Long live to the Horton Machine!

The Horton Machine is our set of tools for geomorphic analysis. It was named after  one of the father of Hydrology and Geomorphology, Robert E. Horton. The GEOframe group contributed since the beginning of it and at present, the tool is maintained by Hydrologis. The presentation below introduces the last stand-alone version of it and, in particular, there is a part dedicated to a tool that Hydrologis dedicated to the GEOframe community for giving a well balanced partition of catchments for hydrological analysis.

Obviously Horton Machine The Spatial Toolbox contains other tools than those for GEOframe, of particular interest are those that support the analysis of LIDAR dataset (L.E.S.T.O.), the use of the GEOpaparazzi (github) and SMASH mobile applications.  

Dr. Silvia Franceschi (GS) is briefly presenting here the tools. The slides of the presentation can be accessed by clicking on the above figure.  Please see the video of the presentation below

Updated material on Horton Machine

The Horton Machine is our set of tools for terrain analysis actually maintained by Hydrologis. They since 2000 and something took care of keeping my tools alive on various platforms: GRASS, JGrass, uDig and now on gvSIG. We also have a porting of the Horton machine that works under GEOframe but is the same codebase.

Silvia Franceschi and Andrea Antonello gave a tutorial at this year gvSIG conference and here it is the material.

You can find the same material also at this osf project. Soon they will follow some theoretical lectures.

Lanscape evolution models (LEMs)

I worked on landscape evolution twenty years ago, mainly during My Ph.D. studies. My literature reference at that time was Bill Dietrich’s one. It would be interesting to know how his collection changed in time te get it updated. My perspective moved in recent years more to Hydrology, but some of the ideas that I collected remained in the background of my mind, and informed my subsequent research. 

Looking now at it, I can say that my work on LEMs followed two main path.   

The first direction was to prove and consolidate analysis tools (my lessons, in Italian, here). These tools (in general, I mean, not specifically mine) do not have evolved much since then, if we exclude that the availability of high resolution data implied some adaptation and offered some opportunity.* They remain the first step, to assess the result of models. In the past I had the impression, that some theories had credit for the insufficient control on  geomorphic characteristics that now can be easily detected.

The second direction was to look for the processes that generate landscape evolution. In my work, the triggering mechanism was channel initiation, counteracted by hillslope-diffusive processes. The first generating fractality, the second destroyng it. However, I soon realise that, in practice, this was interesting but too simple, and certainly the process is mediated by the soil production. So, in my new hypothetical model I would put soil/sediment production in, to limit the landscape change (maybe was this the detachment limitation implied by A. Howard ?). 

The ability to produce soil would differentitate different climates/geological situations. I use both because, it seems to me, that they do not act separately. 

In any case, landscape evolution models usually do not treat  mass wasting  (see also here for other contributions) and usually the effects of the cryosphere (but I could be out-of-date on that side).  Mass wasting is threshold dependent, and the threshold depends both on soil/sediment and climate again. While in other aspects climate probably enters in the picture with  mean properties (this phrase can look a little bit weird, since climate is the supposed mean of weather ) of temperature and precipitation, mass wasting is dependent on the statistics of extreme events which cause soil/sediment failure and transport. 
On the effects of the cryosphere I remember a paper by David Montgomery on the height limits of mountains that introduced the effects of ice and glaciers (another paper is here).

So my next ingredient in the picture would be to have a statistically controlled set of precipitation (a topic on which there is great knowledge) and a set of rules for determining the triggering of mass waste events, and their magnitude. Statistics exist on that aspect that can be used appropriately. 

As I told above, on the actions of the cryosphere I do not have clear indications, but it is known that it has huge and persistent effects ( called paraglacial inheritance), which clearly we did not accounted for in our previous work. Maybe a first approximation would be to avoid glaciated area, but mountains mean, maybe not for much longer, snow and ice.

I am not forgetting to give a little  substance to Tom Dunne phrase:" it is all about climate and tectonics ". My references ob this topic are limited to a recent paper on river and tectonics, published in Nature Geoscience, that felt causally under my attention (referenced here). Some preliminary thinking of mine is also in this  invited poster at EGU 2010.

Last, but not least, ecohydrology has an important role.  There is a persistent trend among fluvial geomorphologists (BTW this is "another" geomorphology type) to consider the effects of vegetation on creation of meanders, bars, and forms. These effects are lived by geographers in the qualitative mood of taking pictures, doing surveyings, writing long an beautiful descriptions, but my shallow opinion is that all of  it could be pursued more quantitatively, by doing models. 
On this topic,  this paper criticised the assumptions of a paper of mine (Ignacio's, Andrea's, Bill's) modeling, I think with some argument.  Vegetation, therefore should be included in new models.

