My Past Research on Cryopheric Hydrology

In [J22] it was demonstrated that a single-layer snowpack model can be sufficiently accurate in describing the evolution of the water equivalent of the snow, as long as the incident radiation is calculated accurately taking care of shadows and the complexity of mountain topography.

Subsequently, the single-layer model was replaced with a multilayer model in order to forecast the evolution of density and of metamorphism of the snow as well as the percolation phenomena within the snowpack, during the thesis of Stefano Endrizzi. Among the various studies carried out, one validates the snow model satellite data derived from MODIS [A41].  Furthermore, the same model was used to study the hydrological evolution of glaciers in Trentino (Alpine) and South America (Equatorial) [A39, A47].  Eventually, the modeling of the cryosphere moved towards considering evolutive processes of permafrost [thesis of Matteo Dall'Amico, and J30], that is the layer of soil subject to temperatures below zero centigrades for more than two consecutive years.  All of these research projects, as well as allowing the aforementioned studies, are necessary to modeling the entire yearly hydrological cycle in mountain environments such as Trentino.

[J30], drawing from an accurate work of reanalysis of process thermodynamics, implements a robust method for the integration of the freezing-soil equation.  The numeric algorithm used is globally convergent Newtonian method that is appropriate for the equations under study.  [J36] is a geomorphological survey of rock glaciers in Trentino, to be subsequently modelled with GEOtop.

References in English


[ J22] - Zanotti, F., Endrizzi, S, Bertoldi, G. e R. Rigon, The GEOTOP snow module, Hydrol. Proc., 18, 3667-3679 (2004), DOI 10.1002/hyp.5794

[j30]- 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

[J36] - R. Seppi, A. Carton, M. Zumiani, M. Dall’Amico, G. Zampedri, R. Rigon, "Inventory, distribution and topographic features of rock glaciers in the southern region of the Eastern Italian Alps (Trentino)" in Geografia Fisica e Dinamica Quaternaria, v. 2012, n. 35(2) (In press)

[A41] Endrizzi S., Bertoldi G., Neteler M., and Rigon R., Snow Cover Patterns and Evolution at Basin Scale: GEOtop Model Simulations and Remote Sensing Observations, Proceedings of the 63th Eastern Snow Conference,


References in Italian

[A47] Noldin I., Endrizzi S., Rigon R., Dall’Amico M, Sistema di drenaggio di un ghiacciaio alpino, Neve e Valanghe, n. 69, 48-52, 2010

My Past Research on Physico-Statistical Modelling of the Water Cycle at Basin Scale

While GEOtop [J24, J25] is for process-based modelling of the mass and energy budgets at a small scale, in order to model larger catchments, which include abstraction works or hydraulic structures, it was decided to implement a new modelling system JGrass-NewAGE [J34].  This system sacrifices process details in favour of  efficient calculations.  It is made of components apt at returning statistical hydrological quantities, opportunely averaged in time and space.  One of the goals of this implementation effort was to create the basis for a physico-statistical hydrology in which the hydrological spatially distributed dynamics is reduced into low dimensional components, when necessary surrogating the internal heterogeneities with "suitable noise" and a probabilistic description.

Unlike other efforts of synthesis, JGrass-NewAge wants to keep the spatial description explicit, at various degrees of simplicity.  This has been made possible by opportune processing of distributed information which, in this way, has become part of the model itself.
From the point of view of the information technology used to implement the modelling  [J41, A44, A49, A50], the system is based on the OMS v 3 system, which allows the use of modern, object-oriented strategies for the structuring of the deployment of the software and, at the same time, furnishing not a model, but various, interchangeable, modeling solutions (MS) that can be adapted to the problems in hand and the practical demands of the problem being solved.
The modeling system, as well as the components to model the physical processes themselves, also includes various tools for the processing of input data (for example, Kriging tools), including all the tools of the Horton Machine [eb3] for the processing of digital terrain data, and the tools for the treatment and interpretation of the output data, for the calibration of model parameters, and (in perspective) for continuous data assimilation.
With this in mind, an effort that is currently being made is that of creating an opportune digital watershed scheme that can accommodate the needs of the various modeling conceptualizations and the identification of areas that are hydrologically "similar" that can be treated conjointly during the calculation of flows and storage. At the moment, model solutions use standard implementations.  [J34, J41, A50] contains the description of the rainfall-runoff part of the modelling system; [J43] is a verification of the radiation budgets components; [J44] is an example of simplified snow modelling.  As a standard, any components is verified by itself against the data relative to the process that it describes, using various automatic calibration procedures, and quantitative objective functions. [J34, J41] using the infrastructure show how increased geomorphological (and processes) information affects the quality of reproduction of the hydrologic response. [j44] explains the watershed partition, based on a generalisation of the Pfafstetter numbering scheme, that guide the functioning of the JGrass-NewAGE system.

References 

In English:

[J24] - Rigon R., Bertoldi G e T. M. Over, GEOtop: A distributed hydrological model with coupled water and energy budgets, Vol. 7, No. 3, pages 371-388

[J25] Bertoldi G. R. Rigon e T. M. Over, Impact of watershed geomorphic char- acteristics on the energy and water budgets, Vol. 7, No. 3, pages 389-394, 2006

[J34] - Formetta, G.; Mantilla, R.; Franceschi, S., Antonello A., Rigon R., The JGrass- NewAge system for forecasting and managing the hydrological budgets at the basin scale: models of flow generation and propagation/routing, Geoscientific Model Development Volume: 4 Issue: 4 Pages: 943-955, DOI: 10.5194/gmd-4- 943-201, 2011

[A49] Formetta G., Antonello A., Franceschi S., David O. and Rigon R., The informatics of the hydrological modelling system JGrass-NewAge, 2012 International Congress on Environmental Modelling and Software Managing Resources of a Limited Planet, Sixth Biennial Meeting, Leipzig, Germany R. Seppelt, A.A. Voinov, S. Lange, D. Bankamp (Eds.) http://www.iemss.org/society/index.php/iemss- 2012-proceedings, 2012

[j36] - Formetta G., Rigon R., Chavez J.L., David O., The short wave radiation model in JGrass-NewAge System, Geosci. Model Dev., 6, 915-928, 2013, www.geosci-model-dev.net/6/915/2013/
doi:10.5194/gmd-6-915-2013

[J39] - Formetta G., Antonello A., Franceschi S., David O., and Rigon R., Hydrological modelling with components: A GIS-based open-source framework, Environmental Modelling & Software, 5 (2014), 190-200

[j42] - Formetta G., David O., Kampf S., Rigon R., The Cache la Poudre river basin snow water equivalent modeling with NewAge-JGrass, accepted GMD, 2014

[j44] Formetta G. , Antonello A. , Franceschi S. , David O., Rigon R.,  Digital watershed representation within the NewAge-JGrass system. Boletin Geologico y Minero, 125 (3): 371-381, 2014. ISSN: 0366-0176

In Italian:

