The Kinetic Theory in detail

Work in progress 

In Sion I could show only a few slides of each step. This post collects the whole series Statistical physics of soil water (version 2.5.1): the decks, and for each one the Real Book that writes out every step, the storyboard and the notebook that computes its figures. The series is built on the preprint arXiv:2607.09416 and two companion papers, one on the Chapman–Enskog reduction and one on water age.

The idea in a few lines. Richards' equation is usually postulated: mass conservation, the Darcy–Buckingham law, and two curves fitted to data. The series derives it, as the Navier–Stokes equations are derived from the kinetic theory of gases. The state of soil water is the occupancy g(r, x, t), the filled fraction of each class of pores. Water moves among pore classes inside a volume and between neighbouring volumes, which gives a kinetic equation with two currents. When redistribution among the pores is fast with respect to the forcing (small Damköhler number), a Chapman–Enskog expansion returns Richards' equation: the retention curve at order zero, the conductivity at order one. Where the Damköhler number is not small, Richards' equation fails, and that is where dual permeability, preferential flow and hysteresis come from.

Deck 0. The whole story

A talk built on three ideas: the state is a function, Richards' equation is a limit, the age of water is written in the pores. An appendix gives two slides for each deck.
→ Slides · Real Book · Storyboard · Notebook

Part I. The pieces: geometry, potential, state

Deck 1. The nature of hydraulic conductivity. K(θ) from a network of pores: Hagen–Poiseuille in each pore, connectivity between classes, a cutoff fixed by suction. Burdine and Mualem are two bounds of one network; K vanishes at percolation.
→ Slides · Real Book · Storyboard · Notebook

Deck 2. Micro potential and macro potential. Capillary, adsorptive, osmotic and gravitational terms; the potential between two pores and between places. Suction is the level of the largest filled pore, defined only at equilibrium.
→ Slides · Real Book · Storyboard · Notebook

Deck 3. The occupancy as the state. Many occupancies share one water content; this degeneracy is where history dependence comes from. How the occupancy could be measured.
→ Slides · Real Book · Storyboard · Notebook

Deck 3b. Equilibrium occupancies. Gravity, films, solutes and temperature, one at a time, and what each does to the equilibrium step and to a measured retention curve.
→ Slides · Real Book · Storyboard · Notebook

Part II. From the pore to Richards' equation

Deck 4. The kinetic continuum equation. The budget of one pore class in one volume, the exchange between volumes, the limit to a point: one equation, two currents.
→ Slides · Real Book · Storyboard · Notebook

Deck 5. Mass conservation and the forbidden operation. Integrating over pore sizes gives mass conservation, exact and empty; integrating first and then looking for a flux law in θ is the shortcut of the classical theory.
→ Slides · Real Book · Storyboard · Notebook

Deck 6. The right procedure. Two clocks and their ratio, the Damköhler number; the shape of the state is slaved and eliminated.
→ Slides · Real Book · Storyboard · Notebook

Deck 7. Free energy and the Rayleighian. A Fermi–Dirac occupancy minimises the free energy; the kinetic equation descends it.
→ Slides · Real Book · Storyboard · Notebook

Deck 8. The Chapman–Enskog development. The expansion term by term: Richards' equation as a limit, and the band of conditions where it does not hold.
→ Slides · Real Book · Storyboard · Notebook

Deck 9. The spectrum. The conductivity as a sum over relaxation modes; the gap closes at percolation; Burdine and Mualem return as trial functions.
→ Slides · Real Book · Storyboard · Notebook

Part III. Structure and memory

Deck 10. Soil structure and dual permeability. A bimodal pore population splits the spectrum into a fast and a slow band: dual permeability derived, with the exchange coefficient computed.
→ Slides · Real Book · Storyboard · Notebook

Deck 11. Hysteresis. Wetting and drying do not commute: hysteresis as a holonomy, a loop that does not close.
→ Slides · Real Book · Storyboard · Notebook

A first look at water age

Deck 12A. Volume and flux. Tracers see the pores weighted by volume, the water balance by flux: why tracers find preferential flow everywhere while water balances close with Richards' equation.
→ Slides · Real Book · Storyboard

The rest of the work on water age and travel times (StorAge Selection functions derived from the occupancy, the age contrast between storage and discharge, and the lectures Travel times, kinetic edition) is not yet mature, and will have a post of its own.

