Abstract
When considering the establishment of tree protection zones in construction, or in assessing relative damage to a tree for risk or penalty, it would be useful to have a method to predict total root area at some distance from the tree. With such a method, the arborist can assess the level of damage in comparison to some estimate of the total rather than from a loss of possible root zone space based on land area. We used a modification of the pipe model approach to estimate the root cross-sectional area at different distances from the tree as defined by the edge and center of the trunk. We discuss two early studies. The first considers root systems excavated from a limited set of 9 trees over 50 years post-establishment across 3 species. Trees were excavated and roots harvested, cataloged, and imaged for measurement at 1, 2 and 3 meters from the trunk edge of the respective tree. The second study considered 29 digitally mapped root systems of Fraxinus pennsylvanica ‘Patmore’ 9 years post-transplant by developing code for a virtual dissection at specific distances from the tree trunk. The second study observed variability across a tightly defined set of trees. There was a weak relationship between root area at set distances by species, and we found 3 m was a useful distance in the first study. We have a long way to go in development before having a method as a tool for practice, but the approach may be useful with additional observation and study.
Introduction
Tree care professionals are tasked with evaluating tree root system patterns when designating tree root system protection zones, considering risk, or when evaluating damage from an event in proximity to an established tree. Much of the process in developing a plan for tree protection during construction focuses on soil conservation for the benefit of the tree root system (Matheny et al. 2023). Often root location and contribution to total damage in tree protection is a concern for tree mechanical stability (Smiley 2008), or protection for whole plant biological support (Watson et al. 2014). Tree care professionals often seek to understand how many roots are impacted as a portion of the entire root system, or a dose of root impact. Within the literature base, it is established that root system architectures can follow several basic forms from a shallow or platelike form, to a compressive buttress or “heart root” form, to a deeper central post morphology, amongst others (Vogel 1996; Mattheck et al. 2015; Stubbs et al. 2019). Environmental conditions such as wind (Stokes et al. 1995; Tamasi et al. 2005) and obstruction (Smiley et al. 2000; Gilman 2006; Day et al. 2010) influence root colonization patterns. Site-growth factors, coupled with an often-uncertain history of previous construction impacts and artifacts, make it difficult to suggest with any precision the colonization of soil volumes around the tree, to predict a dose of impact to the tree resulting from construction, and cannot be assumed to be in any way symmetrically colonized around the tree trunk or canopy. Technologies such as ground-penetrating radar (GPR) or sonic tomography mapping can be deployed for a non-invasive imaging for inferred root location, size, or density (Cermak et al. 2000; Butnor et al 2003; Barton and Montagu 2004; Bassuk et al. 2011; Rinn 2016). However, the technical expense of tools and the training for signal interpretation limits their generalized use in many applications.
The tree trunk can serve as an accessible integrated measure of water flow capacity within a tree since it handles the vascular connection between root system water foraging and tree canopy water demand. Since its introduction, the pipe model (Shinozaki et al. 1964a, 1964b) has been used to conceptualize or explain the connectedness of the tree vascular system as much as to build allometric relationships within trees and other plants. In concept, it suggests the flow of water to meet photosynthetic and transpiration demand has to be related to the “pipe system” carrying the water to the leaf. As examples, the relation between leaf surface area and the supporting shoot tissues as a function of vascular capacity could be modelled at a flow path of various pipes. The model proposes a relationship often characterized by relating a surface area of leaf tissue, or water demand by leaf to the transverse areas of stem tissue, using active conduction tissues versus inactive zones and other non-conductive cells as a scaling factor (McDowell et al. 2002; Calvo-Alvarado et al. 2008). Alternatively, the cumulative area of branch cross section could be related between hierarchical levels of branch division, and to a limited extent a linkage between root systems to shoot tissues (Oohata and Shinozaki 1979; Lehnebach et al. 2018; Houette et al. 2023). Having been demonstrated as a robust organizational tool, the pipe model to generate study hypotheses has established research record (Lehnebach et al. 2017; Aye et al. 2022). Similarly, fluid flow and ascent of fluid in tree xylem systems have been developed and discussed as a relationship linked to the Hagen-Pouselle law in confined fluid flow and in associated Huber values (Huber 1928; Waring et al. 1982; Tyree and Frank 1991; Mencuccini et al. 2019), and as a parallel to Murray’s (1926) model for blood flow in vascular systems and used in root models (McCulloh et al. 2003; Houette et al. 2023).
