Abstract
Background: Urban tree inventories are fundamental to the monitoring and management of urban forests. Various handheld tools and methods exist to conduct tree mensuration, ranging from the simple stick method to laser rangefinders. This study examines the accuracy and precision of the stick method, clinometer, and laser rangefinder, and introduces tree type (i.e., conifer versus broadleaf) comparisons of accuracy and precision. Methods: Measurements were taken from 127 trees comprised of 85 (66.9%) broadleaf and 42 (33.1%) coniferous trees. Trees were distributed across 4 urban land use types: park, golf course, street, and trail system. A drone-mounted measurement tape was used to determine true height. Results: Measured heights ranged from 4.67 m to 25.71 m (
= 13.19 m). Measurements from the stick method yielded statistically similar results to both the rangefinder and clinometer methods. The methods had a Cronbach’s Alpha of 0.991 (N = 3). Accuracy was highest for the rangefinder and lowest for the stick method. Precision was greatest between the rangefinder and the clinometer. Root-mean-square error (RMSE) and percent error were highest for the stick method and broadleaf trees for all 3 measurement methods. Conclusions: The findings indicate greater accuracy and precision across all tools when measuring conifers. The rangefinder was similar in accuracy to the clinometer, with notable changes in accuracy when using the stick method.
INTRODUCTION
Inventories are a crucial component of urban forest management and arboriculture operations (Lilly et al. 2022). While inventory objectives and collected measurements may differ (Ma et al. 2021), there are several common tree measurements used by arborists and urban foresters. These include spatial attributes, such as location using global positioning system (GPS) coordinates or distance from infrastructure assets, and tree characteristics, such as diameter at breast height (DBH), tree height, crown spread, and percent missing crown (Ma et al. 2021; Lilly et al. 2022). The accuracy and precision of tools used to measure these attributes are important to understanding the validity of the inventory results and the data derived from the measured tree attributes.
While the complex three-dimensional shape of trees allows for many different measurements to be taken, select measurements appear with pronounced frequency within industry literature and formulas, including DBH, tree/crown height and width, and tree condition. The practical uses of such tree measurements may include the design of tree protection zones for construction (Fite and Smiley 2016; Lilly et al. 2022), tree planting hole sizes (Watson and Himelick 2013; Watson 2014), installation of tree support systems (Lilly et al. 2022), determining the target zone during tree risk assessment (Dunster et al. 2017; Smiley et al. 2017), appraisals (Council of Tree and Landscape Appraisers 2020; Lilly et al. 2022), and creating pruning objectives based on clearance distances and limb diameters (Lilly et al. 2019).
The adoption of advanced technology in tree mensuration methodology, such as Light Detection and Ranging (LiDAR), has the potential for increased accuracy beyond that of former methodology (Jones et al. 2016; Parmehr et al. 2016). Additionally, devices such as laser rangefinders or electronic tree calipers have progressed urban foresters’ and arborists’ abilities to measure trees quickly and accurately, and technological advancements are addressing limitations in conventional tree measurement techniques (Binot et al. 1995; Asner et al. 2002; Unger et al. 2014; Song et al. 2021).
Measuring Tree Height
Measuring tree height, including total tree height and live crown height, is important in urban forest inventories for calculating ecosystem services. For example, i-Tree Eco (USDA; Madison, WI, USA) uses tree height to estimate the energy effects that trees have on residential buildings (United States Forest Service 2021). In arboriculture and forestry operations, measuring tree height can help inform whether there is sufficient room to fell a tree. Being able to measure the tree felling radius with reasonable accuracy is imperative to safe operating procedures (Tree Care Industry Association 2014).
There are numerous methods for measuring tree height, including nonelectronic methods (e.g., clinometers), handheld electronic measurement tools (ex., handheld laser rangefinders), and terrestrial, airborne, and mounted measurement equipment (ex., LiDAR) (Wing et al. 2004; Vastaranta et al. 2015). Examining the accuracy of methods is important as measurements of tree height often have significant error (Waguchi 2002).
