The Representation of Hydrological Dynamical Systems Using Extended Petri Nets (EPN)

This work presents a new graphical system to represent hydrological dynamical models and their interactions. We propose an extended version of the Petri Nets mathematical modeling language, the Extended Petri Nets (EPN), which allows for an immediate translation from the graphics of the model to its mathematical representation in a clear way. We introduce the principal objects of the EPN representation (i.e., places, transitions, arcs, controllers, and splitters) and their use in hydrological systems. We show how to cast hydrological models in EPN and how to complete their mathematical description using a dictionary for the symbols and an expression table for the flux equations. Thanks to the compositional property of EPN, we show how it is possible to represent either a single hydrological response unit or a complex catchment where multiple systems of equations are solved simultaneously. Finally, EPN can be used to describe complex Earth system models that include feedback between the water, energy, and carbon budgets. The representation of hydrological dynamical systems with EPN provides a clear visualization of the relations and feedback between subsystems, which can be studied with techniques introduced in nonlinear systems theory and control theory.