Focusing on the pipe model hypothesis, the distance and number of branching connections from the point of stem measurement to the leaf surface demand measurement is a confounding factor (Gering et al. 2015; Lehnebach et al. 2017). This is especially salient to a consideration within large woody plants like trees. There have been fewer root-based studies or applications as compared with leaf to shoot study, likely due to the complications and difficulties related to root system observation and measurement. One study observing plant response to root damage by Benson et al. (2019) considered 18 Quercus virginiana in the range of 28 cm at 1-m elevation in Florida, USA. Here, the roots on trench surfaces were modelled as summations of circular root areas defined by orthogonal diameter measures, then used as a ratio coupled with sapwood as estimated from electrical resistance tomography, asserting a pipe model approach (Benson et al. 2019).
Mangrove (Malpighiales spp.) has also been a focus of root-based pipe model adaptation (Rodtassana and Poungparn 2012). In the case of mangrove, root systems have been parsed into root size categories. The relative similarity of total transverse area within each size category has been used to suggest a pipe model can link smaller roots to larger roots as a reasonable approach (Poungparn et al. 2002; Poungparn et al. 2004; Rodtassana and Poungparn 2012). Given the tendency of mangrove to graft and anastomose into clonal form, selection of isolated replicates has limited the replication in studies with a further limitation to focus on smaller individuals (in the range of 10- to 13-cm diameter at breast height [DBH]). Similar findings on 3 fruit tree and 1 shrub species (Strychnos cocculoides, Strychnos spinosa, Vanqueria infausta, and Grewia flava, respectively) linked root size class totals as a pipe model consideration were observed in Africa (Oppelt et al. 2001). While trunk size was not reported, the ages of test plants were in the 10- to 25-year range with basal stem diameters in the 5-cm range as estimated from their example illustrations. Using 3D digital renderings of a Fraxinus pennsylvanica ‘Patmore’ root system, Houette et al. (2023) found a ratio between branch root diameters and their source root diameters to be normally distributed with the source root being of smaller dimension than the summation of its branches.
A study was developed during Tree Biomechanics Week 2022, taking advantage of a plantation of maturing trees in Shalersville, Ohio, USA. The plan was to test the suitability of the pipe model hypothesis approach on large trees to provide a predictor of cross-sectional area of roots at a series of known distances from the tree trunk center and from the edge of the trunk. A second study was developed to deploy digital models of skeletonized tree root systems to provide a second avenue of building an argument for a trunk to root cross-sectional area relationship (Koeser et al. 2016). Our goal was to provide a method for the tree care professional to use trunk diameter and distance to estimate an expected total root cross-sectional area of woody roots. If the method was demonstrated to be successful, we might then develop a simple field observation tool with larger datasets by which to regulate dose or define damage in the field by counting and cataloguing woody roots as a percentage of a total expected area. In the case of a non-concentric root zone, or unbalanced space from built infrastructure, the information could improve current methods of inspecting the root zone for protection assignment or damage assessment. That tool could be used whether in exploratory trenching or in post-development damage assessment.
