Unit 3: Proximity Analysis and Buffering. Lecture Outline

Transcription

1 Unit 3: Proximity Analysis and Buffering Lecture Outline I. Vector-Based Proximity 1. Proximity involves the calculation of distance between features in a single layer, or between features in multiple layers. Buffering calculates the distance around a feature. a. Both proximity and buffers are typically calculated using straight-line distances (Euclidean distances): d 2 x x y y1 where x 2 and y 2 are the coordinates for the referent point (the from point), and x 1 and y 1 are the coordinates for the to point. Straight-line distances are computed because study areas are usually large-scale and the coordinate systems typically used for large-scale areas are based upon some modification of a Cartesian coordinate system, such as UTM or State Plane projected coordinate systems. These coordinate systems are planar, where straight-line distances are appropriate. b. For small-scale study areas, the more appropriate distance to compute would be the Great Circle distance, using spherical trigonometry and the Geographic Coordinate system: cosd = (sin a * sin b) + (cos a * cos b * cos δλ ) where a and b are the geographic latitudes of A and B, and δλ is the absolute value of the difference in longitude between A and B. Example: Great circle distance between Nome, Alsaska and Miami, Florida: cosd = (sin sin 25.45) + [(cos cos cos( )]

2 2. Proximity operations ask how far away are some features from other features? This can lead to interesting explorations of why this is the case. The results of proximity operations in a GIS will either add fields to an existing table, or create standalone tables that store information about pairwise distances between features. Questions: How close are bars to schools? What houses are far from convenience stores? What are the distances among Mayan temples? How far apart are individual sagebrush plants, on average? What are the distances among kangaroo rat burrows and prairie dog burrows? a. Calculate the distance between each point in a feature layer and all other points in the same layer. The result of this type of operation would be a table containing the distances between all point pairs, including the referent point (distance = 0). Output will be a new field in the existing attribute table. b. Calculate the distance between each point in a feature layer and all other points in a different feature layer. The result of this operation results in a table of distances between features (pairwise distances). The number of records in this table will be (n 1 *n 2 ), where n is the number of features in each of the input layers. This will be a standalone table. c. Calculate the distance between each point in a feature class and the nearest other feature. However, unlike the case of Point distance, distances cannot be computed among point features within the same feature class, but only between features in different feature classes. Also, the Near operation can compute the distance between a point and the closest line feature (polyline). Point distance is restricted to point features only. II. Raster-based Proximity Operations 1. Raster based distance/proximity operations also calculate distances, but rather than storing the output in tables, the results are stored in a new raster layer. Raster distance operations calculate the straight-line (Euclidean) distance to some location, represented by a point, from the center of each cell in an existing raster. This is called a Euclidean distance raster. The values in the output cell represent the distance from the center of that cell to a source point as shown below:

3 Normally, these rasters are displayed as classified quantities, showing concentric circles representing distance to the closest point for each cell:

4 III. Buffering 1. A buffer is a region that is less than or equal to a specified distance from one or more features. Buffers may be determined for any of the 3 spatial objects: point, line or polygon. A buffer can be created outside, inside, or both, in the case of polygon features. Buffer shape can made to vary for the same features. Regardless of the object buffered, the result is always a polygon. By necessity, using the buffer spatial operation creates anew GIS layer, specifically a polygon layer. Point buffers are created by establishing a buffer distance, r, around each point feature. The distance is specified by the user and the buffer distance is used as a radius value. Figure from The process for creating a buffer around a line feature is more involved than for a point. Buffers are created around points that make up a line first and then boundaries in between line points are created using the tangent lines connecting pairs of point buffers. The same principles that apply to buffers for line features are also applied to polygon features. In polygon features, it is the lines forming the boundaries of the polygon that are actually buffered, and not the polygon areas. Similar to line features, buffering polygon features allows several different options. Just like point and line features, the result of the buffer operation for polygon features is a polygon. The resulting area for a buffered polygon feature can be larger or smaller than the original polygon feature, but not the same. 2. How large should the buffer area be? That is, what determines the radius that determines the buffer boundary? Different types of buffers exist depending on how the buffer boundary is

5 defined around a feature or set of features. These consist of arbitrary, causative, measurable, and mandated buffers. a. An arbitrary buffer is simply a guess at how large an area around a feature is necessary for protection, guarding, or otherwise needing special treatment. Such examples include buffer areas around construction sites, crime scenes, and hazardous materials spills. b. A causative buffer is based on a priori knowledge about the area within which the buffer is produced. A causative buffer usually takes into account features from the same or other GIS layers. Many times the features from other layers are used as barriers to modify the boundaries of an arbitrary buffer. Examples might include construction of a smell buffer around a sewer plant based on prevailing winds, or a flood zone buffer that uses topography to define the buffer boundary. c. A measurable buffer is defined by a measurable value. These measurements are not arbitrary but are quite accurate, being based solely on measurable phenomena. Such examples include 2-D pollution zones in various soil types, a blast zone around a stick of 40% nitro, and property boundaries. d. A mandated buffer is defined by some external criteria, usually in the form of laws or regulations, and irrespective of other features in the same or other GIS layers. Examples of mandated buffers are numerous and include no parking zones around fire hydrants, highway widths along road centerlines, and parcel sizes for residential, commercial and industrial zones.