The STRADIVARI project - STudy of the teRrestriAl Hydrology and its feeDback wIth the lower atmosphere and the carbon cycle and Its VARIation under vegetation changes at various scales - 0

 Scientific Challenge and Innovation

The poetic novel "The Man Who Planted Trees" (Giono, 1953) depicts the transformation of a barren wasteland into an ecosystem with a complex hydrological cycle through decades of tree planting. While inspirational, the story raises unresolved hydrological questions about feedbacks between soil, vegetation, climate, hydrology, and ecosystems, questions current models cannot fully address. Current Earth System Models fail to capture critical feedbacks between soil evolution, plant hydraulics, and atmospheric processes required for understanding coupled hydrological and ecosystem functioning (e.g., Miralles et al., 2025) because Earth's system compartments are often treated as silos or parameterized in crucial aspects of their dynamics. This leaves fundamental questions unanswered: Can the compelling ecosystem transformation depicted in Giono's story be quantitatively validated through dynamic modeling?

References

Giono, Jean. 1953. "L'homme qui plantait des arbres." Vogue, Paris.

Giono, Jean. 2015. The Man Who Planted Trees. New York, NY: Random House.

Miralles, Diego G., Jordi Vilà-Guerau de Arellano, Tim R. McVicar, and Miguel D. Mahecha. 2025. "Vegetation-Climate Feedbacks across Scales." Annals of the New York Academy of Sciences 1544(1): 27-41. https://doi.org/10.1111/nyas.15286.

From Parameterized to Dynamic Earth System Coupling

Current ESS Models fail to capture critical feedbacks between soil evolution, plant hydraulics, and atmospheric processes required for understanding coupled hydrological and ecosystem functioning (e.g., Miralles et al., 2025) because Earth's system compartments are often treated as silos or heavily parameterized in crucial aspects of their dynamics. This leaves fundamental questions unanswered: Can the compelling ecosystem transformation depicted in Giono's (1953) "The Man Who Planted Trees" be quantitatively validated through dynamic modeling? STRADIVARI aims to fill this knowledge gap by developing an integrated modeling framework that couples dynamic soil-biota interactions, plant hydraulic strategies, and atmospheric boundary layer processes, replacing the fixed BCs that constrain current models with dynamical feedbacks.

The GEOSPACE framework (D'Amato et al., 2025) demonstrates this integration philosophy through operational coupling of soil heat-water transport (WHETGEO) with transpiration processes (Prospero). In that approach, the dynamic root water uptake responds to evolving soil moisture while simultaneously influencing soil energy balance. This proof-of-concept validates that meaningful process coupling emerges from component interactions without sacrificing individual model integrity and represents a blueprint for the project.

The Figure illustrates the complexity of coupled Earth system interactions using Extended Petri Net notation (Bancheri et al., 2019). Even this simplified representation, which misses the feedback with the atmosphere, reveals multiple interdependencies across water, energy, and carbon budgets. The loops represent dynamic feedback, while solid arrows show water, carbon and energy fluxes that must be tracked simultaneously. Traditional models typically fix the quantity inside a triangle as boundary conditions rather than allowing them to evolve dynamically. For a full explanation of the symbols, please see the cited paper.

STRADIVARI aims to fill this knowledge gap by developing an integrated modeling framework that couples dynamic soil-biota interactions, plant hydraulic strategies, and atmospheric boundary layer processes, replacing the fixed boundary conditions that constrain current models with dynamical feedbacks.

Core Innovation: STRADIVARI represents a fundamental methodological paradigm shift: moving from model-constrained science to science-driven modeling. Traditional Earth System modeling forces researchers to adapt scientific questions to existing tool capabilities, while STRADIVARI inverts this relationship by providing computational infrastructure that adapts to scientific inquiry by design. Rather than solving all Earth System coupling challenges directly, STRADIVARI creates tools facilitating the investigation of process interactions, answering the question "what tools do we need to investigate this process?" This paradigm shift transforms Earth system modeling from isolated research efforts into collaborative knowledge construction. Individual researchers are enabled to contribute specialized process knowledge while the modeling infrastructure integrates these contributions into system-level understanding, creating a positive feedback loop where broader participation accelerates discovery across interconnected Earth system processes.

