It's time to revise the GIUH

GIUH has been a valuable approximate tool for getting the hydrologic response. A review can be found in:

• Rigon, Riccardo, Marialaura Bancheri, Giuseppe Formetta, and Alban de Lavenne. 2016. “The Geomorphological Unit Hydrograph from a Historical-Critical Perspective.” Earth Surface Processes and Landforms, EGU Reprint Series, 41 (1): 27–37

The question of maximum discharges treated inside the theory can be found in

• Rigon, R., P. D’Odorico, and G. Bertoldi. 2011. “The Geomorphic Structure of the Runoff Peak.” Hydrology and Earth System Sciences 15 (6): 1853–63.

The role of hillslope and channels was treated in:

• D’Odorico, P., and R. Rigon. 2003. “Hillslope and Channel Contributions to the Hydrologic Response.” Water Resources Research. https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2002WR001708.

Jointly with my first paper that proved the role of the geometric/topological structure of the river network in forming the hydrologic response,

• Rinaldo, Andrea, Alessandro Marani, and Riccardo Rigon. 1991. “Geomorphological Dispersion.” Water Resources Research 27 (4): 513–25.

these papers constitute, on my side, quite a body of contribution on the topic.  There are other greater contributor and their work is cited in the review paper I cited for first.

However, the theory has some limitations. Its applicability is based on the:

• assumption that the rainfall is uniformly distributed (but C. Cudennec and coworkers were able to generalize it, see review paper)

having some recipes to get the effective runoff (i.e. separation of the total rainfall in quick surface water and baseflow and, besides, in evapotranspiration). Another limitation derives from the fact that

• the river network is dynamic (e.g. https://www.erc-dynet.it/publications/ or previous studies by M. Marani, Biswal and coworkers)

That’s why I went back to consider simpler reservoirs systems to get a clue of the interplay of the acting processes. This research work brought to the studies on representation of these reservoir models, to get the good old models streamlined for their structure, e.g.

• Bancheri, Marialaura, Francesco Serafin, and Riccardo Rigon. 2019. “The Representation of Hydrological Dynamical Systems Using Extended Petri Nets (EPN).” Water Resources Research 55 (11): 8895–8921.

and see especially the interactions among processes. The preprint-paper

• Rigon, R., and M. Bancheri. n.d. “On the Relations between the Hydrological Dynamical Systems of Water Budget, Travel Time, Response Time and Tracer Concentrations.”

is (among other things) a trial to get all the types of lumped models related with understanding where the diverse theories can be plugged together. Maybe a little convoluted as way of thinking but hopefully effective.
Another remark regards that once upon a time I was looking and satisfied with discharge, now I try to check the water and the energy budget and, therefore, the overall budget. Let’s see what comes next and if I am able to close the circle.  For who is still interested to implement a GIUH solver, please look at here.

P.S. - In the whole GEOframe/NewAge stuff, river geomorphology is present through the connectivity of the Hydrologic Response Units. Hence geomorphology is not absent: it is just not present in the simple way allowed by the GIUH that permitted to obtain those remarkable semi-analytic results present in the cited papers. 

The estimation of the discharge through the IUH explained

Time to time I go back to the estimation of the discharge through the Instantaneous Unit Hydrograph theory (IUH). It is interesting that this almost 90 year old concept is still alive and, being threathened by the studies on residence time from the physical point of view, is still valid when operational  activities are involved, and, in any case, as a benchmark tool.
IUH is at the core of our analysis of peak flows and of the code called PeakFlow in the Horton Machine, and it is known that the concept can include geomorphic characteristics. Many then can be interested in knowing how to estimate it and the manuscript you can access in Authorea, gives a definitive guide to do it.

The manuscript, can be found here.

Geomorphological modelling in 2020

This presentation, I gave in Perugia for the Italian Days of Hydrology 2015, is part of the long march towards the construction of a reasonable and modern physico-statistical theory of the water budget at catchment scale. This includes previous talks and posts on Residence/Travel time theories that were recently renewed by the work of my friends Rinaldo, Botter, Bertuzzo, Benettin (the younger scientific brother) and others.

It starts with a little of history, and it follows, at the beginning, the recent paper on GIUH theory.

 I do not pretend the presentation is very clear. Without any doubt it requires more than one reading, and the new ideas are just sketched in the last slide, not fully developed. Personally, however, I fill pretty satisfied with these seeds today, also because I feel that I could grab the core of the travel time distribution theories in a way that is understandable by most.

La teoria dell'idrogramma Istantaneo Unitario

L'idrogramma instantaneo unitario è una teoria semplificata dell'aggregazione e propagazione dei deflussi. Ecco nel seguito, le mie lezioni (per il corso di Costruzioni Idrauliche per Ingegneri Civili a Trento).  In 2016 I restructured it in parts, and according to new pieces of theory that I developed with Marialaura Bancheri and finding new inspiration form works by Gianluca Botter, Enrico Bertuzzo and Andrea Rinaldo on travel times. A good review is certainly Rigon et al., 2015. Unfortunetely slides are (so far) in Italian.

