Canopy: A Multidisciplinary Perspective

• Canopy is a vertically extended upper-layer system that regulates exchanges of radiation, momentum, heat, and mass, with applications in agronomy, forestry, fluid mechanics, and urban science.
• Research on canopy integrates methods like LiDAR segmentation, 3D structural modeling, and evolutionary algorithms to optimize light interception, airflow, and energy dynamics.
• Canopy studies drive actionable insights ranging from optimized crop ideotypes and forest reconstruction to urban microclimate modeling and robotic navigation.

A canopy is a vertically extended upper layer or obstacle field whose geometry regulates exchange processes between an underlying domain and the surrounding environment. In agronomy, it denotes the three-dimensional arrangement of crop leaves that determines light interception; in forestry and remote sensing, it denotes the crown layer and its height, stratification, and sub-canopy structure; in fluid mechanics, it denotes rigid or flexible obstructing elements that alter mean flow, turbulence, and scalar transport; and in urban science, it denotes the built layer formed by buildings or vegetation, often represented as a stack of discrete horizontal strata (Saleem et al., 5 Dec 2025, Hamraz et al., 2016, Chen et al., 2023, Burdet et al., 2014). This breadth of usage reflects a common operational role: canopy structure sets the geometry through which radiation, momentum, heat, mass, and measurements are transmitted, attenuated, or redirected.

1. Meanings and abstractions across disciplines

In plant and forest studies, canopy commonly refers to the leaf-bearing or crown-bearing layer of vegetation. Airborne LiDAR work treats canopy as a vertically structured point cloud that can be peeled into overstory and understory layers, while satellite and airborne mapping studies formalize canopy height as a wall-to-wall raster quantity or as a target variable inferred from optical imagery and LiDAR (Hamraz et al., 2016, Fogel et al., 2024). In crop modeling, canopy is explicitly geometric: a maize canopy can be parameterized leaf by leaf, with each leaf specified by length, width, inclination angle, and azimuthal orientation (Saleem et al., 5 Dec 2025).

In fluid mechanics, canopy denotes an obstructing substrate composed of filaments, stems, rigid elements, or porous drag layers. Direct numerical simulation and large-eddy simulation studies analyze canopy density, zero-plane displacement, canopy drag, and the roughness sublayer, showing that canopies modify both inner-layer and outer-layer turbulence (Chen et al., 2023, Bhuiyan et al., 2020). Flexible-canopy studies extend this notion by resolving fluid–structure interaction for dense arrays of filaments, with canopy compliance affecting drag, flapping regime, and Reynolds-stress anisotropy (Rota et al., 2023).

In urban modeling, canopy has two distinct but related meanings. The urban canopy may be the built layer of streets, walls, and roofs, represented as discrete layers with cumulative floor area, wall length, roof area, and free air plan area (Burdet et al., 2014). It may also denote vegetation belts represented by porosity, leaf area index, and leaf-area density in reduced-order wind models (Pattanapol et al., 27 Sep 2025). This suggests that “canopy” functions less as a taxonomic term than as a geometric and transport-theoretic abstraction.

2. Crop canopy architecture and light-use efficiency

A recent crop-scale formulation appears in the algorithmic design of a maize “smart canopy,” in which each virtual plant consists of 10 leaves arranged on a central stalk and each leaf is represented as a NURBS surface prescribed by four free parameters: length $L_i$, maximum width $W_i$, inclination angle $\theta_i$, and azimuthal orientation $\phi_i$ (Saleem et al., 5 Dec 2025). The optimization variable is therefore a 40-dimensional trait vector,

$$\mathbf{x}=(L_1,W_1,\theta_1,\phi_1,\dots,L_{10},W_{10},\theta_{10},\phi_{10}),$$

and the objective is to maximize intercepted photosynthetically active radiation over hourly timestamps from 07:00 to 20:00 on a representative clear-sky day: $$J(\mathbf{x})=\sum_{t\in\mathcal{T}} A_{\rm PAR}(\mathbf{x},t)\,\Delta t.$$

The computational framework combines a 3D functional-structural plant model with an evolutionary algorithm. A $6\times6$ tiled field with periodic boundary conditions emulates an infinite canopy at $\sim 87\,700$ plants ha$^{-1}$, with per-plant azimuthal jitter of $\pm 10^\circ$. The population size is 100, crossover is two-point crossover on the 40-gene string, mutation is per-gene Gaussian perturbation, and runs extend to 200 generations, with stable fitness typically reached by about 80 generations and a convergence criterion of less than $W_i$0 improvement in best fitness over 20 successive generations (Saleem et al., 5 Dec 2025).