Community Innovation: The GEOframe system technologies, which form the backbone of the project and were designed in anticipation of the FAIR principles of reproducible research and community building, will be extended with AI agents. A domain-specific small language model trained on hydrological literature and extensive GEOframe documentation addresses the fundamental bottleneck by providing accessible interfaces to sophisticated modeling capabilities. This AI assistant will democratize access to complex Earth system modeling by enabling researchers without extensive technical expertise to interact naturally with the modeling framework through conversational interfaces, accelerating scientific discovery and broadening the user community.

References

• Bancheri, Marialaura, Francesco Serafin, and Riccardo Rigon. 2019. "The Representation of Hydrological Dynamical Systems Using Extended Petri Nets (EPN)." Water Resources Research 55(11): 8895-8921. https://doi.org/10.1029/2019wr025099.
• Giono, Jean. 1953. "L'homme qui plantait des arbres." Vogue, Paris.
• Giono, Jean. 2015. The Man Who Planted Trees. New York, NY: Random House.
• Miralles, Diego G., Jordi Vilà-Guerau de Arellano, Tim R. McVicar, and Miguel D. Mahecha. 2025. "Vegetation-Climate Feedbacks across Scales." Annals of the New York Academy of Sciences 1544(1): 27-41. https://doi.org/10.1111/nyas.15286.

Objectives

STRADIVARI leverages established physical foundations, infiltration influenced by soil characteristics evolving through biotic activity (Brinkmann et al., 2010; Meng X et al., 2002), plant hydraulics with detailed transpiration processes (Kennedy et al., 2019; D'Amato and Rigon, 2025), soil and surface evaporation with proper energy partitioning (Or et al., 2013), and atmospheric boundary layer dynamics creating feedback loops with surface processes (Anderson et al., 2003; Siqueira et al., 2008), as launching points for investigating emergent behaviors from coupled system interactions. The modular component architecture, interconnected through supporting software layers (David et al., 2013; Moore and Hughes, 2017), enables exploration of cross-compartmental feedback loops that amplify or dampen climate responses through nonlinear dynamics. While such dynamics are well-documented at regional scales (Gross et al., 2018; Gröger et al., 2021), their investigation at catchment and local scales remains limited. The project's scope, while ambitious in vision, does not pretend to solve all coupling challenges directly but opens pathways toward their resolution. STRADIVARI will concentrate mainly on soil-plant interactions, water and carbon cycle dynamics, and plant-atmosphere exchanges. For atmospheric boundary layer description, the project will develop a hierarchy of models with increasing realism to bridge current modeling capabilities. By dynamically linking hydrology with soil biotic evolution (Meurer et al., 2020) and vegetation dynamics, STRADIVARI transcends traditional approaches through inter-compartmental feedback analyses.

Building on earlier visions (Rigon et al., 2006; Rigon et al., 2022), STRADIVARI couples water and energy budgets with dynamic soil and vegetation processes and atmospheric boundary layer transport equations. This addresses a critical gap: micrometeorological models often lack detailed soil and plant descriptions, while hydrological models miss key atmospheric interactions. Existing efforts suffer from architectural limitations and inflexible frameworks (Telteu et al., 2021). STRADIVARI's component-based architecture overcomes these constraints by enabling seamless process integration while maintaining computational efficiency and addressing theoretical and computational challenges in SPAC modeling, particularly regarding soil-plant, plant-atmosphere, and water-carbon cycle couplings. STRADIVARI adopts a "luthier" approach to ESS modeling, crafting instruments that enable virtuoso scientific performance rather than attempting to resolve all coupling challenges directly. Like a violin maker who provides musicians with tools for artistic expression, STRADIVARI provides researchers with computational infrastructure that embodies new conceptual frameworks for investigating process interactions. This philosophy recognizes that ESS coupling involves phenomena across multiple disciplines, temporal scales, and spatial domains that no single project can fully resolve. Instead, STRADIVARI creates a modular research infrastructure that enables systematic investigation of individual coupling mechanisms, virtual experiments to test competing hypotheses, community collaboration across traditional disciplinary boundaries, and progressive advancement as understanding develops. The project's success lies not in solving ESS coupling but in democratizing access to tools that enable meaningful investigation of these challenges. To accelerate adoption, STRADIVARI integrates Small Language Models with AI agents that provide intelligent assistance to new users and developers, making the modeling framework more accessible and reducing the learning curve for complex Earth system investigations.

