Forecasting Tree Root Architecture as a Complement to Proactive Urban Green Space Design

Mature trees in urban areas bring numerous benefits, including shade, improved air quality, stormwater mitigation, and green spaces for recreation and wildlife habitat (Sander et al. 2010). While young trees are important, mature trees offer greater ecological and social benefits due to their larger size, more extensive root systems, and established canopy structures (Dwyer et al. 1991; Wang et al. 2021). For these reasons, most urban forestry plans describe the importance of protecting and enhancing existing tree cover (Ordóñez and Duinker 2013; Grant et al. 2022). However, a critical need remains to incorporate new trees into urban revitalization, intensification, and neighbourhood expansion projects. Under these circumstances, fostering conditions that allow trees to mature and reach their growth potential can enhance city livability and environmental sustainability (Ordóñez and Duinker 2013).

Proactive site planning by landscape architects and urban planners is paramount when aiming to incorporate trees that survive and reach maturity in urban landscapes. This foresight encompasses both above- and belowground considerations. Above ground, it is crucial to consider factors such as sunlight exposure, wind direction, proximity to buildings or structures, and the space needed for mature canopy spread (Urban 2008). These elements should inform tree species selection and placement to ensure optimal growth. Belowground considerations are equally important, assuming the goal of growing trees to maturity is genuine. Yet, attention to the subterranean requirements for tree growth are often overlooked or misunderstood, or their importance is minimized in the design process (Ow and Ghosh 2017; Fini et al. 2020).

Understanding the growth patterns and architecture of urban tree roots is essential for protecting and managing the urban forest (Day et al. 2010; Jim 2023). Tree root systems acquire water, nutrient, and oxygen resources from the soil and provide structural support for the tree (Gregory 2006; Murray 2008; Urban 2008). In urban settings, root growth is often impacted by a variety of soil conditions, ranging from moisture saturation to drought (Day et al. 2010; Brunner et al. 2015; Ordóñez et al. 2018), localized pockets of nutrients and variable access to oxygen (Randrup et al. 2001), compaction (Alberty et al. 1984; Day et al. 2010; Millward et al. 2011; Page et al. 2015), exposure to environmental toxins (e.g., de-icing salts)(Miron et al. 2022) and physical barriers to growth, such as soil volume, debris, pipes, walls, and pavement (Randrup et al. 2001; Page et al. 2015; Morandage et al. 2021). These belowground factors influence the manifestation of an urban tree’s root architecture, shaping an anatomical component that plays a critical role in the tree’s health and longevity (Brunner et al. 2015) and making practical anticipation of the spatial characteristics of roots complex (Gregory 2006; Day et al. 2010).

Studying living tree root systems is difficult because most roots are only easily observed with excavation (Day and Wiseman 2009; Day et al. 2010). Excavation is often resource-intensive, expensive, invasive, and destructive (Lontoc-Roy et al. 2006; Amato et al. 2008). There are noninvasive root detection methods which can avoid the need for excavation, such as Ground Penetrating Radar (GPR), but detection of roots in urban conditions using this method has proven difficult (Stokes et al. 2002; Danjon et al. 2005) and has been especially challenged by the lack of accurate, objective, and automated methods of mapping tree root systems (Guo et al. 2013; Miron and Millward 2020; Sun et al. 2023).

Incorporating plant growth forecasting methods with noninvasive tree root detection techniques like GPR could aid urban tree planting design. With the necessary parameterization, forecasting models can simulate plant growth’s structural and functional characteristics, enabling the exploration of various future scenarios that inform planting design. Such structural and functional models have been typically deployed in non-site-specific contexts, such as hypothetical pots or containers, thus permitting the study or testing of plant responses to specific growth conditions (Leitner et al. 2010b; Mulia et al. 2010; Dunbabin et al. 2013). Although the majority of plant root architecture modelling examples have focused on nonwoody species, more recent research has expanded these techniques to include tree root systems, underscoring the potential benefits of this integrated modelling approach in a broader range of ecological and urban contexts (Garré et al. 2012).

Root system simulations typically use density-based and architecture models (Gregory 2006). Density-based models simulate the spatial arrangement of root density, disregarding morphological characteristics like root growth direction and distribution (Kalogiros et al. 2016). Conversely, root system architecture models explicitly simulate these morphological characteristics in three dimensions, producing a digital representation of the spatial arrangement, geometries (like diameter and length), and the topology of a root system (Fourcaud et al. 2007; Leitner et al. 2010a; Dunbabin et al. 2013; Pagès et al. 2014). Due to their spatial complexity, these models can be computationally expensive.

