PROMISE Project: A PROcess-based MountaIn permafrost Sensitivity indEx for the Euregio

The recent Blatten event (2025) and the cascade of slope failures of the last few summers in the Alps have made a question unavoidable for our community: where will the next cryospheric mass movement occur, and how likely is it at a regional scale? Comprehensive monitoring of the entire Alpine arc is, and will remain, infeasible. What we need are tools that focus attention — that tell hazard specialists, infrastructure managers and policy makers where to look.

PROMISE — PROcess-based MountaIn permafrost Sensitivity indEx — is our proposal to build one such tool for the Euregio Tyrol–South Tyrol–Trentino, led by Jan Beutel (UIBK), Andrea Andreoli (UNIBZ) and myself (UNITN), with Dominik Amschwand (UIBK) coordinating the scientific deliverables and John Mohd Wani (UNITN) leading the modelling effort. Stephan Gruber (Carleton) and colleagues from the Chinese Academy of Sciences accompany us as international partners.

Photo by B Edmaier: https://www.facebook.com/B.Edmaier/posts/thawing-permafrost-due-to-global-warming-can-trigger-huge-landslides-like-yester/835248057961452/

The idea in one paragraph

Permafrost in mountains is not a uniform sheet of frozen ground that retreats upward as it warms. It is a mosaic — rock walls, talus cones, rock glaciers, ice-cored moraines, scree slopes — and each of these landforms transmits atmospheric warming to the deeper subsurface very differently. Some are buffers (an ice-rich rock glacier with a thick coarse-blocky active layer can stay cold for decades after the climate signal arrives); others are amplifiers (a steep, snow-poor rock wall couples almost directly to the air). PROMISE will produce, for the first time at regional scale in the European Alps, a thermal sensitivity index (thSI) that classifies the Euregio terrain along this buffer–amplifier axis, in the present and into the near future.

The thSI is not a permafrost distribution map. Distribution maps answer: where is permafrost likely to be present? The thSI answers a different and, today, more pressing question: where is the ground thermal regime most vulnerable to ongoing and future change?

Why now, and why this approach

There are precedents — but none for the Alps. Smith & Burgess (2004) built a semi-quantitative sensitivity index for the Canadian Arctic using the buffer-layer model of Luthin & Guymon. The Qinghai–Tibet community has produced beautiful regional assessments (Du et al. 2024 mapped the 1982–2020 trend in soil thermal conductivity, revealing a self-reinforcing degradation: as ground warms toward 0 °C, wetting raises STC, which raises heat flux, which accelerates thaw). But the QTP is a low-relief plateau with fine-grained soils. The Euregio is rugged terrain dominated by coarse-blocky debris, fractured bedrock and snow-driven microclimates. We need a landform-resolved approach.

Two findings from the recent literature anchor our framing:

1. Preconditioning (Hauck & Hilbich 2024). A single hot-dry summer can permanently flip an ice-rich landform from buffered to sensitive: once meltwater drains, the latent-heat reservoir is gone and cannot be refilled. Climate sensitivity is not a static material property.
2. Snow melt-out timing dominates over winter snow thickness for many high-elevation landforms. Once snow exceeds the ~0.6 m decoupling threshold, mid-winter variations matter little; what matters is the snow melt-out date (SMOD), after which the dark debris is exposed to the June sun (Amschwand et al. 2025b).

Both effects make a process-based, time-varying index essential. An empirical regression on today's climatology won't capture them.

The framework: thermal resistance of the snow–active-layer system

The thSI rests on a simple but physically grounded backbone. The heat transfer between atmosphere and permafrost is $Q = \Delta T / R_{tot}$, where the total thermal resistance is additive across the seasonal snow cover and the active layer:

$$ R_{tot} = R_{snow} + R_{AL} = \frac{h_{snow}}{k_{snow}} + \frac{h_{AL}}{\alpha_{eff} C_v} $$

A high (or rising) $R_{tot}$ means climate-robust terrain; a low (or falling) $R_{tot}$ means climate-sensitive terrain. The thSI is then a convex combination of $R_{tot}$ and its relative change with respect to a reference time. Continuous values are binned into four ordinal classes — low, moderate, high, very high sensitivity — following the spirit of Smith & Burgess (2004).

