Maps and Models Dr. Miriam Helen Hill

Behavioral Objectives The student will be able to: Define the vocabulary terms Identify latitude and longitude coordinates Identify map types Identify graph types Identify scale types by name Use a graphic scale

Vocabulary Aerial photograph Globe Platform Attribute query GPS Political map Bar graph Graph Population pyramid Bi-lateral graph Graphic scale Prime Meridian Box-whisker Graticule Projection Bubble graph Greenwich Mean Time Proportional symbols Buffer Hachured contour Proportional symbol map Cadastral map High-low graph Query Histogram Raster Cartographer Historical map Register Cartography History map Remote sensing Central meridian Isoline Remote sensing imagery Isoline interval Remote sensing platform Circle Isoline map Representative fraction Circle graph Large scale Resolution Climatograph Latitude RF Climograph Legend Sanborn map Cohort Line graph Satellite imagery Compromise Longitude Scale Conformal Loss-and-gain chart Scatter diagram Contour line Map Second DD Map reading Silhouette graph Degree Map interpretation Small scale Density Mercator Solar noon DMS Meridian Spatial query Dot density map Minute Stacked bar graph Equivalent Model Stereopair False color image Multiple-line graph Surface graph General reference map Overlay analysis Geographic information science Parallel Thornthwaite diagram Geographic information studies Photogrammetry Topographic profile Geographic information system Topographic quadrangle Geologic map Pixel Triangular graph Universal time Verbal scale Vector Wind rose

Introduction

Geographers use many tools to understand their subjects of study. Many people recognize that geographers are often cartographers or mapmakers. Cartography is the science of mapmaking, a very complex and exacting science. With the advent of computers, the facility to make maps and otherwise represent Earth has changed and expanded. The ways spatial patterns can be represented to enhance visualization and understanding rely on the foundations of cartography but are not limited to the pure conception of a map. This lesson will look at a variety of those tools and the basic knowledge needed to read and interpret graphic depictions of spatial data. A model is an idealized and generalized representation designed to depict the inherent properties, characteristics, and interactions of the subject. Models may be simple or complex and are often useful to explore the impact of changes or variations. Models may be descriptions of common characteristics, illustrations of similar properties or regions, computer simulations, numerical equations, solidly constructed objects, and conceptualizations. A globe is a spherical representation of Earth, an example of a model. The spherical shape demonstrates the shape of Earth. It is not exact, but it is close enough to depict important properties such as how latitude and longitude can be used to find points on Earth’s surface. A globe shows the axis as well as the two main features at the surface, land and water. Various globes may show political boundaries, landform patterns, and ocean currents. A movable circular bar may be attached to represent the circle of illumination. Although maps are a type of model, they are usually classified distinctly. Furthermore, holes can be found in most definitions. A map is generally a flat representation of locations on Earth’s surface. However, not all maps are flat, and neither must they be limited to the surface of Earth. They may not even be solid, because they may be in our minds or in computers. They generally depict locational elements or environmental characteristics in some manner. Map reading involves viewing a map and garnering information from it. Map interpretation involves using the data depicted on the map with other knowledge and data to draw inferences and conclusions. Map use skills, often, enable job performance and routine activities to be more efficient and effective. Another type of model is a graph. Graphs show numerical data in pictorial form. Like maps, they help clarify and summarize patterns and can be read and interpreted. Although the patterns may or may not be spatial, geographic data are often displayed on graphs.