Methods
Study One: Biomechanics Week 2022, Shalersville, Ohio, USA
The first study was developed as an opportunistic study as part of the 2022 Tree Biomechanics Week event in Shalersville, Ohio, USA (41.2333 N, 81.1525 W). The biomechanics week event is designed to bring a community of researchers, students, and practitioner volunteers together to execute small studies within the structure of a single week. The end of the week has featured an educational event in the field to discuss the work and to further build the community. The site is a plantation of multiple species planted in grids as single species plots. The site was maintained as a research plantation for decades, with tractor mowing between trees and open access rows between some research blocks. Trees in the plantation block grids were planted on 6.1-m (20-ft) centers. The wind profile of the site has winds generally from the western direction, which is maintained as a mowed field. The site was planted over several years starting in the 1960s, and several trees had been removed in previous research weeks since 2010.
Three trees each of Platanus × hispanica (plane tree), Tilia cordata (linden), and Liquidambar styraciflua (sweetgum)(Table 1) were selected. While most of the plantation site is on a Ravenna silt loam, the linden and sweetgum were within a section of French-town silt loam, which is generally characterized as having thinner soil layers and less drainage potential (Web Soil Survey 2018; John Siefer personal communication 2018). Species were chosen as opportunity allowed within the plantation grid with space for excavation tools. Trees with obvious or recorded damage were not chosen. For the educational purposes of the event, we chose to select 3 trees across 3 diffuse porous species to capture some of the morphological/architectural variation. Trees were also chosen for their ability to conduct static load pull testing associated with the trenching effort of this study. All trees in the study were within the plantation grid and not on the exposed windward edge of the plantation block. One linden was on the western side of its respective block, which was recessed from the rest of the site edge, suggesting there had been something in the block protecting the tree at some earlier date, much as within the plane tree block, so those trees had some recent wind exposure. All 3 replicates of the sweet-gum were on a research block edge running parallel to the prevailing wind direction, with mowed area for machinery access to the south side of each tree.
Tree replicates used in Study 1. DBH (diameter at breast height)
Trunk diameter at 1.37 m was measured with a diameter tape. Azimuth North was labeled onto the trunk with marking paint. A circle was then marked 3 m from the edge of trunk to mark the first trench measurement zone. This distance was chosen based on data we had developed from root plate dimensions of failed trees after Hurricane Sandy in 2012 (Figure 1), and from the failure ratios established by stem diameter and root plate radius from storm-related tree failures in Germany (Mattheck et al. 1993; Mattheck et al. 2015). As the plantation was established with trees on a 6.1-m center grid pattern, 3 m was felt to be the maximum distance to harvest between the trees with space for the excavator without condemning excessive non-target trees. A large excavator was used to remove soil outside of the measurement zone as a trench, then pressurized air was used to blow away soil from the roots in the trench edge measurement zone. The circumference of the trench was broken down into 45° sections and marked with flags. Root section zone targets for collecting all roots at the measured distance were marked at 3 m from trunk with paint before roots were manually harvested and bagged for later processing. Roots were placed in bags labelled for their distance from trunk and section of collection for a later mapping of harvested roots by count and by cross-sectional area contribution. Once the process was completed, a second trench was created 2 m from the trunk for a root harvest, and a third trench 1 m from the trunk was established and harvested. Finally, linden trees were pulled to failure then lifted to develop a root plate bottom depth measure. Plane trees were lifted, cleaned with air, and skeletonized by removing roots < 3 mm to then photograph, measure root depth under the remaining plate, and to collect all roots from that bottom plane of the plate. Due to time constraints of the Biomechanics Week event, the sweetgum harvests were incomplete, and the trench root collection was simplified to entire trenches rather than section subsets.
A tally of wind-overturned tree root systems across mixed species after Hurricane Sandy (2012) in Central New Jersey, USA. Measured root plate dimension is referenced to tree DBH, here as the windward side distance of the overturned tree root plate, from trunk center to the point of root breakage. The dotted line represents an estimated failure curve developed from an image by Mattheck et al. 2015 as the “VTA windthrow diagram for park and garden trees” describing the same relationship.