The trick is that none of the terms in $R_{tot}$ is a constant. $h_{snow}$ and $k_{snow}$ evolve through the season; $\alpha_{eff}$ in coarse blocks includes non-conductive transfer (subsurface airflow) and depends non-linearly on water/ice content. This is where physically based modelling enters.

The three pillars

PROMISE rests on three tightly coupled work packages.

WP1 — Ground truth (UNIBZ, Andrea Andreoli, Raul-David Șerban). Continuing the PERMAWAT line, the consortium extends the existing 32-site ground-surface-temperature network in Matsch and Schnals (with the iconic Lazaun rock glacier) by adding paired soil-moisture/temperature loggers, and instruments two new permanent permafrost boreholes at Hochebenkar / "Auf dem Grat" in the Rofental — the first permanent permafrost boreholes in Tyrol, filling a long-standing observational gap. From these data, the team derives the full battery of thermal indices (MAGST, FDD/TDD, frost number, zero-curtain, SOD/SDD, SCD, frost-cracking window, ALT, MAGT, dza), and uses the semi-empirical FROSTNUM model (Nelson & Outcalt 1987, updated by Cao et al. 2022) as a first-pass hot-spot screening.

WP2 — Numerical modelling (UNITN, with John Mohd Wani). The role of the Trento group is to convert atmospheric forcing into atmosphere–ground transfer functions using GEOtop 3.0, the process-based, three-dimensional land-surface model that solves the coupled mass and energy balance, the multi-layer snowpack, Richards-equation flow with freeze–thaw, and (where relevant) non-conductive subsurface heat transfer in coarse-blocky terrain (Zegers et al. 2025). Two complementary tracks:

• A point-scale 1D ensemble at the cluster centroids defined by the TopoSUB landscape clustering, designed to provide statistically independent samples across the predictor space and to feed both the per-terrain transfer functions and the ML upscaling.
• Distributed catchment simulations (one in Tyrol, one in South Tyrol, one in Trentino, at 50–100 m resolution) that serve as full-physics process diagnostics — quantifying how much lateral water and heat fluxes, slope-aspect contrasts and terrain heterogeneity matter for the transfer functions.

The 1D ensemble is calibrated against the WP1 thermal indices; the distributed runs use the WP3 snow-cover products as boundary conditions and provide the sanity check on what 1D necessarily misses.

WP3 — Upscaling (UIBK, with the new PhD student). Two preparatory products — terrain classification from sub-3-m DEMs and rock glacier inventories, and a pixel-wise SMOD trend analysis over the Euregio building on the 30-m Landsat product of Bayle et al. (2025) — feed into the final thSI map. We will explicitly test the hypothesis that SMOD trends dominate over $R_{snow}$ variability for most high-elevation landforms, by comparing alternative snow-cover descriptors in the GEOtop ensemble. The upscaling itself follows the TopoSUB hybrid statistical–process approach: cluster the landscape, simulate at centroids, map back to the full Euregio.

What's genuinely new

Three things, I think:

• Forward-looking, not descriptive. The thSI estimates rates of change, not present-day occurrence. It is meant to be read together with conventional permafrost distribution maps (Boeckli et al. 2012), not against them.
• Physics-grounded, not regression-fitted. Every grid cell of the final map is anchored, via the cluster centroid it belongs to, to a GEOtop simulation that explicitly resolves snow dynamics, freeze–thaw, and (where relevant) convective heat transfer in coarse blocks.
• A bridge between communities. Mountain permafrost research is, today, fragmented between detailed point-scale process studies (the Murtèl and Matterhorn traditions) and large-scale Arctic / QTP statistical assessments. PROMISE deliberately operates at the intermediate scale where the Alps actually live.

Caveats — what the thSI is not

This deserves emphasis. The thSI quantifies the thermal-conditioning component of permafrost vulnerability. It does not predict slope failures, rockfall release, or rock-glacier surges. Mechanical instability also depends on lithology, fracture geometry, glacial debuttressing, and meteorological triggers we do not model here. The thSI is meant to be added to — not to replace — the topographic, geological and geomorphological information already available to hazard assessors.