The emergent ideotype has two components. First, it shows vertical stratification of leaf inclination and width: upper leaves have $W_i$1 and narrow width for deep light penetration, whereas lower leaves have $W_i$2 and wider width to capture attenuated light. Second, it shows radial tiling of azimuths, with successive leaves offset around the stalk, breaking standard distichous phyllotaxy to minimize intra- and interplant shading (Saleem et al., 5 Dec 2025). Quantitatively, the optimized canopy intercepts $W_i$3 MWh acre$W_i$4 day$W_i$5 versus a baseline of $W_i$6 MWh acre$W_i$7 day$W_i$8, a relative gain of approximately $W_i$9. Gains remain $\theta_i$0 across Ames, Iowa; Thomas County, Kansas; and Bismarck, North Dakota, and $\theta_i$1 across planting densities from $\theta_i$2 to $\theta_i$3 (Saleem et al., 5 Dec 2025).

The same study argues biological plausibility by linking erect upper leaves and horizontal lower leaves to modern density-tolerant cultivars and by noting that spiral azimuths, though rare in maize, have been observed in lines such as CM158Q. It further identifies leaf-angle loci such as liguleless1 and LAC1 and cites marker-assisted selection and high-throughput CRISPR mutagenesis as routes for stacking optimal trait values (Saleem et al., 5 Dec 2025). A plausible implication is that canopy design in crops is moving from descriptive phenotyping toward explicitly optimized three-dimensional ideotypes.

3. Forest canopy measurement, stratification, and reconstruction

Forest canopy research has increasingly treated canopy as a multiscale measurement target rather than a single surface. In airborne LiDAR segmentation of multi-story stands, canopy stratification is performed by binning the point cloud into a grid with cell size equal to the current average footprint,

$\theta_i$4

defining overlapping locales of radius $\theta_i$5, and identifying canopy modes from the second derivative of a Gaussian-smoothed height histogram. If $\theta_i$6 and $\theta_i$7 are the midpoints of the two highest modes, the threshold for peeling the top layer is

$\theta_i$8

Applied to Robinson Forest, this procedure increased understory recall from approximately $\theta_i$9 to $\phi_i$0, while understory commission increased from approximately $\phi_i$1 to $\phi_i$2; overstory F-score changed by less than $\phi_i$3 (Hamraz et al., 2016). The same study found that understory-layer point densities were often suboptimal, with only the first two layers meeting or exceeding the $\phi_i$4 pt/m$\phi_i$5 threshold recommended for reliable 2.5D tree segmentation (Hamraz et al., 2016).

