Modeling forest stand structure using geostatistics, geographic information systems, and remote sensing

Abstract

Forest management requires the estimation and mapping of forest resources. For reasons of time and cost an exhaustive measurement of every individual tree in a forest is not feasible and the variables of interest are measured at single point locations. However, information, such as basal area and timber volume, is usually required for the entire forest. This leads to methods of interpolating data and estimating the mean value within the area. Forest stand structure is traditionally mapped as polygons. This approach assumes that forest parameters are homogeneous within each polygon and change abruptly at boundaries. Many natural phenomena, however, change gradually over space. Spatial interpolation techniques like geostatistical methods, can be applied to represent forest stand structure as a continuous surface. While traditional statistics assume independent data, geostatistics take a different approach by quantifying and modeling this spatial dependence. Underlying this approach is the expectation that, on average, samples close together have more similar values than those that are farther apart (spatial autocorrelation). This study compared five geostatistical methods of interpolation (ordinary kriging, universal kriging with first-degree trend surface, universal kriging with second-degree trend surface, cokriging, and disjunctive kriging) with three traditional estimation methods (polygonal mapping, inverse distance weighting, and inverse distance weighting squared). These eight techniques were used to spatially interpolate the number of stems, total basal area, and number of seedlings on 82 sample plots in a 121-hectare first-order forest watershed in the USDA Forest Service, Fraser Experimental Forest, Fraser, Colorado. Secondary variables used for cokriging included elevation, a combined value for slope and aspect, and the normalized difference vegetation index (NDVI) from Landsat-TM satellite imagery. The comparison criterion was the mean square error (MSE) calculated by cross validation. For variable number of stems the MSEs ranged from 44.568 to 49.444 with cokriging being the best estimation method and disjunctive kriging giving the poorest results. However, the differences between the various methods were relatively small. The MSEs for variable total basal area ranged from 3.464 to 4.598. The best results were obtained using polygonal mapping, while the poorest results were given by inverse distance weighting squared. Again, the differences between the various methods were relatively small. Variable number of seedlings had the best estimation results applying inverse distance weighting squared (MSE of 69.881). The worst results were obtained using disjunctive kriging (MSE of 118.995). For this variable, the differences in MSEs for the various interpolation methods were much larger than with the other two variables. There was no single "best interpolation method" as the performance of the estimation techniques was different between variables. Overall, however, cokriging performed best, followed by polygonal mapping. By utilizing the spatial cross-correlation between primary and secondary variables the quality of the cokriging estimates was improved as compared to the results of the other kriging methods. Polygonal mapping gave good estimation results for two of the variables under study. Universal kriging with a first- or second-degree trend surface yielded, in general, better results than ordinary kriging. Removing a trend improved the interpolation results for two of the variables in comparison with ordinary kriging. Inverse distance weighting was generally less accurate than the linear kriging methods. Inverse distance weighting techniques outperformed the kriging methods only in the case where the requirements of kriging (approximately normal distribution of the data) were not fulfilled. The disadvantage of inverse distance weighting is that it cannot take the clustering of sample points into account, while kriging methods give less weight to clustered sample points. The nonlinear kriging method (disjunctive kriging) performed least well. This method could only be used if the transformed data were close to being normally distributed. But even in cases where the transformation process was successful, disjunctive kriging results were not better than the other kriging methods. Additional information (in the form of spatially cross-correlated auxiliary variables) seemed to be a more important consideration than whether the estimation method is linear or nonlinear.