Related. The MOOC on the hydrology of soil and the Lausanne lectures for the classical theory; the Sion lectures for the short path through it.

© 2026 R. Rigon, CC BY 4.0 (cover paintings excluded). Notebooks need numpy, scipy and matplotlib.

Slides, Storyboards, RealBooks

For a while now, my lessons have come with three objects instead of one: the slides, a storyboard and a Real Book. Each does a different job, and this post explains which. The first complete set is the one for The Hydrology of Soil, Lausanne version, which I am using for the soil lesson at the University of Lausanne (UNIL). The same scheme is used for the series Statistical physics of soil water.

The slides

The slides are what you see in the classroom, and they carry the story: one idea per slide, a figure or an equation, a few words. On their own they are deliberately incomplete. A slide shows the result of a derivation, not the derivation; it names an assumption, but does not discuss it. The colours of the boxes follow a code that is the same in all my recent decks:

• blue for definitions and facts;
• orange for consequences, assumptions and caveats;
• green for what is new and for pointers forward;
• red for open problems and corrections.

The PDFs are on OSF. Editable versions, PowerPoint files with real text boxes and LaTeX equations that open in Keynote or PowerPoint, are available on request.

The storyboard

The storyboard is the script of the deck. It is a table with one row per slide and five columns:

• the slide number;
• the spoken text, a suggested narration;
• what is on the screen;
• the speaker notes;
• the mounting comments for whoever edits a recording: which build slides were merged, where a figure comes from, what was corrected.

Storyboards were born with the soil MOOC we produced for the EU project EDVANCE, where every episode had to be recorded and edited. I kept them because they answer the question a student asks when looking at a slide alone: what was he saying here? They are also the place where the changes between versions of a deck are listed. Each storyboard now ends with a bibliography in three parts: the sections of Freeze and Cherry's Groundwater (1979, openly available) to read with that deck, the works cited on the slides, and further reading.

The Real Book

The name comes from jazz. The Real Book is the collection of lead sheets that musicians actually play from: the melody and the chords, written out, no frills. My Real Books are the same for a lesson: every step, written out. Where a slide shows a result, the Real Book derives it. It also does the following:

• keeps track of units, the most frequent source of error in this subject;
• gives orders of magnitude;
• states which hypotheses are being used, and where they fail;
• lists the corrections to earlier versions of the slides (every deck has had its share of sign errors and missing factors).

The text uses the same colour code as the slides: Mathematics, Physics, Result and Correction boxes, plus Numbers boxes in the statistical-physics series. Each section starts by saying which slides it covers, and every Real Book opens with a table that maps each slide to the section where it is discussed. You can follow the lesson with the slides and open the Real Book only where a step is not obvious. Or you can read the Real Book from start to end, as a short textbook chapter.

How to use the three together

The three objects are meant to be used together:

• In class, the slides.
• To review a lesson, or to study it without having attended, the slides together with the storyboard.
• To understand where an equation comes from, or to check it, the Real Book.
• To go further, the bibliography at the end of the storyboard.

What they can serve

Beyond my own lessons, the three objects are meant to be reused.

• Students can study a topic without having attended. They can check a derivation step by step and find the one or two readings that matter. The exercises at the end of each Real Book, with answers, help prepare for an exam.
• Teachers can take a deck, or part of it, for their own course. They can cut it, reorder it or translate it, keeping the Real Book as the reference text behind the slides. The mapping from slides to sections makes it easy to see what is lost when slides are removed.
• Anyone recording a lesson or a MOOC has, in the storyboard, the script and the editing instructions ready.
• Researchers and reviewers have, in the Real Book, a place where every equation can be checked. Corrections are listed openly instead of being silently fixed.
• Translators and adapters work from the LaTeX and editable sources rather than retyping from a PDF. This also includes adapting the material to another audience, for instance a shorter lesson for practitioners or a longer one for a doctoral school.

Since the Real Books and storyboards are written in LaTeX, they are easy to keep under version control and to update together with the slides.

