which is the best model ?

Which hydrological model is better ?

Geo

rgia

O’K

eefe

Riccardo Rigon

Fort Collins, USDA/ARS, August 27, 2014

!2

The good old Hydrological cycle

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�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

http://abouthydrology.blogspot.com/2012/02/which-hydrological-model-is-better-q.html

!5

Should we just care of process-based models ?

The criticisms to this type of modelling have foundations.

PeakFlow

GEOtop

NewAgeBoussinesq

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

Full

y C

ou

ple

d

Sub

surf

ace-

Su

rfac

e G

rid

Bas

ed

PeakFlow

GIU

H

Pea

k f

lood

s

So we use different models

GEOtopFu

lly

dis

trib

ute

d

Gri

d b

ased

NewAge

Larg

e sc

ale

mod

elli

ng

Hil

lslo

pe

- St

ream

A

nth

rop

ic I

nfr

astr

uct

ure

s

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

http://abouthydrology.blogspot.com/search/label/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

landslidingevapo-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

!19

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 gpressure 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 curvesFreezing=Drying

R. Rigon

!25


R. Rigon

!26


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, 2011www.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 freezingvariably-saturated soilM. Dall’Amico1,*, S. Endrizzi2, S. Gruber2, and R. Rigon11Department of Civil and Environmental Engineering, University of Trento, Trento, Italy2Department 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 2010Revised: 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, thereis a great interest in the modeling of their behavior. Fewmodels exist that describe this process for both saturated andunsaturated soil and in conditions of freezing and thawing,as the energy equation shows strongly non-linear character-istics and is often difficult to handle with normal methodsof iterative integration. Therefore in this paper we proposea method for solving the energy equation in freezing soil.The solver is linked with the solution of Richards equation,and is able to approximate water movement in unsaturatedsoils and near the liquid-solid phase transition. A globally-convergent Newton method has been implemented to achieverobust convergence of this scheme. The method is tested bycomparison with an analytical solution to the Stefan problemand by comparison with experimental data derived from theliterature.

1 Introduction

The analysis of freezing/thawing processes and phenomenain the ground is important for hydrological and other landsurface and climate model simulations (e.g. Viterbo et al.,1999; Smirnova et al., 2000). For example, comparisonsof results from the Project for Intercomparison of Land Sur-face Parameterization Schemes have shown that the modelswith an explicit frozen soil scheme provide more realisticsoil temperature simulation during winter than those without(Luo et al., 2003). Freezing soil models may be divided intothree categories: empirical and semiempirical, analytical,

Correspondence to: M. Dall’Amico([email protected])

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 ormore experimentally established coefficients (e.g. Anisimovet al., 2002). Analytical algorithms are specific solutions toheat conduction problems under certain assumptions. Themost widely applied analytical solution is Stefan’s formula-tion, which simulates the freezing/thawing front using ac-cumulated ground surface degree-days (either a freezing orthawing index) (Lunardini, 1981). Numerical physically-based algorithms simulate ground freezing by numericallysolving the complete energy equation, and in natural condi-tions they are expected to provide the best accuracy in sim-ulating ground thawing and freezing (Zhang et al., 2008).However, this approach has difficulties, especially regardingthe treatment of phase change, which is strongest in a narrowrange of temperatures near the melting point, and thus rep-resents a discontinuity that may create numerical oscillations(Hansson et al., 2004). Furthermore, the freezing processhas a profound effect also to the water fluxes in the soil, asit changes the soil hydraulic conductivity and induces pres-sure gradients driving water movements. Therefore, a cou-pled mass and energy system is needed to simulate both thethermal and hydraulic characteristics of the soil.The objectives of the paper are: (1) to revisit the theory

of the freezing soil in order to provide the formulation forthe unfrozen water pressure, which can accomodate variably-saturated soils; (2) to outline and describe a numerical ap-proach for solving coupled mass and energy balance equa-tions in variably-saturated freezing soils, based on the split-ting method; (3) to provide an improved numerical schemethat: (i) is written in conservative way, (ii) is based on theglobally convergent Newton scheme, and (iii) can handlethe high non-linearities typical of the freezing/thawing pro-cesses.

Published by Copernicus Publications on behalf of the European Geosciences Union.

