406
• Stratified random sampling (Fig. 15.3b): The area is divided into subareas (strata;
small squares), and simple random sampling is performed in each stratum. This
reduces the variance at the same sampling effort or the sampling effort at the
same variance. Strata can be based on maps of environmental parameters (soil
types, vegetation types, aspect, etc.) and can have any shape. Cost functions can
be included for determining sample size. Generally, more points are sampled in
larger, more variable, or cheaper to sample strata.
• Two-stage sampling (Fig. 15.3c): The area is divided into subareas (also called
principle units, PUs), but only a random subset of these subareas is sampled;
within a subarea, sample points are selected with equal probability. This clustering of points is more time-efficient but less precise than simple random sampling.
• Cluster sampling (Fig. 15.3d): Predefined sets of points (clusters) are sampled.
The starting point of each cluster is selected at random; the geometry of the cluster is independent of the starting point (e.g., transects with equidistant points
extending in opposite, predefined directions from the starting point). The regularity of the clusters makes sampling more time-efficient but less precise than
simple random sampling.
• Systematic sampling (Fig. 15.3e): Similar to cluster sampling, a predefined set of
points is selected at random, but only one cluster is selected (e.g., a random grid);
interference with periodic variations can be avoided by combining systematic
sampling with a random element (e.g., two-stage sampling combined with cluster sampling).
• Spatial systematic sampling (Fig. 15.3f): Randomization restrictions are used at
the coordinate level; the area is split into strata, and one point is selected at random. The points in the other strata are not selected independently but follow a
specific model (e.g., a Markov chain).
It is good practice to conduct a sensitivity analysis for estimating the sample size
needed to detect differences in the parameter of interest with the desired level of
confidence (Johannsen and Daughtry 2009). The sample size needed to estimate a
statistical property with a chosen probability depends on the sampling scheme, the
desired error rate, and the variation of the ecosystem property of interest (which can
be approximated from existing data or a pilot study or based on literature values and
experience). Details for estimating sample sizes for the sampling designs mentioned
above are given by De Gruijter (1999). However, error rates of spectroscopic models of vegetation characteristics also depend on the measurement accuracies of vegetation and spectral data and the tightness of the association between the property of
interest and spectral data. For example, as a rule of thumb, the smaller the amount
of the chemical compound of interest and the less precise the laboratory method
used to determine that compound, the more samples will be needed for building a
sound model. Similarly, for classification models, the number of samples needed to
differentiate classes with a desired accuracy will depend on intra- and interclass
variation or the distinctiveness of classes. In other words, when projecting samples
from different classes into spectral (or more generally, feature) space, model accuracy for class differentiation depends on the number of classes, the spread of the
A. K. Schweiger
• Stratified random sampling (Fig. 15.3b): The area is divided into subareas (strata;
small squares), and simple random sampling is performed in each stratum. This
reduces the variance at the same sampling effort or the sampling effort at the
same variance. Strata can be based on maps of environmental parameters (soil
types, vegetation types, aspect, etc.) and can have any shape. Cost functions can
be included for determining sample size. Generally, more points are sampled in
larger, more variable, or cheaper to sample strata.
• Two-stage sampling (Fig. 15.3c): The area is divided into subareas (also called
principle units, PUs), but only a random subset of these subareas is sampled;
within a subarea, sample points are selected with equal probability. This clustering of points is more time-efficient but less precise than simple random sampling.
• Cluster sampling (Fig. 15.3d): Predefined sets of points (clusters) are sampled.
The starting point of each cluster is selected at random; the geometry of the cluster is independent of the starting point (e.g., transects with equidistant points
extending in opposite, predefined directions from the starting point). The regularity of the clusters makes sampling more time-efficient but less precise than
simple random sampling.
• Systematic sampling (Fig. 15.3e): Similar to cluster sampling, a predefined set of
points is selected at random, but only one cluster is selected (e.g., a random grid);
interference with periodic variations can be avoided by combining systematic
sampling with a random element (e.g., two-stage sampling combined with cluster sampling).
• Spatial systematic sampling (Fig. 15.3f): Randomization restrictions are used at
the coordinate level; the area is split into strata, and one point is selected at random. The points in the other strata are not selected independently but follow a
specific model (e.g., a Markov chain).
It is good practice to conduct a sensitivity analysis for estimating the sample size
needed to detect differences in the parameter of interest with the desired level of
confidence (Johannsen and Daughtry 2009). The sample size needed to estimate a
statistical property with a chosen probability depends on the sampling scheme, the
desired error rate, and the variation of the ecosystem property of interest (which can
be approximated from existing data or a pilot study or based on literature values and
experience). Details for estimating sample sizes for the sampling designs mentioned
above are given by De Gruijter (1999). However, error rates of spectroscopic models of vegetation characteristics also depend on the measurement accuracies of vegetation and spectral data and the tightness of the association between the property of
interest and spectral data. For example, as a rule of thumb, the smaller the amount
of the chemical compound of interest and the less precise the laboratory method
used to determine that compound, the more samples will be needed for building a
sound model. Similarly, for classification models, the number of samples needed to
differentiate classes with a desired accuracy will depend on intra- and interclass
variation or the distinctiveness of classes. In other words, when projecting samples
from different classes into spectral (or more generally, feature) space, model accuracy for class differentiation depends on the number of classes, the spread of the
A. K. Schweiger