Practitioners Guide to the Methodology
Introduction
Concerned with improving the recovery of merchantable volume across a harvest cutover, a harvest supervisor or forest owner will often need to quantify how much is left post harvest. The time and effort spent doing so must be put in context of the value of the potential residue volume remaining, and hence the development of the technique of line intercept sampling (LIS).
The use of LIS for cutover residue assessment is in essence simple and well proven, however many questions arise in its practical use. The aim of this report is to provide a quick reference to a number of practical aspects of the line intersect method for cutover residue assessment for harvest supervisors wishing to understand and implement this technique in different conditions. This is not planned as a conventional review of literature, nor does it introduce any new theory. Instead, it is intended to fill the gap between theory and procedure handbook and to promote the best possible understanding of the method, combined with a brief simulation and worked example.
Line Intercept Sampling
Since its original description for merchantable cutover residue assessment in Kaingaroa Forest by Warren and Olsen in 1964, the line intersect method (LIS) has been extensively used for measuring the quantity of wood lying on or near the ground. A number of people over the years continued to develop the technique (Bailey 1970, Wagner and Wilson 1976, Hall 1986, Bell et al 1996), proof its mathematical basis in depth and extend its application (De Vries 1973), review the practical aspects of LIS to overcome bias and improve precision (Wagner, 1982), and carry out a series of simulation studies (Pickford and Hazard 1978, Bell et al. 1996).
Understanding the Nature of the Line Intersect Method
The line intercept is best pictured as a strip sample of infinitesimal width (Figure 1). The data collected are diameters of wood pieces at their points of intersection with a sample line. The sample line is really a vertical plane, and the tally in effect collects a series of circular crosssectional areas from the intersected wood pieces (Wagner, 1982).
Transect A  Transect B  Transect C  Transect D (LIS)  
Transect Width (m)  10  5  2.5  Infinitely Small 
Transect Length (m)  50  50  50  50 
Area (m2)  500  250  125  Infinitely Small 
Piece Diameter (cm)  50  50  50  50 
Plot Volume (m3)  2.0  1.0  0.5  Infinitely Small 
Volume Per Area (m3/ha)  39  39  39  39^{*1} 
Note: *1 probability theory factor removed for this example as piece is a cylinder and crosses at right angles
Figure 1 – Picturing a strip sample of infinitesimal width
Of course the log shown in Figure 1 cross at right angles for each transect, which is often not the case. Therefore the actual cross sectional areas are really ellipses of various shapes, but a factor derived from probability theory (π/2) allows the cross sectional area to be summed as circles.
Figure 2 – The elliptical crosssection at the intersection of a sample line. Addition of the probability theory factor means only ‘d’ needs to be measured above.
Figure 1, also represents a log with no taper which is often not the case. Because LIS simply collects an unbiased sample of cross sections from the wood pieces lying on the ground, Pickford and Hazard 1978 found by way of a range of simulation studies that LIS was unaffected by any kind of variation in diameter throughout the length of the pieces.
The basic equation is then derived (Wagner 1968):
Equation 1:
Where: V= volume per unit area (m3/ha), d= piece diameter at intersection (cm), L= length of the sample line (m), π^{2}/8= product of π/2 (probability theory factor mentioned above) and π/4 (factor to convert d^{2} to circular area).
Assumptions for use of LIS
LIS as described in Equation 1 embodies several assumptions which are important to consider when implementing or considering any changes to procedure manuals.
Sample Intensity
The precision of the result and hence resulting sample size, as in all sampling procedures depends on the size of the sample and the variability of the residue material assessed.
Before making some practical guidelines the following key principals identified by Wagner (1982) are worthy of taking time to consider:

The level of precision depends primarily on the total size of the sample (total transect line length, not the number of smaller transect sections). Therefore it is not the number of transect sections/hectare that is important but the sum of those sections to the total length of sample e.g. 34 transects*50m=1700m.

Theoretically the size of the cutover area sampled is irrelevant, it is the variability of the material being sampled that counts.

