404
limits of a model’s applicability. Field visits are ideal for investigating how environmental context and time of year influence model performance and for determining
under which conditions a model performs well or poorly.
15.2.3.3 Sampling Design
A good approach to deciding on a sampling design and to planning data collection
for remote sensing of plant biodiversity in general is to start at the end and think
about (i) what type of modeling result or product would be most useful with respect
to the research question (such as a hypothesis test at a given significance level or a
map of a variable with a given accuracy), (ii) what kind of data analysis would lead
to that result, (iii) what data properties are needed for the specific analysis, and (iv)
how these data can be collected efficiently (De Gruijter 1999).
In a spatial context, a sampling design assigns a probability of selection to any
set of points in a research area, while a sampling strategy is defined as the combination of sampling design and the estimator of the variable of interest, for which statistical quality measures (such as bias or variance) can be evaluated (De Gruijter
1999). Sampling designs can be model-based or design-based; the two approaches
use different sources of randomness for sample selection and model inferences
(Brus and DeGruijter 1993; Domburg et al. 1997). Harnessing as much information
about spatial variation as possible, including maps of the study region and theory
about spatial patterns, facilitates finding an efficient sampling design for both
model- and design-based sampling strategies.
Model-based sampling is based on geostatistical theory and evaluates uncertainties by using a fixed set of sampling points while the pattern of the values of interest
varies according to a defined random model of spatial variation (De Gruijter 1999).
Model-based sampling strategies are, for example, used for kriging, a spatial interpolation method that uses measured point values to estimate unknown points on a
surface. The ideal situation for using a model-based sampling scheme is when the
desired result should be the prediction of values at individual points or of the entire
spatial distribution of values in the research area (i.e., a map), when a large number
of sample points can be afforded to calculate the variogram (~100–150 sample
points, Webster and Oliver 1992), and, most importantly, when a reliable model of
spatial variation is available, the spatial autocorrelation is high, and there is a strong
association between the model of spatial variation and the variable of interest. The
association between a geostatistical model and the variable of interest is particularly
important, because the final inferences about the spatial distribution of the variable
of interest are based on the model of spatial variation (De Gruijter 1999; Atkinson
1999). However, it is often difficult to decide if model assumptions are acceptable
because several decisions for defining the spatial structure (e.g., about stationarity,
isotropy, and the variogram) are subjective (Brus and DeGruijter 1993).
Ecological systems are often too complex to use model-based inference with
much confidence (Theobald et al. 2007). Nevertheless, if a tight relationship
between a geostatistical model and nature is expected, model-based sampling
A. K. Schweiger
limits of a model’s applicability. Field visits are ideal for investigating how environmental context and time of year influence model performance and for determining
under which conditions a model performs well or poorly.
15.2.3.3 Sampling Design
A good approach to deciding on a sampling design and to planning data collection
for remote sensing of plant biodiversity in general is to start at the end and think
about (i) what type of modeling result or product would be most useful with respect
to the research question (such as a hypothesis test at a given significance level or a
map of a variable with a given accuracy), (ii) what kind of data analysis would lead
to that result, (iii) what data properties are needed for the specific analysis, and (iv)
how these data can be collected efficiently (De Gruijter 1999).
In a spatial context, a sampling design assigns a probability of selection to any
set of points in a research area, while a sampling strategy is defined as the combination of sampling design and the estimator of the variable of interest, for which statistical quality measures (such as bias or variance) can be evaluated (De Gruijter
1999). Sampling designs can be model-based or design-based; the two approaches
use different sources of randomness for sample selection and model inferences
(Brus and DeGruijter 1993; Domburg et al. 1997). Harnessing as much information
about spatial variation as possible, including maps of the study region and theory
about spatial patterns, facilitates finding an efficient sampling design for both
model- and design-based sampling strategies.
Model-based sampling is based on geostatistical theory and evaluates uncertainties by using a fixed set of sampling points while the pattern of the values of interest
varies according to a defined random model of spatial variation (De Gruijter 1999).
Model-based sampling strategies are, for example, used for kriging, a spatial interpolation method that uses measured point values to estimate unknown points on a
surface. The ideal situation for using a model-based sampling scheme is when the
desired result should be the prediction of values at individual points or of the entire
spatial distribution of values in the research area (i.e., a map), when a large number
of sample points can be afforded to calculate the variogram (~100–150 sample
points, Webster and Oliver 1992), and, most importantly, when a reliable model of
spatial variation is available, the spatial autocorrelation is high, and there is a strong
association between the model of spatial variation and the variable of interest. The
association between a geostatistical model and the variable of interest is particularly
important, because the final inferences about the spatial distribution of the variable
of interest are based on the model of spatial variation (De Gruijter 1999; Atkinson
1999). However, it is often difficult to decide if model assumptions are acceptable
because several decisions for defining the spatial structure (e.g., about stationarity,
isotropy, and the variogram) are subjective (Brus and DeGruijter 1993).
Ecological systems are often too complex to use model-based inference with
much confidence (Theobald et al. 2007). Nevertheless, if a tight relationship
between a geostatistical model and nature is expected, model-based sampling
A. K. Schweiger