Wider context on this blog

For readers who want to follow the technical thread, the cryospheric work of the group is documented here in some detail:

• Summarizing my cryospheric work (made with good company) — the most recent overview, with all the relevant references.
• Permafrost is not ice — soil-freezing thermodynamics — slides and video on why frozen soil is a multiphase system and why proper models must carry three thermodynamic potentials.
• Freezing soil requires new algorithms — on the Newton–Casulli–Zanolli (NCZ) nested-Newton method that underpins our energy-conserving freezing-soil solver.
• Advances in permafrost modelling: application of the Nested Newton algorithm for solving the heat equation — the follow-up on Tubini, Gruber & Rigon (2021, The Cryosphere).
• New Insights in Permafrost modelling (EGU Wien 2017) — the earlier conceptual setup.
• Snow, Ice and Permafrost — the broader cryosphere framing with Alberto Bellin.
• Advanced Topics in Snow Hydrology — measurements, modelling, remote sensing — context on snow–permafrost interactions.
• All posts tagged Permafrost and Snow.

Timeline and acknowledgements

If funded (decision in March 2027), PROMISE will run May 2027 – April 2030. Field installations and the first GEOtop terrain-specific runs are scheduled for the first year; the snow-cover trend product and the first thSI metrics for the second; the final Euregio thSI map and the dissemination workshops for the third. Data and code will go out FAIR and open-source, through PANGAEA, the partners' geoportals, and the existing GEOtop/GEOframe GitHub repositories.

A warm thank you to Dominik Amschwand and Jan Beutel (UIBK), Andrea Andreoli and Raul-David Șerban (UNIBZ), John Mohd Wani (UNITN), and Stephan Gruber (Carleton), whose combined expertise on rock-glacier thermodynamics, wireless sensor networks, periglacial geomorphology, cryo-hydrological modelling and topographic downscaling makes this proposal possible.

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Riccardo Rigon, with the PROMISE consortium.

TACOS Project: Redefining How We Map and Model Catchments Response

A few minutes before midnight on May 31, we submitted TACOS — Transferability of soil water process understanding Across sCales for flOod and shallow landSlide prediction — to the PRIN 2026 call (Prot. 2026P2HL9S). Five Research Units, 36 months, €1.49 M total budget, €1.19 M requested from MUR.

The question

How much does knowing the soil actually help us predict floods in small ungauged catchments and rainfall-induced shallow landslides — and at which spatial scales does that knowledge pay off?

The question sounds simple but is curiously unresolved. Operational frameworks for ungauged basins lean on climate, topography, and geology; soil tends to be either smoothed away or absorbed into calibration. Yet soil is the first interface water meets in the critical zone — its depth, layering, pore structure, macropore connectivity, hydraulic properties, and antecedent moisture decide whether intense rainfall infiltrates or runs off, and whether a slope holds or fails.

The idea: a data degradation experiment

The methodological heart of TACOS is straightforward to state, and (we believe) unusually clean. Hold the model fixed and progressively coarsen the soil inputs — high-resolution DSM from full field profiles (Scenario A) → national-scale soil databases (Scenario B) → global coarse products like SoilGrids (Scenario C) — then test the predictions against independent flood events and landslide inventories. Pre-declared metrics with a priori tolerances identify the soil-information ceiling: the coarsest scenario for which predictions remain reliable.

The point is not to demonstrate that better soil information is better — that's almost trivially true — but to find where the curve flattens. Where it does, expensive high-resolution soil mapping is not justified by predictive gains. Where it doesn't, it is. This is a decision rule public authorities can actually use to prioritise soil-monitoring investments.

Four knowledge gaps, four work packages

The project addresses four interlocking gaps:

KG1 — Hydrology-oriented soil mapping (WP2, led by RU_UniNA, F. Terribile). Existing maps were built for agronomy; their relevance for hydrological response has rarely been evaluated systematically. We re-derive uncertainty-aware soil classifications explicitly oriented toward hydrological behaviour, combining Sentinel-1/Sentinel-2/PRISMA, machine learning (Random Forest, Gradient Boosting, spatiotemporal Transformers), and targeted field campaigns.

