Beyond and side by side with numerics
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Transcript of Beyond and side by side with numerics
Beyond and side by side with numerics -I
Riccardo Rigon
Dan
ce, H
enry
Mat
isse
, Hot
el B
iron
ear
ly 1
909
Wednesday, April 24, 13
They started from wrong
assumptions, and applying a
perfect logic, they arrived
rigorously to wrong results.
My father in law
Wednesday, April 24, 13
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
Wednesday, April 24, 13
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
Wednesday, April 24, 13
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
Wednesday, April 24, 13
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
Water balance
C(⇥) :=⇤�w()⇤⇥
Richards ++
R. Rigon and E. Cordano
Wednesday, April 24, 13
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
Water balance
ParametricMualem
C(⇥) :=⇤�w()⇤⇥
Richards ++
R. Rigon and E. Cordano
Wednesday, April 24, 13
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
Water balance
ParametricMualem
Parametricvan Genuchten
C(⇥) :=⇤�w()⇤⇥
Richards ++
R. Rigon and E. Cordano
Wednesday, April 24, 13
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
R. Rigon and E. Cordano
Wednesday, April 24, 13
7
What I mean with Richards ++
Extending Richards to treat the transition saturated to unsaturated zone. Which means:
At the transition with saturation
R. Rigon and E. Cordano
Wednesday, April 24, 13
8
So we switch to a generalisedgroundwater equations
which has been obtained by modifying the SWRC
At the transition with saturation
R. Rigon and E. Cordano
Wednesday, April 24, 13
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
Wednesday, April 24, 13
10
dS(U, V, M) = 0
first principle
potential energy
kineticenergy
internalenergy
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
R. Rigon and M. Dall’Amico
Wednesday, April 24, 13
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 areavolume mass
Independent variables
To find how the equations are modified we go to the basics
Soil Freezing
R. Rigon and M. Dall’Amico
Wednesday, April 24, 13
12
Expression Symbol Name of the dependent variable⇤SUc T temperature
- ⇤V Uc p pressure⇤AUc � surface energy⇤MUc µ chemical potential
To find how the equations are modified we go to the basics
So the equation for each phase is:
Soil Freezing
R. Rigon and M. Dall’Amico
Wednesday, April 24, 13
13
dS( ) =�
1Tw
� 1Ti
⇥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
R. Rigon and M. Dall’Amico
Wednesday, April 24, 13
14
first principle
potential energy
kineticenergy
internalenergy
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
R. Rigon and M. Dall’Amico
Wednesday, April 24, 13
15
Dirichlet Boundary Conditions
Dirichlet Boundary Conditions
The Stefan problem
The Stefan problem
R. Rigon and M. Dall’Amico
Wednesday, April 24, 13
16
Ice (thermal conductivity,
thermal capacity)
Water (thermal conductivity,
thermal capacity)
The Stefan problem
The Stefan problem
R. Rigon and M. Dall’Amico
Wednesday, April 24, 13
17
Diffusion of heat through water
The Stefan problem
Diffusion of heat through ice
The Stefan problem
R. Rigon and M. Dall’Amico
Wednesday, April 24, 13
18
Different condition at the interface
The Stefan problem
The Stefan problem
R. Rigon and M. Dall’Amico
Wednesday, April 24, 13
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
�2v1�z2 (t > 0, z < Z(t))
�v2�t = k2
�2v2�z2 (t > 0, z > Z(t))
v1 = v2 = Ti (t = 0, z)
Freezing case (1D discretization)
Equations of the Stefan Problem
The Stefan problem
