Improving RBS estimates - effects of the auxiliary variable, stratification of the crown, and deletion of segments on the precision of estimates

Abstract

Randomized Branch Sampling (RBS) is a multistage sampling procedure using natural branching in order to select samples for the estimation of tree characteristics. The existing variants of the RBS method use unequal selection probabilities based on an appropriate auxiliary variable, and selection with or without replacement. In the present study, the effects of the choice of the auxiliary variable, of the deletion of segments, and of the stratification of the tree crown on the sampling error were analyzed. In the analysis, trees of three species with complete crown data were used: Norway spruce (Picea abies [L.] Karst.), European mountain ash (Sorbus aucuparia L.) and Monterey pine (Pinus radiata D. Don). The results clearly indicate that the choice of the auxiliary variable affects both the precision of the estimate and the distribution of the samples within the crown. The smallest variances were achieved with the diameter of the segments to the power of 2.0 (Norway spruce) up to 2.55 (European mountain ash) as an auxiliary variable. Deletion of great sized segments yielded higher precision in almost all cases. Stratification of the crown was not generally successful in terms of a reduction of sampling errors. Only in combination with deletion of stem segments, a clear improvement in the precision of the estimate could be observed, depending on species, tree, target variable, and definition and number of strata on the tree. For the trees divided into two strata, the decrease in the coefficient of variation of the estimate lies between 10% (European mountain ash) and 80% (old pine) compared with that for unstratified trees. For three strata, the decrease varied between 50% (European mountain ash) and 85% (old pine).

Keywords

• randomized branch sampling
• multistage sampling
• unequal selection probabilities
• auxiliary variables
• pps-sampling