Finally this paper was published in HESS, and can be found at

http://www.hydrol-earth-syst-sci.net/15/1853/2011/hess-15-1853-2011.html with its companion paper and discussions.

It is the fourth of a sequence of papers that started at the very beginning of my hydrological carrier (as from the ISI catalog):

GEOMORPHOLOGICAL DISPERSION, RINALDO, A; MARANI, A; RIGON, WATER RESOURCES RESEARCH Volume: 27 Issue: 4 Pages: 513-525 Published: APR 1991

CAN ONE GAUGE THE SHAPE OF A BASIN, RINALDO, A; VOGEL, GK; RIGON, R; et al., WATER RESOURCES RESEARCH Volume: 31 Issue: 4 Pages: 1119-1127 Published: APR 1995

HILLSLOPE AND CHANNELS CONTRIBUTIONS TO THE HYDROLOGIC RESPONSE: D'ODORICO, P; RIGON, R, WATER RESOURCES RESEARCH Volume: 39 Issue: 5 - Published: MAY 1 2003

But in these papers, we can possibly include, also:

A NOTE ON FRACTAL CHANNEL NETWORKS, MARANI, A; RIGON, R; RINALDO, A, WATER RESOURCES RESEARCH Volume: 27 Issue: 12 Pages: 3041-3049 Published: DEC 1991

GEOMORPHOLOGICAL WIDTH FUNCTIONS AND THE RANDOM CASCADE, MARANI, M; RINALDO, A; RIGON, R; et al., GEOPHYSICAL RESEARCH LETTERS Volume: 21 Issue: 19 Pages: 2123-2126 Published: SEP 15 1994

In fact, all began in trying to understand the topology of river networks with the hope, of which we had confirmations, that topology and geometry play a role in shaping the hydrograph. The discover was that the river networks were fractal (we actually learned it from La Barbera and Rosso, 1989, and Tarboton et al., 1988), and the width function has a multifractal imprint.

However, on these structures, the river networks, the signal passing though has its own dynamics which is advective but also dispersive. How dynamics interacts with geometry? In the first paper on geomorphological dispersion we showed that geometry usually dominates hydrodynamics. So, a precise account for hydrodynamics is usually not necessary to reconstruct the main features of a hydrograph.

A few year later, however, we realized that our model was a little too simple, since using flood wave celerities in channels were not enough to account for the process. We needed at least to include a further celerity, to account for the travel time of water in hillslopes. This was already clearly envisioned at least by Bras and van Der Tak, 1990 but we introduced it in the formalism of the Geomorphological Unit Hydrograph. Besides, we investigated more the role of dispersion. Getting the signal of an ideal uniform rainfall can we solve the reverse problem of understanding the form of the basin which generated a given hydrograph ? While without diffusion and dispersion we were able to statistically reverse the signal, i.e. obtaining basin shapes very similar to the original one, increasing diffusion makes any effort more and more difficult, until the complete loss of any detailed information. However, we were able to characterize diffusion influence on the moments of distribution, and showed that the average residence time is not affected at all by dispersion (therefore it maintains the imprinting of the topology and geometry of the river network) and gave a formula for the second moment of the hydrograph. Works cited in the Peak Flows paper report subsequent research on topic by Saco and Kumar (see References), and by Botter and Rinaldo. Later on, Botter and Rinaldo, 2010 moved also to study the recession curves.

BTW one of the open questions, actually a missing link for completing the whole picture was the inclusion in the picture of a runoff generating mechanism, since all our consideration were essentially based on the assumption that we were able to single out an "effective rainfall", i.e. that part of the precipitation that produces the flood hydrograph. We attacked this problem in D'Odorico and Rigon, 2003 where we implemented a completely saturation excess theory of it, and showed how the extension of partial saturated areas affect heavily the hydrologic response, and therefore the estimation of any residence time statistics (during the writing we found that Sivapalan, Beven and Wood, wow, already tried it in the old-fashioned IUH theory).

