Geog 380 Map, Air Photo, and Satellite Interpretation
Spring, 1999 Name __________________
I. Projections
Introduction
This exercise is adapted from one given to Cartography students (Geog 385) last year. It introduces you to the production of map projections by computer. Not many years ago, cartographers had to construct map projections by hand, perhaps using a calculator in more recent times. Fortunately, the computer takes care of most of the mathematics now. This should leave the cartographer free to design the map using whatever projection suits the situation. But you still need to understand what projections are and their characteristics. Otherwise you won't know how to choose a projection, or what difference it makes -- and it can make a big difference!
You will use a popular map viewing software called ArcView to look at projections. In the past we have used another software packaged called MicroCAM (for microcomputer automated mapping). MicroCAM is free, but it's a little more difficult to use. If you're interested we can show it to you and arrange for getting you a copy.
ArcView is from a company called Environmental Systems Research Institute, or ESRI. ESRI's main product is called Arc/Info. Arc/Info is the largest-selling software for geographic information systems (GIS). ArcView isn't a GIS package per se, but it can do many of the things GIS software can do. Since it can read maps designed for Arc/Info and since it's pretty user-friendly, ArcView is quickly becoming a popular package for many mapping operations.
As you work through the exercise, answer the numbered questions. When finished, turn in this whole exercise. You can also print maps if you like as you go along; just use the File-Print command in the ArcView menu.
I. Log on and Open the "Projection" exercise
To log on, press Control-Alt-Delete to bring up the Log-on dialog box. In the Username box type "380guest". The From box should say "GIC". Type in the Password box "geography". Note: The Username and Password may be different --check with instructor.
This starts Windows. Go to File Manager and double click to open. Click on the H Drive. Then click on H:\Class\380 directory. This will bring "projectn.apr" file to the right side of the tree. Double click on "projectn.apr". This loads ArcView, Projection Exercise. Then go to File-Open, and your first map will appear.
Displayed is a "view" of the world's countries. In the background should be the latitude/longitude grid. On the left side of the view is a legend (not all listed items are drawn yet).
II. Explore ArcView tools and view
Now you will see a few of the characteristics of the ArcView program and the information it provides. Notice along the top of the screen you have the typical Windows menu. Just below it are a couple of rows of tools and buttons that are shortcuts for doing operations on maps. Don't worry about what most of them mean for now.
On the upper right of the ArcView window on the lower tool bar are given two useful pieces of information: the scale of the map and the location of the mouse pointer. Your map may not show a scale right now; it will a little later after you change the projection.
Question 1. Of the three types of scales cartographers use, which is this one? What scale is listed for this map? (If it doesn't appear right now, come back and write it in when it does.)
To see the cursor location, move the mouse over the map and watch the cursor position change.
Question 2. Use the cursor to examine the map's coordinates. (a) What type of coordinates are they? (b) Where are the x (first) coordinates negative? the y (second)?
Although this is a world map like many you've seen, it's not like the globe. As discussed in class, you cannot project any portion of Earth's surface onto a flat map without some distortion.
Question 3. Describe the difference in appearance between this map of the world and how a globe appears, in terms of the shapes and sizes of continents and the latitude-longitude graticule.
The current map is not really even a projection. All that's been done has been to take the latitude and longitude and plot the grid as if it were a simple x,y coordinate system. Each 30° x 30° region here appears square, even though on the globe they are definitely not square, especially near the poles! Hence this "projection" is not a generally suitable one. It has none of the qualities we might want in a projection -- equal-area, conformal, etc. The next step is to start projecting the globe so it has some good qualities.
III. Change to a Different World Projection
To change the projection of a view in ArcView, go to the View menu and select Properties. A dialog box opens that describes characteristics of this view, such as the date it was created. Notice the entry next to map units: it currently reads decimal degrees. This is what you were looking at in the view before. Remember decimal degrees? An example would be 38.25°. The equivalent in degrees, minutes and seconds would be 38° 15' (since 15' is 1/4, or .25, of 60'). ArcView requires that map data be in decimal degrees to be able to alter the projection.
In the dialog box for the View Properties, click on the button labeled Projection... Another dialog box opens with information on projections.
If you're using standard projection types, you'll normally only use two of the lines in this box. The first one, Category, groups projections according to the geographic region you're working with. You can click on the drop-down arrow to see the choices here. Some projections can be used for the world or any part of it, some can only be used for limited geographic areas, and a few may be suitable for both the whole world and small parts of it at larger scales. For now, leave this line labeled as Projections of the World.
The line below, Type, gives projections for the Category the you've selected. Click on the drop-down arrow here and examine the available projections. Some familiar names crop up. Click on Mercator and then on OK to close the projection dialog box. Before closing the View Properties dialog box, note that the map units entry has changed to projected meters. Then click on OK in this dialog box to return to the view.