[A44] Antonello A., Franceschi S., Formetta G., Rigon R., L’infrastruttura NewAGE per la previsione e la gestione dei bilanci idrici a scala di bacino: I - La struttura informatica, in Atti XXXII Convegno di Idraulica e Costruzioni Idrauliche, Palermo, 14-17 Settembre 2010

[A45] Formetta G., Franceschi S., Antonello A., Cordano E., Mantilla R., Rigon R., Il sistema NewAGE per la previsione e la gestione dei bilanci idrici a scala di bacino. II - I modelli di generazione, aggregazione e propagazione del deflusso. in Atti XXXII Convegno di Idraulica e Costruzioni Idrauliche, Palermo, 14-17 Settembre 2010

[A50] Formetta G., Rigon R, Le nuove componenti modellistiche di JGrass-NewAGE, Atti del XXXIII Convegno di Idraulica e costruzioni Idrauliche, Brescia, 10-15 settembre 2012

My Past Research on Shallow Landslide and Mass Flow Triggering

The role of hydrology in triggering mass movements was initially confronted with an implementation of the theories of Montgomery and Dietrich [1994] (MD), and the case of instability caused by surface runoff [A21, A26, A27].  The study then continued with the analysis of transient phenomena, that is the instabilities caused by the propagation of pressure waves in the unsaturated medium  [A31, A32], according to the theory by Iverson [2000] (I), and integrating  the two, MD1994 and I2000, views even in the case of rainfall of varying intensity [A21, J23].
Then, the simplified approach  (important in as so much as it highlighted some qualitative aspects of infiltration in the hillslopes) was supplanted by the use of the GEOtop model for the continual simulation of hydrological variables [A38, J26], and transient effects, within a minimal set of simplifications.  The use of GEOtop has allowed for the separation of the hydrological part, effectively modeled by GEOtop, and the geotechnical part, contained in the GEOtop-FS model [J26].  Particularly, the latter of these was the subject of a probabilistic treatment that introduced uncertainties into the main geotechnical parameters  [J26].
The paper [J26], and the thesis of Silvia Simoni introduced a systematic approach to the identification of areas of instability that made full use of the potential of on-site geophysical measurement campaigns and the a priori characterization of geotechnical properties of the soil in the laboratory, without using back analyses for the calibration of parameters as is generally done by simplified models.  The IRASMOS Reports [rep06, rep07 and rep08] represent a summary of the literature available on this subject which has been eventually refined in [rep09].

The most recent work  has been focused on trying to understand the dynamics of subsurface flow  in  by means of virtual experiments [A43] with GEOtop, and in more conceptualized terms to explicit the role of the variability of depth of soil [J33, J35, thesis of Cristiano Lanni]  with the model denominated CI-SLAM.  The result is the introduction of the concept of "hydrological connectivity" of the hillslopes, which is realized when a perched water table forms that covers the whole basin.  The connectivity concept bridged the gap between hillslope hydrology and basin hydrology, and has also consequences important for hillslopes' stability [J37]. In fact these concepts allows a better statistical identification of landslide areas, than previous similar models.  [J35] also contains a preliminary attempt to use the theories of self-organizing criticality in the context of instability propagation, which, evidently, heralds the actual landslide itself.

Paper [J46] faces the issues related to the choice of a certain parameterisation of the soil retention curves and analyses their relation to hillslope stability. It uses a new theory that uses double porosity, and estimates the stability with the use of the new theories by Lu, Likos and Godt.

References

In English:

[ J23] - D’Odorico, P., Fagherazzi G., Rigon R. Potential for landsliding: Dependenceon hyetograph characteristics J. Geophys. Res., Vol. 110, No. F1, F01007 10.1029/2004JF000127 10 February 2005

[J26] Simoni, S., F. Zanotti, G. Bertoldi and R. Rigon, Modelling the probability ofoccurrence of shallow landslides and channelized debris flows using GEOtop-FS, Hydrol. Process. 22, 532–545, 2008, DOI: 10.1002/hyp.6886

[J33] - Lanni, C.; McDonnell, J. J.; Rigon, R., On the relative role of upslope anddownslope topography for describing water flow path and storage dynamics:a theoretical analysis, Hydrological Processes Volume: 25 Issue: 25 Pages: 3909-3923, DEC 15 2011, DOI: 10.1002/hyp.8263

[J35] - Lanni C., J. McDonnell JJ, Hopp L., Rigon R., "Simulated effect of soil depthand bedrock topography on near-surface hydrologic response and slope stability" in EARTH SURFACE PROCESSES AND LANDFORMS, v. 2012, (In press). - URL: http://onlinelibrary.wiley.com/doi/10.1002/esp.3267/abstract . - DOI: 10.1002/esp.3267

[J37] Lanni C., Borga M., Rigon R., and Tarolli P., Modelling catchment-scale shallowlandslide occurrence by means of a subsurface flow path connectivity index, Hydrol. Earth Syst. Sci. Discuss., 9, 4101-4134, (in press at HESS)

[A31] - E. Cordano, P., Bartolini, Rigon R. A flexible numerical approach to solving a generalized Richards’ equation problem and some applications, 2004

[rep06]- Rigon R., Rickenmann D., Catalogue of causes and triggering thresholds (Ed), IRASMOS EU Project Deliverable 1.1, 2007

[rep07] - Rigon R. (Ed), State-of-the-art models: their transferability and model application, IRASMOS EU ProjectDeliverable 1.2, 2007

[rep08] - R. Rigon, State of the art of prediction techniques, IRASMOS EU Project Deliverable 1.3, 2007

[rep09] - R.Rigon, Franceschi, S., Monacelli, G., and Formetta, G., The triggering of landslides and debris flows and their mapping, Danube Flood Risk EU Project, 2012

[J46] - Ciervo F. ,  Casini F. , Papa M.N. ,  Rigon R., Some remarks on bimodality effects of the hydraulic properties on shear strength of unsaturated soils, Vadose Zone Hydrology, published electronically, doi:10.2136/vzj2014.10.0152, 2015

In Italian:

[A21] - D’Odorico, P., Fagherazzi S., Rigon R. Frane superficiali e idrologia deiversanti: Un possibile metodo di indagine. Atti del XXVIII Convegno di Idraulica e Costruzioni Idrauliche, vol. V, pp.177-184, 2002

[A26] - Tiso, C., Bertoldi G. and R. Rigon. Il modello Geotop-SF per la determinazione dell’nnesco di fenomeni di franamento e di colata. Atti del Convegno Iterpraevent 2004, Riva del Garda, 24-28 Maggio 2004

[A27] - Rigon, R., A. Cozzini, S. Pisoni, G. Bertoldi e A. Armanini. A new simple method for the determination of the triggering of debris flows. Atti del Convegno Interpraevent 2004, Riva del Garda, 24-28 Maggio 2004

[A32] - Cordano, E., Panciera R., Rigon R., Bartolini P. Sulla soluzione diffusiva dell’equazione di Richards. Atti del XXIX Convegno di Idraulica e Costruzioni Idrauliche, Settembre 2004

