geog 360
Vector Data Model
A spatial data model that uses discrete elements such as points, lines, and polygons to represent the geometry of real-world entities.
ellipsoid
a model of the rounded shape of earth
Ellipsoid
a model of the rounded shape of earth slightly flattened at the poles and slightly bulging at the equator.----the ellipsoid has two characteristic dimensions (Figure 3-4). These are the semi-major axis, the radius a in the equatorial direction, and the semi- minor axis, the radius b in the polar direc- tion. The equatorial radius is always greater than the polar radius for the Earth ellipsoid. This difference in polar and equatorial radii can also be described by the flattening fac- tor, as shown in Figure 3-4.
Graticule
a network of lines representing meridians and parallels, on which a map or plan can be represented
WEEK 2 (ch 2)
WEEK 2 (ch 2)
mean sea level
We must emphasize that a geoidal sur- face differs from mean sea level. Mean sea level may be higher or lower than a geoidal surface because ocean currents, temperature, salinity, and wind variations can cause per- sistent high or low areas in the ocean. These differences are measurable, in places over a meter (3 feet), perhaps small on global scale, but large in local or regional analysis. We historically referenced heights to mean sea level, and many believe we still do, but this is no longer true for most spatial data analyses!!!!!!!!!!!!!!!!!!!!!!!!!
Raster Pyramids
We sometimes intentionally increase the size of our raster data sets without increasing the resolution in a process known as pyra- miding. We create pyramids to increase dis- play speeds when viewed at small scales ("zoomed out"). Long redraw times often hinder use of large data sets, particularly when panning frequently. When displayed at very small scales, the cell size of a data set may be smaller than the resolution of the computer screen. A raster data set 1,000,000 pixels across has 1000 times the data that can be displayed on a monitor with 1000 pixel horizontal resolution. However, dis- play software must wade through all 1,000,000 data elements in a row to pick the 1 cell in 1000 to display. While clever soft- ware can help, there are limits to how much we can speed up the redraws. Pyramiding in effect saves subsampled copies of the cells at various resolutions. In our example above, pyramids may do the equivalent of saving every two, every four, every 10, every 30, and every 100 cells, all within the same raster data set. The software then compares the display scale to the dimensions of the data set, and chooses the most appropriate cell resolution to display. Redraws are much faster, and transparent to the user.
Week 4 Chapter 3 Pages 116 - 137
Week 4 Chapter 3 Pages 116 - 137
Week 5 Ch 4: 147 - 169, 183 - 193 Ch 8: 297 - 327
Week 5 Ch 4: 147 - 169, 183 - 193 Ch 8: 297 - 327
geoidal height
difference between ellipsoid and geoid--measured by gravimeters, and satellite-based measurements
data area/pane
occupies the largest part of the map, and contains most of the depicted spatial data.
boundary generalization
the incomplete representation of boundary locations
Goode Homolosine Projection (based on a sinusoidal projection and a Mollweide projection)
--example of an interrupted projection, often used to reduce some forms of distortion. A 20th century map of Earth with equal area of landmasses but interruptions of the oceans to more accurately represent a "flattened" sphere.
Defining coordinates for the Earth's surface is complicated by three main fac- tors.
1. A flat map must distort geometry in some way because the Earth is curved. 2. The second main problem in defining a coordinate system results from the irregular shape of the Earth. 3. Thirdly, our measurements are rarely perfect, and this applies when measuring both the shape of the Earth, and the exact position of features on it.------------Because of these three factors, we often have several different sets of coordi- nates to define the same location on the sur- face of the Earth.
