DEVISE Geomorphometric Descriptions

Author

WYGISC

Documentation Home

Digital Elevation Model (DEM) data

Shuttle Radar Topography Mission (SRTM) tile data used to create the digital elevation model NASA Data

Geomorphometric conversions

The series of geographic coordinate & data transformation functions:

*All multi-scale metrics have 5 variables with window sizes 90, 330, 510, 990, & 1530 meters

Cross-Sectional Curvature (crosc, a multi-scale metric)

Overview:

Cross-sectional curvature is a measurement of how terrain curves perpendicular to the slope direction. The multi-scale terrain parameter function mstp(), designed for this product, is a wrapper that applied the GRASS GIS’s r.param.scale function. For the cross-sectional curvature metric the function used method = “crosc” for its calculation. The cross-sectional curvature Grass function applied formula 1, shown below, to modify each cell in the DEM based on neighboring cells within a window. The window of adjacent cells selected was based on a parameter s. Parameter s is a whole odd number which displayed the number of cells in the side length of a square sample centered around the current cell of interest. Parameter S for the wrapper mstp() included a range of 5 values [3,11,17,33,51] (Cells have a 30 meter length and width).

Metric Scale:

crosc > 0: Convex or the surface is curving upwards in this perspective. A positive value indicates a landform of some sort.

crosc < 0: Concave or the surface is curving downwards in this perspective. A negative value indicates a depression of some sort.

crosc = 0: Flat or linear surface. No relief.

Sources:

Evans, I. S., (1972), Moore, ID., P.E. Gessler, G.A. Nielsen, and G.A. Petersen (1993), Wood, J. (1996), Pike, R.J., I.S. Evans, T.Hengl (2009)

GRASS GIS r.param.scale() function link

Explanation of Cross-Sectional formula: Wood, J. (1996): The Geomorphological characterisation of Digital Elevation Models. Diss., Department of Geography, University of Leicester, U.K online at: http://hdl.handle.net/2381/34503

Formula 1:

\[\text{crosc} = -200 \cdot \text{resoln} \cdot \text{wsize} \cdot \frac{b \cdot d^2 + a \cdot e^2 - c \cdot d \cdot e}{d^2 + e^2}\]

\(a = \frac{\partial^2 z}{\partial x^2}\) - second-order partial derivative in the x direction

\(b = \frac{\partial^2 z}{\partial y^2}\) - second-order partial derivative in the y direction

\(c = \frac{\partial^2 z}{\partial x \partial y}\) - mixed second-order derivative

\(d = \frac{\partial z}{\partial x}\) - first-order slope in x direction

\(e = \frac{\partial z}{\partial y}\) - first-order slope in y direction

\(resoln = \text{map resolution (in map units per pixel)}\)

\(wsize = \text{window size (neighborhood width)}\) - s

Compound Topographic Index (CTI) or Topographic Wetness Index (TWI)

Overview:

CTI quantifies the effect of topography on the location and the amount of soil moisture. The wrapper function cti(), designed for this model, applied the GRASS GIS’s r.topidx function to convert the DEM. r.topidx() applies formula 2 in order to calculate each cell’s CTI value.

Metric Scale:

Higher CTI values indicate areas more likely to accumulate water. Negative values can occur and indicate an area that is more likely to shed water.

CTI > 0: Accumulates water

CTI < 0: Sheds water

Sources:

Moore, ID., P.E. Gessler, G.A. Nielsen, and G.A. Petersen (1993) Terrain attributes: estimation methods and scale effects. In Modeling Change in Environmental Systems, edited by A.J. Jakeman M.B. Beck and M. McAleer Wiley, London, pp. 189 - 214.

