Comparison of plot designs
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This section is largely based on the paper Kleinn and Vilcko (2006a<ref name=KleinnVilcko06a>Kleinn C. and F Vilčko. 2006a. A new empirical approximation for estimation in k-tree sampling. Forest Ecology and Management 237(2):522-533</ref>). | This section is largely based on the paper Kleinn and Vilcko (2006a<ref name=KleinnVilcko06a>Kleinn C. and F Vilčko. 2006a. A new empirical approximation for estimation in k-tree sampling. Forest Ecology and Management 237(2):522-533</ref>). | ||
| + | In [[forest inventory]] planning one needs to define the [[:Category:Plot design|plot type]] to be used. In many cases there are traditions and conventions and not much is thought about the choice of the plot type. | ||
| − | + | The different plot types (1) [[fixed area plots]], (2) [[Bitterlich sampling|Bitterlich plots]] and (3) [[distance based plots]] carry different practical issues of implementation but also different statistical properties. Here, we wish to look at the statistical properties and illustrate them with a simulation study. A tree map of from the Miombo woodlands in Northern Zambia served as [[sampling frame]]. As all tree positions were exactly known by their grid coordinates, simulation of different plot design could be carried out. There, 4969 trees were mapped on an area of 13.44 ha (369.72 trees/ha) with a basal area per hectare of 16.37 m²/ha. | |
| − | The different plot types (1) fixed area plots, (2) Bitterlich plots and (3) distance based | + | |
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| − | In this simulation study, we compared sampling with | + | In this simulation study, we compared sampling with fixed area plots, Bitterlich sampling and distance-based plots. Target variables were [[density]] (number of stems per hectare) and [[basal area]] per hectare. For the distance-based methods we used the empirical estimators (see [[Distance based plots|distance-based plots]]) presented in Kleinn and Vilcko (2006a<ref name=KleinnVilcko06a /ref>) and Eberhardt (1967<ref name=Eberhardt67>Eberhardt LL. 1967. Some developments in distance sampling. Biometrics (23):207-216.</ref>), whereas the first listed one was rated as the most consistently best performer by Magnussen et al. (2008<ref name=Magnussen08>Magnussen S, C Kleinn and N Picard. 2008. Two new density estimators for distance sampling. European Journal of Forest Research 127:213-224.</ref>). |
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| − | In order to make the plot types comparable in terms of expected field effort, we compared ''k''-tree sampling with both fixed area circular | + | In order to make the plot types comparable in terms of expected field effort, we compared ''k''-tree sampling with both fixed area circular plots and [[relascope]] plots that do, on average, yield ''k'' trees per sample point. With 369.72 trees per hectare in our maps, the fixed plot area ''a<sub>k</sub>'' for an expected number of ''k'' trees per sample plot is |
:<math>a_k = \frac{k}{369.72} * 10000 m^2</math>. | :<math>a_k = \frac{k}{369.72} * 10000 m^2</math>. | ||
| − | For relascope sampling, the basal area factor | + | For relascope sampling, the basal area factor <math>baf_k</math> was defined such that the expected number of counted trees is ''k'', that is |
:<math>baf_k = \frac {16.37}{k} \frac {m^2}{ha}</math>. | :<math>baf_k = \frac {16.37}{k} \frac {m^2}{ha}</math>. | ||
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==References== | ==References== | ||
Revision as of 22:26, 9 March 2011
This section is largely based on the paper Kleinn and Vilcko (2006a[1]).
In forest inventory planning one needs to define the plot type to be used. In many cases there are traditions and conventions and not much is thought about the choice of the plot type.
The different plot types (1) fixed area plots, (2) Bitterlich plots and (3) distance based plots carry different practical issues of implementation but also different statistical properties. Here, we wish to look at the statistical properties and illustrate them with a simulation study. A tree map of from the Miombo woodlands in Northern Zambia served as sampling frame. As all tree positions were exactly known by their grid coordinates, simulation of different plot design could be carried out. There, 4969 trees were mapped on an area of 13.44 ha (369.72 trees/ha) with a basal area per hectare of 16.37 m²/ha.
In this simulation study, we compared sampling with fixed area plots, Bitterlich sampling and distance-based plots. Target variables were density (number of stems per hectare) and basal area per hectare. For the distance-based methods we used the empirical estimators (see distance-based plots) presented in Kleinn and Vilcko (2006aCite error: Closing </ref> missing for <ref> tag), whereas the first listed one was rated as the most consistently best performer by Magnussen et al. (2008[2]).
In order to make the plot types comparable in terms of expected field effort, we compared k-tree sampling with both fixed area circular plots and relascope plots that do, on average, yield k trees per sample point. With 369.72 trees per hectare in our maps, the fixed plot area ak for an expected number of k trees per sample plot is
\[a_k = \frac{k}{369.72} * 10000 m^2\].
For relascope sampling, the basal area factor \(baf_k\) was defined such that the expected number of counted trees is k, that is
\[baf_k = \frac {16.37}{k} \frac {m^2}{ha}\].
