A square-grid sampling support to reconcile systematicity and adaptivity in the periodic spatial survey of natural resources

Abstract Spatially balanced sampling is the most efficient design for surveying continuous or spatial populations across space. The spatial sampling of large-scale surveys is mostly based on grids, whose properties drive, and potentially limit, the possibilities of building flexible samples. Conciliating spatial balance and flexibility remains difficult. In particular, periodicity causes high constraints to the sampling particularly when an increase in the frequency of the information delivery is sought. Sampling stratification of adaptive sampling intensity also conflicts the grid-based approach.We show that square grids have geometric homothetic properties that enable to answer these needs by supporting nested hierarchical subgrid sets. These properties can be exploited to cope with both spatial flexibility in the sampling effort and spatio-temporal coordination of samples. Whereas some surveys seemingly do exploit these properties practically across the world, no formal development has been made available in the survey sampling literature across fields of applications.Here we therefore define and demonstrate these properties, and show how they can be used to produce nested hierarchical grids compatible with multiple periodicity values of interest to natural monitoring, and with adapting sampling intensity across space and time. We also provide an original extension of this framework, intended to tune the sampling effort gradually while preserving spatial systematicity. We use the French National Forest Inventory survey to illustrate these properties and their use in a large-scale repeated inventory. We show the flexibility and diversity of sampling schemes that can be initiated with square grids and the limits of their use.