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Hydrological Sclences-Journal-des Sciences Hydrologiques, 42(6) December 1997 859
The potential application of finite element
modelling of flood plain inundation to predict
patterns of overbank deposition
D. J. SIMM
Department of Science, St. Mary's University College, Waldegrave Road, Strawberry Hill,
Twickenham, Middlesex TWI 4SX, UK
D. E. WALLING
Department of Geography, University of Exeter, Amory Building, Rennes Drive, Exeter
EX4 4RJ, UK
P. D. BATES & M. G. ANDERSON
Department of Geography, University of Bristol, University Road, Bristol BS8 1SS, UK
Abstract Mathematical modelling of overbank inundation and flows faces many
problems and is still in its infancy. Work to date has generally been restricted to
small reaches. Large-scale models based on longer reaches of river channel are
likely to be of greater value for engineering and flood plain management purposes,
but the problems associated with the transition from small to large scales need to be
assessed. A large-scale finite element model, RMA-2, has been applied to the flood
plain of the lower reaches of the River Culm in southeast Devon, UK. Patterns of
radiocaesium accumulation by overbank accretion during flood water inundation
were used to assess the potential of using such models for explaining sedimentation
rates and patterns. A strong correlation was found between values of the 137Cs
inventory and surface concentration and the predicted flood water patterns derived
using the RMA-2 model. Except where recession pondage occurs, an inverse
relationship existed between ' Cs deposition and water depth. However, the
discretization model developed cannot presently cope with large-scale compart-
mentalization of flows by barriers to flow and small-scale local features, such as
ditches crossing the flood plain and the microtopography of the flood plain. This
study appraises the potential for using the RMA-2 model to predict patterns of
overbank deposition and represents an initial stage in the development of an
integrated model of hydraulic and sediment dynamics.
Evaluation ie la modélisation en éléments finis de l'Inondation d'un
lit majeur pour la prévision des caractéristiques des dépôts de crue
Résumé La modélisation mathématique des inondations et des crues rencontre de
nombreuses difficultés et en est encore à ses débuts. Le travail effectué jusqu'à ce
jour s'est généralement limité à de petites surfaces. Des modèles à grande échelle
réalisés sur de plus grandes surface de lits de rivières auraient probablement plus de
valeur dans une optique d'ingénierie ou de gestion des plaines inondables, mais les
problèmes liés au passage de la petite à la grande échelle doivent être pris en
considération. Un modèle mathématique à grande échelle, le RMA-2, a été appliqué
aux plaines inondables de la rivière Culm, dans le sud-est du Devon, en
Grande-Bretagne. Des traces d'accumulation de radiocaesium apparues pendant les
inondations dues aux crues peuvent être utilisées pour évaluer le potential
d'utilisation de tels modèles en vue d'expliquer les taux de sédimentation et les
dépôts observés. Une forte corrélation a pu être établie entre le bilan en 137Cs et les
concentrations de surface d'une part et les caractéristiques des eaux de crues prédites
par le modèle RMA-2 d'autre part. Mis à part là où sont observées des flaques
résiduelles, un rapport inverse existe les dépôts de 137Cs et la profondeur de l'eau.
Cependant, le modèle de discrétisation développé ne peut, à l'heure actuelle,
Open for discussion until I June 1998
860 D. J. Simm et al.
surmonter les difficultés dues au compartimentage à grande échelle des courants par
les digues ou barrages et aux caractéristiques locales à petite échelle, comme la
microtopographie des plaines inondables po les rigoles les traversant
transversalement. Cette étude évalue le potentiel d'utilisation du modèle RMA-2
pour prévoir les dépôts sédimentaires et constitue le stade initial du développement
d'un modèle intégré de dynamique hydraulique et sédimentaire.
INTRODUCTION
The mathematical modelling of flood plain flows, for instance using the modified
Saint-Venant equations, has received increasing attention in order to satisfy
engineering and geomorphological needs (Fread, 1985; Bates et al, 1992; Nicholas
& Walling, 1997). Of particular interest are overbank flows and the modelling of the
overbank deposition of fine sediment. Several studies have investigated the
interaction of in-channel and overbank flows and suspended sediment (James, 1986;
Ervine & Ellis, 1987; Pizzuto, 1987), but such work has generally been restricted to
a two-dimensional approach, involving a lateral transect across the flood plain.