ArcView recalculates the coordinates and redraws the world in the Mercator projection. Notice that it doesn't show the extreme polar regions, and goes only to 75° N latitude here.
How is the latitude/longitude graticule different in the Mercator projection from the previous map -- i.e.,
Question 4. How are the boxes of 30° x 30° different? (Review section II if necessary.)
This Mercator view of the world is familiar to many since it's used in many places. Unfortunately, it's one of the worst choices for showing the area relationships of places. Areas near the poles are much larger than they should be relative to equatorial areas. For instance, Greenland appears about the size of South America, when in fact it is about 1/8 as large!
The Mercator projection is great for one main purpose: navigation. It is the only projection that shows compass headings (also called rhumb lines and loxodromes) as straight lines. Setting a compass on a heading and following it is the easiest way to go, so a sailor or pilot can use this map to plot her/his course. But as we'll see, this course wouldn't be the shortest route. In any case, the widespread use of the Mercator projection for navigation led to its use in other places.
The Mercator is also a conformal projection, meaning that shapes of areas are correct. If you look at Alaska here and compare it to the globe, it will look more natural than a non-conformal projection. Another way of defining conformal is to say that angles are preserved correctly from the globe. By definition, parallels and meridians cross at right angles on the globe. Note they cross at right angles here too.
IV. Change to an Equal-Area Projection
Let us change the map to an equal-area projection of the globe. Choose View-Properties again from the menu, and click the Projection button in the dialog box. Click the Type drop-down arrow and click on the Equal-Area Cylindrical projection. Click OK twice to get back to the view. The world is still rectangular like most cylindrical projections, but things are slightly different again.
Question 5. Describe the difference now in the graticule and the shapes and areas of lands near the poles.
It's difficult to have an equal-area map for the world that looks even somewhat natural. Some other compromises have been developed that attempt to be equal-area or nearly so, and show the world with a natural appearance.
Question 6. Change the projection again for each of the projections listed below, and describe for each the shape of meridians and parallels:
Robinson (official National Geographic projection; neither conformal nor equal-area):
Sinusoidal (equal-area but not conformal):
V. Specify Projection Parameters
Go back again to the Projection dialog box (via View-Properties, then click on Projection). You may have noticed in the projection dialog box other entries below the Type line. In creating a projection, you can choose exactly how it's done. ArcView does have its own Standard options for each projection, as indicated in the "radio button" at the top of the dialog box. But you can customize your projection to fit your needs.
Click on the Type, scroll down and choose The World from Space. Notice the actual projection name that appears in the Projection line: Orthographic. You may recall this from the text or lectures. Click OK twice to see this projection. It does look like Earth from space, although technically it's slightly different (you'd have to be infinitely far away to get this exact perspective, but then of course you'd be too far away to see Earth!).
Question 7. Where is this projection currently centered -- that is, where is the center of the circle formed by the disk of Earth?
Now go back to the Projection Properties dialog box (I'll assume you know how to get there from here on). At the top of the dialog box, click on the button labeled Custom. Notice the rest of the box changes. Now click in the line labeled Central Meridian, and replace the entry with a value of -122 (note the negative sign). Then click in the Reference Latitude line and change it to 38. Click OK twice to redraw the map.
Question 8. Where is the map centered now? (That's better, right?)
You can center your map at any location you like to create your own customized map of the globe. When you change the values for items like central meridian, you're changing the parameters of the projection. A parameter is simply a value that plugs into a formula or equation. Remember that west longitude and south latitude are given negative signs. You can try this again once or twice to convince yourself how it works. You can customize other projections too.
VI. Mercator vs. Gnomonic vs. Equidistant Projections
You've seen how projections can preserve or alter the true-shape (conformality) or true-area (equivalence) qualities of the globe. Let's now look at how projections affect a couple of other qualities of the globe. Certain projections can show true distance (equidistance). Also we may want to show great circles as straight lines, since great circles connect places according to the shortest distance on the globe.
Get back to the Projection properties dialog box. First change the button at the top of the dialog box back to Standard, then change the Type back to Mercator, and click OK twice to see the view. You should see the world in the rectangular, exaggerated -- but conformal -- Mercator projection.
You saw above that straight lines on the Mercator are constant compass bearings (loxodromes), which makes it useful for navigation. Remember that those lines are not the shortest distance between two points. Verify this now by measuring the distance between San Francisco and Moscow in the two projections. Use the following procedure.
First, switch your cursor to the measure tool by clicking on the button that looks like a question mark over a ruler, with arrows pointing away from the question mark.
Now when you move the cursor onto the map, it should have a small cross-hair with a ruler. You can measure the distance between two places by clicking with the measure tool on one location, then moving the cursor to the other location. Let's measure the distance between San Francisco and Moscow. To see markers for these two cities, move your cursor to the legend on the left of the map and click in the check-box next to the Cities entry. You should see a marker for each city appear on the map.
