Scales and Hydrology in 2020

Scales & Hydrology
in 2020
Potenza, 24 Febbraio 2017
Mgritte,R.,Larecherchedel’absolu,Oiloncanva,1940
Riccardo Rigon, Marialaura Bancheri, Niccolò Tubini, Giuseppe Formetta, Francesco Serafin

Three quarks for Muster Mark
J. Joyce

The computational effort and the quantity of information to manage in a hydrologcial
modelling project of areas of many thousands or even millions of square kilometers
become easily so demanding to become impossible to support. This statement has
been always a motivation to discard any trial to investigate what could actually be done
or not in advance.
Through the experience made with the model GEOtop, we analyse in this talk the state-
of-art in this field.
The mathematical (formal) aspects of the hydrological problem to treat seamlessly
different spatial and temporal scale, can be framed by saying that model process-based
(as GEOtop) have at their core systems of partial differential equations (PDEs), while
lumped models (with their physics aggregated at the basin or at at hillslope scale)
constitute systems of ordinary differential equations (ODEs). Almost no other choice is
available, if we excludes statistical models and machine learning techniques. Despite
lumped models are built for reducing the degree of freedom of the hydrological
problems through an informed set of simplifications, even they end to produce quite
complicate systems that, as the process based models do, cause identifiability and
computational problems.
However, it is evident that the issues, before to be computational and about information
(the one necessary to obtain a given prognosis), are theoretical. The topic here debated
is which would be, at any scale, the hydrological aspects (or quantities) that dominate
and a certain spatial and temporal scale.
The research questions raised are: which are the techniques and the approaches that
can be used to aggregate the spatial information. Which are the physical-mathematical
directions towards which we should look ?
This talk aims to give some effective indications, immediately practicable by
researchers.

!4
Rigon & Al.
The experience of “Process Based” models
What is a “Process Based” model ?
Fatichi,S; Vivoni e.R.; Ogden F.L.; Ivanov V.Y.; Mirus,B; Gochis, D; Downer C.W.; Camporese, M; Davison J.H.,
Ebel, B; Jones, N; Kim, J., Mascaro, G; Niswonger, R; Restrepo, P.; Rigon, R.; Shen, C.; Sulis, M.,Tarboton, D.; An
overview of current applications, challenges, and future trends in distributed process-based models in
hydrology, Journal of Hydrology, 537 (2016) 45-60, 2016
Paniconi, C., & Putti, M. (2015). Physically based modeling in catchment hydrology at 50: Survey and outlook.
Water Resources Research, 1–46. http://doi.org/10.1002/(ISSN)2169-8996/homepage/billing_faqs.pdf
Freeze and Harlan, Blueprint for a physically-based digitally-simulated hydrological response model, Jour. of
Hydrology, 1969
Abbot et al., An Introduction to the European Hydrological System - Systeme Hydrologique Europeen, SHE. 1.
History and Philosophy of a Physically-Based, Distributed Modeling System 1986
Dunne Saturation
Overland Flow
Unsaturated Layer
Surface Layer
Saturated Layer:
Horton Overland Flow
Modiﬁed from Abbot et al., 1986

!5
Beven, K. J. (2001). How far can we go in distributed
hydrological modelling? Hydrology and Earth
System Sciences, 5(1), 1–12.
“…The modelling results were never published. They were
simply not good enough. The model did not reproduce the
stream discharges, it did not reproduce the measured water
table levels, it did not reproduce the observed
heterogeneity of inputs into the stream from the
hillslopes.”
Critiques were not missing
Rigon & Al.

!6
An analysis of this question reveals a number of issues. These
will be summarised here as the problems of
nonlinearity;
of scale;
of uniqueness;
of equiﬁnality;
and of uncertainty.
Problems
Rigon & Al.

