The tricky Physics of freezing soils

 Soil freezing is one of the most complex physical processes affecting the Earth's hydrological cycle, yet it remains poorly understood despite its critical importance for climate modeling, agriculture, and infrastructure.  This presentation aims to introduce the intricate thermodynamic relationships governing frozen soil behavior and introduces innovative numerical solutions that are revolutionizing how we model these processes.

Modified from Lu and Godt, 2012. Find the presentation by clicking here

"Permafrost is not ice." This seemingly simple observation reflects a profound understanding that frozen soil represents a complex multiphase system where air, biota, liquid water, ice, and soil particles coexist in dynamic equilibrium. The traditional view of soil freezing as a simple phase transition grossly oversimplifies the physics involved.

The presentation emphasizes that proper soil freezing models must account for three fundamental thermodynamic potentials: temperature (or its inverse in non-equilibrium thermodynamics), pressure exerted by the system on the environment, and chemical potential. Each of these potentials drives different aspects of the freezing process and their interactions determine the overall system behavior.

The energy conservation equation reveals the intimate coupling between heat transfer and mass transfer during freezing. When soil freezes, the energy budget becomes strongly coupled to the mass budget and phase transitions, creating a system where small changes in one variable can cascade through the entire soil column. This coupling is mathematically expressed through terms that include both temperature gradients and mass flux divergence, highlighting why traditional approaches that treat heat and water transport separately often fail.

One of the most important insights from recent research concerns how water actually freezes in soil pores. Due to freezing point depression effects, the largest pores freeze first. This sequential freezing process means that as temperature drops, progressively smaller pores freeze, each at different temperatures determined by the complex interplay of solute concentration, pore geometry, and surface tension effects.

The research identifies several mechanisms controlling freezing point depression: the Gibbs-Thomson effect (curvature-induced freezing point depression), solute presence, ice nucleation kinetics, and interactions with pore boundaries. These processes combine to create soil freezing characteristic curves that show unfrozen water content decreasing gradually with temperature rather than exhibiting the sharp transition seen in pure water.

An educated guess in understanding soil freezing comes from recognizing its mathematical similarity to soil drying. The "freezing = drying hypothesis" suggests that during freezing, the effective chemical potential is determined only by liquid water, not the total water content. This insight allows researchers to use established soil water retention theory, such as the van Genuchten or Kosugi models, to predict freezing behavior.

This analogy proves particularly powerful because it enables the use of well-established relationships like Mualem's theory for predicting hydraulic conductivity as a function of unfrozen water content. The result is a unified framework where soil freezing can be modeled using modified versions of the Richardson-Richards equation, the standard equation for unsaturated soil water flow.

The mathematical complexity of coupled heat and water transport in freezing soil creates severe numerical challenges. The governing equations become highly nonlinear, with hydraulic capacity functions that exhibit sharp peaks near the freezing point. Traditional Newton methods fail to converge when solving these systems, leading to computational failures or unphysical results.

The breakthrough solution presented is the nested Newton-Casulli-Zanolli (NCZ) algorithm, which decomposes the nonlinear problem using Jordan decomposition. This approach separates the sharp nonlinear functions into monotonic components that can be solved iteratively. The NCZ algorithm dramatically outperforms traditional Newton methods, allowing stable solutions with large time steps while maintaining energy conservation.

The researchers have implemented these theoretical advances in WHETGEO-1D, a sophisticated modeling framework built on object-oriented programming principles. Unlike traditional procedural codes that hardwire specific equations, WHETGEO uses abstract interfaces and factory patterns to allow flexible combination of different soil water retention curves, hydraulic conductivity functions, and energy budget formulations.

This design philosophy, built on the OMS3 framework, enables rapid model evolution and prevents the "screwdriver problem" where having only one tool leads to seeing every problem as a screw. The modular architecture allows researchers to easily substitute different physical theories while maintaining the same robust numerical solver.

Field applications demonstrate WHETGEO's capabilities across multiple scales and conditions. The model successfully simulates complex scenarios including infiltration events that bring thermal energy deep into soil columns, surface energy exchanges during diurnal cycles, and seasonal freeze-thaw cycles. Comparison studies show that including phase change effects significantly alters predicted soil behavior, with frozen periods exhibiting markedly different hydraulic properties than unfrozen conditions.

The model's efficiency allows simulation of multi-year periods with time steps of hours or days, making it practical for long-term climate studies. This computational efficiency, combined with rigorous energy conservation, makes WHETGEO suitable for integration into larger Earth system models. WHETGEO  is an open source software distributed under the GPL 3.0 license. For learning its use, please browse the GEOframe 2022 Summer School slides and videos.

Bibliography

Amankwah, S. K., A. M. Ireson, C. Maulé, R. Brannen, and S. A. Mathias. 2021. "A Model for the Soil Freezing Characteristic Curve That Represents the Dominant Role of Salt Exclusion." Water Resources Research 57 (8). https://doi.org/10.1029/2021wr030070.

Casulli, Vincenzo, and P. Zanolli. 2010. "A Nested Newton-Type Algorithm for Finite Volume Methods Solving Richards' Equation in Mixed Form." SIAM Journal of Scientific Computing 32 (4): 2225–73.

Dall'Amico, M., S. Endrizzi, S. Gruber, and R. Rigon. 2011. "A Robust and Energy-Conserving Model of Freezing Variably-Saturated Soil." The Cryosphere 5 (2): 469–84. https://doi.org/10.5194/tc-5-469-2011.

Devoie, Élise G., Stephan Gruber, and Jeffrey M. McKenzie. 2022. "A Repository of Measured Soil Freezing Characteristic Curves: 1921 to 2021." Earth System Science Data 14 (7): 3365–77. https://doi.org/10.5194/essd-14-3365-2022.

Groot, Sybren Ruurds de, and Peter Mazur. 1984. Non-Equilibrium Thermodynamics. New York, NY: Dover Publications.

Kosugi, K. 1999. "General Model for Unsaturated Hydraulic Conductivity for Soils with Lognormal Pore-size Distribution." Soil Science Society of America Journal 63 (2): 270–77. https://doi.org/10.2136/sssaj1999.03615995006300020003x.

Lunardini, V. J. 1985. "Freezing Soil Phase Change Occurring over Finite Temperature Difference." Proceedings 4th International Offshore Mechanics Arctic Engineering Symposium. ASM.

Muskat, M., and M. W. Meres. 1936. "The Flow of Heterogeneous Fluids through Porous Media." Physics 7 (September): 346–63. https://doi.org/10.1063/1.1745403.

Tubini, Niccolò. 2021. "Theoretical and Numerical Tools for Studying the Critical Zone from Plot to Catchments." Ph.D., Università degli Studi di Trento. https://iris.unitn.it/retrieve/handle/11572/319821/498093.

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. https://doi.org/10.5194/tc-15-2541-2021.

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. https://doi.org/10.5194/gmd-15-75-2022.

Zhang, Chao, Lingyun Gou, Shaojie Hu, and Ning Lu. 2022. "A Thermodynamic Formulation of Water Potential in Soil." Water Resources Research 58 (9). https://doi.org/10.1029/2022wr032369.

Zhang, Lianhai, Chengsong Yang, Dayan Wang, Peng Zhang, and Yida Zhang. 2022. "Freezing Point Depression of Soil Water Depending on Its Non-Uniform Nature in Pore Water Pressure." Geoderma 412 (115724): 115724. https://doi.org/10.1016/j.geoderma.2022.115724.

OMS Runner Library: Streamlining Hydrological Model Execution

 The OMS Runner Library v1.2.2 represents a significant advancement in hydrological modeling workflow automation, specifically designed to simplify the execution of OMS3 (Object Modeling System) simulations. For hydrologists and water resources engineers working with GEOframe and OMS3, this Python library addresses the seamless integration and execution of simulation models across different computing platforms. What follows assume a lot of knowlege that you can get by looking to some of our Winter Schools or some of our lab classes as  Physical Hydrology (in Italian) or  Biosphere Atmosphere and Climate Interactions. 