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

http://eprints-phd.biblio.unitn.it/335/

!29

Obviously this makes it possible to simulate a lot of new phenomenologies

Sisik, river in the artic tundra

End

rizzi

et A

l., JH

R, 2

01

0

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

02

46

810

1214

Date (dd/mm)

Dis

char

ge [m

3/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�mHs,�SWC,�Biomass,�GAI

StationB1500�mHs,�SWC,�Biomass,�GAI,ET

StationB1000�mHs,�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,�B2000B2

000�m

B1500�m

B1000�m

Snow�Height�[cm] SWC�5cm�[] ET�[mm]

Not�Measured

Not�Measured

r2=0.66RMSE=7.1

r2=0.57RMSE=5.9

r2=0.55RMSE=2.9

r2=0.80

r2=0.78

r2=0.82

Bag�[gDMmͲ2]

RMSE=0.04

RMSE=0.05

RMSE=0.04

r2=0.93RMSE=58.39

Courtesy of G. Bertoldi, EURAC. Complete presentation and reference at:


R. Rigon



!38

The�GEOtop�2.0��– DV��model

Rigon et�al.,�JHM,�2006;�Endrizzi�et�al.�GMDD,�2014.

Processes

Dynamic vegetationmodel (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:

[email protected]@googlegroups.com

If you like you can use it !

R. Rigon

https://code.google.com/p/geotop/

mailto:[email protected]

mailto:[email protected]

!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

Pic

asso

, Dora

Maa

r

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

http://www.javaforge.com/project/oms

!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

!49http://abouthydrology.blogspot.com/2013/06/ezio-todini-70th-symposium-my-talk.html

R. Rigon

Many models is better … but are they consistent ?

http://abouthydrology.blogspot.com/2013/06/ezio-todini-70th-symposium-my-talk.html

!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

728 G. Formetta et al.: Snow water equivalent modeling component in NewAge-JGrass

– particle swarm optimization component (Eberhart andShi, 2001);

– Let us calibrate (LUCA) component (Hay et al., 2006);

– Differential Evolution Adaptive Metropolis (DREAM)component (Vrugt et al., 2009).

The system is based on a hillslope-link geometrical partitionof the landscape, so the basic unit for the water budget eval-uation is the hillslope. Each hillslope, rather than a cell or apixel, drains into a single associated link. The model requiresinterpolation of the meteorological forcing data (air tempera-ture, precipitation, relative humidity) for each hillslope. Thisoperation can be handled by a deterministic inverse distanceweighted algorithm (Cressie, 1992; Lloyd, 2005), kriging(Goovaerts, 1997) or detrended kriging as in Garen et al.(1994) and Garen and Marks (2005).The radiation model (Formetta et al., 2013) implements

algorithms that take into account shadows and complex to-pography. Shortwave radiation under generic sky conditions(all-sky) is computed according to Helbig et al. (2010) andusing different parameterization choices such as Erbs et al.(1982), Reindl et al. (1990) and Orgill and Hollands (1977).The long-wave radiation budget is based on Brutsaert (1982)and Brutsaert (2005).All modeling components (including those not described

here) can be calibrated using one of the automatic calibrationalgorithms implemented: the particle swarm optimization al-gorithm, LUCA and DREAM. Evaluation of each modelcomponent’s behavior is eventually carried out with the useof NewAge-V (verification/validation), which provides someof the classical indices of goodness of fit, such as Nash–Sutcliffe, percent bias, index of agreement and Kling–Guptaefficiency, all defined in Appendix A. The complete inter-operating set of components available so far can be seen inFig. 1.The snowmelt model components, SWE-C, are perfectly

integrated into the NewAge System as presented in Fig. 2. Ituses the kriging tools for spatial interpolation of temperatureand precipitation and another interpolation method, JAMI(Just Another Meteo Interpolator), presented in Formetta(2013) for temperature interpolation. Like the interpolationalgorithms, SWE-C can be applied both to raster grids andto individual points. SWE-C also uses the NewAge short-wave radiation component to estimate the maps of accu-mulated energy in different periods of the year based ontopography, shadow and cloud cover. The SWE-C outputscould be raster maps or time series of snow water equiva-lent and snowmelt for any point within the domain. If cou-pled with runoff modeling, these points could be centroidsof hillslopes. The SWE-C component could be connected tothe NewAge and OMS3 calibration algorithm to estimate thebest model parameter values.The MS shown in Fig. 2 can be further connected to other

available components to obtain an estimation of the runoff,

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 waterequivalent. The user can select and connect different componentsand use automatic calibration algorithms (at the bottom) to optimizemodel parameters.

although demonstration of this application is not the goal ofthis paper.