References 

• Anderson, M. C., et al. 2003. "A thermal-based remote sensing technique for routine mapping of land-surface carbon, water and energy fluxes from field to regional scales." Remote Sensing of Environment 90(4): 521-531.

• Brinkmann, Pernilla E., Wim H. Van der Putten, Evert-Jan Bakker, and Koen J. F. Verhoeven. 2010. "Plant-Soil Feedback: Experimental Approaches, Statistical Analyses and Ecological Interpretations." The Journal of Ecology 98(5): 1063-73.

• 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).

• David, O., J. C. Ascough II, W. Lloyd, T. R. Green, K. W. Rojas, G. H. Leavesley, and L. R. Ahuja. 2013. "A Software Engineering Perspective on Environmental Modeling Framework Design: The Object Modeling System." Environmental Modelling & Software: With Environment Data News 39(c): 201-13.

• Gross, Markus, Hui Wan, Philip J. Rasch, Peter M. Caldwell, David L. Williamson, Daniel Klocke, Christiane Jablonowski, et al. 2018. "Physics–Dynamics Coupling in Weather, Climate, and Earth System Models: Challenges and Recent Progress." Monthly Weather Review 146(11): 3505-44.

• Gröger, Matthias, Christian Dieterich, Jari Haapala, Ha Thi Minh Ho-Hagemann, Stefan Hagemann, Jaromir Jakacki, Wilhelm May, et al. 2021. "Coupled Regional Earth System Modeling in the Baltic Sea Region." Earth System Dynamics 12(3): 939-73.

• Kennedy, D., Swenson, S., Oleson, K. W., Lawrence, D. M., Fisher, R., Lola da Costa, A. C., and Gentine, P. 2019. "Implementing plant hydraulics in the community land model, version 5." Journal of Advances in Modeling Earth Systems 11: 485-513.

• Meng, Xia, Annemieke M. Kooijman, Arnaud J. A. M. Temme, and Erik L. H. Cammeraat. 2022. "The Current and Future Role of Biota in Soil-Landscape Evolution Models." Earth-Science Reviews 226: 103945.

• Meurer, Katharina, Jennie Barron, Claire Chenu, Elsa Coucheney, Matthew Fielding, Paul Hallett, Anke M. Herrmann, et al. 2020. "A Framework for Modelling Soil Structure Dynamics Induced by Biological Activity." Global Change Biology 26(10): 5382-5403.

• Moore, R. V., and A. G. Hughes. 2017. "Integrated Environmental Modelling: Achieving the Vision." Geological Society, London, Special Publications 408(1): 17-34.

• Or, D., P. Lehmann, E. Shahraeeni, and N. Shokri. 2013. "Advances in Soil Evaporation Physics, A Review." Vadose Zone Journal 12.

• Rigon, R., G. Bertoldi, and T. Over. 2006. "GEOtop: A Distributed Hydrological Model with Coupled Water and Energy Budgets." Journal of Hydrometeorology 7: 371-88.

• Rigon, R., G. Formetta, Marialaura Bancheri, Niccolò Tubini, Claudia d'Amato, O. David, and C. Massari. 2022. "HESS Opinions: Participatory Digital Earth Twin Hydrology Systems (DARTHs) for Everyone: A Blueprint for Hydrologists." Hydrology and Earth System Sciences, January, 1-38.

• Siqueira, Mario, Gabriel Katul, and Amilcare Porporato. 2008. "Onset of Water Stress, Hysteresis in Plant Conductance, and Hydraulic Lift: Scaling Soil Water Dynamics from Millimeters to Meters." Water Resources Research 44(1): 1-14.