The stick method, which uses a straight stick and geometric principles to estimate tree height, is one of the most rudimentary methods of tree height measurements. In this study, “stick method” does not refer to the Biltmore stick—a purpose-built measuring tool for tree mensuration—but rather a more simplistic measurement method (Figure 1). The measurer uses a stick the length of their arm, holding the stick outright to form an isosceles triangle. Looking at the top of the tree “through” the top of the stick, the measurer walks toward or away from the tree until the tree’s top is at a point along length c consistent with the top of the stick. Measuring from the feet of the measurer to the base of the tree and adding the length y, the measurer is able to determine the tree height.
Trigonometry of the stick method. Ls = length of stick, which is equal to La = length of arm. Length a, the distance from the eye of the measurer to the base of the tree, is equal to length b, the height from the eye of the measurer to the top of the tree. Length c denotes the hypotenuse of the isosceles right triangle, and y denotes the distance from the eye of the measurer to the ground.
While the use of the stick method has largely been omitted in formal urban forest inventories based on technological advances, the stick method is still used in arboriculture and logging operations for rapid tree height estimates without the need for expensive tree measurement tools. Given its use within arboriculture operations, it has been included within this study. Further, the need to instruct early career professionals and students in the foundational concepts and mensuration methodology is important in establishing a core understanding of urban forestry practices.
Through expansion of the stick method’s simplistic geometric principles via trigonometric calculations, the clinometer introduces more versatility. This is true because a 45° angle is not required to measure tree height with clinometers. However, the use of a clinometer still requires a measuring tape to determine linear distance (the horizontal cathetus) for the trigonometric equation.
By contrast, handheld electronic/laser rangefinders provide a more rapid measurement of tree height, as well as horizontal and angular measurements, without the need for supplemental tools (Wing et al. 2004). While electronic distance measurement tools were adopted into ranging and surveying use in the 1960s, it was only after the tools were made portable that they began to become popular in forestry applications (Liu 1995). Over recent years, rangefinders have become increasingly affordable (Wing et al. 2004). A study by Wing et al. (2004) compared the accuracy of digital rangefinders, finding that some overestimated while others underestimated height; however, it should be noted that the rangefinders tested may have been updated since the study. A requirement of the use of a rangefinder is the ability to send an unimpeded laser pulse from the rangefinder to the tree’s trunk.
Alternative methods have also been made available for assessing height using electronic tools, including the use of smartphone apps. A study by Vastaranta et al. (2015) found that apps underestimated tree heights, reporting height biases between 5.0% and 8.3% and underestimations between 1.0 and 1.8 m.
Within the scholarly literature on more technologically complex height measurement methods, studies have tested the accuracy of aerial and terrestrial laser scanning (Wang et al. 2019); laser scanning and unmanned aerial vehicle (UAV) photogrammetry against handheld laser scanning (Jurjević et al. 2020); smartphone applications in comparison to traditional and spatial methods (Pace et al. 2022); the accuracy of LiDAR against other tree height mensuration methods (Sibona et al. 2017); and the precision of mensurationists in measuring tree height and DBH (Luoma et al. 2017).
For the purposes of this study, the stick, clinometer, and laser rangefinder methods have been selected based on their wide usage among arboriculture and urban forestry operations. The accuracy and precision of these tree height measurement tools are of importance to those undertaking inventories: for field-based arborists and loggers attempting to determine the felling radius of the tree, and for the education of students trying to learn the methods of tree mensuration. For the purposes of this study, accuracy is defined as the proximity of the measured height to the true height. Precision is defined as the consistency of measured height values across all 3 methods.
While a study by Saliu et al. (2021) examines the accuracy and precision of tree height mensuration methods in measuring mangrove trees, this study seeks to examine the accuracy and precision of tree height mensuration methods in urban forest sites and to evaluate the influence of boreal forest conifer or broadleaf tree types on accuracy and precision of measurements.
