Which of the following statements best describes the characteristics of the Mercator projection?

Mercator projection

The Mercator projection is a cylindrical map projection presented by the Flemish geographer and cartographer Gerardus Mercator in 1569. This map projection is practical for nautical applications due to its ability to represent lines of constant course, known as rhumb lines, as straight segments that conserve the angles with the meridians. Although the linear scale is equal in all directions around any point, thus preserving the angles and the shapes of small objects, the Mercator projection distorts the size of objects as the latitude increases from the equator to the poles, where the scale becomes infinite. A classic example of the distortion that this projection causes is that it projects Greenland and Antarctica to appear much larger than they actually are relative to land masses nearer the equator, such as Central Africa. Another distortion this projection causes is that it makes Greenland appear larger than Australia, while Australia is approximately three-and-a-half times larger than Greenland. We have plotted some examples of the Mercator projection to show the distortions in shapes that it causes in Fig. 12.3.

The following equations place the x-axis of the projection on the equator and the y-axis at longitude λ0, such that

x=λ−λ0,y=ln⁡(tan⁡θ+sec⁡θ).

The formulas for the inverse of this projection are given by

θ=2tan−1⁡(ey)− 12π,λ=x+λ0.

Universal Transverse Mercator (UTM)

The Universal Transverse Mercator (UTM) projection, developed by the U.S. Army, is widely used in topographic maps. This projection is recommended for areas lying between 84°N to 80°S. In UTM, the earth surface is divided in 60 zones, each 6° wide in the longitudal direction resulting in rectangular graticule mesh (Fig. 3.16). These are numbered sequentially from west to east. The western edge of the first zone touches the 180° W meridian and the eastern edge of the 60th zone touches the 180° E meridian. In the latitude direction, each zone covers an area of 8° (except the northern most zone that covers 12°). The bottom-most zone (80°S to 72°S) is assigned letter C and the topmost letter X. The origin of each zone is located at a point at the equator where it is intersected by the central meridian of the zone. The eastings of the origin of each zone is 500,000 m. Regarding northings, for the northern hemisphere it is 0 at the equator and for southern hemisphere, it is 1,000,000 m at the equator.

1.10.1 Geospatial Data Acquisition Tools

The importance of geospatial data on estuaries and coastal waters is not in question. The most primitive type of geospatial data is maps. Maps came into general use in the fifteenth and sixteenth centuries in Europe (e.g., the development of the Mercator projection in 1569). Maps have a strong visual impact and are useful for enabling people to grasp particular facts or concepts. Generally, maps include the following information:

cardinal points,

location (latitude and longitude),

height of land,

natural landmarks (mountains, valleys, and plains),

water districts (seas, lakes, and rivers),

administrative boundaries (national, regional, and local),

infrastructures (road, rails, and structures), and

land use (natural vegetation and habitats).

1.10.1.1 Topographic Maps and Bathymetry

A topographic map can be a base map for general use. Since the 1970s, extensive efforts to collect detailed topographic information from aerial photographs have been made. The US Geological Survey (USGS) established protocols for using 1:130K aerial photographs to obtain 5–10-acre resolution, that is, the target mapping unit (TMU). This was followed by protocols for using 1:80K aerial photographs with 3–5-acre TMU. In the 1980s, the USGS’s National High-Altitude Photography Program (NHAP) was started obtaining wider and more precise topographic maps. It used 1:56K colored aerial photographs to obtain 1–3-acre TMU, which was then followed by using 1:40K aerial photographs with ≤1-acre TMU. In the 1990s, topographic map creation entered the digital era. The TMU was set to 0.5–0.1 acre, and topographic data were able to be stored as a global digital elevation model (DEM) instead of a visual image.