What is OMS3?

The Object Modeling System (OMS3) is a Java-based framework widely used in environmental and hydrological modeling. It provides a robust platform for developing, coupling, and executing complex simulation models. However, working with OMS3 often requires dealing with Java classpaths, configuration files, and platform-specific execution commands – tasks that can be time-consuming and error-prone, especially for researchers focused on scientific analysis rather than software engineering.

The Solution: Python Integration

The OMS Runner Library bridges this gap by providing a comprehensive Python interface for OMS3 operations. This is particularly valuable because Python has become the lingua franca of scientific computing, with most hydrologists already familiar with its ecosystem of tools like pandas, matplotlib, and Jupyter notebooks.

The library automatically handles the complexities of Java environment detection, ensuring that Java JDK 11 is properly configured across Windows, macOS, and Linux systems. This cross-platform compatibility is crucial for research teams working in diverse computing environments, from field laptops running Windows to high-performance computing clusters running Linux.

Please find:

Version 1.2.4

• The OMS_v_1_2_4.py It contains the methods to configure and execute OMS3 projects
• A set of Configuration Getter. Notebooks that demonstrate how to prepare an OMS3 project for the execution of its simulation files.
• A set of Runners Notebooks to discover and execute the sim files
• A set of utilities  Notebooks illustrating some method to debug simulations
• The user manual version 1.2.4

Version 1.2.2

• The OMS.py library 1.2.2.
• The Configuration getter
• An example of a very simple application
• The user manual v1.2.2

Key Capabilities

One of the library's standout features is its intelligent simulation management. It can automatically discover simulation files within a project, maintain configuration databases, and execute models either individually or in sophisticated batch processing workflows. For hydrologists working with multiple scenarios – such as climate change impact assessments or calibration procedures – the parallel execution capabilities can reduce computational time.

The library supports various execution patterns: sequential processing for dependent simulations, parallel execution for independent model runs, and asynchronous background processing for long-running computations. This flexibility allows researchers to optimize their workflows based on available computational resources and modeling requirements.

Practical Applications

In practical hydrological applications, this translates to significant productivity gains. A researcher studying watershed responses to different precipitation scenarios can now set up dozens of model runs with just a few lines of Python code, monitor their progress through Jupyter notebooks, and automatically collect results for analysis. The library's integration with popular Python data analysis tools means results can be immediately processed, visualized, and shared.

Users can explore more about GEOframe's capabilities and latest developments at the GEOframe blog, where detailed tutorials and case studies demonstrate advanced hydrological modeling workflows.

The comprehensive logging and error handling features are particularly valuable in operational hydrology contexts, where model reliability and traceability are paramount. The library maintains detailed execution histories, facilitates debugging, and provides clear diagnostic information when issues arise.

Five papers representing my research decade 2015-2024

Ten years ago I wrote a blogspot paper that contained five reference papers of mine. Or, as I wrote, five papers that represented my earlier research. If I have to choose other 5 papers for the most recente decade, I would chose the following. 

Rigon R., Bancheri M., Green T., Age-ranked hydrological budgets and a travel time description of catchment hydrology, Hydrol. Earth Syst. Sci., 20, 4929-4947, 2016

This paper introduces the concept of age-ranked hydrological budgets as a novel framework for understanding catchment water storage and release mechanisms. The work demonstrates how water age distributions can be used to characterize catchment behavior and link storage-discharge relationships with travel time theory. The approach provides a physically-based method for interpreting hydrological responses that bridges the gap between traditional storage-based and travel time-based descriptions of catchment hydrology. The mathematical framework presented offers new insights into how different water ages contribute to streamflow generation and storage dynamics. This contribution represents, IMHO,  a significant clarification of  the travel time in catchment hydrology theory with important implications for water resource management and hydrological modeling. In perspective, some parts of this paper are better treated in subsequent parts, but this was the starting point. For an alternative, maybe more mature, view of the subject, view also the blogpost here. 

Rigon, Riccardo, Giuseppe Formetta, Marialaura Bancheri, Niccolò Tubini, Concetta D'Amato, Olaf David, and Christian Massari. 2022. HESS Opinions: Participatory Digital Earth Twin Hydrology Systems (DARTHs) for Everyone: A Blueprint for Hydrologists. Hydrology and Earth System Sciences.

This opinion paper presents a visionary blueprint for developing participatory Digital Earth Twin Hydrology Systems (DARTHs) that democratize access to advanced hydrological modeling capabilities. The work advocates for open-source, component-based modeling frameworks that enable collaborative development and knowledge sharing across the global hydrological community. We propose a paradigm shift toward more inclusive and participatory approaches to hydrological modeling, emphasizing the importance of reproducible science and community-driven development. The paper outlines the technical and social infrastructure needed to support such systems, including considerations for data sharing, model interoperability, and user engagement. This contribution provides a roadmap for transforming hydrological modeling from isolated research activities into collaborative, community-based endeavors that can better serve societal needs.

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.

This paper presents the comprehensive implementation of WHETGEO-1D, a physically-based model for simulating coupled water, heat, and solute transport in variably saturated soils within the GEOframe modeling system. The work demonstrates advanced software engineering practices applied to geoscientific modeling, including object-oriented design patterns, component-based architecture, and reproducible computational workflows. The model implements sophisticated numerical solutions for Richards' equation coupled with heat and solute transport, providing a robust tool for understanding subsurface processes. The paper emphasizes open science principles through detailed documentation, version control, and community-accessible code repositories that facilitate model reuse and collaborative development. 

D'Amato, Concetta, and Riccardo Rigon. 2025. Elementary Mathematics Helps to Shed Light on the Transpiration Budget under Water Stress. Ecohydrology: Ecosystems, Land and Water Process Interactions, Ecohydrogeomorphology 18 (2).

This paper employs elegant mathematical analysis to illuminate the fundamental relationships governing plant transpiration under water stress conditions. The work demonstrates how relatively simple mathematical formulations can provide profound insights into complex ecohydrological processes, particularly the trade-offs between water use and carbon assimilation. We develop analytical solutions that reveal the underlying mechanisms driving transpiration responses to drought stress, offering new perspectives on plant-water interactions. The mathematical framework presented provides a foundation for understanding how vegetation adapts its water use strategies under varying environmental conditions. This contribution bridges theoretical ecology and practical water management by providing clear mathematical descriptions of transpiration dynamics that can inform both scientific understanding and agricultural applications.

D'Amato, Concetta, Niccolò Tubini, and Riccardo Rigon. 2025. A Component Based Modular Treatment of the Soil-Plant-Atmosphere Continuum: The GEOSPACE Framework (v.1.2.9). GMDD.

This paper introduces GEOSPACE, a comprehensive modeling framework that treats the soil-plant-atmosphere continuum as an integrated system using component-based software architecture. The work represents an advancement in ecohydrological modeling by providing modular, interoperable components that can simulate complex interactions between soil water, plant physiology, and atmospheric processes. The framework is a blueprint representing the state-of-the-art  of plant hydraulics, stomatal regulation, and soil-root interactions within a flexible, extensible software environment. The component-based design allows researchers to customize model configurations for specific applications while maintaining scientific rigor and computational efficiency. 

In the decade I co-authored other relevant papers. You can find them by browsing this blog @Accepted papers  They were concerned mainly with applications and data analysis, while the above papers are more theoretical-numerical investigations. In fact I did not published very much, against the current tendency, but most of my papers represent a step in doing better and understanding better hydrological modeling. 

Po River Basin's Changing Hydro-Climatology (1991-2020) and Future Activities to Prevent Projected Effects on Po Valley Agriculture

This presentation examines preliminary results on the changing hydro-climatology of the Po River Basin from 1991-2020 and its implications for agriculture in northern Italy's Po Valley, representing collaborative work between the University of Trento, Portland State University, and various Italian research organizations.

