modelling environmental systems - k141hydraulika.fsv.cvut.cz/toky/predmety/pz01/ke... · the...

MODELLING ENVIRONMENTAL SYSTEMS PJZ1 PROJECT 04 MARCH 2015

Miroslav Hrncir Czech Republic, Prague

GUY CARPENTER 1 26 February 2015

Modelling Environmental Systems Project Agenda

Unit A: Modelling Environmental Systems – Introduction The role of modelling; objectives and concepts, types of models, model components Modelling procedures; problem definition, boundary conditions, data requirements,

calibration and validation, sensitivity analysis, parameterization, calibration, validation and evaluation Wastewater Networks Modelling in the UK Practical 1: Design of a simple conceptual model

Unit B: Probabilistic Design of Risk Models (fluid mechanics and hydraulics context) Definition of risk, difference between local and global risk models Response surface methodology, how to calculate return periods Design of a probabilistic model for a dam breach & dike overtopping Practical 2: Probabilistic calculations

Unit C: Natural Catastrophe modelling in the context of risk management Natural catastrophes Basic catastrophe modelling principles Catastrophe modelling modular concept and results Practical 3: Flood event case study


Modelling Environmental Systems Project Objectives

On the successful completion of this unit the student will be able to:

Design a simple conceptual model of any environmental system;

Formally identify the structure of a model to represent a specified hydrological system;

Select between alternative approaches to catchment modelling;

Critically evaluate the usefulness of a model;

Apply a model to meet stated objectives;

Understand the concept of probabilistic risk models;

Design a simple probabilistic risk model;

Understand the basic catastrophe modelling principles, concepts and results in the context

of risk management;


Modelling Environmental Systems - Introduction Agenda

1) The role of modelling; objectives and concepts, types of models, model components

2) Modelling procedures; problem definition, boundary conditions, data requirements, calibration and validation, sensitivity analysis, parameterization, calibration, validation and evaluation

3) Wastewater Networks Modelling in the UK

4) Practical 1: Design of a simple conceptual model


Modelling Environmental Systems - Introduction What is a model

What is a model?


Modelling Environmental Systems - Introduction Types of models

Time scale Probability Steady state Event Continuous

Spatial representation Lumped Semi-lumped Distributed

Determinism Deterministic Stochastic

Mathematical solution Conceptual Empirical Mechanistic


The Modelling Process How do we develop a model?

Development of a conceptual model

Model construction

Verification

Calibration

Sensitivity analysis

Validation

Solving the problem

Rei

tera

tion

Parameterisation

Definition of the problem

Eval

uatio

n D

esig

n D

evt


The Modelling Process Definition of a problem

Is a model the most appropriate solution?

What is the purpose of the model?

Purpose will determine the nature of the model

Modelling a system for no purpose is unproductive

Should not be ‘all things to all men’!


The Modelling Process Modelling Terminology

System – a limited part of reality containing

interrelated components

Model – simplified representation of a system

Boundary – edges of the system

Simulation – mathematical representation of a

system

Environment – set of conditions outside the system

being modelled

State and rate variables – State of components – Rate of change

Parameters – Constant values for a system

Driving variables – External variables driving change

Feedback – negative, positive


The Modelling Process The Conceptual Model

• Framework of the system

• Model is a simplification of our own mental model of the system

• Consists of a system boundary, within which are compartments, flows, influences

• What components and flows should be included?

• May be an end in itself - i.e. a learning exercise

“Make things as simple as possible, but no simpler” – Albert Einstein “ … if you cannot retain a handful of causes in your explanation, then your understanding is simplistic. If you require more than a handful of causes, then it is unnecessarily complex. If you cannot explain it to your neighbour, you do not truly understand it”. - Holling, (2000)


The Modelling Process Example Conceptual Model

http://www.ozestuaries.org/oracle/ozestuaries/conceptual_mods/cm_wde.htm


The Modelling Process Model Construction

Implementation of the model

manual calculation, spreadsheet, computer program, graphical package (ModelMaker, Stella)

Mathematical equations - knowledge of process required, sometimes empirical

All components must be quantified

Best to develop bit-by-bit, test, then move on to next bit


The Modelling Process Parameterization

Parameters are constant values in the model

Initially need realistic values - further refinement can come later in calibration

Directly measured from field experiments, laboratory experiments, literature, etc.

Indirectly estimated by optimisation (calibration)


The Modelling Process Why do we verify models?

Check of internal consistency of the model and its software implementation

– mathematically correct

– analysis of dimensions and units

– mass conservation

– detection of violation of natural ranges of parameters and variables

Does it behave as expected?


The Modelling Process Why do we do sensitivity analysis?

