## Elevation Metrics

### Summary

Elevation Metrics are statistical parameters related to point cloud elevation. They are frequently used in regression analysis, especially when correlating field plot measurements with LiDAR data. In this model, 46 statistical parameters related to elevation and 10 parameters related to point cloud density can be calculated. The resultant product is a table in CSV format or a set of TIFF files.

### Principle

**Average Absolute Deviation**: Computed using the following equation:, where Z_{i}represents the elevation of i^{th}point within a statistical unit, Z represents the average elevation of all points within a statistical unit, and n is the number of points in a statistical unit.**Canopy relief ratio**: Computed using the following equation: , where mean represents the average elevation of a statistical unit, min represents the minimum elevation of a statistical unit, and max represent the maximum elevation of a statistical unit.**AIH (15)**: Within a statistical unit, all normalized lidar point clouds are sorted according to the elevation and the cumulative heights of all points are calculated. The cumulative height of X% points in each statistical unit is the statistical unit's AIH. In LiDAR360, 15 AIH can be calculated, including 1%, 5%, 10%, 20%, 25%, 30%, 40%, 50%, 60%, 70%, 75%, 80%, 90%, 95% and 99%.**AIH Interquartile Distance**: Computed using the following equation: , where AIH75% represents the 75% AIH statistical layer, and AIH25% represents the 25% AIH statistical layer.**Coefficient of Variation**: Computed using the following equation: , where Z_{std}represents the standard deviation of elevation within a statistical unit, and Z_{mean}represents the average elevation within a statistical unit.**Density Metrics(10)**: The point cloud data is divided into ten slices with the same height interval from low to high, and the proportion of returns in each height interval is the corresponding density metrics.**Kurtosis**: The kurtosis of the Z value of all points in a statistical unit. The calculation formula is , in which Z_{i}is the height value of the i-th point in each statistical unit, Z is the average height of all points in each statistical unit, n is the point number in each statistical unit, and σ is the standard deviation of point cloud height distribution within a statistical unit.**MADMedian**: The median of median absolute deviation.**Maximum**: The maximum value of Z for all points in a statistical unit.**Minimum**: The minimum value of Z for all points in a statistical unit.**Mean**: The mean value of Z for all points in a statistical unit.**Median**: The median of Z for all points in a statistical unit.**Generalized means for the 2nd power**: Computed using the following equation: , where Z_{i}is the Z value of the i^{th}point in a statistical unit.**Generalized means for the 3rd power**: Computed using the following equation:, where Z_{i}is the Z value of the i^{th}point in a statistical unit.**Elevation Percentile (15)**: Within a statistical unit, all normalized lidar point clouds are sorted by elevation, and then the elevation at which X% of points in each statistical unit is located is the elevation percentile of this statistical unit. In LiDAR360, 15 elevation percentiles are calculated, including 1%, 5%, 10%, 20%, 25%, 30%, 40%, 50%, 60%, 70%, 75%, 80%, 90%, 95% and 99%.**Elevation Percentile Interquartile Distance**: Computed using the following equation: , where Ele75% represents the 75% elevation statistical layer, and Ele25% represents the 25% elevation statistical layer.**Skewness**: This value shows the symmetry of Z values of all the points in each statistical unit. The calculation formula is , in which Z_{i}is the height value of the i-th point in each statistical unit, Z is the average height of all points in each statistical unit, n is the point number in each statistical unit, and σ is the standard deviation of point cloud height distribution within a statistical unit.**Standard Deviation**: The standard deviation of Z for all points in a statistical unit.**Variance**: The variance of Z for all points in a statistical unit.

### Usage

To generate Elevation Metrics, navigate to *ALS Forest > Forest Metrics > Elevation Metrics*.

### Settings

**Input Data**: Ensure that each input point cloud data is Normalize by DEM or Normalize by Ground Points. The input file can be a single file or multiple data files. Point cloud data should be opened in LiDAR360 before being processed.**XSize (meter)(default value is "15")**: The length of a grid size should be greater than an individual tree crown width. For most forest types, the grid size should be greater than 15 meters.**YSize (meter)(default value is "15")**: The width of a grid size should be greater than an individual tree crown width. For most forest types, the grid size should be greater than 15 meters.**HeightBreak (meter)(default value is "2")**: Usually, it is desirable to ignore points below a particular elevation to avoid influence low vegetations (e.g., grass and shrub). The "HeightBreak" parameter can be set in many ALS forestry tools, allowing users to ignore points below a specified height (a value of 2 m is commonly used).**Output Path**: Path of the output file. A corresponding CSV file or a set of corresponding TIFF files will be generated for each input point cloud data, which can be used as an independent variable in the regression analysis.**DefaultValue**: Restore the default parameters.

Note: Only when the point cloud data is loaded in the software can you use the Elevation Metrics function; otherwise, the message "There is no point cloud data meeting the conditions of calculation!" will pop up. If the maximum Z value of the point cloud is greater than 200 m or the maximum Z minus the minimum Z is greater than 200 m, the data is not considered to have been normalized, and the prompt information shown in the figure below will pop up. Click “YES” to keep using this type of data in the operation; otherwise, click "NO" and reselect the input data file.