4 NewAge-SWE evaluation

4.1 Sites and data description

To test the performance of SWE-C, the model is applied inthe upper Cache la Poudre River basin, located in the RockyMountains of northern Colorado and southern Wyoming,USA. This basin is 2700 km2 and has elevations ranging from1590 to 4125m, with mean annual precipitation ranging from330mm at lower elevations to 1350mm at the highest eleva-tions (Richer et al., 2013).Six meteorological stations have precipitation and temper-

ature data in this river basin. These stations are presented inFig. 3, and Table 1 shows their main features. The Hourglass,Deadman Hill and Joe Wright stations are part of the Natural

Geosci. Model Dev., 7, 725–736, 2014 www.geosci-model-dev.net/7/725/2014/

The structure of NewAGE

R. Rigon

!52

Rin

ald

o, G

eom

orp

hic

Flo

od

Res

earc

h, 2

00

6

Someone call them Hydrologic Runoff Units

we call them hillslope-link partition of the basin


R. Rigon

!53

Rin

ald

o, G

eom

orp

hic

Flo

od

Res

earc

h, 2

00

6

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 runoffgeneration models, Duffy’s (Duffy, 1996) and the Hymod model(Moore, 1985; Boyle, 2001). In both cases the model is applied toeach hillslope only and not to the entire basin.

Finally, the discharge generated at each hillslope is routed toeach associated stream link according to Mantilla and Gupta (2005)and Mandapaka et al. (2009) using the index derived from thePfaffstetter [Verdin and Verdin] algorithm to work out all the linksin the network (i.e., discharge is produced for any link of the rivernetwork and not only for its outlet).

All modelling components can be calibrated separately usingone of the automatic calibration algorithms: the Particle SwarmOptimization (PSO) (Kennedy and Eberhart, 1995; Eberhart and Shi,2001), DREAM (Vrugt et al., 2009), and LUCA (Hay et al., 2006). Thecalibration system works in a generic way: either a set of param-eters for a single component or the parameters for a chain ofcomponents can be optimised. More details on calibration usingPSO are presented in Formetta et al. (2011). Moreover, the LUCAcomponent (not a product of this work, but presented in Hay et al.(2006), and ported to this system) offers the possibility to perform amulti-step calibration, tuning parameters of different componentsstep-by-step.

With the above components different modelling solutions canbe instantiated, initialised, and connected in a sequence. In this waythe modeller can build a custom hydrological model and solutionby selecting alternative components to simulate the same hydro-logical processes.

Like the components for the hydro-geomorphological analysis,every hydrological modelling component can be connected, para-meterised, and executed either using the OMS3 console (OMS 3.1)or the OMS3 scripting mode within the uDig Spatial Toolbox. It ispossible to run geomorphological and hydrological routines alltogether with a single script. However, they are usually executedseparately, because the same geomorphological analysis can servemultiple hydrological applications. Once connected and executed in

Fig. 4. Hillslope-link partition of the basin work-flow.

Fig. 5. Interacting NewAge-OMS3 components.

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

Form

etta

et

al.,

Hyd

rolo

gic

al m

od

elli

ng w

ith

com

pon

ents

: A

GIS

-bas

ed o

pen

-sou

rce

fram

ework

, 20

14

!56

Hillslope Storage Dynamics

Surface flows Aggregation

Channel flow

Next time step

JGrass-NewAgeFormetta et al., GTD, 2011, Formetta et al, EM&S, 2014


R. Rigon

!57

a simulation, processes will take advantage of the OMS3 implicitparallelism to improve the computational efficiency in multicore ormultiprocessor machines.

Changing a model component and re-running a simulation re-quires just few minutes if the new component is already present inthe system. If the new component has to be built form scratch, theintegration time increase depends on the time of implementationof the model (i.e. on the complexity of the newmodel). Connectingexisting legacy-codes is also possible. For instance, embedding thedistributed model GEOtop (Rigon et al., 2006a,b) required a coupleof man-months of work.

4. Running JGrass-NewAGE on the Fort Cobb river basin

In order to test the capability of the JGrass-NewAge system anapplication of a model solution on the Fort Cobb river basin ispresented. In this application we have estimated the discharge ofthe basins by interpolating the meteorological data, applying anoptimization component, and have tested the results (Fig. 6).

The Fort Cobb Watershed (Fig. 7), is located in the Central GreatPlains Eco-region in south-western Oklahoma in Caddo and is 813square kilometres in size. Its elevation ranges between 383 m and565 m.

