Part C | 28.1
612 Part C Coastal Design
are almost entirely based on large-scale flume tests
and just recently have been adapted for changed design wave conditions based on such tests [28.1]. Scour
around structures is another example where physical
models are still much in use, in this case because of the
complexity of the three-dimensional (3-D) currents and
turbulence around them. However, in many cases such
a direct application of physical modeling to a problem
is difficult, and such models are then used to look into
the details of processes and to validate numerical models that can be used at larger scales.
Large-scale physical models of tidal systems, rivers,
and estuaries have become too expensive in developed
countries to compete with ever-improving numerical
models, but are still widely used in countries like China,
where labor cost is relatively cheap and there is considerable expertise in dealing with inevitable scale effects.
Combining such models with numerical modeling can
lead to interesting results, and is probably a direction
worth exploring further.
When waves are important and we have to look at
large systems at the same time, physical modeling is
no longer an option. The modeled waves would be too
small to be represented properly, so we will have to look
at other methods.
28.1.2 Analytical Models
First, we turn to analytical models. They can be simple and elegant and provide almost instant insight.
The coastline theory of Pelnard-Considère [28.2] has
shaped our thinking about large-scale coastal evolution,
and analytical and numerical successors of the theory
are still abundantly used [28.3]. Other, more complex,
analytical models explain point bars in rivers and estuaries [28.4], sand waves and tidal sandbanks [28.5], and
though they use strong approximations of the physics,
they tell us which processes are responsible for certain
phenomena we see, so we can make sure that more
complex numerical models reproduce these processes,
which in theory they should, but in practice often fail to
do.
28.1.3 (Semi-)Empirical Models
The next type of models is heavily based on data and
therefore called empirical models. The equilibrium profile model for dune erosion, which has made it into
Dutch law, is a good example [28.1, 6]. Based on the
observation that beach profiles always have the same
shape after a storm, the method consists of shifting that
profile back and forth until the eroded area equals the
accreted area. A more advanced approach for beach
evolution and dune erosion is used in SBEACH [28.7].
SBEACH is a one-dimensional (1-D) (profile) beach
erosion model for storm where net sediment transport
occurs when the local wave dissipation rate is different
from the equilibrium rate. For tidal inlets and estuaries,
there is a host of equilibrium equations [28.8], relating the tidal volume to channel cross-section, to total
channel volume, to ebb delta volume, etcetera. If you
divide a tidal inlet or estuary up into a number of units
(ebb delta, channels, tidal flats) you can define equilibrium situations for each of them. However, that does
not tell you how they get to their equilibrium. To solve
this, semiempirical models were developed, where the
units all try to get to their equilibrium but sediment
has to be transported between them. The rate of sediment exchange depends on how far each unit is from
equilibrium. Stive and Wang use this concept to model
long-term, large-scale effects of sea-level rise and gas
extraction, inlet closure, dredging, and other scenarios [28.9].
Such models have shown a lot of value for specific
situations, where there is a lot of historical data and
nice test cases from the recent past (closure of inlets,
channel deepening for navigation) to calibrate the coefficients in such models. In many places around the
world this is not the case; also, more complex situations or more detailed questions need to be addressed
than can be represented by the semiempirical models
we just discussed. In such cases, we turn to processbased morphodynamic modeling.
28.1.4 Process-Based Models
In process-based models, we start from a detailed
description of processes and let sediment transports,
bottom changes, and the evolving bathymetry follow
from that. It is a bottom-up approach, where we do
not specify any equilibrium situation beforehand but
let the model evolve freely to wherever it wants to
go. Obviously, this raises the question of whether such
an approach can ever lead to sensible solutions in the
longer term. As we will see in the following sections,
there is ample scope for reasonable behavior using this
approach and in the rest of this chapter we will focus on
the process-based approach.
612 Part C Coastal Design
are almost entirely based on large-scale flume tests
and just recently have been adapted for changed design wave conditions based on such tests [28.1]. Scour
around structures is another example where physical
models are still much in use, in this case because of the
complexity of the three-dimensional (3-D) currents and
turbulence around them. However, in many cases such
a direct application of physical modeling to a problem
is difficult, and such models are then used to look into
the details of processes and to validate numerical models that can be used at larger scales.
Large-scale physical models of tidal systems, rivers,
and estuaries have become too expensive in developed
countries to compete with ever-improving numerical
models, but are still widely used in countries like China,
where labor cost is relatively cheap and there is considerable expertise in dealing with inevitable scale effects.
Combining such models with numerical modeling can
lead to interesting results, and is probably a direction
worth exploring further.
When waves are important and we have to look at
large systems at the same time, physical modeling is
no longer an option. The modeled waves would be too
small to be represented properly, so we will have to look
at other methods.
28.1.2 Analytical Models
First, we turn to analytical models. They can be simple and elegant and provide almost instant insight.
The coastline theory of Pelnard-Considère [28.2] has
shaped our thinking about large-scale coastal evolution,
and analytical and numerical successors of the theory
are still abundantly used [28.3]. Other, more complex,
analytical models explain point bars in rivers and estuaries [28.4], sand waves and tidal sandbanks [28.5], and
though they use strong approximations of the physics,
they tell us which processes are responsible for certain
phenomena we see, so we can make sure that more
complex numerical models reproduce these processes,
which in theory they should, but in practice often fail to
do.
28.1.3 (Semi-)Empirical Models
The next type of models is heavily based on data and
therefore called empirical models. The equilibrium profile model for dune erosion, which has made it into
Dutch law, is a good example [28.1, 6]. Based on the
observation that beach profiles always have the same
shape after a storm, the method consists of shifting that
profile back and forth until the eroded area equals the
accreted area. A more advanced approach for beach
evolution and dune erosion is used in SBEACH [28.7].
SBEACH is a one-dimensional (1-D) (profile) beach
erosion model for storm where net sediment transport
occurs when the local wave dissipation rate is different
from the equilibrium rate. For tidal inlets and estuaries,
there is a host of equilibrium equations [28.8], relating the tidal volume to channel cross-section, to total
channel volume, to ebb delta volume, etcetera. If you
divide a tidal inlet or estuary up into a number of units
(ebb delta, channels, tidal flats) you can define equilibrium situations for each of them. However, that does
not tell you how they get to their equilibrium. To solve
this, semiempirical models were developed, where the
units all try to get to their equilibrium but sediment
has to be transported between them. The rate of sediment exchange depends on how far each unit is from
equilibrium. Stive and Wang use this concept to model
long-term, large-scale effects of sea-level rise and gas
extraction, inlet closure, dredging, and other scenarios [28.9].
Such models have shown a lot of value for specific
situations, where there is a lot of historical data and
nice test cases from the recent past (closure of inlets,
channel deepening for navigation) to calibrate the coefficients in such models. In many places around the
world this is not the case; also, more complex situations or more detailed questions need to be addressed
than can be represented by the semiempirical models
we just discussed. In such cases, we turn to processbased morphodynamic modeling.
28.1.4 Process-Based Models
In process-based models, we start from a detailed
description of processes and let sediment transports,
bottom changes, and the evolving bathymetry follow
from that. It is a bottom-up approach, where we do
not specify any equilibrium situation beforehand but
let the model evolve freely to wherever it wants to
go. Obviously, this raises the question of whether such
an approach can ever lead to sensible solutions in the
longer term. As we will see in the following sections,
there is ample scope for reasonable behavior using this
approach and in the rest of this chapter we will focus on
the process-based approach.