Raster Data Model
A data model that uses a grid and cells to represent the spatial variation of a feature; The raster model is used most commonly with variables that may change continuously across a region. Eleva- tion, mean temperature, slope, average rain- fall, cumulative ozone exposure, or soil moisture are examples of phenomena that are often represented as continuous fields.
geoid (lecture)
A geoid is a gravitational surface with "equal gravitational potential" 🡪 it is a measured surface
Public Land Survey System (PLSS)
A land partitioning system used in the United States
Secant (of a circle)
A line that intersects a circle in two points
Geographic Coordinate System
A location reference system for spatial features on the Earth's surface. !!!!!Because the meridians converge, geo- graphic coordinates do not form a Cartesian system. A Cartesian system defines lines on a right-angle, planar grid. Geographic coor- dinates 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 approxi- mately 111.3 kilometers at the equator, but 0 kilometers at the poles. In contrast, the ground distance for a degree of latitude var- ies 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. Because the spherical system for geo- graphic coordinates is non-Cartesian, for- mulas for area, distance, angles, and other geometric properties that work in a Carte- sian coordinates give errors when applied to geographic coordinates. Areas are calcu- lated after converting to a projected sys- tem
Object Data Model
A main goal is to raise the level of abstraction so that the data objects may be conceptualized and addressed in a more natural way. Object models attempt to encapsulate the information and operations (often called "methods") into discrete objects. Object models for spatial data often fol- low a logical model, a user's view of the real objects we portray with a GIS (Figure 2-39). This model includes all the "things" of inter- est, and the relationships among them. Things, or objects, might include power poles, transformers, powerlines, meters, and customer buildings, and relationships among them would include a transformer on a pole, lines between poles, and meters at points along the lines. The logical model is often represented as a box-and-line diagram. Most object models define the proper- ties of each object, and the relationships among the same and different types of objects.
neatline/inset
A neatline is often included to provide a frame around all map elements, and insets may contain additional map ele- ments.
Pointers
A pointer is an address or index that connects one file loca- tion to another. Pointers are a common way to organize information within and across multiple files. Figure 2-44 depicts an exam- ple of the use of pointers to organize spatial data. In Figure 2-44, the polygon is com- posed of a set of lines. Pointers are used to link the set of lines that form each polygon. There is a pointer from each line to the next line, forming a chain that defines the poly- gon boundary. Pointers help by organizing data in such a way as to improve access speed. Unorga- nized data would require time-consuming searches each time a polygon boundary was to be identified. Pointers also allow efficient use of storage space. In our example, each line segment is stored only once. Several polygons may point to the line segment as it is typically much more space efficient to add pointers than to duplicate the line segment.
Raster Cell/discrete data and categorical data
A raster data model may also be used to represent discrete data (Figure 2-33), for example, to represent landcover in an area. Raster cells typically hold numeric or single- letter alphabetic characters. A coding scheme defines what land cover type the dis- crete values signify. Each code may be found at many raster cells.
Chloropleth Map
A thematic map that uses tones or colors to represent spatial data as average values per unit area. Choropleth maps depict quantitative information for areas such as population density. Polygons define area boundaries, such as counties, states, census tracts, or other stan- dard administrative units. Each polygon is given a color, shading, or pattern corre- sponding to values for a mapped variable
datum-2
A useful datum must include a set of points and lines that have been painstakingly surveyed, and that may be used as the start- ing points for subsequent, detailed, local sur- veys. Some authors define the datum as a specified reference surface, and a realization of a datum as that surface plus a physical network of precisely measured points. In this nomenclature, the measured points describe a Terrestrial Reference Frame. This clearly separates the theoretical surface, bench- markthe reference system or datum, from the terrestrial reference frame, a specific set of measurement points that help fix the datum.
Shapefile--pg 70-72
A vector data storage format for storing the location, shape, and attributes of geographic features. Shapefiles are a common vector spatial data format that uses an index to link files. Shapefiles were originally developed by ESRI, inc., as a way to store point, line, and polygon features, although they have since been adopted as a common format for data interchange and analysis. Shapefiles represent layers with a clus- ter of files. Each file has the same base name but a different filename extension, indicated by a suffix, for example, the ".shp" in the filename "boundary.shp." A transportation data layer stored in shapefile format might have the base name of roads, with different suffixes for different files: roads.shp roads.shx roads.dbf roads.prj, etc. --The .shp files contain the coordinates that represent each road, organized by line seg- ments,---Segments in the roads.shp file are indexed by pointers in the roads.shx file. Part of the information stored for a segment is the identifiers of connecting segments. The roads.shx file contains indices that point to the segment records in the .shp files, based on these identifiers. This speeds access, because without indexing, the soft- ware would have to search the .shp file each time it needed to find adjacent segments in a road. The roads.dbf file also uses an index to point to the combined roads in the .shp and .shx files. A group of segments may be used to form a line, and associated with a set of attributes stored in a dbf file, for example, attributes on road name, surface type, or speed limit. By appropriate use of pointers and indices, largely hidden to the user, this group of three shapefiles implements our vector data model.