!7
My ﬁrst answer is
We discover ... that all our laws can be
written in mathematical form; and that
this has a certain simplicity and beauty
about it. So, ultimately, in order to
understand nature it may be necessary to
have a deeper understanding of
mathematical relationships*
R. Feynman
http://abouthydrology.blogspot.it/2013/06/ezio-todini-70th-symposium-my-talk.html
Rigon & Al.

!8
On a practical base
I (we) built GEOtop
mass, momentum and energy conservation
are
the most “true” equations we know
Rigon & Al.

Richards equation is “wrong” !
9
Sure. But then, what else I should use:
•Green-Ampt ?
•SCS ?
•Topmodel ?
•Reservoirs ?
I use all of them when I find convenient.
However, all of them are even more “wrong” than Richards. So for the first
part of this talk I stick with Richards’ assumptions.
Take it as my null hypothesis
Better wrong than “not even wrong”
Rigon & Al.

10
To exaggerate
•energy budget: turbulent flows, heat equation, soil
freezing, snow budget
we added
still Freeze and Harlan, 1968 ?
EndrizziandMarsh,2010;Dall’Amicoetal.,2011,Endrizzietal.,2013
Bertoldietal.,2010a,b
Better wrong than “not even wrong”
Rigon & Al.

11
In What GEOtop is different ?
Water mass budget
Rigonetal,2006;Bertoldietal.,2006
Parflow,AsbyanFalgout,1996
Hydrogeosphere,TherrienandSudicki,1996
Catflow,Zeheetal.,2001
InHM,VanderKwaak,andLoague,2001
Cathy,PaniconiandPutti,1994
tRIBS,Ivanovetal,2004
DHSVM,Wigmostaetal.,1994
Rigon & Al.

12
Energy budget
Rigonetal,2006
BATS,Dickinsonetal.,1986,
NoahLSM,Chenetal.,1996,
LSM,Bonan,1996
SEWAB,Megelkampetal.,1999
CLM,Daietal.,2003
Rigon & Al.

13
Snow height, density, temperature)
Freezing Soil - Permafrost
Snow and freezing soil: see also me on Thursday talk
Zanotti et al, 2004; Dall’Amico et al., 2011
CROCUS,Brunetal.,1992
Alpine3D,Lenhingetal.,2006
Rigon & Al.

14
Many models do the water budget
Many models do the energy budget
Many model do the snow budget
How many models do the whole stuff together ?
Obviously is also matter of the degree of
physical simplification (i.e. the
equations) used.
To study the interactions all is modelled together
Rigon & Al.

15
Some misconceptions about distributed modelling
“Distributed models are overparameterised”
“Model parameters cannot be identified”
“These models require too high computational time”
“They cannot be used for ungauged basins”
“Reality is simpler than that (and we learn just from simple models)”
see also http://www.nature.com/nature/journal/v469/n7328/abs/469038a.html
To sum up our position
not completely wrong but not completely true.
eat the apple before talking!
Rigon & Al.

16
Endrizzi et al. 2014
see also http://abouthydrology.blogspot.com/search/label/GEOtop
The whole story here
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
Abstract. GEOtop is a fine-scale grid-based simulator that
represents the heat and water budgets at and below the soil
surface. It describes the three-dimensional water flow in the
soil and the energy exchange with the atmosphere, consider-
ing the radiative and turbulent fluxes. Furthermore, it repro-
duces the highly non-linear interactions between the water
global climate change. This importance derives on one hand
from the requirement to study more and more complex sys-
tems, and, on the other hand, this representation of more
complex systems can inform decisions about their simpli-
fication (Freeze and Harlan, 1969). In fact, the systems of
equations required for representing such environments areRigon & Al.

