Beyond and side by side with numerics

Beyond and side by side with
numerics -I
Riccardo Rigon
Dance,HenryMatisse,HotelBironearly1909
Wednesday, April 24, 13

They started from wrong
assumptions, and applying a
perfect logic, they arrived
rigorously to wrong results.
My father in law

3
I am here to tell you about
What are the central topics of the work of the modellers
•Find the right equations
Introduzione
R. Rigon
•Find the right numerical methods

4
Are Richards’ equation right ?
Well, they represents mass conservation: and this is a basic principle
However
What happens when soil turns to saturation ?
What happens when soil freezes ?
What happens when warms, goofers or roots escavate the soil ?
Richards ++
R. Rigon

5
What I mean with Richards ++
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
C(⇥) :=
⇤ w()
⇤⇥
Richards ++
R. Rigon and E. Cordano

5
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
Water balance
C(⇥) :=
⇤ w()
⇤⇥
Richards ++

5
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
Water balance
Parametric
Mualem
C(⇥) :=
⇤ w()
⇤⇥
Richards ++

5
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
Water balance
Parametric
Mualem
Parametric
van Genuchten
C(⇥) :=
⇤ w()
⇤⇥
Richards ++

6
What happens when
In terms of soil water content, it cannot become
larger than porosity (if the matrix is considered
rigid).
At the transition with saturation

7
Extending Richards to treat the transition saturated to unsaturated zone.
Which means:

8
So we switch to a generalised
groundwater equations
which has been obtained by modifying the SWRC

9
What about soil freezing ?
In terms of soil water content, it cannot become
larger than porosity (if the matrix is considered
rigid).
Soil Freezing
R. Rigon and M. Dall’Amico

10
dS(U, V, M) = 0
first principle
potential
energy
kinetic
energy
internal
energy
energy fluxes at
the boundaries
second principle
the equilibrium relation becomes:
(But they are not 2 equations. The second is just a restriction on the
first ). Assuming:
K( ) = 0 ; P( ) = 0 ; ( ) = 0
Which equations ?
Soil Freezing

11
Uc( ) := Uc(S, V, A, M)
dUc(S, V, A, M)
dt
=
⇥Uc( )
⇥S
⇥S
⇥t
+
⇥Uc( )
⇥V
⇥V
⇥t
+
⇥Uc( )
⇥A
⇥A
⇥t
+
⇥Uc( )
⇥M
⇥M
⇥t
Internal Energy
entropy area
volume mass
Independent variables
To find how the equations are
modified we go to the basics
Soil Freezing

12
Expression Symbol Name of the dependent variable
⇤SUc T temperature
- ⇤V Uc p pressure
⇤AUc surface energy
⇤M Uc µ chemical potential
To find how the equations are
modified we go to the basics
So the equation for each phase is:
Soil Freezing

13
dS( ) =
1
Tw
1
Ti
⇥
dUw( ) +
pw
Tw
pi
Ti
⇥
dVw( )
µw( )
Tw
µi( )
Ti
⇥
dMw = 0
⇤
⇥
Ti = Tw
pi = pw
µi = µw
the equilibrium relation
becomes:
Flat interfaces at equilibrium
*
* The derivation is not so straightforward and implies the use of Lagrange multipliers. See Muller and Weiss,
2005
Water Freezing

14
first principle
potential
energy
kinetic
energy
internal
energy
energy fluxes at
the boundaries
second principle
but:
(But they are not 2 equations. The second is just a restriction on the
first ). Assume:
Let’s condsider a disequilibrium process
Soil Freezing equations

15
Dirichlet Boundary Conditions
Dirichlet Boundary Conditions
The Stefan problem
The Stefan problem

16
Ice (thermal conductivity,
thermal capacity)
Water (thermal conductivity,
thermal capacity)
The Stefan problem
The Stefan problem

