Comparison of the local pivotal method and systematic sampling for national forest inventories

Background:The local pivotal method(LPM)utilizing auxiliary data in sample selection has recently been proposed as a sampling method for national forest inventories(NFIs).Its performance compared to simple random sampling(SRS)and LPM with geographical coordinates has produced promising results in simulation studies.In this simulation study we compared all these sampling methods to systematic sampling.The LPM samples were selected solely using the coordinates(LPMxy)or,in addition to that,auxiliary remote sensing-based forest variables(RS variables).We utilized field measurement data(NFI-field)and Multi-Source NFI(MS-NFI)maps as target data,and independent MS-NFI maps as auxiliary data.The designs were compared using relative efficiency(RE);a ratio of mean squared errors of the reference sampling design against the studied design.Applying a method in NFI also requires a proven estimator for the variance.Therefore,three different variance estimators were evaluated against the empirical variance of replications:1)an estimator corresponding to SRS;2)a Grafström-Schelin estimator repurposed for LPM;and 3)a Matérn estimator applied in the Finnish NFI for systematic sampling design.Results:The LPMxy was nearly comparable with the systematic design for the most target variables.The REs of the LPM designs utilizing auxiliary data compared to the systematic design varied between 0.74–1.18,according to the studied target variable.The SRS estimator for variance was expectedly the most biased and conservative estimator.Similarly,the Grafström-Schelin estimator gave overestimates in the case of LPMxy.When the RS variables were utilized as auxiliary data,the Grafström-Schelin estimates tended to underestimate the empirical variance.In systematic sampling the Matérn and Grafström-Schelin estimators performed for practical purposes equally.Conclusions:LPM optimized for a specific variable tended to be more efficient than systematic sampling,but all of the considered LPM designs were less efficient than the systematic sampling design for some target variables.The Grafström-Schelin estimator could be used as such with LPMxy or instead of the Matérn estimator in systematic sampling.Further studies of the variance estimators are needed if other auxiliary variables are to be used in LPM.

Sampling strategies for estimating forest cover from remote sensing-based two-stage inventories

Background: Remote sensing-based inventories are essential in estimating forest cover in tropical and subtropical countries, where ground inventories cannot be performed periodically at a large scale owing to high costs and forest inaccessibility(e.g. REDD projects) and are mandatory for constructing historical records that can be used as forest cover baselines. Given the conditions of such inventories, the survey area is partitioned into a grid of imagery segments of pre-fixed size where the proportion of forest cover can be measured within segments using a combination of unsupervised(automated or semi-automated) classification of satellite imagery and manual(i.e. visual on-screen)enhancements. Because visual on-screen operations are time expensive procedures, manual classification can be performed only for a sample of imagery segments selected at a first stage, while forest cover within each selected segment is estimated at a second stage from a sample of pixels selected within the segment. Because forest cover data arising from unsupervised satellite imagery classification may be freely available(e.g. Landsat imagery)over the entire survey area(wall-to-wall data) and are likely to be good proxies of manually classified cover data(sample data), they can be adopted as suitable auxiliary information.Methods: The question is how to choose the sample areas where manual classification is carried out. We have investigated the efficiency of one-per-stratum stratified sampling for selecting segments and pixels, where to carry out manual classification and to determine the efficiency of the difference estimator for exploiting auxiliary information at the estimation level. The performance of this strategy is compared with simple random sampling without replacement.Results: Our results were obtained theoretically from three artificial populations constructed from the Landsat classification(forest/non forest) available at pixel level for a study area located in central Italy, assuming three levels of error rates of the unsupervised classification of satellite imagery. The exploitation of map data as auxiliary information in the difference estimator proves to be highly effective with respect to the Horvitz-Thompson estimator,in which no auxiliary information is exploited. The use of one-per-stratum stratified sampling provides relevant improvement with respect to the use of simple random sampling without replacement.Conclusions: The use of one-per-stratum stratified sampling with many imagery segments selected at the first stage and few pixels within at the second stage- jointly with a difference estimator- proves to be a suitable strategy to estimate forest cover by remote sensing-based inventories.