Key Climate Findings and Scientific Limitations

The core message draws from a referenced Nature Climate Change paper: "More Green and Less Blue Water in the Alps during Warmer Summers," reflecting how global warming increases evapotranspiration (ET) while reducing summer river water availability. The Alps, serving as the region's "water towers," show significant hydrological changes with climate impacts varying by elevation and geographic position across different Alpine subregions.

Critical Reproducibility and Methodological Gaps

However, these results face significant reproducibility challenges. The original study's underlying data were not redistributed, and computational workflows remain unrecorded, hampering independent verification. More fundamentally, the models exhibit important scientific limitations affecting conclusion reliability.

The hydrological models inadequately represent crucial feedbacks between soil-plant systems and the atmospheric boundary layer (ABL)—particularly important in Alpine environments where local topography, vegetation, and atmospheric processes create complex coupling mechanisms. Without proper representation, models may misestimate evapotranspiration rates and warming responses.

Additionally, the research overlooked critical plant physiological responses to global warming. As CO₂ concentrations and temperatures rise, plants exhibit adaptive responses including changes in stomatal conductance, water use efficiency, and photosynthetic capacity. These physiological adjustments can substantially modify transpiration rates and water cycling, potentially altering the "more green water" conclusions.

The STRADIVARI Project Response

These methodological concerns motivated the STRADIVARI project formulation, which will address reproducibility issues through open science practices with fully documented workflows and redistributable datasets. STRADIVARI aims to incorporate:

• Coupled soil-plant-atmosphere modeling with explicit ABL feedbacks
• Physiologically-based plant responses to elevated CO₂ and temperature
• Multi-scale interactions from leaf-level processes to catchment-scale hydrology

The current Po Project partially addresses these limitations by developing comprehensive datasets and model frameworks, though full integration of plant physiological responses and ABL coupling remains work in progress.

Snow Water Equivalent Analysis: Unprecedented Scale with Critical Limitations

The research provides comprehensive Snow Water Equivalent (SWE) data at 500m spatial resolution with daily temporal coverage from 1991-2021—an unprecedented systematic approach to regional snow monitoring. Peak SWE averages 3.34 Gm³ annually, revealing concerning elevation-dependent trends.

Elevation-Dependent Changes and ERA5 Bias Concerns

The 30-year analysis shows dramatic decreases in snow water storage at lower elevations: 28.4% reduction at 0-500m, 21.7% at 500-1000m, and 23.3% at 1000-1500m. Conversely, highest elevations (2500-4500m) show increases of 5.9-9.4%.

However, high-elevation results require careful interpretation due to methodological constraints. Ground-based meteorological stations are sparse at high elevations, necessitating ERA5 reanalysis precipitation data incorporation. Subsequent validation reveals ERA5 likely overestimates high-elevation precipitation, potentially creating artificial increases in modeled snow accumulation above 2500m.

This bias is particularly concerning as independent glaciological surveys suggest actual snow and ice losses even at high elevations, contradicting ERA5-informed analysis. The discrepancy highlights fundamental challenges in mountain hydrology where climate change impacts may be most pronounced but observational data are scarcest.

Implications for Reanalysis Data Usage

These findings provide important cautionary notes for uncritical ERA5 usage in complex mountain terrain. While ERA5 represents advanced global reanalysis, its coarse spatial resolution and interpolation methods may inadequately capture steep gradients and local meteorological processes in Alpine environments. The systematic high-elevation precipitation overestimation demonstrates that ERA5 requires careful validation and bias correction for mountain hydrological studies.

The work underscores critical needs for expanded high-elevation observational networks and improved methods for integrating ground-truth data with reanalysis products, including elevation-specific bias correction techniques.

Hydrological Modeling: Multi-Model Challenges and Uncertainties

As a 4DHydro project outcome, the research employs six hydrological models (TETIS-PO, clm_Rhine, WFLOW-PO, GEOframe-PO, mHM-PO, and PCR-2007PO) to analyze basin water quantities and understand hydrological processes and climate variability responses.

Evapotranspiration Estimation Concerns

The multi-model comparison reveals critical issues warranting examination. Five models consistently estimate ET around 500 mm annually with remarkably constant interannual values, likely reflecting oversimplified responses to stable radiation inputs rather than realistic representation of complex evapotranspiration factors.

This temporal constancy is problematic since real evapotranspiration should exhibit greater interannual variability driven by soil moisture availability, vegetation phenology, atmospheric demand, and temperature fluctuations. The models' failure to capture this variability suggests deficiencies in soil-plant-atmosphere interaction representation.

GEOframe-NewAge exhibits different behavior with more temporal variability but unrealistically low ET estimates. Based on regional expectations, ET should represent 30-40% of annual precipitation. The majority of models better align with these expectations, suggesting GEOframe's estimates may reflect calibration issues or structural limitations.

Model Uncertainty and Validation Needs

These simulations used relatively coarse calibration procedures. More refined approaches incorporating multiple objective functions and longer periods could yield considerably different results. The current analysis likely underestimates true model uncertainty ranges and improvement potential through systematic parameter optimization.

The presentation would benefit from systematic model intercomparison, particularly side-by-side graphical comparisons of simulated versus observed discharges to highlight differences and reveal systematic biases. Such analysis would identify models that consistently over- or under-predict flows across different seasons and conditions.

The observed differences between simulated and measured discharges at annual scales raise important concerns about model reliability for operational applications. For water management, agricultural planning, and climate adaptation, greater precision is essential. Current uncertainty levels may be insufficient for supporting critical infrastructure investments or policy decisions requiring reliable hydrological projections.

Agricultural Implications: Data Quality Concerns and Future Directions

While not directly addressing agriculture yet, the research outlines clear connections through planned Gross Primary Productivity (GPP) analysis at catchment and 1km² scales for both control periods and future projections.

Critical Assessment of Irrigation Data Reliability

A referenced irrigation study shows how intensive irrigation helped buffer groundwater declines in European breadbasket regions, including the Po Valley, suggesting current agricultural practices are adapting to changing water availability. However, significant concerns exist regarding underlying irrigation data reliability.

The fundamental challenge lies in absent comprehensive ground-truth validation for Po Valley irrigation estimates. Current datasets typically rely on remote sensing products, statistical models, and administrative records—each carrying substantial uncertainties that compound when integrated.

Remote sensing approaches face inherent limitations including cloud contamination, mixed pixel effects, and difficulty distinguishing irrigation from natural soil moisture variations. Administrative records often lack spatial precision and may not reflect actual versus permitted irrigation rates. Statistical gap-filling models introduce additional uncertainty layers rarely adequately quantified.

Methodological Concerns in Earth Observation Applications

This exemplifies broader Earth Observation community concerns where tendency exists to advance rapidly toward novel applications without adequately addressing fundamental data quality issues. This "run forward" approach assumes intermediate data products are sufficiently reliable when substantial uncertainties may remain unresolved.

While the irrigation mapping community has made significant algorithmic and multi-sensor fusion progress, methodological innovation emphasis sometimes outpaces systematic validation work needed to establish accuracy levels under different environmental and agricultural conditions.

Path Forward for Agricultural Applications

The Po Valley would benefit enormously from systematic ground-truth irrigation surveys providing validation frameworks for improving remote sensing products. Such surveys should include direct measurements of irrigation timing, volumes, and spatial coverage across representative agricultural areas.

Future work should prioritize robust validation frameworks before advancing to complex integrated analyses, including ground-truth irrigation monitoring networks, systematic accuracy assessments, and uncertainty propagation methods throughout analytical chains.

Future Outlook and Adaptive Strategies

The findings paint a concerning picture for Po Valley agriculture. Reduced snowpack at critical elevations means less water storage for summer irrigation when crops need it most. Combined with increased evapotranspiration from warming temperatures, this creates significant water stress scenarios for one of Europe's most important agricultural regions.

However, the research represents crucial groundwork for developing adaptive strategies to maintain agricultural productivity facing accelerating climate change impacts on Alpine water resources. The honest assessment of limitations demonstrates appropriate scientific conservatism essential for complex mountain hydrological systems where observational uncertainties significantly impact climate change conclusions.

