# Lidar metrics
Here are a list of all lidar metrics that are available in lidar metrics processing algorithms. For each metric there is a set of parameters (if there is parameters) and a list of outputs. These outputs can be available or not depending the output format (raster or vector), this information are given by the columns `Vector` and `Raster`. There is multiple types of metrics so each metric will be tagged with specific badges described below.
| Badge | Description |
| ----------------------------------------------------- | ----------------------------- |
|  | Available with raster output. |
|  | Available with vector output. |
|  | Metric computed per strata. |
|  | Voxel based metric. |
|  | Point based metric. |
Outputs for strata metrics are duplicated for all the strata. Output for a specific strata is: `S_{lower_bound}:{upper_bound}_{output_name}`. For the lower stratum the `lower_bound` is `min` and for the higher stratum the `upper_bound` is `max` to contain all points of lidar point cloud.
## Canopy Cover
 
Compute the canopy cover using a map of small cells. A cell is considered as canopy cell if there is at least one point of lidar poit cloud that is a first return and got a height higher or equal to canopy minimum size. Open/close morpholigical operations are applied to make canopy cover more realistic.
### Parameters
| Name | Type | Description |
| ----------------------- | ------------------------------------- | --------------------------------------------------- |
| `Map resolution` | [numeric: double]
Default: 0.1 | Cell size for canopy map. |
| `Canopy minimum height` | [numeric: double]
Default: 1.30 | Minimum height to consider a point as canopy point. |
| `Open size` | [numeric: integer]
Default: 13 | Size in pixels for morphological opening operation. |
| `Close size` | [numeric: integer]
Default: 21 | Size in pixels for morphological closing operation. |
### Outputs
| Name | Type | Description | Vector | Raster |
| ------------- | ----------------- | ----------------------------------------------- | ------ | ------ |
| `CanopyCover` | [numeric: double] | Canopy cover fraction. Value between 0 and 100. | Yes | No |
## Canopy Relief Ratio
  
Canopy Relief-Ratio (CRR) is a quantitative descriptor of the relative shape of the canopy from altimetry observation ([Geoffrey Parker & all](https://doi.org/10.1016/j.foreco.2003.09.001)).
$$
CRR = \frac{H_{mean}-H_{min}}{H_{max}-H_{min}}\\
$$
Where $H$ is points heights.
### Outputs
| Name | Type | Description | Vector | Raster |
| ----- | ----------------- | ------------------------------------------- | ------ | ------ |
| `CRR` | [numeric: double] | Canopy relief ratio. Value between 0 and 1. | Yes | Yes |
## Effective Number of Layers
  
Compute the Effective Number of Layers ([Martin Ehbrech & all](https://www.sciencedirect.com/science/article/pii/S0168192317301478?via%3Dihub#bib0040)).
$$
ENL = \frac{1}{\sum_{n=1}^{n=N} (\frac{F_{n}}{T})^2} * V_{z}
$$
Where:
- $N$ is Number of voxels strata that contain at least one filled voxel
- $F_{n}$ is the number of filled voxels for stratum i
- $T$ is the total of filled voxels for all strata
- $V_{z}$ is the voxels height
### Outputs
| Name | Type | Description | Vector | Raster |
| ----- | ----------------- | --------------------------- | ------ | ------ |
| `ENL` | [numeric: double] | Effective Number of layers. | Yes | Yes |
## Foliage Height Diversity
  
$$
FHD = -\sum_{i=1}^{i=N} pi * \log{pi}
$$
Where:
- $p_i$ is the proportion of points that lies in the stratum i
- $N$ is the number of strata where $p_i$ > 0
### Outputs
| Name | Type | Description | Vector | Raster |
| ----- | ----------------- | ------------------------- | ------ | ------ |
| `FHD` | [numeric: double] | Foliage Height Diversity. | Yes | Yes |
## Height peaks estimation
  
