Maps have been used throughout history to portray the Earth’s surface, location of features, and relations between features. Traditionally, maps were exclusively hand-drawn or drafted documents. The practice of cartography paralleled the exploration of the world as navigators established loca- tion reference schemes, classifications of features, labeling, and other annotations. Many of the symbols developed are retained in modern maps, such as blue lines for streams, double-line symbols for roads, and contour lines for topography.
As noted in Chapter 1, of the many contributions John Wesley Powell made in his explorations of the western United States, his creation of a map of the previously unknown Colorado River region had perhaps the greatest impact. The map destroyed the mystery of the canyon, showed where it flowed from and to, and showed the relative elevations along the way. That information provided following explorers, engineers, and land developers with a logistical perspective on how to get from here to there, and the land relief to be expected. It was the beginning of a systematic mapping of the West that led to the development of transportation routes, settlements, and irrigation and reservoir projects.
A map can accomplish many things in many ways. When you read a map, you observe the shapes and position of features, some attribute information about a feature, and the spatial relationships between features (Zeiler 1999). Some things that maps accomplish include:
Internal Users Internal Management Organization External Management User Services External Database External
User DatabaseInternal
Input Analysis GIS Database GIS Data Management Output
FiGure 2.3 GIS in an organizational context involves internal and external information exchanges.
Identify what is at a location through placement of a feature’s symbol in a reference frame •
Portray the relationship between features as connecting, adjacent, contained within, inter- •
secting, in proximity, or higher/lower Display multiple attributes of an area •
Allow portrayal of and discernment between distributions, relationships, and trends •
Show classifications of feature attributes and graphic portrayals as thematic maps •
Visually encode feature attributes as text, values, or identifiers •
Detect changes over time using maps prepared at different times •
Integrate data from diverse sources into a common geographic reference, thereby allow- •
ing comparison
In environmental and water resources engineering, maps and plans are a basic medium for design. Infrastructure designs are portrayed in a map format to communicate the exact nature of the project in terms of specific locations and relationships over an area. For example, a sanitary sewer system is shown in Figure 2.4. The layout shows the location and flow path of the collection sewer system. Topographic contours describe the lay of the land. Slope values can be derived and act as input for pipe alignment and diameter computations. Pipe flows are derived from the specific properties and streets in this plan.
2.3.2 coorDinate systeMsanD GeocoDinG
If a map feature is to be comparable in space to other features, it must have a location. Spatial data compiled from various sources must be assembled into a consistent reference frame. All points on the Earth’s surface can be defined in geographic coordinates as latitude, longitude, and elevation above mean sea level. A map projection is a mathematical transformation by which the latitude and longitude of each point on the Earth’s curved surface is converted into corresponding (x,y) or (easting, northing) projected coordinates in a flat-map reference frame (Snyder 1987). Figure 2.5 illustrates the concept of map projection for the equatorial case. If data are available in one map projection and required in another, then specialized GIS software can perform the transformation into the new projected reference frame.
Knowledge of the map scale is needed to properly understand a map’s accuracy. The map scale describes the relationship between the mapped size and the actual size. It is expressed as the ratio (or representative fraction) of the linear distances on the map and corresponding ground distances. Large-scale maps (≈1:1000) cover small areas, but can include a high level of detail. Large-scale maps are most often used for municipal facilities plans, and these maps must be developed using
FiGure 2.4 Portion of a sanitary sewer design plan showing (a) terrain contours and (b) connected
photogrammetric techniques. Small-scale maps (≈1:250,000) depict larger areas with less detail. For example, the U.S. Geological Survey Digital Line Graph (DLG) series is issued as three primary types: (a) large-scale (7.5-min of latitude and longitude) DLGs correspond to the USGS 1:20,000-, 1:24,000-, and 1:25,000-scale topographic quadrangle maps; (b) intermediate-scale (1:100,000-scale) DLGs; and (c) small-scale (1:1,000,000-scale) DLGs for the National Atlas. The 1:24,000 scale is most often used for watershed studies. The 1:100,000 scale is used for national coverage of the U.S. stream network. Details on U.S. map standards can be found at http://nationalmap.gov/gio/standards/.
USGS maps adhere to the National Map Accuracy Standards (USGS 1999). As applied to the USGS 7.5-min quadrangle topographic map, the horizontal accuracy standard requires that the positions of 90% of all points tested must be accurate within 1/50th of an inch (0.05 cm) on the map. At 1:24,000 scale, 1/50th of an inch is 40 ft (12.2 m). The vertical accuracy standard requires that the elevation of 90% of all points tested must be correct within half of the contour interval. On a map with a contour interval of 10 ft, the map must correctly show 90% of all points tested within 5 ft (1.5 m) of the actual elevation.
2.3.3 Data representationsanD Data MoDels
The nature of the data representation has a strong influence on the analysis that can be applied. Spatial data in GIS are most often organized into vector and raster (or surface) data structures (Figure 2.6). In the vector structure, geographic features or objects are represented by points, lines, and polygons that are precisely positioned in a continuous map space, similar to traditional hard- copy maps that identify landmarks, buildings, roads, streams, water bodies, and other features by points, lines, and shaded areas. In addition, each object in the vector structure includes topologic information that describes its spatial relation to neighboring objects, in particular its connectivity and adjacency. This explicit and unambiguous definition of and linkage between objects makes vec- tor structures attractive and allows for the automated analysis and interpretation of spatial data in GIS environments (Meijerink et al. 1994).
On the other hand, surface, or raster (from display technology), data structures divide space into a two-dimensional (2-D) grid of cells, where each cell contains a value representing the attribute being mapped. A raster is an x,y matrix of spatially ordered numbers. Each grid cell is referenced by a row and column number, with the boundary of the grid being registered in space to known coordinates. Raster structures arise from imaging sources such as satellite imagery and assume that the geographical space can be treated as though it were a flat Cartesian surface (Burrough 1986). A point is represented by a single grid cell, a line by a string of connected cells, and an area by a group of adjacent cells. When different attributes are considered, such as soil and land use, each
FiGure 2.5 Geographic coordinates expressed as degrees latitude and longitude represent angular degrees
are represented by separate raster layers. Operations on multiple layers involve the retrieval and processing of the data from corresponding cell positions in the different layers. This overlay con- cept is like stacking layers (2-D grids) and then analyzing each cell location (Meijerink et al. 1994). The simplicity of data processing in raster structures has contributed to its popularity. Both vector and raster structures are valid representations of spatial data. The complementary characteristics of both structures have long been recognized, and modern GIS can process both structures, includ- ing conversions between structures and overlays of both structures. Additional details on GIS data structures are presented in Chapter 3.
Of primary interest for water resources, especially surface-hydrology applications, are represen- tations of topography. Digital elevation model (DEM) is the general term used for topographic data models. DEMs are generally stored in one of three data structures: (a) raster or grid structures, (b) triangulated irregular network (TIN) structures, and (c) contour-based structures. Grid structures consist of a square grid matrix, with the elevation of each grid square (called a pixel) stored in a matrix node. Location is implicit from the row-and-column location within the matrix, given known boundary coordinates. In TIN structures, a continuous surface is generated from interconnected triangles with known elevation values at the vertices of the triangles. For each triangle, the location (x,y) and elevation (z) of the vertices are stored, as well as topological information identifying adja- cent triangles. Triangles vary in size, with smaller triangles clustered in areas of rapidly changing topography and larger triangles in areas of relatively smooth topography. Contour-based structures consist of digitized contour lines defined by a collection of x,y coordinate pairs for contours of specified elevation. DEM data sources are described in Chapter 3.