17
Diffusion of heat through water
The Stefan problem
Diffusion of heat through ice
The Stefan problem

18
Different condition at the interface
The Stefan problem
The Stefan problem

19
⌅⌅⌅⌅⌅⌅⌅⌅⌅⌅⌅⌅⌅⌅⌅⌅⌅⌅⌅⌅⌅⇤
⌅⌅⌅⌅⌅⌅⌅⌅⌅⌅⌅⌅⌅⌅⌅⌅⌅⌅⌅⌅⌅⇥
v1 = v2 = Tref (t > 0, z = Z(t))
v2 ⇥ Ti (t > 0, z ⇥ ⇤)
v1 = Ts (t > 0, z = 0)
⇥1
v1
z ⇥2
v2
z = Lf ⇤w s
dZ(t)
dt (t > 0, z = Z(t))
v1
t = k1
2
v1
z2 (t > 0, z < Z(t))
v2
t = k2
2
v2
z2 (t > 0, z > Z(t))
v1 = v2 = Ti (t = 0, z)
Freezing case (1D
discretization)
Equations of the Stefan Problem
The Stefan problem

20
• Moving boundary condition between the two phases,
where heat is liberated or absorbed
• Thermal properties of the two phases may be different
The Stefan Problem
The Stefan problem

21
⌅⌅⇤
⌅⌅⇥
v1(t, z) = Ts +
Tref Ts
erf · erf z
2
⇥
k1 t
if z ⇤ Z(t)
v2(t, z) = Ti
Ti Tref
erfc
“ q
k1
k2
” · erfc z
2
⇥
k2 t
if z > Z(t)
⌅⌅⇤
⌅⌅⇥
v1(t, z) = Ti
Ti Tref
erfc
“ q
k2
k1
” · erfc z
2
⇥
k1 t
if z > Z(t)
v2(t, z) = Ts +
Tref Ts
erf · erf z
2
⇥
k2 t
if z ⇤ Z(t)
where ζ is the solution of:
Freezing case:
exp( 2
)
· erf
⇤T 1
⇤
k2 (Ti Tref )
⇤T 2
⇤
k1 (Tref Ts) · erfc
⇧
k2
k1
⇥ · exp
⇤
k2
k1
2
⌅
=
Lf ⇧w ⇥s
⇤
⌅
CT 2 (Tref Ts)
where ζ is the solution of:
Thawing case:
exp( 2
)
· erf
⇤T 2
⇤
k1 (Ti Tref )
⇤T 1
⇤
k2 (Tref Ts) · erfc
⇧
k1
k2
⇥ · exp
⇤
k1
k2
2
⌅
=
Lf ⇧w ⇥s
⇤
⌅
CT 1 (Tref Ts)
The Stefan Problem: analitic solutions
The Stefan problem

22
Well, the real case is a little more complicate

23
Water is
•often in unsaturated conditions
•in pores
•it is known that it does not freeze until very
negative temperatures are obtained
Beyond the Stefan problem

24
Unsaturated conditions
•Means that capillary forces acts, i.e. we have to
account for the tension forces that accumulate in
curves surfaces

25
pw = pa wa
⇤Awa(r)
⇤Vw(r)
= pa wa
⇤Awa/⇤r
⇤Vw/⇤r
= pa wa
2
r
:= pa pwa(r)
Young-Laplace equation
pa
pw
the equilibrium condition:
becomes:
What does it means unsaturated conditions

26
⇤
dp
dT
=
sw( ) si( )
vw( ) vi( )
=
hw( ) hi( )
T [vw( ) vi( )]
⇥
Lf ( )
T [vw( ) vi( )]
where Lf = 333000 J/Kg is the latent heat of fusion
Clausius-Clapeyron equation

27
A paradox ?
Water inside a capillary is at a lower pressure than atmosphere.
Therefore it should freeze before (lower the pressure, higher the freezing
temperature.

28
A paradox ?
Instead what happens is exactly the contrary, because for freezing a nucleus of
condensation has to occur
r
with r << r

29
So, actually
The situation at the freezing point is the opposite, and represented by the
blue arrow
Freezing point depression

30
Because,
the smaller the pores,
the larger the freezing point depression
larger pores
freezes before than
smaller pores

31
Because
by means of the Clausius-Clapeyron equation
there is a one-to-one relations between the
size of the pores and the temperature
depression, and because there is
also a one-to-one relationship between the
size of the pores and the pressure
there is a one-one relation among T and