In the final accounting of research data, the plane tree, and the linden were completely harvested, but in some cases, for time constraints, the 8 radial sections were batched into single collections after photo documentation to match a 3D-scanning effort (to develop and test a protocol for future work). The sweetgum trees were not completed, as the time for the excavation and sampling exceeded the time available for the teams in the field and the event timeline. Data is presented as accounting for a partial dataset to inform future efforts.
The collected roots were later processed to develop a clean transverse section thickness of 0.5 to 1.5 cm for each root within the target zone line of the 3-, 2-, or 1-m mark. Roots on the underside plane were also processed noting the specific depth of plane established in the field. Roots greater than 3 mm were used in the sample processing for counts and area scans. The root sections were arranged onto the plate of an Epson® 11000XL scanner (Seiko Epson Corporation, Suwa, Nagano, Japan); the pixel dimensions were known and verified. The image was collected as a .jpeg (after verifying a lack of distortion versus a .tiff image) at 400 dpi. Images were cropped and then non-root pixels were erased by hand, to avoid sample depth capture and shadow in the image. Pixels of root presence were then counted, recorded, and converted to area for each sampling image. Roots have been archived by tree and section grouping for future comparison to 3D images which were collected in the field as part of this harvest (data not shown).
Root area summations by section and as whole tree total at each trench distance were developed as a distance from the trunk edge with an assumption of a centered trunk core. The pipe model hypothesis would suggest that the transverse area of the roots in total might somehow relate to the trunk conducting tissue as a connected transverse section. Accounting for non-conducting cells and the development of heartwood-sapwood balance was deferred to a later analysis once a fundamental pattern was identified. A series of exploratory models were attempted to look for patterning comparing each distance within a tree replicate and across replicates within species and then between species. While we acknowledge there is a difference between the formal pipe model hypothesis and the antecedent of the hypothesis such as posited by DaVinci (MacCurdy 1938; Richter 1939), we sought a uniform distance as a field management-assessment approach informed by the pipe model hypothesis, rather than strictly an application of the model. Radar/donut plots were developed to track both root counts and root cross-sectional area within each section and distance from the trunk. Roots in the bottom plane after total tree excavation were added to the 1-m dataset as there were no roots lower than 1 m found during excavation of the linden and plane tree.
Visual patterning of root area and root occurrence was assessed with an understanding of a generally west to east wind direction. Root cross-sectional totals at each distance were developed and compared between distances within individual trees, and compared to the trunk diameter of the individual.
As an exploratory effort with limited replication, we used scatter plots and simple linear regression (SLR) model approaches in Minitab® version 19 (Minitab Inc., State College, Pennsylvania, USA) to consider the feasibility of developing a simple field method to estimate root areas based on trunk diameter and distance. Scatter plots and ANOVA general linear model processes were deployed to look for similarity within species and between species.
Study 2: Datasets from Koeser et al. 2016 and Miesbauer et al. 2019
For the second study to test the pipe model application, we worked with a dataset developed and detailed by Miesbauer et al. (2019) and Koeser et al. (2016). The dataset consisted of mapped root systems from 29 Fraxinus pennsylvanica ‘Patmore’ individuals from SfM photogrammetry. The trees had been excavated by 244-cm hydraulic tree spades, skeletonized to a minimum root size of 1 cm, then imaged into a series of 3D coordinate system map files. With this data, we sought to look at within-species variability with a closely controlled population of similar subject individuals as we tested the utility of the pipe modelling approach. The trees were 9 years in-field as liner transplants. We deployed pixels in the image as a proxy for area as we were seeking allometric relationships rather than absolute measures. Stated, with reference to root and trunk measures in the image, the pixels could be converted to an estimate area if deemed necessary.