Attempts to incorporate a three-dimensional, spatial component have been restricted
to detailed, small-scale models because of the computational complexities introduced
by the low relief and complex topography of flood plains. Recent research (Howard,
1992; Nicholas & Walling, 1995) has also attempted to combine models of water and
sediment dynamics for short river reaches. Such detailed small-scale modelling
attempts to take account of the fact that overbank deposition is not uniform across the
flood plain, but is highly variable both spatially and temporally. A high spatial
resolution model, such as the 5 X 5 m grid cells employed by Nicholas & Walling
(1995), permits greater flexibility in the modelling of the complex interaction of
variables, notably the topography of the flood plain and flood water inundation
sequences. Although better for representing topographically-driven effects, these
models tend to have a simplified hydraulic representation, which includes steady state
dynamics and a temporally coarse time step (e.g. hourly), and are restricted to the
local scale. In contrast, the RMA-2 model, with 150 X 150 m finite elements over
11 km, requires improved hydraulic representation in order to attain realistic
modelling of water depths and velocity vectors over long reaches. Firstly, the
imposed boundary conditions are further apart and so do not provide a strong
constraint over the internal flows predicted by the model. Secondly, a complex
dynamic hydraulic model which includes all the terms in the momentum equation is
required at long reach scales because it is impossible to make an assumption of
steady state flow as in the model of Nicholas & Walling (1995). The diffusion wave
equation used by those authors is appropriate at local scales but may be problematic
at reach scales.
When models increase their scale of coverage, improved hydraulic representation
is necessary due to backwater effects but this is achieved at the expense of
topographic detail. The modelling of a long reach of flood plain (Baird & Anderson,
1992; Bates et al., 1992) typically faces the need for simplification to cope with scale
factors and computational complexity and, at present, such models are often based
The potential application of finite element modelling of flood plain inundation 861
primarily on water dynamics with little consideration for topography. There is,
however, a need, from both engineering and geomorphological perspectives, to scale
up from small reach studies to longer stretches of river and flood plain. A reach-scale
model could be of value: firstly, in flood plain management and planning by
providing predictions of flood water inundation extent which could be used for flood
hazard zoning; secondly, possible engineering applications include estimation of the
potential for erosion during inundation by identifying points of overbank spillage and
channel breaching and avulsion {cf. Gee et al, 1990). Consequently, it could be of
value in the design of flood mitigation schemes; and thirdly, reconstruction of flood
water behaviour (flow direction, depth and velocity vector plots) could prove
valuable for studies of contemporary flood plain form and development.
Furthermore, from a catchment-wide sediment delivery perspective, a large-scale
modelling approach is necessary to provide meaningful predictions of spatial rates
and patterns of overbank deposition by more realistically modelling sediment
dynamics using basic hydraulic information. Ultimately, such a model could
incorporate both hydraulic and sediment dynamics and could, potentially, be used to
study longer term flood plain aggradation.
The RMA-2 model presented by Bates et al (1992) provides a clear example of
the move towards a long reach modelling approach. The modelling background,
assumptions and limitations of the model are discussed by Bates et al (1992). This
paper will attempt to evaluate the potential for using such a flow model to assist in
the interpretation and explanation of rates and patterns of overbank sedimentation.
The preliminary model results presented by Bates et al (1992) are first used as a
basis for deriving general relationships between hydraulic variables, such as water
depth and flow velocity, and field-based estimates of the rates and patterns of
overbank deposition. Secondly, the potential of a model developed explicitly for
large areas, as distinct from small-scale models, will be assessed, by identifying the
factors which become important at larger scales. The attendant problems of
topographic definition and model resolution which are associated with the
development of such a model will also be addressed.
THE RMA-2 MODEL
The RMA-2 model is a two-dimensional finite element hydrodynamic model that has
recently been applied to river channel and flood plain flows (Gee et al, 1990; Baird
& Anderson, 1992; Baird et al, 1992; Bates et al, 1992). The RMA-2 model can
generate information on inundation extent, flood water depths, velocities and
directions of flow over length scales of the order of 10-100 m for reaches of up to
20 km using basic flood plain topography and upstream discharge data (Bates et al,
1992). The model solves the depth-integrated Reynolds equation for two-dimensional
free-surface flows in a horizontal plane using finite element techniques. It can be
applied to both steady and unsteady flows (Baird & Anderson, 1990). Following the
successful application of the model to a large-scale stretch of the River Fulda,
862 D. J. Simm et al.
Germany (Gee et al, 1990; Baird & Anderson, 1992; Baird et al, 1992), Bates et
al. (1992) applied the model to a similar scale but more complex problem on the
River Culm in southeast Devon in order to investigate the problems and limitations
of representing complex topographic features over reach lengths of 10-20 km. The
RMA-2 model incorporates model attributes (such as the mathematical model,
numerical solution scheme, etc.) which are site independent, and attributes of the
discretization and parameterization (resolution, topography inclusion, etc.) which are
site specific. This paper addresses some of the limiting factors in this second
category.