32
Unsaturated
unfrozen
Unsaturated
Frozen
Freezing
starts
Freezing
procedes

33
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

34
Now
we have enough information to write the right
equations
Perhaps

35
A further assuption
To make it manageable, we do a further assuption. Mainly the freezing=drying
assuption.
Considering the assumption “freezing=drying” (Miller, 1963) the ice “behaves
like air” and does not add furhter pressure terms
Freezing = Drying

36
pw1 = pw0 + pfreez
Freezing = Drying
Freezing = Drying

37
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

38
w =
s
Aw |⇥| + 1
⇥w = ⇥r + (⇥s ⇥r) · {1 + [ (⇤)]
n
}
m
max
w = s ·
Lf (T Tm)
g T ⇥sat
⇥-1/b
Clapp and
Hornberger
(1978)
Luo et al. (2009), Niu and
Yang (2006), Zhang et al.
(2007)
Gardner (1958) Shoop and Bigl (1997)
Van Genuchten
(1980) Hansson et al (2004)
How this reflects on pressure head
Freezing = Drying

39
Unsaturated
unfrozen
Unsaturated
Frozen
Freezing
starts
Freezing
procedes
Soil water retention curves
Freezing = Drying

40
−0.05 −0.04 −0.03 −0.02 −0.01 0.00
0.10.20.30.4
Unfrozen water content
temperature [C]
Theta_u[−]
psi_m −5000
psi_m −1000
psi_m −100
psi_m 0
ice
air
water
...
T := T0 +
g T0
Lf
w0
T* at various saturation contents
= ⇥r + (⇥s ⇥r) · {1 + [ · ⇤w0]
n
}
m
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
Freezing = Drying

41
Freezing = Drying

42
Freezing = Drying

43
-3 -2 -1 0 1
0.00.20.40.60.81.0
n=1.5
temperature [C]
theta_w/theta_s[-]
psi_w0=0 psi_w0=-1000
alpha=0.001 [1/mm]
alpha=0.01 [1/mm]
alpha=0.1 [1/mm]
alpha=0.4 [1/mm]
-10000 -8000 -6000 -4000 -2000 0
0.00.20.40.60.81.0
n=1.5
psi_w0 [mm]
theta_w/theta_s[-]
T=2 T=-2
alpha=0.001 [1/mm]
alpha=0.01 [1/mm]
alpha=0.1 [1/mm]
alpha=0.4 [1/mm]
T > 0
[mm 1
]
n 0.001 0.01 0.1 0.4
1.1 0.939 0.789 0.631 0.549
1.5 0.794 0.313 0.099 0.049
2.0 0.707 0.099 0.009 0.002
2.5 0.659 0.032 0.001 1.2E-4
T = 2 ⇥
C
[mm 1
]
n 0.001 0.01 0.1 0.4
1.1 0.576 0.457 0.363 0.316
1.5 0.063 0.020 0.006 0.003
2.0 4E-3 4E-4 4E-5 1E-5
2.5 2.5E-4 8E-6 2.5E-7 3.2E-8
25
θw/θs at ψw0=−1000 [mm]
Playing with Van Genucthen
Freezing = Drying - Numbers

44
⇤
⇤t
fl
w (⇥w1)
⇥
⇤ •
⇤
KH⇤ ⇥w1 + KH⇤ zf
⌅
+ Sw = 0
Liquid water may derive from
ice melting: ∆θph
water flux: ∆θfl
Volume conservation:
⇤
⌃⇧
⌃⌅
0 ⇥ r ⇥ ⇥ ⇥ s ⇥ 1
r
⌥
w0 + i0 + 1 i
w
⇥
ph
i ⇥ fl
w ⇥ s
⌥
w0 + i0 + 1 i
w
⇥
ph
i
Mass conservation (Richards, 1931) equation:
Richards’ equation
Equation of freezing

45
U = Cg(1 s) T + ⇥wcw w T + ⇥ici i T + ⇥wLf w
U
t
+ ⌥⇥ • ( ⌥G + ⌥J) + Sen = 0
⌃G = T (⇥w0, T) · ⌃⇤T
J = w · Jw(⇥w0, T) · [Lf + cw T]
0 assuming freezing=drying
U = hgMg + hwMw + hiMi (pwVw + piVi) + µwMph
w + µiMph
i
no expansion: ρw=ρi
assuming:0
no flux during phase change
Eventually:
0 assuming equilibrium thermodynamics:
µw=µi and Mw
ph = -Mi
ph
conduction
advection
Energy Equation

