Map Errors Explained

Selecting a geodetic datum (e.g. an idealized geometric description of the Earth’s shape used to define longitude and latitude).
Picking a projection method used to transpose geographic features, defined by points of longitude and latitude, from a curved earth’s surface (defined by the geodetic datum) to a flat paper surface.
Choosing an appropriate scale to print the map.
Data collection.

Each of these steps can be expected to introduce errors that will influence how hikers use maps to navigate the backcountry.

Geodetic Datum Considerations

While maps can be based on any one of a hundred or so existing geometric descriptions of the earth’s average shape called a geodetic datum (e.g. the shape, size and orientation in space of a reference ellipsoid) in practice only 2 datums are important to Washington State hikers. The first, and still very commonly used datum(e.g. USGS Topographic Maps), is the North American Datum of 1927 (NAD 27) which was created using measurements taken over North America relative to a reference point very near the geographic center of the forty-eight Contiguous United States (Meades Ranch;Kansas) to create a simple geometric model of the earth. Thus, NAD27 is a local referencing system which should only be used when making maps of North American. The newer datum is the World Geodetic System of 1984 (for our purposes GRS 1980 and NAD83 datums are just WGS84 with a different name). The WGS84 datum was generated from worldwide satellite data, uses the center of the earth has an origin, and is a reference ellipsoid that best fits an idealized sea level (a.k.a. geoid) worldwide. Thus WGS84 can be used to define longitude and latitude anywhere in the world and WGS84 is the default standard datum for GPS units. While perfectly good hiking maps for Washington can be made using either NAD27 or WGS84 errors come into play when map or GPS information from NAD27 and WGS84 are incorrectly combined. In Washington the difference between WGS 84 and NAD 27 can be over 200 meters. It is also important to remember that all datums use an idealized mathematical abstraction of the physical Earth that is much smoother than the earth’s physical surface . For example, before plotting locations in Mt. Rainier National Park on a map they are first projected onto the datum (e.g. a smooth ellipsoid) and elevation relief is lost. Thus if one calculates the distance from Paradise to the summit of Mt. Rainier by only measuring the lateral distance on a map a significant underestimation of the true distance will be made. To reduce this error you would have to include vertical information in the calculation of distance (e.g. extract elevations from contour lines and calculate the distance along a profile)

Projection Considerations

The Earth is curved and maps are flat. Map projection is the mathematical process of flattening out the curved Earth onto a flat piece of paper or computer monitor. While in theory there is an infinite number of possible map projections there are only a few that hikers of Washington State would typically encounter. These projections include:

All projections (including UTM and Lambert Conformal Conic) always introduce errors. The best a map maker can do is to select the type of distortions that will dominate in his map. For instance, both UTM and Lambert projections minimize angle and shape distortions but accept less accurate representations of distance and area. In general, geometric properties that can be distorted when projecting the curved earth’s surface to a flat paper map include:

These types of distortions are most obvious in small scale (i.e. large area coverage) maps. The classic example of this is the distortions of Greenland and Antarctica that occur on the Mercator Map used in countless class rooms. On this map Antarctica appears to be a huge continent that wraps around the earth and Greenland appears to be just as large as South America although Greenland is merely one-eighth the size of South America. However, projection errors are minor for the large-scale (i.e. only cover small areas) maps that a hiker would normally use. For instance, the projections used with large-scale 7.5-minute USGS topographic map would not introduce any noticeable errors into any bearing or distance measurements that a hiker might make.

Scale Considerations

The scale of a map is usually defined as the ratio of a single unit of distance on the map to the corresponding distance on the ground. The largest scale (the large/small terminology arose from the practice of writing scales as numerical fractions: 1/10000 is larger than 1/10000000) that a hiker would normally use is the 1:24,000 7.5-minute USGS topographic map. Green Trail and Custom Correct map use a significantly smaller scale (but cover a larger area). Highway maps (which a hiker might use to figure out how to drive to the trail head) can be expected to have a scale on the order of 1:1,000,000. It is important to recognize that even the most accurate maps sacrifice a certain amount of accuracy in scale to deliver a greater visual usefulness to its user and each map scale offers a tradeoff between detail and convenience. For instance, 1:250,000 USGS topographic maps do not have the detail necessary for hiking in the backcountry but can provide an overview of large areas of the terrain that can be useful in initial the planning for a backcountry trip. A Green Trail or Custom Correct Maps may not have all the detail that a USGS 7.5 minute topographic map has but they have enough detail for most hiking needs and covers a much larger area (i.e. do not have to paste together a bunch of 7.5 minute maps to avoid “walking out” of the map) and have much more up-to-date trail information.

ANY map scale that a hiker might use always required some generalization in its creation. This generalizing can take on several forms that include: selection, simplification, exaggeration combination, and displacement. In selection the cartographer will only retain and draw certain elements that he deems the most necessary or appropriate. In this method, the most important elements stand out while lesser elements are left out entirely. An example might be the elimination of logging roads on a small scale highway map (on the other hand, logging roads could be very important on a Green Trail scale map). At the opposite extreme it is sometimes necessary to exaggerate features. For example, the width of trails are exaggerated (Table 1) when they are too narrow to be shown on the map at true scale (i.e. on a printed map they would be narrower than could be perceived by the naked eye). The same applies to computer maps where the smallest unit is the pixel. A narrow trail say must be shown to have the width of a pixel even if at the map scale it would be a small fraction of the pixel width. Simplification is a technique where shapes of retained features are altered to enhance visibility and reduce complexity. For example, a river on a highway map would be represented with a single smooth blue line while on a 7.5 minute map variations in width and river bends for the same river would be shown. Features can also be combined when their separation is irrelevant to the map focus. For example, a mountain chain may be depicted as several smaller ridges and peaks with intermittent forest on a 1:100,000 USGS topographic map but be shown as a contiguous chain on a highway map. Displacement is used if features are so close on the ground that they overlap on a map (e.g. the lines used to represent them are wider than the separation) (Table 1). In this case it is necessary to displace the map features from their original projected locations.

Maps are only generalized models of the landscape and are thus always inaccurate to some degree. However, these generalizations can sometimes allow hikers to better comprehend the environment by removing ‘clutter’ or exaggerating narrow trails. Map inaccuracies induced by generalizing need not become serious errors if the map user is aware of them.

Data collection considerations

Data collection can be a source of significant errors. For instance, in the past many trail locations were extracted from aerial photos. Since many of the trails in Western Washington are heavily forested this means that a lot of early trail mapping involved a lot of guess work. Capturing small switchbacks (which can add up to significant distances that the map will not account for if not found) can be particularly problematic under these circumstances. A related problem is that the processing of topographic data in the Olympic Mountains was relatively imprecise due to the scarcity of control and steepness of terrain. In practical terms this means is that the contour lines can be a little bit displaced from more precise data (e.g. GPS tracks). Another major problem with these trail locations is that they are often out-of-date. New mapping of trails with GPS can improve mapping accuracy but GPS can sometimes fail in narrow, deep and forested valleys. Old fashion human error is also a constant concern. All these problems cause a sort of a “man with two watches never knows the time” problem in that different map sources can sometimes show inconsistent trail locations.

In total all these possible errors make calculating extremely accurate trail features sometimes very tricky. Even calculating simple trail distances precisely can be problematic. For instance, with some maps it may not possible to show all the switchbacks. In the worst case the trail is simplified to a straight line. In this case the calculated length from the map will be significantly less then what the hiker will travel. Further, map distances only consider the horizontal distance and ignore vertical distances. With a complex trail, like the North Loop trial, the calculated distances will often be less than the actual distance.