Alexander Ilich December 30, 2023


R-CMD-check CRAN License: GPLv3 DOI

Please cite as

Ilich, A. R., Misiuk, B., Lecours, V., & Murawski, S. A. (2023). MultiscaleDTM: An open-source R package for multiscale geomorphometric analysis. Transactions in GIS, 27(4).


This R package calculates multi-scale geomorphometric terrain attributes from regularly gridded digital terrain models (DTM; i.e. elevation or bathymetry rasters) via a specified window as described in Ilich et al. (2023).

Figure adapted from Wilson et al. (2007)

Install and Load Package

The package can be installed from CRAN using install.packages("MultiscaleDTM") or the development version can be installed from github using the code remotes::install_github("ailich/MultiscaleDTM"). If you are using Windows, you may need to install Rtools using the instructions found here). To install from github you must already have the remotes package installed, which can be installed using install.packages("remotes")

This package relies on the terra package for handling of spatial raster data.

Main Functions

Slope, Aspect and Curvature

\[ Z = aX^2 + bY^2 +cXY+ dX +eY +f \]

Figure adapted from Walbridge et al., (2018)


Figure adapted from Sappington et al. (2007)

Figure adapted from Habib (2021)

\[ \text{VRM} = 1- \frac{\sqrt{\bigg(\sum x\bigg)^2+\bigg(\sum y\bigg)^2+\bigg(\sum z\bigg)^2}}{N} \]

\[ x = sin(\text{slope})*sin(\text{aspect}) \]

\[ y=sin(\text{slope})*cos(\text{aspect}) \]

\[ z=cos(\text{slope}) \]

Figure adapted from Friedman et al. (2012) and created with

Figure adapted from Jenness (2004)

Figure adapted from Cavalli et al. (2008)

Relative Position

Relative position represents whether an area is a local high or low in relation to a reference height. It is calculated as the value of the focal cell minus the value of a reference elevation which is often the mean of included values in the focal window but could also be other functions such as the median, min, or max of included values. Positive values indicate local topographic highs and negative values indicate lows.Relative Position can be expressed in units of the input DTM raster or can standardized relative to the local topography by dividing by the standard deviation or range of included elevation values in the focal window.

Examples of different focal window shapes. Shown are a 13 x 13 cell rectangular window (left), a circular window with a radius of six cells (center), and an annulus window with an inner radius of four cells and an outer radius of six cells (right).


In this tutorial we will calculate most terrain attributes using a 5 x 5 cell rectangular window; however, any rectangular odd numbered window size could be used. Window size is specified using the w parameter. Rectangular window sizes are specified with a vector of length 2 as c(n_rows, n_cols). If a single number is provided it will be used for both the number of rows and columns. Functions that calculate relative position currently support other focal window shapes. In those examples, we will additionally calculate the measures using a circular focal window with a radius of 2 cells, an annulus window with an inner radius of 4 and an outer radius of 6 cells, and a custom focal window. Circular windows are specified by a single number representing the radius, annulus windows are specified with a vector of length 2 of c(inner_radius, outer_radius), and custom windows are specified by a matrix with values showing which data to include (1’s) and which data to exclude (NA’s).

Load packages

library(MultiscaleDTM) #Load MultiscaleDTM package

See package help page


Read in Data

Typically raster data would be loaded into R via terra package’s rast function. We will use instead load a georeferenced version of R’s built in volcano data set using the erupt function.

r<- erupt()

Slope, Aspect, and Curvature

slp_asp<- SlpAsp(r = r, w = c(5,5), unit = "degrees", method = "queen", metrics = c("slope", "aspect", "eastness", "northness"), na.rm=TRUE)

qmetrics<- Qfit(r, w = c(5,5), unit = "degrees", metrics = c("elev", "qslope", "qaspect", "qeastness", "qnorthness", "profc", "planc", "twistc", "meanc", "maxc", "minc", "features"), na.rm = TRUE)

To explore these measures in an interactive environment use explore_terrain() or go to this website


vrm<- VRM(r, w=c(5,5), na.rm = TRUE)

sapa<- SAPA(r, w=c(5,5), slope_correction = TRUE, na.rm=TRUE)

adj_SD<- AdjSD(r, w=c(5,5), na.rm = TRUE)

rie<- RIE(r, w=c(5,5), na.rm = TRUE)

Relative Position

Note, the “s” at the start of some names indicates the attribute has been standardized based on local topography.

rp<- RelPos(r, w=matrix(data = c(1,NA,1), nrow = 3, ncol=3), shape = "custom", fun = "median", na.rm = TRUE)

tpi<- TPI(r, w=c(5,5), shape= "rectangle", na.rm = TRUE)

dmv<- DMV(r, w=2, shape= "circle", na.rm = TRUE, stand="range")

bpi<- BPI(r, w = c(4,6), unit = "cell", stand= "sd", na.rm = TRUE)

Circle and annulus windows for can be specified in either cell units (number of raster cells) or in map units (e.g. meters) which can be useful if your x and y resolutions are not equal. Additionally, the function circle_window and annulus_window can be used to verify that you are specifying your window correctly (NA’s are excluded cells and 1’s are included cells) and can be directly supplied to the w argument instead.

annulus_window(radius = c(4,6), unit = "cell")
##       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]
##  [1,]   NA   NA   NA   NA   NA   NA    1   NA   NA    NA    NA    NA    NA
##  [2,]   NA   NA   NA    1    1    1    1    1    1     1    NA    NA    NA
##  [3,]   NA   NA    1    1    1    1    1    1    1     1     1    NA    NA
##  [4,]   NA    1    1    1   NA   NA   NA   NA   NA     1     1     1    NA
##  [5,]   NA    1    1   NA   NA   NA   NA   NA   NA    NA     1     1    NA
##  [6,]   NA    1    1   NA   NA   NA   NA   NA   NA    NA     1     1    NA
##  [7,]    1    1    1   NA   NA   NA   NA   NA   NA    NA     1     1     1
##  [8,]   NA    1    1   NA   NA   NA   NA   NA   NA    NA     1     1    NA
##  [9,]   NA    1    1   NA   NA   NA   NA   NA   NA    NA     1     1    NA
## [10,]   NA    1    1    1   NA   NA   NA   NA   NA     1     1     1    NA
## [11,]   NA   NA    1    1    1    1    1    1    1     1     1    NA    NA
## [12,]   NA   NA   NA    1    1    1    1    1    1     1    NA    NA    NA
## [13,]   NA   NA   NA   NA   NA   NA    1   NA   NA    NA    NA    NA    NA
## attr(,"unit")
## [1] "cell"
## attr(,"scale")
## [1] "4x6"
## attr(,"shape")
## [1] "annulus"
bpi2<- BPI(r, w = annulus_window(radius = c(4,6), unit = "cell"), stand= "sd", na.rm = TRUE) # equivalent to BPI code from earlier


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