Figure 5‑2 Grid generation examples

Figure 5‑3 Grid sampling examples within hexagonal grid, 1 hectare area

Where a regular cell framework has been generated the software then supports creation of sampling points within each cell — single points in this example. The methods supported are regular (center of cell, Figure 5‑3A); systematic unaligned (Figure 5‑3B) in which the first cell point is selected with random x,y coordinates and subsequent points are selected using the same x or y coordinate as the previous cell, but with one of the two coordinates selected at random, alternating on a column-by-column basis); and random (Figure 5‑3C). In the latter two cases a weighting factor is provided that biases selection towards the center of the cell (100= no bias, 1=maximum bias). Selected sample points that nominally fall inside a cell but outside of the polygon boundary are excluded.

With general purpose GIS packages it is straightforward to generate a random, regular or partially randomized point set (within or externally to the GIS), and then to compute the intersection of this set with pre-defined polygons or grid cells. With this approach simple point-sampling schemes may be created, although precise matching to polygon forms, sample numbers or attribute weightings may be difficult. Purpose-built add-ins, such as Hawth’s Tools for ArcGIS, provide a range of tailored sampling facilities. These include: (i) generation of random points, with a range of selection options (including use of raster or polygon reference layers — see Figure 5‑4A, Mississippi, USA); (ii) random selection from an existing feature set (points, lines, polygons — see Figure 5‑4B, 200 radio-activity monitoring sites in Germany. Random sample of 30 (red/large dots)<100 units of radiation and 30 (crosses)>=100 units of radiation); and (iii) conditional point sampling, designed for case-control analysis and similar applications. The latter facilitates a variety of random point generation methods in a region surrounding specified source points.

Random points in the plane may be used as sampling points or in connection with modeling ― for example as part of a Monte Carlo simulation of a probability distribution. Random points can also be generated on a network. Naturally the distribution of such points will be affected by the distribution of the network links in the plane, and may thus appear clustered with respect to the plane (excluding the network). The corollary of this observation is that a clustered point pattern in the plane that is, in fact, a set of points on a network, may actually be a random uniform distribution when shortest network path distances are used rather than Euclidean planar distances. For example, the set of 100 points in Figure 5‑5A (Tripolis, in Greece) appears to be far from random, but in fact this is a random uniform (Poisson) point set on a network, as shown in Figure 5‑5B. This example was generated using the SANET software, which also provides a wide range of tools for analyzing observed point patterns on or almost on networks such as that illustrated (see further, Section 5.4.1).

The term quadrat sampling is applied to schemes in which information on all static point data (e.g. trees, birds’ nests etc.) is collected using an overlay of regular form (e.g. a square or hexagonal grid). Collected data are then aggregated to the level of the quadrat, whose size, orientation and internal variability will all affect the resultant figures (e.g. counts). Very small quadrats will ultimately contain 0 or 1 point objects, whilst very large quadrats will contain almost all the observations and hence will be of little value in understanding the variability of the data over space. An alternative to procedures based on lattices of quadrats is to “drop” quadrats onto the study area at random. Such quadrats may be of any size or shape, but circular forms have the advantage of being directionally invariant. A disadvantage with this approach is that some areas may be repeat sampled unless precautions are taken to exclude areas once sampled.

Figure 5‑4 Random point generation examples — ArcGIS

Figure 5‑5 Random point samples on a network

SANET software: Prof A Okabe et al; Network data (Tripolis, Greece): S Sirigos; see also Figure 7‑16