10. EIA and uncertainty propagation

What is a environmental impact assessment (EIA)

a procedure which serves to provide information to local authority planners, other regulators and authorising bodies, other interested parties and the general public about certain proposed developments and their likely effects on the environment

What is the aim of EIA

To protect the environment by ensuring that a local planning authority grants planning permission for projects “in the full knowledge of the likely significant effects, and takes this into account in the decision making process”

What is the outline of the EIA process

Screening: Determining whether a project requires an EIA

Scoping: Identifying the various issues that should be covered

Baseline studies

Impact significance assessment

Mitigation

Submission of environmental statement

Decision making

What is project screening

Screening is a procedure used to determine whether a project requires an EIA

What are the 2 types Schedules of projects

Schedule 1 projects always require an EIA

Schedule 2 projects require EIA if they exceed certain thresholds and/or are situated in a sensitive area

What are examples of Schedule 1 projects

Crude oil refineries, power stations and other metal works

What are examples of Schedule 2 projects

fish farming, food industry and shopping centres

What are sensitive areas in the UK

Special scientific interest, national parks and WHO sites

How do you rank risks

Risk = likelihood x consequence

Deterministic model

Do not account for random processes and provide single, supposedly exact, answers

Stochastic models

Account for random processes and provide results in the form of probability distributions

What undermines both the deterministic and stochastic models

model structure uncertainty and parameter uncertainty

What is the three processes of development of mathematical models

1. The conceptual model

2. Governing equations

3. Analytical or numerical solutions

Model structure uncertainty

uncertainty about the acceptability of this deviation (a deviation from the process we are trying to represent)

Model calibration

Finding a set of parameter values that a given mathematical model simulates a set of previously observed measurements to the best of its ability

Measurement error

There will be error in the measurements used to inform the parameter calibration

Model structure error

Parameter values based on previous experience often compensate for model structure errors incurred due to model structure uncertainty

Equifinality

Often it is not possible to constrain all of the unknown parameters using a given set of measurements. This gives rise to equifinality, whereby multiple combinations of parameter values yield identical model responses within a restricted window of behaviour

Extrapolation error

The scenario of interest often represents an extrapolation from a previous domain of experience

how do we end up with our probability distribution of model results

If we account for the randomness associated with model structure and parameter uncertainty within our deterministic model predictions

Uncertainty propagation

The process of propagating knowledge about model structure uncertainty and parameter uncertainty through to model outputs such that model results are stochastic and specified as probability distributions

What is the equation for cumulative distribution function (CDF)

F(x)=[f(x)dx]x -inf

What is the equation for the probability of exceedance

P(X>x)=1-P(X<x)

What is a PDF

PDF is a continuous form of a histogram where the bin widths are infinitesimally small

How can a continuous CDF be found from

F(X) = [f(x)dc] x -inf

What is an important property of the PDF

[f(x)dc]inf -inf =1

How to work out empirical CDF

• Consider N number of measurements, xj

• Let xi(i=1,2,…,N) be the same set but ranked large to small

• i is the rank number and N is the number of samples

What are the two popular heuristic equations in empirical CDF

Gringorten plotting position and Weibull plotting position

Gringorten plotting position

P(X>xi)=i-0.44/N+0.12 (P=probability of non-exceedance, is is the rank number, N is the number of samples)

Weibull plotting position

P(X>xi)=i/N+1 (rank number/number of samples +1)

What does a triangular distribution look like

like a triangle

How to use Monte Carlo simulation (used for propagating parameter uncertainty though to model outputs)

1. Specify parameter distributions

2. Sample a specified number of different parameter sets

3. Run deterministic model for each parameter set

4. Collect all the model results to form a cumulative distribution function

What is a tornado plots

Shows bar charts of rank correlation for each parameter with the highest correlating parameters displayed first

What are the steps to create a tornado plot

1. involves determining the rank number of the model outputs and each parameter

2. the next step is to determine the rank correlation between parameter ranks and output ranks for each parameter

3. determine the P value

4. finally rank all the rank correlations and order the model parameters accordingly in a bar chart

What happens if P>0.05

If P>0.05 a correlation is considered to be not significant, so we set those correlation coefficients to zero

What is a common method of abstracting data from a CDF is to determine…

P10, P50 and P90, which correspond to probabilities of non-exceedance of 10%, 50% and 90%. These can be obtained using the following additional code:

yiSTATS=interpl(PNE,yi,[10 50 90]);