Compute number of modes, maximum mode height, minimum mode height and mode height range from a kernel density estimation of height probability function.
### Outputs
| Name | Type | Description | Vector | Raster |
| ---------------- | ----------------- | ----------------------------------------------- | ------ | ------ |
| `KDE_n_modes` | [numeric: double] | Number of modes. | Yes | Yes |
| `KDE_min_mode` | [numeric: double] | Minimum height mode. | Yes | Yes |
| `KDE_max_mode` | [numeric: double] | Maximum height mode. | Yes | Yes |
| `KDE_mode_range` | [numeric: double] | Range between minimum and maximum height modes. | Yes | Yes |
## Statistics on L moments of heights
  
Compute coefficient of variation, Skewness and Kurtosis of the L moments of points heights.
### Outputs
| Name | Type | Description | Vector | Raster |
| -------------------------- | ----------------- | ------------------------------------------------- | ------ | ------ |
| `Height L Moments cv` | [numeric: double] | Coefficient of variation of L moments of heights. | Yes | Yes |
| `Height LMoments skewness` | [numeric: double] | Skewness of L moments of heights. | Yes | Yes |
| `Height LMoments kurtosis` | [numeric: double] | Kurtosis of L moments of heights. | Yes | Yes |
## Statistics on L moments of intensities
  
Compute coefficient of variation, Skewness and Kurtosis of the L moments of points intensity.
### Outputs
| Name | Type | Description | Vector | Raster |
| ---------------------------- | ----------------- | ---------------------------------------------------- | ------ | ------ |
| `Intensity L Moments cv` | [numeric: double] | Coefficient of variation of L moments of intensities. | Yes | Yes |
| `Intensity LMoments skewness` | [numeric: double] | Skewness of L moments of intensities. | Yes | Yes |
| `Intensity LMoments kurtosis` | [numeric: double] | Kurtosis of L moments of intensities. | Yes | Yes |
## Mean Outer Canopy Height
  
Compute the Mean Outer Canopy Height as the mean of first returns points heights with the assumption that first returns points do not enter the canopy and are representative of the outer surface area ([Jeff W. Atkins & all](https://besjournals.onlinelibrary.wiley.com/doi/10.1111/2041-210X.14040)).
### Outputs
| Name | Type | Description | Vector | Raster |
| ------ | ----------------- | ------------------------ | ------ | ------ |
| `MOCH` | [numeric: double] | Mean Outer Canopy Height. | Yes | Yes |
## Plant Area Density
  