17
Will you suggest, from the point of view of computational time, to use
distributed models (like SHE) and continuous, since we think to use weather
time series of thousands of years ? Personally I see the danger to be
overwhelmed by data, and by so long computational time that we will not
able to perform all the analysis we require with the adequate rigor
(sensitivity analysis, and so on ...).
Different people have different ideas of what a distributed model is. Kampf and
Burges (2007) offered a review a few years ago. However, taking as reference
our GEOtop, that is probably one of the more complex existing hydrological
models, we can observe that it runs, in our laptop, a year long simulation for a
10-20 square kilometer basin at 10 m of resolution, in, say, a day. So,
simulating 1000 years would require approximately 3 years: which is clearly
too long for any project. Using faster machine would probably increase the
time by a factor of two. GEOtop is not parallelized, so, after an investment in
rewriting the code, we could probably cut the time of simulation of a factor 100,
by using also large parallel computers. Thus, we will reduce one year of
simulation to 3/4 days: this could then be feasible. But this is obviously wishful
thinking.
A practical concern from: Which hydrological model (is better) ?
Rigon & Al.

18
However
Condon, L. E., & Maxwell, R. M. (2016). Analyzing the impact of groundwater ﬂow and storage changes on Budyko
relationships across the continental US. Hydrology and Earth System Sciences Discussions, 1–40. http://doi.org/10.5194/
hess-2016-408
Rigon & Al.

19
However
MySnowMaps
Rigon & Al.

20
So the bottom line here is:
Maybe scale problem could became not so
important from the computational point
of view in the next future.
Similar systems can be implemented also for:
• rainfall
• runoff
• evapotranspiration
• groundwater
With resolution of few hundreds meter. Just a problem of investments.
Rigon & Al.
Is the scale problem so important anymore ?

21
This doesn't imply that
nonlinearity;
of scale;
of uniqueness;
of equiﬁnality;
and of uncertainty.
issues are not solved. But that
“…The modelling results were never published. They were simply
not good enough. The model did not reproduced the stream
discharges, it did not reproduced the measured water table levels, it
did not reproduced the observed heterogeneity of inputs into the
stream from the hillslopes.”
maybe this is still
not true
Rigon & Al.
Issues

22
So we do not care anymore about scale issues ?
Certainly not. We want do it more easily. Implying less time and facing a whole
set of interactions and feedbacks. Especially with vegetation and ecosystems.
Some problems complexity grows more than exponentially and are not computable.
Rigon & Al.
What is the real scale problem ?

23
Rigon & Al.
Please join the number and the letter

Scales & Hydrology
simplifications

25
The problem here can be enunciated as follows:
• Do, at certain scale, are we interested just in “averages” of the
hydrological quantities ?
• Are fluxes of the (at boundaries of the control volumes of interest)
computable just on the basis of these averages (or on their
gradients) ?
• How can we exploit the fact that mass, energy and momentum are
conserved
Rigon & Al.Rigon & Al.
Scaling by simpliﬁcation

26
2D - de Saint Venant equations
with some smart subgrid parameterization
(e.g. Casulli, 2009)
1D - Kinematic equation
So many to cite here but ... Liu and
Todini, 2002
Various aggregation strategies
for runoff, including residence
time theories (a.k.a GIUH)
Rodriguez-Iturbe and Valdes, 1979;
Rinaldo et al., 1991,
D’Odorico and Rigon, 2003
Rigon et al. 2016a
Less is more: Ranfall runoff
Rigon & Al.

27
3D-Richards’ equation
(Richards, 1931; Celia et al. 1990)
1D-Richards + Boussinesq
Topkapi
HsB
Topog/Topmodel
CordanoandRigon,2008
(Cordano and Rigon, 2013)
Liu and Todini, 2002
Troch et al., 2003
O’Loughlin, 1986; Beven and Kirkby, 1979
Less is more: soil science
Rigon & Al.

28
Dalton’s Equation
e.g. Brutsaert 1982
Penman
Penman, 1948
Monteith
Monteith, 1965
Priestley-Taylor
Priestley and Taylor, 1972
Less is more: Evapotranspiration
Rigon & Al.

29
Energy Budget
Jordan, 1991
Radiation + Temperature
Brubaker et al., 1996
Hock, 1999
Degree-day (Just
temperature)
Martinec and Rango, 1975
Less is more: snow
Rigon & Al.

