# Surface Parameters (3D Analyst)

## Summary

Determines parameters of a raster surface such as aspect, slope and curvatures.

## Usage

• The output parameters are calculated on a cell-by-cell basis by fitting a local surface around a target cell. The available surface parameter options for the Parameter type parameter (parameter_type in Python) are Slope, Aspect, Mean curvature, Tangential (normal contour) curvature, Profile (normal slope line) curvature, Plan (projected contour) curvature, Contour geodesic torsion, Gaussian curvature, and Casorati curvature.

• All output parameters are calculated using geodesic coordinates and equations.

• When the Slope (SLOPE in Python) option is specified for Parameter type, the output represents the rate of change of elevation for each digital elevation model (DEM) cell. It is the first derivative of a DEM. The range of values from the slope output depends on the type of measurement units.

• When the Aspect (ASPECT in Python) option is specified for Parameter type, the output identifies the compass direction that the downhill slope faces for each location. It is expressed in positive degrees from 0 to 360, measured clockwise from north.

• Curvature is used to describe the shape of a surface. When applied to earth science, it is used to help understand the impacts of gravity, erosion, and other factors upon the surface and is used in conjunction with other surface parameters to identify and classify landforms.

• Mean curvature (MEAN_CURVATURE in Python) —The overall curvature of the surface. It is computed as the average of the minimum and maximum curvature. When this is specified for Parameter type, the output is equivalent to the mean of profile (normal slope line) and tangential (normal contour) curvatures. Its sign, positive or negative, is not a definitive indicator except at extreme values. High positive values indicate areas of maximum denudation, and high negative values indicate areas of maximum accumulation (Minár et al., 2020).
• Profile (normal slope line) curvature (PROFILE_CURVATURE in Python)—The geometric normal curvature along the slope line. Positive values indicate areas of acceleration of surface flow and erosion. Negative profile curvature indicates areas of slowing surface flow and deposition. A positive profile (normal slope line) curvature indicates that the surface is convex at that cell in the direction of the slope. A negative curvature indicates that the surface is concave at that cell in that same direction. A value of 0 indicates that the surface is flat.
• Tangential (normal contour) curvature (TANGENTIAL_CURVATURE in Python)—The geometric normal curvature perpendicular to the slope line, tangent to the contour line. Positive values indicate areas of diverging surface flow. Negative tangential curvatures indicates areas of converging surface flow. A positive tangential (normal contour) curvature indicates that the surface is convex at that cell perpendicular to the direction of the slope. A negative curvature indicates that the surface is concave at that cell in the direction perpendicular to the slope. A value of 0 indicates that the surface is flat.
• Plan (projected contour) curvature (CONTOUR_CURVATURE in Python)—The curvature along contour lines.
• Contour geodesic torsion (CONTOUR_GEODESIC_TORSION in Python)—The rate of change in slope angle along contour lines.
• Gaussian curvature (GAUSSIAN_CURVATURE in Python)—The general curvature of a surface. It is computed as the product of the minimum and maximum curvature and can take negative and positive values. Positive values indicate that the surface is convex at that cell, while negative values indicate that it is concave. A value of 0 indicates that the surface is flat.
• Casorati curvature (CASORATI_CURVATURE in Python)—The general curvature of the surface. It can be zero or always positive. High positive values indicate areas of sharp bending in multiple directions.

The units of all curvature type outputs will be the reciprocal (the square of the reciprocal for Gaussian curvature) of the x,y-units of the Output Coordinate System.

• The Quadratic (QUADRATIC in Python) option of the Local surface type (local_surface_type in Python) parameter does not fit the neighborhood cells exactly. This is the default and recommended option for most data and applications.

• The quadratic surface minimizes the effect of noisy surface data such as a high resolution lidar surface, which is especially important when computing curvature.
• Use the quadratic surface when specifying a neighborhood size that is larger than the cell size and when using the adaptive neighborhood option.
• The Biquadratic (BIQUADRATIC in Python) option of the Local surface type parameter fits the data from the neighborhood cells exactly.

• This option is suitable for a highly accurate input surface.
• If the neighborhood distance is larger than the input raster cell size, the accuracy advantages of the biquadratic surface type will be lost. Leave the neighborhood distance as the default (equal to the cell size).
• The Neighborhood distance (neighborhood_distance in Python) parameter determines the neighborhood size and calculates the surface parameter over this distance from the target cell center.

