Thursday, July 4, 2024

A Ph.D. position on snow modelling and the related runoff production

 APPLY TODAY ! There is an opening until July 10 (<---Here it is the link) for a Ph.D. position on the SpaceItUP and SUPER project(Snow and glacier rUnoff Production in alpine RivER basins 1990-2050)

Due to climate change, the Alpine region is experiencing a reduction in snow quantity (snow droughts) and an increase in evapotranspiration losses (green water), with significant consequences for sustainable water resource management and ecosystem preservation. This project aims to develop new models to quantify snowmelt and evapotranspiration losses, providing practitioners with calculation tools that are different from traditional lumped parameter models but simpler than 3D process-based models. The project also intends to study the water content obtained from snow and glaciers, from the present to 2050, in the Po and Adige river basins, assessing both quantitative and temporal variations in contributions. The primary tools for the analyses will be the open-source models of the GEOframe system, integrated, modified, and improved by the new models. The modeling will be supported by the acquisition of Earth observation products derived from the MODIS and Sentinel platforms, and potentially other platforms as data becomes available. The final product of the research, concerning snow forecasts, will be developed on a regular grid of 250 meters, while flow rates will be produced for each section of interest. The analyses for the control period from 1990 to 2022 will be conducted on both daily and hourly scales, providing a valuable "reference data cube." Future projections will be produced on a monthly scale. As part of enhancing the current state of the art, which is typical for a doctoral project, reliability criteria and error estimation methods will be developed for each produced dataset. The work will be done in collaboration with dr. John Mohd Wani as co-advisor. Collaborations can include working and exchanging ideas with dr. Christian Massari (GS), Professor Manuela Girotto (GS), Prof. Stefan Gruber (GS), Giacomo Bertoldi (GS)Kelly Gleason (GS), Marco Borga (GS) and Stefano Ferraris (GS).
Old work on snow and permafrost of the group can be found here (to be updated soon).
 The deadline is approachinf very fast, therefore APPLY! To better understand the policies of the group, please give a reading here 

Thursday, June 27, 2024

How much snow is in the mountains and what is its fate? by Manuela Girotto

Water resources such as snow or groundwater can be estimated using satellite remote sensing observations and numerical models. Both models and observations have inherent uncertainties and limitations related to observation errors, model parameterization, and input uncertainties. A promising method to alleviate shortcomings in models and observations is data assimilation because it combines existing and emerging observations with model estimates, thus bridging scale and limitation gaps between observations and models. 

Using these tools, we can address the following science questions: How much water is stored as seasonal snow? How much is in the groundwater aquifers? Can we quantify hydrological changes due to human induced processes (e.g., irrigation)? This presentation will focus on the estimation of snow seasonal amounts in mountainous regions, the water towers of the world. They supply a substantial part of both natural and anthropogenic water demands and they are also highly sensitive and prone to climate change. Slides of the talk can be found by clicking on the above figure. 

The presentation was followed by an interesting discussion that you can see here below:

Sunday, June 9, 2024

On catchment analysis (modeling)

In a series of papers (Abera et al., 2016, Abera et al. 2017a, Abera et al., 2017b, Azimi et al., 2023), we have outlined a methodology for studying basins, focusing on specific locations BUT looking especially to the methodologies. They are also summarized in slides that I typically use in my hydrological modeling classes. These slides summarize the analysis requirements in seven key steps, supported by various notebooks that implement the methodologies.