At national scale, canopy is operationalized as a dense raster prediction problem. Open-Canopy provides a 1.5 m benchmark over metropolitan France covering approximately $\phi_i$6 km$\phi_i$7, with $\phi_i$8 one-kilometer tiles and SPOT 6/7 imagery paired with airborne ALS point clouds rasterized at 1.5 m (Fogel et al., 2024). On pixels within the vegetation mask and with $\phi_i$9 m, the best-performing model is PVTv2 pretrained on ImageNet1k and fine-tuned with $$\mathbf{x}=(L_1,W_1,\theta_1,\phi_1,\dots,L_{10},W_{10},\theta_{10},\phi_{10}),$$0, reaching MAE $$\mathbf{x}=(L_1,W_1,\theta_1,\phi_1,\dots,L_{10},W_{10},\theta_{10},\phi_{10}),$$1 m, nMAE $$\mathbf{x}=(L_1,W_1,\theta_1,\phi_1,\dots,L_{10},W_{10},\theta_{10},\phi_{10}),$$2, RMSE $$\mathbf{x}=(L_1,W_1,\theta_1,\phi_1,\dots,L_{10},W_{10},\theta_{10},\phi_{10}),$$3 m, Bias $$\mathbf{x}=(L_1,W_1,\theta_1,\phi_1,\dots,L_{10},W_{10},\theta_{10},\phi_{10}),$$4 m, and tree-cover IoU $$\mathbf{x}=(L_1,W_1,\theta_1,\phi_1,\dots,L_{10},W_{10},\theta_{10},\phi_{10}),$$5 (Fogel et al., 2024). Open-Canopy-$$\mathbf{x}=(L_1,W_1,\theta_1,\phi_1,\dots,L_{10},W_{10},\theta_{10},\phi_{10}),$$6 extends this to canopy-height decrease detection between consecutive years; using thresholded PVTv2 predictions, the reported Precision, Recall, F1, and IoU are $$\mathbf{x}=(L_1,W_1,\theta_1,\phi_1,\dots,L_{10},W_{10},\theta_{10},\phi_{10}),$$7, $$\mathbf{x}=(L_1,W_1,\theta_1,\phi_1,\dots,L_{10},W_{10},\theta_{10},\phi_{10}),$$8, $$\mathbf{x}=(L_1,W_1,\theta_1,\phi_1,\dots,L_{10},W_{10},\theta_{10},\phi_{10}),$$9, and $$J(\mathbf{x})=\sum_{t\in\mathcal{T}} A_{\rm PAR}(\mathbf{x},t)\,\Delta t.$$0, respectively (Fogel et al., 2024).

Several studies push canopy-height mapping to finer resolution or broader generalization. A self-supervised ViT encoder with a convolutional dense prediction decoder trained on aerial LiDAR-derived canopy height maps yields sub-meter canopy height predictions for California and São Paulo with an average MAE of $$J(\mathbf{x})=\sum_{t\in\mathcal{T}} A_{\rm PAR}(\mathbf{x},t)\,\Delta t.$$1 m and ME of $$J(\mathbf{x})=\sum_{t\in\mathcal{T}} A_{\rm PAR}(\mathbf{x},t)\,\Delta t.$$2 m (Tolan et al., 2023). Depth2CHM fine-tunes Depth Anything V2 by converting canopy height $$J(\mathbf{x})=\sum_{t\in\mathcal{T}} A_{\rm PAR}(\mathbf{x},t)\,\Delta t.$$3 into pseudo-depth $$J(\mathbf{x})=\sum_{t\in\mathcal{T}} A_{\rm PAR}(\mathbf{x},t)\,\Delta t.$$4 with $$J(\mathbf{x})=\sum_{t\in\mathcal{T}} A_{\rm PAR}(\mathbf{x},t)\,\Delta t.$$5 m; independent validation reported biases of $$J(\mathbf{x})=\sum_{t\in\mathcal{T}} A_{\rm PAR}(\mathbf{x},t)\,\Delta t.$$6 m and $$J(\mathbf{x})=\sum_{t\in\mathcal{T}} A_{\rm PAR}(\mathbf{x},t)\,\Delta t.$$7 m and RMSEs of $$J(\mathbf{x})=\sum_{t\in\mathcal{T}} A_{\rm PAR}(\mathbf{x},t)\,\Delta t.$$8 m and $$J(\mathbf{x})=\sum_{t\in\mathcal{T}} A_{\rm PAR}(\mathbf{x},t)\,\Delta t.$$9 m at Chinese and U.S. sites, respectively (Lai et al., 6 Feb 2026). For primeval forests in the Yarlung Tsangpo Grand Canyon, PRFXception uses fused GEDI, ICESat-2, Sentinel-2, UAV-LS, and field data to generate a 10 m canopy-height map; reported validation includes RMSE $6\times6$0 m against GEDI/ICESat-2 fusion, $6\times6$1 m against UAV-LS, and $6\times6$2 m against ground plots, and the resulting map identified two previously unknown communities with $6\times6$3 (Fan et al., 2024).