Within the watershed there is the Fort Cobb reservoir, a lake forwater supply and recreational use created by the Bureau of Recla-mation in 1959 by impounding Cobb Creek three miles north of thetown of Fort Cobb. Land use in the watershed includes agriculturalfields, cattle operations, rural communities, and one hog feedingoperation. Most soils in the watershed are highly erodible sandyclays and loams underlain primarily by Permian sandstone, silt-stone, and claystone.

The climate of the basin can be characterized as moist with anaverage annual precipitation of 816 mm and an average tempera-ture of 16 !C.

The JGrass-NewAGE modelling solution is applied for the FortCobb river basin at the Eakly river outlet into the reservoir.

Fig. 6. The workflow for the Fort Cobb river basin application.

Fig. 7. Fort Cobb watershed DEM and measurement stations.

Table 1Meteorological stations used in the Fort Cobb river basin application.

ID Name City Lat Long Elevation (m)

F102 Hydro Caddo 35.4504 "98.5443 524.0F103 Corn Washita 35.4237 "98.7087 484.0F104 Colony Washita 35.3923 "98.6233 484.0F105 Colony Caddo 35.4072 "98.571 493.0F108 Eakly Caddo 35.3611 "98.5712 492.0F109 Eakly Caddo 35.3123 "98.5675 466.0F113 Colony Washita 35.291 "98.6357 465.0

G. Formetta et al. / Environmental Modelling & Software 55 (2014) 190e200196Rainfall-Runoff*

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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

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Watershed model of NewAGE

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Thus we have discharges

Here, Here ... and here again

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Watershed model of NewAGE

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Input Data treatment

Goodness of fit

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JGrass-NewAgeCalibration tools

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G. Formetta et al. / Environmental Modelling & Software 55 (2014) 190e200196Forcings and Calibration

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Channel flow

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G. Formetta et al.: Modeling shortwave solar radiation using the JGrass-NewAge system 919

18 G. Formetta et al.: Modeling short wave solar radiation using the JGrass-NewAge system

Fig. 1. OMS3 SWRB components of JGrass-NewAge and flowchartto model shortwave radiation at the terrain surface with generic skyconditions. Where not specified, quantity in input or output must beintended as a spatial field for any instant of simulation time. ”Mea-sured” refers to a quantity that is measured at a meteorological sta-tion. The components, besides the specfied files received in input,include an appropriate set of parameter values.figure

Fig. 1. OMS3 SWRB components of JGrass-NewAge and flowchart to model shortwave radiation at the terrain surface with generic skyconditions. Where not specified, quantity in input or output must be intended as a spatial field for any instant of simulation time. “Measured”refers to a quantity that is measured at a meteorological station. The components, besides the specified files received in input, include anappropriate set of parameter values.

3 Applications

The capability of the model was tested by combining fourNewAge JGrass components within a OMS script: theSwRB, the (radiation decomposition model) DEC-MOD’s,the kriging and the NewAGE-V (verification) package. Eachpackage is represented in Fig. 1 by a rounded rectangle andthe lines joining the rectangle represent the data that twopackages exchange. According to the convention used, thecomponent on the left provides data to the component onthe right. The model is applied in two different modes: vec-tor mode, providing the radiation results in a number ofpoints defined by the user, and raster mode, providing theradiation result for each pixel of the analyzed basin. Belowwe described the basins used for the verification, commenttheir data, illustrate the verification procedure and finally, wepresent the raster mode application.

3.1 Reference catchments

Three different basins were used in this study: Little WashitaRiver basin (Oklahoma, USA), Fort Cobb watershed (Okla-homa, USA) and Piave River basin (Veneto, Italy). As pre-sented in the next subsections, differences between the twoplaces in elevation range, number of monitoring points, lati-tudes, and complexity of the topography are substantial.