[GRASS GIS’s r.topidx() function] (https://grass.osgeo.org/grass-stable/manuals/r.topidx.html)

Formula 2:

\[ \text{CTI} = \ln\left( \frac{A}{\tan(\beta)} \right) \]

\({A}\) = Upslope contributing area per unit contour length (typically measured in \(m^2/m\))

\(\beta\) = local slope angle in radians

\(\tan(\beta)\) = slope steepness

Martonne’s Dissection Index (diss, a multi-scale metric)

Overview:

Measures the local relief of a cell compared to its neighboring cells. The wrapper function diss(), designed for this model, applied GRASS GIS’s r.neighbors function and r.mapcalc() to calculate the dissection index. r.neighbors collected the grouping of surrounding cells which were used to calculate local relief. The function r.mapcalc() applies formula 3 inside the wrapper to calculate the index. The window of adjacent cells selected was based on a parameter s. Parameter s is a whole odd number which displayed the number of cells in the side length of a square sample centered around the current cell of interest. Parameter S for the wrapper diss() included a range of 5 values [3,11,17,33,51] (Cells have a 30 meter length and width).

Metric Scale:

Martonn’s Dissection Index ranges from 0 to 1.

Values near 1 indicate that the cell is at a local high, and values near 0 indicate a local low.

Sources:

Bolstad, P.V., and T.M. Lillesand. (1992). Improved classification of forest vegetation in northern Wisconsin through a rule-based combination of soils, terrain, and LandsatTM data. Forest Science. 38(1): 5-20.

GRASS GIS r.neighbors() function link

GRASS GIS r.mapcalc() function link

Formula 3:

\[\text{DISS} = \frac{z - z_{\min}}{z_{\max} - z_{\min}}\]

\(z\) = elevation at the focal cell

\(z_{\min}\) = minimum elevation in the surrounding neighborhood (defined by window size s)

\(z_{\max}\) = maximum elevation in the surrounding neighborhood (same window)

Heat Load Index (HLI)

Overview:

Estimates the potential direct solar radiation or relative heat load a location receives, based on slope and aspect. The wrapper designed in this case, hli(), uses the GRASS GIS function’s r.slope.aspect() and r.mapcalc() to apply formula 4.

Metric Scale:

HLI ranges from 0 to 1. O represents the slopes with the lowest direct solar radiation, which are therefore the coldest. 1 represents slopes with the highest direct solar radiation which are therefore the hottest.

Sources:

McCune, Bruce and Dylan Keon, 2002. Equations for potential annual direct incident radiation and heat load index. Journal of Vegetation Science. 13:603-606.

GRASS GIS r.slope.aspect() function link

GRASS GIS r.mapcalc() function link

Formula 4:

\[\text{HLI} = 0.339 + 0.808 \cdot \cos(\phi) \cdot \cos(\beta) - 0.196 \cdot \sin(\phi) \cdot \sin(\beta) - 0.482 \cdot \cos(\gamma)\] \(\phi\) = latitude (in radians)

\(\beta\) = slope (in radians)

\(\gamma\) = folded aspect (in radians)

Longitudinal Curvature (longc, a multi-scale metric)

Overview:

Measures the curvature of the surface in the direction of maximum slope (Wood, J. 1996). The wrapper function mstp(), designed for multi-scale terrain parameters calculations, applied GRASS GIS’s r.param.scale() function to calculate “longc” using formula 5. r.neighbors() collected the grouping of surrounding cells which were used to calculate local relief. The function r.mapcalc() applies formula 3 inside the wrapper to calculate the index. The window of adjacent cells selected was based on a parameter s. Parameter s is a whole odd number which displayed the number of cells in the side length of a square sample centered around the current cell of interest. Parameter S for the wrapper mstp() included a range of 5 values [3,11,17,33,51] (Cells have a 30 meter length and width).

Metric Scale:

A higher curvature value indicates a sharper bend and a lower indicates a softer bend. 0 indicates a flat surface in the longitudinal direction.

Sources:

Evans, I. S., 1972. General geomorphometry, derivatives of altitude, and descriptive statistics. In Chorley, R. J., Spatial Analysis in Geomorphology New York: Harper & Row pp.17 - 90.