[A43] Lanni C., Cordano E., Rigon R., Tarantino A., Analysis of the effect of normaland lateral subsurface water flow on the triggering of shallow landslides witha distributed hydrological model. in from geomorphology mapping to dynamic modelling, Strasbourg: CERG, 2009. Atti di: A Tribute to Prof. Dr. Theo van ASCH, Strasbourg, 6th-7th February 2009

My Past Research on Hydroinformatics, GIS and Modelling by Components

Research in the aforementioned sectors was also carried out with the implementation of  open-source software, coded in C and Java and distributed with a GPL (v 3) license.  Involvement in this topic has been deemed necessary to easy cooperative research, and to improve reuse of codes among researchers and students,  and allow an incremental development of modelling solutions (avoiding to implement again and again the same algorithms at any new generation of students).
The software has been accurately documented [eb1 to eb13] so that it can be easily reused and modified for both research and didactic purposes.  The software originally included a series of C libraries for reading, writing and insertion of comments in the data files, dynamic allocation of memory, the statistical treatment of data aimed  especially at hydrology, hydraulics, and geomorphology, but not limited to these.  On the basis of these libraries, called "Fluid Turtles" and now obsolete, was implemented the initial version GEOtop model [j24, s3]  and an initial version of  the  Horton machine [e.g. eb-3, s3].

However, the traditional software architecture of the Fluid Turtles presented various limitations. Mainly: the lack of an interface for the processing of  input data and the treatment of output data and the difficulty of maintaining and testing the software and its parts each one independently from the others, with the growing number of processes being described [e.g. A44, A49]. In fact, with the increasing number of people working on the code, and with the success of the modelling ideas among users, it became necessary to be able to test and use groups of parts of the models separately (as in JGrass-NewAGE).  It was also envisioned necessary to predispose the models  to be linked (in the future) to external models, such as, for example, those simulating the evolution of the atmospheric boundary layer, or belonging to other domains than hydrology (for instance to build a Decision Support System).
These, and other reasons [J40], have brought through a decade of work, trials and errors, on the one hand, to the development of a new GIS,  JGrass, eventually embedded in uDig,  and, on the other, to the adoption of suitable informatics infrastructure in order to restructure the models in components according to the OMS standard.

In the latest version, JGrass has partially contributed to the uDig "core" [eb10, A49, J41], while the modeling part is migrating to the jgrasstools environment (based on OMS) called Spatial Toolbox.
The last version of the tools has been actually embedded in Hydrologis' S.T.A.G.E which is a stand-alone application connectable, in principle, to any Java GIS (thinking to future versions of uDig or GvSig). The tools for terrain analysis included in STAGE  (a.k.a "The Horton Machine") are well covered by [a57]

Along the years various prototypes where developed around the above infrastructures to connect models to SQL/Geographic databases (Postgresql/Postgis), to visualise results on the Nasa World Wind virtual globe, and to allows scripting to interact with models which were presented in various conferences, and on which we could discuss with those interested.

References

In English:

[ J24] - Rigon R., Bertoldi G e T. M. Over, GEOtop: A distributed hydrological model with coupled water and energy budgets, Vol. 7, No. 3, pages 371-388

[A49] Formetta G., Antonello A., Franceschi S., David O. and Rigon R., The informatics of the hydrological modelling system JGrass-NewAge, 2012 International Congress on Environmental Modelling and Software Managing Resources of a Limited Planet, Sixth Biennial Meeting, Leipzig, Germany R. Seppelt, A.A. Voinov, S. Lange, D. Bankamp (Eds.) http://www.iemss.org/society/index.php/iemss- 2012-proceedings, 2012

[J40] - Formetta G., Antonello A., Franceschi S., David O., and Rigon R., Hydrological modelling with components: A GIS-based open-source framework, Environmental Modelling & Software, 5 (2014), 190-200

[a57]- W. Abera, A. Antonello, S. Franceschi, G. Formetta, R Rigon , "The uDig Spatial Toolbox for hydro-geomorphic analysis" in Geomorphological Techniques, v. 4, n. 1 (2014), p. 1-19.

[eb2-b] Ghesla, E. and R. Rigon, A Tutorial for the Management of Digital Terrain Models, pg. 131, University of Trento, Department of Civil and Environmental Engineering, ISBN 10: 88-8443-155-7, 2006 (Now obsolete)

[eb3] - R.Rigon, E. Ghesla, C. Tiso and A. Cozzini, The Horton Machine, pg. viii, 136, ISBN 10:88-8443-147-6, University of Trento, 2006 (Now obsolete)

[eb4-a] Ghesla E and R. Rigon, A Tutorial for preparing GEOtop Input Files with JGrass, pg. vi, 62, ISBN 10:88-8443-153-0, University of Trento, 2006

* [eb05] Dall’Amico, A., Endrizzi, E., Gruber, S., Rigon R., The GEOtop Manual, Università di Trento, in press, 2013

In Italian:

[A44] Antonello A., Franceschi S., Formetta G., Rigon R., L’infrastruttura NewAGE per la previsione e la gestione dei bilanci idrici a scala di bacino: I - La struttura informatica in Atti XXXII Convegno di Idraulica e Costruzioni Idrauliche, Palermo, 14-17 Settembre 2010

[eb1-a] Antonello, A., S. Franceschi, A. Vitti e R. Rigon, Il Manuale JGRASS 2.0 (In Italiano), pg. 176, ISBN 10:88-8443-144-1, University of Trento, 2006 (Now obsolete)

[eb2-a] Ghesla, E. and R. Rigon, Un tutorial per il trattamento di modelli digitali del terreno con JGRASS - A Tutorial for the treatment of DEMs with JGRASS (in Italian), ISBN 10: 88-8443-146-8, 2006 (Now obsolete)

[eb4-b] Ghesla E and R. Rigon, Un tutorial per la generazione dei file di input per GEOtop utilizzando JGrass, pg. vi, 62, ISBN 10:88-8443-154-9, University of Trento, 2006 (Now obsolete)

* [eb6] Rigon R., Formetta G., Zini M., Franceschi S., Antonello A., La Horton Machine, Università di Trento, in press, 2013


* [eb7] Rigon R., Formetta G., Perathoner L., Iemma A., Franceschi S., Antonello A., Jiffle, una breve introduzione, Università di Trento, in press, 2013

* [eb8] Rigon R., Formetta G., Perathoner L., Franceschi S., Antonello A., Peakflow: teoria e pratica, Università di Trento, in press, 2013

* [eb9] Franceschi S., Rigon R., Formetta G., Perathoner L., Antonello A., Trentop, Manuale d’uso, Università di Trento, in press, 2013

* [eb10] - Antonello A., Franceschi S., Rigon R., Formetta G., Perathoner L., uDig: Installare lo Spatial Toolboox, Università di Trento, in press, 2013

[eb11] - Iemma, A., Antonello A., Franceschi S., Rigon R., Formetta G., Perathoner L., uDig walkthroughs, Lavorare con i formati di GRASS in uDig, Università di Trento, in press, 2013