What about the peak flows ? Here it comes the present paper:

This paper develops a theoretical framework to investigate the core dependence of peak flows on the geo- morphic properties of river basins. Based on the theory of transport by travel times, and simple hydrodynamic characterization of floods, this new framework invokes the linearity and invariance of the hydrologic response to provide analytical and semi-analytical expressions for peak flow, time to peak, and area contributing to the peak runoff. These results are obtained for the case of constant-intensity hyetograph using the Intensity-Duration-Frequency (IDF) curves to estimate extreme flow values as a function of the rain- fall return period. Results show that, with constant-intensity hyetographs, the time-to-peak is greater than rainfall duration and usually shorter than the basin concentration time. More- over, the critical storm duration is shown to be independent of rainfall return period as well as the area contributing to the flow peak. The same results are found when the effects of hydrodynamic dispersion are accounted for. Further, it is shown that, when the effects of hydrodynamic dispersion are negligible, the basin area contributing to the peak discharge does not depend on the channel velocity, but is a geomorphic propriety of the basin. As an example this framework is applied to three watersheds. In particular, the runoff peak, the critical rainfall durations and the time to peak are calculated for all links within a network to assess how they increase with basin area.

Note: I probably forgot some Siva contributions in this story, just do a "Sivapalan" search on the Water Resources Research site to have an idea of his contributions.

References

Botter, G. and A. Rinaldo (2003), Scale effect on geomorphologic and kinematic dispersion, Water Resour. Res., 39, 1286, doi:10.1029/2003WR002154.

Botter, G. (2010), Stochastic recession rates and the probabilistic structure of stream flows, Water Resour. Res., 46, W12527, doi:10.1029/2010WR009217.

La Barbera, P., and R. Rosso (1989), On the Fractal Dimension of Stream Networks, Water Resour. Res., 25(4), 735-741.

Saco, P. M. and P. Kumar (2002), Kinematic dispersion in stream networks 1. Coupling hydraulic and network geometry, , 38, 1244, doi:10.1029/2001WR000695.

Saco, P. M. and P. Kumar (2002), Kinematic dispersion in stream networks 2. Scale issues and self-similar network organization, , 38, 1245, doi:10.1029/2001WR000694.

Saco, P. M. and P. Kumar (2004), Kinematic dispersion effects of hillslope velocities, Water Resour. Res., 40, W01301, doi:10.1029/2003WR002024

M., K. Beven, and E. Wood (1987), On Hydrologic Similarity 2. A Scaled Model of Storm Runoff Production, Water Resour. Res., 23(12), 2266-2278.

Tarboton, D., R. Bras, and I. Rodriguez-Iturbe (1988), The Fractal Nature of River Networks, Water Resour. Res., 24(8), 1317-1322.

van der Tak, L., and R. Bras (1990), Incorporating Hillslope Effects Into the Geomorphologic Instantaneous Unit Hydrograph, Water Resour. Res., 26(10), 2393-2400.

## Saturday, June 18, 2011

## Monday, June 13, 2011

### A New International Network for in Situ Soil Moisture Data

is available from TU Wien. Announcement can be found here on the EOS AGU Journal. The site can be found at https://ismn.geo.tuwien.ac.at/

This is an Initiative of the International Soil Moisture Network about which is available an open access paper on HESS by Dorigo et al.

This is an Initiative of the International Soil Moisture Network about which is available an open access paper on HESS by Dorigo et al.

## Sunday, June 12, 2011

### About peer review and the tyranny of some

I already talke about the review process and some of its excess. Here it is an informed opinion from Nature. Professor Ploegh talks about the danger to require further but not necessary experiments. I strongly agree with him.

### Research topics for my next 20 years

These are the research topics I posted on the call for the doctoral school of Trento (but I update regularly this post -last update is dec 2014). Who wants to know what I did (the basis to know what I will do) can find my papers and my past research topics here.