• It cannot be less than the input raster cell size.
• A smaller neighborhood distance captures more local variability in the landscape, characteristics of smaller landscape features. With high resolution elevation data, larger distances may be more appropriate.
• If the Use adaptive neighborhood parameter is checked (use_adaptive_neighborhood is set to ADAPTIVE_NEIGHBORHOOD in Python), the neighborhood distance will change with variability in the terrain. The neighborhood distance will shrink if there is too much variability in the calculation window.

• Specifying the surface Z unit (z-unit in Python) parameter value is important to ensure the proper computation of the slope output.

If a z-unit is available in the vertical coordinate system of the input raster, it will be applied automatically. It is recommended that you define a z-unit for the input raster if it is missing. You can use the Define Projection tool to specify a z-unit. If it is undefined, meter will be used by default.

• The range of values in the slope output depends on the Output slope measurement (output_slope_measurement in Python) option units:

• Degrees (DEGREE in Python)—The range of slope values is 0 to 90.
• Percent rise (PERCENT_RISE in Python)—The range is 0 to essentially infinity. A flat surface is 0 percent, a 45 degree surface is 100 percent, and as the surface becomes more vertical, the percent rise becomes increasingly larger.
• If the Project geodesic azimuths parameter is checked (project_geodesic_azimuths is set to PROJECT_GEODESIC_AZIMUTHS in Python), the following are true:

• North is always represented by 360 degrees.
• Azimuths will be projected to correct the distortion caused by a nonconformal Output Coordinate System. These angles can be used to accurately locate points along the steepest downhill slope.

• If the Use equatorial aspect parameter is checked (project_geodesic_azimuths is set to USE_EQUATORIAL_ASPECT in Python), aspect will be measured from a point along the equator to correct for the skewing of direction that occurs when approaching the poles. This parameter ensures that the north-south and east-west axes are perpendicular to each other.

Check the Use equatorial aspect parameter if the terrain is near to the north or south pole.

• References:

• James D.E., M.D. Tomer, S.A. Porter. (2014). Trans-scalar landform segmentation from high-resolution digital elevation models. Poster presented at: ESRI Annual Users Conference; July 2014; San Diego, California.
• Minár, J., Evans, I. S., & Jenčo, M. (2020). A comprehensive system of definitions of land surface (topographic) curvatures, with implications for their application in geoscience modelling and prediction. Earth-Science Reviews, 103414. https://doi.org/10.1016/j.earscirev.2020.103414

## Parameters

 Label Explanation Data Type Input surface raster The input surface raster. Raster Layer Output raster The output raster.It will be floating-point type. Raster Dataset Parameter type(Optional) Specifies the output surface parameter type that will be computed.Slope—The rate of change in elevation will be computed. This is the default.Aspect—The downslope direction of the maximum rate of change for each cell will be computed.Mean curvature—The overall curvature of the surface will be measured. It is computed as the average of the minimum and maximum curvature. This curvature describes the intrinsic convexity or concavity of the surface, independent of direction or gravity influence.Tangential (normal contour) curvature—The geometric normal curvature perpendicular to the slope line, tangent to the contour line will be measured. This curvature is typically applied to characterize the convergence or divergence of flow across the surface.Profile (normal slope line) curvature—The geometric normal curvature along the slope line will be measured. This curvature is typically applied to characterize the acceleration and deceleration of flow down the surface.Plan (projected contour) curvature—The curvature along contour lines will be measured.Contour geodesic torsion—The rate of change in slope angle along contour lines will be measured.Gaussian curvature—The overall curvature of the surface will be measured. It is computed as the product of the minimum and maximum curvature.Casorati curvature—The general curvature of the surface will be measured. It can be zero or any other positive number. String Local surface type(Optional) Specifies the type of surface function that will be fitted around the target cell.Quadratic—A quadratic surface function will be fitted to the neighborhood cells. This is the default.Biquadratic—A biquadratic surface function will be fitted to the neighborhood cells. String Neighborhood distance(Optional) The output will be calculated over this distance from the target cell center. It determines the neighborhood size.The default value is the input raster cell size, resulting in a 3 by 3 neighborhood. Linear Unit Use adaptive neighborhood(Optional) Specifies whether neighborhood distance will vary with landscape changes (adaptive). The maximum distance is determined by the neighborhood distance. The minimum distance is the input raster cell size. Unchecked—A single (fixed) neighborhood distance will be used at all locations. This is the default. Checked—An adaptive neighborhood distance will be used at all locations. Boolean Z unit(Optional) The linear unit of vertical z-values.It is defined by a vertical coordinate system if it exists. If a vertical coordinate system does not exist, the z-unit should be defined from the unit list to ensure correct geodesic computation. The default is meter.Inch—The linear unit will be inches.Foot—The linear unit will be feet.Yard—The linear unit will be yards.Mile US—The linear unit will be miles.Nautical mile—The linear unit will be nautical miles.Millimeter—The linear unit will be millimeters.Centimeter—The linear unit will be centimeters.Meter—The linear unit will be meters.Kilometer—The linear unit will be kilometers.Decimeter—The linear unit will be decimeters. String Output slope measurement(Optional) The measurement units (degrees or percentages) that will be used for the output slope raster. This parameter is only active when Parameter type is Slope.Degree—The inclination of slope will be calculated in degrees.Percent rise—The inclination of slope will be calculated as percent rise, also referred to as the percent slope. String Project geodesic azimuths(Optional) Specifies whether geodesic azimuths will be projected to correct the angle distortion caused by the output spatial reference. Unchecked—Geodesic azimuths will not be projected. This is the default.Checked—Geodesic azimuths will be projected. Boolean Use equatorial aspect(Optional) Specifies whether aspect will be measured from a point on the equator or from the north pole. Unchecked—Aspect will be measured from the north pole. This is the default.Checked—Aspect will be measured from a point on the equator. Boolean