To reduce computational requirements while retaining the ability to model complex root-environment relationships, recent advancements have combined root architecture models with density-based models (Leitner et al. 2010c; Mulia et al. 2010; Dunbabin et al. 2013; Pagès et al. 2014). These models vary from focusing merely on three-dimensional geometries (Pagès et al. 2014) to more complex root function simulations involving the interaction of the plant’s geometric and specific biological attributes and require consideration of the spatial location of root geometries (Godin and Sinoquet 2005). RootBox is an example of an open-source root architecture model implemented in MATLAB and authored by David Leitner and Andrea Scnepf, formerly of the University of Vienna’s Computational Science Center (Leitner et al. 2010a; University of Vienna 2023). It is a general-purpose structural architecture model that can integrate with a three-dimensional soil environmental model.

This paper introduces an urban design site assessment protocol incorporating tree root growth forecasting into the existing urban planning processes. As depicted in Figure 1, this protocol enables urban planners, landscape architects, or other planting designers to comprehensively consider above- and belowground factors during site planning and design, including predictions of how a tree’s root system will spatially evolve over time. Specifically, we demonstrate how root architecture forecasting could support the achievement of desired urban greening objectives. While tree root systems have been simulated in prior research, and plant root architecture modelling serves diverse research goals, this study investigates the practicality of RootBox to forecast generalized formal attributes of tree root architecture and predict the interaction of tree root architecture with various hypothetical urban growing conditions.

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Figure 1.

An urban design site assessment protocol with a particular focus on meeting urban greening objectives. In the Model Scoping, the urban forest management objectives, opportunities, and constraints are established as they relate to the insights that can be gained from root architecture forecasting. In Model Design and Parameterization, the RootBox model is calibrated and parameterized, and the encoding of physical and biological modulators of tree root system development over time is performed. In Post-Modelling Assessment, further calibrations are made to update model output based on real-world observation and monitoring of tree and tree-root development over time. In addition, insights gained from the RootBox model runs, such as the forecasted spatial extent of the root system, are operationalized and used to modify the tree management approach or the design of urban greening interventions.

Among various models available to simulate root architecture, RootBox (version 6b) was chosen for the current study because it is a freely available contemporary software that works atop a MATLAB codebase (University of Vienna 2023). The open-source nature of RootBox makes it potentially accessible to a wide range of researchers and practitioners. Its creators provide RootBox as a primary root system architecture model, which can be modified or augmented with new modules that describe root-soil interactions (Leitner et al. 2010a).

Model input parameters control the number and growth of individual roots. For every root type, 16 core growth parameters are set. These are listed and described in Table 1. Each set of growth parameters is tailored for each root type. In the present study, the number of types was limited to 17 for practical reasons of computational efficiency. Root types are based on a standard root architecture nomenclature developed by Zobel and Waisel (2010). There are 4 primary root architectural types: Tap, Basal, Shoot-borne, and Laterals up to the nth order (or the number of successors). In this study, none of the shoot-borne types are used. Minor variations in parameter values are used to create a complete set of 17 types.

Root growth parameter values were selected based on their ability to create generalized tree root morphological characteristics described in the literature. Illustrations provided by Coutts (1987), Stokes et al. (2002), and Danjon et al. (2005), as well as photographs of excavated tree systems in Phillips et al. (2015) and digital reconstructions of the root architecture of excavated trees in Nicoll and Armstrong (1998) and Nicoll et al. (2006), were used for parameter value refinement. Refinement of parameters based on conformance to the literature, or how well they produce architectural attributes reported in tree root system field studies, is typical when calibrating root architectural models (Pagès et al. 2004; Collet et al. 2006). It is often difficult to gauge how changes in a parameter’s value will influence the model output (Dunbabin 2007; Lopez et al. 2011; Stava et al. 2014). As an initial step, recognizably unrealistic parameter values can be ruled out of the final simulations. This decision is similar to the methodological approach Dunbabin (2007) took to assess the importance and sensitivity ofthe parameters ofthe ROOTMAP architecture model (an alternative to RootBox) to simulate agricultural crop-weed competition.

The conformity of root simulations to approximate expected root architecture was assessed relative to the following generalized tree root characteristics:

• (1) Zone of rapid taper (ZRT)—most tree root systems exhibit a rapid change in the average diameter or thickness of roots in the first 1- to 2-m radius from the base of the tree (Day et al. 2010). RootBox cannot create a tapering diameter along one root segment unless the model source code is modified (Leitner et al. 2010a). A substantive revision of the source code was not made for this project. Thus, an alternative approach to root tapering was taken to create a ZRT. Root branching was increased in the first 1- to 2-m radius using 3 generations of short roots that reduced in diameter for each generational segment. Thus, a chain of 3 roots is made to “taper” from the first to the third order root by reducing the radius for each subsequent child root segment. The taper rate conforms to Danjon et al. (2005), who define the ZRT as the distance at which the rate of change in average root diameter exceeds 1.25% per centimeter of elongation.

