Water&life

Water and life
a hydrological perspective of research
Riccardo Rigon
16 December 2015
Whatdowecomefrom?Whatarewe?Wherearewegoing?-P.Gaugen1897

!2
Resembles Life what once was held of Light,
Too ample in itself for human sight?
…
S. Coleridge

!3
1
PROOF
2 R. RIGON ET AL.
Figure 1. A basin Q4subdivided into five HRUs and ‘exploded’ into
paths. Any path can be further subdivided into parts, called ‘states’,
and once each part is translated into mathematics the overall response
is the sum over the parts, having assumed a linear behavior. The blue
dots delineate the position of HRUs outlets. For instance, for HRU 1
the path is H1 ! c1 ! c2, and the travel time distribution is obtained
by the convolution of the probability distribution function in states H1,
c1 and c2, and analogously for the other paths. This figure is available
in colour online at wileyonlinelibrary.com/journal/espl
If an HRU is checked at an arbitrary time, a water molecule
in the HRU will have a residence time, which is the time spent
river courses, especially in the Tropics, were hardly known at
all. Therefore, the paper also tried to use information about
the shape and form of rivers, given by knowledge of Hor-
ton’s law of bifurcation ratios, length ratios, area ratios and
Schumm’s law of slopes (e.g. Rodríguez-Iturbe and Rinaldo,
1997; Cudennec et al., 2004). According to them, a river’s
drainage structure could be summarized by only a few num-
bers, mainly the bifurcation ratio and the length ratio: the
first was used to describe the geometrical extension of the
river network, and the second to provide the mean travel
times in each part of the network. To move from the drainage
structure to the hydrograph, a fundamental hypothesis had to
be made: during floods the wave celerity could be consid-
ered constant along the network, as supported by Leopold
and Maddock (1953). In theory, the constancy of celerity
was necessary only within each partition of the basin (i.e.
in each HRU or state used for its disaggregation) and not in
the overall network (as was actually done in many studies
for practical purposes), and actually this assumption can be
fully relaxed. Formally, the main equation summarizing all of
this reads:
Q.t/ D A
Z t
0
p.t /Je. /d
p.t/ D
X
2€
p .p 1 p /.t/
(1)
where A is the area of the basin, Je is the effective precip-
itation (i.e. the part of precipitation that contributes to the
discharge), p is the instantaneous unit hydrograph (i.e. the
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afterRigonetal,2015
The theory of the Geomorphologic Unit Hydrograph. Starting from the simplest
1
Q(t) = A
X
2
(Jeff ⇤ p 1
⇤ · · · ⇤ p ⌦
)(t)
R. Rigon

!4
1 Various elements here
• A Lagrangian view of the runoff production (integrated at basin scale)
• The geometry and topology of basins as part of the construction of the
probabilities
• The assessment the geometry counts more than the details of the
dynamics in generating the flood wave shape
• The view of basins as fractal geometries
• some analytic result
2
A little change in some paradigm
R. Rigon

!5
2 WATER RESOURCESRESEARCH,VOL. 28,NO. 4, PAGES 1095-1103,APRIL 1992
EnergyDissipation,RunoffProduction,and the Three-Dimensional
Structure of River Basins
IGNACIORODRfGUEZ-ITURBE,I,2ANDREARINALDO,3RICCARDORIGON,'*
RAFAELL. BRAS,2ALESSANDROMARANI,4 AND EDE IJJ/(Sz-VXSQUEZ2
Threeprinciplesof optimalenergyexpenditureare usedto derivethe mostimportantstructural
characteristicsobservedindrainagenetworks:(I) theprincipleofminimumenergyexpenditureinany
linkofthenetwork,(2)theprincipleofequalenergyexpenditureperunitareaof channelanywherein
the network,and(3) the principleof minimumtotal energyexpenditurein the networkas a whole.
Theirjoint applica,tionresultsin a unifiedpictureof themostimportantempiricalfactswhichhave
beenobservedin thedynamicsof thenetworkanditsthree-dimensionalstructure.They alsolink the
processof runoffproductionin thebasinwiththecharacteris.ticsof the network.
INTRODUCTION' THE CONNECTIVITY ISSUE
Well-developedriver basinsare made up of two interre-
latedsystems'the channelnetwork and the hillslopes.The
hillslopescontrolthe productionof runoffwhichin turn is
transportedthroughthe channelnetworktowardthe basin
outlet.Every branch of the network is linked to a down-
streambranchfor the transportation of water and sediment
butit is also linked for its viability, throughthe hillslope
system,toevery otherbranchin the basin.Hillslopesarethe
runoff-producingelements which. the n.etwork connects,
transformingthe spatially distributedpotential ,energyaris-
ingfromrainfallin the hillslopesto kineticenergyin theflow
throughthe channelreaches. In this paper we focuson the
drainagenetwork as it is controlled by energy dissipation
principles.It !spreciselytheneedfor effectiveconnectivity
thatleadsto the treelike structureof the drainagenetwork.
Figure!, from Stevens[1974], illustratesthis point. Assume
onewishestoconnectasetofpointsinaplanetoacommon
outletandfor illustrationpu.rposesassumethat everypoint
isequallydistantfrom its nearestneighbors.Two extreme
case each individualis supposedto operate at his best
completelyobliviousof his neighbors,but the systemas a
whole cannot survive.
Branchingpatterns accomplish connectivity combining
thebestof thetwo extremes;they are shortaswell asdirect.
The drainagenetwork, as well as many other natural con-
nectingpat.terns, is basically a transportationsygtemfor
which the treelike structure is a most appealing structure
from the point of view of efficiency in the construction,
operation and maintenance of the system.
The drainage network accomplishes connectivity for
transportationin three dimensions working against a resis-
tance force derived from the friction of the flow with the
bottomandbanksof the channels, the resistanceforce being
itself a function of the flow and the channel characteristics.
This makesthe analysisof the optimal connectivity a com-
plex problem that cannot be separated from the individual
optimalchannelconfigurationandfrom .thespatialcharac-
terization of the runoff production inside the basin. The
questionis whethertherearegeneralprinciplesthatrelate
thestructureof the network and its individualelementsWith
If geometry counts, from where geometry comes from ?
1096 RODFffGUEZ-ITURBEET AL,' STRUCTUREOF DRAINAGE NETWORKS
233.1,•--303,3
L- 3.73
Fig. 1. Different patterns of connectivity of a set of equally
spacedpointstoa commonoutlet.L r isthetotallengthof thepaths,
andL is the averagelengthof the pathfrom a pointto the outlet. In
theexplosioncase,L•2)referstothecasewhenthereisaminimum
displacementamong the points so that there is a different path
betweeneachpoint and the outlet [from Stevens,1974].
network; (2) the principle of equal energy expenditureper
unit area of channel anywhere in the network; and (3) the
principleof minimumenergyexpenditurein the networkas
a whole. It will be shown that the combination of these
principlesis a sufficientexplanationfor the treelike structure
of the drainagenetwork and, moreover, that they explain
equalthesumofthecubesoftheradiiofthedaughter
vessels(see,forexample,Sherman[1981]).Heassumedthat
twoenergytermscontributetothecostofmaintainingblood
flowin anyvessel:(1) theenergyrequiredto overcome
frictionasdescribedbyPoiseuille'slaw,and(2)theenergy
metabolicallyinvolvedin the maintenanceof theblood
volumeandvesseltissue.Minimizationofthecostfuncfi0a
leadstotheradiusofthevesselbeingproportionaltothelB
powerof the flow. Uylings[1977]hasshownthatwhen
turbulentflowisassumedinthevessel,ratherthanlain'mar
conditions,thesameapproachleadstotheradiusbe'rag
proportionalto the 3/7 power of the flow. The secorot
principlewasconceptuallysuggestedbyLeopoldandLang.
bein[1962]in theirstudiesof landscapeevolution.It isof
interestto addthatminimumrate of workprincipleshave
been appliedin severalcontextsin geomorphicresearch.
Optimaljunctionangleshavebeenstudiedinthiscontextby
Howard[1971],Roy [1983],andWoldenbergandHorsfield
[1986],amongothers.Also the conceptof minimumworkas
a criterion for the developmentof streamnetworkshasbeen
discussedunder differentperspectivesby Yang[1971]a•d
Howard [1990], amongothers.
ENERGY EXPENDITURE AND OPTIMAL NETWORK
CONFIGURATION
Considera channelof width w, lengthL, slope$, andflow
depthd. The forceresponsiblefor theflowisthedownslope
componentof the weight, F1 = ptldLw sin /3 = ptIdLwS
where sin/3 = tan/3 = S. The force resistingthemovement
is the stressper unit area times the wetted perimeterarea,
F2 = •(2d + w)L, where a rectangularsectionhasbeen
assumed in the channel. Under conditions of no acceleration
of the flow, F1 = F 2, and then r = p.qSRwhereR isthe
hydraulicradiusR = Aw/Pw = wd/(2d + w), Awand
beingthe cross-sectionalflow area, andthewettedperimeter
ofthesection,respectively.In turbulentincompressibleflow
theboundaryshearstressvariesproportionallytothesqua•
oftheaveragevelocity,r = Cfpv2,whereCfisadimen.
sionlessresistancecoefficient.Equatingthetwoexpressions
for,, oneobtainsthewell-knownrelationship,S= Cfv2/
(R•/),whichgivesthelossesduetofrictionperunitweightof
flowperunitlengthofchannel.Thereisalsoanexpendi•
1
Why river are more like
this instead that in
other forms ?
E = argmin
Conﬁgurations
(
X
i2all sites
Ai )
R. Rigon