The new slides:

1   - Introduction

2   - Preliminary notions on travel and residence times

3   - Alternative heuristics (demonstration of equivalence by travel time distribution -TTD- and IUH)

4   - Some mathematical aspects of IUH theory

5   - A couple of examples (uniform  and exponential TTD and their names in classical iterpretation)

6   - The geomorphologic instantaneous unit hydrograph GIUH

7   - The width function unit hydrograph WFIUH (for this see also this post on the width function)

8   - The problem of the peak flows and maximum discharge

9   - Geomorphological dispersion (coming soon)

10 - Hillslope and channel contributions (coming soon)

The old slides

Slides e Audio:

1 - Introduzione allo IUH. Audio 2014 (31.1 MB);  Audio 2015 (19.5 Mb);
2 - Alcune distribuzioni dei tempi di residenza (5.8 Mb); Audio 2015: Alcune distribuzione per tempi di residenza (7.2 Mb).
3 - Idrogramma Istantaneo unitario Geomorfologico. Audio 2014  (16.8 Mb). Audio 2015 (20.3 Mb)
4 - Portate massime. Audio 2014 (17.4 Mb).
5 - L'idrogramma istantaneo unitario basato sulla funzione di ampiezza.

The even older ones:

All the old slides together: La teoria dell'idrogramma istantaneo unitario e dell'idrogramma istantaneo unitario 

The geomorphic unit hydrograph from a historical-critical perspective

I have just submitted to the review process a paper on the geomorphic unit hydrograph. (Now published here). It crosses close to four decades of progress the field of describing the treatment of the hydrologic response with the travel time concept, and hopefully was able to convey the core of the ideas behind this very nice (and effective) theory, and to open the way to new researches. The paper was accepted as a "State of  art paper" by Earth Surface Processes and Landforms.

Its abstract:
"In this paper we present a brief overview of Geomorphic Instanteneous Unit Hydro- graph (GIUH) theories and analyze their successful path without hiding their limitations. The history of the GIUH can be subdivided into three major chapters. The first chap- ter is based on the pioneering work by Rodríguez-Iturbe and Valdés (1979), and Gupta and Waymire (1983), which recognized that a treatment of water discharges with ”travel times” could give a rich interpretation of the theory of the Instantaneous Unit Hydrograph (IUH). We show how this was possible, what assumptions were made, which of these assumptions can be relaxed, and which have become obsolete and been discarded. The second chapter focuses on the Width Function Based IUH (WFIUH) approach and its achievements in assessing the interplay of the topology and geometry of the network with water dynamics. The limitations of the WFIUH approach are described, and a way to work around them is suggested. Finally, a new formal approach to estimating the water budget by ”travel times”, which derives from a suitable use of the water budget equation and some mixing hypotheses, has been disentangled and presented."

The little post on the width function can be considered a complementary reading too.  The pre-print of the paper is here.

Bibliography (including some more papers)


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Residence time approaches to the hydrological budgets

The natural evolution of geomorphic unit hydrograph approach to the hydrologic response is the analysis of residence time of water for any of the processes in the hydrological budget. Indeed,  there exists something already done in this direction of research, and can be found in the work of Andrea Rinaldo and collaborators. Gianluca Botter talked about the topic in his speech reported here, in a recent post. Without the claim to be very general, very deep, or very informed, I am collecting here some papers of the group on the subject.
Residence time is important under several aspects. The more direct application of theories per residence time seems to be the estimation of pollutants transport around the catchments, but the use of isotopic tracers to determine the age of water, immediately move their applications also the  understanding of the dynamics of runoff formation with mixing between various "waters". If plants are included, also evapotranspiration can become part of the game thus modifying what we expect (See also the post here with related references). Why not, then, make a step forward and use the theory also for temperature (as a passive tracer) ?
This could disclose a way to follow the entropy production and fluxes in the hydrological cycle at catchment scale: a topic in itself.

References

Benettin, P., A. Rinaldo, and G. Botter (2013), Kinematics of age mixing in advection-dispersion models, Water Resour. Res., 49, 8539–8551, doi:10.1002/2013WR014708.

E. Bertuzzo, M. Thomet, G. Botter, A. Rinaldo, Catchment-scale herbicides transport: Theory and application, Advances in Water Resources 52 (2013), p. 232–242

Botter, G., E. Bertuzzo, and A. Rinaldo (2010), Transport in the hydrologic response: Travel time distributions, soil moisture dynamics, and the old water paradox, Water Resour. Res., 46, W03514, doi:10.1029/2009WR008371.

