Maps represent one of the most important tools that geographers use to communicate information about the spatial associations of the phenomena which they study. We can think of maps as being models, in the sense that they typically aim to reduce the complexity of the real world into something that can be studied more easily. There is a bewildering array of map types; common map types are base maps, which show the essential features of the landscape, and thematic maps, which show the spatial distributions of probably any geographic variable you care to think of. In Canada, base mapping at the federal government level is the referred to as the National Topographic System (NTS).
This lab is largely about how to use NTS maps, plus some Google Earth practice, to address fundamental questions that geographers ask: How can we specify where a place is? (Geographers know where it’s at!). How far is it between two places? In which direction are we going?
After completion of this lab, you will be able to:
- Use geographical coordinates and UTM coordinates to specify locations;
- Understand the applications of map scales;
- Derive distances from a map;
- Use Google Earth to derive coordinates and distances.
The term geographical coordinate refers to the latitude-longitude system, which defines a location using angles measured from some prescribed baseline. Latitude is the angle measured north or south from the equatorial plane to your position. Lines of equal latitude form parallels that run west-east. The Equator is at latitude 0°. Latitude ranges from 90°S (South Pole) to 90°N (North Pole). When using latitude data in purely digital form (i.e. the N or S isn’t specified), northern hemisphere data are considered as positive and southern hemisphere data negative. Unless you’re using purely numerical data, you must specify N or S to avoid ambiguity.
Since parallels must, by definition, be parallel (go figure!) each line of latitude must have a fixed north-south separation between them. On the Earth’s surface, one degree of latitude represents a distance of approximately 111 km. This is a useful thing to remember, because it enables you to estimate the north-south distance between two places if you know their latitudes. For example, the northern boundary of British Columbia is the 60°N parallel, and most of the southern boundary is at the 49th parallel (i.e. 49°N); therefore, a very quick estimate of the distance between the two boundaries is: (60 – 49) 111 = 1221 km.
Longitude is the angle measured west or east from the Prime Meridian (or Greenwich Meridian, since it runs through the observatory at Greenwich, England) to your position. Lines of equal longitude form meridians that run north-south from the North Pole to the South Pole. This means they are not parallel: they are farthest apart at the Equator and converge towards the poles. The Prime Meridian is at longitude 0°. Longitude ranges from 180°W to 180°E. When using longitude data in purely digital form (i.e. the W or E isn’t specified), eastern hemisphere data are usually considered as positive and western hemisphere data negative (but beware – occasionally you may come across the reverse of this convention, for example when using online distance calculators; you need to stay sharp!). Unless you’re using purely numerical data, you must specify W or E to avoid ambiguity. Note that the 180°W meridian is also exactly the same as the 180°E meridian, and is also the general location of the International Date Line.
The distance between individual meridians is ~111 km at the Equator (i.e. same distance as one degree of latitude) and decreases as you get closer to the poles; this means that estimating west-east distances from longitude data is a little trickier than it was with latitude. The simple solution is that the surface distance between two meridians, one degree of longitude apart, is: 111 cos(LAT), where LAT is your latitude. For example, the west-east distance for one degree of longitude in the central area of British Columbia’s (55°N assumed) is: 111cos(55) 64 km.
Geographical coordinates are based on angles, and there are two common ways to express these:
- As a simple decimal. Here are three examples: (i) 50.6°N; (ii) 50.57°N; (iii) 50.56789°N. Obviously, the more decimal places we use, the greater the implied accuracy of the coordinate. Using coordinate (i) would be appropriate when defining the location of a town, for example, because this only requires an approximate value. But if we wanted to define the location of a particular building in that town, then greater precision is required, and the extra decimal places in coordinate (iii) would be needed.
- Using a sexagesimal system, which divides one degree into sixty minutes and one minute into sixty seconds. Here are three examples, exactly the same as those in (a), above: (i) 50° 36′ N; (ii) 50 34′ 12″ °N; (iii) 50 34′ 04.404″ °N. Notice here that if we want to specify very precise locations using the sexagesimal system, we have to add decimal places to the seconds.
Geographic Coordinates on Maps
Different mapping agencies use different ways to denote geographical coordinates on maps, but a common method is to show latitude and longitude markers around the margins. On Canadian 1:50,000 NTS maps (e.g. Figure 12.1), the alternating black and white bar lines along the margins represent minutes of latitude (vertical lines) and longitude (horizontal lines). The latitude increases as one moves northwards (up) away from the Equator and longitude increases as one moves westwards (left) away from the prime meridian. It might also be useful to note that the neatlines (i.e. the actual edge of the map) of NTS maps are defined by parallels and meridians (i.e. the top and bottom edges run exactly west-to-east, and the sides run exactly north-to-south).