ASCII code
American Standard Code for Information Interchange--One of the most common number cod- ing schemes uses ASCII designators. ASCII stands for the American Standard Code for Information Interchange. ASCII is a stan- dardized, widespread data format that uses seven bits, or the numbers 0 through 126, to represent text and other characters. An extended ASCII, or ANSI (American National Standards Institute) scheme, uses these same codes, plus an extra binary bit to represent numbers between 127 and 255. These codes are then used in many programs, including GIS, particularly for data export or exchange. ASCII codes allow us to easily and uni- formly represent alphanumeric characters such as letters, punctuation, other characters, and numbers. ASCII converts binary num- bers to alphanumeric characters through an index. Each alphanumeric character corre- sponds to a specific number between 0 and 255, which allows any sequence of charac- ters to be represented by a number. One byte is required to represent each character in extended ASCII coding, so ASCII data sets are typically much larger than binary data sets. Geographic data in a GIS may use a combination of binary and ASCII data stored in files. Binary data are typically used for coordinate information, and ASCII or other codes may be used for attribute data.
Raster Data-cell center point
An alternative interpretation of the ras- ter cell applies the value to the central point of the cell. Consider a raster grid containing elevation values. Cells may be specified as 200 meters square, and an elevation value assigned to each square. A cell with a value of 8000 meters (26,200 feet) may be assumed to have that value at the center of the cell, but this value will not be assumed to apply to the entire cell.
Polygon Inclusion
An area different in some characteristic from the recorded attributes of the polygon, but not resolved.--paved walkway in between mulched garden bed, eg
true line of scale figure 3-33
Approximate error due to projection distortion for a specific oblique stereographic projection. A plane intersects the globe at a standard circle. This standard circle defines a line of true scale, where there is no distance distortion. Distortion increases away from this line, and varies from -1% to over 2% in this example.
Geoid
As noted in the previous section, the true shape of the Earth varies slightly from the mathematically smooth surface of an ellip- soid. Differences in the density of the Earth cause variation in the strength of the gravita- tional pull, in turn causing regions to dip or bulge above or below a reference ellipsoid (Figure 3-7). This undulating shape is called a geoid.--Geodesists have defined the geoid as the three-dimensional surface along which the pull of gravity is a specified constant. The geoidal surface may be thought of as an imaginary sea that covers the entire Earth and is not affected by wind, waves, the moon, or forces other than Earth's gravity. The surface of the geoid extends across the Earth, approximately at mean sea level across the oceans, and continuing under continents at a level set by gravity. The surface is always at right angles to the direction of local gravity, and this surface is the refer- ence against which heights are measured.
Binary columns
Binary numbers are also formed by rep- resenting values in columns. In a binary sys- tem each column represents a successively higher power of two (Figure 2-43). The first (rightmost) column represents 1 (20 = 1), the second column (from right) represents twos (21 = 2), the third (from right) represents fours (22 = 4), then eight (23 = 8), sixteen (24 = 16), and upward for successive powers of two. Thus, the binary number 1001 rep- resents the decimal number 9: a one from the rightmost column, and eight from the fourth column (Figure 2-43).
cartometric maps
Cartometric maps are those that faithfully represent the relative position of objects and thus may be suitable as a source of spatial data.
Chapter 3----85 - 104 (week 3 continued)
Chapter 3----85 - 104 (week 3 continued)
Triangulated Irregular Network (TIN)
Composite vector data that approximate the terrain with a set of nonoverlapping triangles; typically x,y, and z locations for measured points are entered into the TIN data model. These points are distributed in space and the points may be connected such that the smallest triangle possible spans all 3 points.
