Working Group Biometric Models – Sampling Techniques, Spatial Statistics and Regionalization
Current and finished research projects since 2005
- Clustered subsampling of double sampling for stratification and growth model based updates of past forest inventories
- Development of a Point Transect technique for estimating deadwood abundance in forests
- Measurement of gap patterns by digital height models and applications in beech forests of different utilization intensity
- Small area estimation of stand tables using data of large-scale forest inventories
- Conditional prediction errors for point and area prediction in sample based inventories in forests
- Regionalized estimation of yield and increment in district inventories
- Spatial, GIS-based analysis of game densities estimated by line-transect sampling
Clustered subsampling of double sampling for stratification and growth model based updates of past forest inventories
(doctoral student: MSc Nikolas von Lüpke)
Grant: DFG
Summary:
Double Sampling for Stratification is a sampling design that is widely used for forest and resource inventories worldwide and, particularly, well established for periodic forest inventories of districts in public and private forests in Germany. Spatially clustered subsampling of second-phase units, actually representing a third phase of sampling, can be expected to reduce travelling costs, but will also decrease precision of estimates. Therefore, the proposed project is intended to develop estimators for totals and per hectare values of usual target variables in forest inventories as well as related sampling errors under that new three-phase sampling design. Using real data the trade-off between precision and amount of clustering will be analyzed. A special focus will be on temporary regional or state-wide inventories based on previous double sampling district inventories. In this case additional precision can be gained by updating the previous inventories using growth models. These growth predictions shall be combined with the sample based estimator to form a composite estimator of higher precision.
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Development of a Point Transect technique for estimating deadwood abundance in forests
(doctoral student: MSc Tim Ritter)
Grant: DFG
Summary:
In managed forests the occurrence of deadwood can be regarded as a stochastically rare event with high variance at a small scale and strong clumping (Meyer 1999). Existing sampling techniques (Fixed Radius Sample Plots, Angle Count Sampling, Line Intersect Sampling) do not regard this fact. Point Transect Sampling basically suits better, because at a sample point it does not only regard objects of dead wood within a limited sample plot, but (as a matter of principle) all objects which can be seen from that point. Within the framework of a project funded by the German Research Foundation (DFG), a Point Transect Sampling technique for the estimation of deadwood quantity, which can effectively be integrated into conventional inventories, is to be developed. Based upon a considerable large inventory the new technique is to be compared with existing ones regarding precision and costs.
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Measurement of gap patterns by digital height models and applications in beech forests of different utilization intensity
(doctoral student: M.Sc. Robert Nuske)
Grant: Deutsche Bundesstiftung Umwelt
Summary:
Nature oriented forest management tries to emulate natural disturbances by its silvicultural treatments. While the disparities between natural disturbance and silviculture can never be fully overcome, foresters try to mimic the intensity, frequency, and spatial patterns created by a natural disturbance regime. To assess the silvicultural management one needs meaningful parameters to characterize managed forest as well as comparable (near-) natural forest. This study focuses on the spatial distribution of gaps in the forest canopy which are typically caused by small-scale, low intensity disturbances.
The following map shows the workflow for gap delineation.
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Small area estimation of stand tables using data of large-scale forest inventories
(doctoral student: Dipl. Forst.-Ing. ETH Daniel Bierer)
Grant: Swiss Federal Research Institute WSL
finished 2008
Summary:
One of the most important parameters for characterizing a forest stand is its stand table. In this thesis, the problem of estimating stand tables in stands with only a few sample plots (i.e. in small areas) is considered. An alternative estimation strategy to the common design-unbiased approach is proposed and it will be shown that drastic savings in mean squared error can be achieved by relaxing the restriction of unbiasedness. In contrast to previous works on small area estimation of stand tables, a composite estimator is suggested that takes into account the mean squared errors instead of only the variances of its component estimators. As component estimators serve the common design-unbiased estimator and a synthetic estimator that links external data by kernel smoothing. The weighting scheme of the proposed composite estimator is based on a weight estimator for estimating Schaible’s approximation to the optimal constant weighting scheme. The results of the thesis are promising in that the suggested composite estimator performs well also in stands for which the synthetic component estimator is highly biased. A further appealing property indicated by the results of the thesis is the general applicability of the proposed estimator, i.e. it performs well in mixed and unmixed stands as well as in even and uneven aged stands. Furthermore, the diameter distribution of the subject stand has not to look like a presumed parametric distribution such as the Weibull distribution, i.e. it can have also, for instance, a multimodal distribution. Finally, the suggested estimator is also attractive in terms of simplicity: only (weighted) averages have to be build and no numerical methods for optimization or integrating have to be applied. All these properties make the estimator appropriate for the practical use in forestry.
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Conditional prediction errors for point and area prediction in sample based inventories in forests
(doctoral student: M.Sc. Andreas Dominik Cullmann)
Grant: DFG
finished 2007
Summary:
For prediction in a gaussian random field we give an explicit formulation of the conditional mean squared prediction error. If the prediction method is ordinary kriging we find that this error in most applications is likely to be very close to the ordinary kriging variance. This is additionally demostrated based on a case study. Finally, we discuss the difference between these two errors compared to the error introduced by using estimated instead of true covariance parameters.
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Regionalized estimation of yield and increment in district inventories
(doctoral student: Dipl.-Forstw. Arne Nothdurft)
finished 2007
Summary:
A non-linear hierarchical mixed model approach is used to describe height growth of Norway spruce from longitudinal measurements. The parameter variation in the model was divided into unknown random effects, fixed effects and covariate-dependent effects in order to model tree height growth. The values for fixed effect parameters and the variance-covariance matrix of random effects were estimated. Covariates could only explain up to 10% of parameter variability. Height curves were calibrated by means of BLUPs for the unknown random effects using prior height measurements and evaluated using a separate data set. The resulting curves had a small error variance and plausible shapes.
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Spatial, GIS-based analysis of game densities estimated by line-transect sampling
(doctoral student: M.Sc. Felix Mader)
Grant: Land Niedersachsen (Graduiertenförderung) and DAAD
finished 2007
Summary:
Modelling of game counts (n) per transect segment depending on local geographic information (spatial covariates) using generalized linear models (loglinear model, Poisson-Regression) with spatially autocorrelated errors. Spatial predictions of counts are realized by a geostatistical universal kriging approach.
left: derivation of counts per segment (transect: blue); middle: intersection of segments with other information layers (covariates: elevation, vegetation density and type, distance to water, road etc.); right: predictions of local abundance (darker is higher), blue lines=transects, circles: clusters counted (bigger means larger cluster); equations: (1) estimation of expected counts with offset-term for different segment sizes; (2) covariance matrix among observed positions including nugget-effect and over-dispersion; (3) spatial prediction.
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