GRASS GIS r.param.scale() function link

Wood, J. (1996): The Geomorphological characterisation of Digital Elevation Models. Diss., Department of Geography, University of Leicester, U.K online at: http://hdl.handle.net/2381/34503

Formula 5:

\[longc = -200 \cdot \text{resoln} \cdot \text{wsize} \cdot \frac{a \cdot d^2 + b \cdot e^2 + c \cdot d \cdot e}{d^2 + e^2}\]

\(a = \frac{\partial^2 z}{\partial x^2}\) - second-order partial derivative in the x direction

\(b = \frac{\partial^2 z}{\partial y^2}\) - second-order partial derivative in the y direction

\(c = \frac{\partial^2 z}{\partial x \partial y}\) - mixed second-order derivative

\(d = \frac{\partial z}{\partial x}\) - first-order slope in x direction

\(e = \frac{\partial z}{\partial y}\) - first-order slope in y direction

\(resoln = \text{map resolution (in map units per pixel)}\)

\(wsize = \text{window size (neighborhood width)}\) - s

Mean Slope Formula (mnslp, a multi-scale metric)

Overview:

The mean slope is calculated as the average slope over a defined window. The wrapper function mnslp(), designed for this conversion, applied GRASS GIS’s r.neighbors() and r.aspect() functions internally. r.neighbors() collected the grouping of surrounding cells which were used as a local sample for the average slope. The function r.mapcalc() applied formula 6 inside the wrapper to calculate the index. The window of adjacent cells selected was based on a parameter s. Parameter s is a whole odd number which displayed the number of cells in the side length of a square sample centered around the current cell of interest. Parameter S for the wrapper mnslp() included a range of 5 values [3,11,17,33,51] (Cells have a 30 meter length and width).

Metric Scale:

The slope value with range from 0 to 90 degrees (or equivalent radians), and slope values closer to 0 indicate a flatter surface while values closer to 90 indicate a steeper slope.

Sources:

Evans, I. S., 1972. General geomorphometry, derivatives of altitude, and descriptive statistics. In Chorley, R. J., Spatial Analysis in Geomorphology New York: Harper & Row pp.17 - 90.

Pike, R.J., I.S. Evans, T.Hengl (2009) Geomorphometry: A Brief Guide. Developments in Soil Science, Volume 33. Elsevier B.V. ISSN 0166-2481

GRASS GIS r.neighbors() function link

GRASS GIS r.slope.aspect() function link

Formula 6:

\[\text{mnslp} = \frac{1}{n} \sum_{i=1}^{n} \sqrt{\left( \frac{\partial z}{\partial x} \right)_i^2 + \left( \frac{\partial z}{\partial y} \right)_i^2 }\]

\(\frac{\partial z}{\partial x}\) and \(\frac{\partial z}{\partial y}\) are the partial derivatives (slopes) in the x and y directions.

\(n\) is the number of cells in the neighborhood.

The square root of the sum of squares gives the slope magnitude at each point.

Planform Curvature (planc, a multi-scale metric)

Overview:

Planform curvature is a terrain morphometric parameter that describes the curvature of the terrain in the planform view. More simply planform curvature is a measure of the shape of a surface in the horizontal plane. The multi-scale terrain parameter function mstp(), designed for this product, is a wrapper that applied the GRASS GIS’s r.param.scale() function. For the plan curvature metric the Grass function used the parameter value method = “planc”. The plan curvature Grass function applied formula 7, shown below, to modify each cell in the DEM based on neighboring cells within a window. The window of adjacent cells selected was based on a parameter s. Parameter s is a whole odd number which displayed the number of cells in the side length of a square sample centered around the current cell of interest. Parameter S for the wrapper mstp() included a range of 5 values [3,11,17,33,51] (Cells have a 30 meter length and width).

Metric Scale:

Positive values display a convex curvature. Negative values display a concave curvature. Values near zero display a flat or linear slope.

Sources:

Evans, I. S., 1972. General geomorphometry, derivatives of altitude, and descriptive statistics. In Chorley, R. J., Spatial Analysis in Geomorphology New York: Harper & Row pp.17 - 90.

Gessler, P.E., I.D. Moore, N.J. McKenzie, and P.J. Ryan. (1995). Soil-landscape modeling and spatial prediction of soil attributes. International Journal of GIS. 9(4):421-432.

