Stand metrics¶

A tree inventory measures trees one at a time. Stand metrics summarize the whole plot: how many stems per hectare, how much basal area, how tall the canopy is, how much ground the crowns cover, how crowded each tree is by its neighbors, and (optionally) how much biomass the plot holds. This page is the method specification; every definition names its source. See Run a tree inventory for the steps.

Which trees count¶

The stand figures use the trees that have a DBH at or above the minimum DBH (default 5 cm, a setting). Trees you have marked dead in the Tree Table are left out unless you untick Exclude dead trees. Every figure updates as you change these, or as you edit a tree's status.

Inventories use different minimum diameters, and stems/ha in particular depends strongly on the threshold. Compare stands only at the same minimum.

Plot area¶

Every per-hectare figure divides by the plot area A (m²). By default Phytograph measures it as the area of the convex hull of the plot's ground points (or of all its points, when there are no ground labels). If your plot has a known surveyed area, enter it instead. The summary says which area it used.

Edge effects

A scanned plot has no clean edge. Trees near the boundary have crowns and competitors outside it, and the scanned area rarely matches a surveyed plot exactly. The treatment of trees and crowns cut by the plot edge measurably changes plot-level estimates, and the effect grows as plots get smaller (Mascaro et al., 2011). For small plots, prefer an entered surveyed area. Treat the edge-flagged competition values (see below) as underestimates.

Stand summary¶

With N trees of diameter dᵢ (m), basal area gᵢ = π/4 · dᵢ² and height hᵢ:

Metric	Definition	Source
Stems per hectare	`N / A · 10⁴`	Kershaw et al. (2016); West (2009)
Basal area per hectare	`Σgᵢ / A · 10⁴` (m²/ha)	Kershaw et al. (2016); West (2009)
Quadratic mean diameter (QMD)	`√(Σdᵢ² / N)`: the diameter of the tree of mean basal area	Curtis & Marshall (2000)
Lorey's mean height	`Σgᵢhᵢ / Σgᵢ`: height weighted by basal area	Lorey (1878), as given by Curtis & Marshall (2000)
Mean and maximum height	arithmetic mean and maximum of `hᵢ`	—

QMD rather than the arithmetic mean diameter is the diameter that relates directly to basal area: BA = N · π/4 · QMD². It is always at least the arithmetic mean, since QMD² = mean² + variance (Curtis & Marshall, 2000). Lorey's height weights big trees more, which makes it the right mean height for stand volume (Curtis & Marshall, 2000).

Diameter and height distributions are histograms of the stand trees in classes of a chosen width: 5 cm DBH and 2 m height by default.

Canopy cover¶

Canopy cover is the area of ground covered by the vertical projection of the canopy (Jennings, Brown & Sheil, 1999), as a fraction of the plot:

canopy cover = area(union of crown projections ∩ plot) / A

The crown projections are the convex hulls from the tree inventory. Each is clipped to the plot, and their union is measured on a 0.1 m raster, so the error is at most one cell width along the crowns' outline. On a very large plot, over about 20 million cells at 0.1 m, the cell grows to keep memory bounded. The cell used is reported with the result. Every measured crown counts, whatever the stand filters, because cover describes the canopy, not the tree list.

Canopy cover is not canopy closure, which is the fraction of the sky hemisphere obscured when viewed from one point (Jennings et al., 1999). The summary also reports the summed crown area, Σ crown projection area. It exceeds the union wherever crowns overlap.

Competition¶

Each tree gets three measures of how crowded it is.

Hegyi's index (Hegyi, 1974), in the form stated by Lorimer (1983):

CIᵢ = Σⱼ (Dⱼ / Dᵢ) / distᵢⱼ

The sum runs over every other tree j with a DBH whose stem base lies within the search radius of tree i's stem base. Competition and canopy cover need every tree, so a run restricted to some trees skips them. D is DBH, and dist is the horizontal distance between stem bases in meters (floored at 0.1 m). Large, near neighbors raise the index; a tree that dominates its neighbors has a low one. The search radius is a setting (default 6 m; the default is ours). The index depends on it, so compare indices only at the same radius. n_competitors counts the trees inside the radius.

Crown overlap. crown_overlap_m2 is the sum of the areas where this tree's crown projection overlaps each other tree's. The crowns are convex, so each overlap is an exact convex-polygon intersection. crown_overlap_fraction is the share of this tree's own crown projection covered by at least one other crown (sampled on a 0.1 m grid). Crown overlap here is a geometric description of the projections. TLS studies of crown competition model crowns in 3-D (Seidel et al., 2011; Metz et al., 2013). The classic field index from overlapping zones of influence is Bella's (1971).

Edge flag. edge is true when the search circle reaches past the plot boundary. Competitors outside the plot are then missing, so the index is an underestimate (see Edge effects above).

Biomass (optional)¶

Above-ground biomass (AGB, kg oven-dry mass) per tree, summed to the stand and divided by the plot area for Mg/ha. Choose one method; it applies to every tree:

Chave et al. (2014), pantropical:

AGB = 0.0673 · (ρ D² H)^0.976

D is DBH in cm, H height in m, and ρ wood density in g/cm³. It is fitted to 4,004 harvested trees from 58 tropical sites, with D from 5 to 212 cm. It is for tropical trees, and underestimates by about 20% for the very largest (over 30 Mg) (Chave et al., 2014).