Latitude and Longitude

One of the means by which locations on Earth are identified is by using latitude and longitude. Latitude measures north and south from the equator. Technically, the value is the angle formed between the line from the given point on Earth’s surface to Earth’s center and the line from there to the point on the equator nearest to the original location. Latitude is measured using east-west running lines called parallels, lines that are parallel to the equator. The latitude of the equator is 0°. The highest latitude possible is 90° or ¼ of the way around Earth (360° ÷ 4). Further around the earth means the angle measures less from the opposite side. All latitudes except the equator must be designated as either north or south. 90°N is the North Pole, and 90°S is the South Pole. With the exception of these two locations, a latitude alone defines a parallel of an infinite number of points. A degree (°) is divided into minutes and seconds. While a circle is 360°, a degree is 60 minutes (’), and a minute is 60 seconds (”). This is the same as time if an hour is substituted for a degree. Just as 30 minutes of time is half of an hour, 30 minutes of arc is half of a degree. Coordinates can be expressed in degrees, minutes, and seconds or DMS. They can, also, be converted to decimal degrees or DD, where the divisions of degrees are changed to decimals, such as tenths and hundredths of a degree. In order to locate an individual point, other than the poles, longitude must be provided following the latitude, geographically. Longitude measures east and west from the Prime Meridian that runs through an observatory in Greenwich near London, U.K. The north-south running lines used to measure longitude are meridians, and longitude is the angle measured east and west from the Prime Meridian or Greenwich Meridian. This starting location has a longitude of 0°. The highest longitude possible is half way around Earth or 180° (360° ÷ 2). Other than these two locations, all longitudes must be identified as either east or west of the Prime Meridian. See Figure 1. Longitude is the foundation of time. Earth turns on its axis once every 24 hours. With 360° in a circle, this means that Earth turns 15° in an hour. Solar noon is when the sun is over the meridian of a given location, so every longitude has a different time. To simplify matters, Earth has been generally divided into 24 time zones each differing by an hour. The central meridians have longitudes that are multiples of 15°, and these set the time for that zone. The time zone centered on the Prime Meridian sets Greenwich Mean Figure 1 Latitude and Longitude Time or Universal Time. Time zones to the east are later than times zones to the west, and the new day begins at the International Date Line at 180°. See Figure 2. Political conventions vary this model so that in reality, time zone boundaries are more complex and do not perfectly coincide with the longitude lines or have full hour differences.

Figure 2 Central Meridians and 7.5° Boundaries (Politics Varies the Actual Time Zone Boundaries)

Projections

The spherical nature of Earth creates a major problem for cartographers. Consider trying to flatten an orange peel. It tears and breaks. Mathematical manipulations must be undertaken, then, to represent the spherical Earth’s surface in a flat form. These manipulations make projections. Three major categories of projections are equivalent, conformal, and compromise. An equivalent projection preserves the size of small areas on the map; and, thus, these can be used to compare areas or to explore density, number per area, relationships. Conformal projections maintain the shape of small areas. A map cannot be both equivalent and conformal! Another category of projections is the compromise projection, and these preserve neither area nor shape. Rather, compromise projections moderate and sacrifice both properties to make a nicer looking map. See Figure 3.

Figure 3 Sample Projections Many map projections have been created. The Mercator projection is, perhaps, the most commonly recognized. Although it is made mathematically, the creation can be envisioned by considering a transparent globe marked with the latitude and longitude grid or graticule and the continents. A light bulb placed in the center would project these lines outward beyond the globe. If a rectangular piece of paper were to be wrapped around the globe touching or tangent around the equator, the continents and grid projected on to the surface of the paper would make a Mercator projection. Consider this projection. The parallels are parallel to each other, but they are not evenly spaced with higher latitudes. The meridians are, also, parallel rather than correctly converging toward the poles, and the poles cannot fall on the paper. An area at high latitude is much larger than an equal area near the equator, but the shapes of small areas are retained. Thus, this is a conformal projection. Greenland is a good location to observe to consider the properties of a projection. On the Mercator map, Greenland is huge compared to Saudi Arabia or Mexico, both of which are only a little smaller in area. If dots were placed on the map so one dot was in the center of each 10° area of the grid, the dots would be much more dispersed in Greenland than they would be near the equator. This Mercator projection cannot correctly show spatial distribution. Only projections that are equivalent projections are suited to this task.

