However, here you can find also the Jupyter Notebooks and the data that were used to produce the figures in the presentation. The presentation itself can be found by clicking on the figure above.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.
AboutHydrology
My reflections and notes about hydrology and being a hydrologist in academia. The daily evolution of my work. Especially for my students, but also for anyone with the patience to read them.
Tuesday, April 16, 2024
Elementary Mathematics sheds light on plant Transpiration
Friday, April 5, 2024
A series of talks and material on Transit (Travel) time, Residence time and Response Time
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.
- The view of the catchment as the statistics of elementary water volumes moving stochastically, a storyboard
- Travel Time, Residence Times (Vimeo2024)
- A summary (Vimeo 2022)
- A short note about past and future (Vimeo2022)
- The Python Notebook that created the Figure in slides
- Vimeo 2021-Ita, Vimeo 2021-Eng, Vimeo2022
- Some discussion (In English)
- Previous lesson recap - Blackboard2024
- StorAge Selection Functions (Vimeo2024)
- A summary on SAS, Blackboard2024,
- Some further considerations on our goals - Blackboard2024
- A Python notebook where the age-ranked tables are created within a simple example
- Response time and Life Expectancy (Vimeo2024)
- A post on travel (transit) time, residence time and response time definitions
- A Notebook Estimating the empirical response time probability from the age-ranked (He) table
- Niemi's identity (Vimeo2024)
- Multiple Reservoirs (Vimeo2024)
- Multiple Reservoirs treatment is not that complicate as it can be imagined from theformal mathematics - Blackboard2024
- Partitions (Vimeo2024)
- Pollutants and Tracers (Vimeo2024)
- Q&A - A student asks and I respond on travel times (in Italian)
- Q&A - Another session of explanations
- Klicker session on Travel times, Residence Time, etc. (List of questions and answers by students, Zoom2020)
- More material on travel time, residence time and response time on this blog.
- Old material on the same topic
- Response Times (Vimeo 2023)
- Vimeo2020
- Vimeo 2021-Eng, Vimeo 2021-It
- A little of discussion (in English)
- Pollutants, Tracers, Nutrients Transport (Vimeo2023)
- (Vimeo2022)
- Partitioning the outputs (Vimeo2023)
- (Vimeo2022)
- Benettin, P., Soulsby, C., Birkel, C., Tetzlaff, D., , G. and Rinaldo, A. (2017) Using sas functions and high resolution isotope data to unravel travel time distributions in headwater catchments. Water Resources Research, 53, 1864–1878. URL: http: //doi.org/10.1002/2016WR020117.
- Benettin, Paolo, and Enrico Bertuzzo. 2018. “Tran-SAS v1.0: A Numerical Model to Compute Catchment-Scale Hydrologic Transport Using StorAge Selection Functions.” Geoscientific Model Development Discussions, January, 1–19.
- Benettin, Paolo, Nicolas B. Rodriguez, Matthias Sprenger, Minseok Kim, Julian Klaus, Ciaran J. Harman, Ype van der Velde, et al. 2022. Transit Time Estimation in Catchments: Recent Developments and Future Directions.†Water Resources Research 58 (11). https://doi.org/10.1029/2022wr033096.
- Botter, Gianluca, Enrico Bertuzzo, and Andrea Rinaldo. 2010. “Transport in the Hydrologic Response: Travel Time Distributions, Soil Moisture Dynamics, and the Old Water Paradox.” Water Resources Research 46 (3). http://doi.wiley.com/10.1029/2009WR008371.
- Botter, Gianluca, Enrico Bertuzzo, and Andrea Rinaldo. 2011. “Catchment Residence and Travel Time Distributions: The Master Equation.” Geophysical Research Letters 38 (11). http://doi.wiley.com/10.1029/2011GL047666.
- Drever, Mark C., and Markus Hrachowitz. 2017. “Migration as Flow: Using Hydrological Concepts to Estimate the Residence Time of Migrating Birds from the Daily Counts.” Methods in Ecology and Evolution / British Ecological Society 8 (9): 1146–57.
- Harman, Ciaran J. 2015. “Time-Variable Transit Time Distributions and Transport: Theory and Application to Storage-Dependent Transport of Chloride in a Watershed.” Water Resources Research 51 (1): 1–30.
- Harman, Ciaran J., and Esther Xu Fei. 2024. Mesas.py v1.0: A Flexible Python Package for Modeling Solute Transport and Transit Times Using StorAge Selection Functions.†Geoscientific Model Development 17 (2): 477–95. https://doi.org/10.5194/gmd-17-477-2024.
- Hrachowitz, M., Benettin, P., van Breukelen, B. M., Fovet, O., Howden, N. J. K., Ruiz, L., van der Velde, Y. and Wade, A. (2016) Transit times-the link between hydrology and water quality at the catchment scale: Linking hydrology and transit times. Wiley Interdisciplinary Reviews: Water, 3, 629–657.
- McDonnell, Jeffrey J. 2014. The Two Water Worlds Hypothesis: Ecohydrological Separation of Water between Streams and Trees? Wiley Interdisciplinary Reviews: Water, April. http://doi.wiley.com/10.1002/wat2.1027.
