statistical techniques in geographical analysis

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Statistical Techniques in Geographical Analysis By Damon Verial, eHow Contributor Share Print this article Geographical analysis is the application of analytical techniques to geographical data. Much of the results in this field would not be possible without the strong statistical techniques that support the analysis of data. Geographical analysts rely on many statistical techniques, including probabilistic methods, hypothesis testing, sample selection and statistical inference, to perform analyses that allow for the results in this field. Other People Are Reading How to Select a Data Analysis Technique Techniques of Statistical Analysis 1. Probability o Probability is a useful tool in geographical analysis, especially in situations where hard data does not exist. The application of probability can allow a geographical analyst to make reasonable predictions in these situations. Consider the lack of data regarding how people in the United States migrate and change residences. A geographical analyst can use the probabilities of moving certain distances along with the probabilities of moving certain directions to predict the average migration patterns of citizens of the United States. Hypotheses Tests o In geographical analysis, analysts often want to make meaningful comparisons. However, whether the data be air pollution levels in big cities or state population growth, simply looking at the data to determine if there are differences present is poor method to make this determination.

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Statistical Techniques in Geographical Analysis

Statistical Techniques in Geographical Analysis

By Damon Verial, eHow Contributor

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Print this articleGeographical analysis is the application of analytical techniques to geographical data. Much of the results in this field would not be possible without the strong statistical techniques that support the analysis of data. Geographical analysts rely on many statistical techniques, including probabilistic methods, hypothesis testing, sample selection and statistical inference, to perform analyses that allow for the results in this field.

How to Select a Data Analysis Technique

Techniques of Statistical Analysis 1. Probability

Probability is a useful tool in geographical analysis, especially in situations where hard data does not exist. The application of probability can allow a geographical analyst to make reasonable predictions in these situations. Consider the lack of data regarding how people in the United States migrate and change residences. A geographical analyst can use the probabilities of moving certain distances along with the probabilities of moving certain directions to predict the average migration patterns of citizens of the United States.

Hypotheses Tests

In geographical analysis, analysts often want to make meaningful comparisons. However, whether the data be air pollution levels in big cities or state population growth, simply looking at the data to determine if there are differences present is poor method to make this determination. Statistics offers geographical analysts the ability to use hypotheses tests to conclude with high probability whether differences are present and in what ways the things being compared differ.

Data Selection

Geographical analysis relies heavily on finding data sets with which to perform analyses; yet the choice of data is a complicated procedure. To avoid collecting a biased data set, geographical analysts must employ a suitable sampling method for the situation. How to appropriately select a sample is a well-researched topic of statistics, and geographical analysts make heavy use of the well-founded statistical practice of selecting unbiased, representative samples.

Inference

Often, geographical analysts perform analysis on a small geographical area because of restrictions in funding, time or other resources. In spite of this, analysts execute their analyses with the overall goal of making inferences about larger geographical areas. The problem is that without the appropriate statistical techniques these inferences will not hold. Statistics inference allows analysts to move away from simply describing their sample and move toward using their results to make larger, more general conclusions.

http://www.ehow.com/info_8074582_statistical-techniques-geographical-analysis.htmlhttp://education.nationalgeographic.com/education/geographic-skills/?ar_a=1What is Cartography?

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Cartography is the art and science of map making, practiced by cartographers. Humans have been drawing maps for thousands of years, as part of an effort to understand their environment. The quest for an accurate map drove explorers to adventure to far-flung areas well into the 1700s, and cartographers in the modern day find frequent employment still, thanks to constant political and geological changes around the world. To train in cartography, a student should be prepared to take years of courses in multiple disciplines.

The term comes from two Greek words, chartis, meaning map, and graphos, meaning to draw or write. In historic times, an individual cartographer hand drew a map in entirety, often with limited information. Modern practitioners of cartography have the advantage of computers and other equipment to assist them, making their maps more precise. The science of cartography has also evolved, as many maps have become multimedia data explosions, chock full of information for the reader.

Basic cartography covers two data components. The first is location data, indicating where the area being depicted is located. In ancient maps, location data often showed where something was in relation to something else, but modern maps usually use geographical coordinates such as latitude and longitude to orient their features. The second type of data is attributional data, showing bodies of water, mountains, valleys, hills, and other geographical features of interest and of note.

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A map of the world reflects an immense mathematical and aesthetic challenge, that of translating the globe to a two dimensional surface. Many cartographers have struggled with this issue over the centuries, striving to project the features of the globe accurately and effectively. Numerous approaches have been taken to solve this problem, including the Mercator Projection, a map which distorts geological features north and south of the Equator in order to fit the globe into a neat rectangle. Other maps portray the globe in sections, reducing the amount of distortion necessary.

The skills needed for cartography are immense. Cartography relies heavily on math to represent the Earth, along with science to help describe and understand geological features. Specialized maps may include things like ocean soundings, which requires a knowledge of oceanography, or unique rock formations, which implies geological study of the region. Knowledge of ongoing political events is also important, as nations divide, change names, or disappear more frequently than many people realize.