• (2) Tree root system radial distance—the maximal radius distance of the tree’s root system is commonly estimated in practice and is strongly related to the size of a tree’s diameter at breast height (DBH)(Day et al. 2010). It was assumed that the maximum root system radius was 8 m for all hypothetical scenarios. The length-controlling parameters in RootBox allow for control of the maximum root system extent.

• (3) Root system shape—Stokes and Mattheck (1996) describe 3 types of root system shapes generalized from field observations that are associated with the ability of the root system to provide structural support to the tree (Coutts 1987). Stokes and Mattheck (1996) do not propose a threshold for when a root system is considered as any of the 3 types, and some root forms reported in Danjon et al. (2005) reflect combinations of each type. While establishing a general shape of the root system is challenging, for the present study, the root insertion angles (parameter 3) and segment flexibility (parameter 10) of first-order roots (i.e., root types 1, 2, and 3) are set to ensure that they initiate at angles that bias their direction of growth laterally, emanating from the tree base. A technical limitation of RootBox is that the initial horizontal cardinal direction of root initiation cannot be specified in advance, is determined at random, and thus limits control of growth direction in the horizontal plane.

Generalized ZRT and root system shapes were used to set initial model parameters. Generalization is advantageous because it avoids the methodological problem of calibrating the model to match site-specific measurements, which may not represent common architectural characteristics. Simplification of root traits is also beneficial because it enables species-agnostic features to be built into the simulation, allowing results to be relevant to various site conditions. Estimating formal parameters from the literature is not meant to reproduce a site-specific root system (Dunbabin et al. 2013). Therefore, the model instead aims to implement realistic production rules that include variability.

Scenarios

Four hypothetical scenarios were simulated to capture different and plausible urban site soil conditions. In the first scenario, a “base” soil environment favored root growth from the tree’s base in the upper 0.5 m of soil and, laterally, outward and quasi-parallel to the soil surface. Model parameters discouraged root growth below this plane. This basic soil environment was altered for each subsequent scenario to introduce a growth bias to direct or restrict root growth in specific locations. Additionally, each modeled scenario was iterated 5 times to account for stochastic variation in the results. Growth parameters, except root diameter, are kept constant throughout each scenario.

The soil environment was spatially modelled using a four-dimensional matrix grid (x, y, z, C), where the three-dimensional spatial coordinates are x, y, and z. C is the environmental value assigned to the soil at a location in coordinate space (Figure 2). Multiple C values may be overlayed on top of three-dimensional coordinates. We refer to the matrix as a three-dimensional (3D) environmental affinity/impedance model (EAI). The EAI was created using the MATLAB meshgrid function that can be modified to load values from a comma-delimited value (.csv) file. The values encoded in each EAI grid point can reflect real-world characteristics (e.g., soil bulk density, soil compaction, soil oxygen availability). The EAI spanned a hypothetical 20 m × 20 m (400 m²) with varying resolutions. In the first 4-m distance, grids occurred at every 0.25 m, and after 4 m, every 1 m. The higher resolution of the grid nearer the origin was due mainly to the need to keep computation resources light. At the same time, it was desirable to provide a consistent and small resolution: simulations ran too slowly when the entire grid was at 0.25-m intervals.

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Figure 2.

The RootBox root system architecture growth model is coupled with a three-dimensional environmental affinity and impedance model (EAI). The EAI encodes and summates a variety of factors, such as soil compaction, to direct or retard the development of the root system architecture over time. The EAI has the ability to encode the locations and even the characteristics like size and depth of certain roots from an already existing tree-root system. This helps in fitting the architecture model to these known data points. Time is represented here as the progressive extension of the root architecture in three dimensions, and it is here that variations in the rate or spatiality of the evolution of the root architecture are expressed. This diagram shows 3 time steps (t1, t2, t3), but many more such time steps could be used to model a root over a long time frame. In each time step, the root system is modified—extended, stopped, or trimmed—based on interactions with the EAI.

An EAI may trigger 2 functions: (1) a tropism (or affinity) response which modulates the growth direction of the root, and (2) an elongation response which slows or speeds the rate at which a root will extend. The elongation response was governed by a function that decreases the elongation rate by the value encountered in the EAI. This can be used, for example, to model the impedance of root growth retarding influences, such as high soil bulk density, compacted soil, or low soil oxygen concentration.

Creating a soil environment and setting the response parameters offers a way to control the shape and spatial distribution of the resulting root system. However, the directional tropism function does not compel individual roots to follow a pre-defined pathway, nor do roots grow rigidly towards a directional influence. Instead, the tropism function increases the chances of any root tip orienting in the direction of influence. In this research, EAI values vary between scenarios, but only enough to create localized oddities, such as setting very low EAI values for compacted areas under a sidewalk.