My Past Research on Process Based Physical Modelling on the Hydrological Cycle

The first studies in this field took inspiration from analysis of moisture distribution in the soil, [J14, A8] where it was shown that, during relatively “dry periods, the moisture distribution in the soil can be understood and described with fractal analysis techniques. From these studies, and the desire to model evapotranspiration, eco-hydrological phenomena, hydrology and slope stability, and the evolution of the snowpack, there arose the need to develop an instrument capable of modelling the water cycle and soil moisture dynamics continually over time. These goals were the founding reasons for the implementation of the GEOtop Model [J24, A22]. GEOtop is “terrain-based (it is based on the use of digital terrain models and uses the knowledge of interac- tion between morphology and process) distributed (all the simulated variables are calculated for each pixel of the basin) model of “the water cycle (it simulates all the components of the water cycle, taking account of both the mass budget and the energy budget, the two budget equations being coupled through the temperature of the soil, which controls evaporation, hydraulic conductivity, and accumulation of the snowpack [J22]). A complete description of the model can be found in [J24, A22], articles that present the model system and a practical application to the Little Washita basin in Oklahoma, and, obviously in the manual [eb-05].

The GEOtop model was also applied during the study of the water cycle of Lake Serraia (Trentino, Italy) [A34]. [J25] demonstrates the effects of complex topography and morphology on the water cycle. In particular, one can observe that a more extensive channel network (as might arise in presence of greater slopes or more erodible soil) causes greater surface runoff and less evapotranspiration, which, in the energy budget, causes an increase in latent heat exchange with atmospheric boundary layer. The paper demonstrates, therefore, that topographic effects cannot be neglected in formulating the energy budget of the soil, as most global climate models normally do. Among the more theoretical studies, but essential to the distributed modelling of flows in unsaturated media, are [J27, A29]. In [J28] Richards Equation was perturbatively decomposed into a vertical component and a lateral one. The first dominates the initial phases of infiltration, the second the long-term redistribution of water volumes. With the work reported in [J30] the model was expanded with a soil freezing and thawing module, that allowed the analyses of the PermaNET project to be executed, and other studies performed by other researchers.

Recently, the GEOtop model has been used to estimate the impact of climate change on mountain catchments [rep05]. Ancillary studies have been dedicated to parameter calibration and uncertainties in hydrologic model forecasting [A37, A40].
The article [J38] envisages the restructuring of the GEOtop model with new numeric methods, developed together with Prof Vincenzo Casulli, and the adoption of a non-structured grid for the modeling. However, [J43] represents the state-of art of  GEOtop version 2.0, a milestone in the model history which contains Richards 3D integration, permafrost modelling, a multilayer snow model, renewed options for the treatment of meteo-data and radiation.
[J44] embrace the use of CLM and face the problem of data assimilation complemented by the use of Kriging techniques for filling the missing data.

A small community of users and developers has developed around GEOtop which is steadily growing.

The article [j38] envisages the restructuring of the GEOtop model with new numeric methods, developed together with Prof Vincenzo Casulli, and the adoption of a non-structured grid for the modeling.   [J43] represents the state-of art of  GEOtop version 2.0, a milestone in the model history which contains Richards 3D integration, permafrost modelling, a multilayer snow model, renewed options for the treatment of meteo-data and radiation.
[J44] embraces the use of CLM model, and faces the problem of data assimilation complemented by the use of Kriging techniques for filling the missing data.

References

In English:

[J14] - Rodriguez-Iturbe, I, Gregor K. Vogel, R. Rigon, D. Entekhabi, F. Castelli and A. Rinaldo, On the spatial organization of soil moisture fields, Geoph. Res. Letters, 22(20), 2757-2760, 1995.

[ J22] - Zanotti, F., Endrizzi, S, Bertoldi, G. e R. Rigon, The GEOTOP snow module, Hydrol. Proc., 18, 3667-3679 (2004), DOI 10.1002/hyp.5794

[ J24] - Rigon R., Bertoldi G e T. M. Over, GEOtop: A distributed hydrological model with coupled water and energy budgets, Vol. 7, No. 3, pages 371-388

[ J25] Bertoldi G. R. Rigon e T. M. Over, Impact of watershed geomorphic char- acteristics on the energy and water budgets, Vol. 7, No. 3, pages 389-394, 2006

[ J28] - Cordano E. R. Rigon, A perturbative view on the subsurface water pressure response at hillslope scale, Water Resour. Res., Vol. 44, No. 5, W05407- W05407, doi:10.1029/2006WR005740, 2008 

[j30]- M. Dall’Amico, S. Endrizzi, S. Gruber, and R. Rigon, An energy-conserving model of freezing variably-saturated soil, The Cryosphere Discussion, The Cryosphere Discuss., 4, 1243-1276, doi:10.5194/tcd-4-1243-2010, 2010

[J38] Cordano E., Rigon R., A mass-conservative method for the integration of the two-dimensional groundwater (Boussinesq) equation, submitted to Water Resour. Res., 2012  

[J43] - Endrizzi S., Gruber, S, Dall'Amico M., and Rigon R., GEOtop 2.0: simulating the combined energy and water balance at and below the land surface accounting for soil freezing, snow cover and terrain effects, Geosci. Model Dev.,  7, 2831–2857, 2014, www.geosci-model-dev.net/7/2831/2014/ doi:10.5194/gmd-7-2831-2014

[J44] -  Han X., Lin, X, Rigon R., Jin R., Endrizzi S., Local Analysis of L-Band Microwave Brightness Temperature Assimilation With Geostatistics for Soil Moisture Estimation, PLOSONE, 2015

[A8] - Rodriguez-Iturbe, I., G. K. Vogel, R. Rigon, D. Entekhabi, F. Castelli and A. Rinaldo, Scaling properties of soil moisture, Proceeding of the workshop on climate change and hydrometereological hazards in the mediterranean area, Perugia, 1995 

[A34] - Bertola P., Bertoldi G.,Grisenti P., Piva G., Ragazzi M., Righetti M., Rigon R., Salvaterra M., Soppelsa G., Tomazzolli V., Integrated research on eutrophication processes on Caldonazzo lake (Trento, Italy). Atti del Convegno Simposio Internazionale di Ingegneria Sanitaria e Ambientale, Taormina, 23-26 Giugno, 2004

[A37] - Entezarolmahdi R., G. Bertoldi e R. Rigon, An Automatic “Watershed Model Calibration process, 7th International Congress of Civil Engineering, Teheran, 2006

[A31] - E. Cordano, P., Bartolini, Rigon R. A flexible numerical approach to solving a generalized Richards’ equation problem and some applications, 2004

[A40] Entezarolmahdi R., Rigon R., Bertoldi G., Assessment of parameter uncertainty for physically based hydrologic model, using automatic optimization approach, XXX Convegno di Idraulica e Costruzioni Idrauliche, Roma 2006 

[eb05] Dall’Amico, A., Endrizzi, E., Gruber, S., Rigon R., The GEOtop Manual, Università di Trento, A Draft here, in press, 2012