Two research questions are examined in this paper: (1) “How do accuracy and precision compare between different methods and the established height of the tree?”, and (2) “How does the performance of height measurement tools compare between conifers and broadleaf trees?”
MATERIALS AND METHODS
Sample Sites and Tree Selection
A member of the research team randomly selected and recorded the coordinates of 255 trees at 8 locations within the Rural Municipality of Victoria Beach, Manitoba, Canada, based on a proportionate sampling of the number of accessible trees located at each location (i.e., no trees on private property or in enclosed areas). The selection was controlled such that a clear sight of the tree trunk was always established from at least 1 side of the tree, a clear view of the treetop was present, and no noticeable lean was present. The selected trees were comprised of 136 (53.33%) broadleaf trees and 119 (46.67%) coniferous trees.
A randomized selection of 127 trees (49.80% of the original sample) was taken from the 255 trees of the proportionate sample. The member of the research team who selected the original 255 trees was not aware of the research question being tested. This methodology and randomized selection procedure were done to reduce selection bias, as it was conceived that measurers on the research team might otherwise select easy-to-measure trees (i.e., excurrent or fastigiate trees with live crown tops).
From the 127 trees selected for testing, 71 trees (55.9%) were located in municipal parks, 36 trees (28.3%) were located at the municipal golf course, 16 trees (12.6%) were located along municipal roads (i.e., “street trees”), and 4 trees (3.1%) were located along a forest trail. There were 85 (66.9%) broadleaf trees and 42 (33.1%) coniferous trees.
Height Measurement Methods
To examine the research questions, 3 methods were tested for measuring tree height: the stick method, clinometer (SUUNTO PM-5 Clinometer; Suunto Oy; Vantaa, Finland), and laser rangefinder (Forestry Pro II Laser Rangefinder/Hypsometer; Nikon Vision Co., Ltd.; Tokyo, Japan). A drone (Mavic Air 2; Shenzhen DJI Science and Technologies Ltd.; Shenzhen, China) was used to determine the absolute tree height using an adapted technique from Saliu et al. (2021). Where Saliu et al. (2021) used a Leica distometer (Leica Geosystems; Heerbrugg, Switzerland) to measure to the base of the drone, this study used a measuring line attached to the base of the drone. The drone was flown to the height of the tree and evaluated using a camera mounted on the drone, consistent with the methodology of Saliu et al. (2021). The point at which the measuring tape reached the ground was recorded as the absolute tree height. Slope was controlled for between the point where the measuring tape reached the ground and the base of the tree using an electronic level held against a length of steel. While the absolute height measurement was adjusted for slope, because of the close proximity of the measuring tape to the base of the tree, slope corrections were relatively minor, ranging from 0.40 cm to 12.35 cm.
Per the manufacturer’s recommendations (Nikon Vision Co., Ltd. [date unknown]), the rangefinder was set to the 3-point method for measuring tree height. Using this method, the first measurement is taken horizontally at eye level to the tree, yielding the horizontal distance. The second measurement is taken to the base of the tree, and the third measurement is taken to the top of the tree, yielding the angle between the first and subsequent measurements. The rangefinder automatically calculates and outputs the total tree height.
When using the clinometer to measure tree height, the following formula was used:
This formula is based on the formula described by the Canadian Institute of Forestry (2014) and the Woodland Education Centre (1999).
This study uses a variation of the stick method described in Saliu et al. (2020) and outlined in the Introduction of this paper. The tree height is equal to the length of the measurer’s feet to the base of the tree (length a in Figure 1) plus the distance from the measurer’s point to the tree trunk to the ground (length y) when the top of the tree is at a point along length c.
Implementation of Testing Measures
The selected trees were measured using the drone to determine the absolute tree height, then the author of the study measured tree heights with each of the 3 tested methods. The rangefinder was used first for all 127 trees consecutively, then the clinometer was used, and then the stick method. Tree height measurements were recorded individually, such that the measurer could not see the results yielded by the prior methods. While these additional steps added to the time taken to complete the measurements, it helped to reduce possible bias from the measurer by correcting measurements for greater accuracy or precision.
