Equivalences and differences among various Hydrological Dynamical Systems

In this paper we want to show that once the topology of a Hydrological Dynamical System is determined, the structure of the equations of the Water Budget Dynamical System is determined but with it also the travel time and residence time distributions are. This is obvious since our paper on age-ranked functions but here it is rigorously stated and worked out.

Ideally this paper is also a continuation of the paper on the representation of Hydrological Dynamical systems with Petri Nets of which in some sense, it represents an extension. In a ideal menù, the reader should read first the paper on the historical-critical approach to the GIUH, I would say excluded its last section, then the Age-Ranked paper, then the Petri Net paper and finally this one. Clicking on the Figure you can have the preprint, or on the bibliography below you can have access to all the manuscripts. This is part of my research program on trying a statistical-mechanical approach to hydrological modeling which across all my research activity since the last (almost) thirty years. 

References

• Rigon, Riccardo, Marialaura Bancheri, Giuseppe Formetta, and Alban de Lavenne. 2016. “The Geomorphological Unit Hydrograph from a Historical-Critical Perspective.” Earth Surface Processes and Landforms, EGU Reprint Series, 41 (1): 27–37.
• Rigon, Riccardo, Marialaura Bancheri, and Timothy R. Green. 2016. “Age-Ranked Hydrological Budgets and a Travel Time Description of Catchment Hydrology.” Hydrology and Earth System Sciences 20 (12): 4929–47.
• Bancheri, Marialaura, Francesco Serafin, and Riccardo Rigon. 2019. “The Representation of Hydrological Dynamical Systems Using Extended Petri Nets (EPN).” Water Resources Research 55 (11): 8895–8921.
• Marialaura, Bancheri, Francesco Serafin, and Riccardo Rigon. 2019. “Supporting Material for: The Representation of Hydrological Dynamical Systems Using Extended Petri Nets (EPN).” Water Resources Research.
• Rigon, Riccardo, and M. Bancheri, 2020, “Equivalences and Differences between the Hydrological Dynamical Systems of Water Budget, Travel Time and Tracers Concentration and the Legacy of Models’ Topology.”, submitted to Hydrol. Processes.
• Rigon, Riccardo, and Marialaura Bancheri, 2020. “Supplementary Material, Equivalences and Differences between the Hydrological Dynamical Systems of Water Budget, Travel Time, Response Time, and Tracer Concentrations and the Legacy of Models’ Topology.” submitted to Hydrol. Processes.