Lambert Conf conic vs Tranverse (practical apps)
Continental projections may also be established. Generally, the projections are chosen to minimize area or shape distortion for the region to be mapped. Lambert con- formal conic or other conic projections are often chosen for areas with a long east-west dimension, for example when mapping the contiguous 48 United States. Standard paral- lels are placed near the top and bottom of the continental area to reduce distortion across the region mapped. Transverse cylindrical projections are often used for large north- south continents.
map projection
Datums tell us the latitudes and longi- tudes of features on an ellipsoid. We need to transfer these from the curved ellipsoid to a flat map. A map projection is a systematic rendering of locations from the curved Earth surface onto a flat map surface. Nearly all projections are applied via exact or iterated mathematical formulas that convert between geographic latitude and longitude and projected X an Y (Easting and Northing) coordinates.
Conversion Among Coordinate Systems
Conversion from one projected coordi- nate system to another requires using the inverse and forward projection equations, described in an earlier section, passing through the geographic coordinate set. This allows a flexible conversion between any two projections, given our requirement that both the forward and inverse, or "backward" projection equations are specified for any map projection. For example, given a coor- dinate pair in the State Plane system, you may calculate the corresponding geographic coordinates. You may then apply a formula that converts geographic coordinates to UTM coordinates for a specific zone using another set of equations. Since the backward and forward projections from geographic to projected coordinate systems are known, we may convert among most coordinate systems by passing through a geographic system (Figure 3-48, a). Care must be taken when converting among projections that use different datums. If appropriate, we must insert a datum trans- formation when converting from one pro- jected coordinate system to another (Figure 3-48, b). A datum transformation, described earlier in this chapter, is a calculation of the change in geographic coordinates when moving from one datum to another.
Spherical Coordinate 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 loca- tions on the Earth using angular measure- ments 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 (lamda), is measured around the imaginary axis on which the Earth spins, an axis that goes through the North and South Poles. A second angle of rotation, measured along lines that intersect both the north and south poles, is used to define a latitude. 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 con- verge to intersect at the poles.
Grid North
Direction of north established by grid lines on a map. Note that the use of a projection defines a Cartesian coordinate system and hence cre- ates grid north, a third version of the north- ern direction. Grid north is the direction of the Y axis in a map projection, and often equals or nearly equals the direction of a meridian near the center of the projected area. Grid north is typically different from the norths previously described, magnetic north, toward which a compass points, and geographic north, the pole around which the globe revolves.
vector topology
Enforces strict connectivity and recording adjacency and planarity
SPC and Different datums
Finally, note that more than one version of the State Plane coordinate system has been defined. Changes were introduced with the adoption of the North American Datum of 1983. Prior to 1983, the State Plane pro- jections were based on NAD27. Changes were minor in some cases, and major in oth- ers, depending on the state and State Plane zone. Care must be taken when using legacy data to identify the version of the State Plane coordinate system used because the FIPS and State Plane zone designators may be the same, but the projec- tion parameters may have changed from NAD27 to NAD83.
large scale map
Larger ratio signifies a large scale map. 1:24,000 is considered large-scale relative to 1:100,000. !:24,00 has the larger ratio!!! It is helpful to remember that features appear larger on a large- scale map.!! It is also helpful to remember that large-scale maps of a given paper size show more detail, but less area!!! Maps that cover smaller areas with greater detail.
National Coordinate System
Many governments have adopted a stan- dard project for nationwide data, particularly small and midsized countries where distor- tion is limited across the spanned distances. Many European countries have stan- dard map projections covering a national extent; for example, Belgium, Estonia, and France each have different Lambert Confor- mal Conic projections defined for use on standard nation-spanning maps and data sets, while Germany, Bulgaria, Croatia, and Slovenia use a specialized modification of the transverse Mercator projection. Some countries adopt specific Universal Trans- verse Mercator projections, including Nor- way, Portugal, and Spain. Specifications of these projection parameters may be found in the respective national standard documents. Larger countries may not have a spe- cific or unified set of standard, nationwide projections, particularly for GIS data, because distortion is usually unavoidably large when spanning great distances across both latitudes and longitudes in the same map.
feature maps
Many types of maps are produced, and the types are often referred to by the way features are depicted on the map. Feature maps are among the simplest, because they map points, lines, or areas and provide nom- inal information (Figure 4-5, upper left). A road may be plotted with a symbol defining the type of road or a point may be plotted indicating the location of a city center, but the width of the road or number of city dwellers are not provided in the shading or other symbology on the map. Feature maps are perhaps the most common map form, and examples include most road maps, and standard map series such as the 7.5-minute topographic maps produced by the U.S. Geological Survey.