Base EAI Grid (Scenario 1)

Scenario 1 represents a soil condition without growth impedance or any varying directional bias, a growth condition that may exist in larger urban parks. EAI values are selected to cause the roots to tend outwards and explore the upper 0.5 m of the soil profile (Figure 3).

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Figure 3.

(a) Surface view (ortho-graphic top-down) of the base EAI grid used with Scenario 1. The grid ranges in values from 1 (dark green) to 23 (orange) at the grid’s edges. Grid values are shown on top of the cell colours. The grid spans 20 m × 20 m, but its resolution varies. Grid values increment from smaller values (at the origin point in the center and indicated with a small black border) to larger values at the periphery, because RootBox’s tropism function requires that the directional bias be represented by increasing grid values in the direction of influence. (b) Profile view (i.e., as a slice through the grid and seen from the side) of the base EAI grid of Scenario 1. Dark green values are values that approach zero, and these values limit the extension of root growth below 1 m in depth. The location at (0,0) contains low values (i.e., one) that increase to 23 at the edges (i.e., at 10-m horizontal distance and down to 0.5-m depth). Grid values are highest at 0.1 m below the surface to ensure roots do not collect just below the surface line.

This depth bias was created to ensure the root system exploits soil layers closest to the surface and elongates from the tree base in a radial pattern. The preference of root systems to exploit shallower soil layers and to avoid deeper layers is a common characteristic of most tree root systems (Coutts 1989; Coutts and Nicoll 1991; Crow 2005; Day et al. 2010), although the biological reasons for this growth predilection in shallower soils are diverse.

Nutrient or Water Source (Scenario 2)

For Scenario 2, a hypothetical nutrient or water source is included within the EAI, exemplified by urban conditions where, for instance, there is a sewage or a water pipe leak underground (Randrup et al. 2001), influencing some of the roots to direct towards the nutrient or water source. In actual site growth conditions, it is more likely that only roots within a given proximity to the attraction point will begin moving toward it. Here, grid values remain the same as in Scenario 1, and grid values increase in a localized area at approximately 2.5 m from the tree’s base and 0.3 m below the surface (Figure 4). Grid values are increased within a buffer of 0.75 m on either side, 0.2 m above, and 1.2 m below the point of attraction. The internal location (grid cells) describing the water or nutrient conduit is given a soil value of zero because this represents an impeding obstacle to root growth.

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Figure 4.

(a) Surface view of the EAI of Scenario 2 showing values as they would appear at a 0.5-m depth. High grid values along a conduit that runs across the site represent a hypothetical nutrient or water source. The conduit is located approximately 2.5 m from the base of the tree and between 0.3 and 0.4 m below the surface. The zone of influence where roots start to direct themselves towards the conduit is 0.75 m on either side and 1.2 m below the conduit. (b) Cross-sectional profile of the EAI in Scenario 2.

Sidewalk (Physical Barrier) Underlaid with Compacted Soil (Scenario 3)

A sidewalk is located 1 m away from the tree’s base in Scenario 3. Below the sidewalk is compacted soil to a depth of 0.5 m. Low EAI values reflecting sidewalk compaction trigger tropism and elongation functions, forcing the root to change direction or stop growing underneath the sidewalk (Figure 5). Compaction can either be modelled as a rigid barrier where root growth is forced to stop entirely upon encountering low grid values (e.g., when a concrete sidewalk is encountered), or it can make root growth difficult. In the former case, roots will fail to extend if they enter the volume under the sidewalk. At values of zero, the extension of a root stops immediately. In this scenario, depths between 0 m and 0.1 m represent the hard sidewalk material that will not permit root extension.

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Figure 5.

(a) Surface view of the EAI of Scenario 3. Like Scenario 2, the grid is identical to the base EAI grid of Scenario 1 except for the very low values representing the location of the sidewalk (shown in dark green). The sidewalk is located approximately 1 m from the tree’s base and is 1.5 m wide along the entire site represented by a grouping of low grid values up to 0.5-m deep. (b) Cross-sectional profile of the EAI in Scenario 3.

Weighting the Basic EAI Grid Based on In-Situ Knowledge of Root Location (Scenario 4)

A customized EAI was created in Scenario 4 to represent areas where a hypothetical on-site field investigation has revealed the presence of roots and/or a substantial amount of root biomass. The base EAI grid was weighted to favour these areas of known root presence. The weighting scheme was encoded into a weighting grid multiplied against the base EAI grid to create a tropism response that directs root growth to these locations. A multiplication of base EAI grid values to create tropism bias was used in Scenario 2, but the tendency was localized within a limited zone of influence. Scenario 4 takes a different approach and weights the entirety of the base EAI grid to ensure that the effect of the bias is present in all locations and signals all active root tips.