Everything is released under a Creative Commons Attribution 4.0 licence (CC BY 4.0), except the paintings on the covers, which are copyrighted by the original authors and used according a FAIR use agreement. The materials are a work in progress, and will be improved after the lesson. If you find an error, a missing step or a better reference, please tell me: that is exactly what the Correction boxes are for.

Soil Kinetic Theory - Sion EPFL Lecture

Work in Progress. Links are still missing. Today I am in Sion, at the Laboratory of Catchment Hydrology and Geomorphology (CHANGE) of EPFL, to talk about soil water. The talk goes from the classical picture to the kinetic theory I have been working on in the last months: the state of soil water is a function, the filled fraction of each class of pores, and Richards' equation is the limit of a kinetic equation when water redistributes among the pores faster than it is forced.

There are seven decks. Each comes with its Real Book (every step written out), its storyboard (what I say on each slide) and the notebooks that make its figures.

1. The energy of water in soil. The chemical potential, how it moves water and how it transforms it, pressures and heads, and the retention curve from the pore-size distribution.
   → Slides · Real Book · Storyboard · Notebooks
2. The nature of K. The hydraulic conductivity as the conductance of the network of filled pores: bounds, Burdine and Mualem, percolation.
   → Slides · Real Book · Storyboard · Notebook
3. Soil water budget. From mass conservation to Richards' equation, and the two hypotheses it rests on: instant redistribution and accessibility of all pores.
   → Slides · Real Book · Storyboard · Notebook
4. The micro potential. The potential of water in a pore, and between two pores. Out of equilibrium there is no single ψ.
   → Slides · Real Book · Storyboard · Notebook
5. Occupancy. Many states share the same water content: the state is the function g(r), and its degeneracy is the source of hysteresis.
   → Slides · Real Book · Storyboard · Notebook
6. The kinetic equation. The budget of one pore class, the exchange between neighbouring volumes, one equation with two currents.
   → Slides · Real Book · Storyboard · Notebook
7. The rest of the story. Two slides for each of the decks that follow: Richards' equation as a limit, the two clocks, free energy, the spectrum, dual permeability, hysteresis, and a first look at the age of water.
   → Slides · Real Book · Storyboard · Notebooks

The first and the third deck come from my MOOC; the others from the series Statistical physics of soil water, built on the preprint arXiv:2607.09416 and two companion papers.

Related material. The MOOC on the hydrology of soil; the Lausanne lectures, on the classical theory; and the kinetic theory in detail, with all the decks of the series. Water age and travel times, only glimpsed here, will have a post of their own.

Slides, Real Books, storyboards and notebooks: © 2026 R. Rigon, CC BY 4.0 (cover paintings excluded). Thanks to the colleagues of CHANGE for the invitation.

Before the Kinetic Theory of water flow in porous media - What you need to know about soil - Lausanne (UNIL) seminar

I will give a long lesson on soil water at the University of Lausanne (UNIL) Hydrology lab. These are the slides I plan to use. They are the Lausanne version of The Hydrology of Soil, the course I prepared for the soil MOOC of the EU project EDVANCE, revised for this occasion. The whole course, included the parts which I have skipped here are available at the MOOC site. A last deck opens a window on the work I am doing now on the statistical physics of soil water and which is the topic of my talk at Sion EPFL Hydrology and Geomorphology lab. All the slides and the companion material are available as PDF files in the OSF repository. 

The story runs from what a soil is to the equation we use to describe water moving in it, Richards' equation, and then to the places where that equation stops working. Each deck below is followed by a few lines on what it contains.

Please consider all the material as a work in progress.  Though there should not be error in the hydrology, ll the material can be considered as a preprint to be subject to revision. Not sure, I will be able to tell everything, but parts can be skipped, and the whole amount of material is left to inspection by curious. 

Please find the slides at the links. You'll be maybe surprised to find two two other objects: a storyboard and a Real Book. This post explains what they are. 

0. What soil is

This is an introduction to what I assume to be known. It covers the five constituents that share the soil volume (solid particles, liquid water, ice, gas with its water vapour, and biota), soil profiles and horizons, and texture. That means sand, silt and clay, the particle-size distribution, and the texture triangle. It closes with the key definitions used in the rest of the lesson: masses, volumes and densities, volumetric water content, porosity, and relative and effective saturation.