46
dU
dt
= CT
dT
dt
+ ⇥w (cw ci) · T + Lf
⇥⇤ w
⇤t
⇤ w [⇥w1(T)]
⇤t
=
⇤ w
⇤⇥w1
·
⇤⇥w1
⇤T
·
⇤T
⇤t
= CH(⇥w1) ·
⇤⇥freez
⇤T
·
dT
dt
dU
dt
=
⇤
CT + w Lf + (cw ci) · T
⇥
· CH(T) ·
⇤⇥freez(T)
⇤T
⌅
·
dT
dt
-3 -2 -1 0 1
020406080100140
alpha= 0.01 [1/mm] n= 1.5 theta_s= 0.4
Temp. [ C]
U[MJ/m3]
psi_w0=0
psi_w0=-100
psi_w0=-1000
psi_w0=-10000
-3 -2 -1 0 1
alpha= 0.01 [1/mm] n= 1.5 C_g= 2300000 [J/m3 K]
Temp. [ C]
C_a[MJ/m3K]
1e+011e+021e+03
psi_w0=0 psi_w0=-1000
theta_s= 0.02
theta_s= 0.4
theta_s= 0.8
{Capp
Appearent Heat Capacity

47
⇤
⌃⇧
⌃⌅
⇤U( w0,T )
⇤t
⇤
⇤z ⇥T (⇤w0, T) · ⇤T
⇤z J(⇤w0, T)
⇥
+ Sen = 0
⇤ ( w0)
⇤t
⇤
⇤z
⌥
KH(⇤w0, T) · ⇤ w1( w0,T )
⇤z KH cos + Sw = 0
1D
representation:
Finally the “right” equations

48
GEOtop solver of freezing equations

49
The right numerical methods
Notes on numerics

50
• Finite difference discretization, semi-implicit Crank-Nicholson
method;
• Conservative linearization of the conserved quantity (Celia et al,
1990);
• Linearization of the system through Newton-Raphson method;
• when passing from positive to negative temperature, Newton-
Raphson method is subject to big oscillations (Hansson et al,
2004)
Notes on numerics

51
if ||⌅(⇥)m+1
|| > ||⌅(⇥)m
|| ⌅ ⌅⇥m+1
⇤ ⌅⇥m ⌅⇥⇥ ·
reduction factor δ with 0 ≤ δ ≤ 1.
If δ = 1 the scheme is the normal Newton-
Raphson scheme
Globally convergent Newton Method
Notes on numerics

52
Limitations of the analytical solution:
• homogeneous substance (pure water)
• instant freezing/thawing at 0˚C
• porosity=1
• SFC (soil freezing characteristic curve)
very steep (see VG parameters)
GEOtop
Notes on numerics of GEOtop

53
real soil
• constant Dirichlet conditions at the surface
• no water movement (static conditions) • Richards is OFF
-3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5
0.00.20.40.60.81.0 temperature [C]
Theta_u[-]
modeled SFC for the comparison
real SFC
GEOtop

54
!5 !4 !3 !2 !1 0 1 2
543210
Temp [ C]
soildepth[m]
phase change: simulated and analytical solution
alpha= 0.4 n= 2.5 theta_s= 1 theta_r= 0
sim an (day 0)
sim an (day 15)
sim an (day 30)
sim an (day 45)
sim an (day 60)
sim an (day 75)
time (days)
T[C]
−5−4−3−2−1012
0 15 30 45 60 75
An GEOtop
GEOtop Vs Analytical solution
alpha= 0.4 n= 2.5 theta_s= 1
0.02 m
0.12 m
0.22 m
0.32 m
0.42 m
0.52 m
0.62 m
0.72 m
Oscillations: interface Z=Z(T=0,t) cannot move in a continuum as the analytical
solution. Therefore the interface can be either on the cell i or on the cell i+1 but
not in between.
GEOtop