The products of cartography can be divided into two rough types of map, although they may frequently overlap. A topographical map is one which is designed to be true to the landscape that it is depicting. Topographical maps usually include elevations, major geographical features, and other information which someone who use to orient him or herself. These maps can often be used for decades, unless a major geological event such as a volcanic eruption or earthquake occurs.

A topological map, on the other hand, is used for conveying information such as highway routes, dangerous regions of a country, or population density. Topological maps can sometimes be quite complex, showing multiple important features to readers to highlight and educate, and they change frequently as the lives of the people and places depicted on them change.

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What Are the Cartographic Sciences ?

The cartographic sciences are geodesy, surveying, photogrammetry, remote sensing, geographic information systems (GIS), global positioning systems (GPS) and, of course, mathematics and statistics. In recent years, multimedia and virtual reality became part of the cartographic experience. These are all separate, though somewhat overlapping, disciplines, and they share an intimate relationship with cartography; indeed some have their own cartographic components. A working acquaintance with these fields is an essential part of the education of the modern cartographer.

Geodesy

Geodesy is a very specialized science concerned with determining the shape and size (the 'figure') of the earth--not the solid earth, but the geoid, the surface defined by mean sea level--and establishing a framework of points whose locations are known very precisely in terms of latitude and longitude. This is achieved in two ways, by studying the earth's gravitational field and by conducting very high-accuracy surveying operations. At one time, such work was entirely ground-based, but satellite observations are now routine. Geodesy plays a fundamental role in cartography, for in order to map the earth, it is obviously necessary to know how big and what shape it is and to have reference points of known locations on its surface.

Surveying

If geodesy is unfamiliar to most people, surveying is quite the opposite, for almost everyone has seen the surveyor at work on city streets with transit, level or distance meter. There are many branches of surveying, including engineering surveys (carried out in connection with construction projects), cadastral surveys (concerned with property boundaries), hydrographic surveys (depicting water bodies) and mine surveys (outlining what is underground). The relation between surveying and cartography is very close indeed, and the end-product of the surveyor's work is often a map of some sort. One branch of surveying--topographic surveying-- has the production of maps as its express aim. Surveying, like cartography, has undergone major changes in recent years, but none so dramatic as those being brought about by Global Positioning Systems (GPS).

Global Positioning Systems (GPS)

A constellation of twenty-four satellites operated by the U.S. Department of Defense comprises GPS. It enables surveyors to determine ground locations very precisely at the click of a button on a hand-held receiver under any weather condition. GPS is revolutionizing the practice of surveying at a very fast pace. Today, a position on the earth's surface can be determined within fractions of a centimeter. The standard piece of information provided by a GPS receiver is a readout of the calculated latitude and longitude of a given position. These latitude and longitude positions obtained from a GPS can be plotted on a chart or on a map.

Photogrammetry

Photogrammetry means literally measurement with light and has as its principal aim the production of topographic maps from aerial photographs. An earlier technological change that revolutionized topographic surveying, photogrammetry emerged in the 1930s. Previously topographic maps (large-scale maps in sheet form showing natural and cultural features in the landscape) were produced by traditional ground surveying methods, and while ground surveys are still needed, most of the detail on these maps--the rivers, coastlines, roads, buildings, contours, and so on--is now derived from airphotos. The work is done by the operator of a photogrammetric plotter, a complex piece of machinery that enables one to trace landscape features from a three-dimensional 'model' of the earth's surface created by viewing airphotos stereoscopically. In modern photogrammetry, the movements of the tracing device, or 'floating mark,' are translated directly into digital form and the map is plotted automatically.

Remote Sensing

A more recent discipline, dating from the 1960s, is remote sensing, the process of obtaining information about the earth's surface using sensors carried in aircraft and satellites. Though the discipline is new, the original form of remote sensing--aerial photography--dates from the nineteenth century, and techniques of airphoto interpretation have long been highly developed. All types of remote sensing involve the measurement of electromagnetic energy reflected from or radiated by the earth's surface, and photographic cameras (based on visible light) are now accompanied by other sensing devices operating at longer wavelengths. Examples are thermal scanners in the infrared waveband and radar systems in the microwaves. The information obtained may be in image form (like a photograph) or in digital form, and one of the most intriguing applications of remote sensing is the computer processing of digital multispectral data (data obtained simultaneously in more than one waveband) to produce land cover maps of the earth's surface. Another application of increasing importance is image mapping, the incorporation of a remote sensing image, enhanced by computer processing, into the map itself. Remote sensing, especially sensing from space, is a major source of mappable data, and as such plays a key role in modern cartography.