Slides, Storyboard, Realbook, Notebooks I, II, III

1. The energy of water in soil

This is the longest deck, and the one on which everything else rests. It starts from the forms of energy that water in soil can have, and arrives at the chemical potential as the quantity that tells where water goes. From there it recovers the traditional pressures and heads (matric, osmotic and gravitational). It then treats capillarity: Young–Laplace, Jurin's law and the meaning of a negative pressure. Next comes the passage from single pores to the soil water retention curve, which is the pore-size distribution seen in suction coordinates. The deck ends with hydraulic hysteresis and the parametric forms of the retention curve (Brooks–Corey, van Genuchten, Kosugi, do not worry about, they are explained in the slides).

Slides, Storyboard, Realbook, Notebook

2. Darcy and Buckingham laws

The deck starts from Darcy's experiment, and asks whether Darcy's law can be derived from the Navier–Stokes equations (it can, under well-defined conditions). It then goes down to the pore with the Hagen–Poiseuille law, and back up to the Representative Elementary Volume. In unsaturated soil, Buckingham's law asks whether the flux can keep Darcy's form with a conductivity that depends on water content. Mualem's hypothesis of mutually accessible pores is what makes this work. The deck ends with the van Genuchten–Mualem conductivity and its siblings: Brooks–Corey–Mualem, Kosugi–Mualem and Peters–Kosugi–Mualem.

Slides, Storyboard, Realbook, Notebook

3. Soil water budget

This deck goes from a budget to a differential equation: conservation laws, the divergence operator, and the local form of the balance. Combining continuity, the Darcy–Buckingham law and the retention curve gives Richards' equation. Along the way it pays attention to which potential drives the flow. The excess of potential sits in the largest filled pores, and this is true only at equilibrium. The two foundational hypotheses are stated explicitly: internal redistribution is instantaneous, and all pores are mutually accessible. The deck closes with 1D simulations made with GEOframe (with Niccolò Tubini): sand, clay, ponding, and sand over clay.

Slides, Storyboard, Realbook, Notebook

4. Solving Richards' equation, and its limits

The deck starts with where the parameters come from: pedotransfer functions, from Rawls' regressions to today's tools (Rosetta, euptf and others). It then looks at what the soil column does not contain. Bedrock topography, pipes and macropores control much of the subsurface flow, and flow switches on above thresholds (Tromp-van Meerveld and coworkers; Koestel, Larsbo and Jarvis). It ends with the breakdowns of Richards' equation: hydrophobicity, a conductivity that grows with sample size, fingering and saturation overshoot. A few philosophical remarks on what a model leaves out close the deck.

Slides, Storyboard, Realbook, Notebook

5. The nature of hydraulic conductivity (statistical physics of soil water, Deck 1)

This last deck turns the question around: can K(θ) be derived from the pore space, instead of being postulated? It builds the conductivity from a network of pores: Hagen–Poiseuille in each pore, the connectivity between pore classes, and a cutoff fixed by suction. It then sums the network in parallel, in series and exactly (Kirchhoff's laws, effective medium). Burdine's and Mualem's formulas turn out to be two bounds of the same network. The conductivity vanishes at percolation, and water enters from the boundaries. The same question, one scale up, is the effective conductivity of stochastic hydrogeology. It is the first deck of a series built on the preprint arXiv:2607.09416, in which Richards' equation appears as a limit of a kinetic theory of pore water.

Slides, Storyboard, Realbook, Notebook

The slides of decks 0–4 have accompanying Real Book chapters where every step is written out, and the decks will be improved after the lesson. Comments and corrections are welcome. The paintings that open the decks are by Jay Stratton Noller and Mark Rothko. I thank Chiara Baldo and Lorenzo Duchi, who helped with the MOOC version, and the colleagues at UNIL for the invitation.

Daniele Andreis' PhD.

Under construction

 

Gaia Roati's Ph.D.

Under construction 

Daily Forcings Datasets (Rainfall and Temperature) for hydrological Purposes over the Po river district

If you want to run a hydrological model in the Po basin, or anywhere in northern Italy, the first question is which meteorological forcing to use. A few years ago the choice was short. Today there are at least a dozen gridded products, regional and European, built with different networks, methods and purposes. This post is a review of what is available, written from the point of view of someone who needs daily forcing for water budgets with GEOframe or a similar model.