[rep05] - R. Rigon, A. Bellin, L. Forlin, H. Fowler, S. Blenkinsop, Testing of climate change scenarios on a case-study catchment using different methodologies, Deliverable C2.4 AQUATERRA EU Project, 2005

In Italian:

[A22] - Bertoldi, G., Rigon R., Overt T.M. Un indagine sugli effetti della topografia sul ciclo idrologico con il modello GEOtop. Atti del XXVIII Convegno di Idraulica e Costruzioni Idrauliche, Potenza, pp.313-324, 2002

[A32] - Cordano, E., Panciera R., Rigon R., Bartolini P. Sulla soluzione diffusiva dell’equazione di Richards. Atti del XXIX Convegno di Idraulica e Costruzioni Idrauliche, Settembre 2004

My Past Research on Hydro-geomorphology

The work on evolution of river networks, certainly enters also in this category. Here however, it is reported about those papers that deals directly with quantitative geomorphological analysis.
In most of the papers, the relationships between the various parts of a river basin are analyzed with fractal geometry techniques.  Such knowledge is useful not only for the evaluation of river basin evolution models, but also in  identifying the nature of their hydrological response to given events and their paleoclimate.  In [J2], using the Peano Basin, a mathematical reference structure, it is suggested that the amplitude function of natural networks can be reproduced with a multifractal multiplicative
process.   In [J11] this concept was rigorously formalized in the framework of random multifractal cascades theory.

The fractal properties, that is  power laws relating to  contributing areas and the length of stream reaches, were rigorously analyzed in [J15]. In [J17] more relationships between these characteristic quantities were found and an explanation of the nature of Hack's law is suggested.
In [J27] the structure of the river networks is further investigated by analysing the tributaries statistics. The relationships were verified experimentally by means of Digital Elevation Models (DEM).

Given programs for the extraction of digital terrain models (DEM) and their treatment, the natural development was the implementation of an open-source geographic information system: JGrass [s2].  JGrass, now part of uDig, contains within the package a large amount of GIS methods, jointly known as the Horton Machine [eb-3] to support the most common and some less common tools of analysis for river networks topology,  channel extraction, hillslope delineation. A review of these tools is in [a57].

Papers and work on landslide triggering are also concerned with geomorphology but referred in a different post.

References

[j2] - Marani, A., R. Rigon and A. Rinaldo, A Note on fractal channel networks,Water Resources Research, (27)5, 3041-3049, 1991.

[j11] - Marani, M., A. Rinaldo, R. Rigon and I. Rodriguez-Iturbe, Geomorphological width function and the random cascade, Geophysical Research Letters, 21(19), 2123-2126, 1994.

[j15] - Maritan, A., A. Rinaldo, R. Rigon, I. Rodriguez-iturbe and A. Giacometti, Scaling laws for river networks, Physical Review E , 53, 1510, 1996.

[j17] - Rigon, R., I. Rodriguez-Iturbe, A. Rinaldo, A. Maritan, A. Giacometti and D. Tarboton, On Hack’s law, Water Resources Research, 32(11), 3367, 1996

[s2] Jgrass (since 2002): it is a full featured GIS system built to support the hydro- geomorphological research of the group since the early 2000s. Recently it has been integrated in uDig. Current developments (which go far beyond my contribution) are available at: http://udig.refractions.net/

[eb3] - R.Rigon, E. Ghesla, C. Tiso and A. Cozzini, The Horton Machine, pg. viii, 136, ISBN 10:88-8443-147-6, University of Trento, 2006

[j27] - Convertino, M, Rigon, R; Maritan, A; I. Rodriguez-Iturbe and Rinaldo, A, Probabilistic structure of the distance between tributaries of given size in river networks, Water Resour. Res., Vol. 43, No. 11, W11418, doi:10.1029/2007WR006176, 2007

[a57]- W. Abera, A. Antonello, S. Franceschi, G. Formetta, R Rigon , "The uDig Spatial Toolbox for hydro-geomorphic analysis" in Geomorphological Techniques, v. 4, n. 1 (2014), p. 1-19

My Past Research on the Evolution of River Networks

Chronologically, one of my first interests was modeling the evolution of channel networks according to principles of minimal energy dissipation and self-organization by critical states. These two types of models proved to be capable of reproducing the two- and three-dimensional statistical characteristics of channel networks and natural basins, as well as the fractal and multifractal characteristics. This work, born with the intent of identifying a minimum set of characteristic dynamic elements in the evolution a hydrographic basin, has always been carried out in parallel to the refinement of measurement and analysis techniques of topographic data [J3]. 

The concept of optimality of a hydrographic basin was introduced in [J3, J4, J5]. In these works, the three postulates of optimal channel networks (OCNs) are stated and developed, proving how such principles can have quantitative effects on the morphology of river networks, particularly affecting the structure of slopes and of contributing areas, the geometry of the channels, and the characteristic velocity of the peak flow of a basin. All of these results explain numerous empirical laws and are still the basis of measurement campaigns.

In [J4], that which was postulated in [J3, J5] was verified by numeric simulation. It should be noted that the minimization of dissipated energy generates fractal forms that reproduce the quantitative characteristics of real basin. In [J6] the concept of optimality is further refined by introducing the hillslope contribution and presenting some case studies. In [J6], more tools are introduced for the qualitative comparison between the numeric models and the natural data. In [J8, J9, A6] a model of the evolution of river basins is presented that is based on the concepts of self-organization by critical states. This model proved to be equivalent to optimization model of [J3-J6]. In [J13] the impact of climatic variability on the morphology of the fluvial landscape is simulated, so offering an interpretative framework for some fluvial forms that can be found in nature.

Subsequently, the concept of optimality was refined observing that real basins do not have the configuration that would give an absolute minimum of dissipated energy, but rather that of states of local minimum that are dynamically accessible. From here the concept of feasible optimality was derived [A10, J18, J19]. It was also demonstrated that the states of absolute minimum, dynamically unreachable, have statistical properties that are not realistic, while accessible minimum states have the desired statistical characteristics. A relevant characteristic of the space-time dynamics of hydrographic networks is that they can be described by means of a parameter that can be linked to temperature [J16]. It is therefore possible to define the thermodynamics of the river networks. As with the thermodynamics of other physical systems, the relevant quantities are energy (dissipated in unit time), entropy, and the temperature.

It should be noted that the space-time evolution of river networks happens with an intermittent behavior similar to the concept of point equilibrium proposed for the evolu- tion of the biological species. It was also demonstrated that the temporal dynamics of river networks is coupled with the spatial activity at all scales and that natural networks, therefore, evolve according to conditions of minimum dissipation of energy but in the presence of a great variety of possible dynamic states.

In [J10] an accurate analysis of the fractal and multifractal properties of optimal river networks was carried out. The note [J18] is a review article, sent to the Annual Review of Earth and Planetary Sciences, that treats the aforementioned topics. In [J20] the results of a theorem on network topology that relates the sum of the contributing areas with the contributing areas themselves and hypothesizes that these quantities are analogous to the ratio of metabolic rhythm and mass of living beings. The two quantities are linked an exponential law with an exponent that was proved to be Hack’s exponent.

