Lutz Fehrmann

Comparison of linear and mixed-effect regression models and a k-nearest neighbour approach for estimation of single-tree biomass

Allometric biomass models for individual trees are typically specific to site conditions and species. They are often based on a low number of easily measured independent variables, such as diameter in breast height and tree height. A prevalence of small data sets and few study sites limit their application domain. One challenge in the context of the actual climate change discussion is to find more general approaches for reliable biomass estimation. Therefore, nonparametric approaches can be seen as an alternative to commonly used regression models. In this pilot study, we compare a nonparametric instance-based k-nearest neighbour (k-NN) approach to estimate single-tree biomass with predictions from linear mixed-effect regression models and subsidiary linear models using data sets of Norway spruce (Picea abies (L.) Karst.) and Scots pine (Pinus sylvestris L.) from the National Forest Inventory of Finland. For all trees, the predictor variables diameter at breast height and tree height are known. The data s...

Triangulation based inclusion probabilities: a design-unbiased sampling approach

A probabilistic sampling approach for design-unbiased estimation of area-related quantitative characteristics of spatially dispersed population units is proposed. The developed field protocol includes a fixed number of 3 units per sampling location and is based on partial triangulations over their natural neighbors to derive the individual inclusion probabilities. The performance of the proposed design is tested in comparison to fixed area sample plots in a simulation with two forest stands. Evaluation is based on a general approach for areal sampling in which all characteristics of the resulting population of possible samples is derived analytically by means of a complete tessellation of the areal sampling frame. The example simulation shows promising results. Expected errors under this design are comparable to sample plots including a much greater number of trees per plot.

On the site-level suitability of biomass models

Tree biomass estimates in environmental studies are based on allometric models, which are known to vary with species, site, and other forest characteristics. The UNFCCC published a guideline to evaluate the appropriateness of biomass models before application, but it misleads the concept of model suitability and does also allow the selection of models with systematic deviations in the predictions. Here we present an alternative approach based on non-parametric techniques. The approach was tested for pure stands, but this methodology is likewise applicable to mixed forests. The proposed tests perform well in rejecting a model if the predictions for the targeted population are systematically deviant. It is demonstrated that the suitability of an allometric model is a matter of accuracy. The proposed method also allows localizing the model. The presented approach can improve the transparency of global forest monitoring systems and can be implemented with relatively small effort. Biomass model suitability is often judged by the fitting statistics of the model.Characteristics of the local population are usually ignored in suitability checking.We propose statistical test to evaluate the suitability of biomass models.Biomass model suitability is a matter of accuracy and not precision.A new approach to evaluate model suitability based on statistical tests is presented.

Development of a Compatible Taper Function and Stand-Level Merchantable Volume Model for Chinese Fir Plantations

Chinese fir (Cunninghamia lanceolata [Lamb.] Hook) is one of the most important plantation tree species in China with good timber quality and fast growth. It covers an area of 8.54 million hectare, which corresponds to 21% of the total plantation area and 32% of total plantation volume in China. With the increasing market demand, an accurate estimation and prediction of merchantable volume at tree- and stand-level is becoming important for plantation owners. Although there are many studies on the total tree volume estimation from allometric models, these allometric models cannot predict tree- and stand-level merchantable volume at any merchantable height, and the stand-level merchantable volume model was not seen yet in Chinese fir plantations. This study aimed to develop (1) a compatible taper function for tree-level merchantable volume estimation, and (2) a stand-level merchantable volume model for Chinese fir plantations. This “taper function system” consisted in a taper function, a merchantable volume equation and a total tree volume equation. 46 Chinese fir trees were felled to develop the taper function in Shitai County, Anhui province, China. A second-order continuous autoregressive error structure corrected the inherent serial autocorrelation of different observations in one tree. The taper function and volume equations were fitted simultaneously after autocorrelation correction. The compatible taper function fitted well to our data and had very good performances in diameter and total tree volume prediction. The stand-level merchantable volume equation based on the ratio approach was developed using basal area, dominant height, quadratic mean diameter and top diameter (ranging from 0 to 30 cm) as independent variables. At last, a total stand-level volume table using stand basal area and dominant height as variables was proposed for local forest managers to simplify the stand volume estimation.