- Niemi, Antti J. 1977. “Residence Time Distributions of Variable Flow Processes.” The International Journal of Applied Radiation and Isotopes 28 (10): 855–60.
- 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.
- Rigon, R., and M. Bancheri. “On the Relations between the Hydrological Dynamical Systems of Water Budget, Travel Time, Response Time and Tracer Concentrations.” http://abouthydrology.blogspot.com/2020/05/equivalences-and-differences-among.html.
- Sprenger, M., Stumpp, C., Weiler, M., Aeschbach, W., ST, A., Benettin, P., Dubbert, M., Hartmann, A., Hrachowitz, M., Kirchner, J., McDonnel, J., Orlowski, N., Penna, D., Pfahl, S., Rinderer, M., Rodriguez, N., Schmidt, M. and Werner, C. (2019) The demographics of water: A review of water ages in the critical zone. Rev. Geophys., 2018RG000633.
- Schwemmle, Robin, and Markus Weiler. 2024. Consistent Modeling of Transport Processes and Travel Times: coupling Soil Hydrologic Processes with StorAge Selection Functions. Water Resources Research 60 (1). https://doi.org/10.1029/2023wr034441.
- Velde, Y. van der, P. J. J. F. Torfs, S. E. A. T. M. Van der Zee, and R. Uijlenhoet. 2012. “Quantifying Catchment-Scale Mixing and Its Effect on Time-Varying Travel Time Distributions.” Water Resources Research 48 (6): W06536–13.
- Velde, Ype van der, Ingo Heidbüchel, Steve W. Lyon, Lars Nyberg, Allan Rodhe, Kevin Bishop, and Peter A. Troch. 2014. “Consequences of Mixing Assumptions for Time-Variable Travel Time Distributions.” Hydrological Processes 29 (16): 3460–74.
- Wilusz, Daniel C., Ciaran J. Harman, and William P. Ball. 2017. “Sensitivity of Catchment Transit Times to Rainfall Variability Under Present and Future Climates.” Water Resources Research 53 (12): 10231–56.
Friday, March 22, 2024
4DHydro website
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.
Friday, March 8, 2024
Modelling and Hydrological Modelling
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.
- Models in Science (Vimeo2024)
- Catchment processes (Vimeo2024)
- Further References
- Gao, Hongkai, F. Fenicia, and H. Savenije. 2023. “HESS Opinions: Are Soils Overrated in Hydrology?” Hydrology and Earth System Sciences, July. https://doi.org/10.5194/hess-27-2607-2023.
- Ying Zhao, Mehdi Rahmati, Harry Vereecken, Dani Or. “Comment on ‘Are Soils Overrated in Hydrology?’ by Gao et Al. (2023).” Egusphere -. Accessed March 8, 2024. https://egusphere.copernicus.org/preprints/2024/egusphere-2024-629/.
- Hydrological Models (Vimeo2024)
- Seven steps in hydrological modelling: I - clarifying the purposes, II-geomorphology, IV-pre-analysis of input data (Vimeo2024)
- Integral Distributed Model or Hydrological Dynamical Systems, HDSys (Vimeo2024)
- The representation of Hydrological Dynamical System (Vimeo2024)
- Seven steps in hydrological modelling: IV- setup, V - model calibration/execution/validation (Vimeo2024)
- Seven steps in hydrological modelling: VI- delivery the results, VII- final deployment to stakeholders (Vimeo2024)
- DARTHs (Digital Twins of Earth System)
- A new way to do models
- A final view on Hydrological Dynamical Systems and their application to catchments.
- Hypothesis testing in Hydrological Modelling with HDSys (At the whiteboard)
- Further readings:
Thursday, March 7, 2024
Stock and flow diagrams, a different way to represent dynamical systems
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.Wednesday, March 6, 2024
On Hydrological Models and their choice (and a use of the AboutHydrology mailing list)
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 |
Subsequently, I came across two intriguing papers authored by Melsen, delving into the "sociology of selecting a hydrological model." These papers proved to be quite engaging. Additionally, there are other noteworthy publications exploring similar themes. Notably, among the more recent works, Hamilton et al., 2022, and Horton et al., 2023, deserve special mention. Please find their citation below. In the paper you can easily recover previous relevant literature.
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.
Friday, February 16, 2024
Summarizing my (with a good company) cryospheric work
A little of-of-date itinerary can be found in a previous post here. To understand our progress, three milestone theses summarize the work done
- Matteo's Together, we worked out the Thermodynamics of non equilibrium for ice-systems and the theory of freezing soils. Matteo implemented also an integrator in GEOtop, not the perfect one, but acceptable. Matteo's 2011 paper is a benchmark paper in the topic.
- Stefano's brought GEOtop to some maturity and especially fine tuned the various tools related to snow and ice. Stefano's 2014 paper remains a landmark in our work.
- Niccolò's pushes forward the previous work. Especially remarkable is his work on re-implementing the informatics according to new (for us) concepts in OO programming and using (finally) safe algorithms for the integration of the equations. His WHETGEO and FreeThaw papers are a must read for completeness and clarity.