Geographical Information Systems (GIS)

Another new discipline, perhaps the most exciting of all, GIS is a computer-based system for handling geographical data, that is, data relating to the earth's surface. The word 'handling' conceals a wealth of different operations, however. Some, like data storage and retrieval, are fairly mundane, but others, especially analytical operations like buffering, overlay, network analysis and viewshed modelling, are truly staggering in their potential for solving real-world problems. Maps are integral to a GIS. Data are stored in the computer in the form of 'layers,' each in effect a digital map of some component of the landscape (e.g. a streams layer, a roads layer, a soils layer) and analyses are achieved by performing operations on these layers, sometimes one at a time, sometimes on several layers simultaneously. Each stage in an analysis is displayed in map form on a high-resolution computer monitor, and the end-product is very commonly itself a map. GIS has become a billion-dollar business since the early eighties, which is not surprising given the range of proven applications. These include forest management, urban planning, emergency vehicle dispatch, mineral prospecting, retail outlet location, maintenance of public utilities, and waging war, as well as a host of applications with purely scientific ends.

Mathematics and Statistics

Mathematics and statistics are heavily involved in the mapping process, not only because of the geometric aspects of describing locations in space, but also because of clear needs to describe and summarize the characteristics of spatial data. Through creative mathematical approaches, cartographers may find new solutions to solve spatial problems.

Multimedia (MM)

Computer systems allow for integrated access to a range of data through the means of stimulation of human senses using digital technology. This includes the integration of images, video and graphics, maps and photographs, text and sound and perhaps in the future smell and taste. This technology has a wide range of applications including education, scientific research, military activities and, of course, entertainment.

Virtual Reality (VR)

A computer system that is able to combine a mixture of real world experiences and computer generated material to allow for simulated real world representation produces a "virtual reality." VR addresses the construction of artificial worlds with clear spatial dimensions. The movie "Twister" is an excellent example how VR works. These same kind of images can be very useful for the scientist to model or demonstrate an event such as a natural hazard. Cartographers have a major role to play in the identification of VR as a potential research tool.

Cartography and the cartographic sciences are all concerned in some way with data relating to the earth's surface, whether it be data acquisition, management, analysis or display, and there is a growing trend, driven by a common dependence on computer technology, for the disciplines described here to move even closer together. Reflecting this trend, the term geomatics is used in Canada to denote an integrated multi-disciplinary approach to dealing with earth-related data. In a sense, geomatics is an umbrella term for cartography and the cartographic sciences.

http://www.cca-acc.org/careers-2.aspTypes of Maps:Projections

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A map is a representation of a place. There are many different types of maps that have different uses.

Projections: Maps are called projections because map-makers have to project a 3-D surface onto a 2-D map. A projection is a representation of one thing onto another, such as a curved 3-Dimensional surface (like the Earth) onto a flat 2-Dimensional map. There are 3 major types of projections: cylindrical, conic, and planar.

Since a map is 2-dimensional representation of a 3-dimensional world, compromises must be made in accuracy (some information must be lost when one dimension is ignored). Different maps differ in the relative accuracy of the depiction of the area, the shapes of objects, actual distances, and compass direction. Maps that focus on maintaining one feature (like preserving distance) must distort other features (like area, shape and compass directions).

Maps that accurately reflect area are often called equal-area maps (an example is the Albers equal-area conic map). Maps that maintain the shape of objects are called conformal. Maps that correctly show the distance between points are often called equi-distant maps (note that the shortest distance between two points on a map is generally not a straight line. but a curve). Navigational maps need accurate compass directions maintained on the map (like the Mercator map).

Related Terms:

central meridianA central meridian is a meridian that passes through the center of a projection. The central meridian is often a straight line that is an axis of symmetry of the projection.

conic projectionA conic projection is a type of map in which a cone is wrapped around a sphere (the globe), and the details of the globe are projected onto the cylindrical surface. Then, the cylinder is unwrapped into a flat surface.

cylindrical projection

A cylindrical projection is a type of map in which a cylinder is wrapped around a sphere (the globe), and the details of the globe are projected onto the cylindrical surface. Then, the cylinder is unwrapped into a flat surface, yielding a rectangular-shaped map. Cylindrical maps have a lot of distortion in the polar regions (that is, the size of the polar regions is greatly exaggerated on these maps).

equatorThe equator is an imaginary circle around the earth, halfway between the north and south poles.

geographical coordinate systemA geographical coordinate system is a system that uses latitude and longitude to describe points on the spherical surface of the globe.

latitude

Latitude is the angular distance north or south from the equator to a particular location. The equator has a latitude of zero degrees. The North Pole has a latitude of 90 degrees North; the South Pole has a latitude of 90 degrees South.

longitude

Longitude is the angular distance east or west from the north-south line that passes through Greenwich, England, to a particular location. Greenwich, England has a longitude of zero degrees. The farther east or west of Greenwich you are, the greater your longitude. Midway Islands (in the Pacific Ocean) have a longitude of 180 degrees (they are on the opposite side of the globe from Greenwich).

Mercator projectionA Mercator projection is a type of rectangular map in which the true compass direction are kept intact (lines of latitude and longitude intersect at right angles), but areas are distorted (for example, polar areas look much larger than they really are). Mercator projections are useful for nautical navigation. Geradus Mercator devised this cylindrical projection for use in navigation in 1569.

meridianA meridian a circular arc of longitude that meets at the north and south poles and connects all places of the same longitude. The prime meridian (0 degrees longitude) passes through Greenwich, England.