!6
2
Evolution and selection of river networks: Statics,
dynamics and complexity
Andrea Rinaldo ∗ †
, Riccardo Rigon ‡
, Jayanth R. Banavar §
, Amos Maritan ¶
, and Ignacio Rodriguez-Iturbe ∥
∗
Laboratory of Ecohydrology ECHO/IIE/ENAC, École Polytechnique Fédérale Lausanne EPFL, Lausanne CH-1015, CH,†
Dipartimento IMAGE, Universitá di Padova, I-35131
Padova, Italy,‡
Dipartimento di Ingegneria Civile e Ambientale, Università di Trento, Italy,§
Department of Physics, University of Maryland, College Park, Maryland 20742,
USA,¶
Dipartimento di Fisica e INFN, Padova, Italy, and ∥
Department of Civil and Environmental Engineering, Princeton University
This contribution is part of the special series of Inaugural Articles by members of the National Academy of Sciences elected on May 1, 2012 (AR).
Moving from the exact result that drainage network configurations
minimizing total energy dissipation are stationary solutions of the
general equation describing landscape evolution, we review the static
properties and the dynamic origins of the scale-invariant structure of
optimal river patterns. Optimal Channel Networks (OCNs) are fea-
sible optimal configurations of a spanning network mimicking land-
Rather, each of them can be derived through scaling relations
postulating the knowledge of geometrical constraints. And, as
is common in any good detective novel, our story comes with
unexpected twists. The first surprise was that the observa-
tional exponents do not fall into any known standard univer-
sality class of spanning or directed trees with equal weight. A
General principles acting
22 • The main idea here is that river networks forms on the
basis of minimal energy expenditure
• Maximum Entropy and minimal energy are in fact
principles acting on a large set of systems whose
functioning can be attributed to some “network”
connectivity
• This is still an open question in literature …
PNAS, 2014
Ideas behind
R. Rigon

!7
32 13 April, 1995
Self-Organisation or how forms emerge
and are continuously destroyed by diffusion
Self organising criticality ? And its destruction
R. Rigon

!8
Many evidences showed that it could be the same
Same as optimality ?
R. Rigon

!9
On Hack’s law
Riccardo Rigon,1,2 Ignacio Rodriguez-Iturbe,1 Amos Maritan,3
Achille Giacometti,4 David G. Tarboton,5 and Andrea Rinaldo6
Abstract. Hack’s law is reviewed, emphasizing its implications for the elongation of river
basins as well as its connections with their fractal characteristics. The relation between
Hack’s law and the internal structure of river basins is investigated experimentally through
digital elevation models. It is found that Hack’s exponent, elongation, and some relevant
fractal characters are closely related. The self-affine character of basin boundaries is
shown to be connected to the power law decay of the probability of total contributing
areas at any link and to Hack’s law. An explanation for Hack’s law is derived from scaling
arguments. From the results we suggest that a statistical framework referring to the scaling
invariance of the entire basin structure should be used in the interpretation of Hack’s law.
1. Introduction
Hack [1957] demonstrated the applicability of a power func-
tion relating length and area for streams of the Shenandoah
Valley and adjacent mountains in Virginia. He found the equa-
tion
L 5 1.4A0.6
(1)
where L is the length of the longest stream in miles from the
outlet to the divide and A is the corresponding area in square
miles. Hack also corroborated his equation through the mea-
surements of Langbein [1947], who had measured L and A for
nearly 400 sites in the northeastern United States. Gray [1961]
later refined the analysis, finding a relationship L } A0.568
.
Many other researchers have corroborated Hack’s original
study, and, although the exponent in the power law may slightly
vary from region to region, it is generally accepted to be
slightly below 0.6. Equation (1) rewritten as L } Ah
with h .
0.5 is usually termed “Hack’s law.”
Muller [1973], on the basis of extensive data analysis of
several thousand basins, found that the exponent in Hack’s
equation was not constant but that it changed from 0.6 for
basins less than 8,000 square miles (20,720 km2
) to 0.5 for
basins between 8,000 and 105
square miles (20,720–259,000
km2
), and to 0.47 for basins larger than 105
square miles
(259,000 km2
).
As Mesa and Gupta [1987] point out, Muller’s empirical
observations are not consistent with the implications of the
troduced in the classic paper of Shreve [1966]. In fact, they
theoretically derived the value of Hack’s exponent, h, for the
random topology model of channel networks as
h~n! 5
1
2 Sp 1 ~p/n!1/ 2
p 2 1/n D (2)
where n is the basin’s magnitude. Equation (2) implies a con-
tinuously decreasing h(n) with an increasing n. For n 5
10,100, and 500 the exponent h(n) is 0.68, 0.530, and 0.513,
respectively. When n tends to infinity, h tends to the asymp-
totic value of 0.5. This result makes clear the importance of the
magnitude of the network in the exponent h under the pre-
mises of the random topology model. Further and more gen-
eral results on random trees can also be found in work by
Durret et al. [1991].
The classical explanation for the exponent h being larger
than 0.5 was to conjecture that basins have anisotropic shapes
and tend to become narrower as they enlarge or elongate. The
hypothesis of basin elongation was verified by Ijjasz-Vasquez et
al. [1993] under the framework of optimal channel networks
(OCNs), which are the result of the search of fluvial systems
for a drainage configuration whose total energy expenditure is
minimized [Rodriguez-Iturbe et al., 1992a; Rinaldo et al., 1992].
Thus Hack’s relationship may result from the competition and
minimization of energy in river basins.
Mandelbrot [1983] suggested that an exponent larger than
0.5 in L } Ah
could arise from the fractal characters of river
channels which cause the measured length to vary with the
WATER RESOURCES RESEARCH, VOL. 32, NO. 11, PAGES 3367–3374, NOVEMBER 1996
4
Back almost from where we started
Misura ciò che e misurabile e rendi misurabile
ciò che non lo è.
Measure what is measurable and make
measurable what is not
Galileo Galilei
pretation of the empirical evidence. Specifically, we focus on
the internal structure of basins whose extension is in the range
of 50–2000 km2
. Theoretical and experimental motivations
justify this choice. At lower scales, diffusive processes interact
with concentrative erosive processes responsible for concave
landforms, and area-length relationships are altered. At very
large scales geologic controls dominate. We expect instead that
at medium to small scales, self-organization plays a predomi-
nant role, yielding the observed recurrent characters of river
basins. Furthermore, Montgomery and Dietrich’s [1992] collec-
tion of data shows that a composite data set, from 100 m2
up
to 107
km2
, can reasonably be fitted with an exponent of 0.5 in
Hack’s relation, and hence a large span of orders of magnitude
in basin area is not the most adequate to fit as a whole when
investigating Hack’s equation.
2. Does Hack’s Law Imply Elongation?
This section considers the connection between Hack’s law,
the fractal sinuosity of stream channels, and the elongation of
river basins. The meaning of the terms “elongation” and “frac-
tal sinuosity” first needs to be defined.
The planar projection of river basins may be characterized by
Shapes will be c
for all areas, A,
Alternatively, if
constant, basin
constant we no
Constant a(L)
creasing with A
One interpre
along channels
while s remains
h 5 0.57:
This suggests t
that according t
Another inte
brot [1983] is th
stream length, L
where fL is a
assumed to be s
and thus L } A
The more gene
streams are fra
watershed shap
nent H [e.g., M
1993]:
where H , 1,
and a(L) beco
For H , 1, a(
gation. Using (1
which combined
Thus we have [
which relates se
fL, and Hack’s
Maritan et al. [1
differs from pre
Figure 1. Sketch of a river basin; its diameter, L; and its
width, L'. Some subbasins are also drawn. For any subbasin
the longest sides of the rectangle enclosing the network are
parallel to the diameter L, defined as the straight line from
the outlet to the farthest point in the basin. The shortest sides
are L'.
RIGON ET AL.: ON HACK’S LAW3368
L = ↵A
1
R. Rigon

