The Statistical physics of unsaturated soil water: kinetic theory and non commutative pore water dynamics

 Work in progress

Stomata close to maximize transpiration ?

This is the talk I am going  on EGU 2026 and I co-authored with Concetta D'Amato.  It talks about the complexity behind the plant reactions to various environmental factors and the interactions that control stomata openings. 

The slides of the talk can be found here.  The various figures were created within Jupyter Notebooks that are here with the helps of Claude. Please also consider to watch my other presentation on a new statistical theory on the dynamics of soil water in vadose zone, also presented at EGU 2026. This latter presentation is here. 

EGU WIEN 2026

Please you can find what we present and do at the EGU 2026 General Assembly in Wien. 

The high resolution pdf is here. 

Below one by one the contributions:

• Marianna Tavonatti & Al. (On Tuesday) Pico Presentation

GEOSPACE Validation Paper: Application and Testing in the "Spike II" Lysimeter Experiment

We have just submitted a new paper — A flexible open-source modular framework for ecohydrological modeling: Application and validation of GEOSPACE-1D — by Concetta D'Amato, Paolo Benettin, Andrea Rinaldo, and Riccardo Rigon. It is the natural companion and follow-up to the GEOSPACE framework paper published in Geoscientific Model Development earlier this year, which described the design principles and modular architecture of GEOSPACE. That paper introduced the framework; this one puts it to work.

The validation is built around the "Spike II" experiment, a carefully instrumented lysimeter study carried out in 2018 on the EPFL campus in Lausanne. Four soil columns — a willow tree (L2), two grass-covered lysimeters (L1 and L4), and a bare-soil system (L3) — were monitored over two months, providing high-quality weight-based evapotranspiration estimates alongside measurements of soil water content, pressure, and drainage. These data allow a thorough assessment of the model across contrasting vegetation types and soil configurations.

The core of the paper addresses three questions: Can GEOSPACE reproduce observed ecohydrological dynamics across such diverse conditions? What are the practical advantages of its modular structure? And does it enable novel analyses — the kind that open new scientific doors rather than merely close validation loops?

On performance: GEOSPACE reproduces soil water pressure dynamics, depth-resolved water content, bottom drainage, and evapotranspiration fluxes across all four lysimeters with R² values of 0.87, 0.81, 0.83, and 0.73 for L2, L1, L4, and L3 respectively. Mean residual biases are negligible throughout. The slightly lower performance over bare soil reflects a known structural limitation of the Penman–Monteith formulation for soil evaporation under conditions where thermal inertia matters — an honest diagnosis rather than a defect to be papered over.

On modularity: the willow lysimeter was simulated with three alternative evapotranspiration formulations — GEOET-Prospero-PM, GEOET-Priestley-Taylor, and GEOET-Penman-Monteith FAO — keeping the soil component (WHETGEO) and the partitioning solver (BrokerGEO) identical across all three runs. All formulations close the cumulative water balance (~600 mm over the experiment), but the Prospero-PM formulation captures sub-daily peak dynamics with roughly half the residual spread of the other two. The calibrated Priestley-Taylor α = 4.16 and FAO Kc = 3.9 — both well above standard values — are informative precisely because they expose structural limitations of simplified formulations when applied to a high-transpiration system dominated by stomatal control.

On novel capabilities: the model computes root water uptake (RWU) for every control volume at every time step, yielding a full depth–time distribution of uptake intensity. The willow shifts its water sourcing dynamically in response to moisture depletion and atmospheric demand, with the mean uptake depth varying over time in a way that closely mirrors the measured root density profile. This kind of depth-resolved diagnostic is directly relevant to isotope-based ecohydrology, where xylem water provides only a bulk integrated signal — GEOSPACE's spatial resolution of the RWU can help interpret what that bulk signal actually means.

The paper grew out of Concetta D'Amato's PhD work at the Center Agriculture Food Environment (C3A) at the University of Trento, supported by the WATZON COST Action and the PRIN 2017 WATZON project. Readers interested in the longer history of GEOSPACE and its components can find much of the background documented here on AboutHydrology: see the posts on GEOSPACE and WHETGEO, and in particular the earlier post on Concetta's PhD thesis and the exploration of the SPAC.

The source code is on GitHub at https://github.com/geoframecomponents/GEOSPACE-1D, with a frozen version on Zenodo. All simulation data are openly available. GEOSPACE continues to grow.

Waiting for the official preprint, you can download it here. Here instead, find the supplemental material. 

Three Decades of Snow Water Equivalent Dynamics in the Po River Basin, Italy: Trends and Implications

Seasonal snowpack is a key component of the mountain cryosphere, acting as a vital natural reservoir that regulates runoff downstream in snowfed basins.