30
Models “complexity” and computational time increase
going from bottom up.
More complexity, more processes physics.
Scales of application usually* decrease from top to
bottom
* But not anymore necessarily
Less is more
Rigon & Al.

31
Parameters pretend to be estimated ex-ante
(measured) in more complex models (with a lot of
disclaimers ... obviously)
Are certainly calibrated (ex-post) in the simplest
models (but in some models preserve a physical
significance)
From top to bottom heuristic and statistics
substitute processes analysis
Less is more
Rigon & Al.

32
A more theoretical but abstract treatment of the subject can be found in
Reggiani, P., Sivapalan, M. and Hassanizadeh, S.M., 1998. A unifying framework for
watershed thermodynamics: balance equations for mass, momentum, energy and
entropy and the second law of thermodynamics, Adv. Water Resour., 23, 15-40.
Reggiani, P., Hassanizadeh, S.M., Sivapalan, M. and Gray, W.G., 1999. A unifying
framework for watershed thermodynamics: constitutive relationships, Adv. Water
Resour., 23, 15-40.
Reggiani, P., Sivapalan, M. and Hassanizadeh, S.M., 2000. Conservation equations
governing hillslope responses: exploring the physical basis of water balance, Water
Resour. Res., 36, 1845- 1863.
Well, my opinion on those papers is that they are a must read.
However notation does not help and they lack of insight of physics,
with repect to the more “bottom up” paper and procedures I cited
before. Then .. c’mon everybody when does not what to say talks
about entropy but does not really reveals the mystery around it.
Rigon & Al.
A systematic approach

Scales & Hydrology
The Richards’ case

34
Everything is statistical, and statistics is more than simple integration
integration interpretation simplification
Is
Rigon & Al.
Statistical-Mechanical-Hydrology

35
Soil is made up of various stuff
http://www.directseed.org/soil_quality.htm
Take the case of Richards equation
But we concentrate on pore distribution
Rigon & Al.

36
Interpretation and simplification: As in Mualem (1976), we think that
soil is a bundle of pores and that they are filled (or emptied)
systematically. Filled from the smaller to larger. Emptied from larger to
smaller. Then a partially filled soil is represented by figure below.
Statistics is represented here by the pdf f(r) and the water content is
Interpretation & Simpliﬁcation
Rigon & Al.

37
Thus the variation in time of the water content is:
pores distribution
largest pore size
dimensionless liquid water content
The ﬁrst member of the equation
Rigon & Al.

38
Young-Laplace law
pore radius
liquid water density
acceleration of gravity
surface tension of water
contact angle
water pressure
Rigon & Al.

39
As a result (see Kosugi et al., 2008):
l.h.s. of Richards’ equation
hydraulic capacity
Rigon & Al.

40
r.h.s. of Richards’ equation
We could continue with the r.h.s. of the equation to express
Richards equation as a function of the largest pore size
hydraulic conductivity
details in Rigon et al. 2017 (in preparation)
Rigon & Al.

41
scales up
because we can think to any control volume as a bundle of pores of a
given statistics. For fluxes to be right though some more hypothesis
has to be made.
Rigon & Al.
it scales up

42
Another good example of “scaling up” is offered by
Mualem, Y. (1976). A new model fro predicting the hydraulic conductivity of
unsaturated porous media. Water Resources Research, 12(3), 513–522.
which is also the most cited paper in Water Resources Research.
Rigon & Al.
read the masters!

Scales & Hydrology
ET’s case

44
Admitting that scaling in Richards can be obtained
With other processes like evapotranspiration is more complicated
computationally demanding. Therefore, several eco- carbon285
) concepts that empirically link carbon
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
afterFatichi,PappasandIvanov,2015
Rigon & Al.

