Physical Geography - Version 1 Unit 4 Mapping Earth’s Surface

. A ' I ' Figure Lowest Elevation in California , Basin in Death Valley , California . Image by Jeremy is used under a license . UNIT MAPPING SURFACE Goals Objectives of this unit Understand a map scale , projections , and ways of telling the map user what the map is measuring on Earth surface . Explore the concepts of scale , resolution , and projection . Identify contour intervals on basic topographic maps . Allow students to interpret the distortions of each projection , and to explain how the point of tangency creates different styles of maps and presents different information . Provide students an understanding of latitude and longitude , and how to use this and other coordinate systems . GEOGRAPHY

WHAT IS ?

Cartography is the study , practice , and interpretation of maps . Combining science , aesthetics , and technique , cartography builds on the premise that reality can be modeled in ways that communicate spatial information effectively . The fundamental problems of traditional cartography are to Set the map agenda and select the traits of the object to be mapped . This is the concern of map editing . Traits may be physical , such as roads or land masses , or maybe abstract , such as or political boundaries . Represent the terrain of the mapped object on flat media . This is the concern of map projections . Reduce the complexity of the characteristics that will be mapped . This is also the concern of generalization . Orchestrate the elements of the map to best convey its message to its audience . This is the concern of design . Map Scale The Earth surface has an area of over 500 million and any picture of the earth that you can easily carry can only show general outlines of continents and countries . When we visually represent a region of the world on a map , we must reduce its size to fit within the boundaries of the map . Map scale measures how much the features of the world are reduced to fit on a map or more precisely , map scale shows the proportion of a given distance on a map to the corresponding distance on the ground in the real world . The map scale is represented by a representative fraction , graphic scale , or verbal description . Representative Fraction The most commonly used measure of map scale is the representative fraction ( where a map scale is shown as a ratio . With the numerator always set to , the denominator represents how much greater the distance is in the world . The figure below shows a topographic map with an of , which means that one unit on the map represents units on the ground . The representative fraction is accurate regardless of which units are used the can be measured as centimeter to centimeters , one inch to inches , or any other unit . GEOGRAPHY

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I I ! I ' CONTOUR INTERVAL 40 FEET NATIONAL GEODETIC VERTICAL DATUM OF 1929 Figure Representative Fraction Scale Bars from a Topographic Map . Image is used under a Creative Commons license . Graphic Scale Scale bars are graphical representations of distance on a map . The figure has scale bars for mile , 7000 feet , and kilometer . One important advantage of graphic scales is that they remain true when maps are shrunk or magnified . Verbal Description Some maps , especially older ones , use a verbal description of scale . For example , it is common to see one inch represents one kilometer or something similar written on a map to give map users an idea of the scale of the map . use a scale to describe maps as being or . This description of the map scale as large or small can seem counterintuitive at first . A by map of the United States has a small map scale while a college campus map of the same size is scale . Scale descriptions using the provide one way of considering a scale , since is larger than . Put differently , if we were to change the scale of the map with an of so that a section of road was reduced from one unit to , say , units in length , we would have created a map whose representative fraction is . In general , the larger the map scale , the more detail that is shown CONTOUR LINES Contour lines are the greatest distinguishing feature of a topographic map . Contour lines are lines drawn on a map connecting points of equal elevation , meaning if you physically followed a contour line , the elevation would remain constant . Contour lines show elevation and the shape of the terrain . They useful because they illustrate the shape of the land surface ( topography ) on the map . Here an easy way to understand how to interpret contour lines Take an object GEOGRAPHY

like a ball or a pile of laundry and shine a red laser pointer along the object side . The line you see will look like a contour line on a topographic map . Topographic maps show lines for certain elevations only . These lines are evenly spaced apart . We call this spacing the contour interval . For example , if your map uses a contour interval , you will see contour lines for every 10 feet ( meters ) of elevation lines at , 10 , 20 , 30 , 40 , and so on . Different maps use different intervals , depending on the topography . If , for example , the general terrain is quite elevated , the map might run at to even ( to ) intervals . This makes it easier to read the map , as too many contour lines would be difficult to work with . Figure Mount Fuji with Contour Lines ( Image used with permission . To make topographic maps easier to read , every fifth contour line is an index contour . Because it impractical to mark the elevation of every contour line on the map , the index contour lines are the only ones labeled . The index contours are a darker or wider brown line in comparison to the regular contour lines . You see the elevations marked on the index contour lines only . To determine elevations , pay attention to the amount of space between lines . Ifthe contours are close together , you looking at a steep slope . If the contours have wide spaces in between or are there at all , the terrain is relatively flat . EXTENT VERSUS RESOLUTION The extent of a map describes the area visible on the map , while resolution describes the smallest unit that is mapped . You can think of the extent as describing the region to which the map is zoomed . The extent ofthe map below is national as it encompasses the contiguous GEOGRAPHY