55
time (days)
T[C]
!5!4!3!2!1012 0 15 30 45 60 75
An GEOtop
#layers= 100 , layer D= 200 mm, alpha= 0.4 n= 2.5 theta_s= 1
0.1 m
0.3 m
0.5 m
0.8 m
1.1 m
1.5 m
3 m
4.5 m
grid size=300 mm grid size=200 mm
time (days)
T[C]
!5!4!3!2!1012
0 15 30 45 60 75
An GEOtop
#layers= 100 , layer D= 300 mm, alpha= 0.4 n= 2.5 theta_s= 1
0.15 m
0.3 m
0.5 m
0.8 m
1.1 m
1.5 m
3 m
4.5 m
GEOtop

Beyond and side by side with
numerics - II
Riccardo Rigon
Dance,HenryMatisse,HotelBironearly1909

When you arrive at Naples, you
are not at the South of Italy.
When you are at Reggio
Calabria, you are at the South!
Giuseppe Formetta

58
•Produrre un sistema di supporto alle decisioni (DSS)
•Produrre un sistema “democratico”, facilmente mantenibile, che favorisca
la cooperazione tra ricercatori
•Produrre Ricerca Riproducibile (RRS)
•Adottare un sistema informatico appropriato a trattare i dati di contorno
del solutore numerico
Aver individuato le giuste equazioni e i corretti metodi
numerici non basta
Introduction
R. Rigon

59
MODELS
IS MODELING SCIENCE ?
R. Rigon

60
To sum up
DataParametersEquations
Mass,
momentum and
energy
conservation.
Chemical
transformations
Forcings and
obervables
Equation’s
constant. In time!
In space they are
heteorgeneous
Hydrological models are the interplay of
Models
R. Rigon

61
To sum up
Numerics,
boundary and
initial conditions
Data
Assimilation.
Data Models.
Tools for
Analysis.
Calibration,
derivation from
proxies
DataParametersEquations
Mass,
momentum and
energy
conservation.
Chemical
transformations
Forcings and
obervables
Equation’s
constant. In time!
In space they are
heteorgeneous
Models
R. Rigon

62
Boundary and initial conditions
Equations are not enough
R. Rigon

63
Meteo Forcings
R. Rigon

Hourly:
- Precipitation (quantity and type, spatially distributed)
- Relative humidity (spatially distributed)
- Wind Speed and direction (spatially distributed)
- Solar Radiation (spatially distributed)
64
Required Input Data
R. Rigon

- Soil moisture (profile, in terms of matric potential, spatially
distributed)
- Soil temperature (profile, spatially distributed)
- Surface water (if present)
- Snow cover (if present)
65
Other Input Data
R. Rigon

66
Fields of Parameters
R. Rigon

Data base
Calibrazione
EVALUATION OF
STRATEGIES THROUGH
MODELS
STRATEGIES FOR
POLICY MAKERS
DATA
INTERPRETATION
67
DDS
Modelling is not just for
Modelling
R. Rigon

68
I - Once a model, design and implemented as a monolithic
software entity, has been deployed, its evolution is totally in
the hands of the original developers. While this is a good
thing for intellectual property rights and in a commercial
environment, this is absolutely a bad thing for science and
the way it is supposed to progress.
RobbedfromaCCApresentation
A critique of old modelling style
R. Rigon

69
II - Independent revisions and third-party
contributions are nearly impossible and especially when
the code is not available.
Models falsiﬁcation (in Popper sense) is usually impossible by
other scientists than the original authors.
III- Thus, model inter-comparison projects give usually
unsatisfying results. Once complex models do not
reproduce data it is usually very difﬁcult to
determine which process or parameterization was
incorrectly implemented.
A critique of old modelling style
R. Rigon

70
MODELLING, FOR WHO ?
Which end user do you have in mind ?
SCIENTIST ARE NOT THE ONLY MODELS USERS
R. Rigon

71
Users/Actors
Four types of user have been deﬁned:
• Prime users: take or prepare decisions at a political level
• Technical users: prepare projects or maps for the primary users
• Other end-users: national agencies, representative groups, etc.They
may take or prepare decisions at national or regional level, or represent
stakeholder groups.
• Model and application developers/modellers: build
models and targeted applications
R. Rigon