The Little Washita River basin (611 km2) is located insouthwestern Oklahoma, between Chickasha and Lawtonand its main hydrological and geological features are pre-sented in Allen and Naney (1991). The elevation rangeis between 300m and 500m a.s.l., the main land uses arerange, pasture, forest, and cropland. The mean annual pre-cipitation is 760mm and the mean air temperature is 16 �C.Seventeen meteorological stations of the ARS Micronet(http://ars.mesonet.org/) were used for the simulations andfor each station there are five-minute measurements avail-able of air temperature at a height of 1.5m, relative humidityat a height of 1.5m and incoming global solar radiation. Thedata for the year 2002 were aggregated to an hourly time stepto be used in the simulations. The meteorological station’smain features are reported in Table 2. Figure 4 shows theLittle Washita DEM and the location of the meteorologicalstations.The Fort Cobb Reservoir basin (813 km2) is located in

southwestern Oklahoma. An exhaustive description is givenin Rogers (2007). The elevation range is between 400 and570m above the sea level, main land usages are cropland,range, pasture, forest, and water. The long record mean an-nual precipitation is 816mm and the mean annual air tem-perature is 18 �C. Eight meteorological stations of the ARSMicronet are used for the simulations. The data for the year

www.geosci-model-dev.net/6/915/2013/ Geosci. Model Dev., 6, 915–928, 2013

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Fig. 1. OMS3 SWRB components of JGrass-NewAge and flowchartto model shortwave radiation at the terrain surface with generic skyconditions. Where not specified, quantity in input or output must beintended as a spatial field for any instant of simulation time. ”Mea-sured” refers to a quantity that is measured at a meteorological sta-tion. The components, besides the specfied files received in input,include an appropriate set of parameter values.figure

Fig. 1. OMS3 SWRB components of JGrass-NewAge and flowchart to model shortwave radiation at the terrain surface with generic skyconditions. Where not specified, quantity in input or output must be intended as a spatial field for any instant of simulation time. “Measured”refers to a quantity that is measured at a meteorological station. The components, besides the specified files received in input, include anappropriate set of parameter values.

3 Applications

The capability of the model was tested by combining fourNewAge JGrass components within a OMS script: theSwRB, the (radiation decomposition model) DEC-MOD’s,the kriging and the NewAGE-V (verification) package. Eachpackage is represented in Fig. 1 by a rounded rectangle andthe lines joining the rectangle represent the data that twopackages exchange. According to the convention used, thecomponent on the left provides data to the component onthe right. The model is applied in two different modes: vec-tor mode, providing the radiation results in a number ofpoints defined by the user, and raster mode, providing theradiation result for each pixel of the analyzed basin. Belowwe described the basins used for the verification, commenttheir data, illustrate the verification procedure and finally, wepresent the raster mode application.

3.1 Reference catchments

Three different basins were used in this study: Little WashitaRiver basin (Oklahoma, USA), Fort Cobb watershed (Okla-homa, USA) and Piave River basin (Veneto, Italy). As pre-sented in the next subsections, differences between the twoplaces in elevation range, number of monitoring points, lati-tudes, and complexity of the topography are substantial.

The Little Washita River basin (611 km2) is located insouthwestern Oklahoma, between Chickasha and Lawtonand its main hydrological and geological features are pre-sented in Allen and Naney (1991). The elevation rangeis between 300m and 500m a.s.l., the main land uses arerange, pasture, forest, and cropland. The mean annual pre-cipitation is 760mm and the mean air temperature is 16 �C.Seventeen meteorological stations of the ARS Micronet(http://ars.mesonet.org/) were used for the simulations andfor each station there are five-minute measurements avail-able of air temperature at a height of 1.5m, relative humidityat a height of 1.5m and incoming global solar radiation. Thedata for the year 2002 were aggregated to an hourly time stepto be used in the simulations. The meteorological station’smain features are reported in Table 2. Figure 4 shows theLittle Washita DEM and the location of the meteorologicalstations.The Fort Cobb Reservoir basin (813 km2) is located in

southwestern Oklahoma. An exhaustive description is givenin Rogers (2007). The elevation range is between 400 and570m above the sea level, main land usages are cropland,range, pasture, forest, and water. The long record mean an-nual precipitation is 816mm and the mean annual air tem-perature is 18 �C. Eight meteorological stations of the ARSMicronet are used for the simulations. The data for the year


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G. Formetta et al.: Modeling short wave solar radiation using the JGrass-NewAge system 19

Fig. 2. OMS3 SWRB components of JGrass-NewAge and flowchartfor automatic Jack-Knife procedure. The Jack-knife component(which is not used in the present paper) simply needs to be added tothe basic model solution, and actually just substitutes the the Verifi-cation component of Figure 1

Fig. 2. OMS3 SWRB components of JGrass-NewAge and flowchart for automatic jackknife procedure. The jackknife component (whichis not used in the present paper) simply needs to be added to the basic model solution, and actually just substitutes the the verificationcomponent in Fig. 1

Table 2. List of the meteorological stations used in the simulationsperformed on the Little Washita River basin. ID is the station iden-tification number, city refers to the closest city to the station, Lat.and Long. stand for latitude and longitude, respectively, and eleva-tion and aspect refer to the respective station. Bold font is used toindicate the stations belonging to the validation set.

