Sunday, January 3, 2010

Mean High-Water Mark: Lies, Damned Lies, and Statistics

Early on in the discussion of public rights of passage, the term “mean high-water mark” was used as in being able to portage or carry around an obstruction as long as one stayed below this mark. This term was dropped in favor of carrying in the “least intrusive manner possible.” I think this was a good development. Why? Partly because of statistics.

The mean is one of several statistical measures of central tendency—add all the values of what you’re measuring and divide by the number of values and you get the mean. The other primary measures of central tendency are the mode (the value that occurs most frequently) and the median (the value that has half the items below it and half above it). When a distribution of values is “symmetrical” these three measures are close to each other. But, if your distribution is “skewed” (i.e., assymetrical), the mean is no longer accurate.

Say 20 families in a neighborhood have salaries between $60 K and $140 K, with most in the middle and some on the extremes. With a symmetrical distribution, the mean will be about $100 K and will be a valid measure of typical wealth. But if family A sells their house to someone earning a million dollars, the distribution will be skewed and the new mean (about $190 K) will not represent the typical neighborhood salary. If water levels for a river are symmetrically distributed, the mean is a valid measure. If not (as when rivers are flood-prone or dewatered due to dams), then the mean is not a good measure. The median or mode would be a better measure in such cases.

However, there are more pressing practical considerations suggest that any statistical measure is not very helpful for rights of passage. Until fairly recently, most paddlers would have a difficult time knowing a river’s mean flow. This information is more available now—the U. S. Geological Service has a Web site and you can get a pretty good idea of typical high water levels from scanning their databases. Still, there are problems. While a good number of rivers have gauges, many do not. Dedicated paddlers are fairly good at estimating water levels for a river by looking at the gauges for nearby rivers, but this is not an exact science. Another problem is that gauges are almost always located in fairly wide sections of a river with relatively milder current. Even if we do know a river’s mean high-water mark, it’s not clear how to extrapolate this information to the spot on the river where you need to carry.

A one-foot difference on a downstream gauge can easily translate to a several foot difference in a narrow part of the river, which is where most carries occur. And, the river at a gauge site may be rising, while a section far away is already dropping (or vice-versa). At low levels, lining may be an option and the issue of “mean high-water mark” isn’t too important. In flatwater and easier whitewater, paddlers can usually(!) carry around obstructions that block narrow passages without having to go inland very far. It is in more significant whitewater, with steep banks, ravines and gorges, where the mean high-water mark comes more into play. But how do you figure out where this is? Well, you can’t, unless you know a given river very well.

Debris lines can indicate the highest recent level and stains on ravine walls might do likewise, but these aren’t reliable measures and it is difficult to communicate this type of information to other paddlers or landowners. A lengthy whitewater run may require multiple carries in a variety of environments. Identifying the “mean high-water mark” for each is just not tenable, regardless of what we may know about USGS readings. While the phrase “least intrusive manner possible” is impossible to define, I still think it’s better than referring to a statistical concept that sounds precise but really isn’t.

Photograph: The Boquet River in late June

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