This work, born with the intent of identifying a minimum set of characteristic dynamic elements in the evolution of a hydrographic basin, has always been carried out in parallel to the refinement of measurement and analysis techniques of topographic data [s2,eb3]. Recently, this field of study has produced a work [J26] where the morphometric statistics of tributaries of natural rivers and OCNs are studied. These are related to the characteristics of peak flows and they have ecological implications such as, for example, the velocity of diffusion of waterborne diseases and the diffusion of species along the river network. In Rigon’s work, the morphological relations between the different parts of fluvial basins have been analyzed with ever more refined numeric instruments, to the point of creating a series of GIS methods known as the Horton Machine [eb3].

The paper [J41] is partially a review of old results, that were not collected before, and were overlooked by people because they did not appear in Rodriguez-Iturbe and Rinaldo 1997 book. It includes however some new set of simulation were injection of rainfall is assigned with certain distributions (with given correlation structure) producing differentiated power laws for discharge and contributing areas. Clearly a result to further explore.

References

In English:

[J3] - Rodriguez-Iturbe, I. , A. Rinaldo, R. Rigon, R. L. Bras, A. Marani and E.J. Ijjasz-Vasquez, Energy dissipation, runoff production, and the 3-dimensional structure of river basin, Water Resources Research, (28)4, 1095-1103, 1992.

[J4] - Rinaldo, A., I. Rodriguez-Iturbe, R. Rigon, R.L. Bras, E. J. Ijjasz-Vasquez e A. Marani, Minimum energy and fractal structures of drainage networks, Water Resources Research, (28), 2183, 1992.

[J5] - Rodriguez-Iturbe, I. , A. Rinaldo, R. Rigon, R. L. Bras, A. Marani and E.J. Ijjasz-Vasquez, Fractal structure as least energy patterns: The case of river networks, Geophysical Res. Letters, (19)9, 889-892, 1992.

[J6] - Rigon R., A. Rinaldo, I. Rodriguez-Iturbe, R. L. Bras and E. Ijjasz-Vasquez, Optimal channel networks: a framework for the study of river basin morphology, Water Resources Research, 29(6), 1635-1646, 1993.

[J7] - Ijjasz-Vasquez, E., R.L. Bras, I. Rodriguez-Iturbe, A. Rinaldo and R. Rigon, Are river networks OCN?, Advances in Water Resources, 16, 69-79, 1993.

[J8] - Rinaldo, A., I. Rodriguez-Iturbe, R. Rigon, E. Ijjasz-Vasquez, and R.L. Bras, Self organized fractal river networks, Physical Review Letters,70(6), 822-26, 1993.

[J9] - Rigon, R., A. Rinaldo and I. Rodriguez-Iturbe, On landscape self-organization, Journal of Geophysical Research, 99(B6), 11971-11993,1994.

[J10] - Rodriguez-Iturbe, I., M. Marani, R. Rigon and A. Rinaldo, Self-organized river basin landscapes: fractal and multifractal characteristics,Water Resources Research, 30(12), 3531-3539,1994.

[J16] - Rinaldo, A. Maritan, A. Flammini, F. Colaiori, R. Rigon, I. Rodriguez-Iturbe and J. R. Banavar, Thermodynamics of fractal networks, Physical Review Letters, 76(18), 3364-3367, 1996.

[J18] Rinaldo, A., I. Rodriguez-Iturbe and R. Rigon, Channel Networks, Annual Review of Earth and Planetary Sciences, 26, 289-327, 1998

[J27] - Convertino, M, Rigon, R; Maritan, A; I. Rodriguez-Iturbe and Rinaldo, A, Probabilistic structure of the distance between tributaries of given size in river networks, Water Resour. Res., Vol. 43, No. 11, W11418, doi:10.1029/2007WR006176, 2007

[J41] -Rinaldo,  A., Rigon R., Banavar, J., Maritan, A. and Rodriguez-Iturbe, I., Evolution and selection of river networks: Statics, dynamics, and complexity, PNAS 2014


In Italian:

[A04]- Rigon, R., Il clima è scritto nella forma del reticolo idrografico?, Rapporti e studi della commissione di studio dei provvedimenti per la conservazione e la difesa della cittá di Venezia, Tomo CLI, Classe di Scienze ff. mm. e nn., 1-21, 1992.

[A06] - Rigon, R. - Principi di auto-organizzazione nella dinamica evolutiva delle reti idrografiche, Tesi di Dottorato, Università degli Studi di Genova, Firenze, Padova, Trento, 1994

[A12] - Rigon, R., Che cosa guida i processi morfologici nei bacini fluviali? Reti ottime di canali e la legge di Hack, Atti XXVI Convegno di Idraulica e Costruzioni Idrauliche, Vol II, 121, 1998

My Past Research on Rainfall-Runoff (Peak Flows) Modelling and related topics

These works of mine reagards event base prediction of discharges based on the Geomorphological Unit Hydrograph. They show that the detailed knowledge of a river basin's morphology allows one to frame the main features of the  hydrological response in terms of a minimal set of dynamical parameters.  This is relevant insomuch as the form of river networks can now be derived with automatic high resolution and objective remote-sensing techniques.  Typically, the required dynamical parameters are the mean flow velocity in the network and distribution of residence times of water in the hillslopes.

In this context, the variance of the GIUH is proven to depend mostly on the structure of the pathways followed by the single volumes of effective rainfall from their release points to the control cross-section (geomorphological dispersion) [J1] rather than on the hydrodynamic dispersion; the latter becoming  relevant only at the large scale.
Generally, it is possible to determine with precision the first moment, the variance, the  skewness, and the kurtosis of the hydrological response of a river basin  as a whole [A3, A9].  In [A7, J12] the production mechanisms of effective rainfall and the  characteristic contributions of the hillslopes are studied. As a result it was observed that rarely is the  response time of the hillslopes negligible when calculating the hydrological response of the  river basin as a whole.
In  [A18, A19, J21] the use of width functions in the construction of the GIUH and the concept
of including information about initial moisture conditions for the basis are further developed.
In this way it was observed that, with varying fractions of saturated river basin, the hillslopes
and channels contributed different fractions to the flood wave;  the hillslopes being particularly
important under conditions of extreme saturation of the basin [J21].
The formulation of the GIUH on the basis of width functions has also given semi-analytical
results regarding peak times and maximum discharges for a basin [J31].
All of these studies brought to the implementation of part of the Horton Machine [eb-3], and on the model Peakflow (e.g. http://www.jgrasstools.org).

The post on the lecture given at Montpellier contains the rational and an explicitation of the assumption made in such type of modelling.

More recently, the study of the hydrological response was directed mainly towards the investigation
of runoff production mechanisms on hillslopes (actually in researches related to the hillslope stability),  in relation to the soil depth [J33, J35, J37] and brought new insights to the concept of hydrological connectivity. These studies overcome the results in [A29] that, while interesting, assume simplistic hillslope setups. Parallel efforts, which are reported in Physico-Statistical Modelling of the Hydrological Cycle, were made in overcoming the limitations of event based modelling.