Graticule ( different from grid which represents x and y coordinates).
Maps often depict coordinate lines (Fig- ure 4-4). When the lines represent constant latitude and longitude, a set of coordinate lines is called a graticule. Graticules are particularly useful for depict- ing the distortion inherent in a map projec- tion, because they show how geographic north or east lines are deformed, and how this distortion varies across the map. Grids may establish a map-projected north, in con- trast to geographic north, and may be useful when trying to navigate or locate a position on the map.
Feature Generalization
Modification of features when representing them on a map. may be classed as: Fused: multiple features may be grouped to form a larger feature, Simplified: boundary or shape details are lost or "rounded off", Displaced: features may be offset to pre- vent overlap or to provide a standard distance between mapping symbols, Omitted: Small features in a group may be excluded from the map, or Exaggerated: standard symbol sizes are often chosen, for example, standard road symbol widths, which are much larger when scaled than the true road width.
Globally-applicable ellipsoids
More recently, data derived from satel- lites, lasers, and broadcast timing signals have been used for extremely precise mea- surements of relative positions across conti- nents and oceans. Global measurements and faster computers allow us to estimate glob- ally-applicable ellipsoids. These ellipsoids provide a "best" overall fit ellipsoid to observed measurements across the globe. Global ellipsoids such as the GRS80 or WGS84 are now preferred and most widely used.
developable surface
Most map projections are based on a developable surface, a geometric shape onto which the Earth surface is projected. Cones, cylinders, and planes are the most common developable surfaces. A plane is already flat, and cones and cylinders may be mathemati- cally "cut" and "unrolled" to develop a flat surface . Note that while the most common map projections used for spatial data in a GIS are based on a developable surface, many map projections are not. Projections with names such as pseudocylindrical, Mollweide, sinu- soidal, and Goode homolosine are examples. These projections often specify a direct mathematical projection from an ellipsoid onto a flat surface. They use mathematical forms not related to cones, cylinders, planes, or other three-dimensional figures, and may change the projection surface for different parts of the globe, but generally are used only for display, and not for spatial analysis, because the coordinates systems are not strictly Cartesian.
Continental and Global Projec- tions.
Most world- wide projections are used for visualization, but not quantitative analysis. There are a number of projections that have been widely used for the world. These include variants of the Mercator, Goode, Mollweide, and Miller projections, among others. There is a trade-off that must be made in global projections, between a con- tinuous map surface and distortion.
planar topology
No overlaps among lines of polygons in the same layer
spheroid
Note that the words spheroid and ellip- soid are often used interchangeably. GIS software often prompts the user for a spher- oid when defining a coordinate projection, and then lists a set of ellipsoids. An ellipsoid is sometimes referred to as an "oblate" spheroid. Thus, it is less precise but still cor- rect to refer to an ellipsoid more generally as a spheroid.
Raster data models
Raster data models are the natural means to represent "continuous" spatial fea- tures or phenomena. Elevation, precipita- tion, slope, and pollutant concentration are examples of continuous spatial variables. Raster data sets have a cell dimension, defining the edge length for each square cell (Figure 2-31). For example, the cell dimen- sion may be specified as a square 30 meters on each side. The cells are usually oriented parallel to the x and y directions, and the coordinates of a corner location are speci- fied. There is often a trade-off between spa- tial detail and data volume in raster data sets. The number of cells needed to cover a given area increases four times when the cell size is cut in half (Figure 2-32). Smaller cells provide greater spatial detail, but at the cost of larger data sets. The number of cells in a raster data set depends on the cell size. For a given area, a linear decrease in cell size causes an exponential increase in cell number, e.g., halving the cell size causes a four fold increase in cell number. While raster cells often represent the average or the value measured at the center of the cell, they may also repre- sent the median, maximum, or another statis- tic for the cell area.