In 1996, GTOPO30, a DEM with a horizontal grid spacing of 30 arcsec (∼1 km), was completed. It is derived from several raster and vector sources of topographic information. For easier distribution, GTOPO30 has been divided into 33 tiles that cover the whole world. In 2000, the Shuttle Radar Topography Mission (SRTM) completed collection of elevation data on a near-global scale to generate the most completed high-resolution digital topographic database of the Earth possible at the time. SRTM consisted of a specially modified radar system that flew onboard the space shuttle Endeavour during an 11-day mission in February of 2000. SRTM is an international project spearheaded by the National Geospatial-Intelligence Agency (NGA) and the National Aeronautics and Space Administration (NASA). The SRTM data are available at the USGS’s EROS Data Center for download via file transfer protocol.

Worldwide bathymetry can be obtained from the General Bathymetric Chart of the Oceans (GEBCO). GEBCO aims to provide the most authoritative, publicly available bathymetry of the world’s oceans. It operates under the joint auspices of the Intergovernmental Oceanographic Commission (IOC) (of the United Nations Educational, Scientific and Cultural Organization (UNESCO)) and the International Hydrographic Organization (IHO). GEBCO produces a range of bathymetric data sets and products, including global gridded bathymetric data sets: the GEBCO_08 Grid (at 30-arcsec intervals) and GEBCO One Minute Grid (at 1-arcmin intervals); a global set of digital bathymetric contours; the GEBCO Gazetteer of Undersea Feature Names; the GEBCO Digital Atlas, and the GEBCO world map (Figure 2).

Figure 2. GEBCO World Map based on GEBCO One Minute Grid, a global bathymetric grid with 1-arcmin spacing.

Reproduced with permission from GEBCO world map, http://www.gebco.net/.

The National Oceanic and Atmospheric Administration (NOAA) provided regional sets of digital bathymetry data in the United States as the National Ocean Service (NOS)’s Estuarine Bathymetry. It is a digital raster compilation of NOS’ hydrographic survey data for selected US estuaries. Bathymetry data sets are offered in the DEM format in both 30-m and 3-arcsec resolutions for 70 estuaries. The extent of the bathymetry data for each estuary is defined by the water boundary component of the NOS Coastal Assessment Framework (CAF)’s estuarine drainage area (EDA). While the covered elevations do not extend beyond the high water line, these data provide important information on estuarine resources. Google Earth visualization files have been available for viewing bathymetry and land topography in a combined image since July 2006. Figure 3 shows an example of NOS estuarine bathymetry (combining bathymetry and land topography) for San Francisco Bay.

Figure 3. San Francisco Bay by NOAA’s Special Projects Office.

Projected by Google Earth™.

Google Earth version 5.0 has been equipped with new ocean layers since 2009. It enables users to travel virtually around underwater volcanoes, watch videos about exotic marine life, read about nearby shipwrecks, contribute photos, and watch footage of historic ocean expeditions. It provides accessible and high-quality combined views of topographical maps and bathymetry data.

1.10.1.2 Attribute Map Based on Remote Sensing

Remote sensing is defined as “acquisition of information about the land, sea and atmosphere by sensors located at some distance from the target of study” (Haines-Young, 1994). By using remote sensing, the attributes of land use and land cover can be added to a base map. Certain land covers have different albedos (reflectance of sun light) over different wavelengths (Figure 4; Spalding et al., 1997). Thus, spectral apparatus can detect differences in the surface texture of the Earth.

Figure 4. Typical spectral responses of important ground attributes.

Modified with permission from Spalding, M.D, Blasco, F., Field, C.D. (Eds.), 1997. World Mangrove Atlas. The International Society for Mangrove Ecosystems, Okinawa, Japan, 178 pp.