The paper [j47] is a review taken from a historical-critical point of view of the theory of the geomorphological unit hydrograph that also enlarge the view to the modern theories for describing water fluxes by travel time. It also serves as the starting point for future research in this directions.

References

In English:

[J1] - Rinaldo, A., A. Marani and R. Rigon, Geomorphological dispersion, Water Resources Research, 27(4), 513-525, 1991

[J12] - Rinaldo A., G. K. Vogel, R., Rigon and I. Rodriguez-Iturbe, Can one gauge the shape of a basin?, Water Resources Research, (31)4, 1119-1127, 1995.

[A18] - Rigon, R., Cozzini A., Pisoni S. Getting the Rescaled Width Function and the Derived WGIUH. The Geomatic Workbooks, (http://geomatica.ing.unico.it), 2001

[A19] - Rigon, R., Cozzini A., Pisoni S. Looking for a new method of estimating solid discharges in small alpine watersheds. The Geomatic Workbooks, vol. 2, (http://geomatica.ing.unico.it), 2001

[J21] - D’Odorico, P. e R. Rigon, Hillslope and channel contributions to the hydrologic response, submitted to Water Resour. Res., 2003

[A29] - Panciera, R., Chirico G.B., Rigon R., Grayson R. Contributing Area Dynamics produced by Saturation Excess Runoff. Atti del XXIX Convegno di Idraulica e Costruzioni Idrauliche, Settembre 2004

[eb-3] - R.Rigon, E. Ghesla, C. Tiso and A. Cozzini, The Horton Machine, pg. viii, 136, ISBN 10:88-8443-147-6, University of Trento, 2006

[J31] - R. Rigon, P. D’Odorico, and G. Bertoldi, The geomorphic structure of the runoff peak, Hydrol. Earth Syst. Sci. Discuss., 8, 1031-1058, doi:10.5194/hessd-8- 1031-2011, 2011

[J33] - Lanni, C.; McDonnell, J. J.; Rigon, R., On the relative role of upslope and downslope topography for describing water flow path and storage dynamics: a theoretical analysis, Hydrological Processes Volume: 25 Issue: 25 Pages: 3909-3923, DEC 15 2011, DOI: 10.1002/hyp.8263

[J35] - Lanni C., J. McDonnell JJ, Hopp L., Rigon R., "Simulated effect of soil depth and bedrock topography on near-surface hydrologic response and slope stability" in Earth Surface Processes and  Landforms, v. 2012, (In press). - URL: http://onlinelibrary.wiley.com/doi/10.1002/esp.3267/abstract . - DOI: 10.1002/esp.3267

[J37] - Lanni C., Borga M., Rigon R., and Tarolli P., Modelling catchment-scale shallow landslide occurrence by means of a subsurface flow path connectivity index, Hydrol. Earth Syst. Sci. Discuss., 9, 4101-4134, www.hydrol-earth-syst-sci- discuss.net/9/4101/2012/ doi:10.5194/hessd-9-4101-2012,
HESS

[J47] - Rigon R.,  Bancheri M.,  Formetta G.,  deLavenne A. , The geomorphic unit hydrograph from a historical-critical perspective, accepted in Earth Sci. Proc. & Landforms, 2015


In Italian:

[A3] - Rigon, R., Influenza della morfologia di un bacino montano sui caratteri della risposta idrologica, Atti del XXXII Convegno di Idraulica e di Costruzione idrauliche, Firenze, 1992.

[A7] - Rigon, R., Formulazione del trasporto per tempi di residenza: un‘alternativa ai modelli di pioggia efficace nel calcolo della risposta idrologica, Atti del XXIV Convegno di Idraulica e di Costruzione idrauliche, Napoli, 1994

[A9] - Rigon, R., P. D’Odorico e L. Parra, Metodi geomorfologici di inferenza della risposta idrologica, Atti del XXV Convegno di Idraulica e di Costruzioni idrauliche, Torino, 1996.

[A13] - D’Odorico, P., M. Marani e R. Rigon, Questioni geomorfologiche e previsione delle piene nei bacini fluviali, Atti XXVI Convegno di Idraulica e Costruzioni Idrauliche, Vol II, 73, 1998

[A24] - Rinaldo A., M. Marani, A. Fornasiero, G. Botter, S. Silvestri, A. Bellin, Rigon R., M. Ferri, F. Baruffi, A. Rusconi. Modelli geomorfologici - Montecarlo per la valutazione del tempo di ritorno delle piene fluviali: fiume Brenta chiuso a Bassano. Atti del XXVIII Convegno di Idraulica e Costruzioni Idrauliche, vol. 1, pp.271-278, 2002

Soil Depth Estimation

Estimation of soil depth is crucial for the assessment of hillslope hydrological processes (e.g.
Tromp van Meerveld and McDonnell, 2006) and landslide stability (e.g Lanni et al., 2011, 2012).  Is a topic that had a lot of attention in the community of geomorphologists but indeed it remain still an open. In a recent paper (e.g. Lanni et al., 2012, under the final stage of review in HESS) we wrote a very short review:

"The spatial distribution of soil depth is controlled by complex interactions of many factors (topography, parent material, climate, biological, chemical and physical processes) (e.g., Summerfield, 1997, Pelletier and Rasmussen, 2009, Nicotina et al., 2011). As a result, soil depth is highly variable spatially and its prediction at a point is difficult. Moreover, soil depth survey is time consuming and soil depth is difficult to measure even for small basins (Dietrich et al., 1995). Various methods have been explored to allow the estimation of soil depth over landscapes. A process-based approach was suggested by Dietrich et al. (1995) for predicting the spatial distribution of colluvial soil depth. Based on this approach, topographic curvature may be considered a surrogate for soil production. Heimsath et al. (1997, 1999) validated the relationship between curvature and soil production based on observations of cosmogenic concentrations from bedrock in their Tennessee Valley site in California. This approach was incorporated into a landscape evolution model by Saco et al. (2006) to evaluate the dependence of soil production on simulated soil moisture. Roering et al. (1999) supported the idea that soil production follows a non linear equation and, therefore, modified the dependence of soil depth relationships. However, the various modeling approaches for predicting soil depth over landscapes, described above, showed only partial success (Tesfa et al., 2009).

In contrast to the process-based approaches, a number of studies have applied statistical methods to identify relationships between soil depth and landscape topographic variables (e.g., slope, wetness index, plan curvature, distance from hilltop, or total contributing area) (e.g. Gessler et al., 1993, Tesfa et al., 2009, Catani et al., 2010). Some of these works reported good predictive capabilities for these statistical relationships. For instance, Tesfa et al. (2009) report that their statistical models were able to explain about 50% of the measured soil depth variability in an out-of-sample test. This is an important result, given the complex local variation of soil depth."

Our short review possibly miss some interesting reference as the one by D'Odorico (2000) on a possible bi-stable evolution equation, and our little work in Bertoldi et al. (2006) that generalize Heimsath's to include random variaility in depth. 

