# Dictionary

## Background

Real Twig allows QSM variable names and metrics to be standardized across TreeQSM, SimpleForest, Treegraph, and aRchi. This is done with the `standardise_qsm()` and `tree_metrics()` functions, creating a consistent experience when working with QSMs. Below are detailed definitions of the standard variable names in rTwig.

## Cylinder

All of the variables shown here are created with the `update_cylinders()` function, which should be run as soon as a QSM is imported with rTwig. Unless, `standardise_qsm()` is run, the variable names will vary depending on the particular QSM software used.

#### Cylinder Attributes

`start:` This defines the x, y, z coordinates at the center of the cylinder’s base.

`axis:` This defines the x, y, z axis formed between the cylinder’s base and top.

`end:` This defines the x, y, z coordinates at the center of the cylinder’s top.

`id:` The first cylinder id is 1 and is the base of the tree. The largest id value is equal to the number of rows in the data frame.

`parent:` This shows the relationships between individual cylinders in the QSM. The parent of the first cylinder is always zero, because the base of the tree has no parent. Within a branch, parent cylinders are always one less than their child. At the base of a branch, the parent cylinder is the cylinder the branch is connected to.

`radius:` This is the radius of the cylinder in meters.

`raw_radius:` This is the radius of the cylinder before any possible modifications. If using TreeQSM, this is always the UnmodRadius column. If using SimpleForest or Treegraph, this is a copy of the radius before Real Twig is run. Real Twig always uses this radius in its corrections.

`modified:` This is an average index of if the cylinder radius was an outlier and modified with Real Twig across the QSM paths. A value of 0 indicates that the cylinder was never modified in any path, while a value of 1 indicates that it was modified in every path. A value in between 0 and 1 was modified in only some, but not all of the paths.

`length:` This is the length of the cylinder in meters.

#### Branch Attributes

`branch:` A branch is defined as starting at a new branch order and continuing until a twig is reached. This definition is what TreeQSM and Treegraph use. SimpleForest branches are converted to this definition when standardizing the QSM. The first branch is always the main stem under the rTwig format. Treegraph QSMs retain their definition of branches. TreeQSM and SimpleForest are numbered consecutively in order of the cylinder ids.

`branch_position:` This is an index of the cylinder’s position within a branch. This is the same as TreeQSM’s PositionInBranch definition. The first position is always the base of the branch, and the last position is always a twig or the branch end in the case of a broken branch.

`branch_order:` This is the order of every branch. The smallest branch order zero is always the main stem. First order branches are connected to the main stem, and so on a so forth for higher order branches. A new branch order always begins at a new branching fork, continues to a twig or end of a broken branch, and is one greater than the parent order. This definition is consistent between TreeQSM, SimpleForest, and Treegraph, but the rTwig format always defines the main stem as order zero for consistency.

`reverse_order:` This is the reverse branch order (RBO). Traditional branch ordering is relative to the main stem, and does not tell us anything about the position or size of the branch. Small twigs and large branches can both be first order branches if they are connected to the main stem under the traditional definition. RBO solves this problem by considering the relative position of branches within a QSM. RBO assigns a value of one at the end of twigs or broken branches, and works backwards until the base of the tree is reached, which is assigned the highest RBO. The RBO of any branch is the maximum segment (internode) depth relative to the twigs in a tree.

`branch_alt:` This is the alternate branch index. Alternate branch zero is always the main stem. The rest of the branches are first order branches and all of their children. This is similar to cutting the first order branches off with a saw and labeling them consecutively. If using a SimpleForest QSM, this is the old `branchID` column updated so that the main stem is index zero.

#### Segment Attributes

`segment:` A segment (internode) is a portion of a tree between branching forks (nodes). A new segment begins at every branch fork. Cylinders are a part of a segment until the cylinder has more than one child and a new segment is created. The rTwig format always defines the base of the tree as the first segment.

`parent_segment:` This shows the relationships between segments in the QSM. The parent segment of the first segment is always zero, because the first segment (the base of the tree) has no parent segment. The parent segment is the node the current segment forked from.

`total_children:` This is the total number of cylinders supported by the given cylinder. This is useful to find where branches fork. A value of one means that there are no branching forks. A value of two means that there is one branching fork, etc.

#### Additional Metrics

`growth_length:` This is the growth length in meters of any given cylinder. Growth length can be defined as the sum of the lengths of the cylinders supported by the given cylinder. We can visualize growth length by cutting a tree with a saw at any given point. The cumulative length of this cut portion is the growth length where the part of the tree was cut. The growth length of the base of the tree is the sum of the lengths of all the cylinders in the QSM. The growth length of a twig is simply the length of its cylinder. Growth length reflects a measurement that could be taken on a real tree, but is easier to obtain with QSMs.

`base_distance:` This is the distance in meters of any given cylinder from the base of the tree. This distance is calculated by taking the simplest complete path from the given cylinder to the base of the tree.