Success will require addressing fundamental data quality issues, improving model representations of critical processes, and establishing robust validation frameworks before advancing to policy-relevant applications. Only through such rigorous approaches can the scientific community provide reliable information needed for sustainable water management in agricultural regions facing climate pressures.

Biosphere Atmosphere Climate Interactions lab 2025

Go to the Theory and Concepts page

This page contains the laboratory materials for the BACI2025 course, specifically covering the sections I oversee. The laboratory sessions build upon concepts from the hydrology class while extending into more advanced simulations, including applications of the GEOSPACE system.  GEOSPACE is based upon GEOframe is an open-source, component-based hydrological modeling framework developed primarily by researchers in Italy. It's designed to be modular and flexible, allowing researchers to combine different hydrological processes and models.

Installations

• Conda (Vimeo2025)
• Java: To Install Java go to the Adoptium website select your platform, archiecture and version 11). Dowloand and launch the installer
• OMS material

Generalities about the Object Modelling System

OMS3 (Object Modeling System 3) is a Java-based environmental modeling framework developed by the U.S. Geological Survey (USGS) and Colorado State University. It's designed to facilitate the development, integration, and deployment of environmental and agricultural models.

• OMS3 (Slides) (Video2025, Video)
• Working Environment (Slides) (Video2025, Video)
• Simulation files  (Slides) (Vimeo2025,Video: 1, 2)
• For running an OMS project, see this other post. 

OMS Project that will be used

• Example 0 (Vimeo 2025)
• Other Examples for your inspection
• WHETGEO basic Project 
• Radiation Project
• GEOET basic project

WHETGEO specifically focuses on simulating the coupled processes of water and heat transport, which are crucial for understanding: Soil moisture dynamics, Evapotranspiration processes, Energy balance at the land surface, Groundwater-surface water interactions, Snow and ice processes (where temperature is critical)

• Exploring a WHETGEO project. Everything is explained in the WHETGEO1D_RichardsCoupled_Computational_grid notebook (Vimeo2025)
•  Please also browse directly the files:
• The grid file: ex00_grid.csv , Initial Conditions: ex00_ic.csv, Parameters: (for van Genuchten): Richards_VG.csv, Dictionary: dictionary.csv (Vimeo2025)
• WHETGEO1D.sim (Vimeo2025)
• Analysis of WHETGEO1D.sim (Vimeo2025)
• To run WHETGEO use the Runner_WHETGEO.ipynb notebook (Vimeo 2025)
• Please observe that the oms.py file needs to be in the same folder than the Notebook
• During the course a more solid solution was provided here.
• How to visualize and interpret the data through the Visualize_output.ipynb Notebook (Vimeo 2025)
• Utilities:
• To proper formatting (according to OMS3) rainfall files, peruse the TimeSeriesFormatter.ipynb Notebook (Vimeo2025)
• How to create an empty TimeSeries using TimeSeriesCreator.ipynb (Vimeo2025) 

RADIATION ESTIMATION is preliminary to any Evapotranspiration estimation since our models use it as input. The estimation of radiation, as it results from the theory, needs a few GIS operations to determine the sky view factor and the aspect of the terrain in the point of interest. These operation for the present exercise are skipped and pre-analyzed data are provided. 

• Please see the 05_NET.sim file in the project's simulation folder (Vimeo2025)
• Inputs are in Input_Radiation.ipynb (Vimeo2025)
• Outputs are in the Output_Radiation.ipynb (Vimeo2025)
• The simulation runner is Runner_NetRadiation.ipynb (Vimeo2025)

GEOET  is a group of  components within GEOframe that focuse specifically on evapotranspiration (ET) modeling. At present GEOET includes three main estimator of ET: The Priestley-Taylor, the Penman-FAO and the Prospero one.  

• Exploring a GEOET project

GEOSPACE, the Soil Plant Atmosphere Continuum Estimator in GEOframe (GEOSPACE) is presented in this paper, in particular the one-dimensional development, GEOSPACE-1D. GEOSPACE  (D'Amato et al., 2025) is a sophisticated modeling framework designed to simulate the complex interactions within the soil-plant-atmosphere continuum (SPAC) system.

• Exploring a GEOSPACE project

Go to the Theory and Concepts page

REFERENCES

• Bottazzi, M. 2020. “Transpiration Theory and the Prospero Component of GEOframe.” Edited by R. Rigon and G. Bertoldi. Ph.D., DICAM.
• D’Amato, Concetta. n.d. “Exploring the Soil-Plant-Atmosphere Continuum: Advancements, Integrated Modeling and Ecohydrological Insights.” Ph.D., Università di Trento.
  
• D’Amato, Concetta, Niccolò Tubini, and Riccardo Rigon. 2025. “A Component Based Modular Treatment of the Soil-Plant-Atmosphere Continuum: The GEOSPACE Framework (v.1.2.9).” https://doi.org/10.5194/egusphere-2024-4128.
• 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, 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. https://doi.org/10.5194/gmd-15-75-2022.
  

A CV template for postdocs that I like

I frequently receive PhD applications with standardized EuroPass CVs. While these formats have their place, I find they often lack personality and fail to effectively showcase a candidate's unique qualities. Even when institutions explicitly request standardized formats, these templates rarely help applicants stand out.
Previously, I've written about the differences between CVs and resumes, and shared my own CV on this blog. However, as a senior academic, my format may not be ideal for early-career researchers. 

Recently, I collaborated with one of my former PhD students to refine her curriculum vitae for postdoctoral applications. She created a format that effectively highlights her qualifications while demonstrating alignment with potential supervisors' research directions. I'm sharing this template below as a resource for prospective postdoc candidates.

Important advice: Always tailor your research plans to align with those of the principal investigator issuing the call for which you are writing your resume. Failing to do this significantly undermines your application's chances of success.

While your past achievements matter—they demonstrate your capability to complete projects—what's truly critical is how your future goals complement mine. Unless you've accomplished truly exceptional work (landmark publications or breakthroughs), focus more on articulating how your skills and interests will contribute to advancing our shared research objectives.

Please you can find here:

• A pdf template with fake contents
• A pdf template
• A LaTeX file (hyperlinks not working)
• An HTML file that can be eventually imported and edited in a word processor

The formatting can be improved since I did not dedicate all the time it needed. Obviously each one cane personalize some parts according to their own personality and attitude. Something can be missing. However, it contains what I expect it should be there. 

Using GEOET's Prospero model with minimal variations for simulating the non capacitive energy budget of snow and soil

This post is not self-explanatory and requires digging into other posts and some papers. 

Please review Section 2 of Concetta's paper (https://onlinelibrary.wiley.com/doi/10.1002/eco.70009?af=R) and verify the calculations presented there.

The model in D'Amato and Rigon (2025) uses a non-capacitive approach (it doesn't account for the thermal capacity of plants), and so will be if the same derivation is specialized for snow (or soil), which is a limitation. However, this approach is still more physically based than semi-empirical formulations or degree-day methods commonly used. In the literature, these are referred to as "stationary solutions" of the system. Despite the name, these solutions respond instantaneously to changing boundary conditions (radiation, latent and sensible heat fluxes), as evident in equation (10), which varies with radiation, wind velocity, and roughness.

Equation (10) and subsequent equations in Concetta's paper are essentially the Prospero solutions (though exact implementation should be verified in Concetta's code). The time interval of integration is, in principle instantaneous, but eventually you would like to integrate it over a finite time step (a hour, or a day, for instance). 

A non negligible aspect is that snow can melt into water and for any temperature you get from the energy budget, you need to partition the water in liquid water and ice. For this reason you probably need a partitioning function, like the one used for partitioning precipitation in rainfall and snowfall or you can simply use a melting law like  in simple models but now the temperature used should not be the air tempeature but the snow temperature.  See melting in simple models in  the links below

• Simplified snow models   (Vimeo2024)

for further information. 