`arcpy.ddd.SurfaceParameters(in_raster, out_raster, {parameter_type}, {local_surface_type}, {neighborhood_distance}, {use_adaptive_neighborhood}, {z_unit}, {output_slope_measurement}, {project_geodesic_azimuths}, {use_equatorial_aspect})`
 Name Explanation Data Type in_raster The input surface raster. Raster Layer out_raster The output raster.It will be floating-point type. Raster Dataset parameter_type(Optional) Specifies the output surface parameter type that will be computed.SLOPE—The rate of change in elevation will be computed. This is the default.ASPECT—The downslope direction of the maximum rate of change for each cell will be computed.MEAN_CURVATURE—The overall curvature of the surface will be measured. It is computed as the average of the minimum and maximum curvature. This curvature describes the intrinsic convexity or concavity of the surface, independent of direction or gravity influence.TANGENTIAL_CURVATURE—The geometric normal curvature perpendicular to the slope line, tangent to the contour line will be measured. This curvature is typically applied to characterize the convergence or divergence of flow across the surface.PROFILE_CURVATURE—The geometric normal curvature along the slope line will be measured. This curvature is typically applied to characterize the acceleration and deceleration of flow down the surface.CONTOUR_CURVATURE—The curvature along contour lines will be measured.CONTOUR_GEODESIC_TORSION—The rate of change in slope angle along contour lines will be measured.GAUSSIAN_CURVATURE—The overall curvature of the surface will be measured. It is computed as the product of the minimum and maximum curvature.CASORATI_CURVATURE—The general curvature of the surface will be measured. It can be zero or any other positive number. String local_surface_type(Optional) Specifies the type of surface function that will be fitted around the target cell.QUADRATIC—A quadratic surface function will be fitted to the neighborhood cells. This is the default.BIQUADRATIC—A biquadratic surface function will be fitted to the neighborhood cells. String neighborhood_distance(Optional) The output will be calculated over this distance from the target cell center. It determines the neighborhood size.The default value is the input raster cell size, resulting in a 3 by 3 neighborhood. Linear Unit use_adaptive_neighborhood(Optional) Specifies whether neighborhood distance will vary with landscape changes (adaptive). The maximum distance is determined by the neighborhood distance. The minimum distance is the input raster cell size. FIXED_NEIGHBORHOOD—A single (fixed) neighborhood distance will be used at all locations. This is the default.ADAPTIVE_NEIGHBORHOOD—An adaptive neighborhood distance will be used at all locations. Boolean z_unit(Optional) The linear unit of vertical z-values.It is defined by a vertical coordinate system if it exists. If a vertical coordinate system does not exist, the z-unit should be defined from the unit list to ensure correct geodesic computation. The default is meter.INCH—The linear unit will be inches.FOOT—The linear unit will be feet.YARD—The linear unit will be yards.MILE_US—The linear unit will be miles.NAUTICAL_MILE—The linear unit will be nautical miles.MILLIMETER—The linear unit will be millimeters.CENTIMETER—The linear unit will be centimeters.METER—The linear unit will be meters.KILOMETER—The linear unit will be kilometers.DECIMETER—The linear unit will be decimeters. String output_slope_measurement(Optional) The measurement units (degrees or percentages) that will be used for the output slope raster. This parameter is only enabled when parameter_type = "SLOPE". DEGREE—The inclination of slope will be calculated in degrees.PERCENT_RISE—The inclination of slope will be calculated as percent rise, also referred to as the percent slope. String project_geodesic_azimuths(Optional) Specifies whether geodesic azimuths will be projected to correct the angle distortion caused by the output spatial reference. GEODESIC_AZIMUTHS—Geodesic azimuths will not be projected. This is the default.PROJECT_GEODESIC_AZIMUTHS—Geodesic azimuths will be projected. Boolean use_equatorial_aspect(Optional) Specifies whether aspect will be measured from a point on the equator or from the north pole. NORTH_POLE_ASPECT—Aspect will be measured from the north pole. This is the default.EQUATORIAL_ASPECT—Aspect will be measured from a point on the equator. Boolean