Compute Plant Area Density and derivated metrics. This si a simplified PAD metric computed using gap fraction ([Olivier Martin & all](https://www.sciencedirect.com/science/article/pii/S0168192324004544?via%3Dihub)).
$$
\begin{array}{l}
NRD_{x,y,z} = \frac{N_{x,y,z}}{\sum_{i=0}^z N_{x,y,i}} \\[0.8em]
GF_{x,y,z} = 1 - NRD_{x,y,z} \\[0.8em]
PAD_{x,y,z} = \frac{-\ln(GF_{x,y,z})}{G(\theta) \times D}
\end{array}
$$
where:
- $N_{x,y,z}$ is the number of hits in voxel $V_{x,y,z}$
- $NRD_{x,y,z}$ is the normalized return index
- $GF_{x,y,z}$ Is the gap fraction
### Parameters
| Name | Description | Type |
| ---- | ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ | --------------------------------- |
| `K` | K coefficient performs an inverse linear calibration of LAD (Leaf Area Density) to a known LAI (Leaf Area Index) and represent vegetation efficiency to intercept lidar laser. | [numeric: double]
Default: 1 |
### Outputs
| Name | Type | Description | Vector | Raster |
| --------------------------- | ----------------- | -------------------------------------------------------------- | ------ | ------ |
| `PAD_mean` | [numeric: double] | Plant Area Density mean. | Yes | Yes |
| `PAD_min` | [numeric: double] | Plant Area Density minimum. | Yes | Yes |
| `PAD_max` | [numeric: double] | Plant Area Density maximum. | Yes | Yes |
| `PAD_sd` | [numeric: double] | Plant Area Density standard deviation. | Yes | Yes |
| `PAD_var` | [numeric: double] | Plant Area Density variance. | Yes | Yes |
| `PAD_cv` | [numeric: double] | Plant Area Density coefficient of variation. | Yes | Yes |
| `PAI` | [numeric: double] | Plant Area Index. | No | Yes |
| `PAI_mean` | [numeric: double] | Plant Area Index mean. | Yes | No |
| `PAI_min` | [numeric: double] | Plant Area Index minimum. | Yes | No |
| `PAI_max` | [numeric: double] | Plant Area Index maximum. | Yes | No |
| `PAI_sd` | [numeric: double] | Plant Area Index standard deviation. | Yes | No |
| `PAI_var` | [numeric: double] | Plant Area Index variance. | Yes | No |
| `PAI_cv` | [numeric: double] | Plant Area Index coefficient of variation. | Yes | No |
| `PAD_mean_of_ver_sd` | [numeric: double] | Plant Area Density mean of vertical standard deviation. | Yes | No |
| `PAD_mean_of_ver_cv` | [numeric: double] | Plant Area Density mean of vertical coefficient of variation. | Yes | No |
| `PAD_sd_of_ver_mean` | [numeric: double] | Plant Area Density standard deviation of vertical mean. | Yes | No |
| `PAD_cv_of_ver_mean` | [numeric: double] | Plant Area Density coefficient of variation of vertical mean. | Yes | No |
| `PAD_mean_of_hor_sd` | [numeric: double] | Plant Area Density mean of horizontal standard deviation. | Yes | No |
| `PAD_mean_of_hor_cv` | [numeric: double] | Plant Area Density mean of horizontal coefficient of variation. | Yes | No |
| `PAD_sd_of_hor_mean` | [numeric: double] | Plant Area Density standard deviation of horizontal mean. | Yes | No |
| `PAD_cv_of_hor_mean` | [numeric: double] | Plant Area Density coefficient of variation of horizontal mean. | Yes | No |
| `VCI` | [numeric: double] | Vertical Complexity Index. | No | Yes |
| `VCI_mean` | [numeric: double] | Vertical Complexity Index mean. | Yes | No |
| `VCI_min` | [numeric: double] | Vertical Complexity Index minimum. | Yes | No |
| `VCI_max` | [numeric: double] | Vertical Complexity Index maximum. | Yes | No |
| `VCI_sd` | [numeric: double] | Vertical Complexity Index standard deviation. | Yes | No |
| `VCI_var` | [numeric: double] | Vertical Complexity Index variance. | Yes | No |
| `VCI_cv` | [numeric: double] | Vertical Complexity Index coefficient of variation. | Yes | No |
| `PAD_peak_height` | [numeric: double] | Height of Plant Area Density peak. | Yes | Yes |
| `PAD_skewness` | [numeric: double] | Skewness of Plant Area Density distribution. | Yes | Yes |
| `PAD_kurtosis` | [numeric: double] | Kurtosis of Plant Area Density distribution. | Yes | Yes |
| `PAD_Z_P25` | [numeric: double] | Percentile 25 of Plant Area Density distribution. | Yes | Yes |
| `PAD_Z_P50` | [numeric: double] | Percentile 50 of Plant Area Density distribution. | Yes | Yes |
| `PAD_Z_P75` | [numeric: double] | Percentile 75 of Plant Area Density distribution. | Yes | Yes |
| `PAD_mean_slope` | [numeric: double] | Mean of Plant Area Density slope. | Yes | Yes |
| `PAD_max_slope` | [numeric: double] | Maximum of Plant Area Density slope. | Yes | Yes |
| `PAD_min_slope` | [numeric: double] | Minimum of Plant Area Density slope | Yes | Yes |
| `PAD_mean_curvature` | [numeric: double] | Minimum of Plant Area Density curvature. | Yes | Yes |
| `PAD_max_curvature` | [numeric: double] | Maximum of Plant Area Density slope. | Yes | Yes |
| `PAD_num_inflection_points` | [numeric: double] | Number of inflection points in Plant Area Density distribution. | Yes | Yes |
## Percentiles of height
  