45
computationally demanding. Therefore, several eco- carbon285
) concepts that empirically link
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 Bed
Momentum transfer
Phenology
Disturbances
Atmospheric
deposition
Fertilization
Nutrient resorption
Nutrient
uptake
Nutri
Mineral nutrien
in solution
Miner
immOccluded or not
available nutrients
Primary mineral
weathering
Biological
fixation (N)
Tectonic uplift
Den
Volatil
Growth respiration
Heterotrophic
respiration
Wood turnover
Litter L
Litt
nutrie
symbiosis
Microbial
and soil
fauna
activity
SOM
DOC
leaching
Lea
Fine and coarse
root turnover
Carbon allocation
and translocation
Leaf turnover
Transpiration
Evaporation from
interception
Evaporation/
sublimation
from snow
Evaporation
Snow melting
Infiltration
Leakage
Root water uptake
Base flow
Deep recharge
Runoff
Sensible heat
Albedo
Energy absorbed
by photosynthesis
FIGURE 6 | Ecohydrological and terrestrial biosphere models have components and parameterizations to simulate the (1) surface en
WIREs Water Modeling plant–water
If ⇥ ET =
(Rn G)
(1 + +
rg
ra
)
+
⇤⇥
ra
qa
(1 + +
rg
ra
)
works for this:
Rigon & Al.
is the same true for transpiration ?

46
Admitting that scaling in Richards can be obtained
Why should this work for this ?
How to scale up this complexity ?
demanding. Therefore, several eco-
dels still use simplified solutions of
carbon285
assimilation to the transpired water or intercepted
nges
Longwave
radiation
incoming
gwave
ation
going
atent
eat
Sensible
heat
Soil heat flux
ck Bedrock Bedrock Bedrock
Momentum transfer
Phenology
Disturbances
Atmospheric
deposition
Fertilization
Nutrient resorption
Nutrient
uptake
Nutrients in SOM
Mineral nutrients
in solution
Mineralization and
available nutrients
Primary mineral
weathering
Biological
fixation (N)
Tectonic uplift
Denitrification (N)
Volatilization
Growth respiration
Heterotrophic
respiration
Wood turnover
Litter Litter
Litterfall
nutrient flux
symbiosis
Microbial
and soil
fauna
activity
SOM
DOC
leaching
Leaching
Fine and coarse
root turnover
Carbon allocation
and translocation
Leaf turnover
Transpiration
Evaporation from
interception
Evaporation/
sublimation
from snow
Evaporation
Snow melting
Infiltration
Leakage
Root water uptake
Base flow
Deep recharge
Runoff
heat
drological and terrestrial biosphere models have components and parameterizations to simulate the (1) surface energy
ter cycle, (3) the carbon cycle, and (4) soil biogeochemistry and nutrient cycles. Many models do not include all the
in the figure.
Modeling plant–water interactions
computationally demanding. Therefore, several eco-
hydrological models still use simplified solutions of
carbon285
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
Phenology
Disturbances
Atmospheric
deposition
Fertilization
Nutrient resorption
Nutrient
uptake
Nutrients in SOM
Mineral nutrients
in solution
Mineralization and
available nutrients
Primary mineral
weathering
Biological
fixation (N)
Tectonic uplift
Denitrification (N)
Volatilization
Growth respiration
Heterotrophic
respiration
Wood turnover
Litter Litter
Litterfall
nutrient flux
symbiosis
Microbial
and soil
fauna
activity
SOM
DOC
leaching
Leaching
Fine and coarse
root turnover
Carbon allocation
and translocation
Leaf turnover
Transpiration
Evaporation from
interception
Evaporation/
sublimation
from snow
Evaporation
Snow melting
Infiltration
Leakage
Root water uptake
Base flow
Deep recharge
Runoff
Sensible heat
Albedo
Energy absorbed
by photosynthesis
FIGURE 6 | Ecohydrological and terrestrial biosphere models have components and parameterizations to simulate the (1) surface energy
WIREs Water Modeling plant–water interactions
carbon285
) concepts that em
assimilation to the transpire
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
Momentum transfer
Phenology
Disturbances
A
d
Occl
availa
Prima
wea
Bi
fixa
Growth respiration
Heterotrophic
respiration
Wood turnover
Litter
symbiosis
Microbial
and soil
fauna
activity
SOM
DOC
leaching
Fine and coarse
root turnover
Carbon allocation
and translocation
Leaf turnover
Transpiration
Evaporation from
interception
Evaporation/
sublimation
from snow
Evaporation
Snow melting
Infiltration
Leakage
Root water uptake
Base flow
Deep recharge
Runoff
Sensible heat
Albedo
Energy absorbed
by photosynthesis
Water cycle Carbon cycle
FIGURE 6 | Ecohydrological and terrestrial biosphere models have components and parameterizations to simula
exchanges, (2) the water cycle, (3) the carbon cycle, and (4) soil biogeochemistry and nutrient cycles. Many models
WIREs Water M
carb
assim
Energy exchanges
Longwave
radiation
incoming
Longwave
radiation
outgoing
Shortwave
radiation
Latent heat
Latent
heat
Sensible
heat
Soil heat flux
Geothermal heat
gain
Bedrock Bedrock
Momentum transfer
Rain Snow Photo
Phenology
Fine and
root tur
Carbon a
and trans
Carbo
Transpiration
Evaporation from
interception
Evaporation/
sublimation
from snow
Evaporation
Snow melting
Infiltration
Leakage
Root water uptake
Base flow
Deep recharge
Runoff
Sensible heat
Albedo
Energy absorbed
by photosynthesis
Water cycle
FIGURE 6 | Ecohydrological and terrestrial biosphere models have componen
exchanges, (2) the water cycle, (3) the carbon cycle, and (4) soil biogeochemistry
WIREs Water
Rigon & Al.

