On the tidal prism - channel area relations

We verify the broad applicability of tidal prism cross-sectional area relationships, originally proposed to relate the total water volume entering a lagoon during a characteristic tidal cycle (the tidal prism) to the size of its inlet, to arbitrary sheltered cross sections within a tidal network. We suggest, with reasonable approximation defining a statistical tendency rather than a pointwise equivalence, that the regime of tidal channels may be anywhere related to local landscape-forming prisms embedded in a characteristic spring tide oscillation. The importance of the proposed extension stems from its potential for quantitative predictions of the long-term morphological evolution of whole tidal landforms, in response to forcings affecting tidal prisms. This is the case, in particular, for alterations of relative mean sea levels possibly driven by climate change. Various 1-D and 2-D morphodynamic and hydrodynamic models are employed to evaluate peak flow rates, bottom shear stresses, and the ensuing local tidal prisms. One-dimensional morphodynamic models describing both the longitudinal and cross-sectional evolution of tidal channels are used to verify the validity of the relationship for sheltered sections. Relevant hydrodynamic features determined through accurate 2-D numerical models are compared with those obtained through time-invariant equivalents, defining a mean watershed by an energy landscape from averaged free surface gradients. Empirical evidence gathered within the lagoon of Venice (Italy) supports the proposed extension. We conclude that the geomorphic law relating tidal prisms to channel cross-sectional areas anywhere within a tidal landscape is a valuable tool for studies on long-term tidal geomorphology.