However, reduction of soil depth formation simply to a geometrical factor (as implied by using equations with homogenous parameters) is clearly not enough. Pedologists know it. But so far I found only a few able to enter in the strict path of learning our equations. 

Anyway,  looking for R based hydrological resources I found this explanatory map by Roudier and Beaudette:

Looking at it gives clearly the idea that soil depth does not depend (only) on geometry. Where slope and curvature remain constant, anyway soil depth varies.

It is easy to think that it depend on variability in the geologic substrate,  soil cover (grass, plants), and soil use (for instance grazing or the presence of animals). But there is any pedologist out there which could help us to built a consistent quantitative theory ?

As usual, the references could be a starting point for a more in-depth literature search.

References

Catani, F., Segoni, S., and Falorni, G.: An empirical geomorphology-based approach to the spatial prediction of soil thickness at catchment scale, Water Resour. Res., 46, W05508, doi:10.1029/2008WR007450, 2010. 

Dietrich, W. E., Reiss, R., Hsu, M.-L., and Montgomery, D. R.: A process-based model for colluvial soil depth and shallow landsliding using digital elevation data, Hydrol. Processes, 9, 383 – 400, doi:10.1002/hyp.3360090311, 1995.

D'Odorico, P. (2000), A possible bistable evolution of soil thickness, J. Geophys. Res., 105(B11), 25,927–25,935, doi:10.1029/2000JB900253.

Gessler, P. E., Moore, I. D., McKenzie, N. J., and Ryan, P. J.: Soil landscape modeling and spatial prediction of soil attributes, Int. J. Geogr. Inf. Syst., 9, 421– 432, doi:10.1080/02693799508902047, 1995.

Heimsath, A. M., Dietrich, W. E., Nishiizumi, K., Finkel, R. C.: The soil production function and landscape equilibrium, Nature, 388, 358– 361, doi:10.1038/41056, 1997.

Heimsath, A. M., Dietrich, W. E., Nishiizumi, K., Finkel, R. C.: Cosmogenic nuclides, topography, and the spatial variation of soil depth, Geomorphology, 27, 151– 172, doi:10.1016/S0169-555X(98)00095-6, 1999.

Lanni, C., McDonnell, J.J., and Rigon, R.: On the relative role of upslope and downslope topography for describing water flowpath and storage dynamics: a theoretical analysis, Hydrological Processes, 25(25), 2011.

Lanni, C., McDonnell, J., Hopp, L. and Rigon, R.: Simulated effect of soil depth and bedrock topography on near-surface hydrologic response and slope stability, Earth Surf. Process. Landforms, 2012, doi: 10.1002/esp.3267.

Lanni, C., Borga M., Tarolli P., Rigon R., Modelling shallow landslide susceptibility by means of a subsurface flow path connectivity index and estimates of soil depth spatial distribution , HESSD, 2012

Nicotina, L., Tarboton, D. G., Tesfa, T. K., Rinaldo, A.: Hydrologic controls on equilibrium soil depths, Water Resour. Res., 47, W04517, doi:10.1029/2010WR009538, 2011.

Liu, J., Chen, X., Lin, H., Liu, H., & Song, H. (2013). A simple geomorphic-based analytical model for predicting the spatial distribution of soil thickness in headwater hillslopes and catchments. Water Resources Research, n/a–n/a. doi:10.1002/2013WR013834

Pelletier, J. D. and Rasmussen, C.: Geomorphically based predictive mapping of soil thickness in upland watersheds, Water Resour. Res., 45, W09417, doi:10.1029/2008WR007319, 2009.

Roering, J.E., Kirchner, J.W., and Dietrich, W.E.: Evidence for nonlinear, diffusive sediment transport on hillslopes and implications for landscape morphology, Water Resorces Research, vol. 35(3), 853–870, 1999.

Saco, P. M., Willgoose, G. R., and Hancock, G. R.: Spatial organization of soil depths using a landform evolution model, J. Geophys. Res., 111, F02016, doi:10.1029/2005JF000351, 2006.

Summerfield, M. A.: Global Geomorphology, 537 pp. Longman, New York, 1997

Tesfa, T. K., Tarboton, D. G., Chandler. D. G., and McNamara, J. P.: Modeling soil depth from topographic and land cover attributes, Water Resour. Res., 45, W10438, doi:10.1029/2008WR007474, 2009.

Tromp-van Meerveld, H.J., and McDonnell, J.J.: Threshold relations in subsurface stormflow: 2. The fill and spill hypothesis, Water Resources Research, 42, W02411. 2006.

Frost Heave

Frost heave is a phenomenon of accumulation of ice due  to peculiar thermodynamics circumstances. It is quite an important phenomenon that I encounter during the thesis of Matteo Dall'Amico, and we did not treat (but I  have some ideas about). Causally I found this youtube lecture that illustrate it, and can be used to understand a little more about.

References

1. Taber, S., Frost heaving, J. Geology 37 (1929) 429-461
2. Taber, S. The mechanics of frost heaving, J. Geology 38 (1930) 303-317
3. Dash, J.G., Fu, H. and Wettlaufer, J.S., The premelting of ice and its environmental consequences, Rep.Prog.Phys. 58 (1995) 115-167
4. Rempel, A.W., Wettlaufer, J.S. and Worster, M.G. Premelting dynamics in a continuum model of frost heave, J. Fluid Mech. 298 (2004) 227-244
5. Wettlaufer, J.S. and Worster, M.G. Premelting dynamics, Annu.Rev.FluidMech. 38 (2006) 427-452
6. Wettlaufer, J.S. and Worster, M.G. , Dynamics of premelted films: Frost heave in a capillary, Phys. Rev E., 51(5), 4679-4689, 1995

Henry Darcy

A nice video on Henry Darcy on youtube. You can easily take five minutes to watch it.

Thanks to Emanuele Cordano to have indicated it to me.

Summer School on bio-geo-dynamics and Earth Sytem Sciences: The biophysical processes that shape the Earth

This School, the BESS,  has a long tradition that goes back to 1990 and was recently renewed.
I usually suggests to my students that participating is an important experience for their formation. The lecturers are very distinguished colleagues. The location (Venice and the Istituto Veneto) are fantastic. The topics are of general interest and, if not strictly covering hydrology, they are certainly useful to open the view of hydrologists who think that hydrology is a little more that fitting some data set but want to understand "how nature works".

The topics of this year were:

• Spatial and temporal controls of soil function by Bridget Emmet
• The thermodynamics of the Earth System by Axel Kleidon
• Linking pattern formation and spatial ecology by Ehud Meron
• Complex Dynamics of Forest Ecosystems at Different Scales: From 100 square meters to the Global Scale by Herman Shugart

Fortunately all the lectures are now available as streaming videos (not the slides of the lectures unfortunately) and can be viewed here.

Work of students is available instead here. Thanks to Marco Marani and Andrea Rinaldo for organising it, and thanks to the Istituto Veneto di Lettere Scienze ed Arti for making all the material available, and for supporting all of it.