Internal variability in numerical morphodynamical experimentation

It has long been recognized that the morphodynamics of coastal bays are not fully deterministic but instead exhibit inherent uncertainty. This intrinsic variability is reminiscent of internal variability in climate systems, arising not only from dynamical instabilities but also from the integration of random disturbances. Traditionally, uncertainty in morphodynamic behavior has been investigated through stability analyses. However, traditional assessments of stability have largely focused on the stability property of low-dimensional analysis. In realistic dynamical numerical models, morphodynamic systems are rarely low-dimensional. In these cases, it is often more appropriate to regard the uncertainty as a manifestation of stochasticity. For real-world systems, this raises an important question: when does an observed development lie outside the range of intrinsic variability, implying the influence of an external driver? Answering this is considerably more complex than in controlled numerical experiments, where a single parameter or process can be isolated and modified. In this paper, we examine uncertainty in a relatively simple morphodynamic numerical model of a coastal bay. We show that minor changes in the initial conditions-such as the tidal phase at model initialization-can lead to differences among ensemble members, substantial in local features (e.g., the fine-scale structure of channels) and less so in overall properties, such as mean bay depth and channel number count. Consequently, a robust evaluation of numerical experiments, such as those testing the effects of altered parameterizations, requires explicit estimates of the system's inherent uncertainty so that the "signal" generated by experimental changes can be distinguished from internal variability ("noise").