Raster Values/points and lines (pg 55-56).
Raster values may also be used to represent points and lines lines, as the IDs of lines or points that occur closest to the cell center.
Data Compression
Reducing the amount of space needed to store a piece of data. We often compress spatial data files because they are large. Data compression reduces file size while maintaining the infor- mation contained in the file. Compression algorithms may be "lossless," in that all information is maintained during compres- sion, or "lossy," in that some information is lost. A lossless compression algorithm will produce an exact copy of the original when it is applied and then the appropriate decom- pression algorithm applied. A lossy algo- rithm will alter the data when it is applied and the appropriate decompression algo- rithm applied. Lossy algorithms are most often used with image data, where substan- tial degradation still leaves a useful image, and are uncommonly applied to thematic spatial data, where any data degradation is typically not tolerated. Data compression is most often applied to discrete raster data, for example, when representing polygon or area information in a raster GIS. There are redundant data ele- ments in raster representations of large homogenous areas. Each raster cell within a homogenous area will have the same code as most or all of the adjacent cells. Data com- pression algorithms remove much of this redundancy.
Cartesian Coordinate System
Spatial data in a GIS most often use a Cartesian coordinate system, so named after Rene Descartes, the system's originator. Car- tesian systems define two or three orthogo- nal (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 val- ues 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.
nodes, vertices of lines
Starting points and ending points for a line = node while intermediate points in a line are referred to as vertices
Lambert Conformal Conic Projection
The Lambert conformal conic and the transverse Mercator are among the most common projection types used for spatial data in North America, and much of the world. Note that sets of circles in an east-west row are distorted in the Lambert conformal conic projection (Figure 3-38, top right). Those circles that fall between the standard parallels exhibit a uniformly lower distortion than those in other portions of the projected map. One property of the Lambert confor- mal conic projection is a low-distortion band running in an east-west direction between the standard parallels. Thus, the Lambert conformal conic projection is often used for areas that are larger in an east-west than a north-south direction, as there is little added distortion when extending the mapped area in the east-west direction.
State Plane Coordinate System
The State Plane Coordinate System is a standard set of projections for the United States. The State Plane coordinate system specifies positions in Cartesian coordinate systems for each state. There are one or more zones in each state, with slightly dif- ferent projection parameters in each State Plane zone (Figure 3-40). Multiple State Plane zones are used to limit distortion errors due to map projections.
State Plane Coordinate System
The State Plane coordinate system is based on two types of map projections: the Lambert conformal conic and the transverse Mercator projections. Because distortion in a transverse Mercator increases with distance from the central meridian, this projection type is most often used with states or zones that have a long north-south axis (e.g., Illi- nois or New Hampshire). Conversely, a Lambert conformal conic projection is most often used when the long axis of a state or zone is in the east-west direction (examples are North Carolina and Virginia).
WGS84 (World Geodetic System 1984)
The World Geodetic System of 1984 (WGS84) is a second set of datums devel- oped and primarily used by the U.S. Depart- ment of Defense (DOD). It was introduced in 1987 based on Doppler satellite measure- ments of the Earth, and is used in most DOD maps and positional data. The WGS84 ellip- soid is similar to the GRS80 ellipsoid
Earth's radii
The best estimates of the Earth's radii, a and b, have evolved as measurements sys- tems have improved. Today, the best esti- mate for a is 6,378,137.0 meters (m), and for b 6,356,752.3 m. When a simple spheroidal shape is assumed where a equals b, some number between these two is usually applied, often the mean value of 6,367,444.7 m.