Compute the following percentiles on points heights: 1, 5, 10, 20, 25, 30, 40, 50, 60, 70, 75, 80, 90, 95, 99.
### Outputs
| Name | Type | Description | Vector | Raster |
| ---------------------- | ----------------- | ---------------------- | ------ | ------ |
| `Height percentile_1` | [numeric: double] | 1st height percentile. | Yes | Yes |
| `Height percentile_5` | [numeric: double] | 5th height percentile. | Yes | Yes |
| `Height percentile_10` | [numeric: double] | 10th height percentile. | Yes | Yes |
| `Height percentile_20` | [numeric: double] | 20th height percentile. | Yes | Yes |
| `Height percentile_25` | [numeric: double] | 25th height percentile. | Yes | Yes |
| `Height percentile_30` | [numeric: double] | 30th height percentile. | Yes | Yes |
| `Height percentile_40` | [numeric: double] | 40th height percentile. | Yes | Yes |
| `Height percentile_50` | [numeric: double] | 50th height percentile. | Yes | Yes |
| `Height percentile_60` | [numeric: double] | 60th height percentile. | Yes | Yes |
| `Height percentile_70` | [numeric: double] | 70th height percentile. | Yes | Yes |
| `Height percentile_75` | [numeric: double] | 75th height percentile. | Yes | Yes |
| `Height percentile_80` | [numeric: double] | 80th height percentile. | Yes | Yes |
| `Height percentile_90` | [numeric: double] | 90th height percentile. | Yes | Yes |
| `Height percentile_95` | [numeric: double] | 95th height percentile. | Yes | Yes |
| `Height percentile_99` | [numeric: double] | 99th height percentile. | Yes | Yes |
## Percentiles of intensity
  
Compute the following percentiles on points intensities: 1, 5, 10, 20, 25, 30, 40, 50, 60, 70, 75, 80, 90, 95, 99.
### Outputs
| Name | Type | Description | Vector | Raster |
| ------------------------- | ----------------- | ------------------------- | ------ | ------ |
| `Intensity percentile_1` | [numeric: double] | 1st intensity percentile. | Yes | Yes |
| `Intensity percentile_5` | [numeric: double] | 5th intensity percentile. | Yes | Yes |
| `Intensity percentile_10` | [numeric: double] | 10th intensity percentile. | Yes | Yes |
| `Intensity percentile_20` | [numeric: double] | 20th intensity percentile. | Yes | Yes |
| `Intensity percentile_25` | [numeric: double] | 25th intensity percentile. | Yes | Yes |
| `Intensity percentile_30` | [numeric: double] | 30th intensity percentile. | Yes | Yes |
| `Intensity percentile_40` | [numeric: double] | 40th intensity percentile. | Yes | Yes |
| `Intensity percentile_50` | [numeric: double] | 50th intensity percentile. | Yes | Yes |
| `Intensity percentile_60` | [numeric: double] | 60th intensity percentile. | Yes | Yes |
| `Intensity percentile_70` | [numeric: double] | 70th intensity percentile. | Yes | Yes |
| `Intensity percentile_75` | [numeric: double] | 75th intensity percentile. | Yes | Yes |
| `Intensity percentile_80` | [numeric: double] | 80th intensity percentile. | Yes | Yes |
| `Intensity percentile_90` | [numeric: double] | 90th intensity percentile. | Yes | Yes |
| `Intensity percentile_95` | [numeric: double] | 95th intensity percentile. | Yes | Yes |
| `Intensity percentile_99` | [numeric: double] | 99th intensity percentile. | Yes | Yes |
## Returns proportion
  