Scale

Scale is another important consideration of maps and some models. Scale tells the size relationship between the map or model and the depicted part of Earth. Scale is given as either a verbal scale, a representative fraction, or a graphic scale. A verbal scale tells the scale in words, for example one inch represents one mile or 1” = 1 mile. A good verbal scale will use a unit of one and a unit suitable for measurement on the map. Then it will give what that distance is on Earth in the most simple and understandable manner. The goal of a scale is to communicate the size relationship. A graphic scale is sometimes called a bar scale, because it is a line drawn on the map or model that is marked to show the corresponding distances on Earth. A good graphic scale will have subdivisions to the left of a 0 and at least one full division to the right. The reason for this is to enable direct measurement. When the distance between two locations are marked on the edge of a sheet of paper, the paper can be placed with the right hand mark on the whole division such that the left hand mark falls to the left of the zero within the subdivision where the values can be read more accurately. The graphic scale is the best scale, because reproduction will keep the graphic scale true as changes in the map size occur. The representative fraction or RF is a ratio or fractional scale, such as 1:63360 or 1/63360. The numerator is always one. The form eliminates the measurement unit, because unit/unit equals one; therefore, any system, for example English or metric, can be used. An RF of 1:63360 means one unit on the map is 63360 of the same unit on the ground. For example, one inch is 63360 inches. Converting this to a verbal scale and simplifying 63360 inches results in the verbal scale as 1” = 1 mile. The RF provides the concept behind the terms large scale and small scale maps. It compares the size of the fraction formed by the RF. On a given size page, a large scale map provides much detail about a limited area while a small scale map generalizes about a more extensive area. See Figure 5. Rules for Scale Creation and Conversion

Verbal Scale One inch represents one mile or 1” = 1 mile

1—The unit is ONE 2—The unit is appropriate for the map 3—Measurements are in simplest form

RF 1 or 1/63360 or 1:63360 63360

1—The numerator is ALWAYS ONE. 2—Both numbers represent the same unit of measurement. 3—NEVER give a unit of measurement with the RF; it drops out.

Graphic

(note that this is not the same scale as the above examples)

1—Subdivisions to the left of the zero are required for the scale to be used correctly. 2—One full division is given on the left, and at least one division is on the right. 3—Good solid numbers must appear on both the right and left sides. 4—Be sure to supply Earth’s measurement unit.

Figure 5: Rules for Creating and Converting Scale

Types of Maps

Two broad types of maps are recognized, general reference maps and thematic maps. General reference maps show a wide range of information for undefined purposes. Thematic maps provide information about a narrow topic. Thematic maps may be classified by the type of data provided or the mapping technique. For example, political maps will show boundaries of countries or smaller political units and their subdivisions. A geologic map will show information about the rocks such as age or type. A cadastral map shows parcel or property boundaries. A history map depicts a historical event. A historical map is an old map produced in the past. Sanborn maps are large scale historical maps of urban areas produced for insurance purposes by the company for which they were named. These are useful for studies of urban historical geography. A choropleth map classifies data into groups and uses similar color or shading to show the pattern and simplify interpretation. Darker colors usually mean greater concentrations. This is a very commonly used type of thematic map. Dot density maps use one dot to represent a given number of observations, and an area is filled by the number of dots needed to represent the associated value. The base map must be an equivalent projection, and the map reader must remember that the dots do not illustrate the exact location of the occurrences. At map that shows one dot for one occurrence at a specific location is specifically a dot map. A proportional symbol map displays a frequency of observations by varying the size of a symbol at the location. The symbol may be sized exactly to show the amount, sized based on classifications, or sized based on rules considering visual perception. Consulting the legend or key for information about the symbols used is, thus, required. A cartogram is a value per area map that changes the size of the area to represent the amount. An area with more will be larger than an area with less. The map may show the areas as contiguous or discontiguous. A is similar to a proportional symbol map in that the symbol size represents the associated amount. However, the flow map shows the path or possible path along which something like a commodity moves from one location to another. These illustrate connections between places and the strengths of these connections. Another especially important map type is an isoline map. An isoline map is used to map something that has a continuous distribution or can be measured everywhere. An isoline connects points of equal value. The difference in value between two adjacent isolines is the isoline interval. The isolines shown on the map are always multiples of that interval. They never cross or divide, and they enclose on areas of either higher or lower values. Isolines closer together means more rapidly changing values than those more widely separated. Isolines are given special names based on what is mapped. The list of types is surprisingly long and indicates the significance of this mapping technique. These include include air pressure as isobars, air temperature as isotherms, amount of precipitation as isohyets, cost of travel as isodapanes, and time of flowering plants as isophenes. Among the most important is the contour or contour line, a line connection points of equal elevation. Contour maps are usually produced with other information including political boundaries, roads, hydrology or streams, and other information about the cultural landscape. Such maps are called topographic maps or quadrangles. In the U.S., these maps are produced by the United States Geological Survey. Contours differ from isoline maps in that contours that enclose on areas of lower value are designated by hachured contours or contours with small tic marks pointing downslope. A critical aspect of reading isolines is attention to the trend or the direction of value change. Any time the trend reverses, a isoline value will be repeated.