UTM Equator
The equator is used as the northing ori- gin for all north zones. Thus, the equator is assigned a northing value of zero for north zones. This avoids negative coordinates, because all of the UTM north zones are defined to be north of the equator. University Transverse Mercator zones south of the equator are slightly different than those north of the equator (Figure 3- 46). South zones have a false northing value added to ensure all coordinates within a zone are positive. UTM coordinate values increase as one moves from south to north in a projection area. If the origin were placed at the equator with a value of zero for south zone coordinate systems, then all the north- ing values would be negative. An offset is applied by assigning a false northing, a non- zero value, to an origin or other appropriate location. For UTM south zones, the northing values at the equator are set to equal 10,000,000 meters. Because the distance from the equator to the most southerly point in a UTM south zone is less than 10,000,000 meters, this assures that all northing coordi- nate values will be positive within each UTM south zone (Figure 3-46).
distortion in map projections - figure 3-32 pg 117
The map surface intersects the Earth at two locations, I1 and I2. Points toward the edge of the map surface, such as D and E, are stretched apart. The scaled map distance between d and e is greater than the distance from D to E mea- sured on the surface of the Earth. More sim- ply put, the distance along the map plane is greater than the corresponding distance along the curved Earth surface. Conversely, points such as A and B that lie in between I1 and I2 would appear compressed together. The scaled map distance from a to b would be less than the surface measured distance from A to B. Distortions at I1 and I2 are zero. distortion is usually small near the points or lines of intersection, and increases with increasing distance from the points or lines of intersection.
Datum adjustment
The positions of all points in a reference datum are estimated in a network- wide datum adjustment. The datum adjust- ment reconciles errors across the network, first by weeding out blunders or obvious mistakes, and also by mathematically mini- mizing errors by combining repeat measure- ments and statistically assigning higher influence to more precise measurements. Note that a given datum adjustment only incorporates measurements up to a given point in time, and may be viewed as our best estimate, at that point, of the measured set of locations.
map scale
The relationship between the size of an object on a map and the size of the actual feature on Earth's surface.
Topology
The study of how items are related to one another in space; a configuration. Topological models create an intersection and place a node at each line crossing, record connectivity and adjacency, and maintain information on the relationships between and among points, lines, and poly- gons in spatial data
Dot Density Map
Thematic map that uses dots to represent the frequency of a variable in a given area. Dot-density maps are another map form commonly used to show quantitative data (Figure 4-5, bottom left). Dots or other point symbols are plotted to represent values. Dots are placed in the polygon such that the num- ber of dots equals the total value for the polygon. Note that the dots are typically placed randomly within the polygon area.
GDAL
There is an open source initiative and tool by the name of GDAL, for Geospatial Data Abstraction Library, with provides a cross-platform utility to translate among many common vector and raster file formats.
Raster Layers and assctd attribute tables
This is most common when nominal data are represented, but may also be used with ordinal or interval/ratio data. Just as with topological vector data, features in the raster layer may be linked to rows in an attribute table, and these rows may describe the essential nonspatial characteris- tics of the features. A one-to-one correspondence is rarely used with raster data sets because it often would require an unmanageably large size of attribute table. To avoid these problems, a many-to-one relationship is usually allowed between the raster cells and the attribute table (Figure 2- 36b). Many raster cells may refer to a single row in the attribute column. This substan- tially reduces the size of the attribute table for most data sets although it does so at the cost of some spatial ambiguity
horizontal datum
Through these methods (satellites, surveying, etc) we establish a set of points on Earth for which the horizontal and vertical positions have been accurately determined. These accu- rately determined points and associated mea- sured and mathematical surfaces are datums, references against which we measure all other locations. These well-surveyed points allow us to specify a reference frame, including an ori- gin or starting point. If we are using an ellip- soidal reference frame, we must also specify the orientation and radii of our ellipsoid. If we are using a three-dimensional Cartesian reference frame, we must specify the X, Y, and Z axes, including their origin and orientation. We can choose different values for these various parts of our reference frame, and hence will have different reference frames. All other coordinate locations we use are measured with reference to the cho- sen reference frame. We then must painstak- ingly measure a precise set of highly accurate points, so we can express locations relative to this reference frame. For most of the past 150 years, the most accurate obser- vations were referenced to the sun, stars, or other celestial bodies (Figure 3-12), as they provided the most stable reference frame.
Geodesy
To effectively use GIS, we must develop a clear understanding of how coordinate systems are established for the Earth, how these coordinates are measured on the Earth's curving surface, and how these coordinates are converted for use in flat maps, either digital or paper. This chap- ter introduces geodesy, the science of mea- suring the shape of the Earth, and map projections, the transformation of coordi- nate locations from the Earth's curved sur- face onto flat maps.