!10
42
In this case measuring is measuring terrain. The tools are
Digital Elevation Models … and GISes
British Society for Geomorphology Geomorphological Techniques, Chap. X, Sec. X (2012)
associated properties such as the starting
and ending point’s of a link, elevation drop to
determine average slope of each links, etc.
The example of pfafstteter coding scheme for
channel and hillslope is provided in figure 3
for Posina river basin in North East Italy.
Figure 3: The pfafstetter enumeration
scheme in uDig GIS spatial toolbox for
channel networks and hillslopes for Posina
river basin in Northaest Italy
3.4 Hillslope toolbox
The tools in Hillslope menu are presented in
transversal curvatures, topographic class (Tc)
tool subdivides the sites of a basin in different
topographic classes. The program has two
outputs: the more detailed 9 topographic
classes (Parsons, 1988) and an aggregated
topographic class with three fundamental
classes.
Planar curvature represents the degree of
divergence or convergence perpendicular to
the flow direction, and profile curvature
shows convexity or concavity along the flow
direction. By combing these two landform
curvatures, topographic class (Tc) tools
produce 9 classes, which are three types of
planar (parallel–planar, divergent-planar,
convergent-planar sites), three types of
convex (parallel-convex, divergent-convex,
and convergent-convex sites), and three
concave (divergent-concave, parallel-
concave, and convergent-concave sites).
These attributes can be summarized just in
With I did a few GIS (now all is being ported in
GVsig)
TheuDigSpatialToolboxforhydro-geomorphicanalysisby
computer
RiccardoRigon1
,AndreaAntonello2
,SilviaFranceschi2
,WuletawuAbera1
,Giuseppe
Formetta3
1
DepartmentofCivil,Environmental,andMechanicalEngineering,TrentoUniversity,Italy
(riccardo.rigon@ing.unitn.it)
2
Hydrologiss.r.l.ViaSiemens,19Bolzano(andrea.antonello@hydrologis.com)
3
UniversityofCalabria,Calabria,Italy(giuseppeform@libero.it)
ABSTRACT:Geographicalinformationsystems(GIS)arenowwidelyusedinhydrologyand
geomorphologytoautomatebasin,hillslope,andstreamnetworkanalyses.Severalcommercial
GISpackageshaveincorporatedmorecommonterrainattributesandterrainanalysisprocedures.
Thesesoftwarepackagesare,however,oftenprohibitivelyexpensive.JGrasstoolsinuDigGIS
insteadisfreeandOpenSource.uDigisanopensourcedesktopapplicationframework,builtwith
EclipseRichClient(RCP)technology,whichismainlyforsoftwareandmodelbuildingcommunity.
However,recentlyuDigGISaddedsignificantresourcesforenvironmentalanalysis.Spatial
toolboxofuDigGISisaspecializedGIStoolsfortheanalysisoftopographyforgeomorphometry
andhydrology.Largenumbersoftoolsareembeddedinthetoolboxforterrainanalysis,river
networkdelineation,andbasintopologycharacterization,andaredesignedtomeettheresearch
needsforacademicscientistswhilebeingsimpleenoughinoperationtobeusedforstudent
instructionandprofessionaluse.JGrasstoolsanduDigaredevelopedinJavathatensurethe
portabilityinalloperatingsystemsrunningaJavaVirtualMachine.Theaimofthispaperisto
presenttheSpatialtoolboxofuDigGISforgeomorphologicalstudy.
KEYWORDS:Hydrology,geomorphology,GIS,OpenSource,catchmentanalysis,network
extraction
No more without a GIS ?
R. Rigon

!11
GEOtop: A Distributed Hydrological Model with Coupled Water and Energy Budgets
RICCARDO RIGON AND GIACOMO BERTOLDI
Department of Civil and Environmental Engineering, CUDAM, University of Trento, Trento, Italy
THOMAS M. OVER
Department of Geology/Geography, Eastern Illinois University, Charleston, Illinois
(Manuscript received 1 March 2005, in final form 11 August 2005)
ABSTRACT
This paper describes a new distributed hydrological model, called GEOtop. The model accommodates
very complex topography and, besides the water balance, unlike most other hydrological models, integrates
all the terms in the surface energy balance equation. GEOtop uses a discretization of the landscape based
on digital elevation data. These digital elevation data are preprocessed to allow modeling of the effect of
topography on the radiation incident on the surface, both shortwave (including shadowing) and longwave
(accounting for the sky view factor). For saturated and unsaturated subsurface flow, GEOtop makes use of
a numerical solution of the 3D Richards’ equation in order to properly model, besides the lateral flow, the
vertical structure of water content and the suction dynamics. These characteristics are deemed necessary for
consistently modeling hillslope processes, initiation of landslides, snowmelt processes, and ecohydrological
phenomena as well as discharges during floods and interstorm periods. An accurate treatment of radiation
inputs is implemented in order to be able to return surface temperature. The motivation behind the model
is to combine the strengths and overcome the weaknesses of flood forecasting and land surface models. The
former often include detailed spatial description and lateral fluxes but usually lack appropriate knowledge
of the vertical ones. The latter are focused on vertical structure and usually lack spatial structure and
prediction of lateral fluxes. Outlines of the processes simulated and the methods used to simulate them are
given. A series of applications of the model to the Little Washita basin of Oklahoma using data from the
Southern Great Plains 1997 Hydrology Experiment (SGP97) is presented. These show the model’s ability
to reproduce the pointwise energy and water balance, showing that just an elementary calibration of a few
parameters is needed for an acceptable reproduction of discharge at the outlet, for the prediction of the
spatial distribution of soil moisture content, and for the simulation of a full year’s streamflow without
additional calibration.
1. Introduction: Design prerequisites
The study of river basin hydrology is focused on the
analysis of the interactions between the near-surface
soil and the atmospheric boundary layer (ABL), which
occur mainly through the mediation of the soil itself,
the vegetation, and the turbulent and radiative energy
transfers taking place on the earth’s surface, and pos-
sible feedbacks from the ABL (e.g., soil moisture–
and momentum exchanges between the land surface
and the atmosphere at several scales (Abbott 1992;
Reggiani et al. 1999), with the purpose of creating mod-
els that can provide improved mid- and long-term hy-
drologic forecasts and better prediction of the impacts
on the hydrologic cycle and on the earth’s ecosystems
resulting from changes in land use and in the climate
(Grayson and Blöschl 2000). Though inspired by this
trend toward improved predictions, the initial motiva-
JUNE 2006 R I G O N E T A L . 371
Geosci. Model Dev., 7, 2831–2857, 2014
www.geosci-model-dev.net/7/2831/2014/
doi:10.5194/gmd-7-2831-2014
© Author(s) 2014. CC Attribution 3.0 License.
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
S. Endrizzi1, S. Gruber2, M. Dall’Amico3, and R. Rigon4
1Department of Geography, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland
2Carleton University, Department of Geography and Environmental Studies, 1125 Colonel By Drive, Ottawa,
ON K1S 5B6, Canada
3Mountaineering GmbH, Siemensstrasse 19, 39100 Bozen, Italy
4Dipartimento di Ingegneria Civile, Ambientale e Meccanica e CUDAM, Università di Trento, Via Mesiano 77,
38123 Trento, Italy
Correspondence to: S. Endrizzi (stefano.end@gmail.com)
Received: 4 October 2013 – Published in Geosci. Model Dev. Discuss.: 3 December 2013
Revised: 25 September 2014 – Accepted: 30 September 2014 – Published: 3 December 2014
A second thread
Hyperresolution hydrological modeling
61
R. Rigon