R. Rigon and M. Dall’Amico
Wednesday, April 24, 13
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
R. Rigon and M. Dall’Amico
Wednesday, April 24, 13
21
�⌅⌅⇤
⌅⌅⇥
v1(t, z) = Ts + Tref�Ts
erf � · erf z2⇥
k1 tif z ⇤ Z(t)
v2(t, z) = Ti � Ti�Tref
erfc“
�q
k1k2
” · erfc z2⇥
k2 tif z > Z(t)
�⌅⌅⇤
⌅⌅⇥
v1(t, z) = Ti � Ti�Tref
erfc“
�q
k2k1
” · erfc z2⇥
k1 tif z > Z(t)
v2(t, z) = Ts + Tref�Ts
erf � · erf z2⇥
k2 tif z ⇤ Z(t)
where ζ is the solution of:
Freezing case:
exp(��2)� · erf �
� ⇤T1⇤
k2 (Ti � Tref )
⇤T2⇤
k1 (Tref � Ts) � · erfc��⇧
k2k1
⇥ · exp⇤�k2
k1�2
⌅=
Lf ⇧w ⇥s⇤
⌅
CT2 (Tref � Ts)
where ζ is the solution of:
Thawing case:
exp(��2)� · erf �
� ⇤T2⇤
k1 (Ti � Tref )
⇤T1⇤
k2 (Tref � Ts) � · erfc��⇧
k1k2
⇥ · exp⇤�k1
k2�2
⌅=
Lf ⇧w ⇥s⇤
⌅
CT1 (Tref � Ts)
The Stefan Problem: analitic solutions
The Stefan problem
R. Rigon and M. Dall’Amico
Wednesday, April 24, 13
22
Well, the real case is a little more complicate
R. Rigon and M. Dall’Amico
Wednesday, April 24, 13
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
R. Rigon and M. Dall’Amico
Wednesday, April 24, 13
24
Unsaturated conditions
•Means that capillary forces acts, i.e. we have to account for the tension forces that accumulate in curves surfaces
Beyond the Stefan problem
R. Rigon and M. Dall’Amico
Wednesday, April 24, 13
25
pw = pa � �wa⇤Awa(r)⇤Vw(r)
= pa � �wa⇤Awa/⇤r
⇤Vw/⇤r= pa � �wa
2r
:= pa � pwa(r)
Young-Laplace equation
pa
pw
the equilibrium condition:
becomes:
What does it means unsaturated conditions
Beyond the Stefan problem
R. Rigon and M. Dall’Amico
Wednesday, April 24, 13
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
Beyond the Stefan problem
R. Rigon and M. Dall’Amico
Wednesday, April 24, 13
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.
Beyond the Stefan problem
R. Rigon and M. Dall’Amico
Wednesday, April 24, 13
28
A paradox ?
Instead what happens is exactly the contrary, because for freezing a nucleus of condensation has to occur
r
with r << r
Beyond the Stefan problem
R. Rigon and M. Dall’Amico
Wednesday, April 24, 13
29
So, actually
The situation at the freezing point is the opposite, and represented by the
blue arrowFreezing point depression
Beyond the Stefan problem
R. Rigon and M. Dall’Amico
Wednesday, April 24, 13
30
Because, the smaller the pores,
the larger the freezing point depression
larger pores freezes before than
smaller pores
Beyond the Stefan problem
R. Rigon and M. Dall’Amico
Wednesday, April 24, 13
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
Beyond the Stefan problem
R. Rigon and M. Dall’Amico
Wednesday, April 24, 13
32
Unsaturatedunfrozen
UnsaturatedFrozen
Freezingstarts
Freezingprocedes
Beyond the Stefan problem
R. Rigon and M. Dall’Amico
Wednesday, April 24, 13
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
Beyond the Stefan problem
R. Rigon and M. Dall’Amico
Wednesday, April 24, 13
34
Now
we have enough information to write the right equations
Perhaps
Beyond the Stefan problem
R. Rigon and M. Dall’Amico
Wednesday, April 24, 13
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
R. Rigon and M. Dall’Amico
Wednesday, April 24, 13
36
pw1 = pw0 + �pfreez
Freezing = Drying
Freezing = Drying
R. Rigon and M. Dall’Amico
Wednesday, April 24, 13
37
Unfrozen water content
soil water retention curve
thermodynamicequilibrium (Clausius Clapeyron)
+
⇥w =pw
�w gpressure head:
�w(T ) = �w [⇥w(T )]
How this reflects on pressure head
Freezing = Drying
R. Rigon and M. Dall’Amico
Wednesday, April 24, 13
38
�w =�s
Aw |⇥|� + 1
⇥w = ⇥r + (⇥s � ⇥r) · {1 + [�� (⇤)]n}�m
