Which is the best model ?

Which hydrological model is better ?
GeorgiaO’Keefe
Riccardo Rigon
Fort Collins, USDA/ARS, August 27, 2014

!2
The good old Hydrological cycle
R. Rigon
Introduction

!3
Every Hydrologist would like to have
THE MODEL of IT
But in reality everybody wants just to investigate a limited set of
phenomena: for instance the discharge in a river. Or landsliding , or
soil moisture distribution.
Any problems requires its amount of prior information to
be solved: some problems needs more detailed information of others
R. Rigon
Introduction

!4
For the impatients I reveal the killer before
Up to a point*… there is no the best model
* See Klemes, Dilettantism in hydrology: Transition or destiny?, Wrr, 1986.
* See also: http://abouthydrology.blogspot.com/2012/02/which-hydrological-model-is-better-q.html
End of the story
R. Rigon

!5
Should we just care of process-based
models ?
The criticisms to this type of modelling have foundations.
PeakFlow
GEOtop
NewAge
Boussinesq
SHALSTAB GEOtop-FS The Horton Machine
and we have several models that we use at different scales and for
different purposes
We did not marry process based models
R. Rigon

!6
Boussinesq
FullyCoupled
Subsurface-Surface
GridBased
PeakFlow
GIUH
Peakfloods
So we use different models
GEOtop
Fullydistributed
Gridbased NewAge
Largescalemodelling
Hillslope-Stream
AnthropicInfrastructures
The complexity arrow
R. Rigon
Many models is better

!7
Every one of them:
!
!
!
Perform the mass budget (and preserves mass)
!
Make hypotheses on momentum variations
!
Simplify the energy conservation (and its dissipation)
to a certain degree
!
(Implicitly delineates a way to entropy increase)
R. Rigon
Ours have some in common

!8
!
(Rigon et al., Jour. Hydromet., 2006, Endrizzi et al., GMDD, 2014)
This model focuses on the water and energy budgets at few
square meters scale with the goal of describing catchment
hydrology including (a reasonable parameterization) all
known processes. (Whatever this means)
A first modelling adventure
see also: http://abouthydrology.blogspot.com/search/label/GEOtop
R. Rigon
GEOtop

!9
1. Radiation
4. surface energy balance
- radiation
- boundary-layer interaction
2. Water balance
- effective rainfall
- surface flow (runoff and channel
routing)
- distributed model
- sky view factor, self and cast
shadowing, slope, aspect, drainage
3. Snow-glaciers
- multilayer snow
scheme
- soil
temperature
- freezing soil
5. soil energy balance
- multi-layer vegetation
scheme
- evapotranspiration
6 . v e g e t a t i o n
interaction
R. Rigon
GEOtop

!10
snow, ice, permafrost
water cycle in
complex terrain
landsliding
evapo-transpiration,
energy fluxes
Bertoldi et al., 2006
Bertoldi et al 2010
DellaChiesa et al., 2014
Endrizzi 2007
Dall’Amico 2010
Endrizzi et al,
2010a,b
Endrizzi et al.,
2014
Simoni et al 2008
Lanni et al, 2010
Rigon et al., 2006
Hingerl et al., 2014
Formetta et al., 2014
Why this complexity ?
R. Rigon
GEOtop

!11
Meteo
Rainfall/Snow
Snow/Energy budget
Atm. TurbulenceRadiation
For each time stepGEOtop, NewAge
Al the models the
same strategy but
w i t h d i f f e r e n t
a m o u n t o f
information flowing
R. Rigon
GEOtop ﬂow chart

!12
Richards ++
Surface flows
Channel flow
Next time step
GEOtop
R. Rigon
GEOtop ﬂow chart

!13
First, I would say, it means that it would be better to call it, for
instance: Richards-Mualem-vanGenuchten equation, since it is:
Se = [1 + ( ⇥)m
)]
n
Se :=
w r
⇥s r
C(⇥)
⇤⇥
⇤t
= ⇥ · K( w) ⇥ (z + ⇥)
⇥
K( w) = Ks
⇧
Se
⇤
1 (1 Se)1/m
⇥m⌅2
SWRC +
Darcy-Buckingham
(1907)
Parametric
Mualem (1976)
Parametric
van Genuchten
(1981)
C(⇥) :=
⇤ w()
⇤⇥
Not only this:
What I mean with Richards++
R. Rigon

!14
For instance this:
Extending Richards to treat the transition from saturated to unsaturated
zone. Which means:
R. Rigon

