mapping the distribution of BA, V and N. Kriging computes surfaces of the best linear unbiased estimation of regionalized variables at un-sampled points based on the spatial structure defined by the experimental semi-variogram. Ordinary kriging (the most common type of kriging in practice, particularly in environmental sciences) of the regionalized variable at point is given by (Webster & Oliver, 2000): Where, is the weight associated with the value of at the sampled point with the nonbiased condition:
The accuracy of kriging was measured using the Root Mean Square Error (RMSE): Where is the estimated value of re-gionalized variable at the location of ; N is The number of sample plots and is the mean value of measured samples of interest-ed attribute. The software package used for geostatistical analysis was GS+ version 9 (Gamma Design Software, LLC, Plain Well, MI).
To further understand the spatial dependen-cies of BA, V and N, we computed several indices for quadrat counts (e.g., variance-to-mean ratio, Morisita’s index of dispersion, and Morisita’s standardized index of disper-sion) to analyze separately the spatial point patterns for all trees, trees in different diame-ter size classes, and for beech and hornbeam. The variance-to-mean ratio, attributed to Fisher et al. (1922) is one of the oldest and simplest measures of dispersion. The ratio ( ) usually called the index of disper-sion (I) (Bailey & Gatrell, 1995) and is based on the observation in a random pattern, de-scribed by the Poisson distribution, the vari-ance equals the mean, so I = 1 for a random pattern. Ratios larger than 1 indicate clump-ing, while smaller ratios indicate regular or uniform pattern. The other frequently used quadrat-based dispersion index is the Stand-ardized Morisita index of dispersion. Smith-
Gill (1975) set out to improve Morisita's index (Morisita, 1962) just described by putting it on an absolute scale from -1 to +1. To calculate this index, Morisita's index of dispersion (Id) was first calculated, along with two critical values of the uniform index (Mu) and the clumped index (Mc):
Where n is the sample size, x is the number of individuals, and are the values
of chi-squared with (n-1) degrees of freedom that have 2.5% or 97.5% of the area to the right. Morisita's Id is 1 for a random distribution, >1 for a clumped distribution, and a regular/uniform distribution. The Standardized Morisita index (Ip) is then calculated by one of the four following formulae:
When When When When The Ip ranges from -1.0 to +1.0, with 95% con-fidence limits at +0.5 and -0.5. Random pat-terns give an Ip of zero, clumped patterns give an index value of above zero and uniform patterns below zero.
A total of 309 plots were sampled in the study area. Normalization tests showed that the data were not normally distributed, conse-quently, the data were transformed using the square root and log transforms to more closely approximate normal distributions. Table 1 shows the summary statistics of the sample plots. The distribution of tree sizes in the study area reveals an uneven-aged stand diameter distribution with the majority of trees in the small and medium tree size classes (Table 2) and a few very large trees up to 300 cm d.b.h. (Fig. 2).
Because we did not find any variogram aniso-tropies, we fitted only omni-directional vario-grams using a spherical model to which a nugget effects was added (Fig. 3, Table 3). No spatial auto-correlation was revealed in the experimental variograms for BA and V. Con-sequently, these attributes represented a pure nugget effect. However, N showed a moderate level of spatial auto-correlation (50%).
SD: Standard Deviation; CV: Coefficient of Variation
S, Small size (d.b.h. ≤ 32.5 cm); M, Medium size (32.5 L, Large size (52.5 72.5 cm)
SpD (Spatial Dependence) = (SpD ≥75%, Weak; 25%< SpD <75%, Moderate; SpD ≤ 25%, Strong)
Because BA and V did not show any spatial auto-correlation, kriging interpolation was used only for N (Table 4). A comparison of tables 1 and 4 reveals that the estimated mean stem densities are not very different. However,
compared to the spatially uninformed classic method, a variance reduction in the estimate of N of approximately 72% was achieved using kriging interpolation. Figure 4 shows a kriging map and an error map for stem density over the study area.
.
Evaluating the kriging results of N with the Mean Bias Error and Root Mean Square Error and their respective relative values (Table 5) revealed a low relative Mean Bias Error of less than 10% (MBEr = 6.9%). A cross-validation graph of stem density confirms the accuracy of our estimation (Fig. 5).
Although BA and V did not show any spatial variability when considering all trees, the re-sults were quite different when we computed the experimental variograms by tree size clas-
ses and species, individually. When consider-ing trees of different diameter size classes, the spatial variability of BA (Fig. 6) and V (Fig. 7) clearly weakens from the small diameter size class towards the extra large class, with an approximately moderate spatial dependence observed in the small and medium size classes and only a pure nugget effect in the large and extra large classes. Similarly, when examining the spatial variability of BA by tree species, both beech and horn-beam individually exhibited moderate spatial auto-correlation (Fig. 8) that was completely masked when examining the spatial variability of all species (Fig. 6)
MBE: Mean Bias Error; RMSE: Root Mean Square Error; MBEr: relative MBE; RMSEr: relative RMSE
Point pattern analyses revealed that the spatial distributions of all trees, the two dominant tree
species and all diameter size classes except the extra large class were clumped in the study area (Table 6).