Using terrestrial laser scanning to support biomass estimation in densely stocked young tree plantations

The total area of short-rotation tree plantations is increasing globally, one reason being the need to grow sustainable biomass for bio-energy production. Such stands are usually established with a very high stem density, and inventories for biomass estimation require the adaptation of traditional methods. In this study, we tested a novel, efficient, and non-destructive method for biomass estimation relevant to a high-density, short-rotation oak stand of about 16,500 stems ha−1. We used terrestrial laser scanning (TLS) in a single-scan design to measure diameter at breast height (DBH) of all trees within 2 m-radius sample plots. Allometric models were then used to predict the tree biomass from their diameter. Biomass estimates were compared to the true biomass determined after harvesting of the sample plots. Mean absolute error and mean relative error were 12.9 kg and 16.4%, respectively, and the coefficient of determination of the relationship between traditionally measured and scan-based biomass was r2 = 0.65 (p < 0.001). This TLS-based approach is promising as it considerably reduces fieldwork efforts in dense stands compared with traditional diameter tallying by calipers or tapes.

A new design for sampling with adaptive sample plots

Adaptive cluster sampling (ACS) is a sampling technique for sampling rare and geographically clustered populations. Aiming to enhance the practicability of ACS while maintaining some of its major characteristics, an adaptive sample plot design is introduced in this study which facilitates field work compared to “standard” ACS. The plot design is based on a conditional plot expansion: a larger plot (by a pre-defined plot size factor) is installed at a sample point instead of the smaller initial plot if a pre-defined condition is fulfilled. This study provides insight to the statistical performance of the proposed adaptive plot design. A design-unbiased estimator is presented and used on six artificial and one real tree position maps to estimate density (number of objects per ha). The performance in terms of coefficient of variation is compared to the non-adaptive alternative without a conditional expansion of plot size. The adaptive plot design was superior in all cases but the improvement depends on (1) the structure of the sampled population, (2) the plot size factor and (3) the critical value (the minimum number of objects triggering an expansion). For some spatial arrangements the improvement is relatively small. The adaptive design may be particularly attractive for sampling in rare and compactly clustered populations with an appropriately chosen plot size factor.

ABOVEGROUND AND BELOWGROUND BIOMASS AND CARBON ESTIMATES FOR CLONAL EUCALYPTUS TREES IN SOUTHEAST BRAZIL

Eucalyptus plantations represent a short term and cost efficient alternative for sequestrating carbon dioxide from the atmosphere. Despite the known potential of forest plantations of fast growing species to store carbon in the biomass, there are relatively few studies including precise estimates of the amount of carbon in these plantations. In this study it was determined the carbon content in the stems, branches, leaves and roots of a clonal Eucalyptus grandis plantation in the Southeast of Brazil. We developed allometric equations to estimate the total amount of carbon and total biomass, and produced an estimate of the carbon stock in the stand level. Altogether, 23 sample trees were selected for aboveground biomass assessment. The roots of 9 of the 23 sampled trees were partially excavated to assess the belowground biomass at a single- tree level. Two models with DBH, H and DBH 2 H were tested. The average relative share of carbon content in the stem, branch, leaf and root compartments was 44.6%, 43.0%, 46.1% and 37.8%, respectively, which is smaller than the generic value commonly used (50%). The best-fit allometric equations to estimate the total amount of carbon and total biomass had DBH 2 H as independent variable. The root-to-shoot ratio was relatively stable (C.V. = 27.5%) probably because the sub-sample was composed of clones. Total stand carbon stock in the Eucalyptus plantation was estimated to be 73.38 MgC ha -1 , which is within the carbon stock