Each time we begin a new catchment analysis, please ensure these methodological suggestions are considered. Overlooking them can be quite frustrating. Consistently revisit and apply the reference material to build upon previous work and past achievements. Criticize previous methods if necessary, but do not disregard them.
There are two critical steps that are often neglected. The first is data analysis—specifically, examining data coherence and comparing multiple data sources. This preliminary analysis can provide significant insights before any modeling begins, but it is rarely pursued. Instead, input data are directly used in the model, leading to issues later because something seems off.
The second neglected step is validation. There is a tendency to be satisfied with performance metrics like KGE or Nash-Sutcliffe, but these should be starting points, not final assessments. Other benchmarks, such as those proposed by Addor et al., (2018) should be used to critically evaluate the results, not just applied mechanically.
Recently, Azimi et al., 2023 introduced a more refined analysis method (called in future papers EcoProb), which allows for finer discrimination of model behavior by separating the ranges of response. This method should be considered for more precise analysis.
Additionally, since Abera (and likely earlier), we have tried to refocus our analysis on not just discharges but also on budgets. Understanding budget behavior can reveal significant insights and prevent errors, but it is often sidelined. We need to improve in this area.
Mapping is another crucial aspect. While we often rely on time series plots, spatial representation is essential to show the irreducible spatial heterogeneity. This is evident in soil moisture studies, such as the recent work by Andreis et al., and should also apply to other quantities like snow cover and depth.
I have worked with many of you to create effective graphs and maps. Using a full range of colors is beneficial, but please remember that some journals (AGU and EGU) require color-blind friendly plots. Address this requirement from the beginning to avoid last-minute modifications.

P.S. I - One distinguishing feature of GEOframe compared to other systems is its ability to explore multiple working hypotheses. Although this capability exists, it has not been utilized so far. Let's make full use of it moving forward.

P.S. II - When I read a paper from collaborators, I assume that all materials, including data, software, notebooks, and .sim files, are organized and shared as supplemental material for reproducibility. To achieve this, it is crucial to maintain order and keep the material up-to-date from the beginning. Otherwise, it becomes a nightmare.


Abera, Wuletawu, Luca Brocca, and Riccardo Rigon. 2016. “Comparative Evaluation of Different Satellite Rainfall Estimation Products and Bias Correction in the Upper Blue Nile (UBN) Basin.” Atmospheric Research 178-179 (September): 471–83.

Abera, Wuletawu, Giuseppe Formetta, Luca Brocca, and Riccardo Rigon. 2017. “Modeling the Water Budget of the Upper Blue Nile Basin Using the JGrass-NewAge Model System and Satellite Data.” Hydrology and Earth System Sciences 21 (6): 3145–65.

Abera, Wuletawu, Giuseppe Formetta, Marco Borga, and Riccardo Rigon. 2017. “Estimating the Water Budget Components and Their Variability in a Pre-Alpine Basin with JGrass-NewAGE.” Advances in Water Resources 104 (June): 37–54.

Addor, N., G. Nearing, C. Prieto, A. J. Newman, N. Le Vine, and M. P. Clark. 2018. “A Ranking of Hydrological Signatures Based on Their Predictability in Space.” Water Resources Research 54 (11): 8792–8812.

Azimi, Shima, Christian Massari, Giuseppe Formetta, Silvia Barbetta, Alberto Tazioli, Davide Fronzi, Sara Modanesi, Angelica Tarpanelli, and Riccardo Rigon. 2023. “On Understanding Mountainous Carbonate Basins of the Mediterranean Using Parsimonious Modeling Solutions.” Hydrology and Earth System Sciences 27 (24): 4485–4503.

Monday, June 3, 2024

Roots (plants roots)

 How deep go the roots of a plant ? Certainly it depends on the age of a plant but for having a static idea, nothing is better than the collection of roots drawing that can be found at the Wageningen University repository.

Clicking on the figure, you can access it. 

Friday, May 24, 2024

How to make an iPoster with usual paper media

Most researchers aim to present their work at conferences, often considering an oral presentation as the ideal outcome. Conversely, being assigned to present a poster can sometimes be seen as a second choice. However, I believe this perception overlooks the unique opportunities posters provide. Interacting with attendees at a poster session often leads to more in-depth conversations than those following an oral presentation.

Recognizing this potential, some conferences, such as the European Geosciences Union (EGU), have innovated with new formats like the PICO (Presenting Interactive COntent) sessions. These sessions enhance the traditional poster experience by allowing researchers to present their work on touch screens, making the interaction more dynamic and engaging than paper posters. This approach has gained popularity and expanded over time.

Unfortunately, smaller conferences may not have the resources to provide touch screens for such interactive experiences. As an alternative, I've experimented with a method that partially recreates the PICO experience. The idea is to make the poster more visual and less text-heavy while incorporating QR codes that link to short videos explaining different parts of the poster. These videos can cover the abstract, references, and explanations of figures.