ID City Lat. Long. Elevation Aspect(�) (�) (m) (�)

124 Norge 34.9728 �98.0581 387 138�131 Cyril 34.9503 �98.2336 458 245�133 Cement 34.9492 �98.1281 430 116�134 Cement 34.9367 �98.0753 384 65�135 Cement 34.9272 �98.0197 366 182�136 Ninnekah 34.9278 �97.9656 343 270�144 Agawam 34.8789 �97.9172 388 50�146 Agawam 34.8853 �98.0231 358 212�148 Cement 34.8992 �98.1281 431 160�149 Cyril 34.8983 �98.1808 420 205�150 Cyril 34.9061 �98.2511 431 195�153 Cyril 34.8553 �98.2121 414 165�154 Cyril 34.8553 �98.1369 393 175�156 Agawam 34.8431 �97.9583 397 290�159 Rush Springs 34.7967 �97.9933 439 235�162 Sterling 34.8075 �98.1414 405 15�182 Cement 34.845 �98.0731 370 245�

Table 3. List of the meteorological stations used in the simulationsperformed on the Fort Cobb Reservoir basin. Clarification of col-umn headings as in Table 2.

ID City Lat. Long. Elevation Aspect(�) (�) (m) (�)

101 Hydro 35.4551 �98.6064 504 120�104 Colony 35.3923 �98.6233 484 35�105 Colony 35.4072 �98.571 493 300�106 Eakly 35.3915 �98.5138 472 295�108 Eakly 35.3611 �98.5712 492 40�109 Eakly 35.3123 �98.5675 466 90�110 Eakly 35.3303 �98.5202 430 115�113 Colony 35.291 �98.6357 465 155�

2006 were aggregated to an hourly time step and used in thesimulations.The meteorological stations’ main features are reported in

Table 3 and Fig. 5 shows their position.The Piave River basin area (3460 km2) is located in the

northeastern part of the Italian peninsula. The elevationrange is between 700 and 3160m a.s.l., the main soil usesare (i) crops up to 500m a.s.l., (ii) evergreen and decidu-ous forests at elevations between 500 and 1800m a.s.l., and(iii) alpine pasture and rocks at higher elevations. The meanannual precipitation is around 1500mm and the mean airtemperature is 10 �C.

Geosci. Model Dev., 6, 915–928, 2013 www.geosci-model-dev.net/6/915/2013/

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Fig. 5. The Fort Cobb river basin, Oklahoma (USA). riangles repre-sent the verification set (V-set) and circles represent the calibrationset (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 comparisonbetween measured and modeled incoming solar radiation is represented with scatter plots.

in which R represents the linear correlation coefficientbetween the S and O values, A and B are, respectivelyexpressed in Eqs. (33) and (34):

A = �o�s

, (33)

where �o is the observed standard deviation value and�s is the simulated standard deviation value;

B = µs� µo�o

, (34)

where µs and µo are the means of S and O values. Forthis index, the best agreement is represented with thevalue 1.The kriging package can utilize the most common vari-ogram models (spherical, linear, exponential, gaussian).However, for the cases below only a linear model wasused.

3.3 Raster mode application on the Piave River basin

In order to show the capability of the system in providingsolar radiation maps, a raster mode simulation was set upfor the Piave River basin. Different from the previous vectormode applications, the model results are computed for each

point of the Piave River basin. In order to perform this ap-plication it was necessary to interpolate the air temperatureand relative humidity measurement data for each pixel of thebasins by using a detrended kriging component. The simula-tion time step was hourly and the simulation period was oneday: from 1 January 2010 to 1 February 2010.

4 Results

Results are presented separately for the three case studies.They confirm the results found in the literature, and reveala reasonable agreement between measured and simulateddata.

4.1 Results for the Little Washita River basin

Figure 4 (top right, bottom left and bottom right) showsthe scatter plot between the modeled and the measured to-tal incoming solar radiation in the four stations of the V-set.Table 5 shows the result of the NewAge-V, which accepts

as input measured and modeled time series and provides asoutput the user defined goodness of fit indexes.


