A three-phase sampling procedure for continuous forest inventory with partial re-measurement and updating of terrestrial sample plots

Abstract

For a current inventory using double sampling for stratification with a reduced second-phase sample size, compared with a previous inventory, we develop a threephase sampling procedure that exploits plot data from the previous inventory or their updates based on a growth model to increase precision. The three-phase procedure combines double sampling for stratification with a twophase regression estimator within strata. We consider sampling from an infinite population in the first phase. The combined estimator is tested in a case study using data from two consecutive inventories in four State Forest Districts in Lower Saxony, Germany. Data from a reduced number of sample plots from the second occasion are combined with (1) volumes from the first occasion or (2) growth simulations on the sample plots from the first occasion. The data from the previous inventory or their updates serve as the auxiliary variable for the regression estimator of the strata means of the target variable. This case study indicates a remarkable increase in precision and thereby an enormous cost-saving potential for reduced intermediate inventories in a periodic inventory design with both types of auxiliary variables.

A three-phase sampling extension of the generalized regression estimator with partially exhaustive information

“…The present work generalizes in many respects results (g-weight variances and small-area estimation) given in von Lüpke et al (2012), where the first component is generated by a categorical variable defining strata. In a slightly different context, Fattorini et al (2006) considers the case in which both components are generated by stratification and the null phase is performed with unaligned systematic sampling.…”

Multidimensional scaling of first-return airborne laser echoes for prediction and model-assisted estimation of a distribution of tree stem diameters

“…The information necessary for a design-based stratification may not be available until after the field sampling is complete (Andersen et al 2011;Saborowski et al 2010;Tomppo et al 2008;von Lüpke et al 2012). In this case, a model-assisted inference is still possible, but the additional variance generated from classification errors and random post-strata sample sizes must be taken into account (Cochran 1977, ch.…”

The R Package forestinventory: Design-Based Global and Small Area Estimations for Multiphase Forest Inventories

“…These predictions are produced by regression models that use explanatory variables derived from auxiliary data, commonly in the form of spatially exhaustive remote sensing data in the inventory area. Regression estimators using this concept can consider either one additional sample of plot locations (two-phase or double-sampling) or two additional samples available in different sample sizes (three-phase or triple-sampling), see Gregoire and Valentine (2007); Saborowski, Marx, Nagel, and Böckmann (2010); Mandallaz (2013a,d); von Lüpke, Hansen, and Saborowski (2012). Their application to existing forest inventory systems has already showed their efficiency in terms of cost reduction and gain in estimation precision (Breidenbach and Astrup 2012;von Lüpke and Saborowski 2014;Mandallaz, Breschan, and Hill 2013;Magnussen, Mandallaz, Breidenbach, Lanz, and Ginzler 2014;Massey, Mandallaz, and Lanz 2014).…”