A Theoretical Development and Field Test of a Horizontal Line Sampling (HLS) in Coppice Forests

Schlüsselbegriffe: kosteneffizientes Design, Waldinventur, offener lichter Eichenwald, Quercus brantii, Zagros Wald

Available at https://doi.org/10.53203/fs.2302.1

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Abstract

If available forest inventory techniques or measurement instruments are not satisfying or appropriate for monitoring a particulare forest, options include developing a new inventory technique and/or modifying an available instrument. In this study, we present a new application of horizontal line sampling (HLS) in combination with a crown relascope as a potential alternative to line intersect sampling (LIS) to monitor coppice forests (CF). In CFs, the stem basal area relascope is not applicable, since trees often lack distinct stems and are not visible at breast height. Our study was conducted in an open oak-dominated CF in western Iran and we focussed on two forest attributes: above-ground biomass (AGB) and the total number of trees (N). We assessed the field performance of HLS and LIS in CFs and evaluate various line transect lengths and crown relascope angles. Our results indicate that longer line transects (80 m) produce smaller relative sampling errors compared to shorter ones (20 m) and smaller relascope angles (36.8°) are more precise than larger ones (67.4°). In terms of cost-efficiency, HLS is superior or equivalent to LIS in some cases. While HLS and LIS gave different estimates of AGB and N, the difference was not statistically significant at the 95% level. Both relascope angle and line transect length impact the efficiency of HLS. Our study provides evidence that this technique can be useful for monitoring forest conditions.

Zusammenfassung

Wenn verfügbare Waldinventurtechniken und/oder Messinstrumente nicht ge­eignet sind, um ein ausgewähltes Waldgebiet zu beobachten, dann ist eine Lösung, neue Inventur­techniken zu entwickeln und/oder verfügbare Messinstrumente zu adaptiere­­n. In dieser Studie stellen wir eine neue Anwendung der horizontalen Linien­stichprobe (HLS) in Kombination mit einem Kronenrelaskop vor. Als potenzielle Alternative zur Linienkreuzungsstichprobe (LIS) testen wir hier die HLS in Ausschlagwäldern (CF). In niederwaldähnlichen Ausschlagwäldern ist das Stammgrundflächenrelaskop nicht anwendbar, da Bäume oft keine ausgeprägten Stämme haben und in Brusthöhe oft nicht sichtbar sind. Die Studie wurde in einem offenen und von Eichen dominierten Ausschlagwald im westlichen Iran durchgeführt. Die Studie fokussiert sich auf zwei Waldattribute, oberrirdische Biomasse (AGB) und die Gesamtzahl der Bäume (N). Wir bewerten die Leistungsfähigkeit von HLS- und LIS-Inventurtechniken in CF sowie den Effekt verschiedener Transektlängen und Kronenrelaskopwinkel. Unsere Ergebnisse zeigen, dass eine längere Transektlänge (80 m) einen kleineren relativen Stich­probenfehler aufweist als die kürzere Transektlänge (20 m) und ein kleinerer Relaskop­winkel (36,8°) präziser ist als ein größerer Relaskopwinkel (67,4°). Hin­sichtlich der Kosteneffizienz ist HLS der LIS überlegen oder in einigen Fällen gleichwertig. HLS und LIS ergaben unterschiedliche Schätzungen von AGB und N, aber der Unterschied war statistisch nicht signifikant auf dem 95-%-Niveau. Sowohl Relaskopwinkel als auch Transektlänge haben Auswirkungen auf die Effizienz des HLS. Unsere Studie liefer­­t einen Beleg, dass die HLS-Technik für das Monitoring des Waldzustandes hilfreich sein kann.