`twig_distance:` This is the average distance in meters a given cylinder is away from all supported twigs. This is calculated by finding all complete simple paths from the given cylinder to the supported twigs, summing the lengths, and then dividing by the number of paths.

`vessel_volume:` This is the theoretical cumulative volume of living vessels supported by a given cylinder based on allometric scaling theory. It is the sum of pipe_area * length for all supported cylinders.

`pipe_area:` This is the theoretical cross-sectional area of a given cylinder based on allometric scaling theory. The units and values are the total number of supported twigs.

`pipe_radius:` This is the theoretical radius of a given cylinder based on allometric scaling theory. The units and values are the square root of the total number of supported twigs.

## Metrics

`tree_metrics()` generates multiple detailed metrics, which are described in detail below. The `tree`, `branch`, and `segment` data frames are summaries on an individual tree, branch, or segment level, while the `tree_*_dist`, `branch_*_dist`, and `segment_*_dist` are summarised by `height`, `diameter`, `zenith`, `azimuth`, `angle`, or `order`. All of the outputs are described in detail below:

### tree

`tree_volume_m3:` The total volume of the tree in cubic meters.

`stem_volume_m3:` The total volume of the main stem in cubic meters.

`branch_volume_m3:` The total volume of the branches in cubic meters.

`tree_height_m:` The total height of the tree in meters.

`tree_length_m:` The total length of the tree in meters. This is calculated by summing the length of all of the cylinders in the QSM. This is also equal to the growth length of base of the tree.

`stem_length_m:` The total length of the main stem in meters.

`branch_length_m:` The total length of the branches in meters. This is calculated by summing the length of all of the branch cylinders in the QSM.

`branches:` The total number of branches in the QSM, where a branch begins at a new branch order and ends at a twig.

`branches_alt:` The total number of alternate branches, where an alternate branch is attached directly to the main stem, and contains all connected children.

`max_branch_order:` The maximum branch order in the QSM.

`max_reverse_order:` The maximum reverse branch order in the QSM, which is the maximum node depth from the furthest twig.

`twigs:` The total number of twigs in the QSM.

`twig_length_m:` The total length of the twig cylinders in meters.

`twig_distance_m:` The average distance from the base of the tree to each twig.

`path_fraction:` The average path length (from the base of the tree to the twig) divided by the maximum path length. A path fraction of 1 is a perfect fractal.

`tree_area_m2:` The total surface area of the tree in square meters.

`stem_area_m2:` The total surface area of the main stem in square meters.

`branch_area_m2:` The total surface area of the branches in square meters.

`dbh_qsm_cm:` The diameter at breast height of the QSM at 1.37 meters in centimeters, modified by any tapering.

`dbh_raw_cm:` The diameter at breast height of the QSM at 1.37 meters in centimeters, without any radius modification.

`d_base_qsm_cm:` The diameter of the base cylinder of the QSM in centimeters, modified by any tapering.

`d_base_raw_cm:` The diameter of the base cylinder of the QSM in centimeters, without any radius modification.

`crown_diameter_mean_m:` The average crown diameter in meters.

`crown_diameter_max_m:` The maximum crown diameter in meters.

`crown_diameter_min_m:` The minimum crown diameter in meters.

`crown_projected_area_m2:` The projected crown area in square meters.

`crown_base_height_m:` The base height of the crown in meters.

`crown_length_m:` The length of the crown in meters.

`crown_ratio:` The crown length divided by the total tree height.

`crown_area_m2:` The surface area of the crown in square meters.

`crown_volume_m3:` The volume of the crown in cubic meters.

`vessel_volume:` The vessel volume of the base cylinder in the QSM.

`pipe_area:` The pipe area of the base cylinder in the QSM, equal to the total number of supported twigs.

`pipe_radius:` The pipe radius of the base cylinder in the QSM, equal to the square root of the pipe area.

`start_x:` The x coordinate of the base cylinder in the QSM.

`start_y:` The y coordinate of the base cylinder in the QSM.

`start_z:` The z coordinate of the base cylinder in the QSM.

`modified:` The ratio of cylinders with radii modified by Real Twig, divided by the total number of cylinders in the QSM. This value only exists if Real Twig has been run.

`volume_change_pct:` The percent change in total volume from running Real Twig. This value only exists if Real Twig has been run.

`area_change_pct:` The percent change in total surface area from running Real Twig. This value only exists if Real Twig has been run.

### branch, branch_alt, & segment

`branch:` The id of the branch being summarised.

`branch_alt:` The id of the alternate branch being summarised.

`segment:` The id of the segment being summarised.

`parent_branch:` The parent branch of the branch being summarised.

`parent_segment:` The parent segment of the segment being summarised.

`branch_order:` The branch order of the branch or segment.

`reverse_order:` The reverse branch order of the branch or segment.

`diameter_base_cm:` The diameter of the base of the branch or segment in centimeters.

`diameter_mid_cm:` The diameter of the midpoint of the branch or segment in centimeters.

`diameter_tip_cm:` The diameter of the end of the branch or segment in centimeters.

`volume_m3:` The volume in cubic meters of the branch or segment.