Two locations were chosen to represent areas of the highest directional bias (Figure 6). These were located at the three-dimensional spatial coordinates (in meters): −5.00 (x 1); −3.25 (y 1); −0.50 (z 1) and 3.00 (x2); 3.75 (y2); −0.40 (z2).

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Figure 6.

(a) Surface view of the EAI of Scenario 4. The grid is similar to the base EAI grid of Scenario 1 but is weighted by multiplying by a separate grid of values (not shown). Two black dots represent positions of the highest weighting. These focal points are intended to be the locations of the greatest directional bias (i.e., root attraction). Because the values of the base EAI grid are also weighted, their capacity to modify growth direction is maintained. (b) Profile view of the EAI of Scenario 4.

In this study, we assess root architecture forecasting and its potential use in urban green space planning and design. We have situated the results of this focus into a broader framework that aims to holistically understand urban tree growth in the planning and design process. Critical inputs are identified with model scoping, including canopy goals, biodiversity, root system spatial configuration, local water and nutrient sources, and above- and belowground impedances. In the design phase, three-dimensional environmental affinity and impedance models are created as part of our RootBox modifications and parameterization; these encapsulate the nuanced interactions of a tree root system with its surrounding environment and introduce temporal span and granularity. The final stage—post-modeling assessment—emphasizes iterative validation. This process must be undertaken at future times, where observed real-world growth is compared with root architecture forecasts (see description of Scenario 4). Model parameters may be updated at this stage. Detailed findings follow that illustrate RootBox’s root architecture outputs, assuming several different belowground scenarios.

Surface and profile visualizations of the output root system are used to demonstrate and discuss the architectural response to the EAI created for each scenario. The root system is assessed visually to qualitatively determine whether roots react to tropisms in each scenario by avoiding or failing to grow in impedance areas or opportunistically growing towards attractional biases. Profile views demonstrate examples of rooting depth and distribution. In addition, a 20-m × 20-m grid of cells was used to average root axis depth over the entire root system and to average the depth response to obstacles or areas of attraction.

Average root diameter measurements at defined distance intervals were used to demonstrate the formation of a ZRT because it is a function of distance from the tree’s base. The average root diameter was calculated at defined distance intervals of 0.25 m, 0.5 m, 0.75 m, 1 m, 1.5 m, 2 m, and at every subsequent 1-m increment until a 10-m distance was reached. Distance intervals are expressed as concentric rings.

RootBox was iterated 5 times for each scenario to account for random variations in how the root systems arrange themselves vertically and horizontally. In all scenarios, the root system had a clear tendency to grow outwards and slightly downwards in the first 1- to 2-m horizontal distance from the tree base and then rise again—often touching the soil surface— after this point. This indicated that the base EAI grid influences the shape of the root system in all cases. In Scenario 2, the nutrient or water conduit attracted roots towards and under it, though this seemed to apply only to roots that grew within a 0.75-m distance from the nutrient source, which is the distance at which affinity bias was higher, while in Scenario 3, the root system stopped growing once it reached lower grid values under the sidewalk, while some roots dove under the compaction area to the other side of the sidewalk. Despite growing down and under the sidewalk, the sidewalk cut off most root growth and created a noticeable imbalance in the number of roots passing under it. Scenario 4 resulted in a subtle growth movement towards the input affinity weights and produced architectural and depth attributes that, while similar to those produced in Scenario 1, created roots at the designated locations.

A ZRT occurred in the first 1-m horizontal distance from the tree’s base in all scenarios. In this case, the ZRT was calculated as the distance at which the rate of change in average root diameter exceeded 1.25% per centimeter distance. Generally, there were differences in the distribution of the taper rate between each scenario and in the average root diameters measured at each distance interval.

Base EAI Grid (Scenario 1)

The base EAI grid scenario introduced uniform soil tropism towards the upper 0.5 m of the soil and the outer edges of the grid. Depths below this point became progressively smaller, and after 1 m, depth began to hinder growth by reducing root extension. In one of the model iterations, the horizontal distribution of the roots was highly skewed in one direction. This was due to the random horizontal angle of the starting point ofthe root. However, in 4 out ofthe 5 iterations, roots tended to distribute evenly around the tree base and grow outwards in all directions. Figure 7 shows the distribution pattern of the fifth iteration as an example.

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Figure 7.

(a) Surface view of root distribution for Scenario 1 created with the fifth simulation iteration. Concentric rings are the distance intervals used to sample average diameters for ZRT identification. (b) Cross-sectional profile of Scenario 1 simulated root system. (c) Average depth of root vertices for Scenario 1. Depth values are averaged over a 1-m × 1-m grid cell across all 5 simulation iterations.