47
In fact our models are like this:
and they are called big-leaf models
Rigon & Al.
the big-leaf model

48
The knowledge here is too simplified for being scaled up decently.
My guess:
we should go back to pore scale processes as well and combine
properly with boundary layer dynamics
Schymanski, S. J., & Or, D. (2016). Leaf-scale experiments reveal important omission in the Penman-Monteith equation.
Hydrology and Earth System Sciences Discussions, 0, 1–33. http://doi.org/10.5194/hess-2016-363
Rigon & Al.
new insight are needed

!49
the potential for cumulus convective rainfall. Therefore
vertical radiosonde soundings over adjacent locations
that have different surface conditions offer opportuni-
ties to assess alterations in thunderstorm potential. This
influence of surface conditions on cumulus cloud and
thunderstorm development has been discussed, for ex-
Pielke and Zeng, 1989]. The soundings were made prior
to significant cloud development. The radiosonde
sounding over an irrigated location had a slightly cooler
but moister lower troposphere than the sounding over
the natural, short-grass prairie location. Aircraft flights
at several levels between these two locations on July 28,
Figure 5. Same as Figure 4 except between a forest and cropland. Adapted from P. Kabat (personal
communication, 1999). Reprinted with permission.
Pielke,2001
Feedbacks - Retroazioni
sull’atmosfera
~ 10 km
not disconnect from what happens in the heavens
Rigon & Al.

!50
Not even to life processes
.. 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
Rigon & Al.

Scales & Hydrology
How can we make our model more physically based ?

!52
See my comment here:
http://abouthydrology.blogspot.it/2016/09/on-how-to-make-our-models-more.html
Savenije, H. H. G., & Hrachowitz, M. (2016). Opinion paper: How to make our models more
physically-based. Hydrology and Earth System Sciences Discussions, 1–23. http://doi.org/
10.5194/hess-2016-433*
The title was inspired by this paper
Which was eventually renamed
Catchments as meta-organisms – a new blueprint for
hydrological modelling
Rigon & Al.
Hydrological modelling in 2020

!53
“Alexander von Humboldt (1769–1859) considered nature and its processes
as an inseparable entity, where all forces of nature are connected and
mutually dependent (Wulf, 2015). Although these concepts were not
formulated speciﬁcally to describe the movement of water through the natural
environment, they very pointedly summarize what controls hydrological
functioning at the catchment scale.”
“Ironically, state-of-the-art catchment-scale hydrological models, for varying
reasons depending on the model under consideration, frequently do a poor job
in addressing overall system behaviour emerging from the characteristics
above. This results in many models being inadequate representations of real-
world systems, haunted by large model and/or parameter uncertainties and
unreliable predictions. “
Rigon & Al.

