When considering a forest inventory, as foresters we often need to create a sample plot layout across of net stocked area. As part of our Forest Management Cloud Service, GeoMaster Assessment Planner simplifies the creation of sample plot designs for forest inventory purposes. There are a range of options available to the user in selecting the type of sampling structure to be used for the plot layouts as shown in Figure 1. Plots can be arranged in a systematic grid from a random start point, randomly located (with/without replacement), and distributed via a space-filling algorithm (“Quasi-random“). It is this last option which I wish to cover off in this article as it has some operational benefits which should be highlighted for those dealing particularly with periodic populations.
Figure 1 – Assessment Planner Dialog Box for selection of sampling structure.
Most foresters will be familiar with a systematic sampling grid (Figure 2). It is the most commonly applied technique in selecting sample locations across a forest area and almost used exclusively for a couple of key reasons:
- Complete coverage of the entire stand is ensured.
- No risk plots will clump together into one area, often resulting in an unusually large sample error (like in random plots, Figure 3 and 4 below).
- And traditionally with compass and hip-chain navigation, they are less time-consuming and more cost efficient to install as field crews simply walk in a straight line installing plots at a constant interval.
These benefits cannot be understated when compared with random sampling, as shown in figures 3 and 4 below. We can see using these options in Assessment Planner resulted in clumped (yet completely random) plot locations which often do not cover the area of interest particularly well and would be difficult to navigate to using anything other than a modern GPS unit. That brings me to the now common use of GPS for locating plots in the field. Since 2006 navigation with GPS has reached under the forest canopy and use of GPS is now the common practice for plot locations. To correctly locate random plot locations in the past was difficult and had the potential for bias due to the basic navigation aids we used (compass and slope based cotton trail from a hip chain). With GPS this is now more of a feasible task.
Many studies have found that sample statistics for “Simple Random Sampling” (SRS) apply for systematic grid sampling, and hence the variance and standard error calculations for this remain the same as simple random sampling. Therefore the benefits of systematic sampling over pure random sampling for forest inventories has meant this is now standard international accepted practice (Scheaffer et al. 1990).
Figure 2 – Systematic Sampling Grid
Figure 3 – Random (with replacement)
Figure 4 – Random (without replacement) – note that plot areas no longer overlap
However one of the dangers of systematic grid sampling is periodic populations, for example where plantation rows are very structured and the systematic survey might by chance fall in line with this structured plantation. For example in production thinning, all the plots might fall in an out-row thinning, and if every 10th row is removed, and the distance of the systematic grid was by chance to also equal this distance you end by conducting a survey of just out-rows. Or when a mixed plantation where every xth row is a different species, or the area of interest is long and narrow. These examples are at the extreme end of what we might come across but they need to be carefully considered when selecting a valid systematic sample.
Another reason to be aware of with systematic sampling is that it also requires that the grid size be determined in advance and that all points are sampled once a decision is made to go ahead and use that grid size. Typically, sample points are located on a square grid and if the sample size proves insufficient, often the only way of increasing the number of sample points is to halve the grid size, thereby creating four times as many points. Hence once an initial inventory has been completed using a systematic grid there is no satisfactory method to add just a few more plots without the need to oversample. To get around this we could have created a larger grid than needed and then randomly subsampled, but again this can cause either the disadvantages of simple random sampling or at some point cause over sampling to get your target standard error or PLE.
Quasi-Random Sample Design
This brings us to the option of using sub-random / quasi-random plot based space-filling algorithm. Figure 5 shows the quasi-random plot layout of 10 plots. You can see the space-filling algorithm has “filled out” the space and the plot layout starts to resemble the benefits of the systematic sample (Benefit 1 and 2 shown above for coverage of the extent of the stand and reduction in clumping of plots). With the benefit of GPS, field crews no longer need to walk in straight lines and actually it is far more efficient that they don’t so they can walk around obstacles and with the terrain in movement from plot to plot. Hence the evolution of the option for quasi-random sampling for forest inventory.
Figure 5 – Quasi-random Plot Layout – 10 Plots
It is also accepted that this method has the advantage over pure random locations in that it is easy to replicate the initial sample design and add plot points in an unbiased manner to continue to improve the accuarcy of the initial sample. Figure 6 shows the addition of another 5 plots to the layout shown in Figure 5. You can see the first 10 plots are in the same place and just an additional 5 have been added.
Figure 6 – Quasi-random Plot Layout – 15 Plots
Assessment Planner uses the Halton sequence algorithm and controls the randomness by rotating the layout by a random angle, in units of 10°. If a transect bearing is fixed then the layout will always follow the same pattern (Figure 7 shows you can just enter/copy a fixed bearing into the stratum prescription dialog box or look back at the prescription map to get the transect bearing used). So hence this is particularly useful when the variation of the population is unknown and you wish to add some extra plots to an existing layout in order to reduce the standard error (or PLE). By entering the bearing of the initial sample and supplying a new value for plots required then the initial layout will be reproduced with extra plots interspersed in the gaps.
Figure 7 – Quasi-random Plot Layout – Adding plots to an exisiting plot layout by copying the transect bearing selected initially by random into the prescription dialog in Assessment Planner (a shown on the base of the inventory map)
So how does Quasi-random layouts affect the traditional SRS estimators of variance?
In the same way as systematic sampling makes an assumption of using the SRS estimators of variance, so does the quasi-random sample design.
Acknowledgement to Murray Lawrence for his suggestion of adding this method into GeoMaster Assessment Planner.
If you have any questions on these approaches feel free to contact us.