By examining the derivation of Penn-Monteith-like equations for estimating evapotranspiration, one can uncover valuable insights into plant functionality. In essence, equations talk. For a more comprehensive and in-depth exploration of this topic, refer to this erlier post.
Here below we started a little series of lectures about a statistical way of seeing water movements in catchments that, while having a long history (e.g. Niemi, 1977, Rigon et al, 2016) has been largely renewed recently starting from Botter et al., 2010 and Botter et al., 2011. The material is the same prepared for the Hydrological Modelling class however grouped here separately for the readers convenience.
An alternative perspective is presented here regarding their concepts. While certain passages may pose some challenges, the enhanced comprehension of flux formation processes at the catchment scale is, in my opinion, immensely valuable and well worth the effort. The proposed approach involves the following line of thinking: a) the collective fluxes within catchments result from the cumulative movements of numerous small water volumes (water parcels); b) parcels can be understood through three key distributions: the travel time distribution, the residence time distribution, and the response time distribution; c) the interrelations among these distributions are elucidated; d) linking these distributions to catchment processes is achieved through the formulation of age-ranked distributions within ordinary differential equations; e) the theory developed here represents a generalization of the unit hydrograph theory.
4DHydro is a project that came out from a call for tender by ESA to which we had the pleasure to participate. All the making of the project is, since last week documented on the 4DHydro website that you can find following this link.
Not yet available, soon you'll see here a video explaining what the website is supposed to contain.
These lecture are actually part of the 2024 course in Hydrological Modelling. However because they can be of some more general interest, I am grouping them also here. They try to review the concepts of modelling in general and when applied to hydrology. In the series of lectures there is also a concise overview of catchment processes. The first lecture image, see below, it a Maurizo Cattelan artwork entitled "A donkey among doctors" which is my attitude when I approach the topic.
Stock and flow diagrams (see also here) are a way to represent dynamical system which is the same area covered by EPN ((Extended Petri Nets). They were brought to my attention by the talk John Baez gave at Edinburgh Mathematical Society last December. Fortunately the talk is available on Youtube.
Although I find that the visuals of EPN are more expressive and the accompanying infrastructure is easier for engineers to comprehend, I have come to realize that listening to the talk is incredibly instructive when it comes to realize that EPN falls in the objects of category theory. An intriguing aspect explored in the talk is the representation of open systems within stock-flow graphs. In EPN, it is assumed that a flow box not originating from a place indicates that the system is open. Additionally, when one EPN features an outgoing flow labeled A and another EPN has an input flow with the same label, they can be combined to create a composite graph. However, in this presentation, a new rectangular symbol is introduced for the same purpose.Initially, I was captivated by the visuals that I could incorporate into my presentations. To my pleasant surprise, I discovered that the AboutHydrology mailing list served as a valuable data source. Remarkably, this platform has been active for approximately a decade (I need to verify the exact date of its inception) and has amassed a wealth of information.
 |
| Reproduced from Melsen, 2022 |
References
Hamilton, Serena H., Carmel A. Pollino, Danial S. Stratford, Baihua Fu, and Anthony J. Jakeman. 2022. “Fit-for-Purpose Environmental Modeling: Targeting the Intersection of Usability, Reliability and Feasibility.” Environmental Modelling & Software 148 (February): 105278. https://doi.org/10.1016/j.envsoft.2021.105278.
Horton, Pascal, Bettina Schaefli, and Martina Kauzlaric. 2022. “Why Do We Have so Many Different Hydrological Models? A Review Based on the Case of Switzerland.” WIREs. Water 9 (1). https://doi.org/10.1002/wat2.1574.
Melsen, Lieke A. 2023. “The Modeling Toolkit: How Recruitment Strategies for Modeling Positions Influence Model Progress.” Frontiers in Water 5 (May). https://doi.org/10.3389/frwa.2023.1149590.
The lab is almost half of the class. According to the motto "learning by doing" it covers at least three numerical experiments:
Once precipitations arrive to the ground surface they either infiltrate or generate runoff. We first state how they infiltrate and, actually how water behave in the soil and in the ground. We talk about the complexity of the Earth surface that contains life and call it, the Critical Zone. To study infiltration we introduce the Darcy and Richards equations of which we explain the characteristics.