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Fig. 7. The Figure represents the global shortwave radiation on thePiave area the first october 2010, at four different hours of the day.During the day differently oriented hillslope received the maximumamount of radiation and, at 4 p.m. most of the area is covered byshadows.

Fig. 7. The figure represents the global shortwave radiation on thePiave area on 1 October 2010 at four different hours of the day.During the day, differently oriented hillslope received the maximumamount of radiation and, at 16:00 LT most of the area is covered byshadows.

5 Discussion

5.1 About the SwRB and DRM components’ predictivecapabilities

The model applications are performed in case studies wheretopography has different characteristics: (a) two cases pre-sented gentle topography and high density measurement net-work (for the experimental Little Washita and Fort Cobb wa-tersheds), and (b) the other case presented a typical hydro-logical basin with complex topography, high elevation rangeand few monitoring stations.In all the cases the model was able to simulate the global

shortwave radiation showing relatively good goodness of fitindices as presented in Tables 5 and 6 for Little Washita andFort Cobb, respectively, and in Table 7 for the Piave Riverbasin.The model performs with the similar and acceptable accu-

racy both for Little Washita and Fort Cobb basins. The resultis confirmed by the goodness of fit indices and by the graph-ical analysis.The model performance deteriorated in the Piave case

study. This could be due to the effect of the complex topog-raphy on the computation of the clear sky solar radiation but

also due to the lower measurement station density in highelevation zones.Because of this topographic condition the increasing mea-

surement data uncertainty of the temperature and humidityinfluenced the atmospheric transmittance computations. Thisis confirmed also by the data analysis: for the Piave Riverbasin measurements show lower correlation compared to, forexample, the correlation between measurements at the LittleWashita River basin, where the gentle topography does notplay a crucial role.Regardless, the model was able to reproduce well the

shortwave solar radiation also in the case of complex to-pography. The PBIAS index was equal to 14.80 in the worstcase. According the hydrological model classification basedon PBIAS index, presented in Van Liew et al. (2005) andStehr et al. (2008), the results achieved in our study are clas-sified as “good” and therefore the solar radiation model issuitable to be used for the estimation of incoming shortwavesolar radiation.Finally, Fig. 7 presents the raster mode application of the

model. Maps of incoming solar radiation are presented forfour hours during the daytime. The effect of the complex to-pographic feature of the Piave River basin is evident in theradiation maps. Their patterns change during the daytime ac-cording to the solar position, the surrounding terrain, and theshadow.

5.2 About the possibilities open by the components-based JGrass-NewAGE system

Since the goal of the paper was to show how the componentswork, the statistical analysis of the results was maintained toa simple level. One more accurate procedure of testing thecomponents’ performances would be to apply a jackknifeprocedure to estimate errors (as proposed by Quenouille,1956; Miller, 1974). In this procedure, the V-set, would varyamong all the stations and an overall statistic could be delin-eated.According to Tovar et al. (1995) and Long and Acker-

man (1995) studies, the influence of the aspect of the mea-surement station could have been identified. This operationand analysis is time consuming. It can be possible simply byadding a jackknife component to the structure of the modelat “link time”, i.e., using the script that connects the com-ponents. Figure 2 shows the modeling solution that is nec-essary to apply a jackknife strategy. No modification of thesingle components is necessary to accomplish the task, onlytheir re-arrangements with the addition of the new jackknifecomponent that performs the permutation of the calibrationsites.Other components in the New-AGE system (Formetta

et al., 2011) allow to perform parameter calibration. In thisstudy, no calibration of the four parameters (in Table 1) thatare needed to run the SwRB component was performed.However, it can be easily envisioned using the particle swarm


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Including snow (with various models)

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Formetta et al., Snow water equivalent modeling components in NewAge-JGrass, 2014

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G. Formetta et al.: Snow water equivalent modeling component in NewAge-JGrass 729

Fig. 2. The SWE-C integration into the NewAge system, showing connections with the shortwave radiation component and kriging interpo-lation 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 theCache la Poudre River basin.