An important term is missing from the formulation: heat exchange by conduction with the ground, which should be represented as:

G = C_s T_Δg := C_s (T_g - T_s)

Where:

• C_s is an appropriate exchange coefficient (can be taken as C_s = K/L, where K is the bulk thermal conductivity of the layer and L is its depth)
• T_g is the ground temperature (which could be taken as the multi-annual air temperature average)
• T_s is the snow temperature

Since this flux depends on the independent variable, it introduces additional terms that modify solution (10). Please derive these calculations independently.

Other terms that don't depend on the independent state variables can be included in the S_nk term. With these modifications, the Prospero code can effectively simulate the snow energy budget. Similar arguments apply to soil modeling.

A further consideration is the proper parameterization of the conductances C and C_E fluxes in equation (10), which differ from transpiration cases. For soil, according to Lehman-Or theory, evaporation should be modeled as potential until the water storage exceeds a threshold S_T, then decreasing proportionally with storage below this threshold when implementing an integrated model (Details ? I do not know).

I know that there are several missing aspects in this post. Who is interested, please ask. 

P.S. - These components have then to be carefully coupled to the other components. With respect to this, please consider the following: 

First review the presentation materials I've shared:

Getting new features to the linear systems (Vimeo2025)

The topic is that, based on my analysis, the second option is clearly the one should be applied in integrated distributed models (like GEOframe-NewAGE). However, this means we cannot simply subtract ET (or any other sink) from total rainfall - we need to incorporate this directly into the equation solver. While the example in the presentation uses a linear system with an analytical solution, the same principle applies to our non-linear fluxes where we use numerical integration. Therefore appropriate modifications could be necessary to the basic GEOframe-NewAGE codes. 

A Ph.D. position on Advancing Physics-Informed Machine Learning for Environmental Modeling and Smart Irrigation Systems

Project Overview

This PhD grant, funded by Fondazione Bruno Kessler, aims to develop an advanced Physics-Informed Machine Learning (PIML) framework for modeling complex hydrodynamic and environmental systems. By integrating physical principles with data-driven methods, the research will focus on optimizing next-generation irrigation strategies. The project will harness the synergy between physical laws (as implemented in the GEOSPACE system) and machine learning to enable predictive, real-time, and scalable modeling tools for sustainable water resource management.

Key Objectives

• Design hybrid PIML models that combine governing equations with data-driven predictive models (e.g., neural networks);
• Improve predictive accuracy and generalizability across heterogeneous environmental conditions;
• Incorporate real-time sensor data inputs to refine model states and parameters;
• Benchmark PIML approaches against traditional numerical solvers and/or black-box machine learning models.

Methodological Approach

The core innovation of this project lies in the integration of physical constraints (as derived from GEOSPACE) into machine learning models. Building on recent advances in PIML, the goal is to design, develop, and validate models that enforce conservation laws and boundary conditions within neural architectures. This may involve:

• Embedding partial differential equations (PDEs) directly into the loss functions of machine/deep learning models;
• Developing adaptive training strategies to trade-oO data fidelity and physical consistency;
• Utilizing sensor data to dynamically assimilate environmental variability into model predictions;
• Leveraging high-performance computing to train and deploy models at scale across complex
• domains.

Expected Outcomes

This integration will enable:

• Accurate and efficient modeling of water distribution and use in precision irrigation systems;
• Real-time monitoring and decision-support capabilities for agricultural and environmental applications;
• Enhanced data efficiency and model robustness through physics-based regularization;
• Improved understanding of system dynamics under data-scarce and/or non-stationary conditions.

Implementation Timeline

Months 1–6: Literature review on PIML methodologies;
Months 7–18: Design and develop a core PIML architecture, integrating IoT data sources;
Months 19–24: Validate models using lab-scale and field experimental datasets;
Months 25–36: Upscale models to real-world irrigation systems deployed within ongoing local and EU
projects (e.g., IRRITRE, AGRIF .OODTEF), and quantitatively assess their impact on water-saving strategies.

Possible Collaborations

Fabio Antonelli, Fondazione Bruno Kessler; Sara Bonetti and Concetta D'Amato, EPFL

Info: abouthydrology <at>  gmail.com

Shima Azimi's Thesis and Presentation at graduation

 This is a placeholder

A Ph.D. position ! Advanced Soil Biota-Hydraulics Interface for the WHETGEO-GEOSPACE system

Project Overview

This subproject, funded under the ICOSHELL project, aims to develop an integrated modeling
system that explicitly accounts for the dynamic interactions between soil biota activity and soil
hydraulic properties. Building upon the WHETGEO-1D and 2D frameworks, we will implement a
novel coupling between soil fauna population dynamics and plants root growth, evolving soil
hydraulic characteristics. The modelling system implemented will be eventually used for studying
the feedback between soil-vegetation hydrology.

Key Objectives

• Extend the WHETGEO model architecture to incorporate time-varying soil hydraulic properties influenced by soil biota 
• Implement the Kosugi soil water retention curve model with parameters that dynamically evolve based on biological activity
• Develop and integrate a population dynamics module for key soil engineers (earthworms, ants, termites)
• Create a comprehensive validation framework using laboratory and field experimental
• data

Figure from Enrico Chiesa Master Thesis

Methodological Approach

The core innovation of this subproject is the implementation of a feedback loop between
 biological activity and soil physics. Following Meurer et al. (2020), we will start to model how earthworm populations modify soil structure, but significantly expand this approach by:

• Replacing the van Genuchten model with the Kosugi water retention curve formulation, which provides a more direct physical interpretation of pore size distribution
• Developing a differential equation system where the Kosugi parameters (median pore size and standard deviation) are directly modified by biological activity
• Implementing these dynamics within the robust NCZ algorithm of WHETGEO, ensuring numerical stability across diverse conditions
• The population dynamics will be modeled as a set of ordinary differential equations representing different functional groups of soil engineers, their reproduction, mortality, and activity rates as functions of environmental conditions (temperature, moisture, organic matter)

Expected Outcomes

This integration will allow to better capture:

• The temporal evolution of soil infiltration capacity following land-use changes

• The self-reinforcing positive feedback loops of ecosystem restoration, where initial

vegetation changes trigger soil biological activity that further enhances water retention

• The resilience of soil hydrological function under climate change scenarios

Implementation Timeline

Months 1-6: Preliminary studies, doctoral school activities

Months: 6-18 Implement Kosugi model in WHETGEO framework, develop and integrate

population dynamics module Months 18-24: Validate against experimental data Months 32-36:

Upscale to field applications and integration to estimate catchment scale effects. Study effects of

soil management

Possible collaborations

EPFL Lausannne, Prof. Sara Bonetti and Dr. Concetta D'Amato

Info: abouthydrology <at>  gmail.com

The Marvelous Physics of Plants: a personal Introduction

 "The Marvelous Physics of Plants" presents an exploration of the physics behind how plants function, particularly focusing on water transport mechanisms. The presentation begins with poetic descriptions of plant processes, then explores Erwin Schrödinger's fundamental question about how physics and chemistry can explain the events within living organisms. The authors examine various physics domains relevant to plants: quantum physics, thermodynamics, hydraulics, micrometeorology, stability, and light.

Among the other things,  the authors examine the physical limits of tree height, discussing how hydraulic restrictions ultimately limit how tall trees can grow. They also demonstrate synthetic tree models that scientists have created to replicate these natural mechanisms.

The slides combine mathematical formulations, anatomical diagrams, and experimental results to illustrate the physical principles governing plant function. A video of the talk is also available.

Three Batchelor Graduation Works

The first  Thesis-poster,  by Agnese Cavazzini, supervised by Gaia Roati and me, presents a hydrological study of the Secchia River basin using the GEOframe-NewAGE system. The research analyzes water balance and simulates river flow while generating soil moisture maps to identify drought-prone areas. Key elements include watershed division into sub-basins, mass balance equations, and calibration against measured data. Results show flow simulations at two monitoring stations and soil moisture anomaly maps. The successful implementation provides valuable insights into the basin's hydrological dynamics across Modena, Reggio Emilia, and Mantova provinces. You can get a high resolution poster by clicking on the Figure below..

