Five years ago, when we wrote that any lumped-parameter hydrological model can be represented as an Extended Petri Net, the statement had the flavor of a theorem asserted with a couple of worked examples. Now it has the flavor of a proof by exhaustion. The presentation below, prepared with Marialaura Bancheri and Anna De Nardi, contains the EPN translation of all forty-six conceptual models of the MARRMoT collection (Knoben et al., 2019), from the single-bucket Collie River Basin 1 up to SACRAMENTO, PRMS and CLASSIC. Anna carried out the bulk of this work as her graduation exercise, completing the task I had assigned to my class back in 2021, and I think the result deserves to be seen in its entirety.
The presentation can be found by clicking on the above image.
I will not explain here what an EPN is: the definitive references remain Bancheri, Serafin and Rigon (2019), which introduces the formalism and its exact correspondence with the ordinary differential equations of the water budget, and Rigon and Bancheri (2021), which shows how the same topology carries, almost for free, the travel time, response time and tracer dynamics. A gentler entry point, with slides and a video tutorial, is this older post, and the conceptual background on the equivalences among the various hydrological dynamical systems is discussed here.
What the collection adds is something the papers could not give: the experience of seeing forty-six models side by side under a single graphical grammar. Some things become obvious that the original equations, or the traditional bucket sketches, keep hidden. Family resemblances jump out — the MOPEX series, the Flex variants, the Tank models reveal themselves as small mutations of a shared skeleton, and one starts to suspect that the space of conceptual models is much smaller than the number of their names suggests. Complexity becomes measurable at a glance: you can literally count places, transitions, splitters and see where a model concentrates its assumptions. And the pathologies show up too — when the wiring of a model resists a planar, readable drawing, as it happens with SACRAMENTO, that is telling you something about the model, not about the drawing. In this sense the EPN works as a diagnostic instrument, not merely an illustration.
There is also a forward-looking reason to care. Once a model is a graph with typed nodes, it is data: it can be stored, compared, composed with other graphs, translated automatically into code — which is what we pursue in the GEOframe/OMS3 world — and it connects naturally with the compositional, category-theoretic view of open systems I discussed apropos of stock and flow diagrams. The forty-six drawings below are therefore not an endpoint but a dataset.
All the previous material on the topic is collected under the EPN label of this blog, starting from the original announcement of the WRR paper.
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
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
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 Continuous Space-State Formulations." Geoscientific Model Development. https://gmd.copernicus.org/articles/12/2463/2019/
