Transactions on Ecology and the Environment vol 50, © 2001 WIT Press, www.witpress.com, ISSN 1743-3541
Use of an integrated one dimensional-two
dimensional hydraulic modelling approach for
flood hazard and risk mapping.
E. rank', A. Ostanl, M. ~occato'& G.S. stelling2
'BETA Studio srl, Italy
WL I Delft Hydraulics/ Technical University Delf The Netherlands
Abstract
This paper presents the application of a new software tool for modelling fluvial
and floodplain hydraulics. The software package, developed by WL I Delft
Hydraulics, integrates a one-dimensional (ID) modelling package known as
SOBEK-Flow with a two-dimensional (2D) hydrodynamic prediction package
known as Delft-FLS (Delft Flooding System). In the combined modelling
system, called Delft-1D2D, the 1D channel network and the 2D rectangular grid
hydrodynamics are solved simultaneously using the Delft scheme able to tackle
steep fronts, wetting and drying processes and subcritical and supercritical flow.
The model is applied to simulate the inundation processes on the floodplains of
the Liri-Garigliano catchment in central Italy. The implementation of the model
and results obtained are described, as well as the generation of flood hazard and
risk maps. The results highlight the capability of the software to cope with
problems related to flood hazard and risk mapping.
1 Introduction
Growing population and economic activities in the floodplains have increased
the need for disaster management and flood risk assessment. The initial step of
flood risk assessment is the process of hazard determination. Hazards are
associated with each extreme river stage or discharge, and are defined as
exceedance probability PE of the extreme flood. In practical applications, the
result of hazard determination consists of hazard maps. The hazard map for
floods is the map showing the area under water if a flood of magnitude U
Transactions on Ecology and the Environment vol 50, © 2001 WIT Press, www.witpress.com, ISSN 1743-3541
100 River Basin Managemen1
corresponding to P&)
occurs. Various methods and models can been used to
determine such maps. These can be of different complexity ranging from simply
intersecting a plane representing the water surface with a Digital Elevation
Model (DEM) of the potential flooded area to full three-dimensional solution of
the Navier-Stokes equation with sophisticated turbulence closure [l] (see for
example Tomas and Williams [2], Yunis [3]).
Until recently the most popular approaches to retrieve flood inundation maps
at a reach scale have been one-dimensional finite difference solutions of the full
De Saint Venant equations. In such schemes river and floodplains are described
as a series of cross section perpendicular to the flow direction and are modelled
together. The water level in the main channel and the floodplain is the same and
both river and floodplain store and convey water. Even if these models are of
moderate complexity not always the schematisation used (one-dimensional) is
appropriate to describe the inundation processes both in the floodplain and
(sometime) even in the main channel. Moreover the floodplain areas between
cross-section are not explicitly studied: to produce flood inundation maps one is
forced to interpolate in some way the results obtained at the cross-section
locations. To overcome these limitations, two-dimensional finite element model
have been developed (e.g. Bates et al. [4]). These schemes solve the non-steady
free surface flows in shallow water environments. Water depth and depthaveraged velocity is computed at each node at each time step. These models,
initially developed to study costal and estuarial domains, have been adapted to
simulate the hydraulics of river and floodplain takmg into account processes
such as sub- and supercritical flows and transition from one of theses regimes to
the other, dray areas inside the computational domain, sills and submerged dikes.
Limitations of such models are due to the difficulties to simulate in a efficient
way the behaviour of hydraulic structures (bridges, weirs, etc.) located in the
channel and even the channel itself and the network of minor channels if present.
Such features are very important for a correct description of the hydraulic
behaviour of the study domain but a solution based on a pure two-dimensional
scheme would require a DEM with such a fine resolution to become unfeasible at
a basin scale. Owing to these reasons, in recent years models that integrates onedimensional schemes with two-dimensional schemes have been developed. A
one-dimensional model is used to solve the hydraulics equations in the channel
network, described with cross sections and all the important structures. At each
time step of the simulation the results obtained in the one-dimensional scheme
are used as internal boundary condition for the two-dimensional scheme used to
simulate the inundation processes in the floodplain.
The paper describes the technique adopted for flood risk mapping for
floodplains in the Liri-Garigliano catchment in central Italy. The application of
an integrated one dimensional - two dimensional hydraulic model, developed by
WL I Delft Hydraulics, is described, as well as the use of the flood hazard map
obtained by the model to produce flood risk maps.
Transactions on Ecology and the Environment vol 50, © 2001 WIT Press, www.witpress.com, ISSN 1743-3541
River Basin Management
101
2 Description of the hydraulic model
The Delft-1D2D system is a package designed for the simulation of inundations
when in normal conditions (in case of no flooding) hydrography can be modelled
as a I D network. If large areas are inundated then assumptions for 1D flow are
normally no longer valid. In that case the system becomes truly 2D. The system
is designed to deal with any kind of flows, sub- or supercritical including
hydraulic jumps or floodwave bores.