Coming to  more practical arguments, I was a producer of conceptual models. That story is well documented. Instead looking for more process based models, l can remind the one developed by Gary Wilgoose (see here) with Raphael Bras. While the main actor in developing it was certainly Greg Tucker, Raphael was certainly involved also in the development of CHILDS, another remarkable example of modelling, which can be taken as null hypothesis for any further development (it contains also a treatment of vegetation, but I doubt of the cryosphere). 

I have to warn that the above models are mostly of the fluvial transport type of models, and they do not embed many of the features I listed as relevant above. So, definitely there is a lot of room for new works and developments. 

* - Well, I think that the work of Stefano Orlandini on the detection of drainage directions, and arrived recently, is important and definitive. But sooner or later I will do a more detailed post on the subject of "geomorphometrical" tools.

Geomorphological control on variably saturated hillslope hydrology and slope instability

This paper, which has a long history, treats the influence of geomorphology on stability. Not a new topic indeed, but usually saying that convergent topographies favour landslids was a matter of qualitative arguments.  Here it is made by using DEM analysis, a 3D Richards equation solver, and a sound model for hillslope stability. That's the difference for who can appreciate it.

Please, find the preprint, clicking on the Figure. I think the reading is enjoyable and I hope the Journal will accept it soon. 

Introduzione alla geomorfologia

La geomorfometria è la scienza che studia in modo quantitativo la geomorfologia, specialmente attraverso l'uso dei nuovi strumenti digitali. Da anni ho sviluppato con i miei collaboratori degli strumenti (dei software) di analisi raccolti nella  Horton Machine.

La lezione è divisa in 5 parti:

1- Gli elementi di base. Audio  2014: (18.4 Mb). Audio 2015 (22.9 Mb)
2 - Le grandezze derivate. Audio 2014 (24 Mb). Audio 2015 (10.4 Mb)
3 - Dove iniziano i canali. Audio 2015 (12 Mb)
4 - La sintesi digitale delle conoscenze sui bacini idrografici. Audio 2015 (4.6 Mb)
5 -Leggi geomorfologiche, processi idrologici e geomorfologia, Audio 2014 (22.8 Mb). Audio 2015 (15.4 Mb)

Tutto il materiale di supporto sulla Horton Machine, già nominato sopra,  si trova in quest'altro post.

Bibliografia (citata nelle slides)

Broscoe, A.J., 1995, Quantitative analysis of longitudinal stream profiles of small watersheds, Office of Naval Research, Project NR 389-042, Technical Report No. 18, Department of Geology, Columbia University, New York.

Howard A.D., A detachment-limited model of drainage basin evolution, Water Resources Research, vol. 30, n. 7, p. 2261-2285, 1994.

Leopold, L.B., and Maddock, T., Jr, The hydraulic geometry of stream channels and some physiographic implications: U.S. Geological Survey Professional Paper 252. 57p, 1953 

Maidment D.R., ed., Arc Hydro: GIS for Water Resources, ESRI Press, Redlands, Ca, 2002

Montgomery D.R. & Dietrich W.E., Channel initiation and the problem of landscape scale, Science, vol. 255, p. 826-830, 1992.

Moretti and Orlandini. Automatic delineation of drainage basins from elevation contour data using skeleton construction techniques.  (2007) pp. 1-39

Orlandini et al. On the prediction of channel heads in a complex alpine terrain using gridded elevation data. Water Resour. Res. (2011) vol. 47 (2) pp. W02538

Peckham S., New results for self-similar trees with applications to river networks, Water Resources Research, vol. 31, n. 4, p. 1023–1029, 1995

Peckham and Jordan. Digital Terrain Modelling. Lecture Notes In Geoinformation and cartography (2007) pp. 1-326

Rigon R., I. Rodriguez-Iturbe, A. Rinaldo, A. Maritan, A. Giacometti and D. Tarboton, On Hack's law, Water Resources Research, vol. 32, n. 11, p. 3367, 1996

Rigon R., Ghesla E., Tiso C. & Cozzini A., Cozzini The HORTON machine: a system for DEM analysis : the reference manual . Trento: Università di Trento. Dipartimento di ingegneria civile e ambientale, May 2006. - p. viii, 136, ISBN 10:88-8443-147-6, 

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

Rodriguez-Iturbe, I. and Rinaldo, A.: Fractal River Basins. Chance and Self-Organization, Cambridge University Press, New York, 1997.