KG2 — The scaling problem and the breakdown of continuum assumptions (WP3, led by RU_CNR, M. Rossi). Richards' equation works — until it doesn't. We investigate, experimentally and theoretically, the conditions under which preferential flow, macropore activation, and non-equilibrium effects overtake equilibrium-based formulations. The framework links flow-regime classification to a-priori-evaluable thresholds (soil type, antecedent moisture, rainfall intensity) that determine which governing equation enters the Scale-2 model.

KG3 — The soil-information ceiling (WP4, led by RU_UniPD, M. Borga). The data degradation experiment itself, run inside both hydrological (GEOframe, GEOtop, WHETGEO) and landslide-triggering (GEOtop-LFS, TRIGRS, SlideforMAP, LANDPLANER) frameworks.

KG4 — Regionalisation lacking pedologically meaningful storage (WP5, led by RU_PoliTO, P. Claps). Index-flood regionalisation across ~100 small catchments (FOCA / FOCA2), runoff-coefficient analysis via SEASONEX and SIREN, leave-one-region-out cross-validation with and without soil-derived covariates. If soil information does not reduce quantile error, we say so.

The pilot sites

We work across three nested scales:

• Scale 1 (pore → pedon → hillslope): laboratory infiltration experiments, X-ray microtomography (SkyScan 1273, 3.5 μm/voxel), tracer transport tests, and seasonal/interannual in-situ parameter monitoring.
• Scale 2 (hillslope → small basin): three pilot catchments spanning a useful range — Ressi (0.02 km², Italian pre-Alps; the long-term ecohydrological catchment of the Padova group), Sangone at Trana (145 km², mixed forest–agricultural), Cordevole at La Vizza (7 km², high-elevation Dolomitic). The Collazzone pilot area (Umbria, 90 km²) anchors the landslide work; Langhe (NW Italy, 600 km²) provides the statistical-benchmarking testbed via the 1994 widespread event.
• Scale 3 (regional → territorial): ~100 small catchments nationwide.

The team

The consortium pulls together complementary competences:

• RU_UniTN — R. Rigon, G. Formetta. Coordination, process-based modelling (GEOframe/GEOtop), hydrological connectivity, kinetic theory of unsaturated flow.
• RU_PoliTO — P. Claps (substitute PI), S. Tamea, P. Mazzoglio. Regional hydrology, flood frequency analysis, the FOCA and I²-RED national databases, regionalisation methodology.
• RU_UniNA — F. Terribile, G. Langella, N. Mzid. Pedology, Digital Soil Mapping, EO covariates, LANDSUPPORT legacy.
• RU_UniPD — M. Borga. Mountain basin response, debris flows, hillslope-to-channel transfer indices, geo-hydrological modelling.
• RU_CNR (IRPI / ISAFOM) — M. Rossi, M. Bancheri, R. De Mascellis, S. L. Gariano. Physical infiltration experiments, X-ray CT, shallow-landslide thresholds, preferential flow.

The five RUs commit 38.6 person-months of permanent-staff effort plus 11 new temporary contracts (~228 PM total).

What's next

If funded, TACOS would start in 2027. Either way, the proposal is now part of how I think about soil hydrology: not as a parameter to calibrate, but as an empirically measurable structural control whose value for prediction is a question we can settle by experiment rather than assertion.

The intellectual threads reach back through several conversations on this blog — DARTHs and participatory digital twins; the kinetic theory of unsaturated flow that replaces Richards' equation with a pore-occupancy distribution; the percolation-based reading of field capacity and macropore connectivity; the GEOframe ecosystem. TACOS is where these strands meet operational prediction in ungauged basins, with shallow landslides as the natural companion problem — same soil–water dynamics, different observable.

Thanks to the four co-PIs and their teams for the intense final weeks, and to the RETURN PNRR and AdBPo communities for the questions that made this proposal, in a real sense, write itself.