1 Introduction

A larger number of forest inventory techniques have been proposed to collect the necessary information for forest management planning. In forest inventories, the primary objective is to estimate the parameters with the highest possible accuracy/precision and at a reasonable cost (Kershaw et al. 2016). However, a given forest inventory technique and/or measurement instrument may not be efficient when applying it in different situations and for various purposes. The characteristics of the forest, survey´s objective and costs determine the appropriate inventory technique and measurement instrument to be used. For instance, Schreuder et al. (1987) suggested that HPS is a highly effective technique in estimating stand-level basal area, but it may be less effective in estimating other parameters such as tree density. To improve precision in the estimation of snags, Ducey et al. (2002) utilized a combination of horizontal point sampling (HPS) and horizontal line sampling (HLS). Hence, developing a new inventory technique or modifying the currently used measurement instrument to suit various situations is desirable.

Unlike forests, where a stand is characterized by single-stemmed trees that originate from seed, there is another form of forest around the world, so-called coppice forest (CF) (Scolastri et al. 2017). CF consist of trees that have mainly been regenerated from shoots and a small percentage of seed-originated trees (Scolastri et al. 2017; Iranmanesh et al. 2019). Young tree stems are repeatedly cut down to near ground level, resulting in a stool. These stands are formed through asexually/vegetatively sprouting, which is the most common means of regeneration (Vollmuth 2022). 

CF are an important renewable resource, with the potential to provide products and services such as non-wood products, protection and heritage ecosystem services. While seed-originated trees have short stems and large crowns (Scolastri et al. 2017), in CFs shoots-regenerated trees often lack a distant stem. Vollmuth (2022) conducted a survey in Germany’s coppice forest. The author concluded that coppice forests have high overall biodiversity and that they provide habitats for numerous light-demanding species, that are endangered today. 

The stem basal area relascope is a commonly used instrument in forest inventory for estimating variables such as basal area (BA) and volume (Bitterlich 1984; Lynch et al. 2021). However, in CFs, where trees generated through sprouting and do not have distinct stems, the stem basal area relascope may not be as effective due to the invisibility of the stems in breast height. To address this issue, the crown relascope (CrR, Stenberg et al. 2008) may be an efficient alternative. The CrR is an extension of the stem basal area relascope. CrR estimates vertically projected crown area on the ground or crown cover using tree crown diameter as the criterion for selection. However, the use of CrR requires a larger basal area factor known as the crown basal area factor (CBAF).

Line intersect sampling (LIS) is a well-known and efficient technique for sampling different kinds of features (Kaiser 1983, DeVries 1986, Skidmore and Turner 1992). It has been used for measuring the area of two-dimensional objects (Battles et al. 1996, Ramezani & Holm 2011), in estimating total length of linear features (e.g., Matérn 1964, Corona et al. 2004, Ramezani & Holm 2011), and also to estimate the total number of objects (Gregoire & Valentine 2008). However, LIS may not be efficient for sparse populations (Cooper 1957; Ståhl 1997). In such a population, we may encounter one of the two following situations: either there is a need for a large sample size, or the estimated sampling error (or variance) will be large (Ducey et al. 2002). 

Horizontal line sampling (HLS) was originally developed by Strand (1957) to estimate attributes of standing trees. Lynch (2006) and Marquardt et al. (2010) applied HLS to estimate total amounts of forest attributes in riparian forests. Rice et al. (2014) found that HLS was also effective in partially harvested stands, and it has also been used in forest inventory in Taiwan (Yang & Chao 1987). In HLS, Bitterlich sampling (1984) and LIS features are combined and a stem basal area relascope is often used in estimating forest parameters (Schreuder et al. 1987; Gregoire & Valentine 2008). For quantifying coarse woody debris in a sparse population, Ståhl (1997) developed a transect relascope (TR), which combines LIS and a wide-angle relascope instead of the stem basal area relascope. The method section (2.2) provides detailed description of the estimators and inclusion probabilities of both LIS and HLS. 