!15
So, consider a traditional 1D infiltration problem
R. Rigon
An example

!16
So, consider a traditional 1D infiltration problem
usually it cannot be treated with Richards because of the saturation front
R. Rigon
An example

!17
But GEOtop is also 3D
After Lanni et al, 2010 , unpublished
R. Rigon
GEOtop does 3D

!18
Landsliding
dry case - low intensity precipitation
R. Rigon
GEOtop does 3D

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Landsliding
wet case - high intensity precipitation
R. Rigon
GEOtop does 3D

!20
More complex stuff
Extending Richards to treat the phase transition. Which means essentially to
extend the soil water retention curves to become dependent on temperature.
Unsaturated
unfrozen
Freezing
starts
Freezing
procedes
Unsaturated
Frozen
R. Rigon

!21
pw0 = pa wa
⇥Awa(r0)
⇥Vw
= pa pwa(r0) pi = pa ia
⇥Aia(r0)
⇥Vw
:= pa pia(r0)
pw1 = pa ia
⇥Aiar(0)
⇥Vw
iw
⇥Aiw(r1)
⇥Vw
Two interfaces (air-ice and water- ice) should be considered!!!
Curved interfaces with three phases
Four phases … well interfaces are phases too, indeed
R. Rigon

!22
A further assuption
To make it manageable, we do a further assumption. Mainly the freezing=drying
one.
Considering the assumption “freezing=drying” (Miller, 1963) the ice “behaves
like air” and does not add further pressure terms
Freezing=Drying
R. Rigon

!23
Unfrozen water content
soil water
retention curve
thermodynamic
equilibrium (Clausius Clapeyron)
+
⇥w =
pw
w g
pressure head:
w(T) = w [⇥w(T)]
How this reflects on pressure head
Freezing=Drying
R. Rigon

!24
Unsaturated
unfrozen
Unsaturated
Frozen
Freezing
starts
Freezing
procedes
Soil water retention curves
Freezing=Drying
R. Rigon

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Freezing=Drying
R. Rigon

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Freezing=Drying
R. Rigon

!27
T := T0 +
g T0
Lf
w0
ice content: i =
⇥w
⇥i
w
⇥
⇥w = ⇥r + (⇥s ⇥r) ·
⇤
1 + ⇤w0
Lf
g T0
(T T⇥
) · H(T T⇥
)
⇥n⌅ m
liquid water content:
Total water content:
depressed
melting point
Modified Richards equations
= ⇥r + (⇥s ⇥r) · {1 + [ · ⇤w0]
n
}
m
Water and ice mass budget
R. Rigon

!28
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,
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
The whole story here
see also Dall’Amico Ph.D thesis: http://eprints-phd.biblio.unitn.it/335/
The long story of soil freezing - Chapter 1
R. Rigon

!29
Obviously this makes it possible to simulate
a lot of new phenomenologies
Sisik, river in the artic tundra
EndrizzietAl.,JHR,2010
R. Rigon
Do you care of runoff on frozen soil ?

!30
44
thaw depth: T(z,t)=0 water table depth: ψm(z,t)=0
Stefano Endrizzi, William Quinton, Philip Marsh, Matteo Dall’Amico, 2010 in preparation
R. Rigon

!31
The model allows to show that the runoff
properties of a basin dramatically change when
soil freeze.
Runoff on frozen soil
R. Rigon

!32
Arabba
Pordoi
Caprile
Malga Ciapela
Pescul
Ornella
Saviner
Frozen soil can be combine with the snow module
R. Rigon
Snow generated runoff

!33
Frozen soil can be combine with the snow module
R. Rigon

!34
02468101214
Date (dd/mm)
Discharge[m3/s]
01/10 01/12 01/02 01/04 01/06 01/08 01/10
measuredGEOtop
Discharge at Saviner year 2006−2007
We have to work more here!
R. Rigon

!35
So well tested that is confidently used for real-time
forecasting (driven by ground data)
Use it !
R. Rigon

!36
An experimental elevation transect
Elevation as a proxy of climate change: Mazia Valley, emerging LTER
Station
B2000 m
Hs, SWC,
Biomass, GAI
Station
B1500 m
Hs, SWC,
Biomass, GAI,ET
Station
B1000 m
Hs, SWC,
Biomass, GAI
T~ 3.5K
T~ 3.5K
Courtesy of G. Bertoldi, EURAC. Complete presentation and reference at:
http://abouthydrology.blogspot.com/2014/05/process-based-hydrological-modelling-of.html
R. Rigon
Eco-hydrology of mountain prairies