Graphs

The most common graphs are either line graphs or bar graphs. Other types are occasionally encountered. They help to visualize and understand numerical data. Line graphs usually have an x-axis and a y-axis. The scales on the axes may be arithmetic, semi-logarithmic, or logarithmic. The values may, also, be shown as percentages. Simple line graphs typically show one variable by category or through time. A multiple-line graph shows several variables. A silhouette graph is a line graph that is shaded below the line to emphasize the line. A topographic profile, that plots elevation and location across a transect between two points with a vertical exaggeration to help show the elevation change, might be considered a subtype of a silhouette graph. A surface graph is quite distinct, because it is composed of cumulative line graphs that stack to show the total amount on the top surface. A bi- lateral graph shows two related variable that reach a balanced or equilibrium state when the values are equal. Bar graphs show variables by categories and may be singular or grouped data. Some show values and some use percentages. The bars may be vertical or horizontal. They can, also, be made with symbols. A histogram shows values and the frequencies associated with those values. Stacked bar graphs use additive values like the surface graph to show the total values or display the percentages. Various forms of high-low graphs show ranges of values and their statistics. Some add the mean or median, and some show the additional statistical divisions such a in the box-whisker chart. Loss-and-gain show values above and below a key value. A population pyramid shows male and female populations by age group or cohort. Other graphs include pie charts, proportional symbols, scatter diagrams, circular graphs, triangular graphs, climographs, and other complex graphs. As these types show, graphs can be complex and innovative. Some can be plotted on maps to add a spatial dimension. When the numbers represented are the amount of a whole, they can be converted to a percentage, and that can be shown as the amount of a circle to produce a pie chart. This graph should never be drawn by a 3-D option that is available from graphing software, because that distorts the percentage being shown. This is a frequently encountered graphing error. Proportional symbols are drawn showing symbols scaled to the amounts. Scatter diagrams plot one value against another value. This may be associated with a regression or trend line that represents an expected value. If a third variable is added, making the dot into a proportional symbol, it is a bubble graph. Circle graphs are used in diverse ways and show values with distance from a central point or around a point. They may show transportation costs against distance or travel time. A special kind is a wind rose that shows the number of days the wind blows from a given direction. Another is a climatograph that shows the mean daily temperatures and the total monthly precipitation in a circular pattern. Triangular graphs depict classifications based on three variables. A commonly recognized example is the chart for identifying soil textures. The percentages of clay, silt, and sand determine the texture classification. Climographs show mean monthly temperature as a line graph on one side axis and total monthly precipitation as a bar graph on the other side axis. The total annual precipitation and mean annual temperatures are given with the graph. This aids visualizing climate statistics to help in determining Köppen climate classification. Another climate system focuses on understanding the water-moisture balance of an area. This is portrayed by a Thornthwaite diagram that graphs the total monthly precipitation and the potential evapotranspiration or the maximum amount of water that might be lost to the atmosphere from soil and vegetation. This complex graph that resembles the activities of a checking account with overdraft protection shows a detailed picture of when the soil is dry and when water will runoff and contribute to flood hazards. The diversity of graphs can communicate significant geographical knowledge and understanding.