72
Users/Actors
These groups have been further detailed according to their roles:
• Coders: implement models, applications and tools.
• Linkers: link existing models and applications.
• Runners: execute existing models, but they create and deﬁne
scenarios.
• Players: play simulations and experiments comparing scenarios and
making analyses.
• Viewers: view the players’ results, have a low level of interaction with
the framework.
• Providers: provide inputs and data to all other user roles.
R. Rigon

73
Users/Actors
Roles
Users
Hard
Coders
Soft
Coders
Linkers Runners Player Viewers Providers
Prime
Other End
Users
Technical
Researchers
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Object-oriented software development. O-O
programming is nothing new, but it has proven to be a successful
key to the design and implementation of modelling frameworks.
Models and data can be seen as objects and therefore they can
exploit properties such as encapsulation, polymorphism, data
abstraction and inheritance.
Component-oriented software development. Objects
(models and data) should be packaged in components, exposing for
re-use only their most important functions. Libraries of
components can then be re-used and efﬁciently integrated across
modelling frameworks.Yet, a certain degree of dependency of the
model component from the framework can actually hinder reuse.
NEW (well relatively) MODELING PARADIGMS
ModiﬁedfromRizzolietal.,2005
MODELLING BY COMPONENTS
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Discrete units of software which are re-usable
even outside the framework, both for model components
and for tools components.
Seamless and transparent access to data, which
are made independent of the database layer.
A number of tools (simulation, calibration, etc.) that the
modeller will be free to use (including a visual modelling
environment).
A model repository to store your model (and
simulations) and to share it with others.
BENEFITS
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Tools for studying feedbacks among different processes.
BENEFITS FOR SCIENTISTS
Encapsulation of single processes or submodels
MUCH MORE in the ﬁeld of possibilities
New educational tools and a “storage” of hydrological
knowledge using appropriate onthologies
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T H E R E E X I S T S U C H M O D E L I N G
INFRASTRUCTURE ?
Economic modelling frameworks^. GAMS (general
algebraic modelling system, http://www.gams.com) and GTAP
(global trade analysis program, http://
www.gtap.agecon.purdue.edu ) are some of the most used
modelling systems in the agro-economic domain.They can also
account for social variables, such as unemployment.
^from Rizzoli et al., (Modeling Framework (SeamFrame)
Requirements 2005
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INFRASTRUCTURE ?
Environmental modelling frameworks. If we limit to the
agricultural domain, the list is quite limited.There is no ‘real’
framework according to the deﬁnition, but APSIM, STICS
and CropSyst provide some of the functionalities. In this area
SEAMFRAME is an emerging technology.When we consider
the water management sector, we ﬁnd many examples, such
as TIME (the invisible modelling environment), IMT, OpenMI,
and OMS, and, to a certain respect, JUPITER-API.
^ extended from Rizzoli et al., (Modeling Framework
(SeamFrame) Requirements 2005
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INFRASTRUCTURE ?
Other modelling software environments of notable
interest are SME, MMS, ICMS, Tarsier, Modcom,
Simile, but they are integrated modelling environments, not
frameworks.This means that they can be used to perform
assessments, analyses, decision support, but they do not provide
programming structures such as classes, components, objects,
design patterns to be used to create end-user applications.
^from Rizzoli et al., Modeling Framework (SeamFrame)
Requirements, 2005
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INFRASTRUCTURE ?
Other modelling software environments of notable
interest are SME, MMS, ICMS, Tarsier, Modcom,
Simile, but they are integrated modelling environments, not
frameworks.This means that they can be used to perform
assessments, analyses, decision support, but they do not provide
programming structures such as classes, components, objects,
design patterns to be used to create end-user applications.
^from Rizzoli et al., Modeling Framework (SeamFrame)
Requirements, 2005
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INFRASTRUCTURE ?
Atmospheric Sciences: Earth Sciences Modeling Framework
(ESMF) (including Earth System Curator)
High Performance Computing: Common Component
Architecture (CCA)
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DEPLOYEMENT
PREREQUISITES
ALLOWS WRAPPING OF EXISTING CODES BUT
PROMOTES BETTER PROGRAMMING STRATEGIES
BUILT BY OPEN SOURCE TOOLS
DATA BASE PROVIDED
OGC COMPLIANT
CUAHSI SPECIFICATIONS AWARE
DEPLOYABLE THROUGH THE WEB
CAN BE ENDOWED WITH ONTOLOGIES
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The complete framework
PostGIS
Postgres
Web
services
WMS
WFS-T
WPS
Web
services
WMS
WFS-T
WPS
OMS3
Jgrasstools
JGrass
uDig
Eclipse RCP
H2 spatial
UIBuilder
GRASS
GIS engine
The Horton
Machine
Models
BeeGIS
DEPLOYEMENT
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Java
JGrass
uDig
Eclipse RCP
SOLIDITY: The framework bases on the solid fundaments of the Eclipse RCP
framework first created by IBM.
CONNECTIVITY and USERFRIENDLYNESS:The GIS framework is based on the uDig
GIS framework, specialized in accessibility and remote connections
ANALYSIS: The JGrass extentions define a layer of powerful GIS analysis tools and a
straight connection to the GRASS GIS
MOBILITY:The BeeGIS extentions supply tools for digital field surveying
BeeGIS
DEPLOYEMENT