Station Lat. Long. Elevation (m)

Hourglass 40.25 105.38 2814Joe Wright 40.32 105.53 3085Deadman Hill 40.40 105.46 3115Buckhorn Mountain 40.60 105.28 2256Virginia Dale 40.95 105.21 2138Rustic 40.70 105.70 2347

Resource Conservation Service Snow Telemetry (SNOTEL)network. They provide data (precipitation, air temperatureand SWE) at a daily time step. For the Hourglass stationthe data used start on 1 October 2008 and end on 1 Octo-ber 2013. For the Joe Wright and Deadman Hill stations, thedata used start on 1 October 1999 to 1 October 2013. Forthe Joe Wright station, hourly time series of precipitation, airtemperature and snow water equivalent were also availablefrom 1 October 2008 to 1 October 2013.The Buckhorn Mountain, Rustic and Virginia Dale sta-

tions are part of the National Weather Service CooperativeObserver Program (COOP). They only provide precipitationand air temperature, not SWE. For these three stations, datafrom 1 October 2008 to 1 October 2009 were used for airtemperature and precipitation interpolations in the fully dis-tributed application of the snow model.

Formetta et al.: Snow water equivalent modeling component in NewAge-JGrass 11

Figure 3. Cache la Poudre river basin digital elevation model. Ele-vations are in meters.

www.jn.net J. Name

Fig. 3. Cache la Poudre River basin digital elevation model. Eleva-tions are in meters.


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Formetta et al.: Snow water equivalent modeling component in NewAge-JGrass 15

Figure 8. SWE-C application in distributed mode: snow waterequivalent maps from 1 November to 1 June for the Upper Cache laPoudre 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 PoudreBasin.

and temperature maps was relatively small, and further workis needed to test how the simulated SWE patterns compareto observations. Future work will compare these simulatedSWE patterns to a more complex distributed model simula-tion of SWE and to satellite-derived snow cover patterns.

5 Conclusions

This paper presents a parsimonious snow water equivalentmodel based on water and ice mass balance. The model sim-ulates snowmelt using one of three separate temperature-based formulae where melt rates are a function of either

temperature only or both temperature and solar radiation.The model is integrated into the NewAge-JGrass hydrolog-ical model as an OMS3 component, and for this reason itcan make use of all the OMS3 components of the system:GIS-based visualization, automatic calibration algorithm andevaluation packages. All of these components are applied andverified at three SNOTEL stations located in the Cache laPoudre River basin (Colorado, USA), and the model per-forms well for both daily and hourly time steps, althoughmodel performance degrades from the calibration to the eval-uation periods. This is much more evident at a daily timestep compared to an hourly time step. This outcome suggeststhat both the degree-day and the enhanced degree-day mod-els are very sensitive to the parameter values. Furthermore,they have to be evaluated not only for their performance at in-dividual sites but also for their ability to simulate SWE overtime and space.Using an hourly time step reduces the model performance

degradation when moving from the calibration to the evalua-tion period. Therefore, a possible way to improve forecastingcould be to adopt a time-varying degree-day factor as in To-bin et al. (2013).Finally, the model is applied in distributed mode to sim-

ulate spatial patterns of SWE across the basin. Modelingsnow water equivalent patterns in a distributed mode pro-vides the possibility to compare them with more physi-cally based snow models and the option to verify them withsnow water equivalent remote sensing data. Future researchwill address problems related to modified temperature indexsnow water equivalent models such as the transferability ofparameter values to new locations and time periods, over-parameterization, comparison with physically based snowmodels and the evaluation of how well simulated snow coverspatial patterns reproduce spatial and temporal variability ofthe snowpack.


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Figure 15: The water budget closure based on the use of all the rainfall, discharge and evapotranspiration estimation at annual time scale. Theplots reports for the first sex years of the analysis. The solid line with red band is the annual cumulative T AW (total available water) whichincludes the rainfall input plus the residual storage(P-Q-ET ) remains from the last hydrological year, the dash line with blue band is the annualcumulative ETa, the dot line with black band is annual cumulative discharge at the outlet (Q), and the longdash line with gray band is annualcumulative OUT FLOW (ETa + Q). The lines are the maximum and the minimum estimation value, while the bands are the ranges of error in theestimation.

14

The whole budget

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Observe, that I did not mention the complexity implied by

the Richards equation. !

WHERE IS IT NOW ?

Concluding

Toward some conclusion

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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”

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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”

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Merging the two worlds

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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

http://abouthydrology.blogspot.com/2014/07/uncertainty-and-information-theory.html

!79

We go !

OMS

Conclusion for informatics

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To my former Ph.D. students

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A thank to my Ph.D students: they made it possible

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Find this presentation at

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Other material at

Thank you audience !

R. Rigon

http://www.slideshare.net/GEOFRAMEcafe/which-is-the-best-model

http://www.slideshare.net/posterVienna

which is the best model ?

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