To measure the distance, move the cross-hair cursor over San Francisco, click once, then move the cursor to Moscow, and double-click to finish measuring. The distance between the two cities is shown on the status line at the lower left of the screen. Record the distance under question 9 below, then come back to this point.
To see the effect of different projections on routes between places, turn on the layer called San Francisco - Moscow in the legend by clicking on its check-box. You'll see the two routes drawn: the green one for Mercator, and a red one for the gnomonic projection. The green line follows the line you just drew. The red line follows a polar route (note that the Mercator projection here is only shown to about 75° N, so the top of the gnomonic route is cut off). The polar route looks longer, right? But it's actually shorter!
To see this, go back to the Projection properties dialog box and change the Category to Projections of a Hemisphere. Then click in the Type line and notice the new list of projections. Change the Type to the Gnomonic (North Pole) projection. Press OK twice to return to the map display. Notice a very different perspective on the globe. It looks distorted, but this projection has a special feature. Remember that the gnomonic is the only projection that shows great circles as straight lines. The red line now is straight, showing it to be a great-circle route. The Mercator "route", which you could follow by setting your compass once at the start (on about ENE) and going all the way to Moscow, is actually much longer!
The great circle route requires that you change compass directions along the way. You'd start close to due North, and end up heading close to due South. Hence the compromise most navigators make: draw the great circle route on a gnomonic map, transfer it to the Mercator map (by hand or by computer), and then draw a series of straight lines that approximate the great circle route, but that allow them to follow one compass heading for each segment.
You could measure the length along the gnomonic line, but believe it or not it would give you an incorrect value for the distance! (You can try it & note the distance to compare with the next step if you like.) What we need instead is a projection that has correct distances from one point to another. The answer is an equidistant projection.
Go again to the Projection Properties dialog box, and change the button at the top to Custom, then change the Projection to Equidistant Azimuthal. Change the Central Meridian to -122 (remember the negative sign), and the Reference Latitude to 38 (location of San Francisco). Click OK twice to redraw the map. Notice the center of the map is now San Francisco, just as we asked for.
With measure tool still active (click on its button if necessary), measure the distance again from San Francisco to Moscow and record the distance below. Then answer the question that follows.
Question 9. Distance from San Francisco to Moscow:
- in Mercator projection: _________________km
- in Equidistant projection: _______________km
- difference in distance between the two: _________________km
Why is the distance different in the two projections (refer to your notes or book as necessary)?
A final note on equidistant projections: they only give true distances from the central point. This is the reason we specified that San Francisco should be the center of the projection. Had we done a standard Equidistant Projection (centered on the Pole), we would have gotten another incorrect answer! By the way, we could also have centered the map on Moscow. But the current map will give correct distances from San Francisco to any other point on the globe.
Before proceeding you can turn off the routes by clicking again on the San Francisco-Moscow check-box in the legend.
VII. Projections for Regions
Now we will examine a couple of projections suitable for regions. In mid-latitude regions (mid-latitude means the general area between the tropics and the polar regions), conic projections are very often the most suitable for showing continent-sized areas. Some examples of regions suited to conic projections are China, Europe, Australia, South Africa, and the United States.
Use the Projection Properties dialog box to change the Category of projection to Projections of the United States. Click on Type and examine the list. Notice that only three basic projections are available. Two of these, Albers equal-area conic and Lambert conformal conic, are by far the most used projections to show the United States as a whole. You certainly can use other projections listed in other Categories, such as Mercator or Azimuthal Equidistant. But most of them distort this region much more than the just-mentioned choices. Choose Albers Equal-Area (Conterminous U.S.) and click OK to get back to the map view. The conic method of projection should be evident in the display.
Question 10. Describe the shapes of the parallels and meridians in this projection -- are they straight or curved, are parallels indeed parallel, and do meridians converge toward the poles?
Since we're interested in the United States, let's zoom in on just this area. To do this, click on the zoom tool in the tool bar (it looks like a magnifying glass with a plus sign). Then click and drag a rectangle around the US (you can omit Alaska & Hawaii). The projection gives the U.S. the typical shape you've no doubt seen in maps before.
As is obvious from the name, this projection preserves the globe quality of equivalence. To see a slightly different view, use the Projection Properties dialog box to change the projection type to Lambert Conformal Conic (Conterminous U.S.) (then you may need to zoom back into the U.S.). You'll probably notice little difference between this view and the last. It is subtle, but this one is conformal and is not truly equal-area. But it does illustrate a good point: projections have less effect on the appearance of maps as you get to larger scales.