�maxw = �s ·
�Lf (T � Tm)
g T ⇥sat
⇥-1/bClapp 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
R. Rigon and M. Dall’Amico
Wednesday, April 24, 13
39
Unsaturatedunfrozen
UnsaturatedFrozen
Freezingstarts
Freezingprocedes
Soil water retention curvesFreezing = Drying
R. Rigon and M. Dall’Amico
Wednesday, April 24, 13
40
−0.05 −0.04 −0.03 −0.02 −0.01 0.00
0.1
0.2
0.3
0.4
Unfrozen water content
temperature [C]
Thet
a_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
Soil water retention curvesFreezing = Drying
R. Rigon and M. Dall’Amico
Wednesday, April 24, 13
43
-3 -2 -1 0 1
0.0
0.2
0.4
0.6
0.8
1.0
n=1.5
temperature [C]
the
ta_
w/t
he
ta_
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
0.0
0.2
0.4
0.6
0.8
1.0
n=1.5
psi_w0 [mm]
the
ta_
w/t
he
ta_
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 0.41.1 0.939 0.789 0.631 0.5491.5 0.794 0.313 0.099 0.0492.0 0.707 0.099 0.009 0.0022.5 0.659 0.032 0.001 1.2E-4
T = �2 ⇥C
� [mm�1]n 0.001 0.01 0.1 0.41.1 0.576 0.457 0.363 0.3161.5 0.063 0.020 0.006 0.0032.0 4E-3 4E-4 4E-5 1E-52.5 2.5E-4 8E-6 2.5E-7 3.2E-8
25
θw/θs at ψw0=−1000 [mm]
Playing with Van GenucthenFreezing = Drying - Numbers
R. Rigon and M. Dall’Amico
Wednesday, April 24, 13
44
⇤
⇤t
��fl
w (⇥w1)⇥� �⇤ •
⇤KH
�⇤ ⇥w1 + KH�⇤ zf
⌅+ Sw = 0
Liquid water may derive fromice 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
R. Rigon and M. Dall’Amico
Wednesday, April 24, 13
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) + µwMphw + µiM
phi
no expansion: ρw=ρi
assuming:0 no flux during phase change
Eventually:
0 assuming equilibrium thermodynamics: µw=µi and Mw
ph = -Miph
conduction
advection
Energy Equation
Equation of freezing
R. Rigon and M. Dall’Amico
Wednesday, April 24, 13
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
020
40
60
80
100
140
alpha= 0.01 [1/mm] n= 1.5 theta_s= 0.4
Temp. [ C]
U [M
J/m
3]
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/m
3 K
]
1e+01
1e+02
1e+03
psi_w0=0 psi_w0=-1000
theta_s= 0.02
theta_s= 0.4
theta_s= 0.8 {Capp
Appearent Heat CapacityEquation of freezing
R. Rigon and M. Dall’Amico
Wednesday, April 24, 13
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
Equation of freezing
R. Rigon and M. Dall’Amico
Wednesday, April 24, 13
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
R. Rigon and M. Dall’Amico
Wednesday, April 24, 13
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
R. Rigon and M. Dall’Amico
Wednesday, April 24, 13
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
R. Rigon and M. Dall’Amico
Wednesday, April 24, 13
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
0.0
0.2
0.4
0.6
0.8
1.0
temperature [C]
Theta
_u [-]
modeled SFC for the comparison
real SFC
GEOtop
Notes on numerics of GEOtop
R. Rigon and M. Dall’Amico
Wednesday, April 24, 13
54
!5 !4 !3 !2 !1 0 1 2
54
32
10
Temp [ C]
so
il d
ep
th [
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
−1
01
2
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
Notes on numerics of GEOtop
R. Rigon and M. Dall’Amico
Wednesday, April 24, 13
55
time (days)
T [C
]
!5
!4
!3
!2
!1
01
20 15 30 45 60 75
An GEOtop
GEOtop Vs Analytical solution
#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
!1
01
2
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An GEOtop
GEOtop Vs Analytical solution
#layers= 100 , layer D= 300 mm, alpha= 0.4 n= 2.5 theta_s= 1
0.15 m
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0.8 m
1.1 m
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GEOtop
Notes on numerics of GEOtop
R. Rigon and M. Dall’Amico