• Telteu, Camelia-Eliza, Hannes Müller Schmied, Wim Thiery, Guoyong Leng, Peter Burek, Xingcai Liu, Julien Eric Stanislas Boulange, et al. 2021. "Understanding Each Other's Models: An Introduction and a Standard Representation of 16 Global Water Models to Support Intercomparison, Improvement, and Communication." Geoscientific Model Development 14(6): 3843-78.

• Wilkinson, Mark D., Michel Dumontier, I. Jsbrand Jan Aalbersberg, Gabrielle Appleton, Myles Axton, Arie Baak, Niklas Blomberg, et al. 2016. "The FAIR Guiding Principles for Scientific Data Management and Stewardship." Scientific Data 3: 160018. https://doi.org/10.1038/sdata.2016.18.

Integrating GLEAM Earth Observation data strategy usage within GEOframe

To better understand the previous discussions, let's examine the specific case of GLEAM 3.0 (Martens et al., 2017) and 4.0. GLEAM (Miralles et al., 2025) is a global evapotranspiration product built on multiple Earth Observation (EO) resources. Since evapotranspiration (ET) cannot be measured directly, it must be inferred or modeled from available data. AS you know, GEOframe is our system for doing hydrology. For GEOframe methodologies in catchments application, please see this previous post.

Actually GLEAM operates at 0.1-degree spatial resolution (approximately 11 km grid cells), which is adequate for global analyses but insufficient for our purposes. Our objective requires information at 1km (approximateli 0.01-degree resolution), particularly for applications in complex terrain such as the Alps, where significant topographic variation occurs within very small areas.

From Miralles et al. 2025. References can be recovered there

Earth Observation Resources in GLEAM

According to Miralles et al. (2025), GLEAM utilizes the EO and reanalysis resources listed in Table 1. Below is an analysis of how each resource could be integrated with GEOframe:

Radiation

Current GLEAM approach: 0.1-0.5 degree resolution GEOframe implementation: Point-wise calculations using local solar radiation, filtered through cloud interception and atmospheric scattering models, then topographically corrected using digital elevation models.

Limitations: The coarse satellite resolution is inadequate for rugged terrain. Additionally, GEOframe's current empirical methods lack reliability, often requiring radiation estimates from randomly selected points within catchments, reducing representativeness.

Potential improvements: Satellite data could be fused with ground measurements to enhance overall accuracy.

Air Temperature

GEOframe implementation: Kriging interpolation with drift using ground station data.

Assessment: Generally reliable since temperature varies gradually across space, though canopy effects may introduce complications.

Precipitation

GEOframe implementation: Ground station measurements interpolated using kriging (typically without drift, as drift was found insignificant). Event-specific variograms are employed.

Key challenge: Determining whether kriging interpolation accurately captures storm spatial patterns. Satellite and radar data could provide valuable validation and improvement opportunities. See also the last post here.

Wind Speed

Application: Required for Penman-Monteith formulations.

Potential integration: ERA5 reanalysis data could supplement ground station measurements through data fusion/assimilation approaches, pending reliability validation (see Azimi et al., 2025)

Vapor Pressure Deficit (VPD)

Current use: Input for Penman-Monteith solutions (D'Amato and Rigon, 2025).

Technical note: VPD represents the temperature difference between emitting surfaces and air. Understanding EO estimation methods could enable valuable comparative analyses with the Prospero model (Bottazzi et al., 2021; D'Amato et al, 2025), where VPD emerges from energy budget calculations.

Carbon Dioxide Concentration

Application: Controls transpiration conductance in both Jarvis and Ball-Berry-Leuning parameterizations.

Current status: Available as input parameter in GEOframe for Penman-Monteith and Prospero models but not utilized in Priestley-Taylor formulations.

Snow Water Equivalent (SWE)

GEOframe approach: Calculated from precipitation, temperature, and snowpack evolution models. It should not be confused with Snow Covered Area (SCA).

Improvement opportunities: MODIS snow products offer superior resolution compared to GLEAM's 25 km resolution. For mountainous terrain with 5000 m elevation changes within 25 km, higher-resolution products could provide significant improvements.

Surface Soil Moisture

GEOframe implementation: Prognostic variable within root zone compartment.

Integration potential: Could enable GEOframe calibration if EO resolution and reliability improve. GEOframe soil moisture could be upscaled to match EO data resolution for comparative analysis.