Pike, R.J., I.S. Evans, T.Hengl (2009) Geomorphometry: A Brief Guide. Developments in Soil Science, Volume 33. Elsevier B.V. ISSN 0166-2481

GRASS GIS r.param.scale() function link

Wood, J. (1996): The Geomorphological characterisation of Digital Elevation Models. Diss., Department of Geography, University of Leicester, U.K online at: http://hdl.handle.net/2381/34503

Formula 7:

\[planc = 200 \cdot \text{resoln} \cdot \text{wsize} \cdot\frac{b \cdot d^2 + a \cdot e^2 - c \cdot d \cdot e}{{(d^2 + e^2)}^{3/2}}\]

\(a = \frac{\partial^2 z}{\partial x^2}\) - second-order partial derivative in the x direction

\(b = \frac{\partial^2 z}{\partial y^2}\) - second-order partial derivative in the y direction

\(c = \frac{\partial^2 z}{\partial x \partial y}\) - mixed second-order derivative

\(d = \frac{\partial z}{\partial x}\) - first-order slope in x direction

\(e = \frac{\partial z}{\partial y}\) - first-order slope in y direction

\(resoln = \text{map resolution (in map units per pixel)}\)

\(wsize = \text{window size (neighborhood width)}\) - s

Profile Curvature (profc, a multi-scale metric)

Overview:

Profile curvature is the curvature intersecting with the plane defined by Z axis and maximum gradient direction. The curvature describes the rate of change of slope in the direction of the steepest descent which affects flow acceleration/deceleration. The multi-scale terrain parameter function mstp(), designed for this product, is a wrapper that applied the GRASS GIS’s r.param.scale() function. The Grass GIS function used method = “profc” for its calculation which applied formula 8, shown below, to modify each cell in the DEM based on neighboring cells within a window. The window of adjacent cells selected was based on a parameter s. Parameter s is a whole odd number which displayed the number of cells in the side length of a square sample centered around the current cell of interest. Parameter S for the wrapper mstp() included a range of 5 values [3,11,17,33,51] (Cells have a 30 meter length and width).

Metric Scale:

Positive values describe convex profile curvature which lead to accelerating water flow. Negative values describe concave profile curvature which leads to a decelerating water flow.

Sources:

Evans, I. S., 1972. General geomorphometry, derivatives of altitude, and descriptive statistics. In Chorley, R. J., Spatial Analysis in Geomorphology New York: Harper & Row pp.17 - 90.

Gessler, P.E., I.D. Moore, N.J. McKenzie, and P.J. Ryan. (1995). Soil-landscape modeling and spatial prediction of soil attributes. International Journal of GIS. 9(4):421-432.

Pike, R.J., I.S. Evans, T.Hengl (2009) Geomorphometry: A Brief Guide. Developments in Soil Science, Volume 33. Elsevier B.V. ISSN 0166-2481

GRASS GIS r.param.scale() function link

Wood, J. (1996): The Geomorphological characterisation of Digital Elevation Models. Diss., Department of Geography, University of Leicester, U.K online at: http://hdl.handle.net/2381/34503

Formula 8:

\[profc = -200 \cdot \text{resoln} \cdot \text{wsize} \cdot\frac{a \cdot d^2 + b \cdot e^2 + c \cdot d \cdot e}{(d^2 + e^2){{(1 + d^2 + e^2)}^{3/2}}}\]

\(a = \frac{\partial^2 z}{\partial x^2}\) - second-order partial derivative in the x direction

\(b = \frac{\partial^2 z}{\partial y^2}\) - second-order partial derivative in the y direction

\(c = \frac{\partial^2 z}{\partial x \partial y}\) - mixed second-order derivative

\(d = \frac{\partial z}{\partial x}\) - first-order slope in x direction

\(e = \frac{\partial z}{\partial y}\) - first-order slope in y direction

\(resoln = \text{map resolution (in map units per pixel)}\)

\(wsize = \text{window size (neighborhood width)}\) - s

Surface Area Ratio (SAR)

Overview:

Surface area ratio is a terrain metric that quantifies how much the true surface area of a terrain deviates from the planar area of the corresponding raster cell. The function sar(), designed for this product, is a wrapper that applied the GRASS GIS’s r.slope.aspect() and r.mapcalc() functions to calculate the surface area ratio. The Grass GIS functions applied formula 9, shown below, to modify each cell in the DEM.

Metric Scale:

A surface area ratio greater than 1 indicates higher surface complexity. SAR level increases with surface roughness, and a value of 1 indicates a completely flat surface.