Local Parameter Estimation of Topographic Normalization for Forest Type Classification

Radiometric distortions caused by rugged terrain make the classification of forest types from satellite imagery a challenge. Various band-specific topographic normalization models are expected to eliminate or reduce these effects. The quality of these models also depends on the approach to estimate empirical parameters. Generally, a global estimation of these parameters from a whole satellite image is simple, but it may tend to overcorrection, particularly for larger areas. A land-cover-specific method usually performs better, but it requires obtaining a priori land classification, which presents another challenge in many cases. Empirical parameters can be directly estimated from local pixels in a given window. In this letter, we propose and evaluate a central-pixel-based parameter estimation method for topographic normalization using local window pixels. We tested the method with Landsat 8 imagery and the Advanced Spaceborne Thermal Emission and Reflection Radiometer Global Digital Elevation Model (ASTER GDEM) in very rough terrain with diverse forest types. Visual comparison and statistical analyses showed that the proposed method performed better at a range of window sizes compared with an uncorrected image or with a global parameter estimation approach. The intraclass spectral variability of each forest type has been reduced significantly, and it can yield higher accuracy of forest type classification. The proposed method does not require the a priori knowledge of land covers. Its simplicity and robustness suggest that this method has the potential to be a standard preprocessing approach for optical satellite imagery, particularly for rough terrain.

Two neighborhood-free plot designs for adaptive sampling of forests

Adaptive cluster sampling (ACS) has the potential of being superior for sampling rare and geographically clustered populations. However, setting up an efficient ACS design is challenging. In this study, two adaptive plot designs are proposed as alternatives: one for fixed-area plot sampling and the other for relascope sampling (also known as variable radius plot sampling). Neither includes a neighborhood search which makes them much easier to execute. They do, however, include a conditional plot expansion: at a sample point where a predefined condition is satisfied, sampling is extended to a predefined larger cluster-plot or a larger relascope plot. Design-unbiased estimators of population total and its variance are derived for each proposed design, and they are applied to ten artificial and one real tree position maps to estimate density (number of trees per ha) and basal area (the cross-sectional area of a tree stem at breast height) per hectare. The performances—in terms of relative standard error (SE%)—of the proposed designs and their non-adaptive alternatives are compared. The adaptive plot designs were superior for the clustered populations in all cases of equal sample sizes and in some cases of equal area of sample plots. However, the improvement depends on: (1) the plot size factor; (2) the critical value (the minimum number of trees triggering an expansion); (3) the subplot distance for the adapted cluster-plots, and (4) the spatial arrangement of the sampled population. For some spatial arrangements, the improvement is relatively small. The adaptive designs may be particularly attractive for sampling in rare and compactly clustered populations with critical value of 1, subplot distance equal to the diameter of initial circular plots, or plot size factor of 2.5 for an initial basal area factor of 2.

Moving window-based topographic normalization of optical satellite imagery for forest mapping in mountainous terrain

Relief has a significant impact on image classification in mountain areas because slope and aspect of the terrain together with the illumination geometry (solar zenith, solar azimuth angle and sensor position) make that one and the same land cover class has markedly different spectral signatures within one satellite image. Topographic normalization models help reduce intra-class spectral variability. This study proposes and evaluates a moving window-based rotation-correction topographic normalization model. We tested the algorithm with the latest Landsat 8 imagery in a region with very high forest cover in Shitai County, Anhui Province, China, which is characterized by a rough terrain with very steep slopes. Visual comparison and statistical analysis showed that the proposed method yielded better performance at a range of window sizes compared to uncorrected data or global correction methods. The heterogeneity of spectral signatures inside each land cover class could significantly be reduced, which may be partly due to the fact that a site-specific parameterization was used. Model performance was relatively stable over the tested range of window sizes. This new method for parameter estimation for topographic normalization is simple and straightforward, making this technique a suitable option for standard pre-processing of optical satellite imagery.