I try to contribute to hydrology theoretical development, build tools, and apply them to some case studies (others make mainly experiments or field work: and I appreciate a lot their work. But I will never become what I am not: if you want to deal with experiments and field work, you possibly waste your time with me). So students can get the best from me if they have attitudes that get along with my inclinations. Cause of personal attitudes, programming skills, or the will to pursue them, are necessary to work with me. I use C/C++, R, and Java, and I made some posts to help people to become a little more familiar to some of these tools (R here, and Java here). Other good tools exist: but do not blame me if I do not use Fortran or Python. I did this choice long time ago and I am still convinced it was not wrong.

I produce models, free models, and it is intended that all the tangible work in programming and tools of anyone working with me must be free software.

The goal of this research line is to develop and assess models of shallow terrain instabilities through mathematical and numerical modeling, and the validation of models by means of conceptual and field experiments. These last will be prepared jointly with other institutions, in particular we have an ongoing collaboration with Bologna University for some basins in Val di Fassa, where several data were collected, USGS (Jonathan Godt) and School of Mines (Ning Lu). To get an idea of what I am talking about, you can give a look at this post.

The basis of the research is the use of GEOtop 2.0 and GEotop-SF and their improvements. With regards to hillslope hydrology the issues right now seem to have a reasonable model (or mapping) of the soil depth, a reasonable way to represent it within the constraints of a grid, and the characterization, at the grid cell size, of the relevant hydrological parameters (for which we have some hints deriving from soil scientists).

Besides covering hillslope hydrology issues, this research is intended to move from the simple assessment of triggering through the infinite slope stability model to model of propagation and self-organization of the stresses within hillslopes, and implementing Jonathan's and Ning's new theories.

The candidate needs also to develop tools and techniques for the assessment of the boundary and initial conditions necessary to drive the models and perform innovative statistical analysis on the spatio-temporal patterns produced by the models.

My past research on this topic can be found here.

This regards mainly the development of the JGrass-NewAGE for the complete closure of the hydrological budgets, in medium to large scale modelling. This requires the implementation and testing of new physical-statistical model of the various terms of the hydrological cycle, and their application to case studies at the scale of hundreds to thousands of square kilometers. At the moment the model has a first implementation of all the processes that is going to be thoroughly tested, and the main interest in this research is to go beyond the simple forecasting of hydrological quantities (in space-time) to achieve the estimation of error bounds in the predictions with the application of appropriate calibration methods, and data assimilation procedures. The doctoral work is intended to achieve also the application of models and tools to real cases (as for instance those provided by the DMIP2 project).

My past research and further insight on the topic can be found here.

This study involves the modelling and forecasting of the evolution of the snow cover working with the model GEOtop. Previous Ph.D researchers implemented a one dimensional energy budget of both the snowpack and freezing soil. They also posed the bases for further theoretical and numerical improvements of the model, to a 3D version, and eventually including also different constitutive relations, which could be pursued in this research.

The present proposal is especially dedicated to include (or embed) GEOtop modelling with a data assimilation system dedicated to real-time forecasting of the snow cover, depth, and status. The Ph.D. work could be oriented to assimilate either ground data than remote sensing data.

The work will be made in coordination with Mountain-eering S.r.l, a spin-off of the University of Trento, and Stephan Gruber of University of Carleton (CA).

Starting point for this work is, at the moment, Matteo Dall'Amico Ph.D. thesis and the paper Dall'Amico et al., 2011, which I consider one of my milestones.

Information about my research on Cryospheric processes is here.

Hydrology is a thermodynamical science. Each of its fluxes is waiting for a proper assessment which ties together non-equilibrium thermodynamics, and sound fluid dynamics. Little steps in this direction were already made in studying the interaction and the phase change in frozen ground, but remaining essentially in the framework of the classical quasi-equilibrium thermodynamics. Consistent steps can be made actually for most of the processes, including evaporation and transpiration, flow in soil and groundwater, and freezing soils, building upon rational thermodynamics of irreversible processes, and the mesoscopic thermodynamics. The theoretical work, if possible, should be completed by appropriate numerical work. It is intended that all the tangible work in programming and tools produced as free software, and using free software.

There are no previous results on this topic, however, some preliminary work was made.