Remote sensing uses platforms such as satellites, airplanes, radio-controlled planes, balloons, and kites. The most common and economic platform for obtaining an attribute map for a wide area (national to global) is satellites (Table 1). In 1972, the first Earth observation satellite, Landsat, was launched by the US. It contributed to boosting remote-sensing technologies. The Multispectral Scanner System (MSS) and the Thematic Mapper (TM) are the major apparatuses of Landsat. Landsat maps the world with images covering areas around 185 × 170 km. The satellite is used for land-based resource mining and environmental monitoring. The TM apparatus in particular is used for coastal monitoring through its thermal infrared bands. In the 1980s, Satellite Pour l’Observation de la Terra (SPOT) and NOAA satellites were launched as second-generation satellites. They had high-resolution visible (HRV) imagers up to 10-m spatial resolution and an advanced very high-resolution radiometer (AVHRR) to detect surface temperature distribution. In the 1990s, more varieties of apparatus were developed. European Remote-Sensing Satellite 1 (ERS-1) had an active microwave radiometer to observe land water content. Terra and Aqua had an advanced spaceborne thermal emission and reflectance radiometer (ASTER) and a moderate resolution imaging spectrometer (MODIS), respectively.

Table 1. Summary of main satellites used for land-cover mapping

Satellites	Sensors	Since	Band number and spectral coverage	Spatial resolution(pixel size)	Repetition rate and size of image	Altitude (km)	Suitable mapping scale
Landsat-1,2,3	MSS	1972	0.5–0.6 µm	80 m	16 days	913 and 705	National
1975	0.6–0.7 µm		185 km
1978	0.7–0.8 µm
	0.9–1.1 µm
Landsat-4,5	TM	1982	0.45–0.52 µm	30 m	16 days	705	Local
1984	0.52–0.60 µm	30 m	185 km
	0.63–0.69 µm	30 m
	0.75–0.90 µm	30 m
	1.55–1.75 µm	30 m
	2.08–2.35 µm	30 m
	10.4–12.5 µm	120 m
SPOT-1,2,3	HRV	1986	0.5–0.59 µm	20 m	26 days	833	Local
1990	0.61–0.68 µm	20 m	60 km
1993	0.79–0.89 µm	20 m
	(Panchromatic 0.51–0.73 µm)	10 m
NOAA	AVHRR	1987	0.58–0.68 µm	HRPT, LAC 1 km	Daily	1450	Global and regional
0.725–1.1 µm	GAC 4 km	2 700 × 2 700 km
3.55–3.95 µm
10.5–11.3 µm	GVI 15 km
11.5–12.5 µm
MOS-1	MESSR	1987	0.51–0.59 µm	50 m	17 days	909	Local
0.61–0.69 µm	100 km
0.72–0.80 µm
0.80–1.10 µm
ERS-1 and 2	AM1 (SAR)	1991	5.3 GHz	30 m	3 days	785	Local
100km
Sea Star	Sea WIFS	1994	0.402–0.422 µm	LAC 1.13 km	Daily	705	Global and regional
0.433–0.453 µm	GAC 4.5 km	2 800 km
0.480–0.500 µm
0.510–0.530 µm
0.555–0.575 µm
0.655–0.675 µm
0.745–0.785 µm
0.845–0.855 µm
ADEOS	AVNIR	1996	0.43–0.50 µm	16 m	41 days	797	Local
0.52–0.62 µm	16 m	80 km
0.62–0.72 µm	16 m
0.82–0.92 µm	16 m
0.52–0.72 µm	8 m
SPOT-4,5,6	HRVIR	1996	0.5–0.59 µm	20 m	26 days	833	Local
1999	0.61–0.68 µm	20 m	60 km
2000	0.79–0.89 µm	20 m
	1.55–1.75 µm	20 m
	(Panchromatic 0.61–0.68 µm)	10 m
Landsat-7	ETM+	1998	0.5–0.90 µm	15 m	17 days	705	Local
0.45–0.52 µm	30 m	185 km
0.63–0.69 µm	30 m
0.76–0.90 µm	30 m
1.55–1.75 µm	30 m
2.08–2.35 µm	30 m
10.4–12.5 µm	60 m
Landsat-7	HRMSI	1998	0.5–0.90 µm	5 m	17 days	705	Local
0.45–0.52 µm0.52–0.60 µm	10 m	60 km
0.63–0.69 µm	10 m
0.76–0.90 µm	10 m
	10 m
EOS-AM1, AM2 (Terra)	ASTER	1998	0.52–0.86 µm	15 m	Daily	705	Local
2003	1.60–2.43 µm	30 m	60 km
	8.3–11.3 µm	90 m
EOS-AM1,AM2 (Terra)	MODIS–N	1998	0.659–0.895 µm	250 m	Daily	705	National
2003	0.470–2.13 µm	500 m	2 330 km
	0.415–0.865 µm	1000 m
	0.905–0.940 µm	1000 m
	3.75–14.24 µm	1000 m
EOS-PM1,PM2 (Aqua)	MODIS–N	2007	0.659–0.865 µm	250 m	Daily	705	National
2002	0.470–2.13 µm	500 m	2 330 km
	0.415–0.865 µm	1000 m
	0.905–0.940 µm	1000 m
	3.75–14.24 µm	1000 m