Botter, G., E. Bertuzzo, and A. Rinaldo (2011), Catchment residence and travel time distributions:
The master equation, GEOPHYSICAL RESEARCH LETTERS, VOL. 38, L11403, doi:10.1029/2011GL047666

Botter, G., Catchment mixing processes and travel time distributions, Water Resour. Res., 48, W05545, doi:10.1029/2011WR011160.

F. Comola, B. Schaefli, A. Rinaldo and M. Lehning, Thermodynamics in the hydrologic response: Travel time formulation and application to Alpine catchments, Water resour. Res., Accepted manuscript online: 13 FEB 2015 03:59AM EST | DOI: 10.1002/2014WR016228

Cornaton, F., and P. Perrochet (2006), Groundwater age, life expectancy and tran- sit time distributions in advective-dispersive systems: 1. Generalized reservoir the- ory, Advances in Water Resources, 29(9), 1267–1291, doi:10.1016/j.advwatres.2005. 10.009. 

Cornaton, F. J. (2012), Transient water age distributions in environmental flow systems: The time-marching Laplace transform solution technique, Water Resources Research, 48(3), n/a–n/a, doi:10.1029/2011WR010606. 

Cvetkovic, V., C. Carstens, J.-O. Selroos, and G. Destouni (2012), Water and solute transport along hydrological pathways, Water Resources Research, 48(6), W06,537, doi:10.1029/2011WR011367. 

Ginn, T. R. (1999), On the distribution of multicomponent mixtures over generalized ex- posure time in subsurface flow and reactive transport: Foundations, and formulations for groundwater age, chemical heterogeneity, and biodegradation, Water Resources Research, 35(5), 1395–1407. 

Ginn, T. R., H. Haeri, A. Massoudieh, and L. Foglia (2009), Notes on Groundwater Age in Forward and Inverse Modeling, Transport in Porous Media, 79(1), 117–134, doi:10.1007/s11242-009-9406-1. 

Harman, C. J. (2014), Time-variable transit time distributions and transport: Theory and application to storage-dependent transport of chloride in a watershed, Water Resources Research, doi:10.1002/2014WR015707. 

Kirchner, J., X. Feng, and C. Neal (2001), Catchment-scale advection and dispersion as a mechanism for fractal scaling in stream tracer concentrations, Journal of Hydrology, 254(1-4), 82–101, doi:{10.1016/S0022-1694(01)00487-5}. 

McDonnell, J., et al. (2010), How old is the water ? Open questions in catchment transit time conceptualization, modelling and analysis, Hydrol. Processes, 24(12), 1745–1754.

McGuire, K. J., and J. J. McDonnell (2006), A review and evaluation of catchment transit time modelling, J. Hydrol., 330, 543–563.

Niemi, A. J. (1977), Residence time distribution of variable flow processes, Int. J. Appl. Radiat. Isot., 28, 855–860.

Rinaldo, A. and Rodriguez-Iturbe, I., Geomorphological theory of the hydrologic response, Hydrol Proc., vol 10, 803-829, 1996

Rinaldo, A., K. J. Beven, E. Bertuzzo, L. Nicotina, J. Davies, A. Fiori, D. Russo, and G. Botter (2011), Catchment travel time distributions and water flow in soils, Water Resour. Res., 47, W07537, doi:10.1029/2011WR010478. (See also the complimentary material: here)

van der Velde, Y., P. J. J. F. Torfs, S. E. A. T. M. van der Zee, and R. Uijlenhoet (2012), Quantifying catchment-scale mixing and its effect on time-varying travel time distributions, Water Resources Research, 48, doi:{10.1029/2011WR011310}. 

Weiler, M., B. L. McGlynn, K. J. McGuire, and J. J. McDonnell (2003), How does rainfall become runoff? a combined tracer and runoff transfer function approach, Water Resources Research, 39(11), n/a–n/a, doi:10.1029/2003WR002331. 

IUH and GIUH methods for modelling discharges (in Italian)

This contains the material, in Italian, that I use for my classes. It is old and the new material is here instead.

Please find below the old material with audio lectures.

Le slides sulla teoria dell'idrogramma istantaneo unitario e dell'idrogramma istantaneo unitario GEOmorfologico (credo un metodo non convenzionale di mostrare la materia per un corso di Costruzioni Idrauliche). Audio: IUH (31.1 Mb), Alcuni Tipici IUH (5.9 Mb), GIUH (16.8 Mb), sulle portate massime  (17.4 Mb)

Le note [pdf, 11 Mb] scritte sullo stesso tema e su altri di idrologia, funzionali al corso. Le note hanno ormai qualche anno e non sono completamente allineate con le slides. Tuttavia ritengo sia meglio averle che non averle.

Il tutorial di Peakflow (che è un modello per il calcolo delle onde di piena nei bacini naturali. La parte di teoria contiene una descrizione della teoria del calcolo delle portate massime - alle sezioni 5 e 6 - che è la stessa usata da Trento_p).

For the English an further references on GIUH see the English post (not yet ready).

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

The geomorphic structure of Peak Flows

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.