GPS Coördinates and Notations
GPS stands for the Global Positioning System. I am not competent to discuss the technology underlying GPS: see the Basic concept of GPS section in this Wikipedia article for a simple introduction to GPS intended for non-technical readers, which is followed by a much more complete presentation, still surprisingly accessible to a non-mathematician like myself.
But regardless of how GPS conceptually works, from the satellite signals it receives, a GPS device computes its best approximation to the coördinates of its current location, delivering the result as a latitude (distance north or south of the equator) and a longitude (distance west or east of the Greenwich (England) meridian (“prime meridian”)), both measured in degrees (indicated by the symbol °), minutes (sixtieths of a degree, indicated by the symbol ′), and seconds (sixtieths of a minute, indicated by the symbol ″). Most GPS devices can also deliver the altitude of the current location along with other information, such as the current compass heading, both useful to the hiker.
The primary use of GPS coördinates on this web site is for identifying where a photo was taken. They are extremely useful for this purpose, as they pinpoint a location much more precisely than verbal indications such as “on the Southwest Ridge Road 3.8 km (2.3 mi) south of its junction with Route 19”. How precisely? According to the Wikipedia article referenced above, The standard accuracy of about 15 meters (49 feet) can be augmented to 3–5 meters (9.8–16.4 ft) with DGPS, and to about 3 meters (9.8 feet) with WAAS.
¹ That agrees pretty well with my actual experience with my GPS devices, where, on various hikes, I observed that if I sat on the same end of the same bench, I got slightly different GPS readings each time: the readings varied by as much as .003′ in both latitude and longitude. At 40°N, 1 minute of latitude is 1850.75 m (1.15 mi or 6072 feet), so a difference of 0.003′ works out to a difference of 5.55 m (18 feet). At 74°W, 1 minute of longitude is 1422.66 m (0.884 miles or 4667.5 ft); so, a difference of 0.003′ works out to a difference of 4.28 m (14 feet).² On occasion, usually during two different trips to the same place, I have seen a larger variation—as much as .010′ (18 m (59 ft) of latitude, 14 m (46 ft) of longitude); still, even such a larger imprecision serves very well for specifying the location from which a photo was shot!
Three notations are commonly used for GPS coördinates:
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the ‘df’ form uses degrees and fractional degrees: 40.1915667°
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the ‘dmf’ form uses degrees, minutes, and fractional minutes: 40°11.4940′
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the ‘dmsf’ form uses degrees, minutes, seconds, and fractional seconds: 40°11′29.64″
All three of the values shown above express the identical latitude. The classical ‘dmsf’ form does not seem to be as commonly used on the web for GPS coördinates; while the terse ‘df’ notation is widely used and sometimes is the only offering on a GPS device, for this web site, I chose instead the also widely used ‘dmf’ notation because I find it is much less error prone to record manually as well as being much more useful with paper maps, where degrees and minutes are commonly given and decimal degrees are not³. In any case, the arithmetic for converting between these notations is straightforward and, for those who prefer to not do the calculations by hand, this web site will produce the other two notations given any one of them.
Rarely, I lack for one reason or another the coördinates of the location where I took a photo. When this happens, I show a question mark for one or more of the fractional digits, interpolating from a map or, if I have recorded coördinates for landmarks or for photos near that point, interpolating from those coördinates. Thus, a location shown with question marks, such as 46°52.????′N 60°25.????′W, indicates that I lack precise recorded coördinates for the photo and have approximated them from another source.
For Christmas 2008, my family gave me a Garmin nüvi® 260W GPS device, one of a class known as personal navigation assistants. Although I had known about the existence of the satellites which make GPS possible, had seen a couple of GPS devices in the flesh (one on a lobster boat to keep track of lobster trap locations), and had rather cursorily followed discussion and reviews of them in various Mac-oriented mailing lists, this gift was my first real exposure to GPS. Rather a bit skeptical at first, the device, which I named Griselda, quickly become much more useful to me than I would have ever imagined, though not without some serious quirks.