The computational domain is splitted into a one dimensional network, with
general volumes of arbitrary shapes, and a two dimensional part with rectangular
computational cells. The equations to be solved are based upon the momentum
balance and the conservation of mass. For the momentum balance the ID and the
2D system remain strictly separated. That means that velocities or discharges
belong either to the ID part or to the 2D part. For the conservation of mass,
being a scalar quantity, the appropriate 1D and 2D volumes are combined so that
they share the same water level. See Figure 1.
Both the ID and the 2D grids are staggered (Figure la). This means that, for
the finite volume approach applied, the momentum volumes are different from
the mass volumes. There is no interaction between the ID and the 2D
momentum volumes. This means that vertical velocities and shear stress
interaction between 1D flow and 2D flow are neglected. For each momentum
volume the following law is applied:
Rate of change of momentum + transport of momentum +
integrated hydrostatic pressure +friction-losses=O.
(1)
The numerical implementation is such that in the vicinity of steep gradients
proper shock conditions are being fulfilled, both for 1D and 2D volumes
(Stelling et al. [S]).
The interaction between the 1D and the 2D part takes place via mutual
volumes, see Figure lb. For mutual 1Dl2D mass volumes the following equation
is solved:
where:
combined 1DI2D volume;
velocity in X direction;
Transactions on Ecology and the Environment vol 50, © 2001 WIT Press, www.witpress.com, ISSN 1743-3541
102 River Basin Managemen1
v
h
C
Ax
AY
Qn
i, J, 1, K, L
velocity in y direction;
total water height above 2D bottom;
water level above plane of reference (the same for 1D and 2D);
2D grid size in X (or 9 direction;
2D grid size in y (or j) direction;
discharge in the direction normal to the mass volume faces;
integer numbers for nodal point numbering.
For Figure lb, eqn (2) becomes:
After discretisation in time by the "0 method" the velocities are eliminated by
substitution of the momentum equations into the continuity equation. The
resulting system is linear for purely 2D volumes, but if a 1D part is involved the
equation might be non-linear with respect to the volume V(<). This is solved by
Newton iteration. The resulting linearised equations, per Newton iteration step,
are positive definite and symmetric (Casulli [6]). The method used for the
solution is a combination of the so-called "minimum degree algorithm" (Duff et
al. [7]) and of the pre-conditioned CG (conjugate gradient) (Golub and Van Loan
[W.
The continuity equation is discretised in a way that excludes the possibility of
negative volumes. This allows for very efficient and also realistic flooding of dry
beds when the 1D rivers are flooding their 2D surroundings. In normal
conditions, i.e. if there is no flooding, the 2D part is not activated. This means
that in eqn (2) the uh and vh values a& supposed to be zero.
-I
Figure 1: schematisation of the hydraulic model: a) combined 1Dl2D staggered
grid; b) combined finite mass volume for 1Dl2D computations.
Transactions on Ecology and the Environment vol 50, © 2001 WIT Press, www.witpress.com, ISSN 1743-3541
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3 Flood hazard mapping
To perform a comprehensive analysis of flood hazard, the following three steps
were included in the assessment. The fust step entails a detailed analysis of
recorded critical events as well as the collection of hydro-meteorological data to
perform a statistical evaluation of extreme rainfall events and to generate a
design flood hydrograph. The second step involves the set up and calibration of
the integrated hydraulic model for simulating the flood plain flooding processes.
The third and final step concerns the simulation by the one dimensional-two
dimensional hydraulic model of the flood wave obtained via the rainfall-runoff
model using the design storm defined in the fust step.
The analysis of extreme rainfall events was performed based on a regional
frequency framework in order to reduce parameter uncertainty estimation in
gauged sites and for risk assessment in ungauged sites. The regional rainfall
frequency analysis procedure proposed in the VAPI Project @ossi and Villani,
[g]) was used for this purpose. The regionalization procedure adopted in the
VAPI Project uses a hierarchical approach based on the four parameters TwoComponent Extreme Value (TCEV) distribution (Rossi et al. [10]) and arranged
in three levels, each refemng to a different spatial scale.
A statistical procedure for flood hazard assessment has been used, based on
an extension of the original Italian VAPI procedure for the assessment of flood
peak and volume in natural catchments and a serni-distributed catchment
modelling. Using the recent BLUE hyetograph theory (Veneziano and Villani,
[Ill), the procedure allows to define, for each sub-basin, simultaneous
hyetographs associated to a given flood volume. The hyetograph reflects the
rainfall space-time correlation structure and the response characteristic of the
sub-basins.
4 Application of the methodology
4.1 Study site and flood hazard assessment
The Liri river basin at Sora is located in southern Italy, having a draining area of
377km2 pigure 2). The basin ranges in elevation from 284m a.s.1. to 1040m
a d . . The climate is typically Mediterranean. November is the wettest month and
July is the driest one. Long term mean rainfall ranges between 850 and 1000mm.