United States , while the resolution is the state because states are the finest level of spatial detail that we can see . Figure Map Showing Population Density Over National Extent State Resolution , US Census . Image by Steve Manson is licensed under a license . We often choose mapping resolutions intentionally to make the map easier to understand . For example , if we tried to display a map with a national extent at the resolution of census blocks , the level of detail would be so fine , and the boundaries would be so small that it would be difficult to understand anything about the map . Balancing extent and resolution are often one of the most important and difficult decisions a cartographer must make . The figure below offers two more examples ofthe difference between extent and resolution . Coordinated Projections Locations on the Earth surface are measured in terms of coordinates , a set of two or more numbers that specify a location to some reference system . The simplest system of this kind is a Cartesian coordinate system , named for the 17 mathematician and philosopher Rene Descartes . A Cartesian coordinate system , like the one below , is simply a grid formed by putting together two measurement scales , one horizontal ( and one vertical ( The point at which both and equal zero is called the origin of the coordinate system . In the figure , the origin ( is located at the center of the grid ( the intersection of the two bold lines ) All other positions are specified relative to the origin , as seen with the points at ( and ( GEOGRAPHY

( Figure Sample Coordinate Earth Surface is measured in Terms of Coordinates . Image is used under a license . The geographic coordinate system is designed specifically to define positions on the roughly spherical surface . Instead of the two linear measurement scales and , as with a Cartesian grid , the geographic coordinate system uses an scale , called longitude that ranges from to . Because the Earth is round , or ) and ( or ) are the same grid line , termed the International Date Line . Opposite the International Date Line is the prime meridian , the line of longitude defined as . The scale , called latitude , ranges from ( or ) at the North Pole to ( or ) at the South Pole . In simple terms , longitude specifies positions east and west and latitude specify positions north and south . At higher latitudes , the length of parallels decreases to zero at North and South . Lines of longitude are not parallel but converge toward the poles . Thus , while a degree of longitude at the equator is equal to a distance of about 111 kilometers , or about 69 mi , that distance decreases to zero at the poles . Projection is the process of making a map from a globe . We can think of the earth as a sphere . In reality , it is more of an ellipsoid with a few bulges , but it is fine to think of it as a sphere . To get a sense of how difficult this process can be , imagine peeling the skin from an orange and trying to lay the skin flat . Figure Orange Peel Representing Earth as a Flat Surface . Image is used under a . GEOGRAPHY

As you peel and flatten the skin , you will encounter several problems Shearing stretching the skin in one or more directions . Tearing causing the skin to separate . Compressing forcing the skin to bunch up and condense . Cartographers face the same three issues when they try to transform the globe into a map . If you had a globe made of paper , you could carefully try to peel it into a flat piece of paper , but you would have a big mess on your hands . Instead , cartographers use projections to create useable maps . Figure Shearing , Compression Tension Distortion of Globe ( Steve Manson ) Image is used under a license . PROJECTION MECHANICS The term map projection refers to both the process and product of transforming spatial coordinates on a sphere to a plane . In terms of actual mechanics , most projections use mathematical functions that take as inputs locations on the sphere and translate them into locations on a surface . It is helpful to think about projections in physical terms . If you had a clear globe the size of a beach ball and placed a light inside this globe , it would cast shadows onto a surrounding surface . If this surface were a piece of paper that you wrapped around the globe , you could GEOGRAPHY

carefully trace these shadows onto the paper , then flatten out this piece of paper and have your projection ! Most projections transform part of the globe to one ofthree surfaces , because they are flat or can be made flat plane , cone , and cylinder . The resulting projections are called planar , conical , and cylindrical . We use developable surfaces because they eliminate tearing , although they will produce shearing and compression . Ofthese three problems , tearing is seen as the worst because you would be making maps with all sorts of holes in them . As we see below , however , there are times when you can create maps with tearing , and they are quite useful . Figure Red Lines or Dots Mark the Tangent Line or Point . The Flat Surface Touches the Globe it is The Point on the Projected Map Which Has the Least Distortion . Image is in the public domain . The place where the developable surface touches the globe is known as the tangent point or tangent line . Maps will most accurately represent objects on the globe at these tangent points or lines , with distortion increasing as you move farther away due to shearing and compression . It is for this reason that cylinders are often used for areas near the equator ( great circles ) cones used to map the ( small circles ) and planes used for Polar Regions ( points ) For beginning , understanding the exact mechanics of projections does matter as much as knowing which map properties are maintained or lost with the choice of projection . Projections must distort features on the surface of the globe during the process of making them flat because projection involves shearing , tearing , and compression . Since no projection can preserve all properties , it is up to the to know which properties are most important GEOGRAPHY

for their purpose and to choose an appropriate projection . The properties we will focus on are shape , area , and distance . Note that distortion is not necessarily tied to the type of developable surface but rather to the way the transformation is done with that surface . It is possible to preserve any one of the three properties using any of the developable surfaces . One way of looking at the problem is with distortion ellipses . These help us to visualize what type of distortion a map projection has caused , how much distortion has occurred , and where it has occurred . The ellipses show how imaginary circles on the globe are deformed as a result of a particular projection . If no distortion had occurred in projecting a map , all of the ellipses would be the same size and circular . Conformal Conformal projections preserve shape and angle , but strongly distorts area in the process . For example , with the projection , the shapes of coastlines are accurate on all parts of the map , but countries near the poles appear much larger relative to countries near the equator than they are . For example , is only of the land area of Africa , but it appears to be just as large . Figure The Projection . Image is used under a . GEOGRAPHY

