Modelling Environmental Systems - K141hydraulika.fsv.cvut.cz/Toky/Predmety/PZ01/ke... · The...
Transcript of 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
GUY CARPENTER 2 26 February 2015
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;
GUY CARPENTER 3 26 February 2015
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
GUY CARPENTER 4 26 February 2015
Modelling Environmental Systems - Introduction What is a model
What is a model?
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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
GUY CARPENTER 6 26 February 2015
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
GUY CARPENTER 7 26 February 2015
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’!
GUY CARPENTER 8 26 February 2015
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
GUY CARPENTER 9 26 February 2015
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)
GUY CARPENTER 10 26 February 2015
The Modelling Process Example Conceptual Model
http://www.ozestuaries.org/oracle/ozestuaries/conceptual_mods/cm_wde.htm
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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
GUY CARPENTER 12 26 February 2015
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)
GUY CARPENTER 13 26 February 2015
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?
GUY CARPENTER 14 26 February 2015
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
GUY CARPENTER 15 26 February 2015
The Modelling Process Sensitivity analysis – Model Formulation
Run
off
Rainfall
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The Modelling Process Sensitivity analysis – Discontinuities
0200400600800
10001200140016001800
0 5 10 15 20 25
leaf number
leaf
siz
e (c
m2 )
CERES-Maize
GUY CARPENTER 17 26 February 2015
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
GUY CARPENTER 18 26 February 2015
The Modelling Process Sensitivity Analysis Procedure
Select model
Select parameters to vary
Decide on variation – range, step
Describe sensitivity – Statistics – Graphics
GUY CARPENTER 19 26 February 2015
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
GUY CARPENTER 20 26 February 2015
The Modelling Process Effect on Manning’s n on discharge
GUY CARPENTER 21 26 February 2015
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
GUY CARPENTER 22 26 February 2015
The Modelling Process Sensitivity Analysis – Tornado Graph, Spider Graph
GUY CARPENTER 23 26 February 2015
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
GUY CARPENTER 24 26 February 2015
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!
GUY CARPENTER 25 26 February 2015
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
GUY CARPENTER 26 26 February 2015
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
GUY CARPENTER 27 26 February 2015
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
GUY CARPENTER 28 26 February 2015
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
GUY CARPENTER 29 26 February 2015
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
GUY CARPENTER 30 26 February 2015
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.
GUY CARPENTER 31 26 February 2015
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
GUY CARPENTER 32 26 February 2015
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
GUY CARPENTER 33 26 February 2015
The Modelling Process Solving the problem
Identifying future research
Extrapolation - space, time
Decision-support tool
Optimisation of inputs
Teaching & learning - understanding a system
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The Modelling Process Practical 1 – Conceptual Model
Ornamental lake
Waste water disposal
Oasis
Reed bed
Irrigation