Some topics were removed from here, to give a more sharp idea of what really I want to do. They pertain to my past research and/or to some past period. But they could come back sometimes. Following your own curiosity, you can find them here.

Motivated students are invited to contact me for a possible Ph.D. carrier or post-doc positions. As general attitude in my research I believe that research must be reproducible, and I require the same discipline to my Ph.D. students and collaborators.

I try to contribute to hydrology theoretical development, build tools, and apply them to some case studies (others make mainly experiments or field work: and I appreciate a lot their work. But I will never become what I am not: if you want to deal with experiments and field work, you possibly waste your time with me). So students can get the best from me if they have attitudes that get along with my inclinations. Cause of personal attitudes, programming skills, or the will to pursue them, are necessary to work with me. I use C/C++, R, and Java, and I made some posts to help people to become a little more familiar to some of these tools (R here, and Java here). Other good tools exist: but do not blame me if I do not use Fortran or Python. I did this choice long time ago and I am still convinced it was not wrong.

I produce models, free models, and it is intended that all the tangible work in programming and tools of anyone working with me must be free software.

**Hillslope hydrology, landslide and debris flow triggering, and erosion thresholds**The goal of this research line is to develop and assess models of shallow terrain instabilities through mathematical and numerical modeling, and the validation of models by means of conceptual and field experiments. These last will be prepared jointly with other institutions, in particular we have an ongoing collaboration with Bologna University for some basins in Val di Fassa, where several data were collected, USGS (Jonathan Godt) and School of Mines (Ning Lu). To get an idea of what I am talking about, you can give a look at this post.

The basis of the research is the use of GEOtop 2.0 and GEotop-SF and their improvements. With regards to hillslope hydrology the issues right now seem to have a reasonable model (or mapping) of the soil depth, a reasonable way to represent it within the constraints of a grid, and the characterization, at the grid cell size, of the relevant hydrological parameters (for which we have some hints deriving from soil scientists).

Besides covering hillslope hydrology issues, this research is intended to move from the simple assessment of triggering through the infinite slope stability model to model of propagation and self-organization of the stresses within hillslopes, and implementing Jonathan's and Ning's new theories.

The candidate needs also to develop tools and techniques for the assessment of the boundary and initial conditions necessary to drive the models and perform innovative statistical analysis on the spatio-temporal patterns produced by the models.

My past research on this topic can be found here.

**Distributed Modelling of the Hydrological Cycle at large scales, hydrological predictability and data assimilation**This regards mainly the development of the JGrass-NewAGE for the complete closure of the hydrological budgets, in medium to large scale modelling. This requires the implementation and testing of new physical-statistical model of the various terms of the hydrological cycle, and their application to case studies at the scale of hundreds to thousands of square kilometers. At the moment the model has a first implementation of all the processes that is going to be thoroughly tested, and the main interest in this research is to go beyond the simple forecasting of hydrological quantities (in space-time) to achieve the estimation of error bounds in the predictions with the application of appropriate calibration methods, and data assimilation procedures. The doctoral work is intended to achieve also the application of models and tools to real cases (as for instance those provided by the DMIP2 project).

My past research and further insight on the topic can be found here.

**Distributed Modelling of the Cryospher**eThis study involves the modelling and forecasting of the evolution of the snow cover working with the model GEOtop. Previous Ph.D researchers implemented a one dimensional energy budget of both the snowpack and freezing soil. They also posed the bases for further theoretical and numerical improvements of the model, to a 3D version, and eventually including also different constitutive relations, which could be pursued in this research.

The present proposal is especially dedicated to include (or embed) GEOtop modelling with a data assimilation system dedicated to real-time forecasting of the snow cover, depth, and status. The Ph.D. work could be oriented to assimilate either ground data than remote sensing data.

The work will be made in coordination with Mountain-eering S.r.l, a spin-off of the University of Trento, and Stephan Gruber of University of Carleton (CA).

Starting point for this work is, at the moment, Matteo Dall'Amico Ph.D. thesis and the paper Dall'Amico et al., 2011, which I consider one of my milestones.