The second Thesis-poster, by Lorenzo Dalsasso,  presents a statistical analysis of ground precipitation patterns by Lorenzo Dalsasso. Using hourly precipitation data from three weather stations, the study evaluates which probability distributions best represent precipitation duration, intensity, and intervals between events. A Python notebook with Kolmogorov-Smirnov tests determined that lognormal distributions best fit precipitation durations, Weibull distributions best represent precipitation intensities, and either Weibull (stations ID 40 and 1100) or lognormal (station ID 263) best characterize intervals between precipitation events. The results include detailed statistical parameters for each station. The high resolution poster can be found by clicking on the Figure below. 

Thr third thesis-poster presents Marco Feltrin's study on evapotranspirative fluxes in grapevines by integrating the GEOSPACE ecohydrological model with WiseConn sensor technology (dr. Marco Bezzi). The research compares two rainfall scenarios: a wet scenario (1147 mm of total precipitation) and a dry scenario (682.4 mm of total precipitation) to evaluate plant water stress. Using the one-dimensional GEOSPACE model with data from a vineyard near Verona, results show that the dry scenario led to half the plant transpiration during summer months. The model effectively demonstrates how water content throughout the soil column affects water stress in plants, with practical applications for irrigation management, water conservation, and predicting water availability for viticulture under changing climate conditions.  The high resoltion poster can be found by clicking on the Figure below. 

Biosphere, Atmosphere, Climate Interactions 2025 Class

Go to the lab Page

The second part of this course explores the Soil-Plant-Atmosphere Continuum (SPAC). Below you will find materials covering soil properties, their mathematical representations, and an introduction to plant functioning. Students are expected to review these materials as an assignment before our class discussion of the concepts. In the latter portion of the course, we will conduct numerical experiments together using the GEOSPACE system.

Radiation

• Solar Radiation (Vimeo 2025)
• Effects of terrain on solar radiation (Vimeo2025)
• Long wave radiation (Vimeo 2025)
• Radiation and Canopies 

Water in soils 

 (Storyboard2020)

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.

•  Soils (Vimeo2025)
•  (Vimeo2025-IT) 
• Texture of soils (Vimeo2025)
• Structure of soils (Vimeo2025)
• Textbook: Freeze and Cherry: Groundwater, section 2.8

• Definitions (Vimeo2025)
•  (Vimeo2025-IT)
• Darcy law (Vimeo2025)
• (Vimeo2025-IT)
• Textbook: Freeze and Cherry, Groundwater, section 2.1 and section 2.12
• Buckingham (Vimeo2025)
• (Vimeo2025- IT)
• Complementary reading: Freeze and Cherry, Groundwater, section 2.2
• Mass Conservation (Vimeo2025)
• Capillary Forces (Vimeo2025)

• Soil Water RetentionCurves (Vimeo2025 I, Vimeo2025 II)
• (Vimeo2025-IT)
• SWRC White Board explanation
• On What SWRC depends upon (White Board-IT)
• Complementary reading: Freeze and Cherry, Groundwater, section 2.6
• Hydraulic Conductivity
• Conductivity in unsaturated soils (Vimeo2025)
• (Vimeo2025-IT)
• Saturated conductivity (Vimeo2025)
• (Vimeo2025-IT)
• Textbook: Freeze and Cherry, Groundwater, section 2.3 and section 2.
• Additional material: Ning Lu's lectures on soil water

•  The Richardson-Richards equation  (Storyboard 2020-IT)
•  Richards equation (Vimeo2025)
• Complementary reading: Freeze and Cherry, Groundwater, section 2.6
• Pedotransfer Functions (Vimeo2025 - IT)
•  The groundwater equation (Vimeo2025)
• (Vimeo2025-IT)

• Textbook: Freeze and Cherry, Groundwater (Section 2.9 and section 2.11)

• A deeper view on matric potential 

• The matric potential from chemical potential (Vimeo2025)

Evaporation generalities (Storyboard2020)

A consistent part of root zone and surface water evaporates and returns to the atmosphere to eventually form clouds and precipitation again. The process follows quite complicate routes and is different when happening from liquid surfaces, soil or vegetation (and BTW animals).  In this group of lectures we try to figure out the physical mechanisms that act in the process and give some hint on methods to estimate evaporation and transpiration with physically based models. 

• Definitions  (Vimeo2025)
•  (Vimeo2025-IT)

• Evaporation causes diffusion of water vapor and the Clausius Clapeyron Equation (Vimeo2025)
• (Vimeo2025 I - IT, Vimeo2025 II - IT)
• Turbulent transport of vapor (and other quantities): the Daltonian law (Vimeo2025)
• (Vimeo2025-IT)
• Textbook: M. Bottazzi  (cap. 2.2)
• Whiteboards:
• A short reminder (Evaporation as vapor transport and evaporation as phase transition)
• On the parametrization of turbulence
• And again on the logarithm profile
• Blackboard 2024

• Evaporation as energy flux  (Vimeo2025)
• (Vimeo2025-IT)
• Textbook: M. Bottazzi  (chap. 2.3)

• Schymanski & Or derivation of Penman-Monteith equation (Vimeo2025)
• Textbook: M. Bottazzi  (cap. 2.3.2-2.3.5)
• Brief summary (Vimeo2025)

• Simplification of the P-M solution (PM-FAO e Priestley-Taylor) (Vimeo2024)
• Evaporation form soils  (Vimeo2025)
• (Vimeo2024-IT)
• Textbook: M. Bottazzi  (chap. 2.4.1-2.4.3)

• Transpiration (Vimeo2025)
• (Vimeo2024-IT)
• Textbook M. Bottazzi  (chap. 3.0-3.3)
• Stress Factors (Vimeo2025)
• (Vimeo2024-IT)
• A little of plants Hydraulics (Vimeo 2025)

• Supplemental Material

• Plants marvellous physics 
• (Vimeo2025 - IT)
• From Leaves Old Material to Canopies
•  (Vimeo2024-IT)
• Textbook M. Bottazzi  (chap. 3.4)
• Plants physiology and resistances to transpiration (supplemental material)
  

A little on the carbon cycle

The carbon cycle is intrinsically and fundamentally intertwined with both hydrological and climate cycles, forming an interconnected web of Earth system processes that operate across multiple temporal and spatial scales. While carbon dynamics were historically studied as a separate discipline from hydrology and meteorology, this artificial separation has dissolved as hydrology and meteorology have evolved into a comprehensive Earth System Science that recognizes the profound interconnectedness of all planetary processes. The integration of carbon cycle studies with hydrology represents a paradigm shift in our understanding of how Earth's systems function. Water serves as the primary medium through which carbon moves between the atmosphere, biosphere, hydrosphere, and geosphere, while carbon dynamics simultaneously influence water availability, quality, and distribution patterns. This bidirectional relationship creates a complex network of feedbacks that are not merely numerous, but virtually countless in their manifestations and interactions.

• An overview of the terrestrial carbon cycle for the large to stand scales by Daniela Dal Monech (Vimeo2025)
• A few things about the carbon cycle in terrestrial streams by Enrico Bertuzzo.

Further Reading

D’Amato, Concetta, and Riccardo Rigon. 2025. “Elementary Mathematics Can Help to Shed Light on the Transpiration Budget under Water Stress,” January. https://doi.org/10.1002/ECO70009.

Go to the lab Page

The Hydrological Modeling 2025 class

 Welcome to the 2025 Hydrological Modeling Class!

To better understand the materials provided:

• Storyboards – Summaries of the lectures, usually in Italian.
• Whiteboards – Explanations of specific topics, presented on a whiteboard using Notability on an iPad.
• Slides – Commented in English (available since 2021).
• Videos – Recorded during lectures to complement the slides, with no editing (as post-production would be too time-consuming).
  • 2025 videos are available on a [Vimeo Showcase] (link here).
• Additional information & references – Marked in italics, for the curious and the brave who want to explore further.

