Systems, domains and causal networks

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# Systems, domains and causal networks - PowerPoint PPT Presentation

NRM L06. Systems, domains and causal networks. Andrea Castelletti. Politecnico di Milano. 2. Conceptualisation. Defining Criteria and Indicators. Defining Actions (measures). Identifying the M odel. 1. Reconnaissance. Stakeholders. Schema fisico. Physical scheme of the system.

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NRM

L06

### Systems, domains and causal networks

Andrea Castelletti

Politecnico di Milano

2. Conceptualisation

Defining Criteria

and

Indicators

Defining Actions (measures)

Identifying the Model

1. Reconnaissance

Stakeholders

Schema fisico

Physical scheme of the system

Interceptors 1350 m.

CAMPOTOSTO

Vomano

PROVVIDENZA (P)

Chiarino

Fucino

PROVVIDENZA

Gronda 1100 m.

PIAGANINI

SAN GIACOMO (SG)

Left interceptor 400 m.

Right interceptor 400 m.

Water works

MONTORIO (M)

VILLA VOMANO

Irrigation district

(CBN)

S. LUCIA (SL)

Component: modelling elementary unit.

Every component has a specific function.

The model of the component must describe such a fuction.

Logical components are also allowed.

• Choosing the components depends on:
• relevance of the component to the objective of the modelling exercise
• data availability
Identifying the Model
• Definining the components and the system scheme
• Identifying the models of the components
• Aggregated model
Schema fisico

Irrigation District

(CBN)

Interceptors 1350 m.

CAMPOTOSTO

Vomano

PROVVIDENZA (P)

Chiarino

Fucino

PROVVIDENZA

Interceptor 1100 m.

PIAGANINI

SAN GIACOMO (SG)

Left interceptor 400 m.

Right interceptor 400 m.

MONTORIO (M)

Water works

VILLA VOMANO

S. LUCIA (SL)

Irrigation district

(CBN)

Data analysis: time series provided by Enel

Campotosto:

• level
• aggregated daily flow rate the two intereceptors

Piaganini and Provvidenza:

• level
• daily flow rate from mass balance

Interceptors 1350 m.

CAMPOTOSTO

Vomano

PROVVIDENZA (P)

Fucino

Chiarino

PROVVIDENZA

e.g. Provvidenza:

Interceptor 1100 m.

PIAGANINI

SAN GIACOMO (SG)

Left interceptors 400 m.

only aggregated flow data

Water

works

Right interceptor 400 m.

MONTORIO (M)

During night-time without pumping

VILLA VOMANO

S. LUCIA (SL)

Schema fisico

Irrigation District

(CBN)

Interceptors 1350 m.

CAMPOTOSTO

Vomano

PROVVIDENZA (P)

Chiarino

Fucino

PROVVIDENZA

Interceptor 1100 m.

PIAGANINI

SAN GIACOMO (SG)

Left interceptor 400 m.

Right interceptor 400 m.

MONTORIO (M)

Water works

VILLA VOMANO

S. LUCIA (SL)

Schema fisico (bacini)

Irrigation district

(CBN)

CAMPOTOSTO

PROVVIDENZA (P)

Fucino

PROVVIDENZA

PIAGANINI

Water works ???

SAN GIACOMO (SG)

MONTORIO (M)

VILLA VOMANO

S. LUCIA (SL)

Average water supply from hydropower reservoirs

WW

Some difficulties in the scheme

1. Piaganini:there is no way to compute the indicator for the water works

?

How to solve them…

We need to fix a criterion for disaggregating the total inflow in the two single contributions of the interceptors. How?

Based on the surface and the morphological characteristics of the two catchments (regional analysis) we can assume a similar contribution from the two interceptors.

The hypothesis is validated using some flow rate measures locally available on the interceptors.

Some difficulties in the scheme

1. Piaganini: there is no way to compute the indicator for the water works

2. Campotosto: the contribution from the natural catchment is not accounted for.

Some difficulties in the scheme

1. Piaganini: there is no way to compute the indicator for the water works

2. Campotosto: the contribution from the natural catchment is not accounted for.

3. Provvidenza e Piaganini: understimation of snow-melting in spring and evaporation in summer.

Possible solutions

1. Piaganini: there is no way to compute the indicator for the water works

2. Campotosto: the contribution from the natural catchment is not accounted for.

3. Provvidenza e Piaganini: understimation of snow-melting in spring and evaporation in summer.

The daily inflow can be computed via mass balance using release and pumping data:

Campotosto

Provvidenza

Piaganini

Snow melt is negligible

evaporation is NOT negligible

Piaganini

The estimate is reliable: we can use the new data obtained via mass balance (red) instead of those provided by Enel (blue).

Provvidenza

The estimate is not reliable.

Pumping is adding noise to data.

An understimation of evaporation is anyway evident in the data by Enel.

These data can be corrected by removing from them the evaporation that can be obtained from Piaganini, based on the many similarities between the two reservoirs.

Some difficulties in the scheme

1. Piaganini: there is no way to compute the indicator for the water works

2. Campotosto: the contribution from the natural cacthment is not accounted for.

3. Provvidenza e Piaganini: understimation of snow-melting in spring and evaporation in summer.

this is impossible: at 40° max evap. 3m3/s

Campotosto

Estimate is not reliable.

Oscillation are wider than in Provvidenza:

Pumping, but also the instrument precision (1cm) is amplifying the error

The contribution from the natural catchment is evident, but not easily quantifiable.