!12
What the hell are you doing ?
After a decade of smart models of
river networks and papers on river
hydro-geomorphology Rigon seems
to have abandoned simplicity and
creativity, for choosing
overcomplicate machineries based
on a mechanistic view of the world.
Is, probably, a sign of decline.
(No good research after 45 ?)
But overall, what I'm craving? A little
perspective.
Anton Egò
A debate
62
R. Rigon

!13
JackCook,WoodsHoleOceanographicInstitution
How much water there is on Earth ?
Around 1400 millions of km3
Shiklomanov and Skolov (1983)
A flash back
R. Rigon

!14
Collocazione Area coperta Volume % % delle acque
[106
km2
] [106
km3
] dolci
Oceani 361.300 1.338 96.5 -
Acque di falda 134.8 23.4 1.7 -
Acque di falda dolci 10.530 0.76 30.1
Umidit`a del suolo 82 0.0165 0.001 0.05
Ghiacci e neve perenni 16.2275 24.0641 1.74 68.7
Antartico 13.980 21.600 1.56 61.7
Groenlandia 1.8024 2.340 0.17 6.68
Isole artiche 0.2261 0.0835 0.006 0.24
Aree montane 0.224 0.0406 0.003 0.12
Permafrost 21 0.3 0.022 0.86
Acque nei laghi 2.0587 0.1764 0.013 -
Acque dolci nei laghi 1.2364 0.091 0.007 0.26
Acque salate nei laghi 0.8223 0.0854 0.006 -
Lagune e paludi 2.682.6 0.01147 0.0002 0.006
Acque nei ﬁumi 148.8 0.00212 0.0002 0.0006
Acqua negli esseri viventi 510 0.0012 0.0.0001 0.0003
Acqua nell’atmosfera 510 0.0129 0.001 0.04
Totale d’acqua 510 1385.98561 100 -
Totale d’acqua dolce 148.8 35.02921 2.53 100
From: Global Change in the Geosphere-Biosphere, NRC, 1986, Shiklomanov and Skolov
(1983).
But also: Oki et al., 2001; Shiklomanov, I. A., 2000; Vorosmarty et al., 2000; Hanasaki et
al., 2006
Hydrological storages
Numbers
R. Rigon

!15
modificatodaWallaceandHobbs,1977Energy
R. Rigon
between 0.2 and 4, e.g.. Smil, 2003
possible ~ 10 and 11 respectively over
land masses, after L’Ecuyer et al., 2015

!16
OkiandKanae,2006
Fluxes and Interactions
R. Rigon
πάντα ῥεῖ
A very recent: Rodell et al., 2015

regulates the climate
!17
sustains life on Earth
sculpt Earth’s surfaces
The hydrological cycle
it is at the origin of fundamental ecosystem services
Why it is important
R. Rigon

!18
Venus Earth Mars
96.5% CO2
3.5% N2
93.5% CO2
2.7% N2
78 % N2
31% O2
However
Entanglements
R. Rigon

!19
Studies on photosynthesis say that
O2
is produced by plants splitting the water molecule, while carbon dioxide
oxygen is fixed in plants themselves
So life creates Earth atmosphere
and the hydrological cycle we see
today
Other’s planets has a very different atmosphere
Entanglements and feedbacks
R. Rigon

!20
Dear Anton:
You asked for a little perspective*, which I take seriously. So far
surface hydrology modelling was essentially estimating discharges
Now is:
• water mass conservation
• energy conservation
• appropriate momentum treatment
As proper to any physical science
So
63
R. Rigon
* Quotes

!21
64
This was also a way to cope with the
entire terrestrial water cycle, and
the whole set of processes
according to the basic known laws
How can we deal with nonlinear feedbacks if we
linearised all the interactions ?

!22
GEOtop: a distributed model process based model for the remote sensing era - Princeton 2004
explained after Dietrich et al. 2003
R. Rigon
Does it correspond to realism ?
HenriRosseau,TheDream,1910

!23
Richards equation +
van Genuchten parameterization +
Mualem derived conductivity
Energybudget
(withsomeassumptions)
Flux-gradient relationship
(Monin - Obukov)
Diffusive approximation to shallow
water equation
Double layer vegetation
Radiation
Snowmetamorphism
Many Equations
R. Rigon

!24
Se :=
w r
⇥s r
C(⇥) :=
⇤ w()
⇤⇥
Se = [1 + ( ⇥)m
)]
n
~Jv = K(✓w)~r h
K( w) = Ks
⇧
Se
⇤
1 (1 Se)1/m
⇥m⌅2
<latexitsha1_base64="tYHCApFiY8slQcKMwQxwGacE74A=">AAAA+3icSyrIySwuMTC4ycjEzMLKxs7BycXNw8XFy8cvEFacX1qUnBqanJ+TXxSRlFicmpOZlxpaklmSkxpRUJSamJuUkxqelO0Mkg8vSy0qzszPCympLEiNzU1Mz8tMy0xOLAEKBcQLKBvoGYCBAibDEMpQZoACoHJDdElMRqiRnpmeQSBCG4e0koahuYNHQGhyStfknfsPQoQZGaHyggyo4BQAVIE48g==</latexit>
<latexit sha1_base64="tYHCApFiY8slQcKMwQxwGacE74A=">AAAA+3icSyrIySwuMTC4ycjEzMLKxs7BycXNw8XFy8cvEFacX1qUnBqanJ+TXxSRlFicmpOZlxpaklmSkxpRUJSamJuUkxqelO0Mkg8vSy0qzszPCympLEiNzU1Mz8tMy0xOLAEKBcQLKBvoGYCBAibDEMpQZoACoHJDdElMRqiRnpmeQSBCG4e0koahuYNHQGhyStfknfsPQoQZGaHyggyo4BQAVIE48g==</latexit>
Many Equations
R. Rigon

!25
Many Results
R. Rigon
0
5
10
15
20
25
30
Discharge
[m
³/s]
Precipitation
[m
m
]
11.2009
01.2010
03.2010
11.2010
05.2010
07.2010
09.2010
40
30
20
10
0
m
easured
sim
ulated
Figure
5:
Sim
ulated
and
m
easured
discharge
atthe
gauge
in
Raisting
forthe
hydrologic
year2010.
0
5
10
15
20
25
30
Discharge
[m
³/s]
Precipitation
[m
m
]
01.2011
03.2011
11.2011
05.2011
07.2011
09.2011
40
30
20
10
0
m
easured
sim
ulated
d
m
easured
dischargeatthegaugeRaisting
forthehydrologicyear
36
a)
c)
Hingerletal.,2013

