Topographic Prominence - Calculations and Mathematics

Calculations and Mathematics

When the key col for a peak is close to the peak itself, prominence is easily computed by hand using a topographic map. However, when the key col is far away, or when one wants to calculate the prominence of many peaks at once, a computer is quite useful. Edward Earl has written a program called WinProm which can be used to make such calculations, based on a Digital Elevation Model. The underlying mathematical theory is called "Surface Network Modeling," and is closely related to Morse Theory.

A note about methodology: when using a topographic map to determine prominence, one often has to estimate the height of the key saddle (and sometimes, the height of the peak as well) based on the contour lines. Assume for simplicity that only the saddle elevation is uncertain. There are three simple choices: the pessimistic, or clean prominence, assumes that the saddle is as high as it can be, i.e. its elevation is that of the higher contour line nearest the saddle. This gives a lower bound on the possible prominence of the peak. Optimistic prominence assumes that the saddle is as low as possible, yielding an upper bound value for the prominence. Midrange or mean prominence uses the mean of these two values.

Which methodology is used depends on the person doing the calculation and on the use to which the prominence is put. For example, if one is making a list of all peaks with at least 2,000 ft (610 m) of prominence, one would usually use the optimistic prominence, to include all possible candidates (knowing that some of these could be dropped off the list by further, more accurate, measurements).