When the panel speaks: reading the STRADIVARI evaluation

 A follow-up to "A double failure is a giant failure"

The ERC Step-1 evaluation for STRADIVARI has arrived. I promised in November that when it came I would read it carefully and share what I learned. The verdict: score B, ranking range 75–84%, where the top 37% advanced. So the project sits in the lower-middle of PE10 ADG 2025 — not borderline, not retained.

Let me work through what the four reviewers and the panel actually said, because some of it is fair, some of it is unfair, and one piece of it deserves a longer comment about how reviewing is changing in the age of AI suspicion.

The convergent verdict: "incremental"

The panel summary, and three of the four reviewers, converge on a single word: incremental. Reviewer 1 puts it most plainly — the system "falls more or less in the same category" as existing land-surface schemes and is "essentially built by assembling existing components." The panel adopted this reading almost verbatim: "Coupled atmosphere–land models of the suggested type already exist, and the panel was not convinced how the project would go beyond these existing approaches."

I should take this seriously, and I do. But I also want to say honestly what I think happened.

STRADIVARI was framed around what I called a "luthier" approach: building instruments that enable virtuoso scientific work, rather than promising the breakthrough finding myself. The proposal says it explicitly in Part B2: "The project provides the instruments; the community provides the scientific virtuosity."

This is what I believe. It is also, I now see, almost designed to be scored "incremental" by an ERC ADG panel. ADG rewards a PI who claims they will deliver the breakthrough. By framing my project as infrastructure that enables others to make breakthroughs, I handed the panel the exact line they used. They read my honest description of the project's character back to me as a weakness.

I do not regret the framing. I regret choosing the wrong instrument for it. The "luthier" vision is real, the GEOframe/WHETGEO/GEOSPACE work is real, and the integration questions are real. But ADG is not where that proposal belongs. That is a strategic lesson, not a scientific one.

What was actually in the proposal that nobody saw

The proposal contained several specific theoretical claims that, taken individually, are not incremental. The resilience-vs-optimization framing of plant hydraulics (D'Amato & Rigon 2025), the dynamic-SWRC-under-biota proposal, the deconstruction of the resistance framework so that ABL turbulence is resolved rather than parameterized and conductance is left as a purely physiological quantity — none of these are "assembling existing components." They are theoretical positions. But they appear in the proposal as sub-bullets inside a framework-integration narrative, and Reviewer 1, scanning for novelty, never reached them. Reviewer 3, who engaged scientifically, did not flag them either — which means they were not loud enough.

This is on me. I knew this, and I made the choice to lead with the integrating framework. It was the wrong choice for this audience. Everybody overlooked the citations of Diego Miralles et al. (2025): "Current ESS Models fail to capture critical feedbacks between soil evolution, plant hydraulics, and atmospheric processes required for understanding coupled hydrological and ecosystem functioning because Earth's system compartments are often treated as silos or heavily parameterized in crucial aspects of their dynamics."

The four-pillar problem

R2, R3, and R4 each separately worry about how the four pillars (Soil/Biota, Plant Hydraulics, Carbon, ABL) actually integrate. R2 says the proposal "does not convincingly demonstrate how the different parts will be combined." R4 says the methodology is "overly conceptual, with limited discussion of specific validation metrics, error propagation, or computational performance."

This is a real critique. The three-tier validation and minimum-viable-deliverables structure in B2 is there, but it arrives late and it does not pin the whole project to a single experiment that, if it works, validates the integration. ADG proposals win when there is a falsifiable claim at the centre. STRADIVARI has many — too many to land as one.

The Giono problem, and credit to existing literature

R3 makes a small but accurate point: I opened with Giono's L'homme qui plantait des arbres and never paid the framing off. The tree-planter never returns to the proposal. R3 also flags limited engagement with the existing forest-hydrology literature, which is fair: I cited what I needed for the argument, not what I owed to the field. Both points are correctable in any future writing.

And then: the Beven attribution

This is the part that has stayed with me longest. R3 writes:

"I also have to note one surprising aspect: on page 3 (bottom), the formulation 'parameters as garbage collectors' is used with reference to a paper by Keith Beven. Interestingly, this term can not be found in that publication (or any other publication of Beven), but appears as a (made-up) quote when checking with ChatGPT."