### Code sample

SurfaceParameters example 1 (Python window)

The following sample demonstrates the use of this tool in the Python window.

This example generates a slope raster with output values in percentages using an adaptive neighborhood method. The maximum neighborhood distance is 5 meters.

``````from arcpy.ddd import *
SurfaceParameters("elevation_1m.tif", "C:/data/output/outsurfaceparameters01.tif",
"", "", "5 METERS", "ADAPTIVE_NEIGHBORHOOD", "", "PERCENT_RISE")``````
SurfaceParameters example 2 (stand-alone script)

The following sample demonstrates the use of this tool in a stand-alone Python script.

This example generates a profile (normal slope line) curvature raster using an adaptive neighborhood method. The maximum neighborhood distance is 10 meters.

``````# Name: SurfaceParameters_Ex_02.py
# Description: Derive profile (normal slope line) curvature for a 1m
# resolution elevation raster over an adaptive neighborhood distance of maximum 10m.
# Requirements: 3D Analyst Extension

# Import system modules
import arcpy
from arcpy.ddd import *

# Set environment settings
arcpy.env.workspace = "C:/data"

# Check out the ArcGIS 3D Analyst extension license
arcpy.CheckOutExtension("3D")

# Set local variables
inRaster = "elevation_1m.tif"
outRaster = "C:/data/output/outsurfaceparameters02.tif"
inParameterType = "PROFILE_CURVATURE"
inNeighborhoodDistance = "10 METERS"

# Execute the tool
SurfaceParameters(inRaster, outRaster, inParameterType, "",
SurfaceParameters example 3 (stand-alone script)

The following sample demonstrates the use of this tool in a stand-alone Python script.

This example generates an aspect raster using a neighborhood distance of 5 meters. Correct for direction distortions from using a nonconformal projection.

``````# Name: SurfaceParameters_Ex_03.py
# Description: Derive aspect for an elevation surface over a distance of 5m, correct
# for direction distortion from non-conformal projection system.
# Requirements: 3D Analyst Extension

# Import system modules
import arcpy
from arcpy.ddd import *

# Set environment settings
arcpy.env.workspace = "C:/data"

# Check out the ArcGIS Spatial Analyst extension license
arcpy.CheckOutExtension("3D")

# Set local variables
inRaster = "elevation_1m.tif"
outRaster = "C:/data/output/outsurfaceparameters03.tif"
inParameterType = "ASPECT"
inNeighborhoodDistance = "5 METERS"
inProjectGeodesicAzimuths = "PROJECT_GEODESIC_AZIMUTHS"

# Execute the tool
SurfaceParameters(inRaster, outRaster, inParameterType, "", inNeighborhoodDistance,
"", "", "", inProjectGeodesicAzimuths)``````

## Licensing information

• Basic: Requires 3D Analyst or Spatial Analyst
• Standard: Requires 3D Analyst or Spatial Analyst
• Advanced: Requires 3D Analyst or Spatial Analyst