variance-to-mean ratio; Id, the Morisita’s index; Ip, the Standardized Morisita’s index; *, significant at p
,
The spatial structure of the three forest attrib-utes (i.e., basal area, volume and stem density), expressed by their spatial autocorrelation, differed in this unmanaged natural uneven-aged deciduous forest. Whereas stem density behaved as a regionalized variable and exhibited a moderate spatial structure (Table 3), overall stand basal area and volume did not show any spatial auto-correlation and exhibited a pure nugget effect (Fig. 3). The reason for these apparent differences can be found in the spatial distribution of trees of different diameter size classes. While smaller trees exhibited a clumped spatial distribution, larger trees increasingly tended toward a random and regular spatial distribution. This development toward spatial randomness or regularity with increasing tree size has been demonstrated in many forest types (e.g., Szwagrzyk & Czerwczak, 1993, Zenner & Peck, 2009) and is the main reason why the kriging interpolation method embedded in a geostatistical approach was able to estimate stem density more accurately to reduce the variance for stem density estimation by approximately 70%, and to produce a smaller coefficient of variation with acceptable estimation accuracy (MBEr ≈ 7%; Table 5) in comparison with the spatially uninformed classic approach (Table 1). Because smaller trees were more numerous than larger trees in this old-growth forest (Fig. 2) and each individual tree contributes equally to stem density, the moderate spatial structure of the stem density of the stand is largely driven by the
clumped spatial pattern of the smaller trees (Table 6). This is in stark contrast to the observed lack of spatial structure of the stand basal area and volume (Fig. 3) that are principally driven by the spatial randomness of the larger trees that, despite their low density, account for a large proportion of the growing stock. Thus, the spatial distribution of larger trees has more influence on the spatial structure of the growing stock (basal area and volume) in forests than that of small and medium-sized trees that typically exhibit a moderate spatial structure for basal area, and volume (Figs. 6 and 7). This lack of spatial structure of basal area and volume appears to be independent of changes induced by management, as was shown for a stand in the nearby Namkhane district (Fig. 1) that was subject to a management plan that prescribed a close-to-nature silviculture (Akhavan
The spatial structures of stem density and basal area in the current study are quite different from those reported by Akhavan and Kia-Daliri (2010), who applied the same geo-statistical approach in an eighteen year-old maple (Acer velutinum Boiss.) plantation in the Caspian region of Iran. In that study, stem density did not exhibit any spatial structure whereas basal area did. This was likely due to the regular spacing of the trees and the homogeneity of tree sizes in the plantation that was still in the early stage of stand development. Neither windstorms and droughts nor intra-specific competition had been strong enough to remove stems and break up the initial regular spatial distributions (initial planting space of 3 m × 3 m) after 18 years. Consequently, the regularity of the spatial distributions of the plants remained intact and no spatial auto-correlation was found for stem density. In contrast, the homogeneity of tree sizes in the maple plantation had a low coefficient of variation for d.b.h (35%), which was less than half of the coefficient of variation for d.b.h. observed in this study (79%), was sufficient to induce spatial auto-correlation for stand basal area. However, it is expected that as stem numbers decline until harvesting time (at approximately 80 years), stem density will exhibit spatial auto-correlation and the spatial structure of basal area will disappear as the homogeneity of tree sizes decreases. The low, medium and high density areas that are typically associated with mature, middle-aged, and young stands, respectively, have become clearly visible in the kriged stem density maps (Fig. 4a). These kriged stem density maps, thus, permit an indirect estimation of forest stock for any point in the area. For example, the point I on the digital map of figure 4a has a stem densi-ty of 170 n ha-1. Based on the diameter size classification in table 2, there are 64.6% (110 trees), 17.4% (30 trees), 9.8% (16 trees), and 8.2% (14 trees) of trees in the small, medium, large and extra large size classes at the point I, respectively. Therefore, if we use the mid-point value of each size class (namely, 20, 42.5 and 62.5 cm for the first three size classes, respectively; for the largest size class this depends on the maximum diameter size in the studied area), we can indirectly estimate the growing stock at point I. To obtain a more precise estimate, more and narrower size classes in the upper range of the size distribution would of course be beneficial due to their relatively larger impact on forest volume stock. Nonetheless, the advantage of a geostatistical approach that enables the precise quantification of the statistical error in a kriged error map (Fig. 4b) is that it identifies areas with higher errors that can then be covered with extra sample plots to reduce this estimation error. Each tree species has a specific physiological age and longevity that is reflected in a specific auto-correlation diagram (i.e., variogram) that may be masked when investigating the overall stand structure. While we failed to detect any spatial au-to-correlation for basal area when analyzing all tree species that were present at the same time (Fig. 3), we did detect a moderate spatial structure for basal area for the two dominant species (i.e., beech and hornbeam with clumped spatial distribution; Table 6), individually (Fig. 8). Hence, it appears that the spatial structures of growing stock attributes in mixed stands, which are often uneven-aged in this region, may be weaker than those observed in pure and even-aged stands, particularly if not analyzed separately by species. For this reason, Akhavan and Kia- Daliri (2010) may have been able to detect a spatial structure for basal area in their plantation forest. In general, we hypothesize that if the diameter distribution observed in a natural forest has a narrower range (e.g., no larger trees present) and has no missing size classes (i.e., is without any interruption), the growing stock appears to have a stronger spatial structure with a higher auto-correlation, but this tentative hypothesis needs to be put to more rigorous testing. Geostatistical approaches were instrumental for the identification of the spatial structures of stem density in this natural unmanaged forest. In close-to-nature forestry, which is increasingly being applied throughout the world, kriged stem density maps can provide greater assistance for forest management planning and for the identification of forest development stages (Akhavan
This research was financially supported by Iran National Science Foundation (INSF) with grant No. 88001186 and partially supported by the Research Institute of Forests and Rangelands (RIFR), Iran. The authors thank M. Hasani for assistance with fieldwork and data collection and Kh. Mirakhorlou for assistance with the preparation of maps. | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

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