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# Error and uncertainty

By error I don't mean mistake, like misreading a GPS screen or a map, or referring a location to the GDA datum when the datum was actually AGD66.

Instead, by error I mean that for reasons beyond your control, the place may not be exactly where you say it is, and you don't know how large the discrepancy might be. This kind of 'accuracy' error is unavoidable and usually unmeasurable. The good news is that there are fairly simple ways to deal with it.

## Lat/lon lengths

The length of a degree of latitude is ca 111 km, anywhere in the world. It's the length of an arc segment that follows the Earth's curvature. A degree of longitude also has a length, but that length is dependent on latitude. It equals the cosine of the latitude times ca 111 km. In Tasmania, a degree of longitude varies from ca 85 km on King Island to ca 80 km near South Cape.

One second of latitude, then, is ca 111 km x 1/3600, or ca 31 m, while in Tasmania a second of longitude varies from ca 24 m (N) to ca 22 m (S). This means when you cite a lat/lon to the nearest second, like 42°10'34"S 146°45'14"E, you're implying that you know the latitude ±15 m and the longitude ±12 m.

## Lat/lon and GPS

That's a reasonable uncertainty for a handheld GPS unit. Under good conditions (open sky, clear weather, GPS unit held up and well away from the body so you don't block satellite signals, letting the unit 'settle down' to a reading), a GPS might declare an 'accuracy' of (say) 10 m, but the meaning of that 'accuracy' varies a bit from unit to unit and manufacturer to manufacturer. It generally means that 95% of single, independent readings at a location will be within 10 m of the centre's true lat/lon. In other words, imagine a circle 20 m in diameter and you're at the centre with a GPS. You take a reading under good conditions. The lat/lon of your reading is highly likely to be somewhere inside that 20 m circle. The ±15 m for latitude and ±12 m is about right.

However, most GPS units don't read to the nearest second, but to the nearest tenth of a second, as in 42°10'33.8"S 146°45'14.2"E. The implied uncertainty is ±1.5 m for latitude and ±1.2 m for longitude. Is that believable? No. And it becomes even more unbelievable when GPS conditions aren't ideal. I recommend that you imply a reasonable uncertainty, and round off your lat/lon GPS locations to the nearest second.

If you use another lat/lon format, implied GPS uncertainties are a little less 'roundable'. The fourth decimal place in a decimal-degree latitude, like -42.1761, implies an uncertainty of ±5.5 m; the fifth decimal place in -42.17611 implies ±0.6 m. Four decimal places is optimistic but possible, while five decimal places is over-accurate. The second decimal place in 42°10.57'S implies a reasonable ±19 m, while a third decimal place, 42°10.567'S, implies an unrealistic ±2 m.

See the Google Maps and Google Earth pages for examples of way too accurate lat/lon figures.

## Specifying an uncertainty

An alternative to rounding off is to specify an uncertainty. I recommend using the Darwin Core data standard for spatial uncertainty, which is The horizontal distance (in meters) from the given decimalLatitude and decimalLongitude describing the smallest circle containing the whole of the location (this assumes lat/lon in decimal degrees, but the principle applies to all lat/lon formats).

Specified uncertainty is also good practice if your location isn't a point, but a small area. For example, you might be collecting bugs in a patch of bush ca 40 m long and 20 m wide. You could get a GPS reading in the centre of the patch, then record the location as 42°58'38.8"S 147°03'02.4"E ±20 m, or 42°58'39"S 147°03'02"E ±20 m. The uncertainty '±20 m' fairly well covers the sampling area, in the Darwin Core sense. My own, conservative practice is to say that any GPS reading I take has an uncertainty of ±25 m, and I increase that uncertainty when recording from larger areas rather than points.

## UTM

Error in the UTM system is as large as in lat/lon, with an added complication. A 'full' UTM location is usually given with a 6- or 7-digit easting and a 7-digit northing, as in 55G 479674 5330629 or 55G 0479674 5330629. Whether you get that location from a handheld GPS, or from an online service like LISTmap or Google Earth, those last 1-metre figures (55G 479674 5330629) are obviously approximations.

But how should you round off that grid reference? If you record the location as 55G 479670 5330630, you are still indicating that you know the location to the nearest 1 metre.

This is a tricky problem, and in the past the most common workaround I've seen in Tasmania was to report UTM grid references to the nearest 25 or 50 m, and to explain that 'rounding' process in the metadata for the locations (Grid references rounded to the nearest 50 m). A better solution is to report the full grid reference with an uncertainty: 55G 479674 5330629 (by GPS, ±25 m).