Implementing this iPoster strategy involves some technical steps: recording the videos, uploading supplemental material for immediate access, and creating QR codes. Recording videos is now straightforward; you can use a virtual meeting platform to record yourself presenting the poster. For hosting the videos and additional materials, I prefer using the Open Science Framework (OSF), which allows for the visualization of PDFs, videos, and Jupyter notebooks without needing to download them first. Videos can also be uploaded to platforms like YouTube or Vimeo.

Once you have your materials uploaded, you can generate QR codes using one of the many available online tools. Embed these QR codes into your poster at relevant points. This way, visitors can access the supplementary material directly from their mobile devices while viewing your poster, even if you are not present.

This approach enhances the traditional poster session, making it more interactive and informative. While there is always room for improvement, this method can significantly enrich the experience for both presenters and attendees.

Clicking on the Figure above you can see and download the iPoster Example. This was actually derived from this poster. For a more generic/general post on how to do poster, please give a look to this blog post. 

Everything is improvable !

Thursday, May 16, 2024

GEOframe-New AGE material for beginners

Dear User or Dear Explorer,

Here we aim to summarize some of the material related to GEOframe-NewAGE. The main source is certainly the GEOframe blog:

However, for a logical introduction, it may be useful to start here:

The most recent material on GEOframe-NewAGE is from the latest school, accessible from this point:

By following the links for each day, you can download the slides and watch the lesson videos. 

Another useful resource is provided through hydrological modeling tutorials:

GEOframe's infrastructure is based on the Object Modelling System v3:

Various papers and applications related to GEOframe have been written and developed; you can find them here:

For any further assistance, the GEOframe crew can be reached at

Please feel free to reach out  us if you have any questions. Next Winter School  on GEOframe-NewAGE will be in January 2025 from 7 to11 in Trento University.  Next Summer School (on Land-Atmosphere interactions will be June 2-6 2025.  This Summer will be holding one Summer School on GEOframe-NewAGE in El Cairo and one in Mumbay (both the last weeks of July).

Sunday, May 12, 2024

And finally we talk about isotope concentration

 If I understand correctly, colleagues arre measuring the concentration of an isotope in stream or some other catchment outlet.  This is quite not a measure of the age of water but the latter has to be inferred from  a hypothesis the system behavior, and possibly the knowledge of the distribution of water ages within the control volume, obtained iteratively from an initial data (derived from the isotopic data of precipitation).

Therefore, assume you have measured in the outflow a concentration of 5 of solute X in appropriate units. You mai have  the knowledge of the concentration of the same solute in the water of a given age resident in the control volume. It would be a tuple like (7,3,6,2) where the number of concentration is the number of precipitation happened before the present instant. The 5 units out of the tuple can be taken all from the oldest (7) concentration, from the youngest (3,2) where the 3 are out of the 6 of the penultimate concentration.
Therefore a concentration of 5 can be fitted with a water age of 4 in the first case or (3*2+2*1)/5=1.8 in the second case.

In fact, the concentration doesn't identify  the exact age of the water but rather a range of ages spanning from the "first in first out" age to the "last in first out" age illustrated in the simple example.
Potentially the old water is infinitely old and, therefore, the lower bound could be very large, while the upper bound for the ages is, clearly, related to the last rainfall age.
So, the division between young water and old water is reasonable. Instead of trying to guess the distribution, you're trying to guess parts of its integral.
Then SAS (StorAge Selection functions, see this previous post for understanding what they are) are summarizing the mechanics of mixing inside the control volume. If the waters mix a lot the travel time and the residence time should coincides  because of the uniform selection of isotopes (or tracers) among the various populations. SAS have a non trivial form if the mixing of waters is incomplete.
Due to the localized nature of water physics, the actual travel times are intricately linked to the specific location from which water emerges or is extracted from the soil. Within the unsaturated zone, it's logical to posit that newly introduced water is the first to flow out for two primary reasons: it occupies the empty pores, and these pores are typically where water is loosely retained. However, when young water mixes with old water in the saturated zone, the aquifer's pressure rises, causing a pressure wave that pushes out the oldest water near the streams.
Consequently, in a typical zeroth-order catchment, runoff tends to adhere to a "last in, first out" (LIFO) logic, while subsurface stormwater tends to expel old water first, following a "first in, first out" (FIFO) logic. Consequently, the recession of the flood wave is expected to contain a higher proportion of old water than young water. In this hypothetical simplified model delineating two distinct dynamics, and drawing from the aforementioned insights, it becomes feasible to estimate the global effect of the system, as proposed by Rigon and Bancheri in 2022 and applying the recent methods of TT probability determination.
Vegetation withdrawal we can think to extract water from the places where active roots are, according to root density. Plants with shallow roots should mostly sample young water, while plants with deeper roots wold sample older water but maybe also being effective in mixing water of different ages because of exudation and because of preferential water infiltration close to the roots.
The presentation (under construction) is exemplifying these concepts.

