MARRMOT (and others) models represented using the Extended Petri Nets

 This is a place holder - Document still missing

The draft presented in this post represents all the MARRMoTs hydrological models using the Extended Petri Nets graphs. This show in practice that the statement that all the integral distributed hydrological models  (a.k.a. lumped distributed models, the hydrological dynamical systems, semi-distributed hydrological models) can be represented by means of the EPN is actually true. 

The MARRMoT (Modular Assessment of Rainfall-Runoff Models Toolkit) is a collection of hydrological models designed to simulate rainfall-runoff processes across different scales and conditions. Developed in MATLAB, MARRMoT provides a modular framework that allows researchers to compare, assess, and implement various conceptual hydrological models consistently

Key Features and Purpose:

• Model Variety: MARRMoT includes 47 different rainfall-runoff models, ranging from simple lumped models to more complex, semi-distributed structures.
• Comparative Framework: Its standardized environment enables researchers to test models on the same data sets and conditions, making it easier to assess model performance, suitability, and sensitivity.
• Customization: Users can adapt model configurations or modify parameters within the toolkit to better fit specific research objectives or study basins.
• - Open-source and Accessible: MARRMoT is open-source, encouraging community contributions, modifications, and application across various hydrological research areas.

This toolkit is particularly useful for researchers looking to improve or validate hydrological models and for those who want a structured way to compare the effects of model structure on hydrological simulation outcomes.

Extended Petri Nets (EPNs) are an enhanced version of traditional Petri Nets, a mathematical modeling language originally designed to describe distributed systems with concurrent, asynchronous processes. EPNs incorporate additional features to increase modeling flexibility and allow for more complex system representations. In scientific modeling, they are used for representing and analyzing systems in which discrete and continuous interactions are critical, like biological networks, chemical reactions, ecological models, or engineering processes.

In hydrology, an EPN might represent a soil-plant-atmosphere model, where state variables (such as soil moisture or leaf temperature) are stored in places (nodes) and fluxes (like water or energy flow) are represented as transitions. The EPN structure could allow the model to account for dependencies like temperature effects on transpiration, thus helping visualize and simulate complex feedbacks and interactions in the water cycle.

References

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. https://doi.org/10.1029/2019WR025099.

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.

Knoben, W. J. M., J. Freer, K. J. A. Fowler, M. C. Peel, and R. A. Woods. 2019. “Modular Assessment of Rainfall-Runoff Models Toolbox (MARRMoT) v1.0: An Open Source, Extendable Framework Providing Implementations of 46 Conceptual Hydrologic Models as a Ontinuous Space-State Formulations.” GMDD, February, 1–26.

Knoben, W. J. M., J. Freer, K. J. A. Fowler, M. C. Peel, and R. A. Woods. 2019, “Modular Assessment of Rainfall–Runoff Models Toolbox (MARRMoT) v1.2: An Open-Source, Extendable Framework Providing Implementations of 46 Conceptual Hydrologic Models as Continuous State-Space Formulations.” 2019. Copernicus GmbH. https://doi.org/10.5194/gmd-12-2463-2019-supplement.

Rigon, Riccardo, and Marialaura Bancheri. 2021. “On the Relations between the Hydrological Dynamical Systems of Water Budget, Travel Time, Response Time and Tracer Concentrations.” Hydrological Processes 35 (1). https://doi.org/10.1002/hyp.14007.

Trotter, L., W. Knoben, K. Fowler, M. Saft, and M. Peel. 2022. “Modular Assessment of Rainfall–Runoff Models Toolbox (MARRMoT) v2.1: An Object-Oriented Implementation of 47 Established Hydrological Models for Improved Speed and Readability.” Geoscientific Model Development, August. https://doi.org/10.5194/gmd-15-6359-2022.

Translating MARRmoT representation of models into the Extended Petri Net

 MARRmoT is a toolbox containing several Rainfall-Runoff models. The paper and the description of the toolbox is here. The operation is a smart initiative to include many of the commonly used models in a single place and let the users decide which model is more suitable to their cases. 

Our main interest here is actually devoted to the supplemental material present in MARRmoT where the Authors present the 46 models of the version 1.2. The presentation is clear and well illustrated trough the traditional use of reservoirs. Here I made an exercise for my students in transforming the MARRmoT representation into the  EPN one. EPN, as deducible from the title are  diagrams that allows to represent any Dynamical System (in mathematical or system and control science meaning) with graphics which have a one-to-one correspondence with the equations. To learn briefly how they works, please refer to  these other posts.  We wrote a couple of papers, which are cited below,  describing them and showing how to exploit some of their capabilities. 

From the educational point of view I realized that the students are quite helped and in using them they have a better understanding, and, moreover, a method, to grasp what the lumped hydrological models contains. So, anyone interested, can  find the presentation by clicking on the Figure above and my short talk in the video below.

I gave as an exercise to the class the duty to transform the remaining MAARmoT models into the EPN, and we'll see soon the results.

References

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.

Rigon, Riccardo, and Marialaura Bancheri. 2020. “On the Relations between the Hydrological Dynamical Systems of Water Budget, Travel Time, Response Time and Tracer Concentrations.” Hydrological Processes, no. hyp.14007 (December). https://doi.org/10.1002/hyp.14007.

Rigon, Riccardo, and Marialaura Bancheri. 2020. “On the Relations between the Hydrological Dynamical Systems of Water Budget, Travel Time, Response Time and Tracer Concentrations., Supplemental material” Hydrological Processes, no. hyp.14007 (December). https://doi.org/10.1002/hyp.14007.