Tarboton, D.G., A new method for the determination of flow directions and contributing areas in Grid Digital Elevation Models, Water Resources Research, vol. 33, n. 2, 309-319, http://www.engineering.usu.edu/cee/faculty/dtarb/dinf.pdf 

Tarboton, D.G., R.L. Bras and Rodriguez-Iturbe, 1992, A Physical Basis for Drainage Density, Geomorphology, vol. 5, n. 1/2

Venuleo, S., Analisi teoriche e di campo per la caratterizzazione di bacini idrografici montani,  Tesi di Laurea, Relatori: Rinaldo A., Passadorr, G., Padova, 2014

Wilson, J. P. and J. C. Gallant, (2000), Terrain Analysis: Principles and Applications, John Wiley and Sons, New York, 479 p.

Wood, J.D. (1996) The geomorphological characterisation of digital elevation models PhD Thesis, University of Leicester, UK

A paper on the Horton Machine

The Horton Machine toolset has gained a certain stability during the years, and I currently use it in my Hydrology class. There is a tutorial in Italian and an out-of-date Reference Manual which are waiting for being merged into a unique English Manual. Meanwhile, here it is a paper that explains it, as much as it can be made in a paper. This would be part, after having passed the appropriate peer review, of an open access book of the British Society for Geomorphology, Clarke (2013), section 2.4

The book chapter draft can be found here. The complimentary material to reproduce the manuscript figures can be found in this post.

Reference

Clarke, L.E. (Ed.) Geomorphological Techniques (Online Edition). British Society for Geomorphology, London. ISSN: 2047-0371,

OCNs are back!

OCNs stands for optimal channel networks. They are topological configurations of channels that minimize energy expenditure and reproduce the statistical features of real river networks. They were the main topic of my Ph. Thesis, and go some influence in understanding why in nature, many structures are networks, and two of my most cited papers cover this topic.  Eventually my advisors and co-workers pursue further the studies and pushed forward the research.

In figures above (top) a small random network developed according to an Eden growth procedure which start from the outlets (seeds of the growth), and (bottom) a OCN developed from it.
Recently I was asked to  go back to the topic and do some simulation. For the task, I decided to abandon the old version of the program (first programmed in Mathematica, and secondly in C) and to build a new one in Java. The new version is part of the Java for Hydrologists (and geoscientists) 101 and can be found at github under the project Geoframe (package OCNs). News will follow.

Worth to say, other groups of people are working on OCNs. Notably Lily Briggs and her advisor, prof. Mukkai Krishnamoorthy, are also working on OCNs. She built three-dimensional OCNs. Her paper is  here and her code is here, in Github.

A Geomorphological Assessment of Constable Landscapes

I took this post from the River Management Blog, and the post is by Simon Dixon. John Constable is one the greatest English landscape painter, and, in the words of the blog authors, contributed very much to the idea of what a natural landscape is. However, reading the post, you can realize that his paintings portrait not so natural landscapes.

Click, as usual on the painting to jump on the post.

Paraglacial geomorphology

We often talk about landscape evolution (and I have a little history on the subject). However, we usually forget that from 65Ky and 12Ky of years ago a lot of our Earth was covered by a glaciation. The image below, robbed from a Mr. Kurt Werth presentation at "At North of Trento and South of Bolzano"(1,2,3) Meeting, illustrates the situation in the place where I live, the river Adige basin.

I do not know which is the precision of the map, but it illustrates clearly which was the geneal situation. Cause of this,  many of the geomorphic features we see nowadays where created by the glacier retreat and by subsequent land-sculpting. Alluvial fans (some hundreds of them) were formed later. Big rock avalanches (according also to isotopic measurements) crumbled down among 10Ky and 3Ky ago.
Therefore it is time that  alpine geomorphology (and modelling) put Paraglacial situations inside its horizon. Actual landslides and sediment production is strongly affected by what the glaciers left.

Reference
Ballantyne, C.K. - Paraglacial geomorphology, Quaternary Science Reviews 21 (2002) 1935–2017

Rivers in transitions

An editorial of Nature Geoscience to read.

"Rivers affect landscape structure and function to a much greater extent than might be expected from the fraction of the Earth's surface they cover. Rivers redistribute material as they flow, carving out canyons and building new land offshore. These morphological consequences of river flow are evident in any topographic map of the Earth's surface. ..."

Other links are also available at the page.

Browsing the same number also a commentary is available on the role of rivers, and a paper on river drainage patterns in New Zealand.