📅 24 February 2025 – Part I

Syllabus & Introduction to Hydrological Modeling

In this session, I introduced the course and its learning-by-doing philosophy. We cover all theoretical concepts first, followed by the practical applications (with Professor Giuseppe Formetta).

The real start 

•  Vimeo2025, 
• (Vimeo2024, Vimeo 2021)
• Prerequistes  
• Vimeo2025 - I, 
• Vimeo2024 - I, Vimeo2024-II, Vimeo 2021, Vimeo2022,Vimeo 2023)
• Methods
• Vimeo2025  
• (Vimeo2024 II, Vimeo2023 III,Vimeo2021, Vimeo2022)
• How you will be graded  
• (Vimeo2024, Vimeo 2021, Vimeo 2022,Vimeo2023)
• The Topics  
• Vimeo2025-I, Vimeo2025-II
• (Vimeo2024, Vimeo2023 II, Vimeo Video 2020, Vimeo 2021, Vimeo2022)

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

📅 25 February 2025 – Geomorphometry

This session begins with a discussion of previous lesson topics and the rationale behind introducing geomorphometric concepts. Since catchments are spatially extended, understanding their geometry is essential for studying catchment hydrology.

In the first part, we focus on the geometrical and differential characteristics of topography, including:

• Elevation
• Slope
• Curvature

These parameters are fundamental for extracting the river network and identifying different parts of a catchment.

We then define drainage directions and explore how they are computed using Digital Elevation Models (DEMs)—where topography is discretized on a regular grid. From these drainage directions, we determine the total contributing area at each point of a DEM.

These two key characteristics allow us to:

1. Identify channel heads and extract the river network.
2. Define hillslopes and establish an initial framework for Hydrologic Response Units (HRUs).

• Introduction to Geomorphometry I:
• A little of vocabulary (Vimeo2025, Vimeo 2021)
• Data (Vimeo2025, Vimeo 2024)
• The basics of DEM analysis (All the differential geometry-derived quantities)
•  Elevation, Slopes, (Vimeo2025)
•  Curvatures (Vimeo2025)
• Old videos:  Vimeo 2024, Vimeo 2024, Vimeo 2023 - Part I, Vimeo_2023-Part II, Vimeo 2023 Curvatures) Vimeo 2022 part I, Vimeo 2022, part II, Vimeo2021, YouTube video 2019,YouTube2020, Sintesi in Italiano 2020
• Hydrogeomorphology: the derived quantities, drainage directions and contributing areas (Vimeo2025) 
• (Vimeo2024, Vimeo 2023, Vimeo 2022, Vimeo2021, YouTube video 2019,YouTube2020, Sintesi in Italiano 2020)
• On the estimation of tangential stresses in a curved topography (Whiteboard 2020)
• References for who wants to go deeper
• Peckham, R. J., and G. Jordan. 2007. Digital Terrain Modelling: Development and Applications in a Policy Support Environment. Edited by Robert Joseph Peckham and Gyozo Jordan. New York: Springer, Berlin, Heidelberg. Lecture Notes In Geoinformation and Cartography.
• A Storyboard Italian regarding the geomorphic laws
• Where do channels begin: Extracting channels and hillslope (Vimeo2025)
• (Vimeo 2024, Vimeo2022, Vimeo 2023)
• Old classes: YouTubeVideo 2020 b, Sintesi in Italiano 2020
• Old a little different but useful material: extracting the hillslope (YouTube Video 2019,YouTube2020)
• Channel heads move (Vimeo 2024)

📅 3 March 2025 

• A brief overview about geomorphic laws regarding the river networks and catchments (Vimeo2025). 
• Old Classes: Vimeo 2021, Vimeo2022,Vimeo 2024
• Additional information and references
• Part of the above but presented in a different way. Topological classification of catchments elements: 
• Horton-Strahler Ordering (Whiteboard2020); 
• Pfafstetter (Whiteboard2020; an alternative presentation here) and 
• other ordering schemes (Whiteboard 2020 here).
• Rigon, Riccardo, Ignacio Rodriguez-Iturbe, Amos Maritan, Achille Giacometti, David G. Tarboton, and Andrea Rinaldo. 1996. “On Hack’s Law.” Water Resources Research 32 (11): 3367–74.
• Detecting the human landscape (please try to read and summarize the main concepts): Cao, Wenfang, Giulia Sofia, and Paolo Tarolli. 2020. “Geomorphometric Characterisation of Natural and Anthropogenic Land Covers.” Progress in Earth and Planetary Science 7 (1): 2.
• Other references:
• Older classes in Italian 
• Geomorphology with References
• Various information from the AboutHydrology Blog
• R.Rigon, E. Ghesla, C. Tiso and A. Cozzini, The Horton Machine, pg. viii, 136, ISBN 10:88-8443-147-6, University of Trento, 2006
• W. Abera, A. Antonello, S. Franceschi, G. Formetta, R Rigon , "The uDig Spatial Toolbox for hydro-geomorphic analysis" in Geomorphological Techniques, v. 4, n. 1 (2014), p. 1-19

Q&A - 

Multiple choice questions about Geomorphology (Comment in English 2023) 

Multiple choice questions about Geomorphology in Italian (Comment in English) 

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. 

• Getting the sense of what we are doing (Vimeo2025, Vimeo2022)
• Hydrological data (Storyboard2020 in Italian)
• To which data are we interested in and where can we find them ? (In English)
• Ground data and their interpolation (Vimeo2025)
• Vimeo2024, Vimeo2022, Vimeo 2021,  Zoom2020 
• Thiessen Polygons (Storyboard2020 in Italian)
• Inverse distance Weighting (Storyboard 2020 in Italian)
• Introduction to Kriging Theory:
• Summary (Vimeo2025)
• Vimeo 2021, Vimeo2022, Vimeo2024
• Building the system to solve ( Storyboard 2020), 
• the Kriging's equations (Vimeo2025)
• YouTube2019, Vimeo 2021, YouTube2020, Zoom2020, Vimeo2022, Vimeo2023, Vimeo2024 part1, Vimeo2024 part 

Installations of the software can be found here, at this link.

📅 10 March 2025 

 Interpolations part II

• Where do we stand (at the blackboard, Whiteboard2024)
• Variography (Vimeo2025)
•  Storyboard 2020, 
• YouTube video 2019, YouTubeVideo2020, YouTube2020b, Vimeo 2021, Vimeo2022, Vimeo2023, Vimeo2024

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.

• Catching the errors of estimates (Vimeo2025)
• Storyboard2020 in Italian,
•  Vimeo 2024,Vimeo2023, Vimeo2022, Zoom2020,
• Flow chart and Various types of Kriging (Vimeo2024)
• Storyboard in Italian 2020, Zoom2020
• The Normal score (Vimeo2023)
•  (Vimeo2022)
• Some tools available in OMS3 (Vimeo2022)
• Additional material: 
• Old videos and Material in Italian
• Rainfall and Temperature interpolation for hydrologist.
• References:
• Marialaura Bancheri, Francesco Serafin, Michele Bottazzi, Wuletawu Abera, Giuseppe Formetta, and Riccardo Rigon, The design, deployment, and testing of kriging models in GEOframe with SIK-0.9.8, Geosci. Model Dev., 11, 2189–2207, 2018 https://doi.org/10.5194/gmd-11-2189-2018
• Andràs Bardossy, Introduction to Geostatistics, year unknown.
• Goovaerts, P. (1997). Geostatistics for Natural Resources Evaluation (pp. 1–488). New York : Oxford University Press.
• P.K. Kitanidis, Introduction to GEOstatistics, 1997 https://doi.org/10.1017/CBO9780511626166
• Mitas, Lubos, and Helena Mitasova. 1999. “Spatial Interpolation.” Geographical Information Systems: Principles, Techniques, Management and Applications 1 (2). http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.224.5959&rep=rep1&type=pdf.
• G. Raspa, Dispense di Geostatistica Applicata, Università di Roma 3, 2010

Q&A - 

Spatial Interpolation (Vimeo2023)

Spatial Interpolation (Vimeo 2022)

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.

