Calculate fractal Dimension using the height variation method

Usage

fd_hvar(
  data,
  lvec,
  regmethod = "mean",
  keep_data = FALSE,
  plot = FALSE,
  parallel = FALSE,
  ncores = (parallel::detectCores() - 1)
)

Arguments

data: Digital elevation model of class RasterLayer or dataframe (output of hvar function)
lvec: Vector of scales to use for calculation.
regmethod: Method to use for linear regression between scale (lvec) and height range. One of raw (all data), mean (default) median or ends (minimum and maximum scale only)
keep_data: Keep the data used for fd calculation? defaults to FALSE
plot: Logical. Show plot of scales relative to data?
parallel: Logical. Use parallel processing? Note: parallel must be installed.
ncores: Number of cores to use when parallel = TRUE.

Value

A value for fractal dimension, typically between 2 and 3 or a list if keep_data = TRUE.

Details

Calculates fractal dimension using the height variation regression. If lvec is not specified, a default based on resolution and extent will be used. data can be a DEM or a data.frame with columns labeled l and h for grid cell length and height range of that cell, respectively (output of hvar()). A rule of thumb is that l should range an order of magnitude. However, large ranges also average-out fractal dimension of a surface that might have phase transitions, and therefore a thorough exploration of height ranges is suggested using the plot. regmethod specifies whether data is summarized by taking the mean or median of height ranges across scales or all data is used. regmethod "raw" is not recommended because the regression will give much more weight to the lower scales that include more points and likely underestimate D.

Examples


# \donttest{
dem <- habtools::dem_crop(horseshoe, x0 = -469, y0 = 1267, L = 2, plot = TRUE)

fd_hvar(dem, lvec = c(0.125, 0.25, 0.5, 1, 2))
#> [1] 2.215566
fd_hvar(dem, regmethod = "mean", plot = TRUE, keep_data = TRUE)
#> lvec is set to c(0.062, 0.125, 0.25, 0.5, 1, 2).

#> $D
#> [1] 2.145523
#> 
#> $lvec
#> [1] 0.0625 0.1250 0.2500 0.5000 1.0000 2.0000
#> 
#> $data
#>        l          h
#> 1 0.0625 0.05967467
#> 2 0.1250 0.13053990
#> 3 0.2500 0.25134412
#> 4 0.5000 0.47317257
#> 5 1.0000 0.87658044
#> 6 2.0000 1.05967593
#> 
#> $method
#> [1] "hvar"
#> 
fd_hvar(dem, regmethod = "median", plot = TRUE, keep_data = TRUE)
#> lvec is set to c(0.062, 0.125, 0.25, 0.5, 1, 2).
#> $D
#> [1] 2.118973
#> 
#> $lvec
#> [1] 0.0625 0.1250 0.2500 0.5000 1.0000 2.0000
#> 
#> $data
#>        l          h
#> 1 0.0625 0.05613654
#> 2 0.1250 0.13097851
#> 3 0.2500 0.27393017
#> 4 0.5000 0.63257221
#> 5 1.0000 0.91977016
#> 6 2.0000 1.05967593
#> 
#> $method
#> [1] "hvar"
#> 
fd_hvar(dem)
#> lvec is set to c(0.062, 0.125, 0.25, 0.5, 1, 2).
#> [1] 2.145523
# }