Wednesday, April 24, 13
Beyond and side by side with numerics - II
Riccardo Rigon
Dan
ce, H
enry
Mat
isse
, Hot
el B
iron
ear
ly 1
909
Wednesday, April 24, 13
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
Wednesday, April 24, 13
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
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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
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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. RigonWednesday, April 24, 13
Hourly:
- Precipitation (quantity and type, spatially distributed)
- Relative humidity (spatially distributed)
- Wind Speed and direction (spatially distributed)
- Solar Radiation (spatially distributed)
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Required Input Data
Equations are not enough
R. RigonWednesday, April 24, 13
- Soil moisture (profile, in terms of matric potential, spatially distributed)
- Soil temperature (profile, spatially distributed)
- Surface water (if present)
- Snow cover (if present)
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Other Input Data
Equations are not enough
R. RigonWednesday, April 24, 13
Data baseCalibrazioneEVALUATION OF
STRATEGIES THROUGH MODELS
STRATEGIES FOR POLICY MAKERS
DATA INTERPRETATION
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DDS
Modelling is not just for Modelling
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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.
Rob
bed
from
a C
CA
pre
sent
atio
n
A critique of old modelling style
R. RigonWednesday, April 24, 13
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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
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MODELLING, FOR WHO ?Which end user do you have in mind ?
SCIENTIST ARE NOT THE ONLY MODELS USERS
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Users/ActorsFour 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
SCIENTIST ARE NOT THE ONLY MODELS USERS
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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.
SCIENTIST ARE NOT THE ONLY MODELS USERS
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Users/Actors RolesUsers
Hard Coders
SoftCoders
Linkers Runners Player Viewers Providers
Prime
Other End Users
Technical
Researchers
SCIENTIST ARE NOT THE ONLY MODELS USERS
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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
Mod
ified
from
Riz
zoli
et a
l., 20
05
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
MODELLING BY COMPONENTS
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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
MODELLING BY COMPONENTS
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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
MODELLING BY COMPONENTS
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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 ?
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
MODELLING BY COMPONENTS
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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 ?
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
MODELLING BY COMPONENTS
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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 ?
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
MODELLING BY COMPONENTS
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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 ?