Compute population and proportion of returns and first returns with heights above mean height.
### Outputs
| Name | Type | Description | Vector | Raster |
| -------------------------------------------- | ----------------- | --------------------------------------------------------- | ------ | ------ |
| `Returns above mean height` | [numeric: double] | Number of returns with height above mean height. | Yes | Yes |
| `Returns above mean height percentage` | [numeric: double] | Proportion of returns with height above mean height. | Yes | Yes |
| `First returns above mean height` | [numeric: double] | Number of first returns with height above mean height. | Yes | Yes |
| `First returns above mean height percentage` | [numeric: double] | Proportion of first returns with height above mean height. | Yes | Yes |
## Rugosity
  
Compute Rugosity as the standard deviation of outer canopy heights using first returns only. Rugosity provides an assessment of heterogeneity based on the variability of the system ([Jeff W. Atkins & all](https://besjournals.onlinelibrary.wiley.com/doi/10.1111/2041-210X.14040)).
### Outputs
| Name | Type | Description | Vector | Raster |
| ---------- | ----------------- | ------------------------------------------ | ------ | ------ |
| `Rugosity` | [numeric: double] | Standard deviation of outer canopy heights. | Yes | Yes |
## Statistics of height
  
Compute basic statistics on points height distribution.
### Outputs
| Name | Type | Description | Vector | Raster |
| ------------------------ | ----------------- | ------------------------------------------ | ------ | ------ |
| `Heights_min` | [numeric: double] | Minimum height. | Yes | Yes |
| `Heights_max` | [numeric: double] | Maximum height. | Yes | Yes |
| `Heights_mean` | [numeric: double] | Height mean. | Yes | Yes |
| `Heights_median` | [numeric: double] | Height median. | Yes | Yes |
| `Heights_mode` | [numeric: double] | Height mode (peak). | Yes | Yes |
| `Heights_std` | [numeric: double] | Height standard deviation. | Yes | Yes |
| `Heights_var` | [numeric: double] | Height variance. | Yes | Yes |
| `Heights_cv` | [numeric: double] | Coefficient of variation of height. | Yes | Yes |
| `Heights_iqr` | [numeric: double] | Height interquartile range. | Yes | Yes |
| `Heights_skewness` | [numeric: double] | Skewness of height. | Yes | Yes |
| `Heights_kurtosis` | [numeric: double] | Kurtosis of height. | Yes | Yes |
| `Heights_aad` | [numeric: double] | Average absolute deviation of heights. | Yes | Yes |
| `Heights_mad_median` | [numeric: double] | Mean absolute deviation from height median. | Yes | Yes |
| `Heights_mad_mode` | [numeric: double] | Mean absolute deviation from height mode. | Yes | Yes |
| `Heights_quadratic_mean` | [numeric: double] | Quadratic mean of heights. | Yes | Yes |
## Statistics of intensity
  
Compute basic statistics on points intensitiy distribution.
### Outputs
| Name | Type | Description | Vector | Raster |
| -------------------------- | ----------------- | --------------------------------------------- | ------ | ------ |
| `Intensity_min` | [numeric: double] | Minimum intensity. | Yes | Yes |
| `Intensity_max` | [numeric: double] | Maximum intensity. | Yes | Yes |
| `Intensity_mean` | [numeric: double] | Intensity mean. | Yes | Yes |
| `Intensity_median` | [numeric: double] | Intensity median. | Yes | Yes |
| `Intensity_mode` | [numeric: double] | Intensity mode (peak). | Yes | Yes |
| `Intensity_std` | [numeric: double] | Intensity standard deviation. | Yes | Yes |
| `Intensity_var` | [numeric: double] | Intensity variance. | Yes | Yes |
| `Intensity_cv` | [numeric: double] | Coefficient of variation of intensity. | Yes | Yes |
| `Intensity_iqr` | [numeric: double] | Intensity interquartile range. | Yes | Yes |
| `Intensity_skewness` | [numeric: double] | Skewness of intensity. | Yes | Yes |
| `Intensity_kurtosis` | [numeric: double] | Kurtosis of intensity. | Yes | Yes |
| `Intensity_aad` | [numeric: double] | Average absolute deviation of intensity. | Yes | Yes |
| `Intensity_mad_median` | [numeric: double] | Mean absolute deviation from intensity median. | Yes | Yes |
| `Intensity_mad_mode` | [numeric: double] | Mean absolute deviation from intensity mode. | Yes | Yes |
| `Intensity_quadratic_mean` | [numeric: double] | Quadratic mean of intensity. | Yes | Yes |
## Strata returns proportions
   