!26
HYDROLOGICAL PROCESSES
Hydrol. Process. 18, 3667–3679 (2004)
Published online in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/hyp.5794
The GEOTOP snow module
Fabrizio Zanotti, Stefano Endrizzi, Giacomo Bertoldi and Riccardo Rigon*
Department of Civil and Environmental Engineering CUDAM, Università di Trento, Trento, Italy
Abstract:
A snow accumulation and melt module implemented in the GEOTOP model is presented and tested. GEOTOP, a
distributed model of the hydrological cycle, based on digital elevation models (DEMs), calculates the discharge at
the basin outlet and estimates the local and distributed values of several hydro-meteorological quantities. It solves
the energy and the mass balance jointly and deals accurately with the effects of topography on the interactions
among radiation physics, energy balance and the hydrological cycle. Soil properties are considered to depend on soil
temperature and moisture, and the heat and water transfer in the soil is modelled using a multilayer approach. The
snow module solves for the soil–snow energy and mass exchanges, and, together with a runoff production module, is
embedded in a more general energy balance model that provides all the boundary conditions required. The snowpack
is schematized as a single snow layer where a limited number of physical processes are described. The module can
be seen essentially as a parameter-free model. The application to an alpine catchment (Rio Valbiolo, Trentino, Italy),
monitored by an in situ snow-depth sensor, is discussed and shown to give results comparable to those of more
complex models. Copyright © 2004 John Wiley & Sons, Ltd.
KEY WORDS snow; snowmelt; distributed modelling; energy balance
INTRODUCTION
A suitable model of the hydrological cycle of mountain catchments and basins located at higher latitudes must
account for snow accumulation and melting and for soil freezing. The presence of snow modifies the energy
and mass balances, and snowmelt is responsible for most of the runoff during the melting season. Snowmelt
processes have been modelled with different approaches of variable complexity, ranging from simple methods
based only on temperature measurements (Morris, 1985) to complete multilayer models based on an energy
balance (Marks et al., 1999), like the one-dimensional US Army Cold Regions Research and Engineering
Laboratory Model (SNTHERM; Jordan, 1991). This model makes use of a mixture theory to describe all
the dry air, dry soil and water phases dynamics and thermal constituents, and it requires a large number
of snow layers to be set and short integration intervals for the simulations. SNTHERM is a reference for
the description of point processes (Jin et al., 1999), but owing to its complexity it is not suited to direct
implementation within a distributed model of the hydrological cycle. In fact, it neglects all those phenomena
related to lateral flows and surface conditions whose accurate description could be more important than that
The Cryosphere, 5, 469–484, 2011
www.the-cryosphere.net/5/469/2011/
doi:10.5194/tc-5-469-2011
© Author(s) 2011. CC Attribution 3.0 License.
The Cryosphere
A robust and energy-conserving model of freezing
variably-saturated soil
M. Dall’Amico1,*, S. Endrizzi2, S. Gruber2, and R. Rigon1
1Department of Civil and Environmental Engineering, University of Trento, Trento, Italy
2Department of Geography, University of Zurich, Winterthurerstrasse 190, Zurich, Switzerland
*now at: Mountain-eering srl, Via Siemens 19, Bolzano, Italy
Received: 29 June 2010 – Published in The Cryosphere Discuss.: 11 August 2010
Revised: 18 May 2011 – Accepted: 19 May 2011 – Published: 1 June 2011
Abstract. Phenomena involving frozen soil or rock are im-
portant 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 character-
istics and is often difficult to handle with normal methods
and numerical physically-based (Zhang et al., 2008). Em-
pirical and semiempirical algorithms relate ground thawing-
freezing depth to some aspect of surface forcing by one or
more experimentally established coefficients (e.g. Anisimov
et al., 2002). Analytical algorithms are specific solutions to
heat conduction problems under certain assumptions. The
most widely applied analytical solution is Stefan’s formula-
71
Cryospheric Processes
⇥w = ⇥r + (⇥s ⇥r) ·
⇤
1 + ⇤w0
Lf
g T0
(T T⇥
) · H(T T⇥
)
⇥n⌅ m
R. Rigon

!27
Si può misurare, si può prevedere …
27
R. Rigon

!28
Hydrological modelling with components: A GIS-based open-source
framework
G. Formetta a,*, A. Antonello b,1
, S. Franceschi b,1
, O. David c
, R. Rigon a
a
Department of Civil, Enviromnental and Mechanical Engineering e CUDAM, 77 Mesiano St., Trento I-38123, Italy
b
Hydrologis S.r.l., Bolzano, BZ, Italy
c
Department of Civil and Environmental Engineering, Department of Computer Science, Colorado State University, Fort Collins, CO 80523, USA
a r t i c l e i n f o
Article history:
Received 7 January 2013
Received in revised form
13 January 2014
Accepted 14 January 2014
Available online
a b s t r a c t
This paper describes the structure of JGrass-NewAge: a system for hydrological forecasting and
modelling of water resources at the basin scale. It has been designed and implemented to emphasize the
comparison of modelling solutions and reproduce hydrological modelling results in a straightforward
manner. It is composed of two parts: (i) the data and result visualization system, based on the
Geographic Information System uDig and (ii) the component-based modelling system, built on top of the
Object Modelling System v3. Modelling components can be selected, adapted, and connected according
Contents lists available at ScienceDirect
Environmental Modelling & Software
journal homepage: www.elsevier.com/locate/envsoft
Environmental Modelling & Software 55 (2014) 190e200
One Lesson Learned from GEOtop and GIS research
GEOtop code has a mature C++ implementation of solid algorithms and
physics. However it is conceived as a monolithic structure, in which
improvements can be made with difficulty and after overcoming a huge
learning curve. At the same time, the user experience is far by being optimal,
and must be structurally improved.
Therefore, during the same evolution of the model, it was envisioned to
migrate it towards a more flexible informatics where improvements,
maintenance and documentation and research reproducibility could be
pursued more easily.
Informatics for Hydrology (and geoscience)9
The manifesto (mostly still valid) is here.
R. Rigon

!29
10
Upscaling
Does it means you want more money ?
(An EU officier at the Aquaterra defence in Bruxelles)
NO. It means we want
• t o s i m u l a t e l a r g e b a s i n s , w i t h h u m a n
infrastructure besides the natural complexity.
It requires
• the implementation and testing of new physical-
statistical models.
1
R. Rigon
See also: Botter et al., 2010; Rinaldo et al., 2015

!30
A physical-statistical theory of the Hydrologic cycle
102
Adige River
R. Rigon

!31
A physical-statistical theory of the Hydrologic cycle
10
Blue Nile
3
R. Rigon

!32
RRECTED
PROOF
Journal Code: Article ID Dispatch: 17.11.15 CE:
E S P 3 8 5 5 No. of Pages: 11 ME:
EARTH SURFACE PROCESSES AND LANDFORMS
Earth Surf. Process. Landforms (2015)
Copyright © 2015 John Wiley & Sons, Ltd.
Published online in Wiley Online Library
(wileyonlinelibrary.com) DOI: 10.1002/esp.3855
State of Science
The geomorphological unit hydrograph from a
historical-critical perspective
Riccardo Rigon,1* Marialaura Bancheri,1
Giuseppe Formetta2
and Alban de Lavenne3
1
Dipartimento di Ingegneria Civile e Ambientale, Università di Trento, 38123 Trento, Italy
2
Civil and Environmental Engineering Department, School of Mines, Golden, CO 80401, USA
3
Faculté des Sciences etQ1 Technique, Géo-Hydrosystèmes Continentaux
Received 17 September 2015; RevisedQ2 ; Accepted 6 October 2015
*Correspondence to: Riccardo Rigon, Dipartimento di Ingegneria Civile e Ambientale, Università di Trento, 38123 Trento, Italy. E-mail: riccardo.rigon@ing.unitn.it
ABSTRACT: In this paper we present a brief overview of geomorphological instantaneous unit hydrograph (GIUH) theories and
analyze their successful path without hiding their limitations. The history of the GIUH is subdivided into three major sections The
ﬁrst is based on the milestone works of Rodríguez-Iturbe and Valdés (Water Resources Research 1979; 15(6): 1409–1420) and
Gupta and Waymire (Journal of Hydrology 1983; 65(1–3): 95–123), which recognized that a treatment of water discharges with
‘travel times’ could provide 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 section 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 hypotheses, has been introduced and disentangled.
Copyright © 2015 John Wiley & Sons, Ltd.
KEYWORDS: Geomorphological Unit Hydrograph; Hydrologic Response; Travel time theories
Introduction
Here we discuss the evolution of the geomorphological unit
hydrograph in its attempts to assess the interplay of geomor-
of its parts or a group of hillslopes, that mathematical, phys-
ical or computational arguments suggest to treat as a whole.
For the purposes of modeling, each of these HRUs is consid-
ered, at least initially, as an ‘atomic’ part of the basin in which
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02
03
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Almost back to the beginning
10
In this retrospective of the last 35 years of the geomorphological unit
hydrograph, there is a seed for the next development of a large scale
theory, according to travel times.
4
Q(t) p Q(t ⌧|t) = f(t ⌧|t)J(⌧)

!33
So what is furtherly next ?
R. Rigon
has to be quietly evolved. Numerics revised. Vegetation dynamics
introduced. Informatics changed to the new paradigm of components.
Alternative equations and parameterisations selected. Usability enhanced.
Parallelism introduced. (Big) Data assimilation used.
It is already a good model but:
Towards 3.0

