Data Models IN GIS

Data Models IN GIS

Data in a GIS represent a simplified view of physical entities, the roads, mountains, accident locations, or other features we wish to identify. Data include information on the spatial location and extent of the entities, and information on their nonspatial properties.

   Each entity is represented by a spatial feature or cartographic object in the GIS, and so there is an entity–object correspondence. Because every computer system has limits, only a subset of essential characteristics is recorded. As illustrated in Figure 2-1, we may represent land covers in a region by a set of polygons.

   These polygons are associated with a set of essential characteristics that define each land cover, perhaps vegetation type, ownership, or land use. Essential characteristics are subjectively chosen by the spatial data developer.

    The essential characteristics of a forest would be different in the eyes of a logger than those of a conservation officer, a hunter, or a hiker. Objects are abstract representations of reality that we store in a spatial database, and they are imperfect representations because we can only record a subset of the characteristics of any entity.

   No one abstraction is universally better than any other, and the goal of the GIS developer is to define objects that support the

Figure 2-

intended use at the desired level of detail and accuracy. A spatial data model (Figure 2-2) may be defined as the objects in a spatial database plus the relationships among them.

   The term “model” is fraught with ambiguity because it is used in many disciplines to describe many things. Here the purpose of a spatial data model is to provide a formal means of representing and manipulating spatially referenced information. In Figure 2-1, our data model consists of two parts.

    The first part is a set of polygons (closed areas) recording the edges of distinct land uses, and the second part is a set of numbers or letters associated with each polygon.

   The data model may be considered the most recognizable level in our computer abstraction of the real world.

   Data structures and binary machine code are successively less recognizable, but more computer-compatible, forms of the spatial data Coordinates are used to define the spatial location and extent of geographic objects. A coordinate most often consists of a pair or triplet of numbers that specify location in relation to a point of origin.

   The coordinates quantify the distance from the origin when measured along standard directions. Single or groups of coordinates are organized

to represent the shapes and boundaries that define the objects. Coordinate information is an important part of the data model, and models differ in how they represent these coordinates. Coordinates are usually expressed in one of many standard coordinate systems.

   The coordinate systems are usually based upon standardized map projections (discussed in Chapter 3) that unambiguously define the coordinate values for every point in an area. Typically, attribute data complement coordinate data to define cartographic objects (Figure 2-3). Attribute data are collected and referenced to each object. These

attribute data record the non-spatial components of an object, such as a name, color, pH, or cash value.

   Keys, labels, or other indices are used so that the coordinate and attribute data may be viewed, related, and manipulated together. Most conceptualizations view the world as a set of layers (Figure 2-4). Each layer organizes the spatial and attribute data for a given set of cartographic objects in the region of interest. These are often referred to as thematic layers.

   As an example, consider a GIS database that includes a soils data layer, a population data layer, an elevation data layer, and a roads data layer.

   The roads layer contains only roads data, including the location and properties of roads in the analysis area (Figure 2-4). There are no data regarding the location and properties of any other geographic entities in the roads layer. Information on soils, population, and elevation are contained in their respective data layers.

   Through analyses we may combine data to create a new data layer; for example, we may identify areas that have high elevation and join this information with the soils data.

    This combination may create a new data layer with a new, composite soils/elevation variable. Figure 2-3: Coordinate and attribute data are used to represent entities.

Figure

Coordinate Data

   Coordinates define location in two- or three-dimensional space. Coordinate pairs, x and y, or coordinate triples, x, y, and z, are used to define the shape and location of each spatial object or phenomenon. Spatial data in a GIS most often use a Cartesian coordinate system, so named after Rene Descartes, the system’s originator.

    Cartesian systems define two or three orthogonal (right angle, or 90o) axes. Two-dimensional Cartesian systems define x and y axes in a plane (Figure 2-5, left).

   Three-dimensional Cartesian systems in addition define a z axis, orthogonal to both the x and y axes. The origin is defined with zero values at the intersection of the orthogonal axes (Figure 2-5, right).

   Cartesian coordinates are usually specified as decimal numbers that increase from bottom to top and from left to right. Two-dimensional Cartesian coordinate systems are the most common choice for mapping small areas. Small is a relative term, but here we mean maps of farm fields, land and property, cities, and counties.

   We typically introduce acceptably small errors for most applications when we ignore the Earth’s curvature over these small areas. When we map over larger areas, or need the highest precision and accuracy, we usually must choose a three-dimensional system.

    Coordinate data may also be specified in a spherical coordinate system. Hipparchus, a Greek mathematician of the 2nd century B.C., was among the first to specify locations on the Earth using angular measurements on a sphere.

   The most common spherical system uses two angles of rotation and a radius distance, r, to specify locations on a modeled earth surface (Figure 2-6).