Griselda is capable of displaying the coördinates of a location on request and it, like most similar devices, can deliver coördinates in any of the three usual notations. In GPS devices such as Griselda, however, the focus is on showing one’s location by a symbol (car, arrow) superimposed on a map of the current location: as the device moves across the surface of the earth, the map beneath the symbol moves in real time, keeping the symbol centred on the map. In this way, one can visually ascertain where one is at any given moment (usually, of course, one knows, but occasionally, in a strange city, for example, the visualization can be very useful). Most navigation assistants can compute a route from one location to another and provide detailed spoken turn directions as one follows that route. Most also allow one to record locations (waypoints) as one moves about and nearly all are capable of recording a GPS track log over a period of time. It did not take me long to begin to explore the tools that allow such a track log to be plotted onto a map, very useful, for example, for showing the route of a hike, as here. Google Earth has long been capable of importing a trip log and superimposing it on its imagery on a computer screen, a much larger and more detailed map than is available on the GPS device itself. And various apps, such as Garmin’s BaseCamp©, can do the same on a computer screen using the maps built into the GPS device.
In 2010, I retired my 1998 Camry and bought a new Prius, which I ordered with a built-in GPS device, soon named Prissy. Having a considerably larger display, it has substantial user interface advantages over Griselda for car travel and considerably better maps, but it has other disadvantages, three of them crippling:
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it is fixed to the car’s console and is therefore not portable: I can’t carry it around with me outside the car, e.g., when hiking, as I can Griselda
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it does not allow one access to a track log (though it can display a visual representation for the last 125 miles travelled on its maps if asked to do so) and, even if did, its memory is far more restricted than Griselda’s (a maximum of 100 waypoints vs. Griselda’s 1000)
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it displays coördinates in the classical ‘dms’ notation, i.e., without any fractional seconds, and is therefore significantly less accurate than Griselda
For these reasons, I rarely record its readings and do not use them on this web site.
In 2012, I acquired the Nikon GP-1 GPS accessory, soon named Gypsy, an external add-on for my Nikon D5100 camera attached to its camera strap and plugged into a socket on the side of the camera. When a photo was taken, Gypsy caused the GPS coördinates it had computed to be recorded as part of the metadata (date, camera settings, and the like) stored in the photo itself, obviating the need to manually record the location in a notebook. Photos taken on or after 2012 July 19 generally give the GPS coördinates Gypsy provided that were recorded with the photo. Unfortunately, Gypsy was not without problems. It was sometimes very slow to “warm up” and the gap between the time the camera was turned on and the time Gypsy got around to record GPS coördinates could be a few minutes long—a red LED turned green when Gypsy was ready—though once “warmed up” for the day, the lag was normally a matter of a few seconds; on all too frequent occasion, however, I failed to check that Gypsy was ready, resulting in photos with no GPS coördinates, and, less often, even when I was sure it was ready, I still did not get any coördinates recorded with the photo, for reasons I did not understand. With the passage of time, the cable connecting Gypsy to the camera became problematic, loosening the socket and making Gypsy “stutter”, apparently due to the lack of a reliable electrical contact. Moreover, experience soon taught me that Gypsy’s coördinates were not infrequently well off those I obtained from track logs using other devices, occasionally being off significantly enough to make its readings useless. After a fall on 2015 August 26 on a boat applied enough force to Gypsy to shear off its cable where it enters the camera socket, I replaced the cable, but found the socket had also been damaged enough to render it useless, so I no longer had Gypsy’s services after that date. From this experience, I concluded that an external GPS is at best problematic, but I still very much like the idea of a camera being able to automatically record GPS coördinates with the photo’s metadata and will look for a built-in GPS on my next DSLR.
Given the availability of Prissy and Gypsy, Griselda was put primarily to the task of recording tracks. Alas, its limited battery life of less than four hours was often inadequate even for day hikes and its charging slot also became unreliable when hiking, making battery packs to prolong that life long enough to record a day hike useless because they use the charging slot to deliver their back-up power. Consequently, at the beginning of 2013, I purchased a Bad Elf GPS Pro, subsequently nicknamed Grimelda; this device is strictly a track logger, with a very limited display that can show coördinates, altitude, and heading, but no maps. Paired with an iOS device using Bluetooth, it can display tracks on maps, but such pairing uses up battery life considerably, both on the Bad Elf and on the iOS device, so I rarely use it that way. However, it can hold up to 100,000 track points at a rate of 1 track point per second (for 24 hours, that rate generates 86,400 track points) and its battery lasts without charging longer than I can hike (or drive) in a day. I am now generating track logs for each day I travel, whether on foot or in the car; these track logs, once uploaded to my iMac, can then be used to obtain my coördinates with a time accuracy of one second, quite sufficient to identify the location where a photo was taken even if Gypsy was still unready. Although the Bad Elf claims an accuracy of 2.5 m (8.2 ft), I find considerably greater variability than that in practice, comparable to Griselda, but sometimes not quite as good. Worse, the coördinates it obtains are often different from those Gypsy gets, though plugging both coördinates into Google Earth shows that Grimelda is much more often correct than Gypsy.