Central Meridian UTM
UTM coordinate system is defined so that all coordinates are positive within the zone. Zone easting coor- dinates are all greater than zero because the central meridian for each zone is assigned an easting value of 500,000 meters. This effec- tively places the origin (E = 0) at a point 500,000 meters west of the central meridian. All zones are less than 1,000,000 meters wide, ensuring that all eastings will be posi- tive.
Digital Elevation Model (DEM) or Digital Terrain Model (DTM)
a digital representation of land surface or underwater topography. eg. Raster and Tin data.
Sinusoidal
a graph or a function that has the form of a sine or cosine function
Geodetic Datum
a reference surface. A geodetic datum consists of two major components. The first component is an ellip- soid with a spherical or three-dimensional Cartesian coordinate system and an origin. Eight parameters are needed to specify the ellipsoid: a and b to define the size/shape of the ellipsoid; the X, Y, and Z values of the origin; and an orientation angle for each of the three axes.
attribute table
a spreadsheet-style form where the rows consist of individual objects and the columns are the attributes associated with those objects
Eratosthenes
calculated the circumference of the earth.
negative scale distortion (inside standard circle)
compressed/reduced in size value of -1% for ex
convergent circle
defined as the circle passing through all three points. A triangle is drawn only if the corresponding convergent circle contains no other sampling points. Each triangle defines a terrain surface, or facet, assumed to be of uniform slope and aspect over the triangle.
TIN Model Advantages
density of sampled points can be adjusted to reflect relief incorporate the original sample points easy to calculate elevation, slope, aspect, and line-of-sight
Isopleth maps
display lines of equal value. Isopleth maps, also known as contour maps, display lines of equal value (Figure 4- 5, bottom right). Isopleth maps are used to represent continuous surfaces. Rainfall, ele- vation, and temperature are features that are commonly represented using isopleth maps. A line on the isopleth map represents a spec- ified value, for example, a 10oC isopleth defines the position on the landscape that is at that temperature. Lines typically do not cross, in that there cannot be two different temperatures at the same location. However, isopleth maps are commonly used to depict elevation, and cliffs or overhanging terrain do have multiple elevations at the same loca- tion. In this case the lower elevations typi- cally pass "under" the higher elevations, and the isopleth is labeled with the tallest height
positive scale distortion (outside standard circle)
expanded/increase in size +1% for ex
semi-major axis and semi -minor axis
half of the major axis
ellipsoidal height
height above ellipsoid
Orthometric Height
height above the geoid
Transverse
in a crosswise direction
Vertical Datum (lecture)
measure elevations Height above sea level Arbitrary surface with an elevation of zero Mean Sea Level (MSL) is most common Vertical datums based on sea level, ellipsoid, or geoid
coordinate data
pairs or triplets of numbers that define location, - 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.
indices
plural of index, guides
Common geographic data formats may be placed into three large classes:
raster, vector, and attribute.
Run Length Encoding
replacing a long series of a repeated character with a count of the repetition. Run length coding is a common data compression method. This compression technique is based on recording sequential runs of raster cell values. Each run is recorded as the value found in the set of adjacent cells and the run length, or number of cells with the same value. Seven sequen- tial cells of type A might be listed as A7 instead of AAAAAAA. Thus, seven cells would be represented by two characters. Consider the data recorded in Figure 2-45, where each line of raster cells is represented by a set of run-length codes. In general, run length coding reduces data volume, as shown for the top three rows in Figure 2-45. Note that in some instances run-length cod- ing increases the data volume, most often when there are no long runs. This occurs in the last line of Figure 2-45, where frequent changes in adjacent cell values result in many short runs. However, for most the- matic data sets containing area information, run-length coding substantially reduces the size of raster data sets.
map generalization
the unavoidable approximation of real features when they are represented on a map. Not all the geometric or attribute detail of the physi- cal world are recorded; only the most important characteristics are included. The set of features that are most important is sub- jectively defined and will differ among users.
Voxels
volume elements