Can Large Language Models be useful in Hydrology ?

I've been thinking about the potential utility of Language Model ( LLM ) applications in the field of Hydrology. Understanding requires delving into relevant literature and gaining a deep knowledge of how the statistical principles behind LLM operate (because they are statstical tools). The Wikipedia link above, on  serves as an initial source of information, offering some foundational understanding. But let's say that people working on the topics were rediscovering from a different point of view things already known and relabeling them according to a new jargoon. 

For restablishing a little of reasonable context, I would delve into Cosma Shalizi's opinion to gain deeper insights. Careful reading and analysis ad zoom back to recover missing information is necessary to grasp the nuances. However, reading Percy Liang, lecture notes for CS324, Large Language Models (Stanford) [especially looking to "Introduction", "Modeling" and "Training"]  is a definitive settlement of the matter.

Next, I turn to a valuable resource: a work in progress authored by Sebastian Raschka. This book promises practical exercises to fixing the knowledge, albeit still in development.

Disclaimer: I am in a learning process too. So this page will be subject to modifications.

Exploring the Soil-Plant-Atmosphere Continuum: Advancements, Integrated Modeling and Ecohydrological Insights, a Ph.D. Thesis by C. D'Amato

This thesis aims to address the complex issue of SPA interactions by developing a comprehensive set of models capable of representing the intricate dynamics of this system. At the core of this research lies the integration of sophisticated descriptions of hydrological and plant biochemical processes into a novel ecohydrological model, GEOSPACE-1D (Soil Plant Atmosphere Continuum Estimator model in GEOframe).

Through a combination of theoretical exploration, engineering methodologies, and empirical experiments, this thesis aims to advance our understanding of SPA interactions. The development of adaptable models, represents a significant contribution to the field. The thesis emphasizes the practical implications of employing models to analyze experimental data, thereby enhancing our comprehension of various phenomena.

In conclusion, this thesis provides valuable insights into SPA interactions and lays the groundwork for future research and applications. By embracing the challenge of under- standing and modeling the SPA continuum, this work contributes to the ongoing efforts to address environmental challenges and promote sustainable practices.  The thesis draft can be dowloaded by clicking on the figure. 

 

Elementary Mathematics sheds light on plant Transpiration

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. 

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. The paper, submitted to Ecohydrology, can be found as an Authorea preprint here. 

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
• StorAge Selection functions (Vimeo2022)
• Vimeo 2021-It
• 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)

Some References

• 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.