Most roots remained at, or grew towards, the top 0 to 1 m of soil. Roots that start growing vertically will dive deeper and reach beyond 1 m in depth but gradually move toward the surface. Overall, the number of roots that descended deeper than 0.5 m was relatively small, and most smaller diameter roots tended to occur between 0 to 0.5 m in depth. The ZRT ended at the 0.75-m distance interval (Table 2). At all distance intervals between 0 and 0.5 m, the rate of change in average diameter per centimeter exceeded 1.25%. Still, the most rapid taper occurred between 0- and 0.25-m distance, measured at an approximate 2.84% change per centimeter increment.

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Table 2.

Average modelled root diameter in relation to distance from the tree. Data for scenarios 1 through 3 are presented. The zone of rapid taper (ZRT) is determined based on the percent change in the mean diameter of the root per cm distance from the tree base. The symbol “*” indicates where the ZRT ends.

Nutrient or Water Source (Scenario 2)

The nutrient or water source scenario used the base EAI grid of Scenario 1. However, it introduced an area of higher directional affinity up to 0.75 m on either side and down to a 1-m depth at the location of the source. The values within this envelope were the basic (Scenario 1) grid values multiplied by 3. Figure 8 shows the distribution pattern of the fifth iteration; there is no discernible horizontal growth bias towards the source in any of the iterations. Moreover, the roots’ vertical profile shows an affinity downward near the source. Roots dive deeper into the soil to a maximum of 3-m depth. Similar to other scenarios, root vertices below 0.5-m depth occur more frequently near the source than elsewhere. Like Scenario 1, the ZRT ended at the 0.75-m distance interval. At all distance intervals between 0 and 0.75 m, the rate of change in average diameter per centimeter exceeded 1.25%. Still, the most rapid taper occurred between 0- and 0.25-m distance, measured at 2.55% change per centimeter increment.

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Figure 8.

(a) Surface view of root distribution for Scenario 2 created with the fifth simulation iteration. Concentric rings are the distance intervals used to sample average diameters for ZRT identification. The 2 outer boundaries of the nutrient/water conduit are indicated with dashed lines. (b) Cross-sectional profile of Scenario 2 simulated root system. (c) Average depth of root vertices for Scenario 2. Depth values are averaged over a 1-m × 1-m grid cell across all 5 simulation iterations.

Sidewalk (Physical Barrier) Underlaid with Compacted Soil (Scenario 3)

The sidewalk obstacle and compaction scenario also used the base EAI grid of Scenario 1. This approach introduced an area of high impedance approximately 1 m away from the tree base and down to 0.4-m depth. In all iterations, there was a noticeable horizontal reduction in the number of roots on the far side of the obstacle compared with the near side (where the tree’s base is located) to a depth of approximately 0.5 m (Figure 9). This was borne out in how roots were distributed vertically. In the profile view, many roots failed to grow past the barrier, while those that grew underneath reoriented upwards following emergence on the other side. Because the barrier was located near the soil surface, it impeded many roots that would otherwise tend to grow in the top layers of the soil. Also, this location’s average depth of root vertices was much deeper. As in Scenarios 1 and 2, the ZRT terminated around the 0.75-m distance interval. The most rapid taper occurred between 0- and 0.25-m distance and was an approximate 2.35% change per centimeter increment.

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Figure 9.

(a) Surface view of root distribution for Scenario 3 created with the fifth simulation iteration. Concentric rings are the distance intervals used to sample average diameters for ZRT identification. The 2 outer boundaries of the sidewalk are indicated with dashed lines. (b) Cross-sectional profile of Scenario 3 simulated root system. (c) Average depth of root vertices for Scenario 3. Depth values are averaged over a 1-m × 1-m grid cell across all 5 simulation iterations.

Weighting the Basic Grid Based on In-Situ Knowledge of Root Location (Scenario 4)

Scenario 4 used an EAI grid similar to that of Scenario 1. For this reason, ZRT and maximum spread results are not discussed. It was assumed that these values would be similar to those observed in Scenario 1. Visual assessment of the output root architecture showed a discernible overall difference between the averaged spatial distribution when Scenario 4 and Scenario 1 were compared (Figure 10). In Scenario 4, root growth movement was identifiable towards the presence of EAI-weighted points of directional affinity (i.e., modeled growth toward the hypothetical field surveyed root locations).

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Figure 10.

(a) Surface view of root distribution for Scenario 4 created with the fifth simulation iteration. Concentric rings are the distance intervals used to sample average diameters for ZRT identification. Black dots indicate the known locations of roots (hypothetical). (b) Cross-sectional profile of Scenario 4 simulated root system. (c) Average depth of root vertices for Scenario 4. Depth values are averaged over a 1-m × 1-m grid cell across all 5 simulation iterations.

