A Double-Sampling Extension of the German National Forest Inventory for Design-Based Small Area Estimation on Forest District Levels

Andreas Hill,Daniel Mandallaz,Joachim Langshausen

doi:10.3390/rs10071052

Abstract

The German National Forest Inventory consists of a systematic grid of permanent sample plots and provides a reliable evidence-based assessment of the state and the development of Germany’s forests on national and federal state level in a 10 year interval. However, the data have yet been scarcely used for estimation on smaller management levels such as forest districts due to insufficient sample sizes within the area of interests and the implied large estimation errors. In this study, we present a double-sampling extension to the existing German National Forest Inventory (NFI) that allows for the application of recently developed design-based small area regression estimators. We illustrate the implementation of the estimation procedure and evaluate its potential for future large-scale operational application by the example of timber volume estimation on two small-scale management levels (45 and 405 forest district units respectively) over the entire area of the federal German state of Rhineland-Palatinate. An airborne laserscanning (ALS) derived canopy height model and a tree species classification map based on satellite data were used as auxiliary data in an ordinary least square regression model to produce the timber volume predictions. The results support that the suggested double-sampling procedure can substantially increase estimation precision on both management levels: the two-phase estimators were able to reduce the variance of the one-phase simple random sampling estimator by 43% and 25% on average for the two management levels respectively.

Highlights

The German National Forest Inventory (NFI) provides reliable evidence-based and accurate information of the current state and the development of Germany’s forest over time
We further restricted the calculation of the Pseudo Small Area Estimator (PSMALL) and EXTPSYNTH estimator to small area units with a minimum terrestrial sample size of n2,G ≥ 4 to avoid unstable estimates
The study led to two major conclusions: (1) the EXTPSYNTH and PSMALL estimator generally achieved substantially smaller estimation errors on the two investigated forest district levels compared to the SRS estimator

Summary

Introduction

The German National Forest Inventory (NFI) provides reliable evidence-based and accurate information of the current state and the development of Germany’s forest over time. Sample sizes often drop dramatically when entering spatial units below the federal state level This is true for forest management levels such as forest districts for which the estimation uncertainties turn out to be unacceptably large due to the very limited number of sample plots within these units. For this reason, the German NFI data have not yet been extensively incorporated into operational planning on forest district management levels. In most German federal states, management strategies are still based on expert judgements from time-consuming standwise forest inventories (SFI), which are prone to systematic deviations [3] and do not provide any measure of uncertainty

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