Average monthly minimum temperature in January (coldest month) is 7S°C,
while average monthly maximum temperature in August (warmest month) is
23°C. Land use is dominate by forest (54%) and agriculture (22%). The
catchment topographic, land use and soil properties were represented by way of a
GIS. For the purposes of hydrological analysis, the catchment area was
horizontally discretised to generate a raster map with a lOOm grid spacing. The
DEM was processed to obtain estimated distributed terrain slopes and an
automatically-generated drainage network. Other raster maps representing digital
thematic maps were obtained from maps of the whole basin regarding land use
and geo-lithological characteristics of the basin.
Transactions on Ecology and the Environment vol 50, © 2001 WIT Press, www.witpress.com, ISSN 1743-3541
104 River Basin Management
The analysis of extreme flow events was performed following the regional
analysis procedure proposed in the VAPI Project (Rossi and Villani, [9]).
Accordingly to the Italian national framework on flood risk assessment and
based on the models described above, three different design hydrographs have
been computed for return times (RT, hereafter) of 30, 100 and 300 years with a
resulting value of the design peak discharge of 459, 623 and 771m3/s,
respectively. Results provided by the hydraulic model were analysed in terms of
water depth and velocity to draw maps with three different hazard classes,
ranging between Class A and Class C. In summary, Class A identifies the area
inundated with a water depth greater than lOOcm for the 100 year RT flood event
(standard flood, hereafter) and the area inundated with a water depth greater then
30cm for the standard flood with values of water velocity greater than I d s .
Class B identifies the area comprised between Class A area and the boundary of
the inundated area for the standard flood (Class B is subdivided into three subclasses, related to the water depth corresponding to both the standard flood and
the 30 year RT flood event). Class C identifies the area comprised between Class
B and the boundary of the inundated area related either to the 300 year RT flood
event or to the maximum recorded historical flood event.
The test site is a 13 km long reach of the Liri River between Sora and at Isola
del Liri (approx. 275m a.s.1.) (Figure 3). The river along this reach is floodwalled
along both banks. The floodwalls are vertical walls with heights typically
varying from 1 to 2m but on occasions rising to more than 4m above the
protected floodplain. The channel width between floodwalls is about 45m wide
and the channel depth from invert to floodwall top level is about 8m. Two bridge
crossings are located along the study reach, one at the upstream limit, the other at
Transactions on Ecology and the Environment vol 50, © 2001 WIT Press, www.witpress.com, ISSN 1743-3541
Transactions on Ecology and the Environment vol 50, © 2001 WIT Press, www.witpress.com, ISSN 1743-3541
106 River Basin Management
flood prone area or not. Analysis of the vulnerability map allows to assess the
potential damage.
In the context of the Liri-Garigliano study, vulnerability and damage maps
have been drawn based on the maps of the land use plans (PRG maps), by
considering 4 classes of potential damages (classes D1 to D4, with D1
identifying high damage and D4 low damage). Then, the flood risk map was
built, based on the four damage classes and five hazard classes, identifying four
risk classes (R1 to R4) according to the Table shown in Figure 4. Figure 5
reports the vulnerability, damage and risk flood maps generated for the study
area.
Flood Hazard
Figure 4: Identification of flood risk classes in relation to potential damage and
flood hazard.
5 Conclusions
The Liri-Garigliano flood hazard and risk mapping has highlighted a number of
benefits from using an integrated ID-2D hydraulic modelling system. First, it
represent an accurate and affordable solution for the flood hazard mapping task.
In the specific case study, it was readily apparent that due to the presence of
floodwalls the traditional one-dimensional schematisation could not adequately
represent the floodwaters spilling from the main channel onto the floodplain,
which occurs during the extreme events taken as reference for the flood risk
planning concept. The use of the integrated hydraulic modelling system has
enhanced the reliability of the results of flood hazard mapping.
Second, as legislation becomes more stringent, the importance of being able
to demonstrate how answers have been calculated (sources of data, modelling
assumptions) and the reasons for adopting certain solutions becomes more
critical. Using an accurate and systematic framework helps on providing this and
provides a mechanism for the work to be critically reviewed independently to
verify that the best option is being selected. The system also provides detailed
visualisation of results that would help planners convey both what solutions have
been considered and also why certain options are being recommended or
discarded.
Transactions on Ecology and the Environment vol 50, © 2001 WIT Press, www.witpress.com, ISSN 1743-3541
River Basin Management
107
Figure 5 : Study area: maps of a) hazard, b) potential damage, and c) the
resulting flood risk.
Transactions on Ecology and the Environment vol 50, © 2001 WIT Press, www.witpress.com, ISSN 1743-3541
108 River Basin Management
Acknowledgements
The authors thank the Water Authority of Liri-Garigliano and Volturno for
providing the data used in this study.
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