Transcript Australian Centre for Environmetrics Developing Risk-based guidelines for Water Quality Monitoring and Evaluation Prof.

Australian Centre for Environmetrics
Developing Risk-based guidelines for Water
Quality Monitoring and Evaluation
Prof. David Fox
CSIRO Land and Water
University of Melbourne
Melbourne University Private
Australian Centre for Environmetrics
http://www.deh.gov.au/water/quality/nwqms/
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Chapter 1: Introduction
Chapter 5: Recreational WQ
& aesthetics
• Rational for revision
• Philosophical basis
• Swimming, boating, etc.
Chapter 2: Framework
Chapter 6: Drinking Water
• Key steps
• Important issues
• Safety & aesthetics
Chapter 3: Aquatic Ecosystems
Chapter 7: Monitoring &
Assessment
• Types & levels of protection
• Default & site-specific guidelines
• Use of biological indicators
• Data collection & analysis
Chapter 4: Primary Industries
• Irrigation
• Livestock
• aquaculture
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Environmental monitoring
Aim is to design and
conduct scientifically
credible programs of
environmental surveillance
Compliance monitoring
Aim is discover specific
violations and force
corrective action
information
data
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Risk-based Approaches
Evolution of conventions has a lasting effect on how risk analyses are
conducted:
• USEPA has set mostly conservative defaults.
• US Nuclear Regulatory Commission generally avoids
conservative assumptions, recommending that modelers use
default values that are close to the central tendency of
parameter estimates (Bier 2003).
• The Bayesian perspective is that there is a random variable,
and the job of the analyst is to characterize how variable it may
be.
The approaches share a common belief in the epistemic nature of risk:
there is a state of nature and the job of the risk analyst is to define it.
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Risks and Trade-offs
•
Protector risk = prob. ecologically important impact goes undetected
•
Polluter risk = prob. unimportant impact triggers further action
Protector
Risk
Polluter Risk
Max. polluter risk
Max. protector
risk
Low
High
Level of environmental protection
'Acceptable' region of protection
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Trigger-values
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Trigger-values for physico-chemical stressors
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Setting Risk-based trigger values : Aldenburg & Slob (1993)
mortality
100%
Dose-response curves
for selected species
concentration
Distribtion of NOECS
3
Assumed log-logistic
y
0
0
x
1.111
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Setting Risk-based trigger values : Aldenburg & Slob (1993)
3
Distribution of NOECs for all species
Trigger value
y
0.95
3
0
0
x
y
0
0
x
1.111
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1.111
Example – Modelling Uranium NOECs
Test endpoint
NOEC*
(µg L-1)
Chlorella sp.
Cell division
rate
129
Moinodaphnia
macleayi
Reproduction
18
Hydra viridissima
Population
growth
150
Mogurnda mogurnda
Mortality
400
Species
Melanotaenia
splendida inornata
Chronic
Acute
Mortality
* NOEC: no-observed-effect concentration
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810
Example – Modelling Uranium NOECs
Raw Data: x = {129, 18, 150, 400, 810 }
Trigger value = 0.49 g/L
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Example – Modelling Uranium NOECs
Chronic data: denote by X with pdf f X ( x; )
Acute data:
•
denote by Y
•
distribution of Y/ assumed to be same as distribution of X
where  is acute to chronic ratio.
Given sample of n1 X observations and n2 Y observations, the maximum
likelihood estimator (mle) for  is that value which maximises the likelihood
function:
n1
n2
i 1
j 1
L      f X ( xi ; )  fY ( y j  ; )
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Example – Modelling Uranium NOECs
Data: x = {129, 18, 150 } and y = {400, 810}
 12
1.86110
Likelihood function
exp ll  1   2  t k 
Mle = 7.451
0
0
5
10
15
20
0.03
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25
tk
30
35
40
45
50
50
Example – Modelling Uranium NOECs
Modified Data: x = {129, 18, 150 } and y = {400 / 7.451, 810 / 7.451}
Revised trigger value = 5.34 g/L
cf 0.49 g/L (raw data)
5.8 g/L (DEH value)
3.11 g/L (using default  = 10)
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Bayesian Methods – A Credible Alternative?
Bayesian approach:
Has advantage of introducing subjective assessment / expert opinion
But
May be perceived as being difficult to interpret & lacking objectivity.
London Court of Appeal:
“Introducing Bayes Theorem, or any similar method, into a
criminal trial plunges the jury into inappropriate and unnecessary
realms of complexity, deflecting them from their proper task.”
The Times, November 3 1997
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Example – Modelling Uranium NOECs
A Bayesian Approach
mu
mup
tau
lamda
Y[j]
taup
for(j IN 1 : 2)
X[i]
for(i IN 1 : 3)
http://www.mrc-bsu.cam.ac.uk/bugs/winbugs/contents.shtml
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Example – Modelling Uranium NOECs
A Bayesian Approach
Prior & posterior distributions
0.25
Density
0.20
node
mean
stdev
P2.5
median P97.5
Lamda_post
7.324
3.036
4.075
6.624
node
mean
stdev
P2.5
median P97.5
Lamda_prior
19.951
14.134
2.4
16.669
97.5
117.0
14.92
0.15
0.10
0.05
0.00
0.0
19.5
39.0
58.5
78.0
Data
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82.0
136.5
Variable
lamda_prior
lamda_post
Example – Modelling Uranium NOECs
A Bayesian Approach
Modified Data: x = {129, 18, 150 } and y = {400 / 6.624, 810 / 6.624}
Revised trigger value = 6.64
g/L
cf 0.49 g/L (raw data)
5.8 g/L (DEH value)
3.11 g/L (using default  = 10)
5.34 g/L (using mle  = 7.451)
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Reference site – Test site comparisons
Note:
Reference Site
3
•
Normal distributions not a prerequisite
•
Common distribution not a prerequisite
•
80th. Percentile at reference site must be
based on minimum of 24 data values (2
years monthly data)
y
0
0
x
1.111
Test Site
3
De facto ‘standard’
y
0
0
Test site
median
Ref site 80th.
percentile
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x
1.111
Reference site – Test site comparisons
next level investigation triggered
no action required
w arning - investigation may be necessary
3
Test site median
concentration units
2
1
Reference site P80
0
1
2
3
4
5
6
7
8
Month
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10
11
12
Observations & Challenges
•
Despite early attempts, development and adoption of a
‘standard’ risk metric seems a long way off (never?);
•
Bayesian methods are becoming increasingly popular,
although acceptance may be hampered by biases and
lack of understanding;
•
More attention needs to be given to appropriate
statistical modelling. In particular:
- model choice
- Parameter estimation
- Distributional assumptions
- ‘Outlier’ detection and treatment
- robust alternatives (GLMs, GAMs, smoothers etc).
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