A disclosure: with Hossein Salehi and colleagues I have a dataset of my own in this list (Salehi et al., preprint, currently in open discussion at ESSD). I have tried to judge it with the same yardstick as the others.

What a hydrologist needs from a forcing dataset

Not every good climatological product is a good forcing. For water budgets, these are the requirements I use:

Requirement	Why it matters
Daily time step, with the day aligned to discharge records (00–24)	Snow, soil moisture and routing run daily; misaligned days shift peaks
Precipitation and temperature from the same network and method	Rain–snow partition, melt and ET depend on both; mixing products mixes biases
Tmin and Tmax, or radiation	Needed by Hargreaves or Priestley–Taylor ET and by melt and frost thresholds
Resolution close to the model units, about 1 km in Alpine sub-basins	Aggregating is exact; disaggregating needs assumptions
Coverage of the whole hydrological district, Swiss and French headwaters included	Budgets must close over the basin, not over administrative borders
Uncertainty for each cell and day	So that forcing error can be carried into budgets and calibration
Station data and metadata	So that users can check, re-interpolate or bias-correct
Documented behaviour with elevation and undercatch	High-elevation input errors dominate Alpine budgets
Open licence, persistent identifier, standard format	Reuse, citation, reproducibility (the FAIR principles)
Updates after 2020	Operational water-balance and drought monitoring

No product meets all of them.

The datasets

Dataset	Variables	Period, step	Grid	Method
ARCIS precipitation (Pavan et al., 2019)	P	1961–present, daily (9-to-9 local day)	~5 km	Modified Shepard with topographic distance, on 1,048 homogenized series
ARCIS temperature (Pavan et al., 2026)	Tmin, Tmax	1991–present, daily, monthly updates	~5 km	Piecewise lapse rate, urban and water fraction, in 28 sub-areas; Shepard on residuals
IH-GAR (Manara et al., 2026)	P	1951–2023, daily and monthly	~800 m	Anomaly method: elevation-based normals, monthly anomalies, daily fractions
APGD (Isotta et al., 2014)	P	1971–2008; extended version to 2019	5 km	Anomaly method with PRISM-type normals; Alpine part only
Crespi et al. (2018)	P normals	1961–1990 climatology	~800 m	Local weighted regression on elevation
Crespi et al. (2021)	P, mean T	1980–2018, daily	250 m	Anomaly method; Trentino–South Tyrol only
Salehi et al. (preprint)	P, mean T	1991–2020, daily	1 km	Kriging with daily variograms; daily lapse rate for temperature
EMO-1 (Salamon et al., preprint)	P, Tmin, Tmax, T, wind, radiation, vapour pressure	1990–2024, daily and 6-hourly	~1.5 km	Angular distance weighting
E-OBS	P, T, Tmin, Tmax and more	1950–present, daily	~11 km	Ensemble interpolation
CERRA-Land	P and land variables	1984–present	5.5 km	Regional reanalysis
EEAR-Clim (Bongiovanni et al., 2025)	Station P, T, Tmin, Tmax	to 2020, daily	stations	Quality-controlled, homogenized series, about 9,000 stations
BIGBANG (ISPRA)	Water-balance outputs	1951–2024, monthly	1 km	National monthly water-balance model

A few notes on each family.

ARCIS is the work of the regional meteorological services of north-central Italy. Its strengths are care for the data (homogeneity tests, synchronization of 9-to-9 readings) and the fact that it is updated operationally; its temperature companion (Pavan et al., 2026) handles Po Valley inversions with sub-regional, two-slope lapse rates. Its limits for Alpine hydrology are the 5 km grid and the absence of an elevation model for precipitation: Manara et al. (2026) find ARCIS lower than other products above about 750 m.

IH-GAR (Manara et al., 2026) uses the densest network (7,417 stations in its calibration domain, about 2,000 active each year) and the anomaly method, so its normals capture the increase of precipitation with elevation where stations are missing. Its daily values are built from monthly anomalies and interpolated daily fractions; the paper validates normals and monthly anomalies, but I could not find a validation of the daily fields themselves. Temperature has to come from another product.