!37
Elevation gradient: validation
Multiple variables validation: SWE, SWC, above ground biomass (Bag), ET
Two years of data: calibration in B1500, validation in B1000, B2000
B2000mB1500mB1000m
Snow Height [cm] SWC 5cm [] ET [mm]
Not Measured
Not Measured
r2=0.66
RMSE=7.1
r2=0.57
RMSE=5.9
r2=0.55
RMSE=2.9
r2=0.80
r2=0.78
r2=0.82
Bag [gDMm 2]
RMSE=0.04
RMSE=0.05
RMSE=0.04
r2=0.93
RMSE=58.39
Courtesy of G. Bertoldi, EURAC. Complete presentation and reference at:
http://abouthydrology.blogspot.com/2014/05/process-based-hydrological-modelling-of.html
R. Rigon

!38
The GEOtop 2.0 – DV model
Rigon et al., JHM, 2006;
Endrizzi et al. GMDD, 2014.
Processes
Dynamic vegetation
model (for grasslands)
From Montaldo et al., 2005;
Della Chiesa et al., 2014
R. Rigon

!39
So GEOtop is a succes story !
Is’nt it ?
R. Rigon
A synthesis

!40
You can find the GEOtop code at:
git clone https://code.google.com/p/geotop/
Compiling instructions:
http://abouthydrology.blogspot.com/2014/04/installing-
geotop-on-mac-and-linux.html
Manual:
http://abouthydrology.blogspot.com/2011/08/new-
version-of-geotop-with-draft-user.html
User and Developers:
geotopusers@googlegroups.com
geotopdev@googlegroups.com
If you like you can use it !
R. Rigon

!41
However
Developing GEOtop while learning about the
processes and the appropriate numerics required a
lot of code rewriting.
Every student working on GEOtop cancelled hours of
work of the other students.
The code was built as a “monolithic” software, and
this makes its maintenance very difficult, even
having the source code
R. Rigon
Looking behind to the whole process of building GEOtop

!42
While developing GEOtop, the coded evolved, and
third parties developers, doing applications, got
mad in adapting their code to the new versions.
And
As Olaf D. cites: “A fool with a tool remains a fool”.
And if someone goes crazy in developing a tool
eventually s/he fall in the above case.
R. Rigon
Looking behind to the whole process of building GEOtop

!43
A second model adventure
Picasso,DoraMaar
Deconstructing models
R. Rigon
Modelling a different way or perish

!44
Therefore we have to find a new way to build
models
That enhances
•cooperation among researchers,
•the analysis of hydrological processes,
•the comparison among different modelling solutions,
•the adoption of reproducible research strategies,
•sharing of model codes,
•reproduction of research simulations,
Modern OO tools can help
R. Rigon
Modelling a different way or perish

!45
Modelling by components: a solution
I am in the home of modelling by components, here, but let me repeat for those
are unaware of it. In modelling by components, every process becomes a “piece
of software” that can be programmed and inspected independently from the
other components. Components interact just at run-time, after have been
linked together, for instance with a scripting language, in an intermediate
phase.
R. Rigon
Modelling by components

!46
To make a long story short, we chose OMS
OMS3 can be found at: http://www.javaforge.com/project/
Resources
Knowledge

Base
Development

Tools
Products
OMS3
http://www.javaforge.com/project/oms
R. Rigon
Modelling by components

!47
The framework offers new exciting possibilities
So we have a foundational theoretical
declarations about JGrass-NewAGE
“…This system sacrifices process details in favour of efficient
calculations. It is made of components apt at returning statistical
hydrological quantities, opportunely averaged in time and space.
One of the goals of this implementation effort was to create the
basis for a physico-statistical hydrology in which the hydrological
spatially distributed dynamics is reduced into low dimensional
components, when necessary surrogating the internal heterogeneities
with "suitable noise" and a probabilistic description ….”
R. Rigon
Peruse and abuse of models

!48
In practice what we implemented
is a trade-off between the official morality and a more practical and
agnostic view, where we do not expect to derive the statistical laws first
and implement them eventually, but we adopt right away some solution
that compromise among experimental evidence, scientific knowledge,
mathematical convenience, and computational tractability ... and the
natural laziness that everybody has.
On the other hand, being easy exchanging components (and to a certain
extent to produce them) it is easy (once you have them) to compare
components with the same scope, independently from the heuristic that
generated them.
Being realistic
R. Rigon

!49
http://abouthydrology.blogspot.com/2013/06/ezio-todini-70th-symposium-my-talk.html
R. Rigon
Many models is better … but are they consistent ?