AMI: Active Microwave Instrumentation; ASTER, Advanced Speceborne Thermal Emission and Reflectance Radiometer; AVHRR, Advanced Very High Resolution Radiometer; AVNIR, Advanced Visible and Near Infrared Radiometer; ETM+, Enhanced Thematic Mapper Plus; GAC, Global Area Coverage; GVI, Global Vegetation Index; HRMSI, High Resolution Multispectral Stereo Imager; HRPT, High-Resolution Picture Transmission; HRV, High Resolution Visible; HRVIR, High Resolution Visible and Middle Infrared; LAC, Local Area Coverage; MESSR, Multispectral Electronic Self Scanning Radiometer; MODIS-N, Moderate Resolution Imaging Spectrometer-Nadir; MSS, Multispectral Scanner System; SAR, Synthetic Aperture Radar; Sea WiFS, Sea-viewing Wide Field Sensor; TM, Thematic Mapper.

This progress of satellite-based remote sensing enabled vegetation to be mapped-specific vegetation. For example, extensive efforts to create a global mangrove map have been made using satellite-based remote sensing (Spalding et al., 1997). Furthermore, the oceanic environment, including marine winds, radiative processes, air–sea interaction, wind waves and wind, ice, ocean currents, and land–ocean interactions, have been monitored using satellite images (Jones et al., 1993).

Currently, the state of the ocean layer in Google Earth version 5.0 includes daily dynamic sea-surface temperature (SST) provided by the US Navy. The US Navy creates a high-resolution daily optimal blend of SST data from NOAA, NASA, and the European Organisation for the Exploitation of Meteorological Satellites (EUMETSAT). A view of the most recent available global overlay along with an animation of past months is available.

Cartometric Applications

In the 1400s, advances in ship-building design and other nautical instrumentation technologies were making long-distance exploration into uncharted waters more feasible. This expanding frontier greatly increased geographic knowledge and the need for maps to represent these new discoveries. In addition, ocean-going commerce between nations was becoming an important activity. The portolan chart was one of the first navigational aids that enabled sailors to lay out a sailing course on a map. While these maps were generally produced without showing the graticule, contemporary observation suggests that the equirectangular projection with its square graticule was at least a likely foundation. However, the eventual watershed projection for navigation was the Mercator projection (see Figure 12b), developed by Gerardus Mercator in 1569, and probably one of the most recognizable projections. A conformal cylindric projection, the Mercator, was never intended to be displayed as a world map, although many atlases of the nineteenth and twentieth centuries relied heavily upon this projection for their world maps. Rather, the Mercator projection was designed to permit rhumb lines drawn on the projection to be straight lines. This characteristic was particularly useful to navigators in that they could lay out a rhumb line on the map and then follow its compass direction from the origin to destination.

