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It turns out that version 2.0-0 is only comptable with ArcGIS 10.2 and later. For those running < 10.2 here is the link to version 1.01 of the toolbox.


Geomorphometry and Gradient Metrics Toolbox download version 1.01


A new "major release" 2.0-0 version of the ArcGIS Geomorphometry and Gradient Metrics Toolbox is avaliable. We have addressed a few bugs and added a few new models.


The Geomorphometry and Gradient Metrics Toolbox is an ArcGIS toolbox containing various gradient and geomorphometric metrics used for surface analysis. These metrics have been utilized in a variety of applications including landscape ecology, species distribution, predictive vegetation, and remote sensing studies. Current toolbox version 2.0, compatible with ArcGIS version 10 (tested under SP2&3 and Python 2.5 and 2.6). To install just unzip the download to a permanent location on your harddrive. In ArcGIS (ArcMap or ArcCatalog) open the ArcToolbox window. Right click the ArcToolbox entry at the top of the tree, select “Add Toolbox” navigate to where you unzipped the toolbox and select “Geomorphometry and Gradient Metrics (version a1.0).tbx”. To keep the toolbox across ArcGIS sessions right click the ArcToolbox entry at the top of the tree and select “Save Settings” > “To Default”.


Geomorphometry and Gradient Metrics Toolbox download version 2.0


I am also now distributing the toolbox on ESRI's new BETA ArcScripts page:


ESRI ArcScripts BETA - Geomorphometry and Gradient Metrics Toolbox download version 2.0


Suggested citation:


Evans JS, Oakleaf J, Cushman SA, Theobald D (2014) An ArcGIS Toolbox for Surface Gradient and Geomorphometric Modeling, version 2.0-0.

Available: Accessed: 2015 Dec 2nd.


Here is a paper describing the gradient concept and the expansion of traditional patch based landscape metrics.


Cushman, S.A., Gutzweiler, K., Evans, J.S., McGarigal, K. (2010).  The Gradient Paradigm: A conceptual and analytical framework for landscape ecology [chapter 5] In: Cushman, S.A.; Huettmann, F., eds. Spatial complexity, informatics, and wildlife conservation. New York: Springer. p. 83-108.



Covariance - (float) Calculates covariance between two [x,y] rasters.

Distributional Moments - (float) Calculates statistical moments of a distribution within a specified window with options for: mean, median, mad, variance, standard deviation, skewness, kurtosis, coefficient of variation. Future release(s) will also have skewness and kurtosis.

Gaussian raster - (float) Creates a grid of random Gaussian distributed values where mean and standard deviation can be defined (default mean is 0 and standard deviation is 1).

Invert raster - (float) inverts (flips) the values of a float raster.

Moran’s-I (Not yet implemented) - (float) Calculates the Moran’s-I autocorrelation coefficient.

Random raster (Not yet implemented) - (float) Creates grid of random Gaussian distributed values given defined min-max values.

Slope Impedance – (float) A sigmoidal function for an impedance slope function.

Transformations – (float) Applies statistical transformations. Includes; “standardize” - standardizes values to a mean of 0 and standard deviation of 1; “stretch” – stretches data to specified range; “normalize" - normalizes to a scale 0-1 while retaining

distribution shape: Natural logarithmic; and Square-root.


Dissection - (float) Dissection describes dissection in a continuous raster surface within rectangular or circular window. Martonne’s modified dissection is calculated as:
d=( z - z(min)) / (z(max) - z(min) )


    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.

Roughness - (float) represents the roughness in a continuous raster within a specified window.

    Riley, S. J., S. D. DeGloria and R. Elliot (1999). A terrain ruggedness index that quantifies topographic heterogeneity.

        Intermountain Journal of Sciences, 5(1-4)
    Blaszczynski, J.S., (1997) Landform characterization with Geographic Information Systems. Photogrammetric Engineering and

        Remote Sensing, 63(2):183-191.

Surface Relief Ratio- (float) describes rugosity in an continuous raster surface within a specified window. The implementation of SRR can be shown as: srr=( z(mean) - z(min)) / (z(max) - z(min) )

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

        Am. 82, 1079-1084

Curvature - (float) Surface curvature (concavity/convexity) index (Bolstad’s variant).

    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.
    McNab, H.W. (1989) Terrain shape index: quantifying effect of minor landforms on tree height. Forest Science. 35(1): 91-104.
    McNab, H.W. (1993). A topographic index to quantify the effect of mesoscale landform on site productivity. Canadian Journal of

        Forest Research. 23: 1100-1107.

Slope Position - (float) calculates scalable slope position by subtracting a focalmean raster from the original elevation raster.
Surface/Area Ratio - (float) The Berry (2002) method for surface/area ratio.


    Berry, J. K. 2002. Use surface area for realistic calculations. Geoworld 15(9): 20–1.


Classify Aspect - (integer) Classifies aspect into discrete classes.

Compound Topographic Index (CTI) - (float) is a steady state wetness index. The CTI is a function of both the slope and the upstream contributing area per unit width orthigonal to the flow direction. The implementation of CTI can be shown as: CTI=ln (As / (tan (beta)) where; As=Area Value calculated as (flow accumulation + 1 ) * (pixel area in m2) and beta is the slope expressed in radians.

    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.
    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.

Heat load index - (float) A southwest facing slope should have warmer temperatures than a southeast facing slope, even though the amount of solar radiation they receive is equivalent. The McCune and Keon (2002) method accounts for this by "folding" the aspect so that the highest values are southwest and the lowest values are northeast. Additionally, this method account for steepness of slope, which is not addressed in most other aspect rescaling equations.

    McCune, Bruce and Dylan Keon, 2002. Equations for potential annual direct incident radiation and heat load index. Journal of

        Vegetation Science. 13:603-606.

Linear Aspect - (float) - Transforms circular aspect to a linear variable.

Mean Slope - (float) Mean of slope within a defined window.

Slope 2nd Derivative - (float) Calculates 2nd derivate of slope.

Slope/Aspect Transformations - (float). Options are Stage’s (1976) COS, SIN; or Roberts & Cooper (1989) TRASP (topographic radiation aspect index).

COS AND SIN - An a priori assumption of a maximum in the NW quadrant (45 azimuth) and a minimum in the SW quadrant can be replaced by an empirically determined location of the optimum (Stage, 1976). For slopes from 0% - 100%, the functions are linearized and bounded from -1 to 1. Greater than 100% slopes are treated out of the -1 to 1 range and the model sets all values greater than 100% to 101% and flat areas (-1) to nodata.

TRASP - Circular aspect is transformed to assign a value of zero to land oriented in a north- northeast direction, (typically the coolest and wettest orientation), and a value of one on the hotter, dryer south-southwesterly slopes. The result is a continuous variable between 0 - 1 (Roberts and Cooper 1989).

    Stage, A. R. 1976. An Expression of the Effects of Aspect, Slope, and Habitat Type on Tree Growth. Forest Science 22(3):

    Roberts. D. W., and Cooper, S. V., 1989. Concepts and techniques of vegetation mapping. In Land Classifications Based on

        Vegetation: Applications for Resource Management. USDA Forest Service GTR INT-257, Ogden, UT, pp 90-96


Angle conversion - (float) converts between degrees and radians.

Class Percent - (float) Calculates the percent of a class in an integer raster within a specified window.

Missing Data Fill - Fills in NoData gaps using a specified FocalMedian, FocalMean (for float data) or FocalMajority (for integer data) window.

Sieve - (integer) Smoothes discrete data using a sieve approach. User defines minimal number of cells to be retained. Much more controllable and stable then FocalMajority. Easy way to establish a minimal mapping unit.

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