Our group developed code to import #.stl images into a Blender™ interface to then create a mesh that could be processed within a Python script. We digitally imposed a series of hemispheric planes centered in the trunk center at ground elevation which we defined as the top of the first visual root in the image. We standardized the images and thus pixel dimensions by holding the zoom function in Blender™ to a constant level. To keep the “dissections” at a consistent distance from the trunk (which is more likely in the field), we imposed a sphere radius after first fixing the center of the trunk as the origin point then adding a known distance to the edge of the trunk. Trunk pixels were counted in 3 viewing directions to establish an average trunk diameter pixel count, then divided by 2 to establish trunk radius. Hemisphere radii were imposed relative to the trunk diameter at 0.2-m, 0.5-m, and 1-m distance from the trunk edge. Once imposed, the hemispheric surface was analyzed as a binomial output of 0 = non-root and 1 = root presence. Pixels that were partially filled with root and non-root were tallied as non-root if 49% or less were filled, and as root if 50% or greater were filled. Root pixels were tallied on each hemisphere to be compared with each subsequent hemisphere radius on the tree individual and as compared with the transverse pixel count of the trunk or estimated subsection of trunk (to account for non-functioning xylem vessels such as heartwood).
Summations of root signal pixels at each hemispheric distance were compared to trunk diameter (as converted from pixel to diameter in meters) of each replicate. We report these as non-transformed signal data to avoid the temptation of using the observations in-field. The observations are limited in replication numbers, using one species with a variability that should discourage immediate use as a guideline. Scatter-plots with imposed confidence and prediction bands in ordinary least squares (OLS) regression were developed for trunk diameter and root signal at each set distance to evaluate reasonableness as a useful relationship. A reduced major axis (RMA) regression model would be used for promising scatterplots which could provide an estimate of error and predictive use as a clonal set of trees grown in a uniform site, acknowledging the artifact of planting depth that characterized the initial study (Miesbauer et al 2019). Analysis was conducted in Minitab® version 19.
Results
In the first study, root counts did not present any consistent patterning with reference to prevailing wind direction (Figure 2). Also, there was no consistent or obvious patterning when portioning root area (Figure 3, Tables 2 and 3). While the root systems were present in all sectors of the encircling root harvest trench, as one might expect in a plantation system, the root presence was not balanced around the circumference of the trees in this study. There was no pattern between total root area counts and root size distribution between trees or between sections (data not shown). Root areas at each increasing distance suggested a pattern of decrease in observed root area with distance, but low replication prevented a robust test. There was no consistent relationship between DBH and root area at any of the 3 observation distances. The variability of the linden and planetree systems decreased at the 3 m distance. While the observed root area was consistent in linden between the 2- and 3-m rings, there was a marked decrease in plane tree root area with each increasing distance observation. Sweetgum data (Table 4) did not present any pattern as a species or in combination with the other species in the study.
Tree 1, Platanus× hispanica, root counts by section (i to viii). The underside plane for this tree was established at 35-cm depth, a total of 108 roots intersected the bottom plane. The center clear circle represents the tree trunk.
Tree 1, Platanus × hispanica root cross-sectional area (cm2) totals by section (i to viii). The underside plane for this tree was established at 35-cm depth, a total root area of 222.65 cm2 intersected the bottom plane. The center clear circle represents the tree trunk.
Root cross-sectional area (cm2) for 3 Platanus × hispanica trees excavated at 3 distances from the trunk edge. Roots in bottom plane were harvested after tree lifting and were added to the 1-m ring count summation with no deeper roots noted in the excavation further from the tree in the 2- or 3-m ring trenches.
Root cross-sectional area (cm2) for 3 Tilia cordata trees excavated at 3 distances from the trunk edge. Roots in the bottom plane harvested after tree lifting were to be added to the 1-m ring count summation if they were going downward, which was not observed. In cases where only totals are provided, the rings were not subdivided by section during harvest in interest of data collection in the time limited harvest event.
Root cross-sectional area (CSA)(cm2) for 3 Liquid- ambar styraciflua trees excavated at 2 distances from trunk edge. Roots deeper than 0.5 m were not observed in excavation trenches. Excavation rings were not subdivided into sections during harvest.