There are several items to note in Figure 12.1:
- The marginal information related to geographical coordinates is in black-and-white (i.e. ignore the blue annotations)
- The northwest corner of the map has coordinates of 50°00′ and 119°30′, but we are not told which hemispheres. The map-makers assume that we know that Canada is in the northern and western hemispheres.
- Notice the black and white bars up the side: there are seven of them, each representing one minute of latitude, and therefore the north-south extent of the map shown here is nearly 7 minutes of latitude. Every fifth minute has a label: notice the 55′ marker in the lower-left edge of the map.
- The black and white bars along the top margin each represent one minute of longitude, and therefore the west-east extent of the map shown here is about 8½ minutes of longitude.
- Values of latitude increase bottom-to-top, because we are moving farther away from the Equatorial plane. Values of longitude increase right-to-left, because we are moving farther away from the Prime Meridian.
To determine the geographical coordinates of a location when using a NTS map or Google Earth, look in the Supporting Material section at the end of this lab.
UTM Coordinates and Grid References
The Universal Transverse Mercator (UTM) coordinate system is a type of Cartesian system, which means that a location is specified using a rectangular grid. You will be familiar with simple graphing using an x-axis and a y-axis, in which a point can be located by its x value and y value, as follows: (x,y). The UTM coordinate system is similar, but bigger, since it covers most of the Earth! (UTM doesn’t extend to the polar regions, where a separate system, UPS, applies.) Common mapping software (e.g. Google Earth) and GPS receivers often use full UTM coordinates, so it’s important to understand how they work.
The UTM system divides the Earth into sixty identical north-south strips or UTM zones, each 6 degrees of longitude wide and identified by a number (Figure 12.2). Each zone has a central meridian down the middle. Zone 1 is 180°W-174°W, Zone 2 is 174°W-168°W, and so on. So, for example, we find that British Columbia falls into zones 10 and 11, with the boundary between them at 120°W. Each zone has latitudinal divisions 8° latitude in extent, that have letter designations (with I and O being excluded) starting with C at 80-72°S. The Equator is the boundary between M and N (useful to remember because the letter indicates which hemisphere you’re in: C to M are southern and N to X are northern).
So, with a simple number-letter combination we can easily specify any of the squares (or UTM quadrilaterals as they’re more formally known) shown in Figure 12.2. This is useful information, of course, because it immediately gives us a good idea of where we are.
In each of the northern and southern hemispheres, the UTM zone is treated as a very large (x,y) grid. All zones have a “false origin” (0,0) from which the x value (the easting) and the y value (the northing) are derived (Figure 12.3). This is placed 500,000 m west of the zone’s central meridian, forcing all eastings to be positive (UTM has no negative numbers). In the northern hemisphere, the false origin is at the Equator; in the southern hemisphere it is set at 10,000,000 m south of the Equator (this ensures that all northings are positive numbers).
UTM coordinates give your position in the number of metres east and north of the false origin, so the numbers end up being large! For eastings, six digits are required, but for northings, seven. A full UTM coordinate contains: (zone number + letter), easting, northing.
Here’s a simple example of how UTM works: take a look at Figure 12.3, which shows part of UTM zone 10 (Note that the principles outlined here apply to any zone). We will make a rough estimate of the UTM coordinate of location x. It is in UTM quadrilateral 10P. We can see that it is slightly to the east of the central meridian and therefore we know that the easting must be greater than 500,000m; let’s say that x is 600,000 m east of the false origin. We can also see that x is at about 10°N, which means that we can make an educated estimate of how far north it is from the Equator: recall from above that each degree of latitude represents about 111 km of surface distance. Here, we have ten times 111 km, which is 1110 km, or 1,110,000 m. So, a rough estimate of the UTM coordinate of x is: 10P 600000mE 1110000mN (more usually the coordinate would be written as 10P6000001110000).
Here’s a more realistic example: your friend discovered gold and took a GPS measurement, which was: 11U4347825644518.
Let’s break this down:
11U: we are in UTM zone 11, which is between 120°W and 114°W. The letter U indicates that we must be between 48°N and 56°N (Figure 12.2).
434782: the first six digits represent the easting in metres. Note that the number is a bit less than 500,000 m, so this tells us that we must be slightly west from the zone’s central meridian (see Figure 12.3).