VIII. Projections for Local Areas: UTM and State Plane
Finally, we will look at local areas and projections suitable for those areas. You just saw that at larger scales, projections have little effect on the appearance of areas. Nor is there much error in terms of area or distance. At the local scale, most projections are conformal. Why? Because the ones who care most about accuracy on a local level are surveyors. And surveyors measure land most often in terms of angles between landmarks. Remember the definition of conformal? An important part of it is that conformal projections preserve angles correctly as they are on the globe.
For local mapping, surveyors, cartographers and others often need to pinpoint locations accurately. It's difficult and cumbersome to use latitude/longitude. For instance, a point in parking lot "A" at SSU has been surveyed as being at 38° 20' 34.15210" N, 122° 40' 33.99165" W. Imagine trying to figure the distance between this point and another one nearby with similar digits. It would be like figuring how many seconds there are between 9:23:45.98102 a.m. and 2:53:05.73954 p.m.! The units are too cumbersome.
Instead, a number of grid systems have been set up to make locating places easier. Two of these are important for us: the Universal Transverse Mercator (UTM) and the State Plane Coordinate (SPC) system. Both use conformal projections, but they split up the U.S. into different zones, each with its own independent projection and coordinates. Let's look at each in turn.
Universal Transverse Mercator (UTM)
Go again the Projection Properties dialog box, and change the Category to UTM. In the Type item, notice that the selection is by zones -- in the UTM system, the world is divided into 60 vertical strips, each 6° of longitude wide. Northern California is in zone 10, so select Zone 10 in this item and use OK to get back to the map.
You'll probably get zoomed back out to see most of the Western Hemisphere -- and a distorted one at that. The UTM system is only usable within the 6°-wide zone along the central meridian (north-south line).
Question 11. Describe conceptually how this projection is constructed, in terms of the basic type of projection (planar/cylindrical/conic) and the standard line. (Look at your book/notes and also use the name for a clue.)
Use the zoom tool to drag a box around the Bay Area and zoom into our region. Notice the coordinates in the upper right of the screen. The first number is the x or east-west coordinate, called the easting. The second is the y coordinate and is called the northing. Both coordinates are in meters.
Question 12. Write down the approximate coordinates of the southwestern tip of Point Reyes (peninsula jutting out above San Francisco):
__________________________ meters East,
__________________________ meters North
If a UTM easting is 500,000 m E (i.e., meters East), it means the location is that far east of the origin, which puts the origin 500 km (300 miles) off to the west. Technically, that "origin" really doesn't exist. What has happened is that the central line (meridian) of the zone, which could really be considered the origin, is arbitrarily given an easting of 500,000 m E. So the 500,000 north-south line is actually the center of the zone. Points west of this line are below that value, and points east are higher.
The northing does have a real origin: the equator. The northing value tells how far north the location is from the equator. Hence a northing of 4,500,000 m N is 4,500 kilometers north of the equator.
What makes UTM and the next system valuable is that not only can you locate places with a pair of simple coordinates, but also you can calculate the distance between them very easily, using the famous Pythagorean Theorem. But that's another story.
State Plane Coordinates (SPC)
The last coordinate system we will examine is the State Plane Coordinate System (SPCS) . The SPCS started in the 1930s as a way for surveyors and others to establish accurate coordinates for local areas. The most obvious difference between UTM and SPCS is that while UTM coordinates are in meters, SPCS coordinates are in feet. Another difference is that UTM covers the entire globe, while SPCS is set up only for the United States, though other countries have established similar systems.
Like the UTM system, the SPCS breaks up regions into pieces. But while it only takes about a dozen UTM zones to cover the U.S., the SPCS may have up to ten zones per state for larger states. Hence each SPCS zone is relatively small, only a few counties each. The zone covering Sonoma County goes only from Sonoma and Marin Counties eastward to Lake Tahoe in a narrow band. Counties are not split up but remain in single zones.
Examine the SPCS by going to the Projection Properties dialog box, and click in the Category list. Notice two State Plane choices, for 1927 and 1983. They correspond to the two major geodetic datums set up for the United States: the North American Datum 1927 (NAD27) and the North American Datum 1983 (NAD83). Let's use the NAD83, then select from the Type list California - Zone II (you'll probably need to scroll up a ways to find the California zones). Before closing this dialog box, write down the projection parameters for this zone, which is the one covering Sonoma County :
(Question 13. )
Projection: __________________________
Ellipsoid: __________________
Central Meridian: _____________________
Reference Latitude: ___________________
Standard Parallel 1: ____________________
Standard Parallel 2: ____________________
False Easting: ________________________
False Northing: ________________________
Question 14. Each SPCS zone can have different values for all of the above values except one. What one characteristic will all SPCS zones for 1983 have in common, and why? (You can use the Projection Parameters dialog box to check other zones.)
Now click OK to get back to the view. Use your cursor to point at Point Reyes again and get the SPCS coordinates for the southwestern end of the peninsula:
Easting (x): _________________________
Northing (y): _________________________
Finished.
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