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Connectivity and web standards
Database:
PostGIS-Postgres
H2 spatial
Web services
WMS
WFS-T
soon WPS
DATABASE: The GIS framework is ready to connect
to external relational databases as postgres, mysql or
oracle. To spatial data servers like postgis, Oracle
spatial and Arcsde. It also comes with an internal
spatial database based on H2 (no indexing yet)‫‏‬‫‏‬.
It would be fairly easy to create connections to
RESTful services to acquire data.
WEB SERVICES AND STANDARD WEB PROTOCOLS:
The framework supports OGC web standards
like the web mapping service (WMS), the web
feature service, also in transactional format (WFS-
T). An efforth for the web processing service is
ongoing.
DEPLOYEMENT

87
The analysis engine
OpenMI
GRASS
THE CONSOLE ENGINE: the console engine
supplies a framework for modeling development
and scripting environment for fast
methodology testing.The engine contains already
masses of modules called Horton Machine for
various terrain analyses as well as a stability
model and hydrologic models.
Also the engine gives access to the GRASS
analysis modules.
THE STANDALONE MODE:The need for usage
of the modelling environment on supercomputer
deﬁned a heavily decoupled design for the
console engine. The framework deﬁnes a strict
interface between GUI and analysis engine, which
makes it easy to exploit the console engine in
standalone mode on server-side.
The Horton
Machine
Models
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88
The relationship to OMS3
OMS3
THE OMS3 ENGINE: the console engine exposes a
compiler for an OMS3 based modeling language.This
gives a way to write scripts to execute openmi chained
models.
THE OGC STANDARDS EXTENTION:The need for big
vector and raster data forced the team to extend the
OMS3 standard interfaces with two GIS OGC standards:
the OGC feature model
the OGC grid coverage service (in prototype mode)‫‏‬
OGC IN JGRASS: the OGC feature and grid coverage models are served by the
geotools libraries.The coverage model is based on the Java Advanced Imaging
library and supports tilecaching for processing of large dataset. Coverage data are
passed to native languages as C, C++ and Fortran through the easy adoptable
JNA libraries.
The Horton
Machine
Models
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89
Not just an idea
but a reality
The case of JGrass-NewAGE
The State Of Art of the Project
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Formetta et al., CAHMDA IV Lhasa 2010 - July 21-23
5
Modelling with componentsGIS Integration Multi-platform
Multi-languageOpen-source Reproducible research system
NewAge Goals:
Motivation Outline Hydrological Components Modelling Framework Conclusions
Trento 19 April 2013G. Formetta,
R. Rigon with Hydrologis and G. Formetta

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The RRS concept
Since research and technical work rely on daily use of computer programs
•Models conﬁgurations
•Models setup
•Models input data
•Models output
•Results interpretation
Should be sharable in the easiest way
R. Rigon, G. Formetta, and O. David