• Today's storyboard (here in Italian)

📅 17 March 2025 

Hydrological Models 

For old material give a look to Hydrological Modelling 2023

• Catchment processes (Vimeo2025)
• (Vimeo2024)
• Hydrological Models (Vimeo2025)
• (Vimeo2024)
• Seven steps in hydrological modelling I: clarifying the purposes, geomorphology, pre-analysis of input data (Vimeo2025)
• (Vimeo2024)
• Integral Distributed Model or Hydrological Dynamical Systems, HDSys (Vimeo2025) 
• Zoom2020, Vimeo2021,Vimeo2022,Vimeo2023, Vimeo2024
• The representation of Hydrological Dynamical System (Vimeo2025)
• Zoom2020,Vimeo2021,Vimeo2022, Vimeo2023, Vimeo2024
• Seven steps in hydrological modelling II: setup, model calibration/execution/validation (Vimeo2025)
• Vimeo2024
• Seven steps in hydrological modelling III: delivery the results, final deployment to stakeholders (Vimeo2025 - not recorded)
• Vimeo2024
• DARTHs (Digital Twins of Earth System) (Vimeo2024)
• A new way to do models (Vimeo2024)
• A final view on Hydrological Dynamical Systems and their application to catchments.
  • Hypothesis testing in Hydrological Modelling with HDSys (At the whiteboard)
• Further readings:
•  a blogpost from EGU
• Opinions

📅 25 March 2025 

 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.

• The very simplest linear system (Vimeo2025)
• Vimeo 2022, Vimeo2021 , Vimeo2023, Vimeo2024
• Derivation of the solution of the linear reservoir (Blackboard2024)
• Blackboard2023, Whiteboard2021
• Same derivation as above but from a different source and treated in a general way
• Getting new features to the linear systems (Vimeo2025)
• Vimeo 2022, Vimeo2021, Vimeo2023, Vimeo2024
• Integrating the linear system on the blackboard (Vimeo2025)
• Summarizing the previous class results at the blackboard (Vimeo2022)
• The Nash model  (Vimeo2025)
• Vimeo2023,Vimeo 2022, Vimeo2021,Vimeo2024
• A trick for doing the double integration in the Nash Hydrograph derivation (Blackboard 2024, Blackboard2023, Blackboard2022, Vimeo Whiteboard 2021)
• The S-function (Blackboard2024)

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. 

• The storyboard
• The IUH classic (Vimeo2025)
• (Vimeo2024,Vimeo2023,Vimeo2022, Vimeo2021)

📅 31 March 2025 

• Summarizing the previous class (Vimeo2022)
• The issue of runoff generation 
• the SCS (Vimeo2025)
• Vimeo2024,Vimeo2023 Vimeo2022
• In Italian: Vimeo2021
• Why SCS is actually not a good choice for continuous simulations
• the Hymod model  (Vimeo2025)
• Vimeo2024,Vimeo2023,Vimeo2022, Vimeo2021
• ERM-I (Vimeo2025)
• Vimeo2024 ,Vimeo2023, Vime2022
• In Italian: Vimeo2021-I, Vimeo2021-II

📅 7 April 2025 

• A summary of previous lectures 
• ERM-II (Vimeo2025)
• Vimeo2024, Vimeo2023, Vime2022
• In Italian: Vimeo2021-I, Vimeo2021-II
• Simplified snow models  (Vimeo2025)
• Vimeo2024, Vimeo2023, Vimeo 2022, Zoom2020,Vimeo2021
• MaRRmot survey of models (Vimeo2025)
• MaRRmot supplemental material
• Vimeo2021, Vimeo 2022, Vimeo2024
• A little about models calibration (Vimeo2025)
• (Vimeo2024,Vimeo2022, Zoom2020,Vimeo2021)
• Notes about models validation (Vimeo2025)
• (Vimeo2024)

• Additional material

Digressions I - A Glimpse on distributed process-based models

• GEOtop (Vimeo 2023)
• GEOtop on freezing soil and snow  (Vimeo 2023)

 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. 

• The view of the catchment as the statistics of elementary water volumes moving stochastically, a storyboard
• Travel Time, Residence Times (Vimeo2025 part I, Vimeo2025 part II)
• A summary (Vimeo 2022)
• A short note about past and future (Vimeo2022)
• Vimeo 2021-Ita, Vimeo 2021-Eng, Vimeo2022, Vimeo2024
• Some discussion (In English)
• StorAge Selection Functions (Vimeo2025)
• (Vimeo2024)
• (Blackboard2024 -1, Blackboard2024 -2)

📅 14 April 2025 

• He & She on the blackboard (Blackboard2025)
• Response time and Life Expectancy (Vimeo2025)
• (Vimeo2024)
• A post on travel (transit)  time, residence time and response time definitions
• Niemi's identity (Vimeo2025)
• (Vimeo2024)
• Multiple Reservoirs (Vimeo2025)
• (Blackboard2025)
• (Vimeo2024)
• (Blackboard2024)
• Partitions (Vimeo2025 I, Vimeo2025 II)
• (Vimeo2024)
• Pollutants and Tracers (Vimeo2025)
• (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 (advanced)

• Rigon, R., M. Bancheri, and T. R. Green. 2016. “Age-Ranked Hydrological Budgets and a Travel Time Description of Catchment Hydrology.” Hydrology and Earth System Sciences. https://hess.copernicus.org/articles/20/4929/2016/.
• 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.
• More References in slides

Additional material

Digressions I - A Glimpse on distributed process-based models

• GEOtop (Vimeo 2023)
• GEOtop on freezing soil and snow  (Vimeo 2023)

Digressions II - Radiation -  After all radiation moves it all.

•  Radiation (YouTube 2017). 
• The Sun (YouTube 2017)
• Stefan-Boltzmann law and radiation spectrum (YouTube 2017, Vimeo2021)
• Sun  to Earth (YouTube 2017)
• Coping with latitude and longitude (YouTube 2017,Vimeo2021)
• Atmospheric Absorptions (YouTube 2017,Vimeo2021)
• Clouds (YouTube 2017,Vimeo2021)
• Coping with terrain (YouTube 2017,Vimeo2021)
• Long wave radiation (YouTube 2017, Vimeo2021)
• Table of symbols
• Readings:
• Corripio, J. G. (2002). Modelling the energy balance of high altitude glacierised basins in the Central Andes. Ph.D Dissertation, 1–175.
• Corripio, J. G. (2003). Vectorial algebra algorithms for calculating terrain parameters from DEMs and solar radiation modelling in mountainous terrain. Int. J. Geographical Information Science, 17(1), 1–23. 
• Formetta, G., Rigon, R., Chávez, J. L., & David O. (2013). Modeling shortwave solar radiation using the JGrass-NewAge system. Geoscientific Model Development, 6(4), 915–928. http://doi.org/10.5194/gmd-6-915-2013 
• Formetta, G., Bancheri, M., David, O., & Rigon, R. (2016). Performance of site-specific parameterizations of longwave radiation. Hydrology and Earth System Sciences, 20(11), 4641–4654. http://doi.org/10.5194/hess-20-4641-2016
• Various material from the AboutHydrology blog
• Q&A - Some questions on radiation, your answers and my comments.

Digressions III 

Equations for disease spreading (Out of schedule)

• An unexpected candid way (for naive people like me) to model Covid-19 spreading (Whiteboard2020, Zoom2020)
• But look how it is a more informed model s. 

Digressions IV

Examples of Applications:

• Posina Catchment
• Blue Nile
• Basilicata

Intermedia

• Questions to be answered 
• Some MaRRmot models for the exam