5644518: the last seven digits represent the northing in metres. So, we are 5,644.518 km north of the Equator, which puts us in Canada.
Although the UTM system may seem a little cumbersome at first, we have uniquely identified a point on the Earth’s surface with one coordinate. No other place on the planet has this coordinate. (By the way, the bit about gold was made up, as was the coordinate! Sorry to get your hopes up.)
UTM Grid on NTS Maps
If you examine Canadian 1:50,000 NTS maps, you will see that they are criss-crossed by light blue grid lines. This is the UTM grid, and any light blue text around the map’s margins relates to UTM data. On these maps, the grid lines always form squares 20 mm x 20 mm in size, equivalent to 1 km x 1 km in reality. The blue grid will line up exactly with the map’s margins when the location is at a UTM zone’s central meridian, but will tilt slightly as we move away from it. The full easting and northings are shown only at the map’s corners; for all other places on the map, you have to derive them yourself.
To determine the UTM coordinates of a location when using a NTS map or Google Earth, look in the Supporting Material section at the end of this lab.
6-Figure Grid References
The full UTM coordinate is often unnecessary, especially if you are working in only a limited area, or using just one or a few contiguous map sheets. This is where the grid reference— a 6-figure abbreviation of the full UTM coordinate—comes in handy. The aim of the grid reference is to provide a 3-figure easting and a 3-figure northing. The precision of each is to the nearest 100 m. NTS maps usually provide instructions on how to derive a grid reference, but here’s the gist of it:
Step 1: Easting. Work left-to-right. In the example shown above, the easting is between 16 and 17 – in fact, about eight-tenths the way across the grid square. Think of this easting as being “16.8” – and then drop the decimal point to yield 168.
Step 2: Northing. Work bottom-to-top. In the example shown above, the northing is between 89 and 90 – about six-tenths the way up. So, the northing is “89.6” which gets abbreviated to 896.
Step 3: Put it together. The grid reference 168896 (not 896168).
Finally, note that we can derive 6-figure grid references from a full UTM coordinate. Let’s use the “gold” example one from above: 11U4347825644518. The “11U” part is not used in grid references, but we do need the remaining numerical information:
- Easting: the full easting is 434782. The bit we need is underlined: 434782. Since grid references give estimates to the nearest hundred metres, we want to round off the full easting to the nearest decametre (1 dam = 100 m); in this case, it is 4347.82 dam, which rounds off to 4348 dam. We only want the last three digits, so we end up with a 3-figure easting of 348. (If this was on a NTS map, this would be between the blue grid lines of 34 and 35, and much closer to the 35 line.)
- Northing: the full northing is 5644518. The bit we need is underlined: 5644518. Following the principles as for the easting, we can think of this as being a value of 56445.18 dam, which rounds off to 56445 dam. We only want the last three digits, so we end up with a 3-figure northing of 445. (If this was on a NTS map, this would be halfway between the blue grid lines of 44 and 45.)
So, we end up with a grid reference of 348445 (but not 445348).
The world is big. Maps are small. So, real-world sizes have to be reduced in order to fit the landscape onto a map, and the map scale simply tells us how much size reduction has taken place.
Map scale can be expressed in several different ways:
- Graphic scale: a simple line or bar on the map that states the real-world distance. It is simple and intuitive to use.
- Ratio scale: one unit of linear distance (e.g. millimetre, inch, etc.) on the map represents some number of the same units in reality. In the previous section, reference was made to 1:50,000 maps – this simply means that 1 mm on the map represents 50,000 mm in reality, or 1 inch represents 50,000 inches, and so on. The standard convention is to use the form “1:n“, where n can be any number.
- Verbal scale: typically, a statement that relays the same information as a ratio-type scale. For example: “1 cm represents 1 km” is self-explanatory – it means that a distance of 1 cm on the map is equivalent to one kilometre in reality (so the ratio scale would be 1:100,000). Slightly more esoteric examples are: “5 cm to 1 km”, or “1 cm equals 20 km “, neither of which makes complete grammatical or logical sense, but the meaning should be fathomable for any geographer (the ratio scales are 1:20,000 and 1:2,000,000, respectively).
Being able to convert between different types of scale is a useful skill.