In 2013, I also got my first iPhone, an iPhone 5, and installed the Bad Elf app on it; this allowed me to transfer Grimelda’s track logs back to the iPhone and display them, if needed, on the iPhone’s screen and to then move them to my Mac for permanent storage. Given Prissy’s superior facilities for car navigation, the Bad Elf/iPhone combination worked so well and so smoothly, that Grimelda, with much longer battery life, quickly replaced Griselda in my use. Indeed, it was Grimelda’s track logs, plotted in Google Earth, that showed me how far off base Gypsy could sometimes be, so that I frequently had to override Gypsy’s GPS coördinates with Grimelda’s. Grimelda has continued to work very well in the years since, though in 2017, I had to acquire another after having inadvertently stepped on the first one hard enough to break it; the replacement device is a Bad Elf GPS Pro+ and continues to serve admirably in 2018. Barely changed from the previous one, I have continued to use the name Grimelda for it too.
Other than its Compass app, I was pretty much oblivious to the built-in GPS capabilities of my iPhone 5, but the GPS tracking apps available for the iPhone6s Plus soon came to my attention upon acquiring it in 2015. The first I used heavily was the Trails app, which did a decent job as a GPS track logger (less accurate than Grimelda, but not egregiously off the mark), but its estimates of distances left much to be desired.⁴ The Galileo Pro app also worked about as well as Trails as a track logger, but its maps were not as useful to me as the Trail app’s maps were, so I rarely used it. In 2016, I updated to the iPhone7 Plus and, in 2017, discovered the Gaia GPS app, which does as good a job at track logging as the Trails app and a much better job at measuring distance; with its excellent user interface and fine maps, I quickly switched to it and it is currently my main iPhone hiking app. It is still not as good a track logger as Grimelda, which is likely due to the iPhone’s less expensive built-in GPS, but having immediate access to the track plotted on a map while hiking (even when without cell phone connection, using pre-downloaded maps) has proven a fantastically useful feature, so I am currently using both, but I can envision the day when the iPhone’s GPS will be as good as Grimelda’s and I can send Grimelda off to a happy retirement.
The HoudahGeo app for the Mac is a useful way of coördinating a GPS track log with photos taken on a camera without the ability to automatically “geotag” photos as they are taken. When one takes as many photos as I do, it can be beyond tedious to manually supply GPS coördinates one by one from a track log; the app automates this process and reduces the time required to a minuscule fraction of that taken by the manual process. That said, I have used the app on relatively few occasions, primarily because I have been a bit sloppy about ensuring that the Nikons are set to the proper time—their clocks tend to drift after a few days—while the GPS trackers are on a globally synchronized time, leading to a potential mismatch between the photo and the coördinates. HoudahGeo does have an option to adjust for the difference, but it’s not always clear by how much the times need to be adjusted. Still, in the absence of a built-in GPS, it’s a very useful tool to have in one’s toolbox.
The iPhone 5 and iPhone6s Plus cameras did not produce photos of high enough quality for me to use them for my web site, but the iPhone7 Plus camera is good enough to be sometimes competitive with the Nikons and is usually better in flashless low-light situations; it automatically stores the GPS coördinates with the photos, as Gypsy did.
Photos taken before I acquired Grimelda use coördinates I manually recorded using Griselda or were added after the fact when I knew the correct coördinates from having obtained them on another occasion.⁵ Since Grimelda’s acquisition, however, I normally report in the caption the GPS coördinates recorded in the track log. For those photos taken with the Nikons between 2012 July 19 and 2015 August 26, most of the coördinates are from Gypsy, corrected as needed by those from Grimelda’s track logs. For those taken with the iPhone7 Plus, the coördinates are those from the iPhone7 Plus itself. Given the inherent inaccuracies in all of these devices, they may not be exact, but they should be reasonably close and should place you very precisely within the area from which you should be able to see what I saw. I will continue to give imprecise verbal location identifications for those without GPS devices, as I was before 2009, but the provision of GPS coördinates should greatly improve matters for those who do have them.