Information about my research on Cryospheric processes is here.

**Theoretical and Numerical studies about the non equilibrium thermodynamics applied to Hydrology**

Hydrology is a thermodynamical science. Each of its fluxes is waiting for a proper assessment which ties together non-equilibrium thermodynamics, and sound fluid dynamics. Little steps in this direction were already made in studying the interaction and the phase change in frozen ground, but remaining essentially in the framework of the classical quasi-equilibrium thermodynamics. Consistent steps can be made actually for most of the processes, including evaporation and transpiration, flow in soil and groundwater, and freezing soils, building upon rational thermodynamics of irreversible processes, and the mesoscopic thermodynamics. The theoretical work, if possible, should be completed by appropriate numerical work. It is intended that all the tangible work in programming and tools produced as free software, and using free software.

**Implementation of new methods for integrating Navier-Stokes (NS) equation in rugged terrain**

**Having a nice and suitably implemented method of integration of NS equations is seen as the natural complements to what done so far within GEOtop. Evapotranspiration, snow deposition, the simulation of soil temperature, all require that the interactions with the low atmosphere must be well resolved. The only way I see for doing this is adding a module that solves for turbulence. This work will be pursued in conjunction with Dino Zardi and Michael Dumbser, two outstanding colleagues of my own Department, and Michi Lehning of SLF in Davos and Ecole Politechnique of Lausanne.**

There are no previous results on this topic, however, some preliminary work was made.

**HydroInformatics for Hydrology**

I want to investigate the theory and practice of hydrological modelling under the light of modern software engineering. It is a fact that increased knowledge about processes has not been paired by an adequate development and quality of the software that deploy it in software and models.

Software quality has been overlooked for long time, and has relevant consequences on the daily activity of scientists (not only hydrologists), especially those who use numerical models to interpret experiments, do forecasts, and falsify hypotheses.

The bad quality of software also causes serious obstacles to the real understanding and independent analysis of the algorithms used, and makes overwhelming difficult, if not impossible, the replicability and the reproducibility of any result, thus undermining the foundations of the scientific method.

Beyond the scopes of traditional software engineering, or making easier cooperative programming, enhancing the clarity and efficiency of codes, making easier software maintenance, hydroInformatics

applied to science, must solve the issue related to documentation of algorithms and to develop “design patterns” specific to science and hydrology, promote replicable and reproducible research.

In practice this means to enhance the system that is already at the base of JGrass-NewAGE and individuate design patterns for solver of differential equations compatible with the OMS infrastructure. Eventually this will bring to a new version of GEOtop, completely interoperable with JGrass-NewAGE, parallelised, well documented, flexible and full of alternative processes description with the aim to increase the small communities working with these softwares.

Previous work was summarised in Formetta et al., 2014 but also reading Jgrasstools requirements and David et al., 2013 can be useful. This research will be pursued in tight connection with Olaf David and the ARS/USDA facility in Fort Collins.

**Other info**Some topics were removed from here, to give a more sharp idea of what really I want to do. They pertain to my past research and/or to some past period. But they could come back sometimes. Following your own curiosity, you can find them here.

**Epilogue**

Motivated students are invited to contact me for a possible Ph.D. carrier or post-doc positions. As general attitude in my research I believe that research must be reproducible, and I require the same discipline to my Ph.D. students and collaborators.

## Wednesday, June 1, 2011

### A robust and energy-conserving model of freezing variably-saturated soil

We worked a lot for this paper, where we implemented the freezing = drying theory of frozen soil. The theoretical work behind it open the way to generalizations that we will pursue in the next months. Here it is the abstract:

Phenomena involving frozen soil or rock are important in many natural systems and, as a consequence, there is a great interest in the modeling of their behavior. Few models exist that describe this process for both saturated and unsaturated soil and in conditions of freezing and thawing, as the energy equation shows strongly non-linear characteristics and is often difficult to handle with normal methods of iterative integration. Therefore in this paper we propose a method for solving the energy equation in freezing soil. The solver is linked with the solution of Richards equation, and is able to approximate water movement in unsaturated soils and near the liquid-solid phase transition. A globally-convergent Newton method has been implemented to achieve robust convergence of this scheme. The method is tested by comparison with an analytical solution to the Stefan problem and by comparison with experimental data derived from the literature.

