Environmental Engineering Reference
In-Depth Information
Modelling and Prediction Techniques
improved, and as computer power has developed.
Thus, the use of charts, tables and hand calcula-
tions has gradually given way to computer
models.
The search for better understanding to improve
our predictions has led to greater monitoring of
waves, tides and beaches. An important agent for
this in the UK was the introduction of Shoreline
Management Plans in the early 1990s, which set
a requirement on data gathering for coastal man-
agement and development. Thus, there are now
a growing number of coastal locations for which
there are records covering over 10 years. While
this is not yet adequate for detailed research, the
dataset does provide valuable information for
planning and design.
In all prediction it is important to acknowledge
uncertainty. Sources of uncertainty include:
.
Incompleteness - if not all relevant processes are
taken into account then the predictions are un-
likely to be realistic.
.
Empiricism - design equations are generally
empirical, based on experiments performed at lab-
oratory scale. The measurements have scatter
leading to errors in fitting an equation to the data.
.
Extrapolation - when estimating design condi-
tions some extrapolation is usually required and
there is uncertainty associated with this.
.
Measurement error - the observations used for
design will have uncertainties due to the limita-
tions of the measurement equipment.
.
Non-stationarity - if there is a long-term under-
lying trend (such as a gradual rise in themean level
of the sea), or if the variance of a quantity changes
over time (such as storm intensity or duration),
then due account must be made for this.
While some uncertainty has to be accepted its
effects can be mitigated to some extent by consid-
ering 'worst case scenarios', including factors of
safety based on engineering judgement, and,
where appropriate, by adopting a probabilistic ap-
proach to design that allows uncertainties to be
quantified (e.g. Thoft-Christensen andBaker 1982;
Melchers 1999; Reeve 2010). In the following
sections the basic categories of modelling techni-
ques are described, with some case studies to
illustrate the methods.
One of the first decisions to be taken iswhatmodel
to employ. This will depend on the type and
amount of data available, as well as commercial
considerations. The data will usually be in the
form of:
.
time-series (values at a fixed location at regular
intervals in time);
.
seasonal or annual statistics;
.
average or 'typical' conditions;
.
specified conditions corresponding to a given
return period;
.
qualitative information on past construction of
sea defences, beach nourishment and dredging
operations.
Models for describing coastal processes may be
categorized into four types:
1
Statistical (based on analysis and extrapolation,
requiring long records of observations).
2
Empirical (describing equilibrium conditions,
requiring minimal information).
3
Dynamical (solving the equations of motion,
requiring a moderate amount of data).
4
Hybrid (mixtures of the above types, requiring
a modest amount of data).
Examples ofmethods fromeach of these categories
are given below.
Statistical analysis and extrapolation
Statistical techniques are applied to time series of
waves and beach level measurements to identify
patterns of behaviour. This approach can be suc-
cessful if there is strong periodic behaviour in the
data. Fourier analysis is often themethod of choice.
However, if the spatial or temporal sampling is at
irregular intervals then interpolation to regular
intervals will be necessary. The Empirical Orthog-
onal Function (EOF) technique allows patterns to
be identified from irregularly sampled data and has
been used extensively (e.g. Winant et al. 1975;
Reeve et al. 2001;Miller andDean 2007). However,
extrapolation into the future is not so straightfor-
ward. Both Fourier and EOF methods are based on
an assumption that the data record is statistically