92Formetta et al., CAHMDA IV Lhasa 2010 - July 21-23
10
Model setting
Hillslope
Features
Basin splitted
in hillslopes
Outline Calibration Issues Data AssimilationMotivation Hydrological Component
Trento 17 June 2011G. Formetta, Trento 24 June 2011
Outline ConclusionsInformatic StructureHydrological Components
Leipzig 05 July 2012G. Formetta,
Hydrologis, R. Rigon and G. Formetta

93
1
Model setting
Network splitted
in links
Links
Features
Outline Calibration Issues Data AssimilatMotivation Hydrological Component
Outline Calibration IssuInformatic Structure Hydrological Components
Motivation Outline Hydrological Components Modelling Framework Conclusion
Hydrologis, R. Rigon and G. Formetta

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16
Interpolation Problem
Verification Procedure
Outline Calibration IssuesInformatic Structure Hydrological Components
1) Start from a complete dataset
Outline ConclusionsInformatic StructureHydrological Components

95
21
Precipitation Interpolation: Krigings

96
28
Shortwave Energy Model: raster mode application on Piave river
Simulation time step: hourly
Simulation Period: 01/10/201-
02/10/2010

97
29
NewAge-OMS3 automatic calibration algorithms
Generic Parameter set
Optimal Parameter set
Uncertainty:
•  catchment heterogeneity
•  model limitations
•  measurement techniques

98Formetta et al., CAHMDA IV Lhasa 2010 - July 21-23
34
Outline Calibration IssuesInformatic Structure Hydrological ComponentsOutline ConclusionsInformatic StructureHydrological Components
Basin Delineation Conclusions
Formetta G., ARS-USDA-Fort Collins (CO)
Motivation Hydrological Components
Formetta G., David O. and Rigon R.
Little Washita river basin: Rainfall-Runoff modelling solution

99
39
Something more than a classical model
Rome 09 March 2011Trento 17 June 2011G. Formetta, Trento 24 June 2011
Different possibility to run OMS3 components
uDig 1.3.1 Spatial Toolbox
Trento 24 June 2011
Hydrologis, R. Rigon, G. Formetta, and O. David

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40
Rome 09 March 2011Trento 17 June 2011
OMS3 Console

101
41
Rome 09 March 2011Trento 17 June 2011G. Formetta, Trento 24 June 2011
OMS3 Console
Command Line

102
42
Rome 09 March 2011G. Formetta,
What is a .sim file?

103
The file structure is different
respect to a common .sim file:
- Model: here the model has to
be calibrated
- PSO Parameters: here have
to be assigned
- Model Parameters to optimize:
here have to be assigned
- Objective Function, Model output
and measurements: here have to
be assigned
Particle Swarm calibration .sim file
Outline ConclusioInformatic StructureHydrological Components
Motivation Outline Hydrological Components Modelling Framework Conclus

104
EPILOGUE
OUR AIM IS NOT TO MODEL EVERYTHING*OR
DO A MODEL OF EVERYTHING BUT GIVE A
S P A C E W E R E D I F F E R E N T , E V E N
CONTRADICTORY, IDEAS,AND DATA CAN BE
EXPLOITED IN A WAY WHICH PROPELS
COLLABORATIVE EFFORTS BY SCIENTISTS
AND USERS.
*“Correctly interpreted, you know, pi contains the entire history of the human race.”
-Dr. Irving Joshua Matrix, from M. Gardner,“The magic numbers of dr. Matrix”
The Overall Goal
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Direct Contributors:
Andrea Antonello uDig and jgrasstools core developer and architect
Giacomo Bertoldi GEOtop developer (energy budgets, vegetation)
Emanuele Cordano GEOtop developer (Richards equation, I/O)
Matteo Dall’Amico GEOtop developer (permafrost, GEOtop-mono)
Stefano Endrizzi GEOtop developer (energy budgets, snow, permafrost)
Giuseppe Formetta JGrass-NewAGE developers
Silvia Franceschi Jgrasstools models developer and architect
Riccardo Rigon All the merits go to the others
Erica Ghesla, Andrea Cozzini, Silvano Pisoni and others contributed to original version of the
Horton Machine
Acknowledgements
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G.Ulrici-2000?
Thank you
R. Rigon

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