!34
computationally demanding. Therefore, several eco-
hydrological models still use simpliﬁed solutions of
carbon285
) concepts that empirically link carbon
assimilation to the transpired water or intercepted
Energy exchanges
Longwave
radiation
incoming
Longwave
radiation
outgoing
Shortwave
radiation
Latent heat
Latent
heat
Sensible
heat
Soil heat flux
Geothermal heat
gain
Bedrock Bedrock Bedrock Bedrock
Momentum transfer
Rain Snow Photosynthesis
Phenology
Disturbances
Atmospheric
deposition
Fertilization
Nutrient resorption
Nutrient
uptake
Nutrients in SOM
Mineral nutrients
in solution
Mineralization and
immobilizationOccluded or not
available nutrients
Primary mineral
weathering
Biological
fixation (N)
Tectonic uplift
Denitrification (N)
Volatilization
Growth respiration
Maintenance respiration
Fruits/flowers production
Heterotrophic
respiration
Wood turnover
Litter Litter
Litterfall
nutrient flux
DecompositionMycorrhizal
symbiosis
Microbial
and soil
fauna
activity
SOM
DOC
leaching
Leaching
Fine and coarse
root turnover
Carbon allocation
and translocation
Carbon reserves (NSC)
Leaf turnover
Transpiration
Evaporation from
interception
Evaporation/
sublimation
from snow
Evaporation
Throughfall/dripping
Snow melting
Infiltration
Leakage
Root water uptake
Lateral subsurface flow
Base flow
Deep recharge
Runoff
Sensible heat
Albedo
Energy absorbed
by photosynthesis
Water cycle Carbon cycle Nutrient cycle
FIGURE 6 | Ecohydrological and terrestrial biosphere models have components and parameterizations to simulate the (1) surface energy
exchanges, (2) the water cycle, (3) the carbon cycle, and (4) soil biogeochemistry and nutrient cycles. Many models do not include all the
components presented in the ﬁgure.
WIREs Water Modeling plant–water interactions
More thermo-mechanistic ?
So what is furtherly next ?afterFatichi,PappasandIvanov,2015
R. Rigon
Maybe, but without forgetting the “less is more” lesson.

!352005 drought-afflicted ecohydrological system. The result-
ing weighted-cut process network for July 2005 is visual-
ized in Figure 8. The first salient observation is that the
drought process has fewer couplings than the healthy
process network; in fact, roughly half of the couplings
disappear during the drought state (adjacency matrix re-
drought because of insufficient information input from the
synoptic weather patterns. The moisture fluxes which carry
the information may be reduced below a key threshold
during drought.
[63] The absence of information flow from the ABL
subsystem to the turbulent subsystem means that the circu-
Figure 7. The process network for July 2003, a healthy system state. Types 1, 2, and 3 relationships
result in the interpretation of the system as three subsystems linked at time scales ranging from 30 min to
12 h. Thin arrows represent type 2 couplings. Thick arrows represent type 3 couplings. A type 1
‘‘synoptic’’ subsystem including GER, q, Qs, Qa, and VPD forces the other subsystems at all studied time
scales from 30 min to 18 h. A type 2 ‘‘turbulent’’ self-organizing subsystem including gH, gLE, NEE, and
GEP exists with a feedback time scale of 30 min or less and inhabits a feedback loop with P and Rg at
time scales from 30 min to 12 h. The P, CF, and Rg variables form a loose subsystem of mixed types,
which interact with each other on a time scale of roughly 12 h.
W03419 RUDDELL AND KUMAR: ECOHYDROLOGIC PROCESS NETWORKS, 1 W03419
So what is furtherly next ?
More thermo-mechanistic and networks ?
We cannot deny that our universe is not a chaos; we recognise being, objects that
we recall with names. These objects or things are forms, structures provided of a
certain stability; fill a certain portion of space and perdure for a certain time …”
(R. Thom, Structural stability and morphogenesys,1975)
afterRuddelandKumar,2009
R. Rigon

!36
True for life, true for tomorrow hydrology
.. though warned at the outset that the subject-matter was a difficult one a
…, even though the physicist’s most dreaded weapon, mathematical
deduction, would hardly be utilized. The reason for this was not that the
subject was simple enough to be explained without mathematics, but rather
that it was much too involved to be fully accessible to mathematics
What is life ?
E. Schroedinger
The large and important and very much discussed question is: How can the
events in space and time which take place within the spatial boundary of a
living organism be accounted for by physics and chemistry? The preliminary
answer which this little book will endeavor to expound and establish can be
summarized as follows: The obvious inability of present-day physics and
chemistry to account for such events is no reason at all for doubting that they
can be accounted for by those sciences
A programmatic manifesto based on Schroedinger booklet
R. Rigon

!37
I do not believe
In holistic views
not based on a formal and quantitative (in some sense, mathematical,
even if of maybe a new mathematics) approach.
R. Rigon
Certainly we need of a theory of interactions which helps us to simplify
complexities and scale up from the
but despite the critical role that stomata play, the
details of their regulation are still not fully under-
stood.84
Ultimately, stomata are largely regulated
biologically, and it is through these tiny apertures
(or lack thereof if leaves are shed) that vegetation
imprints a unique signature on the water cycle.
Each stoma is surrounded by a pair of guard
cells that are, in turn, in contact with multiple epider-
mal cells (Figure 2). Stomata tend to open when
guard cells increase their turgor (the sum of water
potential and osmotic pressure, see Eq. (4)), while an
increase in epidermal cell turgor results in the oppo-
site reaction, exerting a hydromechanically negative
feedback85–87
(Figure 2(b)). As the guard cell turgor
is the sum of osmotic pressure and water potential,
stomatal apertures are controlled by both hydraulic
and chemical factors88
(Figure 2(c)). Stomata close
when water potential in the leaf drops because of a
large transpiration flux or low water potential in the
upstream xylem conduits.89–91
The hydraulic control
acts directly in the reduction of guard cell turgor,
while chemical signals are less well quantified.92
However, it is well established that chemical factors
are essential for stomata opening in response to
light.93–95
Furthermore, chemical compounds, such
as ABA, are typically released in response to water
stress from the leaves and roots96–98
and contribute
to a reduction in the stomatal aperture.99
Release of
ABA is an important evolutionary trait as in early
plants such as lycophyte and ferns, stomatal closure
is purely hydraulically controlled.100
A differential
sensitivity of stomata aperture to chemical com-
pounds is a likely explanation why certain plants
close stomata considerably in response to dehydrata-
tion, keeping a fairly constant leaf water potential
(commonly referred to as ‘isohydric behavior’), while
others tend to keep stomata open to favor carbon
assimilation, experiencing larger fluctuations and
lower values of the leaf water potential (‘anisohydric
behavior’).
Models have been presented to mechanistically
describe stomatal behavior and reproduce the
hydraulic dynamics in the leaf86,101–108
or simply to
reproduce functional relations in agreement with
observations.80,109,110
Models that represent the
exact mechanisms through which stomata respond to
1
0.8
0.6
0.4
0.2
0
0 1 2
Pg (MPa)
Palisade
mesophyll
Spongy
mesophyll
Epidermal cell Guard cell
Atmosphere
Cuticle
Phloem
Xylem
Pe = 0
Pe = 1.5
Hydraulic only
Hydraulic + chemical
Hydromechanical
feedback
3 4 5
Relativestomatalaperture
0.25
0.2
0.15
0.1
0.05
0
0 –0.5 –1 –1.5 –2
ψg (MPa)
ψm
ψe ψg
ψa
ψg
ψi
ψx,v
gs(molH2O/m2s)
(a)
(b)
(c)
FIGURE 2 | A leaf is mostly composed of mesophyll and epidermal cells. The mesophyll is subdivided into palisade and spongy mesophyll. The
epidermis secretes a waxy substance called the cuticle to separate the leaf interior from the external atmosphere. Among the epidermal cells, there
are pairs of guard cells. Each pair of guard cells forms a pore called stoma. Water and CO2 enter and exit the leaf mostly through the stomata.
The vascular network of the plant is composed of xylem (blue) that transports water to the leaf cells and of phloem (red), which transports sugars
from the leaf to the rest of the plant. Water that exits the xylem is evaporated in the leaf interior (dashed lines). The terms Ψx,v Ψm, Ψe, Ψg, Ψi,
and Ψa are the water potential in the xylem of the leaf vein, mesophyll cell, epidermal cell, guard cell, leaf interior, and atmosphere, respectively.
Stomatal aperture responds positively to guard cell turgor pressure (Pg) and negatively to epidermal cell turgor pressure (Pe) (hydromechanical
feedback). The conductance of the stomatal aperture (gs) decreases with water potential in the leaf because of a combination of hydraulic and
chemical factors.
WIREs Water Modeling plant–water interactions
To the