Significant leaps in transportation occurred in the twentieth century, which ushered in the ‘air-age’. Projections were called upon that highlighted a view of the Earth from space and allowed, for instance, airline routes to be correctly displayed. The gnomonic projection (see Figure 13a), known for centuries, was re-introduced since it shows all great circles and therefore the shortest routes as straight lines. Other projections utilized during this time included the azimuthal equidistant and orthographic. For instance, the azimuthal equidistant projection (see Figure 13b) shows the entire world in a circle and allows the distance from the center of the projection to any point to be accurately computed. On the other hand, Richard Edes Harrison’s Look at the World: The Fortune Atlas for World Strategy relied heavily upon the orthographic projection (see Figure 13c) to show the spatial association of various landmasses around the world.

The launch of satellites and the ability to track their paths on the Earth required the creation of special projections. In the early 1970s the United States launched Landsat, a government-funded satellite program. Developing a projection that displayed the ground track of the satellite’s swath path at correct scale that was also conformal proved to be a problem. John Snyder, a chemical engineer, developed the space oblique Mercator projection as a solution to the problem. Later, in 1977, a cylindric projection was developed by Snyder that displayed the ground tracks of the Landsat satellite as straight lines (see Figure 14). Today, satellite ground-tracking maps rely upon the equirectangular projection, with curved rather than straight orbital paths being shown.

7.4 Map Projections

A map projection is a method of representing the surface of the Earth on a two-dimensional plane. This is the process of creating a map of the Earth's surface all of which distort the Earth's surface in some way as originally proved by Gauss who said that no sphere can be represented on a plane without distortion. These distortions can be minimized depending on the specific application of the map projection. Because there are many different applications, there are a consequent large number of different map projections. Only a few types will be presented here as examples, but the interested reader can find many volumes that are addressed to subject of map projections (e.g. Martín-Asín, 1990; Kraak and Ormeling, 1996).

For simplicity it will be assumed that the Earth's surface is a sphere rather than the precise ellipsoid or geoid as discussed earlier. The purpose of a map projection is to specify the transformation between the curved elliptical surface of the Earth and the flat planar surface of the map. One example is the Albers projection shown here in Fig. 7.24.

This projection is a conic, equal area map projection that uses two standard parallels. This particular projection shows areas correctly, but to do so, it alters the shapes and scales of these areas. It is used by the US Geological Survey and the US Census Bureau.

The most widely used map project is the “transverse Mercator”, which is convenient for large-scale maps as it preserves size and shape for areas within the same limited range of latitudes. The projection geometry is described here in Fig. 7.25, which reveals that this is a cylindrical projection with the tangent points of the cylinder at both poles. A particular “transverse Mercator” projection called the Universal Transverse Mercator (UTM) is probably the most recommended one from latitudes 84°N to 80°S (Fig. 7.26A). For polar regions for latitudes North of 84°N, and South of 80°S, the Universal Polar Stereographic (UPS) is widely used (Fig. 7.26B). Both are coordinate systems that use a metric-based Cartesian grid laid out on a conformally projected surface. The properties of the UTM are as follows: it is conformal (shapes are preserved), its central meridian is automecoic (distances are preserved), the equator and the central meridian intersection is the origin of the (x,y) coordinates, which are expressed in meters. The whole globe is “sliced” in 60, 6° fuses, with the Greenwich meridian lying between fuses 30 and 31. The advantage is that no point is too far away from the central meridian, so the distortions in the fuse are small, but this benefit is achieved at the expense of the discontinuities.

The transverse Mercator projection is mathematically the same as the standard Mercator projection except that it is oriented around a different access. The standard Mercator projection has the cylinder oriented North-South (Fig. 7.27), which results in the familiar stretching of the meridional lines as higher latitudes.

Once the choice is made between projecting on to a cylinder, a cone or a plane, the shape of the map features must be specified. This is done by specifying how the projection surface is located relative to the globe. It may be normal so that the map surface of symmetry coincides with the Earth's axis or it may be transverse that is at right angles to the Earth's axis. The map surface may be tangent in just touching the Earth's surface or it may be secant where the map plane intersects or “slices” through the globe.

