Internal connectivity of meandering rivers: Statistical generalization of channel hydraulic geometry

The geometry of rivers has been characterized in terms of downstream and at-a-station hydraulic geometry, based on individual cross sections. Such analyses do not, however, provide insight as to how these cross sections are connected. We generalize the concept of hydraulic geometry, using data on bathymetry from four reaches of meandering rivers that include at least five bends. We quantify connectivity in terms of the probability that a connected path exists such that a given attribute remains within specified bounds along it. While the concept is general, here we apply it to vessel navigability. We develop a predictor for navigability in meandering rivers, which requires only the following, relatively easily obtained input: vessel draft, vessel width, bankfull depth, bankfull width, relative difference between current and bankfull water surface elevation, and length of desired navigation path. The predictor is applicable to both bankfull and below-bankfull stage. A key input parameter is the standard deviation of the probability distribution of depth. This parameter, in and of itself, yields no information on connectivity as it does not capture the spatial orientation of depth variation. We find, however, that (a) the probability function for connectivity does depend on this parameter, and (b) its use allows for an approximate similarity collapse of the probability function, so providing a quasi-universal predictive relation applying to all four reaches. The results also suggest potential application to more complex forms for connectivity that involve other or multiple in-stream physical variables.