Mollweide projectionA Mollweide projection is a type of sinusoidal projection map in which the entire surface of the Earth is shown within an ellipse. Lines of latitude are parallel to the equator, but lines of longitude are curved in such a way that area distortion is minimal. The distortion is greatest at the edges of the ellipse. This type of projection was created by Carl B. Mollweide in 1805.

Orthographic projectionAn Orthographic projection is a type of map in which is essentially a drawing of (one side of) a globe. There is a lot of distortion of area in this type of map, but one gets the idea that the globe is being represented.

Orthophanic projectionThe Orthophanic (meaning 'right appearing') projection, also called the Robinson projection, is a widely-used type of map in which the Earth is shown in a flattened ellipse. In this pseudocylindrical. projection, lines of latitude are parallel to the equator, but lines of latitude are elliptical arcs. In a Robinson projection, area is represented accurately, but the distances and compass directions are distorted (for example, compass lines are curved). This type of projection was first made in 1963 by Arthur H. Robinson.

parallelA parallel (of latitude) is a line on a map that represents an imaginary east-west circle drawn on the Earth in a plane parallel to the plane that contains the equator.

planar projectionA planar projection is a type of map in which the details of the globe are projected onto a plane (a flat surface) yielding a rectangular-shaped map. Cylindrical maps have a lot of distortion towards the edges.

Robinson projectionThe Robinson projection is a widely-used type of map in which the Earth is shown within an ellipse with a flat top and bottom. In this pseudocylindrical. projection, lines of latitude are parallel to the equator, but lines of latitude are elliptical arcs. In a Robinson projection, area is represented accurately, but the distances and compass directions are distorted (for example, compass lines are curved). This type of projection was first made in 1963 by Arthur H. Robinson; it is also called the Orthophanic projection (meaning 'right appearing').

sinusoidal projectionA sinusoidal projection is a type of map projection in which lines of latitude are parallel to the equator, and lines of longitude are curved around the prime meridian.

Winkel Tripel projectionA Winkel Tripel projection is a type of preudocylindrical projection map in which both the lines of latitude and longitude are curved. The Winkel Tripel projection was adopted by the National Geographic Society in the late 1990s (replacing the Robinson projection).

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Mapping Toolbox ... Coordinate Systems Projected Coordinate Systems Projections and ParametersThe Three Main Families of Map Projections

Unwrapping the Sphere to a PlaneCylindrical ProjectionsConic ProjectionsAzimuthal Projections

Unwrapping the Sphere to a Plane

Mapmakers have developed hundreds of map projections, over several thousand years. Three large families of map projection, plus several smaller ones, are generally acknowledged. These are based on the types of geometric shapes that are used to transfer features from a sphere or spheroid to a plane. As described above, map projections are based on developable surfaces, and the three traditional families consist of cylinders, cones, and planes. They are used to classify the majority of projections, including some that are not analytically (geometrically) constructed. In addition, a number of map projections are based on polyhedra. While polyhedral projections have interesting and useful properties, they are not described in this guide.

Which developable surface to use for a projection depends on what region is to be mapped, its geographical extent, and the geometric properties that areas, boundaries, and routes need to have, given the purpose of the map. The following sections describe and illustrate how the cylindrical, conic, and azimuthal families of map projections are constructed and provides some examples of projections that are based on them.

Cylindrical Projections

A cylindrical projection is produced by wrapping a cylinder around a globe representing the Earth. The map projection is the image of the globe projected onto the cylindrical surface, which is then unwrapped into a flat surface. When the cylinder aligns with the polar axis, parallels appear as horizontal lines and meridians as vertical lines. Cylindrical projections can be either equal-area, conformal, or equidistant. The following figure shows a regular cylindrical or normal aspect orientation in which the cylinder is tangent to the Earth along the Equator and the projection radiates horizontally from the axis of rotation. The projection method is diagrammed on the left, and an example is given on the right (equal-area cylindrical projection, normal/equatorial aspect).

For a description of projection aspect, see Projection Aspect.

Some widely used cylindrical map projections are

Equal-area cylindrical projection

Equidistant cylindrical projection

Mercator projection

Miller projection

Plate Carre projection

Universal transverse Mercator projection

Pseudocylindrical Map Projections

All cylindrical projections fill a rectangular plane. Pseudocylindrical projection outlines tend to be barrel-shaped rather than rectangular. However, they do resemble cylindrical projections, with straight and parallel latitude lines, and can have equally spaced meridians, but meridians are curves, not straight lines. Pseudocylindrical projections can be equal-area, but are not conformal or equidistant.

Some widely-used pseudocylindrical map projections are

Eckert projections (I-VI)

Goode homolosine projection

Mollweide projection

Quartic authalic projection

Robinson projection

Sinusoidal projection

Conic Projections

A conic projection is derived from the projection of the globe onto a cone placed over it. For the normal aspect, the apex of the cone lies on the polar axis of the Earth. If the cone touches the Earth at just one particular parallel of latitude, it is called tangent. If made smaller, the cone will intersect the Earth twice, in which case it is called secant. Conic projections often achieve less distortion at mid- and high latitudes than cylindrical projections. A further elaboration is the polyconic projection, which deploys a family of tangent or secant cones to bracket a succession of bands of parallels to yield even less scale distortion. The following figure illustrates conic projection, diagramming its construction on the left, with an example on the right (Albers equal-area projection, polar aspect).