It follows that for a given total line length the number of sections is within limits immaterial. For example; 20 sections of 50m should provide the same standard error as 10 sections of 100m each.

Transect sections may be either physically separated or parts of a longer continuous line.

Precision is also related to concentration, that is to the number of intersections per unit length of transect line.

Unnecessary precision is costly, to double the precision (half the standard error), would require for times the total transect length.
These principles require some practical comments: It seems unrealistic to spread a scatter of transect lines across a too larger area (point 2). It also makes sense to cover the entire cutover area with several shorter transects than few larger transects (point 3). This helps by taking advantage that transects can be separated (point 4) and provides better statistical understanding of the concentration of pieces across the cutover (point 5). It is recommended that this is done in at least 10, but preferably 20 transect sections to gain stability in the precision (point 3 and 5). It is important that these transect sections be independent from each other for the principals of random sampling to apply, therefore they must not be too close nor too short to provide this (hence joining of 2 or 3 sections for the right angled transect or the equilateral triangle transect and distributing these on a systematic grid). Precision of 2030% probable limit of error (PLE (95%CI/mean)) will suit most cutover residue assessment applications, but for some it might be that 40% PLE would be acceptable (point 6). For example 40% PLE on a cutover with 20m3/ha merchantable volume is ±8m3/ha. If the tolerance is 5m3/ha you can still with great confidence conclude the cutover exceeds tolerance. If a royalty payment is due a higher precision might be required, but if this was just a key performance indicator (KPI) for the harvesting operator’s contract then this would be likely be fine.
Table 2 which has been adopted by Warren and Olsen in 1964 after a range of pilot studies still provides practical guide on total transect length by variability of residue material to be assessed. For example this indicates that for a 2030% PLE that at least 20 to 32 line transect segments of 50m right angles (10001600m) will be suitable depending on the expectation of residue material onsite (or 13 to 21 equilateral triangles). Therefore many practitioners have implemented a sampling design of at least 1 day’s assessment across cutover area of any size. Then depending on the confidence required and the results further sampling can be completed.
Table 3 outlines a workflow example for initial setting of a sample size.
Table 2 Total transect length for varying residue volumes (adapted from Warren and Olsen 1964)
*Expected PLE shown in Red, PLE of 20% shown in yellow, PLE range to 30% in orange and 40% in pink
Table 3 Practical Guideline Steps for Sample Size Definition
Steps  Example Workings to Provide an Indicative Sample Size 
Define expectation of residue volume  1012m^{3}/ha 
Define expectation of precision  Expectation of residue merchantable <=5m^{3}/ha onsite, 30% PLE would likely be the outer limits to provide confidence that the contractor has exceeded 5m^{3}/ha 
Calculate total length of transect  Total transect length 724m (from table 2) 
Decide on transect plot subsample type (right angled transect or equilateral triangles)  Right angled transects in 50m segments. 
Divide the total transect length into a minimum of 10 to 20 transect sections.  15 plots 
Plot Layout  Typically systematic random sampling grid is used, but consider using Quazirandom plot layout to allow for increased sampling if required. 
Additional Outputs from LIS
Information about piece lengths, end diameters, defects can be determined by measuring additional attributes on all pieces or subsampling a portion of the transect line. This is covered in detail by Wagner (1982). One that will likely be of interest to harvest supervisors wanting to more understanding on the type of volume, is piece length distribution per unit area. This will require additional information to be collected and therefore may reduce the cost effectiveness of the main sample. If there is a demand for this procedures could be expanded to include additional measurements or classification.
References
Bell, G. et al., 1996. Accuracy of the line intersect method of postlogging sampling under orientation bias. Forest Ecology and Management, 84(13), pp.23–28.
Hall, P., 1998. Logging Residue at Landings. , (May), pp.1996–1998.
Howard. J, Ward. F 1972 Measurement of Logging Residue – Alterative applications of the Line Intersect Method. USDA Forest Service Research Note PNW183
Wagner, C.E. Van, 1982. Practical aspects of the line intersect method.
If you would like more information on the line intercept method, please contact our technical resources team.