Atmospheric Sciences: Earth Sciences Modeling Framework (ESMF) (including Earth System Curator)
High Performance Computing: Common Component Architecture (CCA)
MODELLING BY COMPONENTS
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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
PostGISPostgres
Webservices
WMSWFS-TWPS
Webservices
WMSWFS-TWPS
OMS3
Jgrasstools
JGrassuDig
Eclipse RCP
H2 spatial
UIBuilder
GRASS
GIS engine
The Horton Machine
Models
BeeGIS
DEPLOYEMENT
R. Rigon with HydrologisWednesday, April 24, 13
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Java
JGrassuDig
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-PostgresH2 spatial
Web services
WMSWFS-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
R. Rigon with HydrologisWednesday, April 24, 13
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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
DEPLOYEMENT
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The relationship to OMS3
OMS3THE 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 modelthe 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 MachineModels
DEPLOYEMENT
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Not just an idea but a reality
The case of JGrass-NewAGE
The State Of Art of the Project
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90Formetta et al., CAHMDA IV Lhasa 2010 - July 21-23
5
Modelling with components GIS Integration Multi-platform
Multi-language Open-source Reproducible research system
NewAge Goals:
Motivation Outline Hydrological Components Modelling Framework Conclusions
Trento 19 April 2013 G. Formetta,
The State Of Art of the Project
R. Rigon with Hydrologis and G. FormettaWednesday, April 24, 13
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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
The State Of Art of the Project
R. Rigon, G. Formetta, and O. DavidWednesday, April 24, 13
92Formetta et al., CAHMDA IV Lhasa 2010 - July 21-23
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Model setting
Hillslope Features
Basin splitted in hillslopes
Outline Calibration Issues Data Assimilation Motivation Hydrological Component
Trento 17 June 2011 G. Formetta, Trento 24 June 2011
Outline Conclusions Informatic Structure Hydrological Components
Leipzig 05 July 2012 G. Formetta,
Motivation Outline Hydrological Components Modelling Framework Conclusions
Trento 19 April 2013 G. Formetta,
The State Of Art of the Project
Hydrologis, R. Rigon and G. FormettaWednesday, April 24, 13
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Formetta et al., CAHMDA IV Lhasa 2010 - July 21-23
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Model setting
Network splitted in links
Links Features
Outline Calibration Issues Data Assimilation Motivation Hydrological Component
Trento 17 June 2011 G. Formetta, Trento 24 June 2011
Outline Calibration Issues Informatic Structure Hydrological Components
Leipzig 05 July 2012 G. Formetta,
Motivation Outline Hydrological Components Modelling Framework Conclusions
Trento 19 April 2013 G. Formetta,
The State Of Art of the Project
Hydrologis, R. Rigon and G. FormettaWednesday, April 24, 13
94Formetta et al., CAHMDA IV Lhasa 2010 - July 21-23
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Outline Calibration Issues Data Assimilation Motivation Hydrological Component
Trento 17 June 2011 G. Formetta, Trento 24 June 2011
Interpolation Problem Verification Procedure
Outline Calibration Issues Informatic Structure Hydrological Components
1) Start from a complete dataset
Outline Conclusions Informatic Structure Hydrological Components
Leipzig 05 July 2012 G. Formetta,
Motivation Outline Hydrological Components Modelling Framework Conclusions
Trento 19 April 2013 G. Formetta,
The State Of Art of the Project
R. Rigon, G. Formetta, and O. DavidWednesday, April 24, 13
95Formetta et al., CAHMDA IV Lhasa 2010 - July 21-23
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Precipitation Interpolation: Krigings
Motivation Outline Hydrological Components Modelling Framework Conclusions
Trento 19 April 2013 G. Formetta,
The State Of Art of the Project
R. Rigon, G. Formetta, and O. DavidWednesday, April 24, 13
96Formetta et al., CAHMDA IV Lhasa 2010 - July 21-23
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Shortwave Energy Model: raster mode application on Piave river
Simulation time step: hourly
Simulation Period: 01/10/201- 02/10/2010
Motivation Outline Hydrological Components Modelling Framework Conclusions
Trento 19 April 2013 G. Formetta,
The State Of Art of the Project
R. Rigon, G. Formetta, and O. DavidWednesday, April 24, 13
97Formetta et al., CAHMDA IV Lhasa 2010 - July 21-23
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NewAge-OMS3 automatic calibration algorithms
Generic Parameter set
