Stochastic Modeling of a fuzzy index to determine the - IDAEA-CSIC

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Stochastic Modeling
of a fuzzy index to
determine the
quality of water in
the Cauca River
Diana Carolina Osorio García
Christian Piamba Ceballos
William Ocampo-Duque
* Marta Schuhmacher
Water pollution limits its use for human
consumption and for the development of a
region's economy.
2
3
Water requires an intelligent management as finite
natural resource in harmony with the ecosystem
(Water Framework Directive).
Ecological assessment (EU Water Framework Directive)
classification & presentation
Water-quality status = Chemical status + Ecological status / potential
Chemical status
Bad status
biotic
elements
abiotic
elements
Bad
status
Poor
status
Ecological status
Good status
Moderate
status
(differs moderately
from type specific
conditions)
Good
status
(slight changes
from type spec.
conditions)
target
status
yardstick
High
status
(close to
undisturbed
conditions)
max. ecol. reference
potential
Ecological status
Do the biological quality
meet reference conditions?
yes
no
Do the biological quality
deviate slightly from
reference conditions?
Do the physico-chemical
conditions meet
high status?
yes
no
no
yes
yes
Do the physico-chemical conditions:
(a) ensure ecosystem functioning, and
(b) meet the EQSs for specific pollutants?
no
Classify on the basis of
the biological deviation
from reference conditions
Do the hydro-morphological
conditions meet
high status?
Is the deviation
moderate?
yes
no
yes
High
status
Good
status
Moderate
status
Poor
status
greater
Is the deviation
major?
yes
greater
Bad
status
• The integration of water quality variables is
essential in the processes of
environmental decision making.
• To that, it is essential to develop tools that
they manage uncertainty and variability
4
General Objective
To improve the environmental assessment
with self-interpretable water quality
indicators to control the subjectivity and
uncertainty present in these complex
environmental problems.
5
Specific Goal
1.- To developed a conceptual model to assess water quality in
rivers from a perspective of environmental risk assessment,
integrating a posibilistic model (Fuzzy) with a probabilistic model
(Montse Carlo)
to manage the uncertanty and the variabilty.
2.- To apply the model to a case study (Cauca river basin,
Colombia)
Cauca river
Tramo Suarez- La Virginia
19 Monitoring stations
Samples
●I Tram (Suarez- Puente
Hormiguero) : 24
●II Tram (Canal Navarro-Puente
Mediacanoa) : 32
●III Tram (Rio Frio-Puente la
virginia) : 20
Yeasr of study : 2002, 2006,
Parameters:
pH, Oxígeno disuelto (OD),
Coliformes fecales (CF),
Demanda bioquímica de
oxígeno (DBO5), Temperatura
(T), Fosfatos totales (FT),
Nitratos(N), Turbiedad (Tur),
Sólidos totales (ST). 2009
Fuzzy Inference System
Water quality
indicator 1
Water quality
indicator 2
…
Water quality
indicator 3
“ Inputs are crisp
numbers limited
to a range”
Rule 1
Rule 2
Rule 3
Σ
Water Status:
9 Excellent
9 Good
9 Average
9 Poor
Rule 4
…
“All rules are evaluated
in parallel using fuzzy
reasoning”
“Results of rules
are aggregated”
“The result
are crisp
number”
Fuzzy inference in risk assessment
Membership functions
Membership Functions
9
Inference rules
Antecedent:
If x is A and y is B
Consequent:
then z is C
They simulate the expert knowledge
x, y, z are “variables”; A, B, C are “qualifiers”
Examples:
If BOD5 is “low” then Water Quality is “Good”
If BOD5 is “medium” then Water Quality is “Average”
If BOD5 is “high” and DO is “low” then Water Quality is “Poor”
3.2 Mechanism of Fuzzy inference
μ A∩B ( x) = min(μ A ( x), μ B ( x))
Mechanism of Fuzzy inference
Results –Water Quality
The Ebro basin
Ocampo-Duque et al., Assessing water quality in rivers with fuzzy inference
systems: a case study. Environment International, 2006
22
Simulation tool: Monte Carlo Method
Method of
generating
random numbers
Data Processing
Exit
OD
Calidad del Agua
FIS
DBO
Non-parametric Distributions
1. Histogram
2. Estimation by
nuclei
Kernel Gaussian Function
Kernel Gaussiana
Stochastic simulation
Quantity of dates
• Tram I : 24
• Tram II : 32
• Tram III : 20
Probability distribution
2006 TRAM I
Coliform
Temperat Turbied
Sólidos
Fosfatos
es
ura
ad
Totales
Fecales
Serie
OD
PH
DBO
Nitratos
Distribució
n:
5,7
6,81
1,78
0,4
Mejor
Ajuste:
Min
Extreme
Weibull
Pareto Lognormal Gamma
Logistic
Anderson0,6918
Darling:
1,1661
0,8335
7,9438
1,5215
1,8256
0,4998
1,4446
0,2766
Valor - P:
0,000
---
0,000
0,000
0,000
0,327
0,000
0,495
0,43
11201,33
21,13
172,37
0,03
186,98
Lognorm
Logistic Lognormal
al
Results for Cauca river
Tram II
2009
2006
2002
Tram I
Results
Tram III
Results. Comparation with other index
2002
2006
2009
Tramo 1
Tramo 2
Tramo 3
Media
Mala
Mala
Media
Mala
Mala
Media
Mala
Mala
2002
2006
2009
Tramo 1
Tramo 2
Tramo 3
Aceptable
Inadecuada
Inadecuada Buena
Buena
Aceptable
Buena
Inadecuada
Buena
2002
2006
2009
Tramo 1
Tramo 2
Regular
Regular
Tramo 3
Mala
Regular
Regular
Mala
Regular
Regular
Mala
Conclusions
• It should ensure the integration of different
disciplines tools to understand and solve
environmental problems.
• Stochastic analysis is necessary, as these
are similar to the behavior of surface
sources, which are probabilistic and not
deterministic .
Thanks for your atention
http://www.tecnatox.cat
Acknowledgements: Spanish Agency for International Development cooperation (AECI)
Thanks to the CVC for providing information for water quality parameters.
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