In the second study, we assigned hemispheric domes at radii of 0.2 m, 0.5 m, and 1 m beyond the radius of the trunk based on the dimensions of the tree spade used to harvest the root systems for the digital maps. Beyond this point, there were gaps due to the spade geometry when imposing the sphere. Of those sphere surface root counts, we observed a weak relationship at the 1-m plus trunk radius in scatterplots (Figure 4). For 0.2-m and 0.5-m radii models, we observed nonsignificant relationships of SLR models with r2 at 0.0047 and 0.0063 respectively. The root signal count in the 0.5-m radius dome was on the scale of 3× higher than the 0.2-m sphere and 2× higher than the 1-m sphere (Table 5). We interpret the signal density pattern as an artifact of the imagery and the code we developed for this initial test.
Fitted line plot of trunk diameter influence on root surface area counts for an imposed digital surface sphere at 1 m from the trunk edge across 29 Fraxinus pennsylvanica ‘Patmore’ trees (Minitab® 19 graphic output).
Signal counts from edge surfaces of virtual dissections of excavated Fraxinus pennsylvanica ‘Patmore’ root systems (Miesbauer et al. 2019).
Discussion
We describe observations on a limited dataset of trees excavated during a week-long research-education event to build a conversation as much as to build a field-based assessment tool based on a broad conceptual model. Given low replication, the results are not definitive but suggest a value in building a larger data library. For our observations, the trench excavation at a maximum of 3 m was a pragmatically selected distance within the planting grid of a plantation system. This distance also happened to fall within a pattern observed in tree failures as described earlier. To move further away from the tree would have placed the effort closer to a neighboring tree and its colonization influence, potentially confounding our observation. We did not explore the influence of root grafting within the species blocks as an influence on the ultimate model relationship and did not directly observe grafting or network anastomosis within the trenching zone. Given the size, location, and known history of the trees in the study, the 3-m distance would have been between 6.6× to 12.1× the tree DBH; falling within Best Management Practice recommendations in tree protection (Matheny et al. 2023). Our study was to look toward a bio-mechanical modelling-anchorage question which often overlaps with the protection question. Tree protection considers plant biological stress and response to trenching or soil disruption. In protection assignments, the spread of the root system as predicted by tree dimension is often used rather than a comparable percentage of total root cross-sectional area (Gilman 1989; Day et al. 2010). While the replication is low, there is evidence to at least defend an argument to develop a larger dataset at the 3- and 2-m distances, despite the labor challenges.
Our work did not consider a defined area of sapwood but considered the entire bole of the tree inclusive of phelloderm and phloem layers for a rapid method of targeting an excavation zone for assessment. The width of an observation trench would most often exceed influence of the outer tissue layers in the placement of the trench. For a more formal research application of a pipe model, the calculation of sapwood area, the proportion of sapwood in vessel elements, and the radial size distribution of said elements would be desirable. In addition, it would be useful to discretize functional vascular transmission proportions of the roots in cross section as partitioned across root size classes. Whether using sonic tomography toward that purpose or making a direct measure in a more tangible (if less definitive in function) increment core observation, scaling the trunk can be very useful toward a direct modelling application.
Similarly, our work did not partition the root area into active and non-active vascular transport zones. We did, however, find that the fast collection of the root sections in-field was useful insomuch as scanning the root sections as groupings of roots provided an organized archive for measurement and image analysis that was preferable to a modelling of roots as circles from measured caliper diameters.