Each tree was measured with all measurements taken from the same compass bearing from the measurer to the tree. The direction of measurement was established where slope was as close to 0° as possible and where there were no impediments to the laser pulse nor measurement tape. The same top point of the tree was used for the 3 measurements as was used with the drone.
Statistical Analysis
The measurements were recorded in Excel (Microsoft 2021) and analyzed using SPSS (IBM Corp. 2020). Three null hypotheses were tested. The first null hypothesis was that there were no differences in the comparative precision between the 3 methods of testing tree height. The second null hypothesis was that the methods were individually accurate to the absolute tree height, as measured with the drone. The third null hypothesis was that accuracy and precision of the methods were equal in measuring conifers and broadleaf trees. The statistical analyses used 90%, 95%, and 99% confidence intervals based on the testing method for forestry scales in Kozak et al. (2008).
Cronbach’s Alpha in SPSS (IBM Corp. 2020) was used to determine the accuracy of the tests given that the measurements were essentially tau-equivalent (Graham 2006). The comparison of precision between the paired comparisons of the 3 measures—or “concurrent validity”—was tested using correlations between the 3 methods.
RESULTS
Descriptive Overview and Correlation of Methods to Absolute Tree Height
Table 1 shows the descriptive statistical overview of the data amongst different methods. The average (mean) absolute tree height of the measured trees was 13.19 m (standard deviation = 4.11 m). The minimum absolute tree height was 4.67 m, and the maximum absolute tree height was 25.71 m.
Summary of descriptive statistics of data collected by tested methods, measured in meters (m).
The mean absolute error (MAE) of the rangefinder was 0.52 m (standard deviation = 0.25 m), closer to the true tree height than the clinometer (MAE = 0.64 m [standard deviation = 0.28 m]) and the stick method (MAE = 0.95 m [standard deviation = 0.46 m]).
Accuracy Testing
The Cronbach’s Alpha Reliability Testing performed for the 3 methods determined a Cronbach’s Alpha of 0.991 (N = 3) with a standardized items Cronbach’s Alpha of 0.992. As the Alpha value approaches a value of 1.00, the methods of measurement are more consistent (Tavakol and Dennick 2011). Interpretation of this Alpha value is guided by the acceptability of error in the measured variable. The inter-item correlation matrix findings were Rangefinder-Clinometer = 0.985; Clinometer-Stick Method = 0.976; Rangefinder-Stick Method = 0.964. If the rangefinder method or clinometer method were removed from the test, Cronbach’s Alpha would decrease to 0.988 and 0.981, respectively. Removing the stick method from the test resulted in an increase in Cronbach’s Alpha to 0.992. This finding indicates that the stick method is the least consistent measurement compared to the other measurement methods.
Figures 2, 3, and 4 show the variation of the 3 methods from the absolute tree height. The solid red linear regression line of y = x (equation: y = 0 + 1 × x) shows the line of perfect accuracy in measurements. Points located above the line are overestimated height measurements, and points located under the line are underestimated. Thus, a greater distance from the red line indicates greater inaccuracy in height measurement. As can be observed in comparing the 3 figures, Figure 4—the stick method—had the greatest error and therefore the least accuracy.
Scatter plot diagram showing the absolute tree height (x) and rangefinder measurements (y). The goodness-of-fit line (y = x) (solid red) indicates the line of accurate measurement. The black dashed line indicates the linear regression relationship between the absolute tree height and the rangefinder measurements.
Scatter plot diagram showing the absolute tree height (x) and clinometer measurements (y). The goodness-of-fit line (y = x) (solid red) indicates the line of accurate measurement. The black dashed line indicates the linear regression relationship between the absolute tree height and the clinometer measurements.