In previous examples of HLS applications, the same instrument – a stem basal area relascope – was generally used as in horizontal point sampling (HPS). However, this study presents a new application of HLS in combination with CrR in a coppice forest. The study compares the field performance, precision, and time efficiency of HLS and LIS inventory techniques. The main objective is to estimate forest attributes such as above-ground biomass (AGB) and the total number of trees (N) in a CF where trees do not have distinct stems. Additionally, the study assesses the performance of HLS and LIS at varying transect lengths (80, 40, and 20 m) and relascope angles (36.8, 53.1, and 67.4°). While sample size has an obvious effect on the precision of estimates, it is not examined in this study.

2 Material and methods

2.1 Study area

The study was conducted in an open, oak-dominated coppice forest (CF) (Quercus brantii) in Lorestan province, western Iran (Zagros forests, see Fig. 1). Quercus brantii is a significant tree species in the western forests of Iran. These oak stands are often found mixed with Juniperus excelsa M. Bieb, Amygdalus scoparia Spach., Pistacia atlantica Desf. and Acer monspessulanum L. Due to human impact, only 7% of the oak forests are considered forests, while the remaining 93% are in coppice form (Iranmanesh et al. 2019; Mahdavi et al. 2020). We note that according to FAO, forest land is defined as land covering more than 0.5 hectares with trees higher than 5 meters and a canopy cover of more than 10 percent. Zagros forests cover an area of approximately 5 million hectares and are classified as semi-arid, accounting for 40% of Iran’s forests. The elevation of the study area ranges from 1860 m to approximately 2070 m above sea level, with a mean annual precipitation of 530.15 mm and a mean annual temperature of 18.3° C (Sagheb-Talebi et al. 2003). Zagros forests are non-timber-oriented and provide valuable ecosystem services such as water resources, climate regulation, and biodiversity conservation. The social economy of Zagros forests is closely linked to the sustainable use and management of the forest ecosystem, with activities including ecotourism, handicrafts, and value-added processing of forest products (Salehi 2009; Riyahi 2010). CFs have been a crucial source of energy in the form of firewood and charcoal for rural people for thousands of years. Animal husbandry is a common land use practice in the Zagros forest (Safari & Sohrabi 2019). Fire frequently occurs in the Zagros forest during the summer and early autumn months. This fire season coincides with the dry and hot periods. Wildfires play a natural role in maintaining forest health and biodiversity. Some tree species in the Zagros forest have adapted to fire and depend on it for their regeneration and growth (Javanmiri pour 2021).

2.2 Sampling design

In this study, we laid out a systematic array of 25 m × 25 m line grids over the study area (about 10.4 ha) in a GIS environment. A total of 166 points were located in the study area, of which 30 were randomly selected and established in the field using a global positioning system (GPS). These locations served as the midpoints of the line transects. The transects were laid out using measuring tape and a hand compass, with orientations determined according to a uniform distribution [0, 2π]. To avoid boundary bias, we applied the walk-back method (Gregoire & Valentine 2008, p. 299), where if a boundary is intersected by a transect, the intersection point with the boundary serves as the starting point and we walk back towards the original sampling location.

We made a simple crown relascope (CrR) using wooden pieces and string (Fig. 2). A common and practical way to determine the desired angle for constructing a relascope is to use a reach-to-width ratio (R:W) (Table 1). Using CrR, the crown basal area factor (CBAF, m² ha^-1) is the amount of crown basal area per hectare that each sampled tree represents. Under CrR, crown cover (CrC) can be estimated by counting the average number of tree crowns (t) that appear wider than the crown relascope’s angle and multiplying the result by a predefined CBAF (m² ha^-1), CrC = t × CBAF. For instance, CBAF 2500 (m² ha^-1) means that one tallied tree corresponds to 2500 m² of crown cover area per hectare.

The next section provides a brief overview of the inclusion probabilities of trees when using LIS and HLS, as well as the estimators associated with these inventory techniques. 

a) Line intersect sampling (LIS)

In LIS, the surveyor walked along the line transects and an object (tree) was included in the sample if the tree crown projected on the ground crossing a line transect. Then, the crown diameter of the selected trees was measured using measuring tape.

