Integrating remote sensing and past inventory data under the new annual design of the Swiss National Forest Inventory using three-phase design-based regression estimation

In 2009, the Swiss National Forest Inventory (NFI) turned from a periodic into an annual measurement design in which only one-ninth of the overall sample of permanent plots is measured every year. The reduction in sample size due to the implementation of the annual design results in an unacceptably large increase in variance when using the standard simple random sampling estimator. Thus, a flexible estimation procedure using two- and three-phase regression estimators is presented with a special focus on utilizing updating techniques to account for disturbances and growth and is applied to the second and third Swiss NFIs. The first phase consists of a dense sample of systematically distributed plots on a 500 m × 500 m grid for which auxiliary variables are obtained through the interpretation of aerial photographs. The second phase is an eightfold looser subgrid with terrestrial plot data collected from the past inventory, and the third and final phase consists of the three most recent annual subgrids with the current state of the target variable (stem volume). The proposed three-phase estimators reduce the increase in variance from 294% to 145% compared with the estimator based on the full periodic sample while remaining unbiased.