A caution that applies to all products built from normals. IH-GAR, APGD and Crespi et al. (2021) obtain daily values by scaling station anomalies with elevation-aware normals. A normal is the number of wet days times their intensity, so this scaling can turn a higher frequency of rain at altitude into heavier storms. Monthly totals stay correct; daily wet-day frequency and intensity at altitude are worth checking before using these products as daily forcing.

APGD (Isotta et al., 2014) remains the Alpine reference for daily precipitation and shows the sharpest valley gradients. It covers only the Alpine part of the basin and is not updated.

EMO (Thiemig et al., 2022, and EMO-1) is the most complete in variables, open and updated. It is worth knowing how it is built in the Alps: EMO-5 imports about 5,000 APGD grid points as virtual stations, and its direct Italian station input is small. In the Alpine part of the Po basin it largely re-grids APGD.

E-OBS and CERRA-Land are useful for large-scale consistency, but too coarse, or too model-dependent, for Alpine sub-basins.

Our dataset was designed as hydrological forcing: precipitation and temperature from the same network (1,583 precipitation and 1,555 temperature stations, from the Po River District Authority and EEAR-Clim), on a 1 km grid, over the whole district plus a 20 km buffer. The review it received was useful and sometimes hard. The precipitation field is smoother than ARCIS, IH-GAR and APGD in some Alpine valleys, Valtellina above all. The lapse rate is one per day for the whole domain, so it misses local inversions. The record stops in 2020, and ordinary kriging of daily totals spreads small amounts across the wet/dry boundary. In the revision we are testing, on the gauges and within single events, whether elevation acts on the number of wet days or on storm intensity, and we will build precipitation from occurrence and intensity separately. What it adds is the daily variograms, the daily lapse rates and the per-cell uncertainty, which we will release with the fields.

How many stations, in the same area?

Comparing station totals is misleading, because each product covers a different domain. What matters is how many stations support the field inside the area you model. For the Po River District with a 20 km buffer (about 90,000 km²):

Dataset	Stations in the district	Basis
Salehi et al., precipitation	472 (1991–2000), 954 (2001–2010), 1,108 (2011–2020) active per day	Exact
ARCIS precipitation	roughly 500–580	Estimate, scaled by area from about 1,000 series per year
ARCIS temperature	roughly 570 (1991) to 930 (after 2013)	Estimate, scaled by area from their Fig. 1a
IH-GAR	roughly 1,100–1,400 active per year	Estimate, from their station density
EMO	few direct Italian stations; APGD points in the Alps	Thiemig et al. (2022)

The estimates assume uniform station density and should be replaced by real counts. They still show a point that is easy to miss: station support changes a lot over time. Our network more than doubles after 2000, and any network that grows this much makes trends from the gridded series suspect unless the series are homogenized and the network is controlled, as ARCIS and IH-GAR do.

Fitness for water-budget modelling

Dataset	P and T, same network	Tmin/Tmax	≤ 1.5 km	Whole district	Per-cell uncertainty	P with elevation	Homogenized	After 2020
ARCIS P + T	same agencies, different methods	yes	no	Italian part	no	no	yes	yes
IH-GAR	P only	no	yes	yes	no	normals	yes	to 2023
APGD	P only	no	no	Alps only	ensemble version on request	normals	no	to 2019
EMO-1	yes	yes	yes	yes	yes (EMO-5)	limited	no	yes
E-OBS	yes	yes	no	yes	ensemble spread	no	no	yes
Salehi et al.	yes	mean T only	yes	yes	yes, kriging variance and cross-validation	tested and rejected	no	no

My reading, by use:

• Long-term climate and trends: ARCIS and IH-GAR, which are homogenized and designed for it.
• Precipitation totals in Alpine basins: IH-GAR, or APGD up to 2019; check ARCIS above 750 m.
• Operational monitoring: ARCIS precipitation and temperature, updated monthly.
• Daily forcing for a distributed model of a Po sub-basin: EMO-1 if you need many variables and recent years; our dataset if you want precipitation and temperature from one regional network with their uncertainty, with the caveats above; and in any case a check of the totals against IH-GAR at altitude.