Thursday, May 2, 2024

Large Language models in Earth Observation

If you've grasped the concepts discussed in the previous post, you're likely poised to explore how to effectively integrate them into your hydrological endeavors. However, you're not starting from scratch. Institutions like ESA and NASA have already outlined some of their applications through a series of posts and contributions. Machine Learning undoubtedly plays a significant role in Earth Observation and remote sensing analyses (see for instance here for an overview) or browse the activities of the RSLab for a perspective from the University of Trento. 

Here they are a list of interesting links that I collected:

After having read them I found that those links are give suggestions but at the end kind of work around the technical questions which I am looking for. 
I am sure that there exist many other resources on this topic, so, please do not hesitate to point my attention to them and I'll make the list grow. 

Tuesday, April 30, 2024

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.

Monday, April 29, 2024

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. 


Tuesday, April 16, 2024

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.

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.

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: // 
  • 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).
  • 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).
  • Botter, Gianluca, Enrico Bertuzzo, and Andrea Rinaldo. 2011. “Catchment Residence and Travel Time Distributions: The Master Equation.” Geophysical Research Letters 38 (11).
  • 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. v1.0: A Flexible Python Package for Modeling Solute Transport and Transit Times Using StorAge Selection Functions.†Geoscientific Model Development 17 (2): 477–95.
  • 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.
  • 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.”
  • 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).
  • 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. 

The final idea about the practice to do model is expressed in the paper and in the various posts that regard DARTHs which can be find here.  Among people that more reflected on Hydrological Modelling there is certainly Keith Beven [GS]. To get a glimpse of his contributions, please see this other post which contains some of his relevant papers. 

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.
Personally, I find the solution in EPN more intuitive, although it may be considered less abstract. Nevertheless, I have come to realize that a similar graphical approach could prove beneficial in extending EPN to represent not only ODE systems but also PDE systems.

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. 


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.

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).

Melsen, Lieke A. 2023. “The Modeling Toolkit: How Recruitment Strategies for Modeling Positions Influence Model Progress.” Frontiers in Water 5 (May).

Friday, February 16, 2024

Summarizing my (with a good company) cryospheric work

The hydrological cycle is significantly influenced by the presence of water in its condensed states in middle and extreme latitudes. Various hydrological parameters change below 0  Celsius, such as water viscosity, thermal capacity, and hydraulic conductivity. Consequently, mainstream hydrology treatments that neglect freezing provide incorrect results in winter, high elevations, and the far north and south for most of the year. In the current state of global warming that threatens the cryosphere which is progressively disappearing, it is even more crucial to address its dynamics

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.

Our work's focus was primarily on the critical zone, where we modified the Darcy-Buckingham law to account for freezing and thawing and their related hydrological and mechanical effects. We primarily focused on the hydrological effects neglecting the mechanical ones but not neglecting the energy budget, a common practice in hydrology, which is obviously not possible. Consequently, we faced the necessity to simultaneously solve both the mass budget and the energy budget.