In 20 Pinus sylvestris trees linking total trunk xylem area and coarse root area (root size undefined) at the distal edge of the zone of rapid taper (distance undefined), Hari et al. (1986) observed a strong allometric relationship connecting the root area to trunk area in felled trees which were later excavated. Further, in Pseudotsuga menziesii var. menziesii, a strong relationship between the trunk sapwood and root sapwood of 12 trees was developed from felled and excavated trees (Gould and Harrington 2008). Within the Benson et al. (2019) study, use of sonic tomography was used to estimate sapwood in a ring-porous species to great advantage. In earlier work, this same team noted differences between ring porous and diffuse porous estimate reliability using the sonic method, suggesting the research applicability might be more approachable than generalized field use for sapwood calculation, at least for the near future (Benson et al. 2018). Since our study did not calculate the proportion of the trunk that was conducting sapwood, our ratios are skewed toward a much lower value as a ratio of root area to total trunk area. In any case, the patterning if observable would be evident and could lead to a best method to refine the relationship as a field assessment tool.
We had developed a series of concentric trenches with our 3-m trench approximating the 9× to 12× trunk diameter treatments across the Q. virginiana tree size distribution in Benson et al. (2019). Our limited root area data follows the general trend observed in that study for 2 of our 3 species. We note the total cross-sectional area of roots (CSA) generally decreased within sweetgum and plane tree replicates. CSA in linden was level between the 2- or 3-m rings but decreased from the 1-m ring.
The pattern of root CSA decrease from 1 m to 2 m is consistent with a zone of rapid taper (Lyford and Wilson 1964; Fayle 1968; Eis 1974; Fayle 1983). Particularly for compressive buttress (Vogel 1996)— otherwise termed heart root models (Dupuy et al. 2005)—the zone close to the trunk would have additional root CSA in the structural support function while at distance the surface area of multiple roots (Stokes 2002) would provide translation of loads to soil, and the roots assume a rope-like morphology more consistent with vascular transport, with a reported bias of root CSA in the windward direction (Stokes et al. 1995). We did not see a colonization patterning in our trees, but we also chose trees within a plantation grid sheltered from the known wind direction.
We observed some deeper root development in Platanus × hispanica and thus established a method to count at the 1-m distance. Incomplete harvests prevented any depth observation close to Liquidambarspp. trunks. No roots were observed growing deep in the 2-m trenches. We did not see Tilia spp. root penetration below 35 cm in the soil profile on this site. Our study observed planetree root systems that were visually consistent with a heart root system morphology. While not fully excavated, the sweetgum systems were also following a pattern not definitive but not inconsistent with a heart root system. Static pulling data collected as part of the excavation of the linden and sweetgum (data not shown) suggested a high anchorage remained after the 2-m trench, suggesting a heart root plate and deeper rooting close to the trunk. The linden displayed a shallow plate-like root architecture, lacking any deep striking roots or major oblique roots with a maximum depth of less than 35 cm; in contrast to some expectations (Ashby 1962; Fayle 1962; Burns and Honkala 1990). While we cannot attribute this colonization pattern specifically to soil profile influence, we did note the visual evidence of slow drainage on the site by way of ground vegetation pattern as confirmed by characteristics of the soil profile as published in the soil survey.
For the expense of such effort, both in the time and labor of establishing research study trees for harvest and in the harvest itself, there is merit in building a general root collection protocol and an organized foundation of observations over time and species. This would likely have to be opportunistic in land clearing events, or possibly deployment of air excavation followed by digital imaging to reduce the destructive nature of the harvest and labor in excavation.
We note that in the imaging analysis in Study 2, there are times when the computer system cannot discretize the quality of root intersections beyond the source image “visual” signal as represented in digital space, and the source image may not have accurately captured root intersections deeper in the root plate. As a result, there may be a density artifact in proximity of the trunk in an image file. We acknowledge that results would change if we chose a higher resolution image for analysis, as the pixel size would be smaller, so the binary separation of root signal would gain precision. The code we developed for measuring a root signal needs additional signal conditioning. Specifically, an improved code would need to establish the maximum orthogonal difference of 2 diameters in signal to then establish a transverse section root area versus an oblique section if the root was running along a portion of the imposed sphere surface. That error would inflate any summation or root signal at any distance from the trunk.
