Approaches for the optimisation of double sampling for stratification in repeated forest inventories

Abstract

Double sampling for stratification is an efficient sampling scheme that could prove its practicability in different forest inventories. Nevertheless, further increases of efficiency are desired. Several approaches for achieving this aim are presented and discussed separately in this thesis. The approaches are tested in case studies with data from the Forest District Inventory of Lower Saxony. The first approach (chapter 2) deals with double sampling for stratification in repeated inventories. A Composite Estimator is constructed with data from the current inventory occasion and simulation results of the preceding occasion. Therein the sample size of the current inventory can be reduced, whereas the full number of sample plots of the previous occasion is used for simulations. Even though such an estimator can be constructed, the case study indicates that no, or at least no sufficient, increase of efficiency can be achieved. This can be explained by the big differences between the results of the reduced, current terrestrial inventory and the predicted volumes of the simulations. An increase of the efficiency of this approach can only become possible through further developments of forest growth models. With a three-phase sampling design, that combines double sampling for stratification and double sampling for regression, a higher efficiency can, however, be achieved for applications in repeated inventories (chapter 3). Estimators for the mean and the variance are presented that are based on the so-called infinite population approach in the first phase. The correlations between current inventory data and growth-simulations on the basis of the previous inventory are used in this approach. Instead of the simulations, the data of the previous inventory can simply be used directly for calculating the correlations. However, using the simulations as regressors mostly leads to better results. The efficiency of the presented three-phase design is higher than the one of the classical two-phase design if the sample size of the second inventory occasion is reduced and a decrease in precision is accepted. Thus, the use of the data from a previous inventory occasion in terms of a strata-wise regression estimator could be shown to be successful and superior to the Composite Estimator. Another presented method is the expansion of the double sampling for stratification design by clustered sub-sampling to a three-phase design (chapter 4). For the Ratio-to-Size approach as well as for the unbiased approach estimators for the mean and the variance are given. Compared to pure double sampling for stratification, using this three-phase design cannot increase the efficiency in the corresponding case study. Reasons for this might be seen in the small spatial extent of the forest districts and the high sampling density in there. Meaningful applications of this procedure are possibly thinkable in large areas with bad infrastructure. In a further case study, it is aimed to cluster existing sample points into clusters of homogenous size (chapter 5). This clustering shall help to optimise the travel time for the inventory of sampling points. Therefore, seven different methods are tested and their results are compared. Moreover, the quality of the solutions is evaluated through a comparison with optimised benchmark-solutions. It becomes obvious that three algorithms of the Vehicle Routing Problem are well suited for generating such clusters of homogenous size. Three clustering-algorithms as well as using planning units as clusters do not produce clusters of very homogenous size, and can thus not be recommended.