We sometimes hear the terms “small-scale map”, “medium-scale map” or “large-scale map”, and it can be confusing. Perhaps the simplest way to think about this is to realise that a large-scale map will show a given feature larger on the map than a small-scale map would. Think about fitting a map of Canada on this page – you have to shrink the country very small in order to do so, and British Columbia would occupy only a small part of the page. This is a small-scale map. Now envisage a map only of British Columbia on this page – obviously, we can make it larger, and so the scale has become larger, although it would still not be considered a large-scale map. An example of a large-scale map is a 1:50,000 map sheet, where the map shows the landscape in fine detail.
Again (because it’s important!), map scale always boils down to this basic ratio:
(the length of a feature on the map) : (the real-life length of the same feature)
…and the units must be identical either side.
On your map the straight-line distance between your house and the shopping mall is 120 mm. In reality, this distance is 2.4 km. So, your map’s scale is: 120mm : 2.4km = 120mm : 2,400,000mm = 1:20,000.
Deriving Distances from a Map
Conceptually, this is simple: measure the distance on the map and multiply it by the scale. For example, 45 mm on a 1:50,000 map represents (4550,000) mm in reality, or 2250 m.
Measuring straight-line distances is easily achieved with a ruler, of course. Alternatively, you could use the edge of a piece of paper and find the map distance and then compare it to the graphic scale bar.
Measuring distances along curvilinear features (e.g., roads, rivers, etc.) is more complicated. It’s possible to use a ruler and then treat the curved lines as a series of straight segments (Figure 12.6b). Although this method will tend to underestimate the distance, it will certainly give a rough estimate that’s usable. Accuracy can be improved by using shorter straight segments (Figure 12.6c), but this comes at a cost of extra time and effort required.
If you are using a hard-copy map, an alternative method of measuring curved lines is to use an opisometer (also called a map measurer).
To derive distances in Google Earth, look in the Supporting Material section at the end of this lab.
Finally, there are also trigonometric methods to derive straight-line distances that use geographical or UTM coordinates but these are beyond the purview of this lab.
The following lab exercises provide some practice at applying the concepts discussed above. You will need a calculator, plus an internet connection to download a map and access Google Earth. Some of the exercises may be easier if you are able to print the relevant portion of the map. The exercises should take you 1½ to 3 hours to complete.
- Using only Figure 12.1, address the following questions:
a. Derive the latitude and longitude of the 669-metre summit about a kilometre NW of McKinley Reservoir. Express your final answer to the nearest 10″ (i.e. round off to 00″, 10″, 20″, etc.).
b. What feature is at 49° 55′ 40″ N, 119° 23′ 30″ W?
- Use Google Earth to:
a. Check your answer to 1(a). (Not for marks)
b. Find out what feature is at 43° 38′ 33″ N, 79° 23′ 13″ W.
- You are exploring BC’s beautiful landscapes and are wondering if this is a safe place to pitch your tent. What do you think? Your GPS receiver indicates that you are here: 54.1895° N, 131.6471° W. (Note: this GPS receiver has been set at “decimal degrees.” You will need to change the options in Google Earth – see the Supporting Material section.)
- Click here to download the 1:50,000 NTS map sheet 01N10 (St. John’s) 8th edition map sheet. Use only this map for the following questions:
a. Derive the latitude and longitude of the steel mill by Octagon Pond, Paradise (lower-left part of map). Express your final answer to the nearest 10″.
b. What feature is at 47° 34′ 13″ N, 52° 40′ 55″ W? (PS: Do you happen to know why this place is famous?)
- Using only Figure 12.1, address the following questions:
a. Derive the full UTM coordinate of the 669-metre summit a kilometre NW of McKinley Reservoir. Express your final answer to the nearest 50 m (i.e. round off to …00m or …50m; this is equivalent to the nearest whole millimetre of measurement on the original map).
b. Convert your answer for (a) to a 6-figure grid reference.
c. What do you find at 11 U 328600 5533850?
d. If you worked at the feature at 207306, what are you most likely doing?
- Use Google Earth to:
a. Check your answer to 5(a).
b. Find out what feature is at 12 U 308700 5509275.
- You are hiking in BC’s beautiful mountains but have wandered away from the trail (pay better attention next time!). Luckily, you brought a GPS receiver with you and can find your location, which is 11 U 355653 5886735. Use Google Earth to find out exactly where you are and describe the location.
- Use the same 1:50,000 NTS map sheet as the previous section.
a. Derive the full UTM coordinate of the South Head navigation light at the entrance to St. John’s Harbour (see the map’s legend for the symbol for a navigation light; you will also have to search the map for the UTM zone information). Express your final answer to the nearest 50 m.
b. Convert your answer to 8(a) to a 6-figure grid reference.
c. What feature has a UTM easting-northing of 22 T 354100 5278750?
d. Why would the feature at 776644 be a good place to eat your sandwiches?