Modern Mapping Practices

With the advent of computers, geographical tools have been expanded and revolutionized. The amount and kinds of data about Earth have changed and multiplied exponentially. Remote sensing, the collection of environmental information from a distance without direct contact, originated as a distinct scientific discipline when cameras were put first on pigeons and in balloons and later on airplanes to make aerial photographs. Photogrammetry involves making measurement from aerial photographs. These photos have many practical applications such as for mapping, studying land use change, or environmental monitoring. When two photos are taken so that they overlap correctly, they can be viewed in 3-D and are stereoscopic pairs or stereopairs. This use of stereopairs expands the interpretation possibilities. Now these capabilities are being incorporated into computer displays. Rockets and satellites, also, serve as remote sensing platforms to hold the imaging equipment. Digital data are replacing photographic techniques. Now some satellites carry multispectral scanners that measure the amount of radiation given off by a surface in wavelengths that can and cannot be detected by human vision. As the instrument detects an area, it registers a value between 0 and 255 (256 values) and assigns it to that picture element, pixel. The size of the area is the resolution, and resolution relates to the level of detail that can be discerned in an image. Each sensor in the instrument is measuring values in different bands, and these values together comprise datasets that can be manipulated to produce satellite imagery or remote sensing imagery. The numbers are displayed as colors or gray-scales or manipulated and analyzed together with other bands or images to identify patterns and trends. They may be printed as false color images, especially where different bands are combined or where the bands are invisible wavelengths. This data format is called raster and uses the same concept as the computer monitors, ink jet printers, digital cameras, and .jpg files. Rasters are cells with a single value or associated attribute. Another data format is vector. Vector data are composed of points, lines, and polygons. A point is a single coordinate location. It may be the location of a fire hydrant or a traffic accident. A line is constructed of at least two points. A line may be a street or a stream. A polygon is an area bounded by lines. An area feature may be a parcel or a state. These examples may change as the scale or resolution is altered. A city on a large scale map may be a polygon, but for a small scale map, it may need to be a point. Vector data is associated with digitizing tablets and plotters as well as Adobe Illustrator .ai files. The global positioning system, GPS, is one means by which locations can be identified. GPS relies on a device that connects with at least three satellites. After calculating the length of time between the sending and receiving of signals and knowing the position of the satellites, triangulation identifies the location of the GPS device. The output can serve as input for vector-based mapping software. The devices have, also, been paired with datasets and more complex computer software and mapping capabilities. Thus, GPS and remote sensing are becoming increasingly integrated into geographic information systems (GIS). The acronym GIS, also, refers to the associated field of studies called either geographic information science or geographic information studies. Originally, GIS were designed to use and manipulate vector data, but extensive raster capabilities have been incorporated into some of the software. GIS analysis is best associated with the concept of overlay analysis. Each separate dataset is added to the project so that the layers register or the locations match from one layer to another. The layers can then be analyzed and manipulated to solve spatial problems. For example, a doctor may desire to live within five miles of the hospital where he will practice and be searching to buy a five bedroom house. The hospital can be selected from a layer of emergency facilities, and a five-mile buffer, a zone surrounding a feature, could be created. Next, a spatial query or search could select the properties from the real estate for sale layer that lie within that buffer zone. Next, an attribute query could search the associated tabular data of those parcels to produce a list of the properties with five bedrooms. GIS has revolutionized mapmaking and spatial analysis. It is a powerful tool used by public and private agencies and increasingly impacts our everyday lives such as through MapQuest and Google Earth. Much of business data has spatial attributes, so it can be mapped and studied. Site location analysis and target marketing help businesses to be more efficient and effective, thereby, increasing profits. GIS is used for facilities management, transportation planning and routing, crime mapping, utility infrastructure control, tax assessment, environmental management, and in the four sectors of emergency management. It offers many career opportunities and is a growing industry. The benefits of using maps and models are being recognized by employers. GIS skills are in high demand.

Maps and Graphs

Activity One: Using the map below, complete the table.

Point Latitude Longitude Point Latitude Longitude A M B N C O D P E Q F R G S H T I U J V K W L South Pole

Activity Two: Using the map below, complete the table to the NEAREST thirty seconds. Point Latitude Longitude Point Latitude Longitude A E B F C G D H

Activity Three: Using the map figures below, complete the table by identifying the name of the type of map illustrated.

Map Type Map Type A H B I C J D K E L F M G N

Activity Four—Using the graphs below, complete the table by identifying the name of the type of graph illustrated.

Graph Type Graph Type A N B O C P D Q E R F S G T H U I V J W K X L Y M

MAP AND GRAPH APPENDIX

Map A

Map B

Map C

Map D

Map E

Map F

Map G

Map H

Map I (NOTE DATE)

Map J

Map K

Map L

Map M

Map N

Graphs

Graph A Graph B

Graph C

Graph D

Graph E

Graph F

Graph G

Graph H

Graph I

Graph J

Graph K

Graph L

Graph M

Graph N

Graph O

Graph P

Graph Q

Graph R

Graph S

Graph T

Graph U

Graph V

Graph W

Graph X

Graph Y