Our outputs in the smaller sphere radii were consistent with the work of Houette et al. (2023) which was developed from a portion of a total root system within the same tree harvest dataset and discusses the massing of signal image in the root plate interior. As with that study, we observe a more normal image with fewer intersecting impediments in our 1-m sphere as the location is on the periphery of the harvested tree image (Houette et al. 2023). While we observed a relationship at the largest sphere surface, we cannot make any assertion that there is a predictive relationship, even with 29 trees of the same species as a cultivar population within a common growing plantation. We know we have an artifact within the sample based on the planting depth variable in the original design of the plantation study which ultimately influenced our positioning of the sphere based on the cut trunk surface (Koeser et al. 2016; Miesbauer et al. 2019). We do not know if the cultivar was a rooted cutting stock or a grafted scion on a seedling root stock. We are thus limited in making an inference on species level variability. Reworking and then rerunning the model is a short-term goal, and then the model outputs might improve.
Conclusions
Our initial goal was to evaluate the idea of predicting total root cross-sectional area at a distance from the tree as a function of the trunk diameter of the tree. Having a predictive tool, we could inform assessment of root protection or root damage when gauging either proportion of root system damage or in assignment of protection zone boundary. With such an estimator, the tree care professional might estimate the level of damage in comparison to some estimate of the total root CSA rather than from estimating loss of possible root zone space based on land area. Toward that end, we look to a modification of the pipe model approach to estimate the root cross-sectional area at different distances from the tree as defined the edge and center of the trunk. We have a long way to go in developing and collating datasets before having a method as a tool for practice. We acknowledge there are many variables which influence the patterns of root growth and the relative efficiency of root function which would impact the ultimate ratio of root area to trunk area in any specific instance of an individual tree, impacting the robustness or sensitivity of such a method.
We suggest that 3 m is a data-supported distance for observation in terms of anchorage assessments based on tree failure data, but also relevant for protection zone establishment and tree biological response; larger distances should be considered specific to current best management practice recommendations for deciduous hardwoods in the 25- to 45-cm DBH range.
From the second study, we can suggest there is a consistency in the relationship across a small range of diameters in a younger cohort of observed tree root systems. We could develop a more sophisticated model, checking the assumptions and invoking the confined flows of Hagen-Pouselle Law or the restatement of Murray’s law for r4 or r3 balancing equations, or we might organize on the location and branching ordination of a pipe model approach or DaVinci’s allometric advice. While those allometric approaches might be useful in carbon modelling or other involved analysis, it would not necessarily improve use in the field as pragmatic guidance to one’s observations when confronted by a largely unknown, hidden system which is the hallmark of a root system on a client property.
Conflicts of Interest
The authors reported no conflicts of interest.
Acknowledgements
We are dedicating this manuscript to the memory of Mark Hoenigman (1957–2024). Mark was a mentor to all, an inestimable leader, an indispensable logistics wizard in the development and execution of the Tree Biomechanics Week series of events, as well as an incredibly gifted cook and excellent conversationalist. Mark will be missed by the tree care community, and we acknowledge that this work, and indeed all the research conducted during Tree Biomechanics Week, would not have been possible without his dedicated leadership. We thank the many students and professional volunteers over multiple projects that have contributed to the data disclosed in this piece; there are over 30 with a conservative count. Different aspects of the work have been variously funded by United States Department of Agriculture (USDA) National Institute of Food and Agriculture funding through the McIntire-Stennis Program. Work was possible through various USDA Forest Service, Tree Fund, and International Society of Arboriculture grants, along with multiple sponsors to support Biomechanics Week events. Funding from the John and Eleanor Kuser endowment for the Faculty Scholar in Urban and Community Forestry was instrumental in supporting the students and the work associated with this pair of studies.
- © 2025 International Society of Arboriculture
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