Canopy reconstruction is also extending below the observed crown envelope. ForestGen3D trains a conditional DDPM on co-registered ALS/TLS tree clouds, learning to generate TLS-like structure $6\times6$4 conditioned on sparse ALS input $6\times6$5 (Castorena et al., 19 Sep 2025). Its geometric containment prior uses the ALS convex hull $6\times6$6, with empirical expected point containment of $6\times6$7 on held-out test trees and out-of-hull distances below $6\times6$8 m on average in landscape deployment (Castorena et al., 19 Sep 2025). Yet an explicit limitation remains: canopy height alone does not capture wood density or multi-layer structure (Fogel et al., 2024). That limitation helps explain the parallel development of stratification, generative reconstruction, and multimodal fusion.

4. Canopies as momentum sinks and turbulence modifiers

In fluid mechanics, canopy is a model of distributed drag and displaced origin. For rigid filament canopies, outer-layer similarity can be assessed with the diagnostic function

$6\times6$9

where $\sim 87\,700$0 and $\sim 87\,700$1. Rather than determining $\sim 87\,700$2 from a local log-law fit, one study chooses $\sim 87\,700$3 and $\sim 87\,700$4 by minimizing the mean-square deviation between canopy and smooth-wall diagnostic functions above the roughness sublayer (Chen et al., 2023). The resulting trends are density dependent: dense canopies with $\sim 87\,700$5 have $\sim 87\,700$6 and $\sim 87\,700$7; intermediate densities have $\sim 87\,700$8 and $\sim 87\,700$9; sparse canopies at sufficiently high $^{-1}$0 recover $^{-1}$1 and $^{-1}$2. In no case does $^{-1}$3 drop by more than approximately $^{-1}$4 relative to the smooth-wall value (Chen et al., 2023).

At atmospheric scale, explicit forest-canopy drag is often represented in resolved momentum equations as

$^{-1}$5

with an additional canopy-induced dissipation term in the TKE equation (Tolladay et al., 2021). In WRF simulations of neutral flow across a forested ridge, the explicit-canopy approach uses $^{-1}$6 m, $^{-1}$7 m$^{-1}$8, and $^{-1}$9, and it outperforms a roughness-length surrogate. Mean-wind RMSE across measurement sites is $\pm 10^\circ$0, $\pm 10^\circ$1, and $\pm 10^\circ$2 m/s for explicit-canopy runs at 2, 4, and 6 m resolution, versus $\pm 10^\circ$3, $\pm 10^\circ$4, and $\pm 10^\circ$5 m/s for roughness-only runs; the roughness-length approach also underpredicts turbulence over flat forested ground and yields insufficient vertical turbulence extent (Tolladay et al., 2021). This directly challenges the common simplification that tall canopies can be reduced to an increased $\pm 10^\circ$6.

Subgrid treatment is also canopy sensitive. In large-eddy simulation of forest-like canopies, a vortex-stretching SGS model resolves about $\pm 10^\circ$7 more TKE than a classical Deardorff TKE model, while immersed-solid and immersed-canopy representations differ in coherent-structure intermittency but keep integral quantities such as $\pm 10^\circ$8, $\pm 10^\circ$9, and TKE profiles within $W_i$00 of each other (Bhuiyan et al., 2020). Sweep and ejection events dominate momentum transport, contributing approximately $W_i$01 and $W_i$02 of total $W_i$03, respectively (Bhuiyan et al., 2020).

For flexible canopies, fluid–structure interaction introduces a distinct control parameter, the Cauchy number

$W_i$04

Direct simulations over $W_i$05 show two flapping regimes: a structure-dominated regime for $W_i$06, with peaks at the natural bending frequency, and a turbulence-dominated regime for $W_i$07, with peak frequency $W_i$08 (Rota et al., 2023). The flow exhibits three turbulence layers—an in-canopy layer, a canopy-interface layer, and an outer layer—distinguished using Lumley-triangle invariants (Rota et al., 2023).

Wildfire-plume simulations add another canopy role: modulation of buoyant flow. Large-eddy simulations with no canopy, homogeneous canopy, edge canopies, and gap canopies show that canopy structure changes plume tilt, pressure gradients, and TKE budgets, with buoyant production dominating shear production and the largest TKE occurring in the gap-canopy configurations (Cervantes et al., 16 Oct 2025). A plausible implication is that the canopy concept in fluid mechanics is best understood as a geometry-dependent closure problem rather than a single drag coefficient.