Some widely-used conic projections are

Albers Equal-area projection

Equidistant projection

Lambert conformal projection

Polyconic projection

Azimuthal Projections

An azimuthal projection is a projection of the globe onto a plane. In polar aspect, an azimuthal projection maps to a plane tangent to the Earth at one of the poles, with meridians projected as straight lines radiating from the pole, and parallels shown as complete circles centered at the pole. Azimuthal projections (especially the orthographic) can have equatorial or oblique aspects. The projection is centered on a point, that is either on the surface, at the center of the Earth, at the antipode, some distance beyond the Earth, or at infinity. Most azimuthal projections are not suitable for displaying the entire Earth in one view, but give a sense of the globe. The following figure illustrates azimuthal projection, diagramming it on the left, with an example on the right (orthographic projection, polar aspect).

Some widely used azimuthal projections are

Equidistant azimuthal projection

Gnomonic projection

Lambert equal-area azimuthal projection

Orthographic projection

Stereographic projection

Universal polar stereographic projection

For additional information on families of map projections and specific map projections, see Supported Map Projections.

http://www.mathworks.com/help/map/the-three-main-families-of-map-projections.htmlCylindrical Projection

A cylindrical projection map is the most common type of map that we see. Imagine placing the movie screen around the globe in a cylinder shape. The projection that results is depicted in this image. Notice that areas close to the equator have very little distortion. However, the closer to the poles that one travels, the more distorted the map becomes. In this example, Greenland appears to be many times larger than it really is.

Conic Projection

A conic projection map is created by placing a cone shaped screen on a globe. The resulting projection is more accurate than the cylindrical projection map discussed above. However, the further we travel down the map, the more distorted and less accurate the map becomes.

Plane Projection

A plane projection is created by placing an imaginary screen directly above or below a globe. The image that would result is called a plane projection. This type of map projection is not commonly used.

Interrupted Projection

There are many different types of interrupted projection maps. These types of maps try to depict the continents as accurately as possible by leaving blank space in the less important areas of the map, such as in the oceans.

Map Projections - types and distortion patterns

The shape of the Earth is represented as a sphere. It is also modeled more accurately as an oblate spheroid or an ellipsoid. A globe is a scaled down model of the Earth. Although they can represent size, shape, distance and directions of the Earth features with reasonable accuracy, globes are not practical or suitable for many applications. They are hard to transport and store; for example you can not stuff a globe in your backpack while hiking or store it in your cars glove compartment. Globes are not suitable for use at large scales, such as finding directions in a city or following a hiking route, where a more detailed image is essential. They are expensive to produce, especially in varying sizes (scales). On a curved surface, measuring terrain properties is difficult, and it is not possible to see large portions of the Earth at once.

Maps do not suffer from the above shortcomings and are more practical than globes in most applications. Historically cartographers have tried to address the challenge of representing the curved surface of the Earth on a map plane, and to this end have devised map projections. A map projection is the transformation of Earths curved surface (or a portion of) onto a two-dimensional flat surface by means of mathematical equations. During such transformation, the angular geographic coordinates (latitude, longitude) referencing positions on the surface of the Earth are converted to Cartesian coordinates (x, y) representing position of points on a flat map.

Types of map projections based on developable surface

One way of classifying map projections is by the type of the developable surface onto which the reference sphere is projected. A developable surface is a geometric shape that can be laid out into a flat surface without stretching or tearing. The three types of developable surfaces are cylinder, cone and plane, and their corresponding projections are called cylindrical, conical and planar. Projections can be further categorized based on their point(s) of contact (tangent or secant) with the reference surface of the Earth and their orientation (aspect).

Keep in mind that while some projections use a geometric process, in reality most projections use mathematical equations to transform the coordinates from a globe to a flat surface. The resulting map plane in most instances can be rolled around the globe in the form of cylinder, cone or placed to the side of the globe in the case of the plane. The developable surface serves as a good illustrative analogy of the process of flattening out a spherical object onto a plane.

Cylindrical projection

In cylindrical projections, the reference spherical surface is projected onto a cylinder wrapped around the globe. The cylinder is then cut lengthwise and unwrapped to form a flat map.

Tangent vs. secant cylindrical projection

Cylindrical projection - tangent and secant equatorial aspect USGSThe cylinder may be either tangent or secant to the reference surface of the Earth. In the tangent case, the cylinders circumference touches the reference globes surface along a great circle (any circle having the same diameter as the sphere and thus dividing it into two equal halves). The diameter of the cylinder is equal to the diameter of the globe. The tangent line is the equator for the equatorial or normal aspect; while in the transverse aspect, the cylinder is tangent along a chosen meridian (i.e. central meridian).

In the secant case, the cylinder intersects the globe; that is the diameter of the cylinder is smaller than the globes. At the place where the cylinder cuts through the globe two secant lines are formed.

