On the drainage density of tidal networks

The drainage density of a network is conventionally defined as (proportional to) the ratio of its total channelized length divided by the watershed area, and in practice, it is defined by the statistical distribution and correlation structure of the lengths of unchanneled pathways. In tidal networks this requires the definition of suitable drainage directions defined by hydrodynamic (as opposed to topographic) gradients. In this paper we refine theoretically and observationally previous analyses on the drainage density of tidal networks developed within tidal marshes. The issue is quite relevant for predictions of the morphological evolution of lagoons and coastal wetlands, especially if undergoing rapid changes owing, say, to combined effects of subsidence and sea level rise. We analyze 136 watersheds within 20 salt marshes from the northern lagoon of Venice using accurate aerial photographs and field surveys taken in different years in order to study both their space and time variability. Remarkably, the tidal landforms studied show quite different physical and ecological characteristics. We find a clear tendency to develop characteristic watersheds described by exponential decays of the probability distributions of unchanneled lengths, and thereby a pointed absence of scale-free distributions which instead usually characterize fluvial settings. We further find that total channel length relates well to watershed area rather than to tidal prism, a somewhat counterintuitive result on the basis of dynamical considerations. Finally, we show that in spite of the apparent site-specific features of morphological variability, conventional measures of drainage density appear to be quite constant in space and time, indicating a similarity of form. We show that such similarity is an artifact of the Hortonian measure. Indeed, important morphological differences, most notably in stream (or link) frequency reflecting the true extent of branching innervating the marshes and the sinuosity of tidal meandering, may only be captured by introducing measures of the