In a random sampling design (as our case), the inclusion probability of tree i (π_i,LIS), is:

where cd_i (m) is the tree crown diameter of tree i, l is transect length (m), and A is the total area (ha) (see Fig. 3, right).

The Horvitz-Thompson (HT) estimator of LIS to estimate the total above-ground biomass (AGB) for a single sampling unit, j (line transect) is 

and to estimate the total number of trees (N) the estimator is 

where, AGB_i (kg) is the above-ground biomass of tree i, and m is the total number of trees sampled in the j th line. 

A general HT estimator for the population total in a sample of n lines (the averaging across n sampling units) is 

b) Horizontal line sampling (HLS)

In HLS, crown relascope (Fig. 2) was used when the same surveyor walking along the same line transects as in LIS. The surveyor sighted both sides of the transects and viewed all candidate trees through the relascope angle. Any tree with crown diameter greater than the width of the projected angle from the relascope was chosen as a sample tree. In this way, trees were sampled with probability proportional to their crown basal area. Note that we adopted modified sausage sampling (Gregoire & Valentine 2008, p 362), where trees selected from the sample locations were omitted. Thus, in such a procedure, the inclusion probability is the same as under the conventional HLS.

Under HLS procedure, tree i, is selected if its perpendicular distance from the transect is within a limiting distance (R_i). In contrast to LIS, a tree is selected into a horizontal line sample without crossing directly by line transects. Under HLS, the inclusion probability of tree i (π_i,HLS), in a random sampling design, is (see Fig. 3, left):

where R_i (m) is the limiting distance from which a tree appears exactly as wide as the measurement instrument that defines the sighting angle. According to Stenberg et al. (2008), R_i for crown relascope can be calculated as:

where r_i (m) is the tree crown radius of tree i, and V is relascope angle determined by the measurement instrument and a design parameter that is constant for all trees. Thus, the inclusion probability π_i,HLS can be expressed with replacing R_i as:

Using HLS, the HT estimator of AGB for a single sampling unit, j is:

and the estimator of N for a single sampling unit, j is:

In the case of HLS, the estimator of the population total in a sample of n lines is:

For both attributes ABG and N the average per hectare can be estimated with

In the study, we predicted tree-level biomass using the following equation fitted by Iranmanesh et al. (2014). The equation is based solely on the tree-level crown diameter and is defined as

where cd is the tree crown diameter (m). The authors developed Equation 11 using 30 sampled Quercus brantii trees. They found a strong and nonlinear relationship (R² = 0.97) between above ground biomass (AGB) and tree crown diameter (cd). The study area had a mean annual rainfall sum of 567 mm and a mean annual temperature of 15.5 °C.

2.3 Time study

The study recorded the time required in seconds per length unit for data acquisition, including measuring the diameter of the crown projected on the ground of sampled trees using a standard tape and walking to the sample trees. The work was carried out by a three-person crew. 

2.4 precision assessment

As both inventory techniques offer design-unbiased estimates for the population total N and AGB, the comparison between the two techniques was based on the smallest cost-variance. The variability between line transects was used to characterize the sampling variability on the total estimates. The estimator of variance of the population total, τˆ_y is defined as (Thompson 2002):

where τˆ_{y, j} is individual estimate of the population total of a single transect, j and τˆ_y is the average of the all n transects. The relative sampling error (SE %) for the population 

It should be noted that the sample size for all combinations of three relascope angles and three line transect lengths was the same (i.e., 30 line transects).

2.5 Efficiency evaluation 

The relative efficiency (RE) method is a commonly used approach to assess the efficiency of different forest inventory techniques (Husch, 1963), where both costs (time) and sampling error are considered. By this method, a forest inventory technique (here LIS), serves as the reference. RE can be computed by:

where %SE_HLS and %SE_LIS are the relative sampling errors of HLS and LIS, respectively. T_HLS and T_LIS are the total time needed for inventory techniques HLS and LIS, respectively. When RE < 1, HLS is more efficient than LIS; when E > 1, the converse is true.