A sphere or globe is the only way to depict the Earth that exhibits constant scale throughout the entire map in all directions. A flat map cannot achieve this property for any area regardless of projection method or limited size of the area of interest. Scale depends on location on the Earth, but not on orientation. Scale is constant along any line of parallel (latitude) in the direction of the latitude.

Map projections can be classified by the type of projection surface onto which the globe is projected. Examples are cylindrical (e.g., Mercator), conical (e.g., Albers), and azimuthal or planar (e.g., stereographic used frequently for polar maps). Another way to classify map projections is according to the properties that they preserve such as: preserving direction (azimuthal), preserving local shape (conformal or orthomorphic), preserving area (equal-area), preserving distance (equidistant), and preserving the shortest route (gnomonic). Because a sphere cannot be flattened, it is impossible to have a map projection that is both equal-area and conformal. There are, of course, many other mathematical formulations for map projections that do not fit easily into any of these classification schemes.

The National Atlas of the United States uses a Lambert azimuthal, equal-area projection to display the country: it is a particular mapping from a sphere to a disk, which accurately represents area in all regions of the sphere, but it does not accurately represent angles. Conformal maps are used for navigational or meteorological charts. The US Geological Survey uses a conformal projection for many of its topographic maps. Equidistant projections are used for radio and seismic mapping and often for ship navigation. Aeronautical charts employ maps that preserve direction and are called again azimuthal or zenithal projections.

4.2 Rigid Body Rotation

Using Euler's Fixed Point Theorem, one can conveniently express the displacement of a plate by a rotation around its Euler pole (see Chapter 7 by Stein and Klosko). To describe the motion of, say, the North American Plate, one does not have to specify how many kilometers San Francisco moved in which direction, or what happened to New York, etc. Let us write the rotation of Plate A relative to Plate B as ARB, its Euler pole as APB, and relative velocity and relative angular velocity as AVB, and AωB. When plate tectonics was introduced, its goal was to substantiate the supposed rigid motion of plates. For this purpose, the proof that actual plate motions satisfied Euler's theorem was sufficient. Consider the case of two plates A and B (Fig. 8). The plate tectonic theory predicts the following: (1) The direction of the relative motion between A and B, i.e., the direction of the transform fault, should be parallel to the small circle on the globe with APB as its pole; (2) the magnitude of the relative velocity should be in proportion to sin(q), where q is the angular distance from APB. A more intuitive picture would be a world map using a Mercator projection, but with the Euler pole APB as its pole. We see that the direction of the relative motion (i.e., the transform fault) is parallel to the lines of “latitude,” and the length of the vector that represents the relative velocity is constant regardless of “latitude.” Confirmation of these predictions was the starting point of plate tectonics.

McKenzie and Parker (1967) investigated the relative motion of the Pacific Plate and the North American Plate, and saw that the projections onto the horizontal plane of slip vectors of several earthquakes at the boundaries of these two plates were nearly parallel to the lines of “latitude” in a Mercator projection with Euler pole at 50°N, 85°W. The Euler pole position was determined from the directions of San Andreas Fault and the average slip vectors of aftershocks of the 1964 great Alaskan earthquake in the Kodiak Island region of the Aleutians.

Morgan (1968) began independently with the same concept, but expanded it to encompass the global view. He took into consideration not only slip vectors of earthquakes and the directions of transform faults, but also the distribution of the spreading rate estimated from the width of geomagnetic stripes. For example, he determined the Euler pole of the relative motion between the American and African Plates (1) from the points of intersection of great circles perpendicular to both transform faults and slip vectors of earthquakes associated with the Mid-Atlantic Ridge and (2) by matching the distribution of spreading rates with the relations of sin(q). These independent estimates agreed well.

Le Pichon (1968) was inspired by Morgan's work and enthusiastically proceeded to undertake a systematic verification of the plate theory. He divided the Earth's surface into six large plates, and tried to find, by the method of least squares, the set of plate motions that would best fit with both the width of geomagnetic stripes and the strikes of the transform faults. He then drew a Mercator projection with the Euler pole thus obtained as its pole, and demonstrated that the two “shoulds” stated above were satisfied.