5. Urban canopy and built-environment processes

Urban-canopy modeling formalizes the built layer as a set of discrete strata that exchange heat with buildings and the atmosphere. In a multilayer formulation, each horizontal layer $W_i$09 is assigned cumulative floor area $W_i$10, wall length $W_i$11, roof area $W_i$12, and free canopy plan area $W_i$13, and the canopy potential temperature satisfies a layerwise energy balance coupled to a simplified 2R–C building-energy model and the CitySim radiosity solver (Burdet et al., 2014). The coupled system allows morphology to affect both radiative access and microclimate. Under identical density and envelope U-values, lower-story solar access in open blocks is on average seven times that of straight slabs, the convex slab gains roughly $W_i$14 more solar input than the straight slab, and absolute heating plus cooling demand decreases by approximately $W_i$15, $W_i$16, and $W_i$17 for convex slabs, uniform open blocks, and height-varied open blocks, respectively (Burdet et al., 2014).

Vegetated urban canopies are also modeled as drag-inducing porous belts. A lightweight 2-D RANS method maps a user-specified leaf area index to porosity via

$W_i$18

then inverts porosity to local LAI, divides by grid-measured canopy thickness $W_i$19 to obtain leaf-area density $W_i$20, and applies a quadratic drag term in the momentum equation (Pattanapol et al., 27 Sep 2025). For a belt with LAI $W_i$21, the model reproduces the approach region, in-canopy deficit, and leeward wake, with wake levels within $W_i$22 of wind-tunnel measurements using default $W_i$23 and $W_i$24 (Pattanapol et al., 27 Sep 2025). The formulation is explicitly described as designer-friendly and computationally efficient for early-stage screening (Pattanapol et al., 27 Sep 2025).

The canopy concept further appears in building ventilation studies, where surrounding buildings form a resolved urban canopy that governs local pressure and flow alignment. Coupled indoor–outdoor LES of four ventilation configurations—cross, corner, dual-room, and single-sided—show that canopy density, wind angle, and house location can alter ventilation rates by $W_i$25 (Bachand et al., 6 Aug 2025). High-density canopies reduce the nondimensional ventilation rate $W_i$26 by approximately $W_i$27 on average, low-density canopies increase $W_i$28 by approximately $W_i$29, and cross-ventilated rooms perform best when wind aligns with the straight ventilation axis (Bachand et al., 6 Aug 2025). These results imply that the urban canopy is not merely a background roughness parameter; it is an active geometric control on energy demand, wind sheltering, and indoor exchange.

6. Canopy access, manipulation, and operationalization

Canopy has also become an operational environment for robotics. The AMBER platform is an aerially deployable crawler designed for adaptive locomotion and manipulation within tree canopies, combining compliant microspine-based tracks, a dual-track rotary gripper, and an elastic tail (Wigner et al., 8 Dec 2025). Experiments report stable attachment under roll up to $W_i$30, climbing on branches inclined up to $W_i$31, average speed $W_i$32 cm/s on horizontal branches, and yaw steering up to $W_i$33 before only two carriers remain engaged and tipping occurs (Wigner et al., 8 Dec 2025). Power measurements show $W_i$34 W in static perching, $W_i$35 W in horizontal crawling, and $W_i$36 W at peak load, compared with approximately $W_i$37 W for a hovering DJI F450 with a $W_i$38 kg payload (Wigner et al., 8 Dec 2025). The deployment workflow—drone approach, aerial perch, tethered lowering, branch traversal, and recovery—treats the canopy as a physically navigable network rather than only as an observed surface (Wigner et al., 8 Dec 2025).

Across these literatures, several recurrent themes emerge. First, canopy geometry is repeatedly parameterized through vertical layering, azimuthal arrangement, porosity, LAD, or frontal density. Second, simple proxies are useful but incomplete: roughness length can miss explicit-canopy turbulence, canopy height alone can miss multi-layer structure, and sparse aerial sensing can miss sub-canopy detail (Tolladay et al., 2021, Fogel et al., 2024, Castorena et al., 19 Sep 2025). Third, current work increasingly couples canopy representation to optimization, diffusion-based generation, or field-deployable robotics. This suggests that the contemporary scientific meaning of canopy is not limited to a visible upper cover; it is a structured medium whose geometry can be measured, inferred, optimized, and traversed.