!54
They have good points
“capacity of the ecosystem to manipulate the system in
response to the temporal dynamics of the atmospheric drivers, as
encapsulated in the above two quotes, is only insufﬁciently or often
not at all accounted for in these models.”
“many others rely on simple and straightforward aggregation
of processes from the lab scale to the catchment scale,
assuming that there is no structure and organization in
the system”
Although most models take Newtonian theory at heart, as best
they can, what they generally miss is Darwinian theory on
how an ecosystem evolves and adjusts its environment to
maintain crucial hydrological functions.
Rigon & Al.

!55
http://seismo.berkeley.edu/~kirchner/reprints/2002_55_Kirchner_gaia.pdf
https://en.wikipedia.org/wiki/Gaia_hypothesis
Rigon & Al.
in late XX century

!56
Rigon & Al.
in late XX century

!57
“River networks morphology self-organise to obtain
minimal energy expenditure”
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
manyof themostimportantempiricalrelationshipsobserved
in the internal organizationof the network and its linkage
with the flow characteristics.The firstprincipleexpressesa
local optimal condition for any link of the network. The
secondprinciple expressesan optimal conditionthroughout
the network regardlessof its topologicalstructureand later
on in this paperwill be interpretedin a probabilisticframe-
work. It postulates that energy expenditure is the same
everywhere in the network when normalizedby the area of
the channelon which it takes place.Thus evenwith the first
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), Aw and
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•
of energyrelatedto themaintenanceof thechannelw•ch
mayberepresentedby F(soil,flow)P•L whereF( ) isa
complicatedfunctionofsoilandflowpropertiesrepresenf•
theworkperunittimeandunitareaofchannelinvolved'm
theremovalandtransportationof thesedimentwhich0th-
erwise would accumulatein the channel surface.Fromthe
equationsofbedloadtransportonemayassumethatF =
KTmwhereK dependsonlyonthesoilandfluidprope•es
and m is a constant.
In a channelof lengthL andflow Q therateofene•
Energy dissipation, runoff production and the three dimensional structure of river networks
Rigon & Al.

!58
Rigon & Al.
in late XX century

!59http://www.larssono.com/musings/sandpile/
Rigon & Al.
the emerging of power laws