Analysis of how changes in particular inputs affect model output

Most of the variation in output is caused by a small number of input variables

Varying an input in small steps can help detect unwanted discontinuities

Aid to verification to check model formulation check for errors (e.g. discontinuities)

Aid to parameterisation identify most sensitive parameters and focus effort on

gaining accurate values

Quantification of uncertainty stochastic methods


The Modelling Process Sensitivity analysis – Model Formulation

Run

off

Rainfall


The Modelling Process Sensitivity analysis – Discontinuities

0200400600800

10001200140016001800

0 5 10 15 20 25

leaf number

leaf

siz

e (c

m2 )

CERES-Maize


The Modelling Process Types of Sensitivity Analysis

One-at-a-time sensitivity analysis – Response to variation in one input at a time – Useful for revealing discontinuities

Factorial sensitivity analysis – Sensitivity of a factor often dependent on values of other

parameters – Inputs varied according to a factorial design – e.g. two-level: each input can be low or high – May be computer intensive for large numbers of factors


The Modelling Process Sensitivity Analysis Procedure

Select model

Select parameters to vary

Decide on variation – range, step

Describe sensitivity – Statistics – Graphics


The Modelling Process Sensitivity Analysis Procedure

Select model

Select parameters to vary

Decide on variation – range, step

Describe sensitivity – Statistics – Graphics

Case Study

AP

u s rn

=

12

23

Where V is the velocity A is the cross sectional area r is the hydraulic radius = A/P where P is the wetted perimeter s is the slope of the water surface n is the roughness of the channel


The Modelling Process Effect on Manning’s n on discharge


The Modelling Process Sensitivity Analysis - Statistics

Absolute sensitivity: Average linear sensitivity:

−

−

=

III

OOO

ALS12

12[ ][ ]12

12

IIOOAS

−−

=

0

20

30

40

50

0 0.5 1.5 2 2.5 3.5 4 4.5 5

O2

O1

I 1 I 2

A

B

Model input

Model output


The Modelling Process Sensitivity Analysis – Tornado Graph, Spider Graph


The Modelling Process Sensitivity Analysis – Summary

Response of model to changes in parameters

Useful information for a variety of purposes

Graphs are a simple but effective tool


The Modelling Process Why do we calibrate models?

All models empirical at some level

Some parameters have no physical meaning and values need to be assigned

Other parameters may be measurable but are fitted

Adjustment of some parameters so that model output matches real-world data

Concentrate on parameters to which model is most sensitive

Not too many (usually 1 or 2) – can make most models fit the data if enough parameters are altered!


The Modelling Process Calibration Process

Apply model

Compare

Change parameter

Use Accept

Reject

Select parameters to calibrate (sensitivity analysis may be helpful)

Split data sets – save some independent data for validation

Change and monitor model’s response with respect to real data – trial and error – optimisation – e.g. minimising least-squares


The Modelling Process Calibration Process – Things to think about!

Need to beware of obtaining unrealistic values (e.g. physically impossible) - can constrain range

Need to beware of local optima which may not be close to the global optimum – try different starting points

Model equifinality is possible - different parameter sets will give the same response

Are calibrated parameters correlated - can’t change one without the other


The Modelling Process Validation

From the Latin validus = ‘strong’

Comparison with independent data

Does the model fulfil the purpose for which it was designed?

Data used for model development, parameterisation, calibration & validation should be different


The Modelling Process Validation – Scattergram, regression, 1:1 line

0

50

100

150

200

250

300

0 50 100 150 200 250 300

Observed, Mm3

Pred

icte

d, M

m3

y = 0.89x + 14.75R2 = 0.84

0

50

100

150

200

250

300

0 50 100 150 200 250 300

Observed, Mm3

Pred

icte

d, M

m3

95% confidence interval 0.79 < x < 0.987.7 < c < 21.8

0

50

100

150

200

250

300

0 50 100 150 200 250 300

Observed, Mm3

Pred

icte

d, M

m3

95% confidence interval 0.79 < x < 0.987.7 < c < 21.8


The Modelling Process Validation – Time Series

0

20

40

60

80

100

1201 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12

1985 1986 1987 1988 1989 1990

NSE = 0.80

------ Simulated____ Observed

∆y = (mi – oi)

SS = Σ(mi – oi)2


The Modelling Process Validation – Goodness of Fit Statistics

Statistic Formula Meaning

Mean bias error ( )MBE

nm oi i

i

n

= −=∑1

1

A measure of the overall bias of the model. It may be positive or negative indicating that the model over, or under estimates.

Root mean square error ( )∑

=

−=n

iii om

nRMSE

1

21 A measure of the absolute differences between the observed and model predicted data.

Weighted sum of squares (chi squared)

( )χ

ε2

2

2=−

∑m oi i

i

Similar to the RSME but weighted according to the error in the observed data.


The Modelling Process Validation – Nash-Sutcliffe Efficiency

0

1

2

3

4

5

6

Jan/1

985

Jul/1

985

Jan/1

986

Jul/1

986

Jan/1

987

Jul/1

987

Jan/1

988

Jul/1

988

Jan/1

989

Jul/1

989

Jan/1

990

Jul/1

990

m3 /s

ObservedSimulated ( )

( )∑

∑

=

=

−

−−= n

ii

n

iii

oo

omNSE

1

2

1

2

1

NSE = 0.80


The Modelling Process Reiteration

Development of a conceptual model

Model construction

Verification

Calibration

Sensitivity analysis

Validation

Solving the problem

Rei

tera

tion

Parameterisation

Definition of the problem

Eval

uatio

n D

esig

n D

evt


The Modelling Process Solving the problem

Identifying future research

Extrapolation - space, time

Decision-support tool

Optimisation of inputs

Teaching & learning - understanding a system


The Modelling Process Practical 1 – Conceptual Model

Ornamental lake

Waste water disposal

Oasis

Reed bed

Irrigation

modelling environmental systems - k141hydraulika.fsv.cvut.cz/toky/predmety/pz01/ke... · the...

Documents