Šumarski list, Vol. 134 No. 5-6, 2010.
Izvorni znanstveni članak
Using Geostatistics in Forest Management
Damir Klobučar
; Hrvatske šume Direkcija Zagfreb
Sažetak
The possibilities of forest measurements have been signifi cantly improved nowadays, by using georeferenced maps, implementing re mote sensing, developing artificial intelligence, using the global positioning system and geographical information system. Moreover, the exact position (x, y) of the measurement (of variables) of the specific location (Z) in the forest allows the monitoring of the information and the analysis of the so called con tinuous model of spatial variation, as opposed to the discrete model of spatial variation which is assumed to be homogeneous.
Ever since geostatistics was introduced to geoscinces (Krige 1951, Mathe ron 1965), it has been implemented in many areas whose interest lies in analy zing spatial data. Geostatistics is based on the concept of regionalized variable (which means that the value of the variable depends on the sampling area).
The goal was research and presentation of using geostatistics in the forest management, with the aim of improving the present approach to using and mapping the forest inventory data for Croatia. The geostatistical analysis was performed on a part of an management unit “Banov Brod”, Pitomača forestry administration, for three structural elements (variables): number of trees (N), basal area (G) and volume (V). The research included the compartments /subcompartments 9a, d, e, 10 a, b (Figure 1), with the total area of 69, 57 ha.
In order to determine the anisotropy, semivariogram surface maps of each of the elements were made. The semivariograms were used as a measure of spatial dependence, and experimental and theoretical semivariograms were calculated. The experimental semivariogram for each structural element was calculated after multiple fitting of number and width of lags. The parameters used for Ordinary Kringing interpolation of each of the structural elements were obtained from the theoretical semivariogram model.
The interpolation of structural elements was also conducted by using the inverse distance method. The testing of the interpolation model was done by using a numeric cross-validation approach. Furthermore, the usefulness of making a variogram cloud in the spatial structural elements’ analysis was shown. Three programs were used during this project: VARIOWIN 2.21; SUR FER 8.0™, and STATISTICA 7.1 ™.
Semivariogram surface maps for the three analyzed structural elements did not indicate the presence of anisotropy (Figure 2). As anisotropy was not determined and omnidirectional experimental semivariogram were calculated (Figure 3). All experimental semivariograms can be considered reliable be cause they contain a great number of pairs of data. What they have in common is the existence of hardly explainable high nugget, that is the difference in the values of close samples or measurement errors, as well as the range, which is bigger than the sampling interval. The omnidirectional experimental semivariogram of the tree volume and basal area (Figures 3a, b) start oscillating very soon, which shows that there is no large range of these two structural elements in any direction. The omnidirectional experimental semivariogram of the number of trees increases relatively quickly so this structural element shows the poorest spatial correlation (Figure 3c). The omnidirectional experi mental semivariogram is approximated with the theoretical (Table 2, Figure 3). Sample distribution maps (Figures 4, 5 and 6) show an estimated value of structural elements on either coordinates (x, y).
Structural elements’ assessments through kriging and inverse distance method are tested with cross-validation and a root mean square error was used as an accuracy benchmark (Table 4). The mean square errors of asses sment methods are very similar and therefore inconclusive when determining which interpolation method is more acceptable. Thus, a testing of the value differences between the measured data and interpolation methods for the three structural elements (number of trees, basal area and volume) was done by using the analysis of variance of repeated measurements. As visible in Table 5, statistically significant difference between the measurement data and interpolation methods of kriging and inverse distance was not determined.
During the assessment of structural elements’ value (Figures 7, 8, 9) it is visible that the kriging assessment is more compatible with range of measure ment values for all three structural elements, while inverse distance method measurements have a significantly lower value range (in other words model cells assessment tend to be around the mean value of incoming data). Conse quently, this research considers kriging as the acceptable interpolation met hod when compared to inverse distance method.
The making of semivariogram cloud is a useful tool because it allows the observation of each variable (structural element) as a distance function (shown on the x-axis) between measured data (variogram values between pairs are shown on the y-axis) within the analyzed area (view of the forest are with locations where measurements were done) on an interactive interface.
In geostatistics the size of area and variable is not a limiting element. Any variable obtained through forest inventory, by tree type or total, can be obser ved by using a geostatistical analysis. The only condition is that some form of autocorrelation is assumed between them.
Since forest inventory is conducted periodically, the geostatistical method which allows the possibility of monitoring forests in space (spatial structure), also allows monitoring forests in time. The changes of variable(s) in space and time (change of structural elements’ values by tree type and total, health of forests, etc.), as well as the forest management itself, can thus be monitored by continuously mapping two or more successive measurements. In addition, the above mentioned approach also enables the control of forest measure ments.
By doing the forest inventory, a lot of information is gathered on the state of forests. Geomathematical tools (geostatistical and neural) enable the data to be used in a more relevant and rational way in space and time, in order to manage forests in a more optimal way.
Ključne riječi
forest inventory; forest management; geostatistics; kriging; semivariogram.; structural elements
Hrčak ID:
57004
URI
Datum izdavanja:
30.6.2010.
Posjeta: 2.327 *