Scatter plot diagram showing the absolute tree height (x) and stick method measurements (y). The goodness-of-fit line (y = x) (solid red) indicates the line of accurate measurement. The black dashed line indicates the linear regression relationship between the absolute tree height and the stick method measurements.
Each method is ascribed a linear relationship which describes how the method’s height measurements relate to the absolute tree height. According to the best-fitting linear relationship of y = −0.65 + 1.04 × x, the stick method is accurate at 16.25 m, increasing in inaccuracy (measured in meters) at lesser or greater tree heights. Below 16.25 m, the stick method increases in inaccuracy, generally underestimating the tree height. Above 16.25 m, the stick method again increases in inaccuracy, but now generally overestimating the tree height. By comparison, the linear relationships of the true tree height and the measured values obtained with the rangefinder and clinometer indicate general tendencies to underestimate tree height. Whereas the ascribed line for the rangefinder highlights greater error in measurement (measured in meters) at the high end of the range of measured tree heights (Figure 2), the opposite is true for the clinometer which shows decreasing error towards the high end (Figure 3).
In evaluating the linear relationship denoted by the black dashed lines in Figures 2, 3, and 4, note the coefficient of determination (R2 linear) value is reported on the upper-right corner of the associated black dashed line. This coefficient of determination value describes the predictive capacity of the linear relationship ascribed to the select method, expressed on a scale of 0 to 1, with a higher value indicating greater predictability. The coefficient of determination is highest for the rangefinder method at 0.987 (98.7%), with the clinometer method having a 0.983 (98.3%) coefficient of determination. The stick method had the lowest predictability along its linear relationship determined by this study (y = −0.65 + 1.04 × x) with a coefficient of determination of 0.945 (94.5%).
While the evaluation of the coefficient of determination is relevant to assessing the predictability of the linear regression, it is not appropriate for determining the goodness-of-fit to the absolute tree height. The R2 values given in the figures show the variation of the measurements from the modeled linear relationship ascribed by the black dashed line. To measure accuracy, the R2 value of the goodness-of-fit evaluation, shown in Figures 2, 3, and 4 as the red solid line, must be evaluated along the linear correlation of y = x (y = 0 + 1 × x).
The evaluation of the accuracy of the measurements relative to the absolute tree height about the linear regression goodness-of-fit line at y = x can be measured quantitatively using root-mean-square error (RMSE). RMSE shows the standard deviation of the residuals, or how far away the blue circles on the scatter plots fall from the red line, as seen in Figures 2, 3, and 4. As the RMSE approaches a value of 0, the measurement method employed (stick method, clinometer, or rangefinder) is shown to be of increasingly greater accuracy. That is to say that an RMSE value of 0.5 shows more accuracy than a value of 0.9.
Table 2 shows the results of the test for RMSE of the 3 methods relative to the absolute tree height. The rangefinder method had an RMSE of 0.7235; the RMSE for the clinometer method was 0.8022; and the RMSE for the stick method was 0.9723. This indicates that the rangefinder has greater accuracy than the clinometer, which, in turn, has greater accuracy than the stick method.
Root-mean-square error (RMSE) for tested methods of rangefinder (RF), clinometer (Clino), and stick method (SM) computed for all trees, conifers, and broadleaf types.
Precision
Table 3 shows the Pearson correlation between the height values obtained by the 3 mensuration methods and absolute tree height. All measures were significantly correlated, P < 0.001, meaning that correlations were statistically different from 0 at the 99.9% confidence level. As the correlation value approaches a value of 1.000, there is greater precision (consistency) between the 2 measures. The lowest correlation was between the rangefinder and the stick method, R(127) = 0.964, P < 0.001. This comparatively low correlation indicates that the compared precision of the rangefinder to the stick method is the lowest.
Pearson correlations between measurement methods and absolute tree height of 127 measured trees. All correlations are significant at P < 0.001 (2-tailed).
