R/lsm_l_pafrac.R

In landscapemetrics: Landscape Metrics for Categorical Map Patterns

#' PAFRAC  (landscape level)
#'
#' @description Perimeter-Area Fractal Dimension (Shape metric)
#'
#' @param landscape A categorical raster object: SpatRaster; Raster* Layer, Stack, Brick; stars or a list of SpatRasters.
#' @param directions The number of directions in which patches should be
#' connected: 4 (rook's case) or 8 (queen's case).
#' @param verbose Print warning message if not sufficient patches are present
#'
#' @details
#' \deqn{PAFRAC = \frac{2}{\beta}}
#' where \eqn{\beta} is the slope of the regression of the area against the perimeter
#' (logarithm) \eqn{N \sum \limits_{i = 1}^{m} \sum \limits_{j = 1}^{n} \ln a_{ij} = a + \beta N \sum \limits_{i = 1}^{m} \sum \limits_{j = 1}^{n} \ln p_{ij}}
#'
#' PAFRAC is a 'Shape metric'. It describes the patch complexity of the landscape while being
#' scale independent. This means that increasing the patch size while not changing the
#' patch form will not change the metric. However, it is only meaningful if the relationship
#' between the area and perimeter is linear on a logarithmic scale. Furthermore, if there
#' are less than 10 patches in the landscape, the metric returns NA because of the small-sample
#' issue.
#'
#' \subsection{Units}{None}
#' \subsection{Range}{1 <= PAFRAC <= 2}
#' \subsection{Behaviour}{Approaches PAFRAC = 1 for patches with simple shapes and
#' approaches PAFRAC = 2 for irregular shapes}
#'
#' @seealso
#' \code{\link{lsm_p_area}},
#' \code{\link{lsm_p_perim}}, \cr
#' \code{\link{lsm_c_pafrac}}
#'
#' @return tibble
#'
#' @examples
#' landscape <- terra::rast(landscapemetrics::landscape)
#' lsm_l_pafrac(landscape)
#'
#' @aliases lsm_l_pafrac
#' @rdname lsm_l_pafrac
#'
#' @references
#' McGarigal K., SA Cushman, and E Ene. 2023. FRAGSTATS v4: Spatial Pattern Analysis
#' Program for Categorical Maps. Computer software program produced by the authors;
#' available at the following web site: https://www.fragstats.org
#'
#' Burrough, P. A. 1986. Principles of Geographical Information Systems for
#' Land Resources Assessment. Monographs on Soil and Resources Survey No. 12.
#' Clarendon Press, Oxford
#'
#' @export
lsm_l_pafrac <- function(landscape, directions = 8, verbose = TRUE) {
    landscape <- landscape_as_list(landscape)

    result <- lapply(X = landscape,
                     FUN = lsm_l_pafrac_calc,
                     directions = directions,
                     verbose = verbose)

    layer <- rep(seq_along(result),
                 vapply(result, nrow, FUN.VALUE = integer(1)))

    result <- do.call(rbind, result)

    tibble::add_column(result, layer, .before = TRUE)
}

lsm_l_pafrac_calc <- function(landscape, directions, verbose, resolution = NULL){

    # convert to matrix
    if (!inherits(x = landscape, what = "matrix")) {
        resolution <- terra::res(landscape)

        landscape <-terra::as.matrix(landscape, wide = TRUE)
    }

    # all values NA
    if (all(is.na(landscape))) {
        return(tibble::tibble(level = "landscape",
                              class = as.integer(NA),
                              id = as.integer(NA),
                              metric = "pafrac",
                              value = as.double(NA)))
    }

    # get number of patches for each class
    number_patches <- lsm_c_np_calc(landscape,
                                    directions = directions)

    # summarise for total landscape
    number_patches <- sum(number_patches$value)

    # PAFRAC NA for less than 10 patches
    if (number_patches < 10) {

        pafrac <-  NA

        if (verbose) {
            warning("PAFRAC = NA for NP < 10",
                    call. = FALSE)
        }

    # calculate pafrac as regression between area and perimeter (beta)
    } else {

        # get patch area
        area_patch <- lsm_p_area_calc(landscape,
                                      directions = directions,
                                      resolution = resolution)

        # get patch perimeter
        perimeter_patch <- lsm_p_perim_calc(landscape,
                                            directions = directions,
                                            resolution = resolution)

        regression_model <- stats::lm(log(area_patch$value) ~
                                          log(perimeter_patch$value))

        pafrac <- 2 / regression_model$coefficients[[2]]
    }

    return(tibble::tibble(level = "landscape",
                          class = as.integer(NA),
                          id = as.integer(NA),
                          metric = "pafrac",
                          value = as.double(pafrac)))
}