Data availability and FAIR principles

Dataset	Identifier and access	Licence	Station data
ARCIS	arcis.it, no DOI	check the site	no
IH-GAR	UNIMI Dataverse, doi:10.13130/RD_UNIMI/CSYYAP	check the repository	no
APGD	MeteoSwiss, doi:10.18751/Climate/Griddata/APGD/1.0, registration	non-commercial use	no
Crespi et al. (2018)	ISAC-CNR	CC BY-NC-ND 4.0	no
Crespi et al. (2021)	PANGAEA, doi:10.1594/PANGAEA.924502	CC BY 4.0	partly
EMO-1	JRC Data Catalogue	CC BY 4.0	no
E-OBS, CERRA-Land	Copernicus Climate Data Store	open	partly (E-OBS)
EEAR-Clim	Zenodo, doi:10.5281/zenodo.10951609	CC BY 4.0	yes
Salehi et al.	Zenodo, doi:10.5281/zenodo.19207256	CC BY 4.0	no (sources: Po District Authority, EEAR-Clim)

The weakest point is common to all regional grids: none releases the input station series, because they belong to the regional services. EEAR-Clim is the exception and a real step forward. A second gap is code: among these products, only EMO and ours (GEOframe Krigings, GPL-3) point to open interpolation code.

What is still missing

• A daily product that brings in the elevation dependence of precipitation where it acts, on wet-day frequency, on intensity or both, with an explicit uncertainty for every day and cell.
• Validation of daily fields at the daily scale, including wet-day frequency and extremes, for products built from monthly components.
• Independent checks of precipitation at altitude, through water budgets closed on gauged basins with storage and evapotranspiration estimated independently. Snow undercatch cannot be seen by comparing gauges with gauges.
• Open station data. Without it, every dataset is a black box that can only be compared with other black boxes.

References

• Bongiovanni, G., et al. (2025). EEAR-Clim: a high-density observational dataset of daily precipitation and air temperature for the extended European Alpine region. Earth Syst. Sci. Data, 17, 1367–1391. doi:10.5194/essd-17-1367-2025
• Crespi, A., Brunetti, M., Lentini, G., Maugeri, M. (2018). 1961–1990 high-resolution monthly precipitation climatologies for Italy. Int. J. Climatol., 38, 878–895. doi:10.1002/joc.5217
• Crespi, A., Matiu, M., Bertoldi, G., Petitta, M., Zebisch, M. (2021). A high-resolution gridded dataset of daily temperature and precipitation records (1980–2018) for Trentino-South Tyrol. Earth Syst. Sci. Data, 13, 2801–2818. doi:10.5194/essd-13-2801-2021
• Isotta, F. A., et al. (2014). The climate of daily precipitation in the Alps. Int. J. Climatol., 34, 1657–1675. doi:10.1002/joc.3794
• Manara, V., et al. (2026). A new daily high-resolution gridded precipitation dataset for the Italian Greater Alpine Region (1951–2023). J. Hydrol.: Reg. Stud., 67, 103776. doi:10.1016/j.ejrh.2026.103776
• Pavan, V., et al. (2019). High resolution climate precipitation analysis for north-central Italy, 1961–2015. Clim. Dyn., 52, 3435–3453. doi:10.1007/s00382-018-4337-6
• Pavan, V., et al. (2026). A new operational dataset of gridded minimum and maximum temperature over north-central Italy 1991 to present. Climate Services, 43, 100689. doi:10.1016/j.cliser.2026.100689
• Salamon, P., et al. EMO-1: an improved version of the high-resolution multi-variable gridded meteorological dataset for Europe. Earth Syst. Sci. Data Discuss., essd-2025-723
• Salehi, H., et al. (2026). A 30-year 1-km daily precipitation and air temperature dataset for the Po River District (Italy). Earth Syst. Sci. Data Discuss. doi:10.5194/essd-2026-467
• Thiemig, V., et al. (2022). EMO-5: a high-resolution multi-variable gridded meteorological dataset for Europe. Earth Syst. Sci. Data, 14, 3249–3272. doi:10.5194/essd-14-3249-2022
• Copernicus Climate Data Store: E-OBS and CERRA-Land
• ISPRA, BIGBANG national water balance: workshop presentation, March 2026