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

A few historic papers on geomorphology from the Bill Dietrich collection

I did my Ph.D. on landscape evolution models, and at that time I collected, among other stuff, the papers that Bill Dietrich was used to distribute for reading to his students. Here the list of the historic (before 1980) papers in that group.

Gilbert, G.K., Report on the geology of the Henry Mountains (Utah): US Geographical an Geological, Survey of the Rocky Mountains Region, Washington D.C., 1877

Gilbert, G.K., The convexity of hilltops, Journal of Geology, 17(4), 344-350, 1909

Davis, W.M., The convex profile of badlands divides, Science, 20: 245, 1892

Horton, R. E. Erosional development of streams, and their drainage basins: hydrophysical approach to quantitative morphology, Bulletin of the Geological Society of America, 56: 275-370, 1945

Penck W., Morphological Analysis of landforms, London Macmillan, 1953

King, L.C., The uniformitarian nature of hillslopes, Trans. Edimburgh Geological Society, 17: 81-102, 1957

Culling, W.E.H. Analytical theory of erosion, Journal of Geology 68, 336-344, 1960

Hack, J.T., Interpretation of erosional topography in humid temperate regions, American Journal of Science, 258A: 80-97, 1960

Anhert, F.,  The role of the equilibrium concept in the interpretation of landforms of fluvial erosion and deposition, L'Evolution des Versants. Liege. Universite' de Liege, 23-14, 1967

Kirkby, M.J., Hillslope process-response models based on the continuity equation, Inst. British Geographers. Spec. Publ., 3:15-30, 1971

Smith, T.R., and F.P Bretherton, Stability and the conservation of Mass in Drainage Basin Evolution, Water Resources Research, 8(6): 1506-1529, 1972

For the longer series by Mike Kirkby look here.

Where do channels begin ?

It is the title of a famous paper by David Montgomery and Bill Dietrich about channel initiation which appeared in Nature, in 1988, and was followed by a subsequent paper (in 1994 on Water Resources Research): and BTW by many others in the following years to confirm, and using their findings.

So we know much more than then about. However, those pioneering contribution, did refer to what happens in sloped but hilly environments, of Oregon and California. What about the Alps ?

Recent work by Paolo Tarolli brought some quantitative light on the issue. He presented his work at last January Cathy meeting that can be summarized as follows:

-the availability of very detailed laser scanner of topography allows a great opportunity to use objective methods to single out channels' head.
- in a region of the Italian Alps (Dolomites) were surveyed at least two main processes that drive channel initiation: i) channel heads formed essentially by surface runoff (mass wasting, in form of debris flows or "more traditional" erosion), ii) and areas where geology and groundwater seeping upward exercise important controls on channel initiation.
- Wavelet analysis allows to smooth the topography the right way to use in sequence "curvatures" for channels head initiation.

I hope it will not pass to much time before we can bring these tools inside our jgrasstools.

For who is interested, relevant papers are listed below:

References

David R. Montgomery & William E. Dietrich,Where do channels begin? , Nature 336, 232 - 234 (17 November 1988); doi:10.1038/336232a0

MONTGOMERY and DIETRICH. Source Areas, Drainage Density, and Channel Initiation . Water Resour. Res. (1989) vol. 25 (8) pp. 1907-1918

Orlandini, S., Tarolli, P., Moretti, G., Dalla Fontana, G. (2011). On the prediction of channel heads in a complex alpine terrain using gridded elevation data, Water Resources Research, 47, W02538, doi:10.1029/2010WR009648

Passalacqua, P., Tarolli, P., Foufoula-Georgiou, E. (2010). Testing space-scale methodologies for automatic geomorphic feature extraction from LiDAR in a complex mountainous landscape, Water Resources Research, 46, W11535, ISSN: 0043-1397, doi:10.1029/2009WR008812.

Pirotti and Tarolli. Suitability of LiDAR point density and derived landform curvature maps for channel network extraction. Hydrol. Process. (2010) vol. 24 (9) pp. 1187-1197

Sofia, G., Tarolli, P., Cazorzi, F., Dalla Fontana, G. (under review). Channel heads and channel network identification from high-Resolution DTM: a statistical approach, Hydrol. Earth Syst. Sci., ISSN: 1027-5606.

Tarolli, P., Dalla Fontana, G. (2009). Hillslope-to-valley transition morphology: new opportunities from high resolution DTMs, Geomorphology, 113, 47-56, doi:10.1016/j.geomorph.2009.02.006