Let me be direct. The "garbage collectors" formulation was a shortcut of mine — a paraphrase that condensed something I take to be implicit in Beven (2006) and the equifinality literature, attributed informally with a (sensu Beven, 2006). It was not a quotation, and I did not present it as one. It was a writing shortcut, and a sloppy one, because attaching anyone's name to a paraphrase in an ADG proposal asks for a higher bar of fidelity than that.

I take the correction. Beven did not write those words, I should not have invoked him for them, and a future version of this argument will either find the exact passage or carry the claim in my own voice without his name attached.

But I want to say something about the second half of R3's remark, because it is no longer about my proposal — it is about how reviewing is changing.

R3 verified the phrase by querying ChatGPT and found it appears there as a "made-up quote." That is offered, in the review, as evidence of fabrication. It is presented in a tone that suggests the proposal itself may have been generated, or at least drafted unchecked, by an AI. This is not stated, but the implication is in the air, and the panel has now seen it.

Here is what I want to register. The search for hallucinations is beginning to exceed the people doing it. A reviewer who finds a phrase that does not appear in the cited source has, in 2025, two possible explanations: the author paraphrased badly, or an AI made it up. The second hypothesis is now reached so quickly that it crowds out the first. In my case the first was correct. I made the shortcut myself — the dumb old-fashioned way, sitting at a keyboard, trying to compress two paragraphs of Beven into seven words. That this looks identical, from the outside, to an AI hallucination is not a reason to stop writing carefully. It is a reason that every attribution must now survive the test of being searchable, verifiable, and grounded — because the cost of an unverifiable phrase is no longer "you paraphrased loosely" but "you may not have read the source." That is a real shift in what scientific writing has to do, and we should name it.

A second point worth making: a proposal that also foregrounds AI integration (the SML / OMS4 component) creates extra surface for this suspicion. The proposal is, in some sense, a candidate hypothesis for its own AI-suspicion test. I had not seen that read coming, and I should have.

What the panel said about me, the PI

All four reviewers were generous about the track record. R4 was particularly clear: "highly accomplished and internationally recognised," with the GEOtop/GEOframe/OMS lineage giving "strong credibility." R3 mentioned the AboutHydrology mailing list (almost 7000 subscribers, for those keeping count). R1 and R2 both said I had the necessary qualifications.

I mention this not to console myself but because it locates the problem precisely. The PI was not the problem. The project, as written, was. That is the more useful diagnosis, even if it is the harder one.

What I take from this

A few things, in plain form:

The "luthier" framing is honest, but ADG is the wrong instrument for it. Either Synergy, or a single-PI proposal built around one falsifiable theoretical claim with the infrastructure as means, would fit better.

The deepest scientific moves in STRADIVARI need to be the centre of any future proposal, not the load-bearing sub-bullets of an integration narrative.

The Beven shortcut is fixed for the future. Every named attribution gets verified or removed. Not because reviewers might think it was an AI, but because they are now correct to check, and the burden of verification has shifted onto authors in a way that did not exist five years ago.

The questions STRADIVARI raised — about dynamic feedbacks the current LSM/ESM generation parameterizes away, about whether minimum-energy-dissipation principles extend to the coupled vegetation-soil-atmosphere system, about whether plant strategies are optimal or resilient — are unresolved. The panel did not say otherwise. They said I had not convinced them I would resolve them inside 60 months with this team and this instrument. That is a different claim, and it does not retire the questions.

The proposals stay on OSF for anyone who wants to read what worked, what did not, and what the panel said about it. As the November post put it, a double failure is a giant failure. But it is the kind of failure that produces a written record, and a written record is more useful than a private wound.

Onward.

Musical Coda

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

I am giving this talk at the EGU General Assembly 2026 in Vienna last week, in the Hydrological Sciences division. The argument, in a single sentence: Richards' equation is not wrong, but it is the equilibrium limit of a deeper kinetic theory — in the same sense that the Navier–Stokes equations are the hydrodynamic limit of the Boltzmann equation for a gas. Mario Putti twenty years ago once asked me, "if not Richards, what else?"; this is my attempt at an answer that arrives after year dedicated to properly solve Richards equation, before with GEOtop and later with WHETGEO. 