Optimal Parameter set
Uncertainty: • catchment heterogeneity • model limitations • measurement techniques
Motivation Outline Hydrological Components Modelling Framework Conclusions
Trento 19 April 2013 G. Formetta,
The State Of Art of the Project
R. Rigon, G. Formetta, and O. DavidWednesday, April 24, 13
98Formetta et al., CAHMDA IV Lhasa 2010 - July 21-23
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Outline Calibration Issues Data Assimilation Motivation Hydrological Component
Trento 17 June 2011 G. Formetta, Trento 24 June 2011
Outline Calibration Issues Informatic Structure Hydrological Components Outline Conclusions Informatic Structure Hydrological Components
Leipzig 05 July 2012 G. Formetta,
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
Motivation Outline Hydrological Components Modelling Framework Conclusions
Trento 19 April 2013 G. Formetta,
The State Of Art of the Project
R. Rigon, G. Formetta, and O. DavidWednesday, April 24, 13
99Formetta et al., CAHMDA IV Lhasa 2010 - July 21-23
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Something more than a “classical” model
Outline Calibration Issues Data Assimilation Motivation Hydrological Component
Rome 09 March 2011 Trento 17 June 2011 G. Formetta, Trento 24 June 2011
Different possibility to run OMS3 components
uDig 1.3.1 Spatial Toolbox
Trento 24 June 2011
Outline Calibration Issues Informatic Structure Hydrological Components Outline Conclusions Informatic Structure Hydrological Components
Leipzig 05 July 2012 G. Formetta,
Motivation Outline Hydrological Components Modelling Framework Conclusions
Trento 19 April 2013 G. Formetta,
The State Of Art of the Project
Hydrologis, R. Rigon, G. Formetta, and O. DavidWednesday, April 24, 13
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Formetta et al., CAHMDA IV Lhasa 2010 - July 21-23
40
Something more than a “classical” model
Outline Calibration Issues Data Assimilation Motivation Hydrological Component
Rome 09 March 2011 Trento 17 June 2011
uDig 1.3.1 Spatial Toolbox
OMS3 Console
Different possibility to run OMS3 components
Outline Calibration Issues Informatic Structure Hydrological Components Outline Conclusions Informatic Structure Hydrological Components
Leipzig 05 July 2012 G. Formetta,
Motivation Outline Hydrological Components Modelling Framework Conclusions
Trento 19 April 2013 G. Formetta,
The State Of Art of the Project
Hydrologis, R. Rigon, G. Formetta, and O. DavidWednesday, April 24, 13
101Formetta et al., CAHMDA IV Lhasa 2010 - July 21-23
41
Something more than a “classical” model
Outline Calibration Issues Data Assimilation Motivation Hydrological Component
Rome 09 March 2011 Trento 17 June 2011 G. Formetta, Trento 24 June 2011
OMS3 Console
Command Line
uDig 1.3.1 Spatial Toolbox
Outline Calibration Issues Informatic Structure Hydrological Components Outline Conclusions Informatic Structure Hydrological Components
Leipzig 05 July 2012 G. Formetta,
Different possibility to run OMS3 components
Motivation Outline Hydrological Components Modelling Framework Conclusions
Trento 19 April 2013 G. Formetta,
The State Of Art of the Project
Hydrologis, R. Rigon, G. Formetta, and O. DavidWednesday, April 24, 13
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Formetta et al., CAHMDA IV Lhasa 2010 - July 21-23
42
Something more than a “classical” model
Outline Calibration Issues Data Assimilation Motivation Hydrological Component
Rome 09 March 2011 G. Formetta,
What is a .sim file?
Outline Calibration Issues Informatic Structure Hydrological Components Outline Conclusions Informatic Structure Hydrological Components
Leipzig 05 July 2012 G. Formetta,
Motivation Outline Hydrological Components Modelling Framework Conclusions
Trento 19 April 2013 G. Formetta,
The State Of Art of the Project
Hydrologis, R. Rigon, G. Formetta, and O. DavidWednesday, April 24, 13
103Formetta et al., CAHMDA IV Lhasa 2010 - July 21-23
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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 Conclusions Informatic Structure Hydrological Components
Leipzig 05 July 2012 G. Formetta,
Motivation Outline Hydrological Components Modelling Framework Conclusions
Trento 19 April 2013 G. Formetta,
The State Of Art of the Project
R. Rigon, G. Formetta, and O. DavidWednesday, April 24, 13
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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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105
Direct Contributors:
Andrea Antonello uDig and jgrasstools core developer and architectGiacomo 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 developersSilvia Franceschi Jgrasstools models developer and architectRiccardo 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
R. RigonWednesday, April 24, 13