Inflow from Enel (blue) and from water balance (red) are not usable. What can we do?

Interceptors

1350 m

Provvidenza

Piaganini

CAMPOTOSTO

Reservoir

The valure for each year is obtained

Montorio

Natural inflow to Campotosto

Can we evaluate the significancy of the inflow contribution from the natural Campotosto’s catchment?

Water balance for the i-th year in Montorio

- Internal pumping to the system

- Error on the level negligible

The estimate is an annual value: how to move to a daily one?

From which

Some difficulties in the scheme

1. Piaganini: there is no way to compute the indicator for the water works

2. Campotosto: the contribution from the natural cacthment is not accounted for.

3. Provvidenza e Piaganini: understimation of snow-melting in spring and evaporation in summer.

Schema fisico

Irrigation District

(CBN)

CAMPOTOSTO

PROVVIDENZA (P)

Fucino

PROVVIDENZA

PIAGANINI

Topological Scheme

SAN GIACOMO (SG)

MONTORIO (M)

VILLA VOMANO

S. LUCIA (SL)

Identifying the Model
• Definining the components and the system scheme
• Identifying the models of the components
• Aggregated model
Schema fisico

Irrigation District

(CBN)

CAMPOTOSTO

PROVVIDENZA (P)

Fucino

PROVVIDENZA

PIAGANINI

SAN GIACOMO (SG)

MONTORIO (M)

VILLA VOMANO

S. LUCIA (SL)

Campotosto lake

Simplification

Let’s assume that only one criterion needs to be satisfied: flood reduction in the town of Campotosto (on the lake shores)

The (lake’s) domain

The whole set of quantities and information about the lake:

• inflow
• release
• level
• water characteristics
• biota
• algae
• ...
• batimetry
• topography
• stage-discharge function of the spillway
• ...
• Regione Lombardia (water authority)
• ...

(at+1)

Models are a simplified representation of reality;

They should reproduce those features of the system that are important for the scope of the Project.

The first step to create a model is to select the essential variables within the domain.

(rt+1)

(ht)

The domain is the first level of abstraction of reality. It does not require any assumption about the mathematical relationships linking the variables.

It is not a representaton of reality, but a partition of knowledge.

The (lake’s) domain

The whole set of quantities and information about the lake:

• inflow
• release
• level
• water characteristics
• biota
• algae
• ...
• batimetry
• topography
• stage-discharge function of the spillway
• ...
• Regione Lombardia (water authority)
• ...

(at+1)

(rt+1)

(ht)

An important convention

The subscript of a variable is the time instant at which it takes deterministically known value.

et+1

at+1

Are the variables well defined?

It is very important that the domain is defined in strict collaboration with the concerned Stakeholders.

Sharing and agreeing on the assumptions made at this point is key to obtain a “trusted” model of the system.

Inflow at+1:

total inflow in the interval [t,t+1)

It is better to divide it into:

et+1 = inflow from the natural catchment

wt = pumping from hydropower plant downstream

wt

Which unit of measurement? m3/s or m3 ?

Are the variables well defined?

YES, as long as we do not find errors: only falsification is possible.

Identifying the model:the causal network

Release decision

Is it a good representation of the real cause-effect relationships?

Causal network of the lake

Loops are not allowed. An effect can not cause itself!!

Is it a good model of reality?

NO, evaporation is missing....

Causal network of the lake

How to check if the network is a good model?

- A priori: good sense, Analyst’s intuition

- A posteriori: accuracy of the model identified starting from the network

deterministic

disturbance

disturbance

input

input

internal

variables

disturbance

input

random

disturbance

Classification of the variables

state

control

output

The stateis composed of all the variables that are necessary to describe the past history of the system, and, once these are known, the future evolution of the system is completely defined by the sole inputs.

set of the feasible controls

output transformation function

The model structure

state transition function

These two equations include all the information available in the network.

In the network the internal variables are explicitely considered.

up planning decision

wtdeterministic disturbance

utcontrol

et +1 random disturbance

input

From now on vectors will be in bold, e.g.xt is the state vector

!

In general: variables

state xt

ouptut yt

Models interact with the outside only through inputs and ouputs. What happens inside is important only as far as it affects the ouptuts.

time-varying model

In general: structure

state transition function

This is a

DYNAMIC SYSTEM

Models are OBJECTS in the computer-science meaning of the word

with the following associated expressions

output transformation function

proper model

improper model

et+1incoming flow

model

utwithdrawal decision

yt diverted flow

only the output

transformation function

yt=ht(ut,et+1)

!

Time-varying is not a synonymus of dynamic

Not always systems are dynamic

Not always the state appears in the system dynamics.

E.g.: diversion dam

this is a non-dynamic model

given

the initial state

Simulation

established

a time horizon H (starting from time 0 and ending at time h)

the input trajectories

simulation is aimed at computing

the state trajectories

the output trajectories

given

the initial state

Simulation

established

a time horizon H (starting from time 0 and ending at time h)

the input trajectories

using the model recursively

38

causal network

mental model

Conclusions

domain

• Next step:
• implicitly or explicitly define
• the state transition function
• - the output transformation function

How to classify model ?

with respect to

the aumount of a priori information one has to know about the ongoing processes

the nature

of their functions

Bayesian Believe Networks
• Mechanistic models
• Empirical models
• Markov models