`area_m2:` The surface area in square meters of the branch or segment.

`length_m:` The length in meters of the branch or segment.

`height_m:` The height above the ground in meters of the branch or segment.

`angle_deg:` The angle in degrees of the branch or segment.

`azimuth_deg:` The azimuth in degrees of the branch or segment.

`zenith_deg:` The zenith in degrees of the branch or segment.

`growth_length:` The growth length of the branch in meters.

`cylinders:` The total number of cylinders in the branch or segment.

`segments:` The total number of segments in the branch.

`children:` The sum of the supported children in the branch or segment.

`base_distance_m:` The shortest path distance in meters to the base of the tree from the base of the branch or segment.

`twig_distance_m:` The average distance in meters to the supported twigs from the base of the branch or segment.

### *_height_dist

The height distributions are calculated on the tree, branch, and segment level. Branch column names containing `_1` summarise only the first order branch cylinders, similar to the output of TreeQSM.

`height_class_m:` The one meter height class of the tree, branch, or segment cylinders.

`volume_m3:` The volume in cubic meters of the tree, branch, or segment cylinders per height class.

`area_m2:` The surface are in square meters of the tree, branch, or segment cylinders per height class.

`length_m:` The length in meters of the tree, branch, or segment cylinders per height class.

`branches:` The number of branches in the height class.

`segments:` The number of segments in the height class.

### *_diameter_dist

The diameter distributions are calculated on the tree, branch, and segment level. Branch column names containing `_1` summarise only the first order branch cylinders, similar to the output of TreeQSM.

`diameter_class_cm:` The one centimeter diameter class of the tree, branch, or segment cylinders.

`volume_m3:` The volume in cubic meters of the tree, branch, or segment cylinders per diameter class.

`area_m2:` The surface are in square meters of the tree, branch, or segment cylinders per diameter class.

`length_m:` The length in meters of the tree, branch, or segment cylinders per diameter class.

`branches:` The number of branches in the diameter class.

`segments:` The number of segments in the diameter class.

### *_zenith_dist

The zenith distributions are calculated on the tree, branch, and segment level. Branch column names containing `_1` summarise only the first order branch cylinders, similar to the output of TreeQSM.

`zenith_class_deg:` The ten degree zenith class of the tree, branch, or segment cylinders.

`volume_m3:` The volume in cubic meters of the tree, branch, or segment cylinders per zenith class.

`area_m2:` The surface are in square meters of the tree, branch, or segment cylinders per zenith class.

`length_m:` The length in meters of the tree, branch, or segment cylinders per zenith class.

`branches:` The number of branches in the zenith class.

`segments:` The number of segments in the zenith class.

### *_azimuth_dist

The azimuth distributions are calculated on the tree, branch, and segment level. Branch column names containing `_1` summarise only the first order branch cylinders, similar to the output of TreeQSM.

`azimuth_class_deg:` The ten degree azimuth class of the tree, branch, or segment cylinders.

`volume_m3:` The volume in cubic meters of the tree, branch, or segment cylinders per azimuth class.

`area_m2:` The surface are in square meters of the tree, branch, or segment cylinders per azimuth class.

`length_m:` The length in meters of the tree, branch, or segment cylinders per azimuth class.

`branches:` The number of branches in the azimuth class.

`segments:` The number of segments in the azimuth class.

### *_angle_dist

The angle distributions are calculated on the branch and segment level. Branch column names containing `_1` summarise only the first order branch cylinders, similar to the output of TreeQSM.

`angle_class_deg:` The ten degree angle class of the branch or segment cylinders.

`volume_m3:` The volume in cubic meters of the branch or segment cylinders per angle class.

`area_m2:` The surface are in square meters of the branch or segment cylinders per angle class.

`length_m:` The length in meters of the branch or segment cylinders per angle class.

`branches:` The number of branches in the angle class.

`segments:` The number of segments in the angle class.

### *_order_dist

The order distributions are calculated on the branch and segment level. Branch column names containing `_1` summarise only the first order branch cylinders, similar to the output of TreeQSM.

`branch_order:` The branch order.

`reverse_order:` The reverse branch order.

`volume_m3:` The volume in cubic meters of the branch or segment cylinders per order.

`area_m2:` The surface are in square meters of the branch or segment cylinders per order.

`length_m:` The length in meters of the branch or segment cylinders per order.

`branches:` The number of branches in the order.

`segments:` The number of segments in the order.

### stem_taper

`height_m:` The height in meters above the ground of the main stem.

`diameter_cm:` The diameter in centimeters at the given height.

### spreads

`azimuth_deg:` 20 degree azimuth classes.

`height_class:` 1 meter height classes.

`spread_m:` The crown spread in meters at the given azimuth and height.

### vertical_profile

`height_class:` 1 meter height classes.

`avg_spread_m:` The average crown spread in meters at the given height.

### cloud

The simulated point cloud used to calculate many of the metrics.

### version

The version of `rTwig` used to create the metrics.

### run_date

The date and time the metrics were generated.