Influence of Tree Type on Accuracy and Precision
Table 2 highlights that the RMSE of all 3 methods was higher when measuring broadleaf trees in comparison to coniferous trees. This indicates greater inaccuracies in height measurement when measuring broadleaf trees. Caution should be applied in reviewing the RMSE between broadleaf trees and coniferous trees based on the differing sample sizes.
The MAE of the rangefinder when measuring conifers was 0.41 m (standard deviation = 0.22 m), compared to a larger MAE, 0.58 m (standard deviation = 0.25 m), when measuring broadleaf trees. Similarly, when measuring conifers and broadleaf trees, the clinometer yielded a MAE of 0.56 m (standard deviation = 0.24 m) and 0.69 m (standard deviation = 0.29 m), respectively. The stick method yielded MAEs of 0.70 m (standard deviation = 0.28 m) and 1.07 m (standard deviation = 0.49 m), respectively.
Because of the potential amplification of error in measurements of shorter trees, understanding the percent error is an opportunity to standardize the errors across all tree heights, which is important in the comparison of 2 subgroups. Knowing from the RMSE data that the precision of methods of measurement differ among conifers and broadleaf trees, the percent-error box plots are shown by conifer and broadleaf classifications (Figure 5). The box plots illustrate the percent error of the 3 methods. There is a noticeably larger percent-error variation (i.e., greater range) in measurements of broadleaf trees than conifers, which is especially true for the stick method.
Box plots showing percent error of the tree measurement methods for broadleaf and conifer trees. The box plots indicate the middle 50% of the percent-error values, with the midline showing the median value and whiskers showing the minimum and maximum of the range (upper and lower 25% of percent-error value), excluding outliers. Open circles (○) indicate high potential outliers, and asterisks (*) indicate high extreme values.
The Pearson correlations for the measurement methods are shown for conifer and broadleaf trees in Table 4, which show both accuracy (methods compared to actual tree height) and precision (methods compared to each other). The loss of power in correlation coefficients between methods and the actual tree height (i.e., moving towards 0) for all methods when measuring broadleaf trees indicates reduced accuracy of measurements compared to conifers. Similarly, the loss of power in correlation coefficients compared between methods indicates reduced precision when measuring broadleaf trees.
Pearson correlations between measurement methods and absolute tree height of 42 coniferous trees and 85 broadleaf trees. All correlations are significant at P < 0.001 (2-tailed).
DISCUSSION
Comparing the Methods
The findings of the Pearson correlations between the 3 methods are all significant and above 0.800, a common threshold for testing concurrent validity of measurements (the comparison of precision between 2 measurements). Tests for concurrent validity of measurements determine the concurrent validity between a proposed test and a validated measure. Because the rangefinder and clinometer are commonly used tools in tree inventories, they can be considered validated measures. Based on these significant, substantial correlations, this study has demonstrated that the stick method is concurrently valid with both the clinometer method and the rangefinder method. The concurrent validity of the stick method to the 2 other methods demonstrates that the height measurements obtained using the stick method are valid, and, based on these findings, further analyses of the 3 methods can be conducted.
Despite the concurrent validity of the stick method to the rangefinder and clinometer, the Cronbach’s Alpha findings demonstrate that the stick method is the least reliable/accurate method of the 3 methods for tree height mensuration.
The rangefinder method was found to be the most accurate method about the line y = x (Figure 2 and Tables 3 and 4). As noted in both Figures 2 and 3, the rangefinder method and clinometer method generally have an underestimation-relationship with the absolute tree height across the interval of heights measured in this study. However, in contrasting the 2 methods, the rangefinder produces greater inaccuracy (underestimation) in height measurements with greater tree height, whereas the clinometer has greater inaccuracy (underestimation) in height measurements at reduced tree heights. Because the tree heights measured are not large trees within the scope of the global forest landscape, the increased inaccuracy of rangefinders with greater tree height is problematic for accurate measurements of large trees. However, it should be noted that the figures provide a measurement of the tree height in meters; therefore, the percent error of the measurements may still be within an acceptable region.
