A general formalism for the distribution of the total length of a geophysical parameter along a finite transect

The distribution of the total length of a geophysical parameter along a finite linear transect is required to determine confidence intervals for its true mean fractional coverage. The distribution is analogous to the total time a queue is busy within a finite time interval. As posed as a queuing problem, this distribution has been the subject of study for the last 40 years using a variety of approaches. Using a heuristic approach, the general equation for the distribution is derived within a geophysical context. As an example, the general equation for the distribution is applied to an exponential field and validated against a published simulation of an exponential field of leads in ice floes. The formalism allows for exact confidence intervals to be derived, and its application to hypothesis testing and experimental design in remote sensing is discussed.