A New Sampling Framework for Spatial Surveys with Application to the French National Forest Inventory

Abstract

Abstract The French National Forest Inventory (NFI) employs a two-stage two-phase sampling scheme summarized by the following key steps: first, the territory is divided into a spatial grid, and cells are randomly selected from this grid. Within the selected cells, additional random sampling of points is conducted. Subsequently, classification of the selected points is performed using auxiliary information from photo-interpretation. This information is used to draw a sub-sample that leads to field measurements. We evaluate the efficiency of the French NFI’s sampling design when the Horvitz–Thompson and post-stratified estimators for the total are used in the first and second phases, respectively. Given the complexity of the French NFI’s sampling design, a new theoretical framework is introduced for two-stage two-phase sampling schemes to facilitate design-based inference, combining inference methods for both finite and continuous populations. Horvitz–Thompson type estimators for the total and post-stratified estimators are proposed alongside variance estimators. Their performances are assessed through a simulation study, comparing the French NFI’s sampling design using alternative methods. The results indicate that the strategy formed by the French NFIs sampling design and proposed estimators may be effective in practice. The proposed framework is general and can be applied to other forest and environmental surveys.