!38
”So, where is the gold medal ?” I.R.I
Giving water to people and ecosystem
R. Rigon

!39
Getting new generation of students having success
MObyGISgettingtheEdison-EnergyPrize
R. Rigon

!40
Entropy 2014, 16 3484
Figure 1. Quantiﬁcation of the entropy or exergy budgets in the Critical Zone at different
spatial scales.
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Getting the fluxes and thermodynamics right at various scales
QuijanooandLin,Entropy,2014
R. Rigon

!41
Nothing can be achieved without good and sound science
R. Rigon
Science is not a commodity but at the core of our well being

!42
Without them it would not be possible
Sandro Marani Andrea Rinaldo Ignacio Rodriguez-Iturbe
The Masters
R. Rigon

!43
Giacomo Bertoldi
Reza Entezarolmahdi
Andrea Antonello
Silvia Franceschi
Fabrizio Zanotti
Emanuele Cordano
Stefano Endrizzi
Silvia Simoni
Agee Bushara
Matteo Dall’Amico
Cristiano Lanni
Giuseppe Formetta
Fabio Ciervo
Wuletawu Abera
Marialaura Bancheri
Francesco Serafin
The Students who actively participated
R. Rigon

!44
Find this presentation at
http://abouthydrology.blogspot.com
Ulrici,2000?
Other material at
Questions ?
R. Rigon

Find what is missing
Riccardo Rigon
16 December 2015
JoshSmith

!46
GEOPHYSICALRESEARCHLETTERS,VOL.22,NO. 20,PAGES2757-2760,OCTOBER15,1995
On thespatialorganizationof soilmoisturefields
IgnacioRodriguez-Imrbe,GregorK.Vogel,RiccardoRigon•
DepartmentofCivilEngineering,TexasA&MUniversity,CollegeStation,Texas
Dara Entekhabi
DepartmentofCivilandEnvironmentalEngineering,M.I.T., Cambridge,Massachusetts
Fabio Castelli
Istitutodi Idraulica,Universithdi Pemgia,Pemgia,Italy
Andrea Rinaldo,
Istitutodi Idraulica"G. Pleni," Universithdi Padova,Padova,Italy
Abstract. We examine the apparent disorder which
seemsto characterizethe spatial structure of soilmois-
ture by analyzinglarge-scaleexperimentaldata. Specif-
ically,we addressthe statisticalstructureof soilmois-
ture fields under different scales of observation and findß
unexpectedresults. The varianceof soil moisturefol-
lowsa powerlaw decayasfunctionof the areaat which
theprocessis'observed.Thespatialcorrelationremains
unchangedwith the scaleof observationand follows
a power law decaytypical of scalingprocesses.Soil
moisture also showsclear scalingpropertieson its spa-
tial clusteringpatterns. A well-definedorganizationof
statistical character is found to exist in soil moisture
patternslinking a large rangeof scalesthroughwhich
the processmanifestsitselfandimpactsotherprocesses.
We suggestthat suchscalingpropertiesare crucialto
our currentunderstandingand modelingof the dynam-
icsof soil moisture in spaceand time.
Introduction
Many outstandingissuesin earth and atmospheric
sciences[Eagleson,1994],suchas sub-gridscalepa-
rameterizationofgeneralcirculationmodels[Entekhabi
andEagleson,1989;AvissarandPielke,1989],hydro-
logicresponseofriverbasins[Eagleson,1978]andland-
atmosphere feedbacks[Delworthand Manabe,1988,
1989],hingein the characteristicsof soilmoisturepat-
terns in spaceand time.
In thispaperweaddressthe apparentdisorder(and
the noteworthyimplications)ofthe spatialandtempo-
ral structureofsoilmoisture.Indeed,probablythemost
1OnleavefromDipartimentodi !ngegneriaCivilee Ambien-
tale, Universirkdi Trento, Trento, Italy
Copyright1995bytheAmericanGeophysicalUnion.
challengingand fascinatingaspectin the studyof soil
moisture is the continuousspectrum of temporal and
spatial scales,from centimetersto thousandsof kilo-
meters and from minutes to severalmonths, which are
embedded one into another. The phenomenain these
scalesare not independentbut the structureof the spa-
tial andtemporalpatternsareaffectedby very different
variables and mechanisms.
This paper focuseson spatial scalesof tens of me-
ters to hundredsof kilometers with temporal scalesof
the order of one day. This scalerange is of great in-
terestin hydrologyfrom the point of view of localand
regionalwaterbalance,basinresponse,dynamicsofsoil-
water-vegetationsystemsandthe translationof locally
measuredfluctuations,tolargerscales.The objective
is to study the links betweenthe propertiesof the soil
moistureprocesswhenobservedat differentscales.The
emphasisis on the spatialcharacterof the fluctuations
of soil moisture. The temporal aspect is not a struc-
tural part of the analysis,it only playsa role in the
time variability that the field undergoeswhen its evo-
lution is followedthroughoutseveraldays.
Description of data
The soilmoisturedatausedin thispaper[Jacksonet
al., 1993;Allen andNaney,1991;Jackson,1993]have
beencollectedby NASA, the US DepartmentofAgricul-
ture and severalagenciesduring the socalledWashita
'92 Experiment. This was a cooperativeeffort between
NASA, USDA, severalother governmentagenciesand
universitiesconductedwith the primary goal of gather-
ing a time seriesof spatially distributed data focusing
on soil moisture and evaporative fluxes.
Data collection was conducted from June 10 to June
18, 1992. The regionreceivedheavyrainsovera period
beforethe experimentstarted with the rain endingon
June 9 and no precipitation occurring during the ex-
5
Soil moisture statistics
R. Rigon
2.5 3.0 3.5
Log distance (m)
Figure 2. Correlation functionof the relativesoilmois-
ture field. The processis describedin 200 m by 200 m
pixels and the correlation is estimated at distancesmul-
tiple of 200 m. The slopesof the fitting linesare: day
11,-0.33; day 14,-0.35; day 18,-0.48.
portance. From the theoretical point of view it opens
the door to an unifying- acrossscales- type of analy-
(a) showsexamplesof the powerlawsobtainedfor the
size distributions of the soil moisture islands. The level
is decreasedwhen advancing in time in order to keep
an adequate sample size becauseof the drying effect.
In all casesthe fitting is excellentwith exponentsin the
range0.75 to 0.95. This implies[Mandelbrot,1975]a
very rough fractal perimeter for the soil moistureclus-
ters. The fractal characteristicsappear to depend on
the crossinglevel pointing out the likely multiscaling
structure of the field.
Other types of clustering patterns were studied for
sisofthe spatialshapespresentin soilmoisture.From. theWashitadata. AnexampleofthisisshowninFigure
the practical point of view it allows the quantitative
probabilisticassessmentof the patchesof differentsoil
moisture levels.
' • 0 ..... day14S>0.50
-0.5 .35
-1.5
-2.0
-2.5
.............. , ........ J ......
5 6 7
Loga (m2)
Figure 3. (a) Probabilitydistributionofthesizeofsoil
moistureislandsabovedifferentthresholds.The slopes
3 (b). In all casesthe powerlaw fitting is excellent
confirmingthe scalingnature of the spatial patterns.
We finally notice that the sizeof the area involvedin
the Washira '92 experimentmakesit unrealisticthat the
scalingdetectedin the soil moisturefieldshasany re-
lation with the dynamicsof soil-atmosphereinteraction
phenomenaor with any appreciablespace-timeorgani-
zation of rainfall. We also observe that from the surface
runoffviewpointthereisnot muchredistributionexcept
through the channelnetwork which will take lessthan
one day to move the water out of the regiononceit
reachesthe network.Also,fromthe viewpointofsignif-
icant moistureredistributionthroughundergrounddy-
namics, the time scalesinvolved make that mechanism
ineffectivefor the type of data at hand[Entekhabiand
Rodriguez-Iturbe,1994].
Some statistical properties of the
porosity field
The abovereasoningsuggeststhat the spatialscaling
of soil moistureat the scalesof this study is a conse-
quenceofthe existenceofspatialorganizationin the soil
properties which command the infiltration of moisture.