- Address all of the following. Remember to show your work.
a. On a 1:50,000 map, what does a length of 50 mm represent?
b. On a 1:250,000 map, what does a length of 50 mm represent?
c. The straight-line distance from point A to Point B is 14 km. What length would this be on a 1:20,000 map?
d. Convert the verbal scale “One centimetre equals four kilometres” to a ratio scale.
e. Assume that you need to use a part of a standard 1:50,000 NTS map in your next term paper, but you had to shrink the map in order to fit it on the page. On your new map, the length of ten grid squares is 137 mm.
i. Is your map a smaller scale or larger scale than 1:50,000? Explain.
ii. Calculate the scale of your map.
- Use Figure 12.1 to address the following questions:
a. How long is the runway at Kelowna airport (in metres)?
b. What is the straight-line distance (in metres) between the 636-metre summit of Mount Dilworth and the 595-metre summit at 262346?
c. What is the shortest distance (in kilometres) by road between the two junctions at 254343 and 286323?
- Use Google Earth to check your answers to Question 10. (Not for marks)
- At the beginning of this lab, we encountered the relationship between geographical coordinates and surface distance: one degree of latitude or longitude represents a certain distance. We can check this using Google Earth. (This question is not for marks.)
a. The rough estimate of the distance between BC’s southern and northern boundaries was 1221 km– check this.
b. Go to BC’s northern boundary at 60°N. Measure the distance along the boundary between 120°W and 125°W. What is the surface-distance equivalent of one degree of longitude? Confirm that the cos(LAT) relationship holds true.
c. Now repeat 12(b), but at the southern boundary between 115°W and 120°W. Confirm that the cos(LAT) relationship holds true.
- One of the most fundamental issues in geography is location—Where am I? Where is this place? Where is that place in relation to the other place? Think about the different ways in which location can be defined and specified. Think about how would tell someone exactly where you are right now—the square metre of Earth’s surface that you are currently occupying! How would your description be different if you simply wanted to give the general location of the town that you are in?
- You have arranged a hiking trip for yourself and some inexperienced friends. You haveprinted out some UTM topographic maps and brought along a couple of GPS units (you knew your friends wouldn’t). Unfortunately, none of them know how to read a map or use GPS! How would you describe to your friends how to locate themselves on the map using the UTM coordinates obtained from the GPS unit?
- Google Maps has crashed, but Google Earth is fine (somehow) and you need to figure out how to get from Kelowna, BC to Fort St John, BC. You know that you can look up both Kelowna and Fort St John and pin them in Google Earth, and that enabling the “Roads” layer will give you all major roads in BC. How could you figure out the distances of different path options and choose the quickest route?
Firstly, take another look at Figure 12.1. We are going to get the coordinates of Wilson Landing.
In Figure 12.7(a) below, we can estimate the latitude and longitude: we are slightly north of 49° 59′ N and slightly west of 119° 29′ W. Estimating by eye, the arrows indicate that we will add about one-quarter to one-third of one minute of arc to this estimate (i.e., distances D1 and D2 in 12.7(a)). To get an answer better than a simple by-eye estimate, we should make measurements on the map (see below). Note that the grey arrows depicting measurements are parallel to the map’s neatlines and not the blue grid squares.
Deriving latitude (Figure 12.7(b)). We are looking to derive the proportion of one minute of arc that is between the 49° 59′ N parallel and Wilson Landing: distance D1. On the original map used in here, the proportion is 11mm:37mm. Therefore, distance D1 must be 11/37th of one minute of arc = (11/37) 60 seconds = 18 seconds.
Deriving longitude (Figure 12.7(c)). We are looking to derive the proportion of one minute of arc that is between the 119° 29′ N meridian and Wilson Landing: distance D2. On the original map used in here, the proportion is 8mm:24mm. So, distance D2 is 8/24th of one minute of arc = (8/24) 60 seconds = 20 seconds.
The geographical coordinate of Wilson Landing: 49° 59′ 18″ N, 119° 29′ 20″ W.