Standard statistical procedures were employed to analysis the data. Specifically, a one-way ANOVA was used to test for significant differences between the inventory techniques sued to estimate N and AGB. Additionally, a multiple regression analysis was conducted to examine the combined effect of predictor variables-line length and relascope angle-on response variable SE %.

3 Results

Figure 4 shows the estimates of the total N and AGB obtained using inventory techniques tested. The error bars represent confidence intervals. Although HLS and LIS produced different estimates, the difference was not statistically significant at a 90% confidence level (p=0.874 and p=0.876 for N and AGB, respectively), as shown in Tables A1 and A2. This result can be expected, since both inventory techniques are design-unbiased. In most cases, longer line transects resulted in smaller confidence intervals.

Figure 5 displays the relative sampling errors (SE%) for N and AGB using two inventory techniques (LIS and HLS), three line transect lengths, and three relascope angles. In general, HLS is more precise than LIS. This result is expected since HLS covers a larger stand area than a comparable LIS, increasing the probability of sampling more trees. Additionally, in most cases, longer line transects result in lower relative sampling errors (SE%).

The results of the multiple regression analysis, shown in Figure 6, indicate a negative relationship between the relative sampling error (SE%) and line transect length. This implies that an increase in the length of the line transect is associated with a decrease in the SE%. Conversely, there is a positive relationship between SE% and relascope angle, which means that an increase in the relascope angle is associated with an increase in the SE%.

Table 2 provides the average time (in seconds per meter) for two inventory techniques and three relascope angles. It is important to note that the walking costs between sampling lines were not included.

Table 3 presents the relative efficiency (RE%) of three line transect lengths and three relascope angles. In some cases, the RE is less than or equal to 1. This indicates that in these cases, HLS is superior to LIS.

4 Discussion

Monitoring forest change and forest degradation is important in sustainable development and management of forest landscapes (Li et al. 2021). Therefore, efficient collection of forest information will play a significant role in improving the management of forest landscape (Moradi et al. 2022).

4.1 Estimation of N and AGB

The application of horizontal line sampling (HLS) in coppice forests, particularly in combination with crown relascope, is novel. As a result, there was no prior knowledge of an appropriate crown basal area factor (CBAF) and its impact on estimates. CBAF was determined by practical convenience. Previous studies have shown that estimates of forest attributes are highly related to basal area factor (BAF) when using horizontal point sampling (HPS) (Brooks 2006; Lindemuth 2007). Our results show that there is no significant difference among the three CBAFs tested in estimating the total number of trees (N) and above-ground biomass (AGB). Thus, choosing much larger or smaller CBAFs may lead to significant estimates of N and AGB.

In this study, it is impossible to determine the most accurate inventory technique due to the lack of a reference value for N and AGB. Further simulation studies are needed to determine the most accurate inventory technique in coppice forests. Under a simulatio­­n study, it is also possible to test very large or small CBAFs.

4.2 Statistical properties 

In general, line intersect sampling (LIS) resulted in higher variance, which was expected as the inclusion zone for trees in LIS – the “imaginary rectangle” – is smaller than in horizontal line sampling (HLS). Our results indicate that, in most cases, HLS is more efficient than LIS in terms of relative sampling error (SE %). This finding is consistent with Stenberg et al. (2008), where a Crown Relascope (CrR) was compared to LIS for estimating crown cover area in boreal forests. However, the authors combined CrR with horizontal point sampling (HPS) and did not consider costs.

Although horizontal line sampling (HLS) with V1 resulted in the smallest sampling error for all three line lengths and for both the total number of trees (N) and above-ground biomass (AGB) (Fig. 5), it is not cost-effective. This is because many trees are sampled, making it time-consuming to use V₁. One way to overcome this drawback – the walking time to sampled trees – is to use ground-based horizontal laser scanning to measure tree crown diameter. As our results show, HLS is superior to line intersect sampling (LIS) in terms of variance (Fig. 5). However, in terms of cost-efficiency, HLS is not effective in some cases because it is more time-consuming than LIS (Table 3).

