This study starts from a pore scale view of flow in soil and aggregate it at the representative elementary volume, (REV), scale according to statistical assumptions, to obtain

new forms of the Richards equation. Flows are assumed to happen under normal and/or freezing conditions and under evapotranspiration demand. Transitions from unsaturated to saturated conditions will be properly accounted in all types of flow. The theoretical work at the basis of this proposal is contained in Dall’Amico et al. 2011 and

Tubini, 2017. At the beginning the system will be modeled by coupling the water budget equation and the energy budget equation, neglecting vapor mass budget, as usually done. The candidate should take care of integrating the equations with appropriate and sound numerical methods that guarantee mass and energy conservation, following the footsteps of the work by Casulli and Zanolli (2010) and work for possible extensions.

There are various possible further development of this research. One is to couple the water and energy budget with surface waters simultaneously solved, another is to deal with water vapor explicitly. Others developments could come ongoing.

The informatics behind the code will follow (and, in case co-develops) the developments pursued by dott.

Serafin, Ph.D. work inside the Object Modelling System, version 3 or subsequent (OMS3, David et al., 2013), that will take care implicitly of execution of parallel processes and will provide various services to computation (e.g. Serafin, 2016).

All the code developed will be done in

Github (or similar platform), inside the GEOframe community and will be Open Source according to the GPL v3 license.

The candidate will take care of implementing, besides the code, the appropriate procedures for continuous integration of the evolving source code, and s/he will be also asked to maintain a regular rate of commits to the common open platform. Despite these conditions, and being free and open source, the code will be intellectual property by the coder. This will be guaranteed also by the components-based infrastructure offered by OMS3, which allows to better define the contributions of anyone. (See also:

For incoming students,

The tales of open source codes).

The implementation part will be followed, accompanied by testing activities, either for mathematical consistency, than for physical consistency with experiments and field measurements. These will be made especially by Dr.

Stephan Gruber (

GS) group at Carleton University, where the candidate will be asked to spend some periods od his/her doctorate. Participation to experimental activities will not be intended to be purely passive, the candidate will be asked to actively participate as much as feasible and reasonable to any part of the research.

The Ph.D. student is intended to produce, besides working and tested codes, also at least three papers in major journals (VQR Class A), of which, at least one as first Author. Duration of the doctoral studies could be three or four years.

This project can enter either the curriculum C (Environmental Engineering) or the curriculum A (Modelling and Simulation) of our doctoral school.

For information please refers to riccardo.rigon <at> unitn.it

**Essential References**
Casulli, V., & Zanolli (2010). A nested newton-type algorithm for finite volume methods solving Richards' equation in mixed form. SIAM J. SCI. Comput., 32(4), 2225–2273.

M. Dall’Amico, S. Endrizzi, S. Gruber, and R. Rigon,

An energy-conserving model of freezing variably-saturated soil, The Cryosphere, 5, 469-484, 2011, doi:10.5194/tc-5-469-2011.

David, O., Ascough, J. C., II, Lloyd, W., Green, T. R., Rojas, K. W., Leavesley, G. H., & Ahuja, L. R. (2012).

A software engineering perspective on environmental modeling framework design: The Object Modeling System. Environmental Modelling and Software, 39, 1–13.

http://doi.org/10.1016/j.envsoft.2012.03.006
Serafin, F., About graphs, DSL and replicable research, 2016,

http://abouthydrology.blogspot.co.at/2016/11/about-graphs-dsl-and-replicable.html
Tubini, N. (2017, March 31).

Theoretical Progress in freezing-thawing process studies. (R. Rigon, F. Serafin, & S. Gruber, Advisors.).