   The first angle of rotation, the longitude (), is measured around the imaginary axis on which the Earth spins, an axis that goes through the North and South Poles. Zero is set for a location in England, and the angle is positive eastward and negative westward (Figure 2-6).

   The zero longitude, also known as the Prime Meridian or the Greenwich Meridian, was first specified through the Royal Greenwich Observatory in England, but measurement improvements, crustal movements, and changes in conventions now place zero longitude about 102 meters

(335 feet) east of the Greenwich Observatory. East or west longitudes are specified as angles of rotation away from the zero line.

   A second angle of rotation, measured along lines that intersect both the north and south poles, is used to define a latitude ( Figure 2-6). Latitudes are specified as zero at the equator, a line encircling the Earth that is always halfway between the North and South Poles.

   By convention latitudes increase to maximum values of 90 degrees in the north and south, or, if a sign convention is used, from -90 at the South pole to 90 at the North pole.

   Lines of constant longitude are called meridians, and lines of constant latitude are called parallels (Figure 2-7) . Parallels run parallel to each other in an east-west direction around the Earth.

   The meridians are north/south lines that converge to intersect at the poles. Because the meridians converge, geographic coordinates do not form a Cartesian system. A Cartesian system defines lines on a right-angle, planar grid. Geographic coordinates occur on a curved surface, and the longitudinal lines cross at the poles.

    This convergence means the distance spanned by a degree of longitude varies from south to north. A degree of longitude spans approximately 111.3 kilometers at the equator, but 0 kilometers at the poles. In contrast, the ground distance for a degree of latitude varies only slightly, from 110.6 kilometers at the equator to 111.7 kilometers at the poles.

    The slight difference with latitude is due to a non spherical Earth, something we’ll describe a bit later. Convergence causes distortion in regular geometric figures specified in geographic coordinates (Figure 2-8, left).

   For example, “circles” with a fixed radius in geographic units, such as 5o, are not circles on the surface of the globe, although they may appear as circles when the Earth surface is “unrolled” and plotted with distortion on a flat map; note the erroneous size and shape of Antarctica at the bottom of Figure 2-8.

   Because the spherical system for geographic coordinates is non-Cartesian, formulas for area, distance, angles, and other geometric properties that work in a Cartesian coordinates give errors when applied to geographic coordinates.

   Areas are calculated after converting to a projected system, described later in this chapter. There are two primary conventions used for specifying the magnitudes of latitude and longitude (Figure 2-9). The first uses a leading letter, N, S, E, or W to indi-

cate direction, followed by a number to indicate location. Northern latitudes are preceded by an N and southern latitudes by an S; for example, N90o, S10o.

   Longitude values are preceded by an E or W, respectively; for example W110o. Longitudes range from 0 to 180 degrees east or west.

   Note that the east and west longitudes meet at 180 degrees, so that E180o equals W180⁰ Signed coordinates are the second common convention for specifying latitude and longitude in a spherical system. Northern latitudes are positive and southern latitudes are negative, and eastern longitudes positive and western longitudes negative.

   Latitudes vary from -90 degrees to 90 degrees, and longitudes vary from -180 degrees to 180 degrees. By this convention the longitudes “meet” at the maximum and minimum values, so -180o equals 180o. Coordinates may easily be converted between these two conventions.

    North latitudes and east longitudes are converted by removing the leading N or E, respectively. South latitudes and west longitudes are converted by first removing the leading S or W, respectively, and then changing the sign of the remaining number from a positive to a negative value.

   Spherical coordinates are most often recorded in a degrees-minutes-seconds (DMS) notation; N43o 35’ 20” for 43 degrees, 35 minutes, and 20 seconds of latitude.

    In DMS, each degree is made up of 60 minutes of arc, and each minute is in turn divided into 60 seconds of arc (Figure 2-10).

    This yields 60 times 60 or 3600 seconds for each degree of latitude or longitude. Note that the ancient Babylonians established these splits, of 360 degrees for a complete circle, with degrees and minutes subse-

quently divided into 60 units, and we’ve carried this convention down to today. Spherical coordinates may also be expressed as decimal degrees (DD). When using DD the degrees take the usual -180 to 180 (longitude) and -90 to 90 (latitude) ranges, but minutes and seconds are reported as a decimal portion of a degree (from 0 to 0.99999...). In our previous example, N43o35’ 20” would be reported as 43.5888. DMS may be converted to DD by: DD = DEG + MIN/60 + SEC/3600 (2.1) Examples of the forward and reverse conversion between decimal degrees and degrees-minutes-seconds units are shown in Figure 2-11. Figure 2-10: There are 360 degrees in a complete circle, with each degree composed of 60 minutes, and each minute composed of 60 seconds.