Sources:

Berry, J. K. 2002. Use surface area for realistic calculations. Geoworld 15(9): 2021.

Evans, I. S., 1972. General geomorphometry, derivatives of altitude, and descriptive statistics. In Chorley, R. J., Spatial Analysis in Geomorphology New York: Harper & Row pp.17 - 90.

Pike, R.J., I.S. Evans, T.Hengl (2009) Geomorphometry: A Brief Guide. Developments in Soil Science, Volume 33. Elsevier B.V. ISSN 0166-2481

GRASS GIS r.slope.aspect() function link

GRASS GIS r.mapcalc() function link

Formula 9:

Surface Area is the 3D surface area derived from the slope of the terrain in a raster cell.

Planar Area is the 2D area of the raster cell.

\[SAR = \frac{A_{\text{surface}}}{A_{\text{planar}}}\]

If the slope \(\theta\) is steep, the surface area increases, and SAR>1. A higher SAR indicates more surface roughness or terrain complexity.

Surface Cosine of Slope Angle (SCOSA)

Overview:

SCOSA quantifies how much the slope of a surface reduces the effective surface area as projected onto the horizontal surface. It is the cosine of the slope angle or the inverse of Surface Area Ratio (SAR). The function scosa(), designed for this product, is a wrapper that applied the GRASS GIS’s r.slope.aspect() and r.mapcalc() functions to calculate the Surface Cosine of Slope Angle. The Grass GIS functions applied formula 10, shown below, to modify each cell in the DEM.

Metric Scale:

\(\theta\) = 0 degrees \(cos(0)\) = 1 : Flat Area

\(\theta\) > 0 degrees \(cos(\theta) < 1\): Steeper Areas

As \(\theta\) increases. SCOSA decreases, and the amount of surface area that can be projected onto a horizontal surface decreases as well.

Sources:

Evans, I. S., 1972. General geomorphometry, derivatives of altitude, and descriptive statistics. In Chorley, R. J., Spatial Analysis in Geomorphology New York: Harper & Row pp.17 - 90.

Pike, R.J., S.E. Wilson (1971). Elevation relief ratio, hypsometric integral, and geomorphic area altitude analysis. Bull. Geol. Soc. Am. 82, 1079-1084

GRASS GIS r.slope.aspect() function link

GRASS GIS r.mapcalc() function link

Formula 10:

\[\theta = artan(\sqrt{d^2 + e^2})\] \[SCOSA = cos(\theta) = \frac{1}{\sqrt{1+d^2 + e^2}}\] \[SCOSA = cos(\text{slope in radians})\]

\(d = \frac{\partial z}{\partial x}\) - Slope in the x direction

\(e = \frac{\partial z}{\partial y}\) - Slope in the y direction

Slope Position (Spost, a multi-scale metric)

Overview:

Quantifies the vertical position of a pixel relative to its surrounding terrain. The function spost(), designed for this conversion, is a wrapper that applied the GRASS GIS’s r.neighbors() and r.mapcalc() functions. These Grass GIS functions in combination applied formula 11, shown below, to modify each cell in the DEM based on neighboring cells within a window. The window of adjacent cells selected was based on a parameter s. Parameter s is a whole odd number which displayed the number of cells in the side length of a square sample centered around the current cell of interest. Parameter S for the wrapper spost() included a range of 5 values [3,11,17,33,51] (Cells have a 30 meter length and width).

Metric Scale:

Spost > 0: The focal cell is higher then its neighbors, which indicates it exists on a landform.

Spost < 0: The focal cell is lower then its neighbors, which indicates it exits in a depression.

Spost ~= 0: The focal cell exits mid-slope.

Sources:

Evans, I. S., 1972. General geomorphometry, derivatives of altitude, and descriptive statistics. In Chorley, R. J., Spatial Analysis in Geomorphology New York: Harper & Row pp.17 - 90.

Gessler, P.E., I.D. Moore, N.J. McKenzie, and P.J. Ryan. (1995). Soil-landscape modeling and spatial prediction of soil attributes. International Journal of GIS. 9(4):421-432.