Conformal projections should be used if the main purpose of the map involves measuring angles or representing the shapes of features . They are very useful for navigation , topography ( elevation ) and weather maps . A conformal projection will have distortion ellipses that vary substantially in size but are all the same circular shape . The consistent shapes indicate that conformal projections ( like this projection of the world ) preserve shapes and angles . This useful property accounts for the fact that conformal projections are almost always used as the basis for large scale surveying and mapping . Figure The Preserves Shape Angle but Distorts Area . Image is used under a license . Equal Area For projections , the size of any area on the map is in true proportion to its size on the earth . In other words , countries shapes may appear to be squished or stretched compared to what they look like on a globe , but their land area will be accurate relative to other landmasses . For example , in the projection , the shape of is significantly altered , but the size of its area is correct in comparison to Africa . This type of projection is important for quantitative thematic data , especially in mapping density ( an attribute over an area ) For example , it would be useful in comparing the density of Syrian refugees in the Middle East or the amount of cropland in production . GEOGRAPHY

Figure Projection . Image is used under a . As we can see with an projection , however , the ellipses maintain the correct proportions in the sizes of areas on the globe but that their shapes are distorted . projections are preferred for thematic mapping , especially when map users are expected to compare sizes of area features like countries and continents . Figure Area is Preserved , But Shapes Are Heavily Distorted . Image is used under a . GEOGRAPHY

Equidistant projections , as the name suggests , preserve distance . This is a bit misleading because no projection can maintain relative distance between all places on the map . Equidistant maps are able , however , to preserve distances along a few specified lines . For example , on the Azimuthal Equidistant projection , all points are the proportionally correct distance and direction from the center point . This type of projection would be useful visualizing airplane flight paths from one city to several other cities or in mapping an earthquake epicenter . Azimuthal projections preserve distance at the cost of distorting shape and area to some extent . The flag of the United Nations contains an example of a polar azimuthal equidistant projection . Figure Azimuthal Equidistant All Points are the Proportionally Correct Distances from a Central Point . Image is used under a A . Compromise , Interrupted , Artistic Projections Some projections , including the Robinson projection , strike a balance between the different map properties . In other words , instead of preserving the shape , area , or distance , they try to avoid extreme distortion of any ofthese properties . This type of projection would be useful for a world map . GEOGRAPHY

Figure Robinson Projection of the World . Image is used under a . Compromise projections preserve not one property but instead seek a compromise that minimizes distortion of all kinds , as with the Robinson projection , which is often used for scale thematic maps of the world . Other projections deal with the challenge of making the globe flat by tearing the earth in strategic places . Interrupted projections such as the interrupted Homolosine projection represent the earth in lobes , reducing the amount of shape and area distortion near the poles . The projection was developed in 1923 by John Paul to provide an alternative to the projection for portraying global areal relationships . The Interrupted Homolosine preserves area ( so it is or equivalent ) but does not preserve shape ( it is not conformal ) Figure The Homolosine Projection of the World . Image is used under a . GEOGRAPHY

PUBLIC LAND SURVEY The combination of a topographic map and this system can be used to locate features within a few acres and is a primary means of subdividing tracts of land for sale . The organization of the system is based on the definition of and principal meridians . The position of a baseline and meridian within a region may or may not coincide with latitude and longitude . Townships are areas of miles on a side ( 36 . mi ) bordered on the east and west by range lines and the north and south by township lines . Each township is subdivided into 36 sections of mile on each side . When is it broken down even smaller into quadrants , which are where we come across A mile increments , otherwise known as . Ultimately this system was designed when man headed west , and each person was allotted a parcel of land , and this was the best way to divide up the land since surveying at that time was too slow and expensive to complete . Principal meridian ! I ' In In no la us la ?

31 iii II Si i I . 12 50 line HIS I Figure The Public Land Survey ( Image is in the public domain . GEOGRAPHY Students explored the concepts of scale , resolution , and projection . All maps also use a projection that can be formed from a developable surface and can preserve one or two properties at most . In cartography , a map projection is a way to flatten a surface into a plane to make a map . This requires a systematic transformation of the latitudes and of locations from the surface of the globe into locations on a plane . All projections of a sphere on a plane necessarily distort the surface in some way and to some extent . Depending on the purpose of the map , some distortions are acceptable , and others are not therefore , different map projections exist to preserve some properties ofthe body at the expense of other properties . Latitude and longitude coordinates specify point locations within a coordinate system grid that is fitted to sphere or ellipsoid that approximates the Earth shape and size . To display extensive geographic areas on a page or computer screen , as well as to calculate distances , areas , and other quantities most efficiently , it is necessary to flatten the Earth . GEOGRAPHY