The formulation of the equations can be found in the theses and papers cited above, and you will realize that establishing a correct relation between the Darcy scale energy content and the corresponding water (liquid or solid) is the main challenge. Proper physics requires the consideration of interfaces between the phases: air-water-soil-ice. While a complete understanding of this relation has not been yet achieved, some working approximations have been obtained. Looking at the two compartments, snow and ice in the soil, they differ in many aspects, with snow lacking soil and being affected by its aerial origin. Both snow and ice in the soil have their own complexities, which affect their evolution. They often interact and the fate of the soil with or without snow is quite different.

While determining the correct equations would be satisfactory goal for many, it remains unresolved how to numerically estimate these equations. It turns out that these mildly nonlinear equations pose problems when solved using the usual algorithms based on variations of the Newton method. Convergence of the numerical methods is not guaranteed, and many workarounds have been deployed to overcome these difficulties, often leading to issues with mass and energy conservation principles.

Fortunately, Casulli and Zanolli (2010) found a method to address these challenges. The fundamental paper can be found in bibliography, and a progressive approach to its formulation can be obtained by reading Casulli's lecture notes and completed by watching videos in this blog. Ideally, attending Casulli's annual school in Trento, held every second half of January after our GEOframe winter school, would provide the best understanding. Tubini's recent papers are the result of this approach, and FreeThaw and WHETGEO are concrete implementations of these algorithms in Java/OMS/GEOframe.

Another aspect to consider is the implementation of these algorithms in informatics. Concepts related to this can be found in parts of Tubini's thesis and the related papers, especially Tubini and Rigon, 2022.

Finally, as a source of information, all of these models' open-source codes can be found on GitHub, both for the older GEOtop and the more recent GEOframe model components.


Casulli, Vincenzo, and ZANOLLI. 2010. “A Nested Newton-Type Algorithm for Finite Colume Methods Solving Richards’ Equation in Mixed Form.SIAM Journal of Scientific Computing 32 (4): 2225–73.

Dall’Amico, Matteo. 2010. “Coupled Water and Heat Transfer in Permafrost Modeling.” Edited by Riccardo Rigon and Stephan Gruber. Phd, University of Trento.

Dall’Amico, M., S. Endrizzi, S. Gruber, and R. Rigon. 2011. “A Robust and Energy-Conserving Model of Freezing Variably-Saturated Soil.” The Cryosphere.

Endrizzi, Stefano. 2007. “Snow Cover Modelling at a Local and Distributed Scale over Complex Terrain.” Ph.D. Thesis, January, 1–189.

Endrizzi, S., S. Gruber, M. Dall’Amico, and R. Rigon. 2014. “GEOtop 2.0: Simulating the Combined Energy and Water Balance at and below the Land Surface Accounting for Soil Freezing, Snow Cover and Terrain Effects.” Geoscientific Model Development 7 (6): 2831–57.

Tubini, N. 2021, June. “Theoretical and Numerical Tools for Studying the Critical Zone from Plots to Catchments.” Edited by R. Rigon and S. Gruber. Ph.D., Dipartimento di Ingegneria Civile, Ambientale e Meccanica, Università di Trento.

Tubini, Niccolò, Stephan Gruber, and Riccardo Rigon. 2021. “A Method for Solving Heat Transfer with Phase Change in Ice or Soil That Allows for Large Time Steps While Guaranteeing Energy Conservation.” The Cryosphere 15 (6): 2541–68.

Tubini, Niccolò, and Riccardo Rigon. 2022. “Implementing the Water, HEat and Transport Model in GEOframe (WHETGEO-1D v.1.0): Algorithms, Informatics, Design Patterns, Open Science Features, and 1D Deployment.” Geoscientific Model Development 15 (1): 75–104.

Thursday, February 1, 2024

Hydrological modelling 2024

Welcome to the 2024 Hydrological modelling class. To understand better what is below: 
  • storyboard is a summary, usually in Italian, of the lecture
  • A whiteboard is an explanation of a particular topic made on the whiteboard (using Notability on the iPad)
  • Slides are commented in English (since 2021)
  • Videos are available to comment the slides. They are usually recorded during the lectures with no editing at all (which would be too much time expensive). 2024 Videos are uploaded to a Vimeo Showcase that can be found here
  • Additional  information (only for the brave or the curious) and references are in italics

2023-02-19 - I  - Syllabus - Introduction 2 Hydrological Modelling 

Here  I introduced the class. Its learning by doing philosophy (altered by the necessity due to COVID-19 times that impose to do first the all the theoretical parts and subsequently all the practical parts hoping that they can be done in presence). 
To begin is also worth to have a little (philosophical) analysis of what a model is. This is what done in the following parte of the lecture
2024-02-22 - Geomorphometry   - Discussion of previous lesson topics. The rational of introducing these concepts  is that catchments are spatially extended and in this course we are interested to deal with catchments hydrology. 