Vegetation Optical Depth (VOD)

Definition: Proxy for vegetation biomass and cumulative transpiration (assuming linear correlation).

Current status: Not implemented in GEOframe.

Integration potential: Could be connected to Leaf Area Index (LAI), which is used in both interception and transpiration calculations.

Fraction of Absorbed Photosynthetic Radiation (fPAR)

Current status: Not used in GEOframe, which employs total radiation instead.

Advantage: Available at appropriate spatial scales for potential integration.

Leaf Area Index (LAI)

Applications: Useful for both interception and transpiration calculations (when using Penman-Monteith or Prospero models).

Integration potential: High, given its direct relevance to existing GEOframe processes.

Vegetation Height

Value: Excellent spatial resolution and direct application in aerodynamic resistance calculations.

Integration status: Not currently used but could be easily incorporated into GEOframe.

Land Cover Fraction

Current status: Not implemented in GEOframe.

Potential application: Could enhance transpiration estimations.

Soil Properties

Current status: Not utilized, as no GEOframe parameters currently depend on soil characteristics.

Future applications: Could become relevant if replacing reservoir-based root zone approaches with simplified versions of WHETGEO (Tubini and Rigon, 2022) or GEOSPACE (D'Amato and Rigon, 2025b).

GLEAM Methodological Components and GEOframe Integration

Rainfall Interception

GLEAM approach: Utilizes the van Dijk-Bruijnzeel model (van Dijk et al., 2001), developed from global experimental datasets.

GEOframe current implementation: Uses the Gash model.

Integration opportunity: Adding a van Dijk-Bruijnzeel component to GEOframe could enhance model compatibility and performance. Notably, Zhong et al. (2022) successfully constrained interception estimates using fPAR, providing valuable insights for EO integration.

Potential Evapotranspiration

GLEAM approach: Employs the Penman equation for potential ET estimation.

GEOframe compatibility: This methodology is already available in GEOframe, enabling direct reproduction of GLEAM's approach. However, D'Amato et al. (2025) implement a more sophisticated Penman-Monteith formulation than GLEAM, allowing for comparative analyses.

Aerodynamic conductance: GLEAM uses Thom's equation, which differs from GEOframe's current formulation but could be easily implemented. Both approaches require roughness length and zero displacement height parameters that can be derived from EO vegetation retrievals.

Soil Moisture Integration

GLEAM4 advancement: Incorporates data assimilation using European Space Agency (ESA) Climate Change Initiative (CCI) surface soil moisture data through a Newtonian Nudging scheme. The method decomposes soil moisture into anomalies and computes uncertainties using triple collocation (Miralles et al., 2025).

GEOframe current approach: Relies solely on root zone reservoirs for ET sources.

Enhancement opportunities:

• Adding ET sources from groundwater reservoirs through minor modifications to GEOframe's groundwater component
• Implementing GLEAM4's multi-layer running water balance approach, which considers constant root depth per land cover fraction

Physical realism considerations: While GLEAM4 moved from reservoir models (similar to GEOframe) to multi-layer approaches, GEOframe could implement GEOSPACE (D'Amato et al., 2025) to achieve superior physical realism compared to GLEAM4. However, the reliability of satellite-derived soil moisture estimates requires careful validation.

Stress Function Formulations

GEOframe current approach: GEOET (GEOframe's transpiration component) employs empirical schemes following Jarvis or Ball-Berry-Leuning (BBL) parameterizations.

GLEAM4 innovation: Introduces an innovative deep neural network approach replacing traditional semi-empirical stress computations. As described by the authors: "GLEAM4 replaces the original semi-empirical computation based on soil moisture and vegetation optical depth (VOD) with the deep neural network approach presented in Koppa et al., 2022."

Neural network advantages: The approach recognizes that actual-to-potential transpiration ratios are controlled by numerous environmental variables with non-linear interactions, including:

• Soil moisture and VOD
• Vapor pressure deficit (VPD)
• Incoming solar radiation (SWi)
• Air temperature (Ta)
• CO2 concentration
• Wind speed (u)
• Leaf Area Index (LAI)

Training methodology: The neural network learns universal transpiration stress functions using global eddy-covariance and sap flow data, with separate parameterizations for tall and short vegetation.

Implementation potential: Incorporating this neural network approach could represent a significant alternative for GEOframe, moving beyond traditional empirical formulations to data-driven, physically-informed methods.

Implementation Considerations

Full understanding and implementation of these methodological improvements requires careful examination of Miralles et al. (2025) and its supporting literature. The integration of these approaches could substantially enhance GEOframe's capabilities while maintaining compatibility with global EO datasets.

Conclusions

While GLEAM provides a comprehensive framework using multiple EO resources, significant opportunities exist for improving spatial resolution and integrating these datasets with process-based models like GEOframe. The main challenges involve resolution limitations and the need for validation of empirical methods against ground-truth data. The methodological advances in GLEAM4, particularly the neural network-based stress functions and improved data assimilation schemes, offer promising directions for enhancing GEOframe's predictive capabilities. Overall GLEAM should not be considered as a EO dataset but a modeling product. Describing it as an EO product makes it more objective that it is actually. Other global products on ET are available. Ecostress (Pierrat et al., 2025) is a recent notable example. A scrutiny similat to the one applied to GLEAM can be made with that platform too, but I let you as an exercise.

This post is part of the dissemination material of the Space It Up project funded by the Italian Space Agency, ASI, and the Ministry of University and Research, MUR, under contract n. 2024-5-E.0 - CUP n. I53D24000060005.

References

• Azimi, Shima, Christian Massari, Gaia Roati, Silvia Barbetta, and Riccardo Rigon. 2025. “A New Tool for Correcting the Spatial and Temporal Pattern of Global Precipitation Products across Mountainous Terrain: Precipitation and Hydrological Analysis.” Journal of Hydrology 660 (133530): 133530. https://doi.org/10.1016/j.jhydrol.2025.133530.
• Bottazzi, M., M. Bancheri, M. Mobilia, and G. Bertoldi. 2021. “Comparing Evapotranspiration Estimates from the Geoframe-Prospero Model with Penman–Monteith and Priestley-Taylor Approaches under Different Climate Conditions.” WATER. https://www.mdpi.com/2073-4441/13/9/1221.
• 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). https://doi.org/10.1002/eco.70009.
• 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.
• 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.
• Dijk, A. I. J. M. van, and L. A. Bruijnzeel. 2001. “Modelling Rainfall Interception by Vegetation of Variable Density Using an Adapted Analytical Model. Part 1. Model Description.” Journal of Hydrology 247 (3–4): 230–38. https://doi.org/10.1016/s0022-1694(01)00392-4.
• Koppa, Akash, Dominik Rains, Petra Hulsman, Rafael Poyatos, and Diego G. Miralles. 2022. “A Deep Learning-Based Hybrid Model of Global Terrestrial Evaporation.” Nature Communications 13 (1): 1912. https://doi.org/10.1038/s41467-022-29543-7.
• Martens, Brecht, Diego G. Miralles, Hans Lievens, Robin Van Der Schalie, Richard A. M. De Jeu, Diego Fernández-Prieto, Hylke E. Beck, Wouter A. Dorigo, and Niko E. C. Verhoest. 2017. “GLEAM v3: Satellite-Based Land Evaporation and Root-Zone Soil Moisture.” Geoscientific Model Development 10 (5): 1903–25. http://www.geosci-model-dev-discuss.net/gmd-2016-162/.
• Pierrat, Zoe Amie, Adam J. Purdy, Gregory Halverson, Joshua B. Fisher, Kanishka Mallick, Madeleine Pascolini-Campbell, Youngryel Ryu, et al. 2025. “Evaluation of ECOSTRESS Collection 2 Evapotranspiration Products: Strengths and Uncertainties for Evapotranspiration Modeling.” Water Resources Research 61 (6). https://doi.org/10.1029/2024wr039404.
• Miralles, Diego G., Olivier Bonte, Akash Koppa, Oscar M. Baez-Villanueva, Emma Tronquo, Feng Zhong, Hylke E. Beck, et al. 2025. “GLEAM4: Global Land Evaporation and Soil Moisture Dataset at 0.1 Resolution from 1980 to near Present.” Scientific Data 12 (1): 416. https://doi.org/10.1038/s41597-025-04610-y.
• Zhong, Feng, Shanhu Jiang, Albert I. J. M. van Dijk, Liliang Ren, Jaap Schellekens, and Diego G. Miralles. 2022. “Revisiting Large-Scale Interception Patterns Constrained by a Synthesis of Global Experimental Data.” https://doi.org/10.5194/hess-2022-155.

Integrating Earth Observation Data in Hydrological Modeling: Challenges and Opportunities

Some time ago, I wrote about the need for remote sensing experts to collaborate more closely with hydrologists to improve both hydrological forecasting and remote sensing applications. While the communities have largely continued working separately (and who am I to challenge such a fruitful paradigm?), my involvement in several projects with ASI (the Italian Space Agency) and ESA (the European Space Agency) has made this integration an unavoidable priority for me. This means I must become an Earth Observation (EO) scientist myself to cover the gap.  First question actually would be:, is the EO data resolution enough for hydrologic simulations ? (The answer here is usually no, it is usually not, but we have, as usual,  to survive with this and understand how the coarser resolution can be useful. Paraphrasing a well know motto: EO are usually wrong but can be useful).

Two Categories of Earth Observation Data

Earth Observation (EO) data can be broadly divided into two categories: quantities we routinely observe on the ground and those we typically do not (or could but usually don't) measure directly.

Ground-Measured Quantities

For simplicity, let's assume proximal data are correct, subject to verification and cross-checking with EO and modeled data. The first category includes rainfall, air temperature, point discharge measurements, surface water levels, groundwater storage (though less frequently measured), solar radiation, soil moisture (rarely measured), wind speed and evapotranspiration if we fully trust eddy covariance towers, which I don't take for granted.

EO-Derived Quantities

The second category encompasses snow cover, depth, and water content, along with soil moisture, vegetation water content, and evapotranspiration. It also includes various ancillary data such as albedo, leaf area index, land cover and land use classifications, surface temperature (which is distinct from the air temperature we typically measure), groundwater storage variations, precipitable water content, cloud cover, atmospheric liquid water content, and other quantities I'm not recalling at the moment. (Yes evapotranspiration is also on this side)

Challenges with Ground-Measured Quantities

For ground-measured quantities, comparing data sources is essential, acknowledging that ground measurements are generally more accurate but come with important caveats. There exists a fundamental scale mismatch where ground measurements are point observations, while EO measurements represent areal averages derived from radiation or gravity observations. Following Rodriguez-Iturbe and Mejia (1974), connecting point values to areal values requires careful assumptions about spatial scaling. Additionally, any systematic differences between ground and EO measurements must be identified and eliminated through proper bias correction procedures. How EO data are biased if compared to ground stations ?

However, ground data are spatially sparse. Obtaining geographic information requires interpolation, typically using methods like Kriging that preserve spatial correlation structure. Yet hydrological processes may be spatially nonlinear, raising the question: Do EO data, even if biased, better reproduce the spatial structure of hydrological variables?

If so, merging ground and EO data could yield superior spatial fields—an approach we pursued in Azimi et al. (2025). These quantities share another important characteristic: they can be produced by hydrological models and serve as inputs, validation data, or assimilation targets to improve model performance (which raises questions about how we evaluate "improvement").

Challenges with EO-Derived Quantities

The second category presents different challenges. These are primarily ancillary quantities that help estimate hydrological variables—leaf area index being the classic example for estimating transpiration, since plants without leaves don't transpire. Each quantity must find its proper role in hydrological models to be truly useful, requiring them to become model parameters.

The key question becomes: How can we effectively use these data in models?

While leaf area index integration seems straightforward, the data become useless if transpiration is estimated using temperature-only formulas. Similarly, how do we use land use data in models? What model characteristics connect to "land use" if it's not an explicit parameter?

Dal Molin et al. (2020) provide an interesting answer: geological setting relates to model structure within the framework of Hydrological Dynamical Systems (reservoir-based hydrological models). This expands possibilities but complicates the connections.

Another crucial question: Are these data actually necessary for the modeler's purpose?