!47
Potential for landsliding: Dependence on hyetograph characteristics
Paolo D’Odorico
Department of Environmental Sciences, University of Virginia, Charlottesville, Virginia, USA
Sergio Fagherazzi
Department of Geological Sciences and School of Computational Science and Information Technology, Florida State
University, Tallahassee, Florida, USA
Riccardo Rigon
Dipartimento di Ingegneria Civile e Ambientale, Universita´ di Trento/CUDAM, Trento, Italy
Received 27 January 2004; revised 8 November 2004; accepted 14 December 2004; published 10 February 2005.
[1] This paper examines the effect of hyetograph shape on the potential for landsliding in
soil-mantled landscapes. An existing pore pressure response model (Iverson, 2000) is used
to study the effects of unsteady rainfall infiltration in hillslopes, and the effect of slope and
convergent topography is expressed using a steady state model of slope-parallel
subsurface flow. Slope stability is assessed using an infinite slope analysis. This theoretical
framework is coupled with simple hyetograph models and to intensity-duration-frequency
functions to determine the return period of landslide-triggering rainfall. Results also
show that hyetographs with a peak at the end of a rainfall event have a stronger
destabilizing effect than hyetographs with a constant rainfall or with a peak at the
beginning of a storm. Thus the variability of hyetograph shapes adds uncertainty to the
assessment of landsliding triggered by rainfall.
Citation: D’Odorico, P., S. Fagherazzi, and R. Rigon (2005), Potential for landsliding: Dependence on hyetograph characteristics,
J. Geophys. Res., 110, F01007, doi:10.1029/2004JF000127.
1. Introduction
[2] The stability of hillslopes and hollows is affected by
extreme rainfalls which increase the soil water pressure and
consequently reduce the shear strength of the aggregates,
favoring the instability of the soil mantle. The triggering of
landslides by rainfall has been studied on different slopes,
bedrock substrates, soil depths and ages, and with different
vegetation [O’Loughlin and Pearce, 1976; Sidle and
Swanston, 1982; Reneau and Dietrich, 1987; Trustrum
and De Rose, 1988; Montgomery et al., 1998; Iida, 1999;
Wieczorek et al., 2000; Morrissey et al., 2001]. The
process-based assessment of whether a slope is stable or
unstable is important to landslide hazard assessment,
mapping of landslide-prone areas [Montgomery and
Dietrich, 1994; Dietrich et al., 1995; Iida, 1999], and
studies of landform evolution [e.g., Benda and Dunne,
1997a, 1997b; D’Odorico and Fagherazzi, 2003], as
well as to investigations of the dependence of landslide
frequency on soil mechanical properties, land cover, and
topography [e.g., Sidle and Swanston, 1982; Sidle, 1987;
Iida, 1999].
[3] This paper puts together an existing body of modeling
approaches and hydrological concepts in a methodology to
calculate the return period of landslide-triggering precipi-
duration, and frequency of precipitation (through the IDF
curves expressed as power laws [e.g., Koutsoyiannis and
Foufoula-Georgiou, 1993; Burlando and Rosso, 1996]);
(2) the relative importance of long-term (slope-parallel)
flow with respect to short-term (vertical) infiltration in the
triggering of landslides; and (3) the influence of the shape
of the storm hyetographs on the return period of landslide-
triggering precipitation.
[4] We assume that the pressure head transient observable
in the course of a rainstorm is due to the unsteady vertical flow
through the soil profile, while slope-parallel subsurface flow
is assumed to occur at a longer timescale and to determine
the prestorm wetness conditions. We therefore couple a
model of subsurface lateral (steady) flow [Montgomery
and Dietrich, 1994; Iida, 1999] with a model of transient
rainfall infiltration [Iverson, 2000] to determine the hydro-
logic conditions that cause slope failure. The return period
of these hydrologic conditions is determined through the
intensity-duration-frequency relations of extreme precipita-
tion. Moreover, simplified models of the complex temporal
structure of storm hyetographs are used here to study the
effect of hyetograph shape on slope stability.
2. Spatial and Temporal Variability of Soil Water
JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 110, F01007, doi:10.1029/2004JF000127, 20058
R. Rigon
HYDROLOGICAL PROCESSES
Hydrol. Process. 22, 532–545 (2008)
Published online 8 October 2007 in Wiley InterScience
(www.interscience.wiley.com) DOI: 10.1002/hyp.6886
Modelling the probability of occurrence of shallow landslides
and channelized debris flows using GEOtop-FS†
Silvia Simoni,* Fabrizio Zanotti, Giacomo Bertoldi and Riccardo Rigon
Department of Civil and Environmental Engineering, CUDAM, University of Trento, Trento, Italy
Abstract:
This paper describes a coupled, distributed, hydrological-geotechnical model, GEOtop-FS, which simulates the probability of
occurrence of shallow landslides and debris flows. We use a hydrological distributed model, GEOtop, which, models latent and
sensible heat fluxes and surface runoff, and computes soil moisture in 3-D by solving Richards’equation numerically, together
with an infinite-slope geotechnical model, GEOtop-FS. The combined model allows both the hydraulic and geotechnical
properties of soil to be considered and realistically modelled. In particular, the model has been conceived to make direct use
of field surveys, geotechnical characteristics and soil moisture measurements. In the model the depth of available sediments
is also used to characterize the hydraulic properties of the area examined.
To account for the uncertainty related to the natural variability in the factors influencing the stability of natural slopes, the
safety factor is computed with a probabilistic approach. In order to determine the likelihood of slope failures, soil parameters
are assigned distributions instead of single deterministic values.
The analysis presented was carried out for an alpine watershed, located in the Friuli region, Italy, for which some geological
and geotechnical data were available. In the past, this watershed experienced landslides and debris flows during intense storms
following long and moderate intensity rainfall events. The distributed coupled GEOtop-FS model was calibrated by reproducing
some of these events and validated in order to map future failure probabilities. Copyright © 2007 John Wiley & Sons, Ltd.
KEY WORDS shallow landslides; failure probability; soil characterization; stability analysis
Received 9 June 2006; Accepted 5 October 2006
INTRODUCTION
The triggering point of shallow landslides, that eventually
turn into debris flows or mudflows in channeled areas,
cannot currently be predicted NRC-National Research
create interpretative maps that show the potential extent
of landslide activity (Glade et al., 2000; Pitman et al.,
2003). The products of this analysis are often landslide
susceptibility maps (Guzzetti et al., 1999) produced with
542 S. SIMONI ET AL.
Figure 8. Variation of the probability of failure, in terms of percentage, with volumetric soil moisture evolution [ ]. Water content rea
maximum value at day 90 which corresponds to a higer probability of failure. Grey areas (15% total catchment area) represent expose
characterized by a very steep topography, where the slope angle is larger than the internal friction angle, and areas with scarce sediment av
layer could drive the stability of the more superficial lay-
ers; therefore stability results must be considered from
bottom-up, bearing in mind that, for a given pixel, the
depth of slipping soil is given by the weakest layer.
The stability analysis with respect to time is shown in
Figures 10 and 11. For a given depth (layer), they dis-
play the variation with time of stable and unstable areas,
respectively, highlighting that unstable areas increase 0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Area%
Landslide triggering

!48
11Carbonate pseudotachylytes: evidence for
seismic faulting along carbonate faults
Alﬁo Vigano`,1
Simone Tumiati,2
Sandro Recchia,3
Silvana
Martin,4
Marcello Marelli5
and
Riccardo Rigon1
volume 23 number 3 june 2011

Information
Riccardo Rigon
16 December 2015
JacquelineHumphries,HowthisWorks,2007

!50
me
http://abouthydrology.blogspot.it/search/label/Me-Myself-I
my past Research
with papers pdfs
http://abouthydrology.blogspot.it/search/label/My%20Past%20Research
my future Research
http://abouthydrology.blogspot.it/search/label/Research%20Topics
About
R. Rigon

!51
About
R. Rigon
GEOtop
JGrass-NewAGE
The Horton Machine
was in Grass, Jgrass, dig, STAGE and will be in GVSig
http://abouthydrology.blogspot.it/2015/02/geotop-essentials.html
http://abouthydrology.blogspot.it/2015/03/jgrass-newage-essentials.html
http://abouthydrology.blogspot.it/2014/05/the-udig-spatial-toolbox-paper.html

!52
About
The future of my past research topics
(with or without me) is a complex question. I will try to answer in a
blog-post, in the first days of January 2016.
R. Rigon
See: http://abouthydrology.blogspot.com

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