A natural extension of the plate tectonic methodology is its use for quantitative reconstruction of continents and ocean basins in the geologic past. Where dated sea-floor spreading magnetic lineation patterns are available on both sides of a ridge, the part of the sea floor between the ridge and an isochron can be resorbed by appropriately rotating the plates and this gives past positions of the plates (continents and ocean basins). Le Pichon (1968) pioneered this type of reconstruction, which has been followed by many, including McKenzie and Sclater (1971) for the Indian Ocean and Pitman and Talwani (1972) for the Atlantic Ocean. Where subduction plays major role, namely, the Pacific Ocean, it is not possible to estimate the past position of continents from magnetic lineations alone, but the evolution of the Pacific Ocean itself and its margin can be discussed (Hilde et al., 1977).

UNIVERSAL MERCATOR GRID SYSTEM

Although latitude and longitude and the Public Land Survey are the most often used system for determining locations on the earth, a third method, which is somewhat more complicated, called the Universal Tranverse Mercator (UTM) Grid System, is also shown on most topographic maps published by the USGS. This is based on the transverse Mercator projection and covers the earth's surface between 80 south and 84 north latitudes.

The UTM system involves establishing 60 north-south zones, each of which is six degrees longitude wide. In addition, each zone overlaps by two degrees into adjoining zones. This allows easy reference to points that are near a zone boundary, regardless of which zone is in use for a particular project. Each UTM zone is assigned a number. Grid zone 1 is assigned to the 180 meridian with zones numbered consecutively eastward. A false origin is established 500,000 m west of the central meridian of each UTM zone. In the Northern Hemisphere, this origin is on the equator; in the Southern Hemisphere it is 10,000,000 m south of the equator. A square grid, with lines extended north and east from the origin, provides a basic locational framework. With this framework, any point on the earth's surface, within each zone, has a unique coordinate. UTM coordinates are shown on the edges of many USGS topographic maps.

Although the latitude and longitude system is used for locating points on a sphere, the UTM system is a location grid that uses straight lines that intersect at right angles on the flat (plane) map sheet. Each UTM grid area is divided into true squares, each consisting of 100,000 m2. Because meridians of longitude converge at the poles, the straight lines of UTM do not follow the lines of longitude on a map.

GIS as Threat

Google Earth abandons many of the cherished icons of cartography such as projections, rendering them largely irrelevant, and in this sense can be seen as threatening to a discipline's cherished expertise. Similarly, GIS enables anyone equipped with data and a few simple tools to produce a map that previously would have required the expertise of a trained cartographer. While great efforts have been made by developers of the more elaborate GIS packages to include support for sophisticated cartographic techniques, such as methods of cartographic generalization and alternative techniques for assigning class intervals to choropleth maps, nevertheless it is easy to find examples of the misuse of GIS. For example, several recent news stories of the missile threat of North Korea have included maps purporting to show the areas reachable by missiles of a given range launched from Pyongyang – by drawing concentric circles on a Mercator projection. Any cartographer, and hopefully most trained GIS users, would know that the scale of the Mercator projection changes rapidly at high latitudes, and that on this projection the locus of equal distance from Pyongyang is only a circle when the distance is vanishingly small. Unfortunately, the result is a severe underestimate of the areas that can be reached (Figure 1).

It is sometimes argued, therefore, that GIS, and the popularization of digital geographic information technologies in general, represents a threat to the field of cartography – that ‘GIS is killing cartography’. Map making, it is argued, is a sophisticated pursuit that is best left in the hands of experts. Maps are often persuasive, capable of influencing opinion and policy; and just as the playing of concert pianos is limited to a few experts, so also the creation of maps should be limited to trained professionals. Attempts have been made in several jurisdictions to restrict mapping practice to accredited professionals, in some cases with success.