See the blue grid and the blue numbers in Figure 12.1. We are going to get the grid reference of Wilson Landing. Firstly, work left to right: Wilson Landing is between grid lines 21 and 22 (interpolated from the blue numbers along the top of map). Moving right from the 21 grid line, Wilson Landing is about six-tenths the distance to the 22 grid line, therefore the easting part of the grid reference is 216 (you can think of it as 21.6, but without the decimal point). Secondly, working bottom to top, we can see that Wilson Landing is between horizontal grid lines 40 and 41, and about three-tenths the distance between them: so, the northing part of the grid reference is 403. Put the easting and northing together to get a grid reference of 216403 (but not 403216).
Again, we’ll use Wilson Landing in Figure 12.1 as our working example. Firstly, we need to know the UTM quadrilateral, but this information isn’t shown in Figure 12.1 – but it would be found on the original map sheet; in this case, it happens to be 11U (FIgure 12.8).
Next, work on the easting: at the top corner of the map sheet we can see the true easting given for one of the blue grid lines: 322000 mE. The grid line to the left is 1000 m away and so must have an easting value of 321000 mE. Wilson Landing lies between the two. To get the best estimate of the easting, we should measure how far it is from the 321000m grid line to our location: in this case, on the original map, it is 13 mm, to the nearest whole millimetre (it’s not usually valid to use a finer precision than this). At a scale of 1:50,000, 13 mm represents 650 m in reality, and so this distance is added to the 321000m to get our full easting: 321650 mE. Take a similar approach to find the northing: the top-most horizontal blue grid line has a full northing of 5541000 mN (see the blue number in the upper-left part of Figure 12.1), and so the next grid line to the south must have a value of 5,540,000 m. Making a measurement on the map, we find that Wilson Landing is about 300 m north of the latter grid line and therefore the full northing is 5540300 mN. Put it all together to get a UTM coordinate of 11U3216505540300.
To use geographical coordinates: Tools–Options-<select the 3D View tab> and make your choice in the Show Lat/Long section. You will see the cursor’s coordinates at the bottom of the screen.
To use UTM coordinates: Tools–Options-<select the 3D View tab> and choose Universal Transverse Mercator. You will see the cursor’s coordinates at the bottom of the screen.
To derive a straight-line distance: Tools-Ruler and in the pop-up box select Line. Mouse-click once to start a line; click a second time to end the line.
To derive a curved-line distance: Tools-Ruler and in the pop-up box select Path. Mouse-click once to start a line; every successive click adds a node to the path. Use Clear to end the process.
To show or hide labels: Tools–Options-Layers-<select or de-select Borders and Labels under the tab>, go to the Show Lat/Long section and choose Universal Transverse Mercator
If you don’t know the map sheet’s number: access the GeoGratis web site at http://www.geogratis.gc.ca and select the Geospatial Product Index. You can then zoom in or out of the map and the map codes will appear. For example, zoom in on Vancouver: you will first see 92 appear, then a grid with letter codes, and then number-letter-number codes which are the 1:50,000 map IDs; downtown Vancouver is map sheet 92G06. You may get access to the maps directly from here, but if not go to the next step.
If you know the map sheet’s number: GeoGratis’s ftp site is at: http://ftp.geogratis.gc.ca/pub/nrcan_rncan/raster/topographic/50k/. You will find *.tif and *.pdf files available; these are scanned versions of the original NTS map sheets.
- Figure 12.1 NTS 1:50,000 map sheet 82E14 (Kelowna) 4th edition © Natural Resources Canada is licensed under a All Rights Reserved license
- Figure 12.2 UTM quadrilaterals between 72°S and 72°N © Ian Saunders is licensed under a CC BY-NC-SA (Attribution NonCommercial ShareAlike) license
- Figure 12.3 Component of UTM zone 10 © Ian Saunders is licensed under a CC BY-NC-SA (Attribution NonCommercial ShareAlike) license
- Estimating UTM coordinates © Ian Saunders is licensed under a CC BY-NC-SA (Attribution NonCommercial ShareAlike) license
- Figure 12.4 Scale from NTS 1:50,000 map sheet 82N05 (Glacier) 3rd edition © Natural Resources Canada is licensed under a All Rights Reserved license
- Figure 12.5 Curved lines as straight-line segments © Ian Saunders is licensed under a CC BY-NC-SA (Attribution NonCommercial ShareAlike) license
- Estimating latitude and longitude © Ian Saunders is licensed under a CC BY-NC-SA (Attribution NonCommercial ShareAlike) license
- Grid Zone Designation from NTS 1:50,000 map sheet 82E14 (Kelowna) 4th edition © Natural Resources Canada is licensed under a All Rights Reserved license