Principles and methods of spatial sampling have been described briefly in Section 2.3.8 and some of the general concepts are explored in more detail in Dixon and Leach (1977, CATMOG 17) and more recently in Delmelle (2008). In this subsection we focus on 2D sampling, but similar concepts apply to 1-D (transect) and 3D (volumetric) sampling. When spatial samples are subsequently analyzed, many factors have to be taken into consideration, such as: sample size; how representative the sample is; whether the sample might be biased in any way; whether temporal factors are important; to what extent edge effects might influence the sample and the subsequent analysis; whether sampled data has been aggregated; how the data measurements were conducted (procedures and equipment); whether sampling order or arrangement is important; to what extent can the measured data samples be regarded as being from a population? In short, the full range of classical sampling issues must be considered coupled with some specifically spatial factors.

Amongst the most commonly applied sampling schemes are those based on point sampling within a regular grid framework. Figure 5‑1 illustrates a number of the simplest schemes based on 100 sample points. The first (Figure 5‑1A) shows a set of regularly spaced sample points in a sample square region. Systematic sampling of this type, and variants such as that shown in Figure 5‑1D in which the start points of each sequence are selected with a random offset, suffer from two major problems: (i) the sampling interval may coincide with some periodicity in the data being studied (or a related variable), resulting in substantial bias in the data; and (ii) the set of distances sampled is effectively fixed, hence important distance-related effects (such as dispersal, contagion etc.) may be missed entirely. Purely random sampling, as illustrated in Figure 5‑1B has attractions from a statistical perspective, but as can be seen, marked clustering occurs whilst some areas are left without any samples at all. A number of solutions to these problems are used, often based on combining the coverage benefits of regular sampling with the randomness of true random selection. Figure 5‑1C illustrates this class of sampling schemes, with each sample point being selected as a random offset from the regularly spaced (x,y) coordinates shown by the + symbols. The degree of offset determines how regular or how random the sampled points will be. Note that some clustering of samples may still occur with this approach. In each of these examples the point selection is carried out without any prior knowledge of the objects to be sampled or the environment from which the samples are to be drawn. If ancillary information is available, it may alter the design selected. For example, if samples are sought that represent certain landscape classes (e.g. grassland, deciduous woodland, coniferous woodland, etc.), then it is generally preferable to stratify the samples by regions that have been separated identified as forming these various classes. Likewise, if 100 samples are to be taken, and it is known that certain parts of the landscape are much more varied than others (in respect of the data to be studied) then it makes sense to undertake more samples in the most varying regions.

In addition to fixed sampling schemes, adaptive schemes can be applied which may offer improvements in terms of estimating mean values and reducing uncertainty (providing lower variances). Typically an adaptive scheme will involve four steps: apply a coarse resolution fixed scheme (e.g. as per Figure 5‑1C ) to the study area; record data at each sampled location; compute decision criteria for continued sampling; and extend sampling in the neighborhood of locations that meet the decision criteria. For example, if recorded values of Cadmium in soil samples at certain locations exceeds a pre-defined threshold, then additional samples might be taken radially around the initial threshold locations. Alternatively, the initial values at each location might be used to compute an experimental variogram (see Section 6.7.1.7), from which estimates values and variances of these values can be computed using Kriging methods (see Section 6.7.2). Locations with high Kriging variance (i.e. poorly represented) could then be identified and additional sampling designed to reduce this uncertainty.