Based on the lower predictability of the stick method and its reduced accuracy as found in the linear regression (Figure 4) and relationship to the line y = x (Tables 3 and 4), it is more challenging to create an evaluative model that can help correct errors in tree height measurements, especially with greater variation about the line y = x. From the viewpoint of a practitioner, knowing that a measurement device tends to under- or overestimate allows for on-the-spot corrections, especially within a felling situation where one might choose to give themselves an “extra bit of room.” Because of the crossover between underestimation and overestimation, it is challenging to have a general rule of thumb for field use.
Future research examining the accuracy and precision of common arborist and urban forester mensuration tools should seek to average the measured values across multiple measurements conducted by different measurers. This would help control for error by the individual measurer and introduce additional statistical tests for inter-coder reliability and the extent of variation between the 3 measures.
Measurements by Tree Type
All 3 methods were more accurate (i.e., reduced RMSE and higher Pearson correlations) when measuring conifers. The average RMSE difference was 0.2321 between conifer and broadleaf measurements. This might be attributed to the clearer identification of the top of the tree for conifers as opposed to broadleaf trees, which helps the measurer to identify the treetop more readily. This finding is consistent with the limitations described in the evaluation of smartphone apps by Vastaranta et al. (2015), who surmised that inaccuracies in tree height measurement may arise as a result of misidentification of the true highest branch or foliage of the tree. Decurrent or fastigiate trees with sparse foliage spread across many upright branches may create difficulty in determining the most suitable measuring point for tree height. Because this study used the same measuring point consistently, another hypothesis is that there is less movement of the apical point of a conifer versus a broadleaf tree, introducing a more static measurement point.
Further research on accuracy and precision of measurement tools may choose to examine methods using more specific qualitative growth form descriptions, which may be beneficial in modeling measurement differences between tree genera.
Implications for Arborists and Urban Foresters
Although the duration of each method per tree was not measured in this study (although it would certainly be a worthy study in the future), anecdotally, the rangefinder was substantially faster, measuring trees in less than a quarter of the time used for the clinometer and stick methods. In addition to the shorter time required to take a measurement and the greater accuracy, the benefit of the rangefinder is that it reduces the influence of human error in calculations, as the calculations are performed by the unit itself.
The accuracy of the rangefinder was highest, and, as a result, should be considered a best practice for tree height measurement during inventories. Because the rangefinder involves no calculations on the part of the user, it may become especially pertinent for urban forest inventories completed with the help of volunteers/citizen scientists, a practice that is becoming increasingly common (Harrison et al. 2020). Using more user-friendly technology may decrease error and will make it easier to teach volunteers the tree mensuration methods.
The stick method had greater error than the other 2 methods in all cases, even under the application of improved practices. While the recorded measurements for inventory data analysis benefit from the least error (i.e., rangefinder), the RMSE findings of the stick method may still be within tolerable error for height measurements in a tree felling context. Thus, despite the greater error, the stick method may remain a suitable method for felling purposes in determining the extent of the felling radius.
Future research on tree height measurements may look at measurer reliability across different methods, especially with different levels of experience and/or training. Additionally, expanding this study into an area with higher trees will better demonstrate the precision and accuracy of these methods among higher tree heights.
Opportunities and Limitations of the Methods
The results examine the reliability of the methods which includes human error. As is true for all 3 methods, human error can result from deviation from the methods’ best practices or from inaccuracies in determining the highest point on the tree. Spending additional time to walk around the tree and determine the highest point is integral to measuring a more accurate total tree height.
Several conditions exist for the use of the stick method. In using the stick method, the ground between the tree and the observer must be level, and the top of the tree must be close to true vertical above the base of the tree. Any deviation from the 2 prior conditions will result in error in estimated tree height using the stick method. Should the tree’s top not be vertically above the base, the stick method will yield an overestimate when the assumed right angle is actually acute and an underestimate when the angle is obtuse. The amplification of error with leaning trees will be most influential when the tree leans directly towards or away from the position of the observer.