Compute population and proportion of returns and first returns per stratum.
### Outputs
| Name | Type | Description | Vector | Raster |
| ----------------------------------------------- | ----------------- | ----------------------------------------------------------- | ------ | ------ |
| `returns` | [numeric: double] | Number of returns. | Yes | Yes |
| `returns_proportion` | [numeric: double] | Proportion of returns. | Yes | Yes |
| `returns_above_lower_bound` | [numeric: double] | Percentage of returns above lower bound of stratum. | Yes | Yes |
| `percentage_of_returns_above_lower_bound` | [numeric: double] | Number of first returns. | Yes | Yes |
| `first_returns_above_lower_bound` | [numeric: double] | Proportion of first returns. | Yes | Yes |
| `percentage_of_first_returns_above_lower_bound` | [numeric: double] | Percentage of first returns above lower bound of stratum. | Yes | Yes |
| `density_proportion` | [numeric: double] | Proportion of total vegetation that lies in current stratum. | Yes | Yes |
## Heights strata statistics
   
Compute statistics on points heights for each stratum.
### Outputs
| Name | Type | Description | Vector | Raster |
| ------------------ | ----------------- | ----------------------------------- | ------ | ------ |
| `Heights std` | [numeric: double] | Heights standard deviation. | Yes | Yes |
| `Heights var` | [numeric: double] | Heights variance. | Yes | Yes |
| `Heights cv` | [numeric: double] | Coefficient of variation of height. | Yes | Yes |
| `Heights skewness` | [numeric: double] | Skewness of heights. | Yes | Yes |
| `Heights kurtosis` | [numeric: double] | Kurtosis of heights. | Yes | Yes |
| `Heights min` | [numeric: double] | Minimum height. | Yes | Yes |
| `Heights max` | [numeric: double] | MAximum height. | Yes | Yes |
| `Heights mean` | [numeric: double] | Heights mean. | Yes | Yes |
| `Heights median` | [numeric: double] | Median of heights. | Yes | Yes |
## Intensities strata statistics
   
Compute statistics on points intensities for each stratum.
### Outputs
| Name | Type | Description | Vector | Raster |
| ---------------------- | ----------------- | --------------------------------------- | ------ | ------ |
| `Intensities std` | [numeric: double] | Intensities standard deviation. | Yes | Yes |
| `Intensities var` | [numeric: double] | Intensities variance. | Yes | Yes |
| `Intensities cv` | [numeric: double] | Coefficient of variation of intensities. | Yes | Yes |
| `Intensities skewness` | [numeric: double] | Skewness of intensities. | Yes | Yes |
| `Intensities kurtosis` | [numeric: double] | Kurtosis of intensities. | Yes | Yes |
| `Intensities min` | [numeric: double] | Minimum intensity. | Yes | Yes |
| `Intensities max` | [numeric: double] | MAximum intensity. | Yes | Yes |
| `Intensities mean` | [numeric: double] | Intensity mean. | Yes | Yes |
| `Intensities median` | [numeric: double] | Intensity median. | Yes | Yes |