The tangent and secant lines are important since scale is constant along these lines (equals that of the globe), and therefore there is no distortion (scale factor = 1). Such lines of true scale are called standard lines. These are lines of equidistance. Distortion increases by moving away from standard lines.

In normal aspect of cylindrical projection, the secant or standard lines are along two parallels of latitude equally spaced from equator, and are called standard parallels. In transverse aspect, the two standard lines run north-south parallel to meridians. Secant case provides a more even distribution of distortion throughout the map. Features appear smaller between secant lines (scale < 1) and appear larger outside these lines (scale > 1).

Cylindrical aspect equatorial (normal), transverse, oblique

Cylindrical projection - transverse and oblique aspect USGSThe aspect of the map projection refers to the orientation of the developable surface relative to the reference globe. The graticule layout is affected by the choice of the aspect.

In normal or equatorial aspect, the cylinder is oriented (lengthwise) parallel to the Earths polar axis with its center located along the equator (tangent or secant). The meridians are vertical and equally spaced; the parallels of latitude are horizontal straight lines parallel to the equator with their spacing increasing toward the poles. Therefore the distortion increases towards the poles. Meridians and parallels are perpendicular to each other. The meridian that lies along the projection center is called the central meridian.

In transverse aspect, the cylinder is oriented perpendicular to the Earths axis with its center located on a chosen meridian (a line going through the poles). And the oblique aspect refers to the cylinder being centered along a great circle between the equator and the meridians with its orientation at an angle greater than 0 and less than 90 degrees relative to the Earths axis.

Examples of cylindrical projections include Mercator, Transverse Mercator, Oblique Mercator, Plate Carr, Miller Cylindrical, Cylindrical equal-area, GallPeters, HoboDyer, Behrmann, and Lambert Cylindrical Equal-Area projections.

Conical (conic) projection

In conical or conic projections, the reference spherical surface is projected onto a cone placed over the globe. The cone is cut lengthwise and unwrapped to form a flat map.

Tangent vs. secant conical projection

Conic projection - tangent and secant USGSThe cone may be either tangent to the reference surface along a small circle (any circle on the globe with a diameter less than the spheres diameter) or it may cut through the globe and be secant (intersect) at two small circles.

For the polar or normal aspect, the cone is tangent along a parallel of latitude or is secant at two parallels. These parallels are called standard parallels. This aspect produces a map with meridians radiating out as straight lines from the cones apex, and parallels drawn as concentric arcs perpendicular to meridians.

Scale is true (scale factor = 1) and there is no distortion along standard parallels. Distortion increases by moving away from standard parallels. Features appear smaller between secant parallels and appear larger outside these parallels. Secant projections lead to less overall map distortion.

Conical aspect equatorial (normal), transverse, oblique

The polar aspect is the normal aspect of the conic projection. In this aspect the cones apex is situated along the polar axis of the Earth, and the cone is tangent along a single parallel of latitude or secant at two parallels. The cone can be situated over the North or South Pole. The polar conic projections are most suitable for maps of mid-latitude (temperate zones) regions with an east-west orientation such as the United States.

In transverse aspect of conical projections, the axis of the cone is along a line through the equatorial plane (perpendicular to Earths polar axis). Oblique aspect has an orientation between transverse and polar aspects. Transverse and oblique aspects are seldom used.

Examples of conic projections include Lambert Conformal Conic, Albers Equal Area Conic, and Equidistant Conic projections.

Planar projection Azimuthal or Zenithal

In planar (also known as azimuthal or zenithal) projections, the reference spherical surface is projected onto a plane.

Tangent vs. secant planar projection

Planar (azimuthal) projection - tangent and secant USGSThe plane in planar projections may be tangent to the globe at a single point or may be secant. In the secant case the plane intersects the globe along a small circle forming a standard parallel which has true scale. The normal polar aspect yields parallels as concentric circles, and meridians projecting as straight lines from the center of the map. The distortion is minimal around the point of tangency in the tangent case, and close to the standard parallel in the secant case.

Planar aspect polar (normal), transverse (equatorial), oblique

The polar aspect is the normal aspect of the planar projection. The plane is tangent to North or South Pole at a single point or is secant along a parallel of latitude (standard parallel). The polar aspect yields parallels of latitude as concentric circles around the center of the map, and meridians projecting as straight lines from this center. Azimuthal projections are used often for mapping Polar Regions, the polar aspect of these projections are also referred to as polar azimuthal projections.

In transverse aspect of planar projections, the plane is oriented perpendicular to the equatorial plane. And for the oblique aspect, the plane surface has an orientation between polar and transverse aspects.

These projections are named azimuthal due to the fact that they preserve direction property from the center point of the projection. Great circles passing through the center point are drawn as straight lines.

Examples of azimuthal projections include: Azimuthal Equidistant, Lambert Azimuthal Equal-Area, Gnomonic, Stereographic, and Orthographic projections.

Azimuthal Perspective Projections

Some classic azimuthal projections are perspective projections and can be produced geometrically. They can be visualized as projection of points on the sphere to the plane by shining rays of light from a light source (or point of perspective). Three projections, namely gnomonic, stereographic and orthographic can be defined based on the location of the perspective point or the light source.

