Two-phase sampling for stratification in the Swiss National Forest Inventory

The Swiss National Forest Inventory (NFI) provides estimates of states and changes in Swiss forests based on data collected on permanent sample plots across the forested area of Switzerland (www.lfi.ch/en). To obtain representative estimates at regional scales, the data from the unique sample plots must be upscaled using statistical methods. To perform this upscaling, the Swiss NFI relies on the concept of two-phase sampling for stratification. The calculations are done within the software “Data Analysis Application” (DAA) developed by the Swiss NFI and hosted at WSL. 

This document originated from a DAA validation process carried out by Jeanne Portier, Brigitte Rohner and Anne Herold in 2023. It has since evolved into this comprehensive documentation designed to describe the DAA and make its concept and application accessible to a broader audience compared to previous documentations with a more technical focus. 

This document is structured in three chapters: 

• Chapter I is about the theory and concepts behind the two-phase sampling for stratification and the DAA. It aims at defining and describing the basic concepts, the terminology and the statistical notation that need to be well understood to comprehend the functioning of the DAA. It relies mainly on section 20.4 in Traub et al. (2019), on the various chapters of the html NAFIDAS DAA documentation that is accessible internally by WSL employees at file://wsl.ch/memo/fe/prj/LFI/Alle/NAFIDAS/DAA_Python/daadoc/index.html, and on the set of equations formulated by Adrian Lanz, which are provided in Chapter III of this document.
• Chapter II deals with the translation of the theory and concepts introduced in Chapter I into the SQL code at the core of the DAA. It aims at supporting the understanding of the code and workflow from the data retrieval to the final result tables. It is therefore describing how, in practice, the DAA works using examples of test cases that are associated with parameter sets (criteria that users must define to obtain the results table they are interested in).
• Chapter III is a reproduction of two internal documents developed by Adrian Lanz in 2017, which detail the mathematical foundation on which the DAA relies. The first document describes state estimation while the second document explains change estimation. 

It is important to note that the DAA is in constant development. Although the conceptual framework described in this document should remain valid on the long-term, its implementation in the code of the DAA is constantly improved by the programmer for practical, computational, reproducibility, or readability reasons. The implementation of additional features such as panel analysis leads to changes and enhancements of the DAA. In addition, maintenance and performance issues trigger adaptations. Consequently, this can result in some differences between the code described in Chapter II of this document and the actual code of the DAA at a later point in time. The final results should not be affected by any of these changes.