Perhaps not, if the goal is simply discharge forecasting, since calibration procedures have proven effective at compensating for missing data and model's structure (as shown in the 4DHydro project outcomes). However, if the objective is reproducing realistic water budgets, these data may be essential, making assessment of all intermediate steps necessary, as shown in the 4DHydro Science Case 5. 

Conclusions

This blogpost does not aim to be comprehensive but just an aid to start the discussion. Two clear conclusions emerge from this analysis. First, EO ancillary data are required only if models have mechanisms to utilize them effectively. Second, they may not be necessary for all modeling purposes, particularly when the primary objective is discharge forecasting rather than comprehensive water budget reproduction.

Ultimately, new data should either increase the precision and accuracy of predictions or enhance our understanding of hydrological process mechanisms. The challenge lies in determining when and how to integrate these diverse data streams effectively.  The final goal is what stated in the last paragraph of this post, which I invite you to read again. 

Space It Up project funded by the Italian Space Agency, ASI, and the Ministry of University and Research, MUR, under contract n. 2024-5-E.0 - CUP n. I53D24000060005.

Cited References (an absolutely insufficient sample of the possible ones)

Azimi, Shima, Christian Massari, Gaia Roati, Silvia Barbetta, and Riccardo Rigon. 2025. “A New Tool for Correcting the Spatial and Temporal Pattern of Global Precipitation Products across Mountainous Terrain: Precipitation and Hydrological Analysis.” Journal of Hydrology 660 (133530): 133530. https://doi.org/10.1016/j.jhydrol.2025.133530.

Molin, Marco Dal, Mario Schirmer, Massimiliano Zappa, and Fabrizio Fenicia. 2020. “Understanding Dominant Controls on Streamflow Spatial Variability to Set up a Semi-Distributed Hydrological Model: The Case Study of the Thur Catchment.” Hydrology and Earth System Sciences 24 (3): 1319–45. https://doi.org/10.5194/hess-24-1319-2020.

Rodriguez‐Iturbe, I., and J. M. Mejía. 1974. “On the Transformation of Point Rainfall to Areal Rainfall.” Water Resources Research. https://doi.org/10.1029/WR010i004p00729.

Methodology and tools for analyzing the hydrology of catchments: four papers and a set of slides and videos.

Recently I recommended 5 papers of mine, which I consider  representative of my recent work. However, they are on the side of the theory/numerics/informatics work. Not less important are those that could be erroneously classified as applications. The four papers presented here, in fact, represent more than a straightforward run of models to individual catchments. They deploy a comprehensive methodology that integrates traditional surface water systems with new features and methods. Their approach combines mixed-resolution spatial discretization through strategic Hydrological Response Unit (HRU) refinement with accurate pre-analysis of the input multi-source validation using neutron probes (as representative of local field measurements), satellite data, and conventional discharge observations.

The modular GEOframe implementation provides flexible model configuration while preserving physical consistency and enabling validation of individual modeling components. A key finding across these papers is that careful analysis of input data can guide model organization and improve  predictions. Each paper targets complete water budget estimation, identifying inconsistencies and providing more robust assessments of catchment hydrology than traditional modeling approaches than the traditional simulation based on discharge alone.

These studies introduce  analytical tools that should become standard practice for catchment hydrology modelers and gently use Earth Observations in their specific contexts. The collective work establishes a framework where data-driven model organization, multi-source validation, and comprehensive water budget analysis modelling try to converge to advance our understanding of hydrological processes at the catchment scale.  Part of the lesson learned from these papers has been also summarized in the set of "Seven Steps in Modeling a catchment", a series of slides and videos that can be considered complementary to reading the papers.  

Much more can be done using the flexibility of the GEOframe system which remains undisclosed.

References

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. https://doi.org/10.5194/hess-21-3145-2017.

Andreis, D; Formetta, G.;Bancheri, M. and Rigon R., Multiple Resolution Analysis of an Alpine Basin. submitted to Water Resources Research, 2025. Preprint

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. https://doi.org/10.1016/j.advwatres.2017.03.010.

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. https://doi.org/10.5194/hess-27-4485-2023.

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. A video on these slides can be found here. 

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.