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 on 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 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 environment.
The Quadratic option of the Local surface type parameter (local_surface_type = "QUADRATIC" in Python) 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 option of the Local surface type parameter (local_surface_type = "BIQUADRATIC" in Python) 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, such as 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 = "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 ensures 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 Slope measurement (output_slope_measurement in Python) parameter measurement units:
- Degree (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 = "PROJECT_GEODESIC_AZIMUTHS" in Python), the following are true:
- North is represented by 360 degrees.
- Azimuths will be projected to correct the distortion caused by a nonconformal Output Coordinate System environment value. These angles can be used to accurately locate points along the steepest downhill slope.
Check the Project geodesic azimuths parameter if you're using the Surface Parameters output as a back direction input for the Input back direction or flow direction raster (in_back_direction_raster in Python) parameter for a tool in the Distance toolset.
If the Use equatorial aspect parameter is checked (project_geodesic_azimuths = "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.
Use the Input analysis mask parameter (in_analysis_mask in Python) to limit the analysis to specific locations of interest within the input surface raster. The locations can be defined by raster or feature data. The Input analysis mask parameter will take priority over the Mask environment setting.
When the Input surface raster (in_raster in Python) value and the Input analysis mask raster data (in_analysis_mask in Python) are of the same cell size and the cells are aligned, they will be used directly in the tool. They will not be resampled internally during tool operation.
If the cell size is different, the output cell size will be the maximum of the inputs, and the Input surface raster value will be used internally as the snap raster. If the cell size is the same but the cells are not aligned, the Input surface raster value will be used internally as the snap raster. Either of these cases will trigger an internal resampling before the extraction operation is performed.
For additional information, see the Cell Size and Snap Raster environment topics.
See Analysis environments and Spatial Analyst for additional details on the geoprocessing environments that apply to this tool.
- James, D. E., Tomer, M. D., and Porter, S. A. 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., and Jenčo, M. A comprehensive system of definitions of land surface (topographic) curvatures, with implications for their application in geoscience modelling and prediction. Earth-Science Reviews, 103414, 2020. https://doi.org/10.1016/j.earscirev.2020.103414