!60
On the coupled geomorphological and ecohydrological
organization of river basins
Kelly K. Caylor a,*, Salvatore Manfreda a,b
, Ignacio Rodriguez-Iturbe a
a
Department of Civil and Environmental Engineering, Engineering Quadrangle, Princeton University, Princeton, NJ 08540, USA
b
Dipartimento di Ingegneria e Fisica dellÕAmbiente, Universita` degli Studi della Basilicata, Potenza I-85100, Italy
Received 17 March 2004; received in revised form 27 August 2004; accepted 27 August 2004
Abstract
This paper examines the linkage between the drainage network and the patterns of soil water balance components determined by
the organization of vegetation, soils and climate in a semiarid river basin. Research during the last 10 years has conclusively shown
an increasing degree of organization and unifying principles behind the structure of the drainage network and the three-dimensional
geometry of river basins. This cohesion exists despite the infinite variety of shapes and forms one observes in natural watersheds.
What has been relatively unexplored in a quantitative and general manner is the question of whether or not the interaction of veg-
etation, soils, and climate also display a similar set of unifying characteristics among the very different patterns they presents in river
basins. A recently formulated framework for the water balance at the daily level links the observed patterns of basin organization to
the soil moisture dynamics. Using available geospatial data, we assign soil, climate, and vegetation properties across the basin and
analyze the probabilistic characteristics of steady-state soil moisture distribution. We investigate the presence of organization
through the analysis of the spatial patterns of the steady-state soil moisture distribution, as well as in the distribution of observed
vegetation patterns, simulated vegetation dynamic water stress and hydrological fluxes such as transpiration. Here we show that the
drainage network acts as a template for the organization of both vegetation and hydrological patterns, which exhibit self-affine char-
acteristics in their distribution across the river basin. Our analyses suggest the existence of a balance between the large-scale deter-
minants of vegetation pattern reflecting optimality in the response to water stress and the random small-scale patterns that arise
from local factors and ecological legacies such as those caused by dispersal, disturbance, and founder effects.
Ó 2004 Elsevier Ltd. All rights reserved.
Keywords: Soil moisture dynamics; Plant water stress; River network; Geomorphology; Ecohydrology; Semi-arid; Vegetation patterns
1. Introduction
Recent years have seen dramatic advances in the
quantitative description of the geomorphologic struc-
features whose basic characteristics remain unchanged
regardless of scale, geology, or climate [18]. Despite
the deep symmetry of structural organization in geo-
morphologic properties, the convergence of the biologi-
Advances in Water Resources 28 (2005) 69–86
www.elsevier.com/locate/advwatres
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
-0.2
-0.1
0
0.1
0.2
x
10
4
10
5
10
6
10
7
10
-3
10
-2
10
-1
T
0.8
1
(a)
(b)
(c)
∆χ
a
(x)
P[T≥t]
0.43
K.K. Caylor et al. / Advances in Water Resources 28 (2005) 69–86 83
Statistical organisation “at large”. Exceedance of upstream total evapotranspiration
Rigon & Al.
eco-hydrology

!61
Does the Thermodynamics of the Earth System has a subchapter in Hydrology ?
Rigon & Al.
Thermodynamics

!62
The law of the instrument
Rigon & Al.

!63
My own path in two questions
(Where is the great optimism of the old century ?)
Where are the experiments ?
Where is the mathematics?
Rigon & Al.
My own tradition

!64
Where are the measurements ?
I mean which type of measurements can we depict to identify spatial and temporal patterns ?
Are power laws the only way to identify organisation ?
How can we use these measurements to constrain our models ?
Can information theory help ?
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 g , g , NEE, and
W03419 RUDDELL AND KUMAR: ECOHYDROLOGIC PROCESS NETWORKS, 1 W03419
Rigon & Al.
My own tradition

!65
Where is the mathematics?
Can we formulate a mathematics of the interactions ?
My own idea is that this mathematics comes out from networks (graph) analysis
I think that an interesting working hypothesis is that "the whole is the sum of its parts
and the interactions among the parts", and that part of the quality of the system, seen
as a whole, derives from parts' interactions and feedbacks. A system is itself a quite
unidentified entity, and its definition is certainly recursive, meaning that, most of the time,
a system is a system of systems, and reality is “stratified”. But having a "basic system" at
some scale should be feasible.
Rigon & Al.
My own tradition

!66
Look at the interfaces !!!
Rigon & Al.
My own advise

!67
Ezio Todini 70th Symposium: my talk
Sparse thoughts (on the foundations of a Thermodynamics of Hydrological Systems)
Reservoirology
On " How to make our models more physically-based"
Critical Zone
Which Hydrological model is better ?
What is life ? (by Erwin Schroedinger) and Hydrology
Some talk and thoughts I’ve not already mentioned
Rigon & Al.
Link to posts in my blog: some further reading for a sleeping night

!68
Find this presentation at
http://abouthydrology.blogspot.com
Ulrici,2000?
Other material at
Questions ?
Rigon & Al.
https://www.slideshare.net/GEOFRAMEcafe/scales-and-hydrology-in-2020

Scales and Hydrology in 2020

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