Another dimension to this argument surfaced in the early 1990s as part of a rapidly emerging social critique of GIS. In the late 1980s, Brian Harley had introduced the concepts of deconstruction to cartography, arguing that all maps were social constructions that could be read as texts for evidence about the agendas of their makers. These arguments found ready acceptance, since maps have always been important as tools of power, and mapmakers have often followed quickly on the heels of conquerors. The selection of features for maps, and the styles in which selected features are rendered, are part of the process of cartographic design, and clearly open to conscious or subconscious manipulation for purposes that range from visual clarity to more sinister coercion.

At the time, cartographers saw GIS as a new and wildly popular tool that appeared insensitive to these ethical arguments. GIS seemed to be grounded in the naïve assumption that one could achieve a scientifically rigorous description of the world, and store it in precise form in a digital computer – that the contents of a GIS database represented the results of objective, replicable scientific measurement. The ability to compute measures such as area to large numbers of decimal places served to reinforce this view, and it was clear that GIS was being marketed by commercial software developers as a scientifically rigorous approach to geographic problems. To cartographers influenced by Harley, GIS users were the barbarians, sensitized to none of the nuances of mapping practice or to the tension between cartography as science and cartography as art.

These critiques came to a head in the early 1990s, and led to a series of meetings in which each side slowly achieved an understanding of the other's position. Today, the social context of GIS is one of the major themes of GIS research, and many developments have addressed the issues raised by Harley and others. The notion of objective truth, reflected in the use of such terms as accuracy and error, has been replaced by concepts of uncertainty and of the relationship between truth and power, in the realization that many aspects of GIS practice are not replicable, that many of the key definitions are inherently vague, and that seemingly objective technologies can be molded to the agendas of their owners and sponsors.

V Additional Topics in Surveying

5.4.3.2 SIFT System

The NOAA propagation database is described in detail in Gica et al. (2008). SIFT system is based on a unit source function methodology, whereby the model runs are individually scaled and combined to produce arbitrary tsunami scenarios. Each unit source function is equivalent to a tsunami generated by a Mw 7.5 earthquake with a rectangular fault 100 km by 50 km in size and 1 m slip. These are similar to the T1 Mw 7.5 events (see Table 5.1). The faults of the unit functions are placed adjacent to each other. When the functions are linearly combined, the resultant source function is equivalent to a tsunami generated by a combined fault rupture with assigned slip at each subfault.

The MOST model that is used to generate the scenarios and the bathymetry for the Pacific Ocean is based on the Smith and Sandwell (1994) 2 arc minute data set. The model utilizes the bathymetry data in the original Mercator projection format of the Smith and Sandwell data, where the grid cells become smaller for locations farther away from the equator. The data are subsampled to twice coarser resolution (4 arc minutes at the equator) of the original data set. There are currently a total of 1400 unit sources distributed throughout the Pacific, Atlantic, and Indian Oceans. These are arranged in several rows along known fault zones, to cover areas of potential tsunami sources. The rake is set at 90°, as in T1. The main differences with the T1 scenarios are that the dip and depth vary according to known assessments of the fault geometries (Kirby et al., 2006). Where depth estimates are not available, the depth of the top row of sources is set at 5 km and the depth of the lower rows of sources depends on the dip of the top rows.

Other relevant specific details of the model configuration are: spatial resolution: 4 arc minutes, minimum offshore depth: 20 m, time step: 15 s, sea level (and depth-averaged currents) at every fourth grid point are saved every four time steps (i.e., 1 min) and the model is run for 24 h of model time.

For the model forecasts considered here, the NOAA system uses inversion techniques to select the best combination of unit source functions in order to match observations of sea level from the tsunami meters (Gica et al., 2008; Titov et al., 2005). The inversion is done by performing a positively constrained combined at least-squares fit of model-data comparisons for all DART locations for a given combination of unit sources. The inversion defines the scaling coefficients for each unit source in the combination.