In this first part we deal with the geometrical (differential) characteristics of the topography. Elevations, slopes, curvatures. They will be necessary later to extract the river network and the parts of a catchment.
In this class we define also what the drainage directions are and how they are computed in the case of DEMs (a topography discretized over a regular grid).  From drainage directions are determined the total contributing areas in each point of  a DEM. These two characteristics are eventually used to determine  the channels head and extract the river networkIn turn, the extraction of the channel network allows for the extraction of hillslope and a first definition of  the Hydrologic Response Units (HRU). 
    Q&A - 

    2024-02-29 -  Interpolations 
    This lecture, assuming that now you have at least the concepts of what a catchment is and theoretically you know how to extract it and subdivide it in parts, deals with the data to feed catchments hydrology models. Because catchments have a spatial distribution, then also the driving data must be distributed. We need therefore methods of interpolation. 

    2024-03-04 -  Interpolations part II. 
    In this class we try to understand how to estimate the errors over the estimates. Besides we introduce a method (the Normal Score) to avoid to obtain negative values when positive interpolated values are required.
    Q&A - 
    Spatial Interpolation (Vimeo2023)

     Hydrological Models. This is a class about hydrological models, so what are they ?

    The title is self-explanatory. A theoretical approach to modelling is necessary because we have to frame properly our action when we jump from the laws of physics to the laws of  hydrology. Making hydrology we do not have to forget physics but for getting usable models we have to do appropriate simplifications and distorsions. The type of model we will use in the course are those in the tradition are called lumped models. Here we also introduce a graphical tool to represent these models.
    2024-03-06-Hydrological Models 

    For old material give a look to Hydrological Modelling 2023
     Linear Models for HRUs

    Once we have grasped the main general (and generic) ideas, we try to draw the simplest systems. They turn out to be analytically solvable, and we derive their solutions carefully. From the group of linear systems springs out the Nash model, whose derivation is performed.  Obviously, it remains the problem to understand how much the models can describe "reality". However, this an issue we leave for future investigations.
    • Summarizing the previous class results at the blackboard(Vimeo2022)
     A little more on the IUH and looking at the variety of HDSys models

    We introduced previously without very much digging into it the concept of Instantaneous Unit Hydrograph. Here we explain more deeply its properties, Then we observe that there are issues related to the partition of fluxes and we discuss some simple models for obtaining them. Not rocket science here. The concept that we need those tools is more important than the tools themselves. We also observe that linearity is not satisfactory and we give a reference to many non linear models. Finally we discuss an implementation of some of the discussed concepts in the System GEOframe. 
    Intermediate exam (2024-04-22)

     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. This view has a long history but recently had a closure with the work of Rinaldo, Botter and coworkers. Here it is presented an alternative vie to their concepts. Some passages could be of some difficulty but the gain in understanding the processes of fluxes formation at catchment scale is, in my view, of great value and deserves some effort.  The way of thinking is the following: a) the overall catchments fluxes are the sum of the movements of many small water volumes (molecules); b) the water of molecules can be seen through 3 distributions: the travel time distribution, the residence time distribution and the response time distributions; c) the relationships between these distributions are revealed; d) the relation of these distributions with the the treatment of the catchments made through ordinary differential equations is obtained through the definition of age ranked distributions; e) The theory this developed is a generalizations of the unit hydrograph theory. 
    Some References (advanced)
    Additional material

    Digressions I - A Glimpse on distributed process-based models

    Digressions II - Radiation -  After all radiation moves it all.
    Digressions III 
    Equations for disease spreading (Out of schedule)
    Digressions IV

  • Examples of Applications: