1. Focal and Zonal Functions RNR 419/519

2. Focal Functions Focal (or neighborhood) functions compute an output grid in which the output value at each cell location is a function of the input cells in the specified neighborhood “around” each output (or target) location. Neighborhoods can be different sizes and geometries. Different arithmetic and statistical functions can be applied to summarize a neighborhood values. Example: Output = focalsum (Input, rectangle, 3,3)

3. Neighborhoods

4. Types of Neighborhood Statistics

5. Focal Functions process each cell Output = focalsum(input) If a cell of NoData is present in the neighborhood, it will be ignored in the processing. If the entire neighborhood consists of cells of NoData, the output cell value will be NoData.

6. Special Focal Functions Slope Aspect Curvature (slope of the slope) Filters Block (non-overlap) FocalFlow (flow into an individual cell) Flow Direction (flow between cells) –Flow Accumulation

7. Slope Reference: Burrough, P. A. and McDonell, R.A., 1998. Principles of Geographical Information Systems (Oxford University Press, New York), p. 190. Based on Horn (1981) A third-order finite difference estimator using the 8 outer points of a 3x3 neighborhood. Slope can be expressed as a percent or degrees. Degrees range between 0 and 90 and percent ranges between 0 and infinite.

8. Slope Computations where Conversion: 57.29578 degrees/radians

9. Slope Computations Cellsize = 5 units

10. Slope Computations There are problems at the edges and slope is highly influenced by the surface (e.g. DEM) resolution.

11. Aspect Aspect identifies the downslope direction of the maximum rate of change in value from each cell to its neighbors. Aspect can be thought of as the slope direction. The values of the output raster will be the compass direction of the aspect. Aspect uses the same base equations as Slope.

12. Aspect Computations The aspect value is then converted to compass direction values (0–360 degrees), according to the following rule: if aspect < 0 cell = 90.0 - aspect else if aspect > 90.0 cell = 360.0 - aspect + 90.0 else cell = 270 - aspect

13. Aspect Computations Since Aspect > 0° and < 90° Direction = 270 - 89.24 = 179.24° (almost due south)

14. Flow Direction The direction of flow is determined by finding the direction of steepest descent, or maximum drop, from each cell. –maximum drop = change in z-value / distance The distance is determined between cell centers. Therefore if the cell size is one, the distance between two orthogonal cells is one and the distance between two diagonal cells is 1.414216, the square root of two. If the maximum descent to several cells is the same, the neighborhood is enlarged until the steepest descent is found.

15. Block Function In a block function, the maximum, minimum, mean, etc. values are calculated for a fixed set of non-overlapping windows or neighborhoods. The resulting value for an individual neighborhood is assigned to all cell locations contained in the minimum-bounding rectangle of the specified neighborhood.

16. Zonal Analysis by Attribute

17. Zonal Statistics

18. Other Zonal Tools