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Geography 2240A/B

Lecture 1 Objectives 1. How to produce maps • To illustrate reports and papers 2. How maps are made • To help understand them (e.g. more skeptical about contours after you have drawn some) • To understand their possibilities and limitations 3. Some basic computer graphic skills • Background for other courses in remote sensing, GIS • Preparation of web graphics Cartography ­ Definition: o The art and science of making maps ­ Art: o Design:  Aesthetics – For an attractive map  Functionality – For a useful map o Creativity  Cartographers have to follow certain conventions  But there is still room for individuality, creativity ­ Science: o Surveying – Accurate measurement of location o Data collection – Contents of the map o Perception – How we extract information from a map ­ History of cartography: o Amajor area of study itself Maps ­ Definition: o “…graphic representations that facilitate a spatial understanding of things, concepts, conditions, processes or events…” o (from Harley, J.B. and Woodward, D., The History of Cartography, Vol. 1) o Many textbooks give inadequate definitions, biased towards modern geographic maps ­ Plans and charts: o No different from maps o Plan – Usually refers to a map of a small object like a building, room or even a machine o Chart – Usually refers to a map used for navigation o But they are both just types of map. The distinction is arbitrary and unnecessary Coordinates Location On The Earth ­ Coordinate reference points: o Earth is nearly spherical (within 0.5%) o Assume it is a perfect sphere o Earth rotates around its axis of rotation o Main reference line for coordinates o Meets surface at north and south poles o Equator defined by plan perpendicular to axis, passing through the planet’s centre ­ Latitude o Angular distance north or south from equator to poles o Geocentric Latitude –Angle between the equatorial plane and radius (centre of Earth to a point) o Geographic Latitude – Angle between the equatorial plane and vertical line at a point ­ Longitude o Measured east or west from a meridian (line from pole to pole) o International convention: Prime meridian runs through the Greenwich Observatory in London, England o Measured 180 degrees to East and West (rarely: 360 degrees around the globe, east from the prime meridian) o Two angles, latitude N or S of the equator and longitude E or W from the prime meridian, define a position on the globe Location On AMap ­ Latitude and longitude: o Grid drawn on map or marked along the edges o E.g. Apoint is at 45 degrees, 50 minutes 22 seconds north, and 78 degrees, 20 minutes, 10 seconds west o Written as: 45° 50’22” N, 78° 20’10” W o Check out this link for more information: ­ Universal Transverse Mercator (UTM) grid (military grid) o Universal – Covers the whole world o Transverse Mercator – Map projection it is based on o Square grid, 1km spacing o Drawn in long narrow strips (zones) – Total of 60 zones o Each zone covers 80° N to 80° S, only 6° of longitude wide o Poles mapped separately with a grid centred on the pole o Check out this link for more information: ­ Grid reference: o Like stating x-y coordinates on a graph o Edges of map are labelled like axes of a graph o Give Easting – Distance in east-west direction, estimated to a tenth of a grid square (100m for a 1km grid) o Give Northing – Distance north-south estimated to 1/10 square  Example: 43.7 easting, 55.3 northing, written as 427553 o But note that this is an abbreviated grid reference, just used for convenience. 100km north or east of here would be another place with the same numbers. The full reference avoids this – see link below. Afull grid reference tells us which zone we are in and gives unambiguous coordinates, as in the linked example o Check this link for more information: ­ Arbitrary grid of letters or numbers o Common on street maps Lecture 2 Map Scale, Directions Scale ­ Precise geometric relationship between a map and the region it portrays o One of the most important characteristics of a modern map o Most maps are greatly reduced in size compared to their subjects, so scale is a small fraction ­ Definition: o Ratio of the size of the map to its subject o Scale = Distance on a map / distance on the ground ­ Example: o Two points on the ground are 1000m apart o Represented on the map by points only 1cm apart o Calculate scale as follows:  1cm represents 1000m  1000m = 100,000cm  So 1cm represents 100,000cm  So scale = 1cm / 100,000cm = 1/100,000 ­ Scale is a fraction expressed in 3 ways: o Representative Fraction (RF) – E.g. 1 : 100,000 o Verbal Scale – ‘One cm represents one km’ o Graphic Scale – Aline labeled with the distance it represents ­ Graphic scale remains accurate if map is enlarged or reduced. Verbal ad RF scales do not ­ On a graphic scale, the intervals must be convenient round numbers Scale Examples ­ Example: Ground distance = 5 km, map distance = 2 cm o Step 1: 2 cm represents 5 km (write in full) o Step 2: 1 cm represents 2.5 km (divide so left side = 1) o Step 3: 1 cm represents 250,000 cm (convert to same units) o Step 4: Scale is 1: 250,000 (express as a representative fraction) ­ Example: Distance on map = 3.5 cm, map scale = 1: 15,000 o What is the real distance? o Step 1: 1 cm represents 15,000 cm (express scale in words, same units as your measurement) o Step 2: 3.5 cm represents (3.5 x 15,000) cm = 52500 cm (multiple both sides by map distance) o Step 3: 3.5 cm represents 525 m (convert to more convenient units) o Answer: 525 m Scale ­ Large and small scales: o Scale is a fraction o ½ is larger than ¼ o 1/5000 is larger than 1/100,000 o 1: 5000 is a larger scale than 1: 100,000 o ‘Large scale’depends on context but usually refers to scales larger than about 1: 50,000 (Note: This has nothing to do with an expression like ‘a large-scale construction project’) ­ Enlarging or reducing: o Scale is map distance / ground distance o If the map is made larger (on photocopier etc.) the map distance increases, so scale changes o Larger map = larger scale, smaller map = smaller scale o Multiple the map distance by the percentage change and recalculate scale ­ Example: Map distance = 1 cm, Ground distance = 1 km o Scale = 1: 100,000 o Enlarge by 141% on photocopier o Map distance = 1.41cm, Ground distance = 1km o Scale = 1.41/100,000 = 1: 70,921 Directions ­ Three main ways to express a direction o Points of the compass  Acceptable for rough directions, not for exact work  Directions usually lie between points of the compass, however often you subdivide o Bearing (numerical version of #1)  Step 1: Look due north if the point you are interested in is at all north of you. Look due south if it is south of you  Step 2: Turn towards east or west until you face the point  Step 3: Measure the angle of that turn  Step 4: Express the bearing using all three pieces of information from step 1, 2, and 3: • North 30° West • North 45° East • South 12° West • South 87° East o Azimuth  Step 1: Look due north  Step 2: Turn clockwise until you face the point you are interested in  Step 3: Measure the angle of the turn.  This angle is the north azimuth, usually just called  azimuth: • 330 degrees • 45 degrees • 192 degrees • 93 degrees  Be able to convert between bearings and azimuths! o Adding Angles  Useful in surveying and navigating   Remember: 60’ = 1° 60’ = 1’  35° 22’ 40” + 5° 15’ 30” = 40° 38’ 10” Definition Of North ­ Three common approaches: o True North (from the latitude – longitude grid)  Points exactly at the north geographic pole (axis of rotation) o Magnetic North (the direction a compass needle points)  Points along magnetic field lines, roughly toward the north magnetic pole (in NWT)  Differs from True North in most places because magnetic and geographic poles are not the same  Changes over time as the magnetic pole drifts  Position of magnetic north must be recalculated if map is more than a few years old  Rate of change printed on edge of map  Example: • “Magnetic North was 7° 30’ west of true north in 1985, decreasing at 12’ annually” • So in 1992, after 7 years: o Magnetic North will be 7° 30’ west of true north, minus 7 times 12’ = 84’ o 84’ = 1° 24’ o So in 1992 magnetic north is 6° 6’ west of true north o Grid North (refers to UTM grid)  Same as True North as the centre of each six degree UTM zone  Changes to each side because the square grid does not follow the convergence of meridians towards the pole  Most topographic maps show the three Norths in a margin  Some maps show only one North. If it is not true North, it must be identified Lecture 3 Elevation, Slope, Contours Elevation ­ Measuring elevation o Need a datum (reference level) to refer to o Use sea level (mean sea level, or high water mark on a coast, etc.) o Easy to measure at sea or on the coast o Estimated under the land (imaginary water level in a canal crossing the land from coast to coast) o This global shape of the sea surface is called the geoid o It differs from the spheroid (flattened sphere) by 80 to 100 m maximum. All heights are measured from this datum o Geoid now measured by satellites o Elevations relative to geoid measured by surveying o Check out this link for more information: o   ­ Depicting elevation o Earliest method: pictures of hills (since 2000 B.C.) o Hachuring: Slopes shown by many small lines pointing downhill. Steeper slope, thicker hachures, so steep slopes look darker. Common 1700 – 1900 o Contours:Acontour is a line joining points with the same elevation. Popular since 1800 o Shaded relief: Shows hills and valleys as if illuminated by sun o Check out this link about interpreting contour maps: (Note: Not all contour maps are of elevations!) Height And Slope ­ Measuring heights on a contour map: o Find the point you want to know the height of o Find the elevations of the contour lines on each side of it o Estimate the height of the point between those elevations o Example: If a point is ¼ of the way between 250m and 300m contours, we estimate its height as 250 plus ¼ of the contour interval (in this case 50m) = 250 + 50/4 or 262.5m (As this is an estimate only, don’t suggest you know it to within 0.5m; round to the nearest 10m, and call it 260m) ­ Measuring slopes on a contour map: o Find the point at which you want to know the slope o Find the elevations of the contour lines on each side of it o Measure the distance between the contour lines (at right angles to the lines themselves) o Slope = “rise over run”, or vertical height increase over horizontal distance o Example: If two contour lines are 300m apart (use map scale to find the distance between them!) and they represent elevations 50m apart, then rise = 50m, run = 300m. Slope = 50/300. But we don’t write it that way…  Percentage slope: Do the division, multiple by 100: (50/300) x 100 = 17%  Slope as an angle: Do the same division: 50/300 = 0.16667. This is the tangent of the angle of slope  We need the angle whose tangent is that number. On a calculator, having found that number, press INV TAN or 2ND TAN (or however your calculator gets to the “inverse tangent” function)  In this case the angle is 9.5 degrees  Note: The ‘run’can be the distance between any two points, not just between two contour lines. You just need to know the elevation of each point and the distance between them o Check out this link about calculating slopes Constructing Isolines (contours) ­ Continuous data only! o We need to estimate elevations between measured points o This is only valid for continuous data ­ Collection of data: o Values measured only at specific locations o Impractical to measure everywhere o Best results if we measure at significant locations o Example:  Estimate elevation of a point on a hillside  Easy if we know the elevation at top and bottom of the hill  Impossible if we have elevations only on hilltops or only in valleys  Surveyors measure significant elevations: • Points at bases of hills • Along tops of ridges • Anywhere the slope of the ground changes  Assumption: Between those places the slope is constant o Easy to measure significant points if we know where they are
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