Cushman, S.A, K. McGarial, K. Gutzwiller and J.S. Evans. (2010). The gradient paradigm: A conceptual and analytical framework for landscape ecology.

GRASS GIS r.neighbors() function link

GRASS GIS r.mapcalc() function linK

Formula 11:

\[spost = z_c - \bar{z_n}\] \(z_c\): The elevation of the focal cell

\(\bar{z_n}\): The mean elevation of the neighboring cells in the window of size s

Surface Relief Ratio (SSR, a multi-scale metric)

Overview:

A measure of relative elevation within a landscape unit, quantifying how close the highest elevation point is to the total relief of the area. The function srr(), designed for this conversion, is a wrapper that applied the GRASS GIS’s r.neighbors() and r.mapcalc() functions. These Grass GIS functions in combination applied formula 12, shown below, to modify each cell in the DEM based on neighboring cells within a window. The window of adjacent cells selected was based on a parameter s. Parameter s is a whole odd number which displayed the number of cells in the side length of a square sample centered around the current cell of interest. Parameter S for the wrapper srr() included a range of 5 values [3,11,17,33,51] (Cells have a 30 meter length and width).

Metric Scale:

SRR ~= 0: A flat area with. Low relief relative to the focal elevation.

SRR ~= 1: A complex area with high relief relative to the elevation.

Sources:

Pike, R.J., S.E. Wilson (1971). Elevation relief ratio, hypsometric integral, and geomorphic area altitude analysis. Bull. Geol. Soc. Am. 82, 1079-1084

Evans, I. S., 1972. General geomorphometry, derivatives of altitude, and descriptive statistics. In Chorley, R. J., Spatial Analysis in Geomorphology New York: Harper & Row pp.17 - 90.

Gessler, P.E., I.D. Moore, N.J. McKenzie, and P.J. Ryan. (1995). Soil-landscape modeling and spatial prediction of soil attributes. International Journal of GIS. 9(4):421-432.

GRASS GIS r.neighbors() function link

GRASS GIS r.mapcalc() function link

Formula 12:

\[SRR = \frac{(z_{max} - \bar{z})}{z_{max} - z_{min}}\] \(\bar{z}\): The elevation mean of the neighboring cells in the window.

\(z_{max}\): The maximum elevation of the neighboring cells.

\(z_{min}\): The minimum elevation of the neighboring cells.

Sine of Slope Aspect (ssina)

Overview:

The north-south orientation of terrain or the sine of the aspect. The function ssina(), designed for this conversion, is a wrapper that applied the GRASS GIS’s r.slope.aspect() and r.mapcalc() functions. These Grass GIS functions in combination applied formula 13, shown below, to modify each cell in the DEM.

Metric Scale:

ssina = 1: South facing slopes

ssina = -1: North facing slopes

ssina = 0: East or West facing slopes

Sources:

McCune, Bruce and Dylan Keon, 2002. Equations for potential annual direct incident radiation and heat load index. Journal of Vegetation Science. 13:603-606.

Gessler, P.E., I.D. Moore, N.J. McKenzie, and P.J. Ryan. (1995). Soil-landscape modeling and spatial prediction of soil attributes. International Journal of GIS.

GRASS GIS r.slope.aspect() function link

GRASS GIS r.mapcalc() function link

Formula 13:

\[ssina = sin(\theta)\]

\(\theta\): The aspect angle

Topographic Position Index (TPI, a multi-scale metric)

Overview:

A metric to quantify how a location’s elevation compares to the average elevation in its local window. The function tpi(), designed for this conversion, is a wrapper that applied the GRASS GIS’s r.neighbors() and r.mapcalc() functions. These Grass GIS functions in combination applied formula 14, shown below, to modify each cell in the DEM based on neighboring cells within a window. The window of adjacent cells selected was based on a parameter s. Parameter s is a whole odd number which displayed the number of cells in the side length of a square sample centered around the current cell of interest. Parameter S for the wrapper tpi() included a range of 5 values [3,11,17,33,51] (Cells have a 30 meter length and width).

Metric Scale:

TPI > 0: The focal cell is higher than its surroundings.

TPI < 0: The focal cell is lower than its surroundings.

TPI = 0: The focal cell lies mid-slope.