!50
JGrass-NewAGE
(Formetta et al., GTD, 2011)
This model focuses on the hydrological budgets of medium
scale to large scale basins as the product of the processes
“averaged” at the hillslope scale with the interplay of the
river network.
JGrass-NewAGE a.k.a. NewAGE

!51
G. Formetta et al.: Snow water equivalent modeling component in NewAge-JGrass
ation component (Eberhart and
) component (Hay et al., 2006);
Adaptive Metropolis (DREAM)
, 2009).
lope-link geometrical partition
unit for the water budget eval-
illslope, rather than a cell or a
ciated link. The model requires
gical forcing data (air tempera-
midity) for each hillslope. This
deterministic inverse distance
1992; Lloyd, 2005), kriging
ed kriging as in Garen et al.
(2005).
metta et al., 2013) implements
ount shadows and complex to-
n under generic sky conditions
ng to Helbig et al. (2010) and
on choices such as Erbs et al.
nd Orgill and Hollands (1977).
et is based on Brutsaert (1982)
(including those not described
ne of the automatic calibration
particle swarm optimization al-
M. Evaluation of each model
tually carried out with the use
lidation), which provides some
oodness of ﬁt, such as Nash–
Fig. 1. The NewAge system showing all the modeling compo-
nents, starting from the top: the uDig Geographic Information Sys-
tem (GIS), the meteorological data interpolation tools, energy bal-
ance, evapotranspiration, runoff production-routing and snow water
The structure of NewAGE
R. Rigon

!52
Rinaldo,GeomorphicFloodResearch,2006
Someone call them Hydrologic Runoff Units
we call them hillslope-link partition of the basin
R. Rigon

!53
Rinaldo,GeomorphicFloodResearch,2006
For each of the variable of the hydrological cycle
a statistics is made for each hillslope and a single value is returned
so, we have 5 values of the prognostics quantities here, that are space
time-averages of what happens inside each hillslope
R. Rigon

!54
They are estimated
for each hillslope
•mean or suitable rainfall
!
•mean or suitable radiation (we exploit some old idea by Ian Moore)
!
•mean or suitable evapotranspiration
!
•mean or suitable snow cover
!
•mean or suitable runoff production
R. Rigon

!55
Subsequently, the user can choose between two different runoff
Fig. 4. Hillslope-link partition of the basin work-ﬂow.
G. Formetta et al. / Environmental Modelling & Software 55 (2014) 190e200 195
So components for watershed partition
The treatment of the topographic data first
R. Rigon
Formettaetal.,Hydrologicalmodellingwithcomponents:AGIS-basedopen-source
framework,2014

!56
Hillslope Storage
Dynamics
Surface flows
Aggregation
Channel flow
Next time step
JGrass-NewAge
Formetta et al., GTD, 2011,
Formetta et al, EM&S, 2014
R. Rigon

!57Fig. 6. The workﬂow for the Fort Cobb river basin application.
G. Formetta et al. / Environmental Modelling & Software 55 (2014) 190e200
Rainfall-Runoff*
R. Rigon
framework,2014

!58
When runoff is collected
then is routed, for small basins, with a modification of the Muskingum-Cunge
algorithm, or directly with a semi-implict solver of the de Saint-Venant 1D
R. Rigon
Watershed model of NewAGE

!59
Thus we have discharges
Here, Here ... and here again
R. Rigon
Watershed model of NewAGE

!60
Input Data treatment
Goodness of fit
Next time step
JGrass-NewAge
Calibration tools
R. Rigon
Formetta et al., GTD, 2011,
Formetta et al, EM&S, 2014

Forcings and Calibration
R. Rigon
framework,2014

!62
Hillslope Storage
Dynamics
Surface flows
Aggregation
Channel flow
Next time step
Radiation
R. Rigon
Formettaetal.,ModelingshortwavesolarradiationusingtheJGrass-NewAge
system,2013

!63
G. Formetta et al.: Modeling shortwave solar radiation using the JGrass-NewAge system 919
Fig. 1. OMS3 SWRB components of JGrass-NewAge and flowchart
to model shortwave radiation at the terrain surface with generic sky
conditions. Where not specified, quantity in input or output must be
intended as a spatial field for any instant of simulation time. ”Mea-
Fig. 1. OMS3 SWRB components of JGrass-NewAge and flowchart to model shortwave radiation at the terrain surface with generic sky
conditions. Where not specified, quantity in input or output must be intended as a spatial field for any instant of simulation time. “Measured”
efers to a quantity that is measured at a meteorological station. The components, besides the specified files received in input, include an
appropriate set of parameter values.
Radiation
R. Rigon
system,2013