The core object is a filling distribution g(r, x, t) : ℝ⁺ → [0, 1] that gives the volume fraction of pores of radius r that are water-filled at position x and time t. Theta is recovered as θ[g] = φ ∫₀^∞ g(r) f(r) dr. Hysteresis becomes the non-commutativity [W, D] ≠ 0 of the wetting and drying operators — geometry, not memory. Richards' equation is recovered as the small Damköhler limit Da → 0, with K(ψ) emerging as a derived transport coefficient built from the connectivity kernel C(r, r') rather than being postulated.

Materials

• Slides (PDF)  the deck I'll use in the presentation.
• Storyboard (DOCX)  the slide-by-slide reading guide, in five columns: spoken text, visual content, speaker notes, mounting comments. Useful if you want to present the same material yourself, or if you just want to follow along with what I actually said.
• Extended version of the slides — give me a few days — an annotated version with the full speaker text, more references, and the bits I had to cut for time.

Notebooks

These are the Jupyter notebooks I used to generate some of the figures in the slides, plus a few that produce supporting evidence in the supplementary material of the upcoming PRE papers. All run on top of OpenPNM 3.x and a small custom Y–L percolation code.

• Hysteresis_SWRC.ipynb — drainage and wetting branches in the (ψ, S_e) plane on a 3D pore network, with internal scanning curves. The figure on slide 9 of the talk comes from here. The notebook also documents an algorithmic artifact near the air-entry value (the missing air-trapping term during imbibition) — which is honest enough that I left it in.
• OpenPNM_Da_overshoot.ipynb — non-equilibrium overshoot in (θ, ⟨r⟩) and the universality crossover when the pore-size distribution becomes bimodal, governed by the Bhattacharyya overlap of the two modes.
• Percolation_K_threshold.ipynb — the percolation scaling K ∝ (θ − θ_c)^t with t ≈ 2, with finite-size scaling on three lattice sizes.
• subsection_pnm_mapping.tex — a short LaTeX subsection on how a two-tier pore-network maps onto the kinetic theory through a bimodal f(r) and a block-structured C(r, r'). Background reading for the OpenPNM notebooks.

Please find them zipped at this link.

Two upcoming papers

The full theoretical development is in two manuscripts, going to arXiv soon and submitted thereafter to Physical Review E --- give me a couple of weeks after EGU26:

1. The Statistical Physics of Unsaturated Soil Water: kinetic theory and non-commutative pore-water dynamics — the long paper. Builds the kinetic equation from the network thermodynamics, identifies the Onsager–Rayleigh gradient-flow structure, and proves that hysteresis is a geometric property of the configuration bundle (not a memory effect).
2. Richards' equation as a hydrodynamic limit: Chapman–Enskog derivation from the kinetic equation for unsaturated soil water — the short companion. Walks through the Chapman–Enskog expansion that recovers Richards' equation in the Da → 0 limit, with K(ψ) derived from the connectivity kernel.

Where this connects

The framework absorbs and extends a number of existing approaches that have been circling the same physics from different angles:

• Mixed-form Richards as the Da → 0 limit, with K(ψ) derived rather than postulated.
• Hassanizadeh–Gray as a thermodynamically consistent extension — pore-class-resolved here.
• Phase-field methods (Cahn–Hilliard) as gradient flow on a free energy — with explicit pore-network connectivity through C(r, r').
• Lucas–Washburn and its fractal variants as the single-capillary kinetic building block of C(r, r').
• Percolation-based hillslope frameworks with Damköhler and Péclet, where macropore activation is the Da > 1 transition.
• Compressible statistical soil mechanics (Einav–Liu 2023) — same occupancy dynamics governs the (ψ, σ') coupling.
• Freezing soil thermodynamics (Rempel et al. 2023, and our own work with Wani and D'Amato) — same kinetic framework with capillary pressure replaced by freezing-point depression.

This kinetic theory is not a parallel universe to Richards. It absorbs the existing physics, and it opens new measurements — directly observing g(r) is the obvious next experimental challenge

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.