Sources:

Gessler, P.E., I.D. Moore, N.J. McKenzie, and P.J. Ryan. (1995). Soil-landscape modeling and spatial prediction of soil attributes. International Journal of GIS. 9(4):421-432.

Evans, I. S., 1972. General geomorphometry, derivatives of altitude, and descriptive statistics. In Chorley, R. J., Spatial Analysis in Geomorphology New York: Harper & Row pp.17 - 90.

Cushman, S.A, K. McGarial, K. Gutzwiller and J.S. Evans. (2010). The gradient paradigm: A conceptual and analytical framework for landscape ecology. Chapter 5 in S.A. Cushman and F. Huettman (eds). Spatial Complexity, Informatics and Wildlife Conservation, Springer, New York.

Evans, J.S. and S.A. Cushman (2009) Gradient Modeling of Conifer Species Using Random Forest. Landscape Ecology 5:673-683.

GRASS GIS r.neighbors() function link

GRASS GIS r.mapcalc() function link

Formula 14:

\[ TPI = z - \bar{z}\] \(z\): The elevation at the focal cell

\(\bar{z}\): Average elevation within the window

Transformed Aspect (trasp, a multi-scale metric)

Overview:

A linear transformation of aspect that adjusts for the southwest-facing slopes being drier and northeast-facing slopes being wetter. The function trasp(), designed for this conversion, is a wrapper that applied the GRASS GIS’s r.slope.aspect() and r.mapcalc() functions. These Grass GIS functions in combination applied formula 15, shown below, to modify each cell in the DEM based on neighboring cells within a window. The window of adjacent cells selected was based on a parameter s. Parameter s is a whole odd number which displayed the number of cells in the side length of a square sample centered around the current cell of interest. Parameter S for the wrapper trasp() included a range of 5 values [3,11,17,33,51] (Cells have a 30 meter length and width).

Metric Scale:

trasp = 0: Southwest facing aspect

trasp = 1: Northeast facing aspect

trasp = 0.5: Northwest or Southeast facing aspect

Sources:

McCune, Bruce and Dylan Keon, 2002. Equations for potential annual direct incident radiation and heat load index. Journal of Vegetation Science. 13:603-606.

Evans, J.S. and S.A. Cushman (2009) Gradient Modeling of Conifer Species Using Random Forest. Landscape Ecology 5:673-683.

GRASS GIS r.slope.aspect() function link

GRASS GIS r.mapcalc() function link

Formula 15:

\[TRASP = \frac{cos(\frac{\pi}{180}(\theta - 30))}{2}\] \(\theta\): Aspect in degrees

Terrain Ruggedness Index (tri, a multi-scale metric)

Overview:

Quantifies the the topographic heterogeneity of a landscape by measuring the variation in elevation between the focal cell and its surrounding neighbors. The function tri(), designed for this conversion, is a wrapper that applied the GRASS GIS’s r.neighbors(). This GRASS GIS function applied formula 16, shown below, to modify each cell in the DEM based on neighboring cells within a window. The window of adjacent cells selected was based on a parameter s. Parameter s is a whole odd number which displayed the number of cells in the side length of a square sample centered around the current cell of interest. Parameter S for the wrapper tri() included a range of 5 values [3,11,17,33,51] (Cells have a 30 meter length and width).

Metric Scale:

TRI Values

Level = 0 to 18.519 meters

Nearly Level = 18.519 to 41.469 meters

Nearly level = 18.520 to 41.469 meters

Slightly rugged = 41.470 to 71.699 meters

Moderately rugged = 71.700 to 103.864 meters

Highly rugged = 103.865 to 134.430 meters

Extremely rugged = 134.431 = 242.804 meters.

Sources:

Evans J.S., M.A. Murphy, Z.A. Holden, S.A. Cushman (2011). Modeling species distribution and change using Random Forests CH.8 in Predictive Modeling in Landscape Ecology

GRASS GIS r.neighbors() function link

Metric Scale context link

Formula 16:

\[TRI = \sqrt{\sum{(x_i - E)^2}}\]

\(x_i\): All cells within the window s by s

\(i\): The number of cells within the sample window

\(E\): The focal cell within the window