!64
to model shortwave radiation at the terrain surface with generic sky
conditions. Where not specified, quantity in input or output must be
intended as a spatial field for any instant of simulation time. ”Mea-
Fig. 1. OMS3 SWRB components of JGrass-NewAge and flowchart to model shortwave radiation at the terrain surface with generic sky
conditions. Where not specified, quantity in input or output must be intended as a spatial field for any instant of simulation time. “Measured”
efers to a quantity that is measured at a meteorological station. The components, besides the specified files received in input, include an
appropriate set of parameter values.
Radiation
R. Rigon
system,2013

!65
G. Formetta et al.: Modeling shortwave solar radiation using the JGrass-NewAge system
for automatic Jack-Knife procedure. The Jack-knife component
(which is not used in the present paper) simply needs to be added to
the basic model solution, and actually just substitutes the the Verifi-
OMS3 SWRB components of JGrass-NewAge and flowchart for automatic jackknife procedure. The jackknife component (which
sed in the present paper) simply needs to be added to the basic model solution, and actually just substitutes the the verification
ent in Fig. 1
R. Rigon
Radiation - II
system,2013

!66
Fig. 5. The Fort Cobb river basin, Oklahoma (USA). riangles repre-
sent the veriﬁcation set (V-set) and circles represent the calibration
set (C-set). The comparison between measured and modeled incom-
ing solar radiation is represented in term of scatter plots.
Fig. 5. The Fort Cobb Reservoir basin, Oklahoma (USA). Triangles represent the V-set and circles represent the C-set. The comparison
between measured and modeled incoming solar radiation is represented with scatter plots.
in which R represents the linear correlation coefﬁcient
between the S and O values, A and B are, respectively
expressed in Eqs. (33) and (34):
A =
o
s
, (33)
point of the Piave River basin. In order to perform this ap-
plication it was necessary to interpolate the air temperature
and relative humidity measurement data for each pixel of the
basins by using a detrended kriging component. The simula-
tion time step was hourly and the simulation period was one
day: from 1 January 2010 to 1 February 2010.R. Rigon
Radiation: test at stations
after Formetta et al., GMD, 2013

!67
G. Formetta et al.: Modeling shortwave solar radiation using the JGrass-NewAge system
Fig. 7. The Figure represents the global shortwave radiation on the
Piave area the first october 2010, at four different hours of the day.
During the day differently oriented hillslope received the maximum
amount of radiation and, at 4 p.m. most of the area is covered by
shadows.
Fig. 7. The figure represents the global shortwave radiation on the
Piave area on 1 October 2010 at four different hours of the day.
During the day, differently oriented hillslope received the maximum
amount of radiation and, at 16:00 LT most of the area is covered by
shadows.
also due to the lower measure
elevation zones.
Because of this topographic
surement data uncertainty of t
influenced the atmospheric tran
is confirmed also by the data
basin measurements show lowe
example, the correlation betwe
Washita River basin, where the
play a crucial role.
Regardless, the model was
shortwave solar radiation also
pography. The PBIAS index w
case. According the hydrologic
on PBIAS index, presented in
Stehr et al. (2008), the results a
sified as “good” and therefore
suitable to be used for the estim
solar radiation.
Finally, Fig. 7 presents the r
model. Maps of incoming sola
four hours during the daytime.
pographic feature of the Piave
radiation maps. Their patterns c
cording to the solar position, th
shadow.
5.2 About the possibilities
based JGrass-NewAGE
Since the goal of the paper wasR. Rigon
Radiation: daily total radiation over an area
system,2013

!68
Hillslope Storage
Dynamics
Surface flows
Aggregation
Channel flow
Next time step
Evapotranspiration
Radiation
R. Rigon

Forcings and Calibration
R. Rigon
framework,2014

!70
Hillslope Storage
Dynamics
Surface flows
Aggregation
Channel flow
Next time step
JGrass-NewAge
(Formetta et al., GTD, 2011
Evapotranspiration
Radiation
Including snow
Including snow (with various models)
R. Rigon
Formetta et al., Snow water equivalent modeling components in NewAge-JGrass, 2014