4.3 Relationship between sampling error and line length and relascope angle 

Our results indicate that both relascope angle and line length impact the relative sampling error (SE %). Rice et al. (2014) also found that for a given line length, a larger relascope angle can produce a higher sampling error. Our results suggest that longer line transects and/or smaller relascope angles lead to better precision estimates. However, Schreuder et al. (1987) found in a simulation study that longer lines with a large angle can be efficient, which they attributed to dense undergrowth in the study area - a factor not present in our study. Previous studies have shown that HLS is equivalent or superior to HPS in various respects (e.g., Ríos et al. 2000; Schreuder et al. 1987). Kenning et al. (2005) found that HLS was more efficient in sampling basal area compared to fixed area sampling. However, no comparison study has been conducted between HLS and LIS, making direct comparison of results difficult.

A wide-angle relascope was used by Cooper (1957, 1963) and Stenberg et al. (2008) to estimate the number of shrubs (N) and canopy cover area (CCA) in shrubland and boreal forest stands, but the authors applied HPS. They found that HPS was also superior to LIS. Using HPS, CCA can be estimated simply by counting sampled trees and multiplying by a constant expansion factor – the crown basal area factor. However, to estimate other forest attributes such as above-ground biomass (AGB) and N, the tree crown diameter of sampled trees must be measured.

4.4 Caveats and shortcomings

There are several sources of bias when using Horizontal Line Sampling (HLS): (a) deviations from the line transect when walking along it; (b) not operating the relascope horizontally; (c) overlapping of tree crowns; and (d) non-circularity of tree crowns. As Stenberg et al. (2008) concluded, CrR appears to be effective and applicable in forest stands where there is no overlapping of tree crowns. Fortunately, this is the case in our study area – a low-density, open coppice forest. Ståhl (1997) also found that the relative superiority of HLS was larger in populations where the intensity of population elements was low. The last source of bias was not included in this study, but it would be an interesting research topic to explore the extent of bias. For this purpose, a true value is needed.

4.5 A vision for the future of HLS and crown relascope research

In this study, line transects were established randomly. However, Gregoire and Valentine (2008) describe a systematic alternative for deriving element inclusion probabilities and corresponding estimators. Under a systematic design, the probability of including a tree depends on the width of the inclusion area for the tree in a direction perpendicular to the sample line. One advantage of a systematic sampling design is that it allows for the estimation of total without the need for the total area of the study tract (Lynch, 2006).

In this study, the sample size is fixed (i.e., 30 line transects). However, it is well-known that sample size can substantially impact the precision of estimates. Woldendorp et al. (2004) and Ramezani and Holm (2010) demonstrated in simulation surveys how sample size and line transect length can influence the precision of estimates. It would be interesting to conduct a similar survey for CrR and HLS, considering a combination of different sample sizes, line transect lengths, and relascope angles. It would also be interesting to compare crown relascope to fixed-area sampling, a widely used forest inventory technique.

5 Conclusions

In this study, we explored a new application of Horizontal Line Sampling (HLS) in combination with CrR to estimate attributes of coppice forests (CFs). Our suggested combination is easy to implement in the field and, in some cases, more efficient than Line Intersect Sampling (LIS) for estimating forest attributes in CFs. While this study focused on standing trees, we speculate that HLS and CrR may also be useful for inventorying other sparse populations such as downed wood in CFs.

Both relascope angle and line transect length impact the performance of HLS. The technique used in our research may be replicated in other CFs with similar characteristics and stand structures. Our study provides evidence that this technique can also support forest degradation monitoring.

Acknowledgment

We would like to express our gratitude to four anonymous reviewers for their valuable comments on the manuscript.

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