Introducing a specialized concomitant-variable hidden semi-Markov model tailored for the analysis of marine count data in the Venice Lagoon, this study offers a robust framework to comprehensively explore hourly exceedances of flooding limits. Addressing the challenge of zero counts, a customized zero-inflated Poisson distribution is integrated into the model. The methodology goes beyond traditional approaches by incorporating a discrete set of unobservable environmental states that evolve dynamically over time within a (non-homogeneous) hidden semi-Markov chain. A notable enhancement to the conventional hidden semi-Markov approach is introduced by integrating regression-dependent state-specific duration parameters. These parameters are strategically modeled as a function of a well-defined endogenous variable, providing an added layer of adaptability and precision in capturing the complexities inherent in real-world scenarios. The proposed methodology employs a robust maximum likelihood estimation, optimizing the log-likelihood function to infer model parameters. Through this comprehensive approach, the study aims to deliver a nuanced understanding of the intricate interplay between weather states, environmental variables, and observed marine count data in the Venice Lagoon. This model is not only tailored to address the unique challenges posed by marine count data but also presents an innovative approach to capturing the evolving dynamics of environmental states and their influence on flooding events in this vulnerable ecosystem.