# Curvature (3D Analyst)

## Summary

Calculates the curvature of a raster surface, optionally including profile and plan curvature.

## Usage

• The primary output is the curvature of the surface on a cell-by-cell basis, as fitted through that cell and its eight surrounding neighbors. Curvature is the second derivative of the surface, or the slope-of-the-slope. Two optional output curvature types are possible: the profile curvature is in the direction of the maximum slope, and the plan curvature is perpendicular to the direction of the maximum slope.

• A positive curvature indicates the surface is upwardly convex at that cell. A negative curvature indicates the surface is upwardly concave at that cell. A value of 0 indicates the surface is flat.

• In the profile output, a negative value indicates the surface is upwardly convex at that cell. A positive profile indicates the surface is upwardly concave at that cell. A value of 0 indicates the surface is flat.

• In the plan output, a positive value indicates the surface is upwardly convex at that cell. A negative plan indicates the surface is upwardly concave at that cell. A value of 0 indicates the surface is flat.

• Units of the curvature output raster, as well as the units for the optional output profile curve raster and output plan curve raster, are one hundredth (1/100) of a z-unit. The reasonably expected values of all three output rasters for a hilly area (moderate relief) can vary from -0.5 to 0.5; while for steep, rugged mountains (extreme relief), the values can vary between -4 and 4. Note that it is possible to exceed this range for certain raster surfaces.

## Syntax

Curvature_3d (in_raster, out_curvature_raster, {z_factor}, {out_profile_curve_raster}, {out_plan_curve_raster})
 Parameter Explanation Data Type in_raster The input surface raster. Raster Layer out_curvature_raster The output curvature raster. Raster Dataset z_factor(Optional) Number of ground x,y units in one surface z unit.The z-factor adjusts the units of measure for the z units when they are different from the x,y units of the input surface. The z-values of the input surface are multiplied by the z-factor when calculating the final output surface.If the x,y units and z units are in the same units of measure, the z-factor is 1. This is the default.If the x,y units and z units are in different units of measure, the z-factor must be set to the appropriate factor, or the results will be incorrect. For example, if your z units are feet and your x,y units are meters, you would use a z-factor of 0.3048 to convert your z units from feet to meters (1 foot = 0.3048 meter). Double out_profile_curve_raster(Optional) Output profile curve raster dataset. This is the curvature of the surface in the direction of slope. Raster Dataset out_plan_curve_raster(Optional) Output plan curve raster dataset. This is the curvature of the surface perpendicular to the slope direction. Raster Dataset

## Code Sample

Curvature example 1 (Python window)

This example creates a curvature raster from an input surface raster and also applies a z-factor.

```import arcpy
from arcpy import env
env.workspace = "C:/data"
arcpy.Curvature_3d("elevation", "c:/output/outcurv01", 1.094)```
Curvature example 2 (stand-alone script)

This example creates a curvature raster from an input surface raster and also applies a z-factor.

```# Name: Curvature_3d_Ex_02.py
# Description: Calculates the curvature of a raster surface,
#              optionally including profile and plan curvature.
# Requirements: 3D Analyst Extension

# Import system modules
import arcpy
from arcpy import env

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

# Set local variables
inRaster = "elevation"
outRaster = "C:/output/outcurv02"
zFactor = 1.094

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

# Execute Curvature
arcpy.Curvature_3d(inRaster, outRaster, 1.094)
```

## Licensing Information

ArcView: Requires 3D Analyst or Spatial Analyst
ArcEditor: Requires 3D Analyst or Spatial Analyst
ArcInfo: Requires 3D Analyst or Spatial Analyst

6/10/2013