!71
Fig. 2. The SWE-C integration into the NewAge system, showing connections with the shortwave radiation component and kriging inte
ation algorithm. The connection with the particle swarm optimization algorithm is presented as a red dashed line.
Table 1. Meteorological stations used in test simulations for the
Formetta et al.: Snow water equivalent modeling component in NewAge-JGrass
R. Rigon

!72
Formetta et al.: Snow water equivalent modeling component in NewAge-JGrass 15
Figure 8. SWE-C application in distributed mode: snow water
equivalent maps from 1 November to 1 June for the Upper Cache la
Poudre basin.
www.jn.net J. Name
Fig. 8. SWE-C application in distributed mode: snow water equiva-
lent maps from 1 November to 1 June for the upper Cache la Poudre
Basin.
and temperature maps was relatively small, and further work
temperature only or bo
The model is integrated
ical model as an OMS3
can make use of all the
GIS-based visualization,
evaluation packages. All
veriﬁed at three SNOTE
Poudre River basin (Co
forms well for both dai
model performance degr
uation periods. This is
step compared to an hou
that both the degree-day
els are very sensitive to
they have to be evaluated
dividual sites but also fo
time and space.
Using an hourly time
degradation when movin
tion period. Therefore, a
could be to adopt a time
bin et al. (2013).
Finally, the model is
ulate spatial patterns of
snow water equivalent pR. Rigon

!73
1995 1996
1997 1998
1999 2000
0
500
1000
1500
0
500
1000
1500
2000
2500
0
500
1000
1500
0
500
1000
1500
2000
0
500
1000
1500
2000
0
1000
2000
3000
Jan 1995 Apr 1995 Jul 1995 Oct 1995 Jan 1996 Jan 1996 Apr 1996 Jul 1996 Oct 1996 Jan 1997
Time
BasinmeanwaterFluxes(mm)
Figure 15: The water budget closure based on the use of all the rainfall, discharge and evapotranspiration estimation at annual time scale. The
plots reports for the ﬁrst sex years of the analysis. The solid line with red band is the annual cumulative TAW (total available water) which
includes the rainfall input plus the residual storage(P-Q-ET) remains from the last hydrological year, the dash line with blue band is the annual
cumulative ETa, the dot line with black band is annual cumulative discharge at the outlet (Q), and the longdash line with gray band is annual
cumulative OUTFLOW (ETa + Q). The lines are the maximum and the minimum estimation value, while the bands are the ranges of error in the
estimation.
14
The whole budget
R. Rigon
Aberaetal.,inpreparation,2014

!74
Observe,
that I did not mention the complexity implied by
the Richards equation.
!
WHERE IS IT NOW ?
Concluding
Toward some conclusion
R. Rigon

!75
A rigorous statistical theory would be needed that
allows for
!
•doing rigorously such simplifications*, not just on the basis of the personal Art
of modelling^;
!
•quantify the uncertainty remained after the simplifications**
*for a derivation of part of it see Cordano and Rigon, 2008 and BTW compare it with the abstract view
Reggiani et al., 1999
^Art will remain, anyway ...
** The distribution around the mean quantities could not be sharp. Variances can be important ...
A need of a “statistical theory”
R. Rigon

!76
The more “reductionist” GEOtop
!
could be used to test the solutions implemented in the simplified NewAGE and
evaluate the non-acceptable behaviors.
Obviously, this is not as simple as
it can be, because GEOtop itself
comes with its simplifications and
errors
A need of a “statistical theory”
R. Rigon

!77
Merging the two worlds
R. Rigon

!78
In general, when building our models, we should
have a clear and disenchanted vision of their
limits, a theory for their errors, and the idea of
the measures (if we do not have controlled
experiments) to falsified them. The best would
be to have a theory* correlating the information
(of the signal) we need to reproduce with the
complexity of the model needed to get it, so we
do not exaggerate with detailed descriptions of
the (micro-)physics, at finer scales, which are not
required at the larger ones.
Conclusion for physics
R. Rigon
For tentative studies about the relation of modelling and information theory see also: http://
abouthydrology.blogspot.com/2014/07/uncertainty-and-information-theory.html

!79
We go
!
OMS
Conclusion for informatics
R. Rigon

!80
To my former Ph.D. students
R. Rigon
A thank to my Ph.D students: they made it possible

!81
Find this presentation at
http://abouthydrology.blogspot.com
Ulrici,2000?
Other material at
Thank you audience !
R. Rigon
http://www.slideshare.net/GEOFRAMEcafe/which-is-the-best-model

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