Jenkins et al. (2003), United States species groups:

AGB = exp(β₀ + β₁ ln D)

D is DBH in cm. The equations cover trees of 2.5 cm DBH and up. Choose one of the ten species groups; its coefficients (Jenkins et al., 2003, Table 4) apply to every tree:

Group	β₀	β₁	Max DBH (cm)
Aspen / alder / cottonwood / willow	−2.2094	2.3867	70
Soft maple / birch	−1.9123	2.3651	66
Mixed hardwood	−2.4800	2.4835	56
Hard maple / oak / hickory / beech	−2.0127	2.4342	73
Cedar / larch	−2.0336	2.2592	250
Douglas-fir	−2.2304	2.4435	210
True fir / hemlock	−2.5384	2.4814	230
Pine	−2.5356	2.4349	180
Spruce	−2.0773	2.3323	250
Woodland (juniper / oak / mesquite)	−0.7152	1.7029	78

No log-bias correction is applied, as in the published equations. Trees larger than the group's maximum DBH are still estimated, but the tree count beyond that range is reported. Chojnacky, Heath & Jenkins (2014) update these equations with more groups.

QSM volume × wood density:

AGB = V · ρ · 1000

V is the tree's woody volume in m³ from its QSM (see Batch QSM below), and ρ is the basic wood density in g/cm³. On 65 harvested eucalypts this estimate agreed with the weighed biomass far better than allometric equations did (concordance 0.98 against 0.68–0.78; Calders et al., 2015). It needs a QSM per tree, and a QSM needs a well-scanned woody structure.

ρ is one value for the whole stand (a setting, default 0.5 g/cm³). In a mixed stand it is an average, and biomass inherits its error.

A tree the chosen method cannot estimate (no DBH, no height, no QSM) is left out of the total, and the summary says how many were.

Batch QSM¶

A QSM can be built for every segmented tree in one run. Each tree is read from the cloud separately (as in the inventory). If the cloud carries leaf/wood labels, only the wood points are used, since a QSM models the woody structure. A tree with more points than the per-tree budget (default 60,000, as for a single QSM) is thinned on a voxel grid, which keeps the point spacing even; taking every k-th point would keep the scan's near-range density bias. The QSM reconstruction itself is the same pipeline as a single QSM. Each tree's metrics (woody volume, trunk diameter, height, branch counts) join its table row and export as a QSM metrics CSV, and each model is added to the scene.

References¶

Bella, I.E. (1971). A new competition model for individual trees. Forest Science 17(3):364–372.
Calders, K., Newnham, G., Burt, A., Murphy, S., Raumonen, P., Herold, M., Culvenor, D., Avitabile, V., Disney, M., Armston, J. & Kaasalainen, M. (2015). Nondestructive estimates of above-ground biomass using terrestrial laser scanning. Methods in Ecology and Evolution 6(2):198–208.
Chave, J. et al. (2014). Improved allometric models to estimate the aboveground biomass of tropical trees. Global Change Biology 20(10):3177–3190.
Chojnacky, D.C., Heath, L.S. & Jenkins, J.C. (2014). Updated generalized biomass equations for North American tree species. Forestry 87(1):129–151.
Curtis, R.O. & Marshall, D.D. (2000). Technical note: Why quadratic mean diameter? Western Journal of Applied Forestry 15(3):137–139.
Hegyi, F. (1974). A simulation model for managing jack-pine stands. In: Fries, J. (ed.) Growth Models for Tree and Stand Simulation. Royal College of Forestry, Stockholm, Research Notes 30, pp. 74–90.
Jenkins, J.C., Chojnacky, D.C., Heath, L.S. & Birdsey, R.A. (2003). National-scale biomass estimators for United States tree species. Forest Science 49(1):12–35.
Jennings, S.B., Brown, N.D. & Sheil, D. (1999). Assessing forest canopies and understory illumination: canopy closure, canopy cover and other measures. Forestry 72(1):59–74.
Kershaw, J.A., Ducey, M.J., Beers, T.W. & Husch, B. (2016). Forest Mensuration, 5th ed. Wiley-Blackwell.
Lorey, T. (1878). Die mittlere Bestandeshöhe. Allgemeine Forst- und Jagdzeitung 54:149–155.
Lorimer, C.G. (1983). Tests of age-independent competition indices for individual trees in natural hardwood stands. Forest Ecology and Management 6:343–360.
Mascaro, J., Detto, M., Asner, G.P. & Muller-Landau, H.C. (2011). Evaluating uncertainty in mapping forest carbon with airborne LiDAR. Remote Sensing of Environment 115(12):3770–3774.
Metz, J., Seidel, D., Schall, P., Scheffer, D., Schulze, E.-D. & Ammer, C. (2013). Crown modeling by terrestrial laser scanning as an approach to assess the effect of aboveground intra- and interspecific competition on tree growth. Forest Ecology and Management 310:275–288.
Seidel, D., Leuschner, C., Müller, A. & Krause, B. (2011). Crown plasticity in mixed forests — quantifying asymmetry as a measure of competition using terrestrial laser scanning. Forest Ecology and Management 261(11):2123–2132.
West, P.W. (2009). Tree and Forest Measurement, 2nd ed. Springer.