Proactive site planning is crucial for landscape architects and urban planners aiming to integrate mature trees into urban landscapes. This planning encompasses both aboveground and subterranean factors. Above ground, elements such as sunlight exposure, wind patterns, and proximity to urban infrastructures should be acknowledged and guide tree species choice and placement (Urban 2008). Understanding and prioritizing the oft-misunderstood environment in the subterranean realm is vital for tree maturation (Ow and Ghosh 2017; Fini et al. 2020). The role of urban tree roots, responsible for water, nutrient, and oxygen absorption and structural reinforcement (Gregory 2006; Murray 2008; Urban 2008), is paramount. Urban soil conditions present a range of challenges, from fluctuating moisture content to physical barriers like pipes and pavements (Randrup et al. 2001; Page et al. 2015; Morandage et al. 2021). The structure of these roots plays a critical role in ensuring the tree’s health and longevity (Brunner et al. 2015).

Non-invasive root detection techniques, such as GPR, are valuable in identifying existing root locations (Guo et al. 2013; Miron and Millward 2020; Sun et al. 2023) and could provide data for validating or even enhancing models like RootBox (see Scenario 4). However, while GPR can locate roots, it does not elucidate the potential growth patterns in varied urban soils of a newly planted tree. For such guidance, root forecasting models like RootBox become invaluable. Plant root modeling is not a new area of research (see Dupuy et al. [2010] for a review of root modeling history). Most of this research has focused on agricultural crops (Ma et al. 2007), and limited studies have investigated tree roots. A model focused on tree root branching density was developed by Dupuy et al. (2005) and tested with Maritime pine (Pinus pinaster). These authors found that density functions provided a localized morphological perspective that closely resembled real root systems in depth and branching angle. More recently, Perona et al. (2022) developed the Root Distribution Model (RDM) that maps root systems in different climates, utilizing physical parameters related to soil and moisture for calibration. The RDM can be adapted to scenarios influenced by rain or water fluctuations, making it valuable for studying environmental impacts on root distribution.

Although the idea of using RootBox to predict tree root growth is not unique, our implementation of it is innovative in terms of its practical use in urban areas. In addition, incorporating a forecasting tool into the urban planning process, which enables spatial tree root forecasting based on different scenarios, can encourage significant conversations among stakeholders regarding the underground realm that has traditionally been a mysterious “black box.” We understand that there are other models that could be used in urban planning besides RootBox. However, our contribution lies in recognizing the importance of a spatial tree root forecasting approach to ensure the survival and growth of trees in future cities. The following paragraphs provide more information and context on the results of our RootBox simulation scenarios.

In the resulting architectures, the average diameter of all roots within the first 0.75 m showed a high taper rate that aligns with the rate proposed by Danjon et al. (2005). The ZRT, which is the distance along the root axis where the diameter change rate per centimeter exceeds 1.25%, was used to measure this rate. However, in this study, the ZRT was measured by determining the change in the average diameter at defined intervals over a horizontal distance instead of measuring individual root axes in any direction. Our simulations slightly underestimated the reported size in the literature, but this was due to the parameters used in the simulations, which could be further adjusted to increase the size of the ZRT.

RootBox can simulate a ZRT, but the parameters for creating one must be set indirectly. This is done by creating multiple short roots near the tree’s base, with each successive root having a smaller diameter than its predecessor. While RootBox does not allow for direct root thickening, this feature was added by modifying the parameters to create a root-thickening proxy (Leitner et al. 2010a). However, current simulations only allow for young roots to grow with the same diameter they will have at the end of the simulation, whereas root thickening is a characteristic found in older trees (Coutts 1987; Wagner et al. 2011). RootBox does not have a feature for creating a root collar, which is important for determining the final radius of the ZRT and total root spread. In RootBox, all first-order roots grow from the same origin point. A shortlength, vertically oriented root with a large diameter can be created to incorporate the root-collar diameter.

The simulations kept the root growth parameters constant to make it easier to compare different scenarios. The diameter, length, and number of successors were not allowed to vary, which limited the range of variability in the simulation output. However, the maximum depth that individual roots reached varied, with some roots penetrating below 1 m. This was not due to any specific type of root, but rather the initial angle at which the roots began to grow and their ability to deviate from that angle during extension (Armstrong and Heimsch 1976; Coutts 1987; Danjon and Reubens 2008). This stochastic behavior contributed to a lack of control over the output of the model. Some roots may grow deeper in real-world environments to access scarce hydrological resources near the surface (Day and Wiseman 2009). Forecasting root growth and its spatial characteristics is challenged by not knowing the originating location of roots (root collar) or the direction in which they initially grew from the tree base.