Similarly, should the ground between the tree and the observer not be level, the stick and clinometer methods will yield an overestimate, provided that the observer and the base of the tree are at the same level and a depression or ridge exists between the observer and the tree’s base and the measuring tape is laid on the ground.
Because both methods are contingent on the ability to measure the horizontal distance accurately using a measuring tape, their application will also be limited by hindrances to measuring a clear path from the observer to the tree trunk. As such, the use of the stick method or clinometer when working in an area with large brush accumulation can be limited. However, when used in a felling scenario, where the measurer wants to know where the top of the tree is likely to reach, foot placement where the top of the stick aligns with the top of the tree from the measurer’s perspective will roughly estimate the felling radius of the tree, as is true when the clinometer reads 45°.
This same situation with large brush accumulation is also detrimental to the use of the rangefinder, however. The measurer must be able to determine the location of the base and trunk of the tree, and this may not be possible with interference between the base and/or trunk of the tree and the rangefinder. In an urbanized environment, this may be less frequently encountered, although shrubbery surrounding the tree can impede the application of the rangefinder. In such cases, a second person can stand next to the trunk of the tree and provide a reflective point for the rangefinder. Alternatively, the stick method or clinometer can be used with the measurer making use of a measuring tape to measure from the base of the tree to a position where a clinometer can be used or at the 45° angle with a stick.
This introduces another benefit of the clinometer over the stick method: the ability to use the clinometer at varying distances. As the clinometer is not contingent on maintaining a 45° angle, the clinometer can be used at a closer range than the stick method. Additionally, elevation corrections for the clinometer are more readily determinable, although requiring additional measurements of the distance parallel to the slope and the degrees of slope (Rheinhardt et al. 2013).
In much the same manner that statistical tests hold various assumptions and conditions, so too do the measuring instruments in urban forestry. The foundational condition which underpins the use of the rangefinder is a clear, unhindered ability to see the tree’s trunk, base, and top. Any hindrance to viewing the trunk can cause the laser pulse to misread, resulting in inaccurate measurements by distorting the true horizontal distance, thus detrimentally impacting the tangent functions which yield tree height. The clinometer and the stick method share the condition that the measurer must be able to measure using a tape measure along a horizontal gradient, although the stick method has the further condition that the measurer must maintain an isosceles right triangle. The overarching benefit of the stick method is that it comes at no cost and a stick can be sourced by an arborist at most every job site, while the rangefinder is more accurate and faster to use, yet more expensive, although the cost may be offset by the swiftness of the tool. Meanwhile, the clinometer finds itself as an intermediary between the 2 others.
CONCLUSION
This study demonstrates the accuracy and precision of the rangefinder above the clinometer and stick method. While the rangefinder was determined to be the most accurate, the clinometer was close in accuracy. The 2 methods were closer in precision to each other than to the stick method. Using the stick method, reasonable accuracy and precision within the 95% confidence interval was achieved, particularly in measuring conifers; however, deviation from the absolute tree height varied greatly for some measurements. Further, the findings demonstrate that measurements of tree height of conifers under all 3 methods are more accurate and precise than tree height measurements of broadleaf trees. This research is applicable to the evaluation of suitable mensuration techniques for the determination of tree height.
The use of the stick method, which remains an informal mensuration practice among loggers and arborists, can be considered reasonably accurate within +/− 1.5 m and may be considered an affordable, accessible option for determining the felling radius when used according to established procedures. These findings may also be helpful in field-based education, demonstrating the accuracy of various methods in an urban forest context.
Because of the adoption of rangefinders in more recent inventories, this research demonstrates how technology has increased the accuracy of measurements in urban forest inventories. Analyses of common field-based practices are important to promoting applicable standards of practice, and this research helps validate the use of common handheld apparatuses for tree height measurements for varying contexts.
Footnotes
Conflicts of Interest:
The author reported no conflicts of interest.
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