The paper and the previous discussion paper can be freely downloaded at The Cryosphere site

For who is interested, a nice companion of the paper is the reading of Matteo Dall'Amico thesis, where there is some other remarkable material, and an introduction to equilibrium Thermodynamics that can make happy those who never really understood the notation used by thermodynamicists. Matteo and I made an effort to derive the basic thermodynamics from some postulates (derived from Callen's book), and use the normal algebra (the one we learn at the beginning of our undergraduate studies): I think we were quite successful, and for us Thermodynamics is not anymore the "a dismal swamp of obscurity", as C. Truesdal said. Also the books by Garbrect-and -Bohren, and Muller-and-Weiss were very useful to achieve our results.

Please take the time to read the reviews which added very informed and beautiful literature, and knowledge to the first paper.

References

Bohren C. F., and Albrecth B. A., Atmospheric Thermodynamics, Oxford University Press, 1998

Callen, H. B., Thermodynamics and an Introduction to Thermostatistics, J. Wiley and Sons, 1985

Muller, I., and Weiss, Entropy and Energy: A Universal Competition, Springer, 2005

Truesdall, C., The tragicomical history of thermodynamics 1822-1854, Springer Verlag, 1980 (the sentence is at page 6)

For who interested in thermodynamics, I found also another couple of good books:

Ganguly A., Thermodynamics in Earth and Planetary Sciences, Springer, 2010

Zdunkowski W., and Bott, A., Thermodynamics of the Atmosphere: A Course in Theoretical Meteorology, Cambridge University Press, 2004

Phenomena involving frozen soil or rock are important in many natural systems and, as a consequence, there is a great interest in the modeling of their behavior. Few models exist that describe this process for both saturated and unsaturated soil and in conditions of freezing and thawing, as the energy equation shows strongly non-linear characteristics and is often difficult to handle with normal methods of iterative integration. Therefore in this paper we propose a method for solving the energy equation in freezing soil. The solver is linked with the solution of Richards equation, and is able to approximate water movement in unsaturated soils and near the liquid-solid phase transition. A globally-convergent Newton method has been implemented to achieve robust convergence of this scheme. The method is tested by comparison with an analytical solution to the Stefan problem and by comparison with experimental data derived from the literature.

The paper and the previous discussion paper can be freely downloaded at The Cryosphere site

For who is interested, a nice companion of the paper is the reading of Matteo Dall'Amico thesis, where there is some other remarkable material, and an introduction to equilibrium Thermodynamics that can make happy those who never really understood the notation used by thermodynamicists. Matteo and I made an effort to derive the basic thermodynamics from some postulates (derived from Callen's book), and use the normal algebra (the one we learn at the beginning of our undergraduate studies): I think we were quite successful, and for us Thermodynamics is not anymore the "a dismal swamp of obscurity", as C. Truesdal said. Also the books by Garbrect-and -Bohren, and Muller-and-Weiss were very useful to achieve our results.

Please take the time to read the reviews which added very informed and beautiful literature, and knowledge to the first paper.

References

Bohren C. F., and Albrecth B. A., Atmospheric Thermodynamics, Oxford University Press, 1998

Callen, H. B., Thermodynamics and an Introduction to Thermostatistics, J. Wiley and Sons, 1985

Muller, I., and Weiss, Entropy and Energy: A Universal Competition, Springer, 2005

Truesdall, C., The tragicomical history of thermodynamics 1822-1854, Springer Verlag, 1980 (the sentence is at page 6)

For who interested in thermodynamics, I found also another couple of good books:

Ganguly A., Thermodynamics in Earth and Planetary Sciences, Springer, 2010

Zdunkowski W., and Bott, A., Thermodynamics of the Atmosphere: A Course in Theoretical Meteorology, Cambridge University Press, 2004

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