Gnomonic Projection (also known as Central or Gnomic Projection)

Gnomonic Projection USGSThe point of perspective or the light source is located at the center of the globe in gnomonic projections. Great circles are the shortest distance between two points on the surface of the sphere (known as great circle route). Gnomonic projections map all great circles as straight lines, and such property makes these projections suitable for use in navigation charts. Distance and shape distortion increase sharply by moving away from the center of the projection.

Stereographic Projection

Stereographic projection USGSIn stereographic projections, the perspective point is located on the surface of globe directly opposite from the point of tangency of the plane. Points close to center point show great distortion on the map. Stereographic projection is a conformal projection, that is over small areas angles and therefore shapes are preserved. It is often used for mapping Polar Regions (with the source located at the opposite pole).

Orthographic Projection

Orthographic projection USGSIn orthographic projections, the point of perspective is at infinite distance on the opposite direction from the point of tangency. The light rays travel as parallel lines. The resulting map from this projection looks like a globe (similar to seeing Earth from deep space). There is great distortion towards the borders of the map.

Map projection types based on distortion characteristics

As stated above spherical bodies such as globes can represent size, shape, distance and directions of the Earth features with reasonable accuracy. It is impossible to flatten any spherical surface (e.g. an orange peel) onto a flat surface without some stretching, tearing, or shearing. Similarly, when trying to project a spherical surface of the Earth onto a map plane, the curved surface will get deformed, causing distortions in shape (angle), area, direction or distance of features. All projections cause distortions in varying degrees; there is no one perfect projection preserving all of the above properties, rather each projection is a compromise best suited for a particular purpose.

Different projections are developed for different purposes. Some projections minimize distortion or preserve some properties at the expense of increasing distortion of others. The choice of a projection for a map depends on such factors as the purpose for which the map will be used, the area being mapped, and the maps scale (distortion is more pronounced in small-scale mapping).

Measuring map scale distortion scale factor & principal (nominal) scale

As mentioned above, a reference globe (reference surface of the Earth) is a scaled down model of the Earth. This scale can be measured as the ratio of distance on the globe to the corresponding distance on the Earth. Throughout the globe this scale is constant. For example, a 1:250000 representative fraction scale indicates that 1 unit (e.g. km) on the globe represents 250000 units on Earth. The principal scale or nominal scale of a flat map (the stated map scale) refers to this scale of its generating globe.

However the projection of the curved surface on the plane and the resulting distortions from the deformation of the surface will result in variation of scale throughout a flat map. In other words the actual map scale is different for different locations on the map plane and it is impossible to have a constant scale throughout the map. This variation of scale can be visualized by Tissot's indicatrix explained in detail below. Measure of scale distortion on map plane can also be quantified by the use of scale factor.

Scale factor is the ratio of actual scale at a location on map to the principal (nominal) map scale (SF = actual scale / nominal scale). This can be alternatively stated as ratio of distance on the map to the corresponding distance on the reference globe. A scale factor of 1 indicates actual scale is equal to nominal scale, or no scale distortion at that point on the map. Scale factors of less than or greater than one are indicative of scale distortion. The actual scale at a point on map can be obtained by multiplying the nominal map scale by the scale factor.

As an example, the actual scale at a given point on map with scale factor of 0.99860 at the point and nominal map scale of 1:50000 is equal to (1:50000 x 0.99860) = (0.99860 / 50000) = 1:50070 (which is a smaller scale than the nominal map scale). Scale factor of 2 indicates that the actual map scale is twice the nominal scale; if the nominal scale is 1:4million, then the map scale at the point would be (1:4million x 2) = 1:2million. A scale factor of 0.99950 at a given location on the map indicates that 999.5 meters on the map represents 1000 meters on the reference globe.

As mentioned above, there is no distortion along standard lines as evident in following figures. On a tangent surface to the reference globe, there is no scale distortion at the point (or along the line) of tangency and therefore scale factor is 1. Distortion increases with distance from the point (or line) of tangency.

Map scale distortion of a tangent cylindrical projection - SF = 1 along line of tangency

Scale distortion on a tangent surface to the globeOn a secant surface to the reference globe, there is no distortion along the standard lines (lines of intersection) where SF = 1. Between the secant lines where the surface is inside the globe, features appear smaller than in reality and scale factor is less than 1. At places on map where the surface is outside the globe, features appear larger than in reality and scale factor is greater than 1. A map derived from a secant projection surface has less overall distortion than a map from a tangent surface.

Map scale distortion of a secant cylindrical projection - SF = 1 along secant lines

Scale distortion on a secant surface to the globe

Tissot's indicatrix visualizing map distortion pattern

A common method of classification of map projections is according to distortion characteristics - identifying properties that are preserved or distorted by a projection. The distortion pattern of a projection can be visualized by distortion ellipses, which are known as Tissot's indicatrices. Each indicatrix (ellipse) represents the distortion at the point it is centered on. The two axes of the ellipse indicate the directions along which the scale is maximal and minimal at that point on the map. Since scale distortion varies across the map, distortion ellipses are drawn on the projected map in an array of regular intervals to show the spatial distortion pattern across the map. The ellipses are usually centered at the intersection of meridians and parallels. Their shape represents the distortion of an imaginary circle on the spherical surface after being projected on the map plane. The size, shape and orientation of the ellipses are changed as the result of projection. Circular shapes of the same size indicate preservation of properties with no distortion occurring.