RootBox has been designed to control the shape and distribution of roots to mimic realistic root system profiles. It does this by incorporating tropism and elongation functions. The elongation function is activated when the EAI affinity values are low and impedance values are high, which restricts the growth of root tips that penetrate these depths. In simulations, most roots stop growing beyond a depth of 1 m. The low affinity grid values at greater depths represent a hypothetical water table, as per studies conducted by Ballantyne (1916), Armstrong and Heimsch (1976), and Coutts (1987). It is also common to find higher soil-penetration resistance at greater soil depths, as observed by Hernanz et al. (2000). The tropism and elongation functions built into RootBox allow for significant control of the roots’ output shape and vertical distribution to reproduce realistic root system profiles. The elongation function reacted with low soil affinity grid values to reduce the extension of root tips that penetrated these depths.

In urban or constrained growing conditions, certain roots will delve into deeper soil layers to obtain resources that may not be available near the surface (Day et al. 2010). This growth pattern can be replicated by ensuring that the grid values deep below the surface are higher than the surrounding values, forming a pocket of high tropism or affinity and low impedance. The roots can easily grow through to these depths since EAI values do not hinder the extension of roots.

Determining the direction in which a root system grows towards a nutrient or water source is a complex process. The direction of growth is influenced by several factors that can either encourage or discourage it. These factors must be balanced to determine the ultimate path the root takes (Walk et al. 2006; Mulia et al. 2010). In Scenario 2, the EAI affects growth direction, but a more complex algorithm is needed to accurately model the ecological controls on directional growth. This study does not aim to develop such algorithms, but it is an important consideration for future research.

When faced with Scenario 3, roots are hindered by EAI values that impede their growth. In such cases, some large roots may grow beneath the area of impedance and then emerge on the far side, towards the surface. It is realistic for the model output to show limited root extension due to highly compacted soil. However, it is important to note that roots may react differently to compaction impedance, with some even increasing their growth rate through compacted soil (Coutts 1987; Alameda and Villar 2009).

In Scenario 4, we adjusted the base EAI used in Scenario 1 to create a global directional growth affinity bias towards 2 specific locations. This was done to test the efficiency of RootBox’s tropism function in optimizing the spatial arrangement of roots to match the potential site measurements of tree root location. The weighting was applied to direct the roots toward these locations while maintaining the bias of the periphery and upper soil layers. The results showed a noticeable difference in root growth near these 2 locations. As with the EAI model in Scenario 2, localized weightings successfully attracted roots to deeper areas around an area of affinity. However, the magnitude of weighting relative to other variable values could be used to strengthen the directional signalling to tree roots in order to increase the chances that the root will match a known location. A limitation of the model is that existing root architectures and their topology cannot be specified in advance, and a user cannot specify arbitrary starting geometries from which the modeling process could begin. A modification to the source code to include this feature could be made in future research.

The modeling with RootBox described in this work represents a promising tool for simulating the urban tree root systems that can generate actionable forecasts of their spatial development, which is useful knowledge for urban planning and design schemes that aim to expand long-term tree cover. It allows the modeling of root system architecture, reflecting traits common to various tree species and approximating urban soil conditions. Additionally, tropism and elongation functions in the software enable users to simulate root responses to the growth affinities and impedances found in urban conditions, presenting a foundational framework for urban tree root modeling. However, the research does not confirm the model’s precision or accuracy in predicting specific tree root systems on particular sites. Future studies should aim to align the model’s outcomes more closely with empirical data, refining the RootBox parameters to incorporate field-derived information to enhance the accuracy of root architecture representations.

A model sensitivity analysis is also absent from this study, which would be useful for determining the impact ofparameter changes on the model’s outcomes. Such an analysis could provide better user control and help align the model’s forecasting with knowledge of root locations after tree planting (Saltelli et al. 2010; Pianosi et al. 2016). Finally, the application of RootBox as it is presented in this work, while versatile and adaptable, may require users to have some programming skills to customize its parameters for specific urban settings. A logical next step would be to integrate RootBox with industry-standard computer-aided drawing (CAD) tools to make root forecasting available at the landscape architecture stages of urban planning.

For landscape architects and urban planners, the successful integration of trees into new or revitalized cityscapes requires comprehensive foresight. Above the soil, factors such as sunlight, wind direction, and proximity to structures play a crucial role in determining tree health and growth. Yet, just as vital are the often overlooked belowground considerations. To genuinely realize the vision of mature trees thriving in urban settings, planners must also account for the subterranean needs of trees, emphasizing the importance of visible and hidden growth factors in urban design.

In this study, we provide a broader context for the importance of considering the belowground requirements of urban trees. We then focus on tree root growth forecasting using a uniquely parameterized instance of RootBox and argue that a modeling tool such as this can complement existing decision-making by allowing the creation of forward-looking scenarios. While our presentation of RootBox’s capabilities does not represent an “off-the-shelf’ solution, we believe that its further integration into software-aided design is urgently required to ensure that future urban greening efforts can proactively overcome the limitations of knowledge about, and avoid the past pitfalls imposed by, the subterranean cityscape.

The authors reported no conflicts of interest.