 In mid- and low-elevation mountain regions such as the European Alps, snow processes, such as accumulation and ablation, are highly sensitive to climate change, having direct implications for hydrological forecasting and water availability. In this study, we present the analysis of a 30-year (1991–2021) long dataset of snow water equivalent (SWE) in the Po River District, Italy, which includes parts of the Alps and Apennines. The data is available at a 500 × 500 m2 spatial resolution and at a daily temporal scale (Dall’Amico et al., 2025). This data was generated using the “J-Snow” modeling framework, which integrates the physically based GEOtop model with in situ snow height observations and earth observation snow cover products such as MODIS. Our results show that the long-term (30 year) basin-wide mean annual SWE volume equals 3.34 Gm3. The elevation-wise statistical analysis of key snow volume and duration metrics shows that the most pronounced snow water equivalent losses occur below 2000 m a.s.l. Below this threshold, both snow volume metrics and duration metrics show a significant decrease, indicating decrease in snow water storage and earlier melt. Above this elevation, the snow volume metrics show increasing trend while as the duration metrics continue to show a shortened (decreasing trend) snow season except at the highest elevations (> 2500 m). The findings of this study highlight the changes to the mountain seasonal snow storage and the timing of snow disappearance across the Italian Alps. This combined effect highlights a fundamental shift in the hydrological regime of the Po River Basin, with significant implications for water availability and management under ongoing climate change. The data used in this paper are those freely available in Dall'Amico et al., 2025. 

References

Dall’Amico, Matteo, Stefano Tasin, Federico Di Paolo, Marco Brian, Paolo Leoni, Francesco Tornatore, Giuseppe Formetta, John Mohd Wani, Riccardo Rigon, and Gaia Roati. 2025. “30-Years (1991-2021) Snow Water Equivalent Dataset in the Po River District, Italy.” Scientific Data 12 (1): 374. https://doi.org/10.1038/s41597-025-04633-5.

Wani, John Mohd, Kelly E. Gleason, Matteo Dall’Amico, Federico Di Paolo, Stefano Tasin, Gaia Roati, Marco Brian, Francesco Tornatore, and Riccardo Rigon. 2025. “Three Decades of Snow Water Equivalent Dynamics in the Po River Basin, Italy: Trends and Implications.” EGUsphere. https://doi.org/10.5194/egusphere-2025-5520.

From Snow Depth to Streamflow: Reducing Snowfall Uncertainty in Alpine Headwaters with Sentinel-1 based snow depth retrievals

In mountainous regions, the sparse distribution of precipitation gauges at high elevations is a major source of uncertainty in snowfall estimation. This matters beyond the local scale: uncertainties originating in headwater areas propagate through hydrological modelling, affecting the estimation of all water balance components downstream. Yet establishing dense gauge networks in complex mountain terrain remains logistically and economically challenging — which makes it worthwhile to ask whether remote sensing can fill the gap.

This study assimilates Sentinel-1 C-band snow depth observations into the snow module of the GEOframe hydrological model, coupled with a snow-density scheme, to jointly update snow depth, snow water equivalent (SWE), and snowfall estimates. The method is applied to two key Alpine catchments: the Aosta River catchment and the headwaters of the Piemonte catchment in the upper Po River basin. Both are critical contributors of snowmelt-driven discharge to the Po Valley — sustaining its agricultural water supply — and both suffer from limited high-elevation gauge coverage.

Results show that assimilating satellite-derived snow depth systematically increases snowfall estimates across elevation gradients relative to the model's partitioned snowfall, and substantially improves simulated river discharge during the snowmelt season. Notably, similar improvements persist in years without active data assimilation, suggesting that the approach has a lasting positive influence on model state and performance.

This work¹ has been submitted to The Cryosphere and is currently under review.

References

Azimi, S., Girotto, M., Rigon, R., Roati, G., Barbetta, S., and Massari, C.: From Snow Depth to Streamflow: Reducing Snowfall Uncertainty in Alpine Headwaters with Sentinel-1 Based Snow Depth Retrievals, EGUsphere [preprint], https://doi.org/10.5194/egusphere-2026-793, 2026.

Girotto, Manuela, Giuseppe Formetta, Shima Azimi, Claire Bachand, Marianne Cowherd, Gabrielle De Lannoy, Hans Lievens, et al. 2024. “Identifying Snowfall Elevation Patterns by Assimilating Satellite-Based Snow Depth Retrievals.” The Science of the Total Environment 906 (167312): 167312. https://doi.org/10.1016/j.scitotenv.2023.167312.

Where do we stand

 Aristotle had it all wrong.

Dalton, Horton, Sherman and Leopold played the starting gong.

Eagleson, Rodriguez-Iturbe went for a grand theory, in which they believed.

Ignacio (Vujica teaches) dated with randomness.

It is (dis-)organized complexity, Jim Dooge said.

Richards, Richardson, Harlan and Freeze insisted on using PDEs.

Horton said the runoff is infiltration excess,

Dunne said that it is saturation excess,

Hewlett and Hibbert said that overland flow is not necessary.

Tracer research screwed it all up.

Darcy and Buckingham — it is all a matter of gradients, they thought.

Beven and Germann set up a mountain of doubts.

And many, I forgot, I do not know.

(Klemeš complains.)

Now we do not really know what we know,

except that we know more than before,

better data we have,

satellites see it all (but what you see, you do not believe).

Modelers give numbers without caring,

machine learning thinks it can do all without understanding —

and because we did not have it when we thought we did,

they probably sing the right song.

Musical coda