Equal Area Projection Equivalent or Authalic

Gall-Peters cylindrical equal-area projection Tissot's indicatrix Eric Gaba Wikimedia Commons user: StingEqual area map projections (also known as equivalent or authalic projection) represent areas correctly on the map. The areas of features on the map are proportional to their areas on the reference surface of Earth. Maintaining relative areas of features causes distortion in their shapes, which is more pronounced in small-scale maps.

The shapes of the Tissots ellipses in this world map Gall-Peters cylindrical equal-area projection are distorted; however each of them occupies the same amount of area. Along the standard parallel lines in this map (45 N and 45S), there is no scale distortion and therefore the ellipses would be circular.

Equal area projections are useful where relative size and area accuracy of map features is important (such as displaying countries / continents in world maps), as well as for showing spatial distributions and general thematic mapping such as population, soil and geological maps. Some examples are Albers Equal-Area Conic, Cylindrical Equal Area, Sinusoidal Equal Area, and Lambert Azimuthal Equal Area projections.

Conformal Projection Orthomorphic or Autogonal

Mercator - conformal projection Tissot's indicatrix Eric Gaba Wikimedia Commons user: StingIn conformal map projections (also known as orthomorphic or autogonal projection) local angles are preserved; that is angles about every point on the projected map are the same as the angles around the point on the curved reference surface. Similarly constant local scale is maintained in every direction around a point. Therefore shapes are represented accurately and without distortion for small areas. However shapes of large areas do get distorted. Meridians and parallels intersect at right angles. As a result of preserving angles and shapes, area or size of features are distorted in these maps. No map can be both conformal and equal area.

Tissots indicatrices are all circular (shape preserved) in this world map Mercator projection, however they vary in size (area distorted). Here the area distortion is more pronounced as we move towards the poles. A classic example of area exaggeration is the comparison of land masses on the map, where for example Greenland appears bigger than South America and comparable in size to Africa, while in reality it is about one-eight the size of S. America and one-fourteenth the size of Africa. A feature that has made Mercator projection especially suited for nautical maps and navigation is the representation of rhumb line or loxodrome (line that crosses meridians at the same angle) as a straight line on the map. A straight line drawn on the Mercator map represents an accurate compass bearing.

Preservation of angles makes conformal map projections suitable for navigation charts, weather maps, topographic mapping, and large scale surveying. Examples of common conformal projections include Lambert Conformal Conic, Mercator, Transverse Mercator, and Stereographic projection.

Equidistant Projection

Equirectangular (equidistant cylindrical) projection Tissot's indicatrix Eric Gaba Wikimedia Commons user: StingIn equidistant map projections, accurate distances (constant scale) are maintained only between one or two points to every other point on the map. Also in most projections there are one or more standard lines along which scale remains constant (true scale). Distances measured along these lines are proportional to the same distance measurement on the curved reference surface. Similarly if a projection is centered on a point, distances to every other point from the center point remain accurate. Equidistant projections are neither conformal nor equal-area, but rather a compromise between them.

In this world map equidistant cylindrical projection (also known as plate carre), Tissots ellipses are distorted in size and shape. However while there are changes in the ellipses, their north-south axis has remained equal in length. This indicates that any line joining north and south poles (meridian) is true to scale and therefore distances are accurate along these lines. Plate carre is a case of equirectangular projection with Equator being a standard parallel.

Equidistant projections are used in air and sea navigation charts, as well as radio and seismic mapping. They are also used in atlases and thematic mapping. Examples of equidistant projections are azimuthal equidistant, equidistant conic, and equirectangular projections.

True-Direction Projection Azimuthal or Zenithal

Gnomonic projection Wikimedia CommonsDirections from a central point to all other points are maintained accurately in azimuthal projections (also known as zenithal or true-direction projections). These projections can also be equal area, conformal or equidistant.

The gnomonic map projection in the image is centered on the North Pole with meridians radiating out as straight lines. In gnomonic maps great circles are displayed as straight lines. Directions are true from the center point (North Pole).

True-direction projections are used in applications where maintaining directional relationships are important, such as aeronautical and sea navigation charts. Examples include Lambert Azimuthal Equal-Area, Gnomonic, and azimuthal equidistant projections.

Compromise Projections

Robinson projection Eric Gaba Wikimedia Commons user: StingSome projections do not preserve any of the properties of the reference surface of the Earth; however they try to balance out distortions in area, shape, distant, and direction (thus the name compromise), so that no property is grossly distorted throughout the map and the overall view is improved. They are used in thematic mapping. Examples include Robinson projection and Winkel Tripel projection.

http://geokov.com/education/map-projection.aspx

Listing and description of various map projections