Although the RMA-2 model does not presently incorporate a sediment transport
component its ability to produce detailed spatial patterns of velocity vectors and
depth information clearly has potential for predicting sediment deposition. The
potential for using the model in this way has been assessed by comparing
independent field observations of overbank sedimentation rates with the model
output. Recent advances in the use of caesium-137 (137Cs) measurements to document
medium-term rates and patterns of flood plain sedimentation afford an essentially
unique means of assembling the spatially distributed information on sedimentation
rates required for such comparison.
THE USE OF CAESIUM-137 MEASUREMENTS
Caesium-137 is an artificial fallout radionuclide associated with the testing of
thermonuclear weapons which offers considerable potential for sediment tracing
studies (Walling & Bradley, 1990). It has a half-life of 30.2 years. The
introduction of measurable quantities of 137Cs into the environment commenced in
the early 1950s and the main period of fallout deposition occurred in the 1960s,
peaking in 1963-1964 (Ritchie & McHenry, 1990). In most environments, fallout
137
Cs reaching the land surface is preferentially absorbed by fine sediment and its
subsequent redistribution occurs in asscociation with the movement of soil and
sediment particles. It may thus be mobilised by hillslope erosion processes,
transferred downstream during storm events, and deposited during overbank
inundation of the flood plain (cf. Walling & Bradley, 1990). Within the past
decade, caesium studies have become increasingly used in flood plain studies to
document the spatial and temporal patterns of the overbank deposition of fines (cf.
Walling et al, 1989, 1992) because it can provide information on medium-term
deposition patterns. With the exception of the presence of Chernobyl-derived 137Cs
in some areas, there are generally no problems of interference from additional
sources. By comparing the ,37Cs inventory of a flood plain core with the inventory
associated with an undisturbed control site located above the level of inundation it
is possible to identify positive and negative residuals, indicative of a predominance
of deposition and scour respectively. Inventories with the same value as the
baseline represent either no deposition or equilibrium between deposition and scour
over the time period.
The potential application of finite element modelling of flood plain inundation 863
THE STUDY REACH
The river channel and flood plain reach used for evaluating the RMA-2 model is a
14.1 km stretch of the River Culm (Fig. 1), a tributary of the River Exe in southeast
Devon, which is delimited by two gauging stations with an altitudinal difference of
24 m. The lowland flood plain ranges from 70 to 450 m wide, with a gravel bed
channel 8-12 m wide. Bates et al. (1992) present a detailed case study of the
application of the RMA-2 model to a single site (SX 95 99) upstream of Rewe
(Fig. 1) for a 1-in-l year flood event (>65 m3 s"1), which provides the basis for the
comparisons made in this paper.
The combination of regular flooding downstream of Cullompton (ST 02 07),
relatively high sediment concentrations, and the predominance of suspension load,
typically 95% <63 /an and 70% < 2 /xm (Walling & Bradley, 1989), promotes
relatively high overbank deposition rates compared to other flood plains. An average
accumulation rate of 177 g m"2 year4 (0.2 mm year"1) has been reported for the study
site based on sediment traps positioned on the flood plain (Simm, 1993). The
enhanced overbank deposition rates and the use of the caesium technique, which
documents deposition over a period of 36 years or so, overcome the inherent
difficulties of quantifying the relatively low accretion rates often experienced on
lowland flood plains.
The study site (SX 95 99) near Rewe (Fig. 1) forms a branched section,
producing an "island" approximately 600 m by 300 m in the River Culm
immediately downstream of Columbjohn (SX 957 997), with the channels rejoining
500 m downstream at Rewe Barton (SX 946 994). The channels and surrounding
ditches have a complex history (Hooke, 1977; Simm, 1993). Most are man-made
former mill leats with associated weirs dating from the late eighteenth and early
nineteenth centuries. For instance, the weir immediately downstream of
Columbjohn Bridge (SX 958 997) fed mills near Brookleigh (SX 953 989) and the
leat rejoined some distance downstream. The northern branch, flanked by a road,
between Columbjohn and Rewe is a man-made section. Fences, dense hedgerows
and ditches split the site into three compartments (Fig. 2(b)). The central (field B)
and western (field A) compartments are characterised by complex microtopography
and are regularly inundated, although flood water depths are typically only of the
order of a few centimetres. Field A is crossed by a distinct linear depression,
running centrally and parallel to the fence separating fields A and B, which acts as
a secondary channel during inundation. The eastern compartment (field C), with
the exception of a scroll depression in a meander (location D on Fig. 1), is mostly
flat and featureless, and is less frequently inundated. Pronounced levees are found
around the tight meander at location D and at the southern end of field A, whilst
elsewhere the levee is poorly defined. The site is readily inundated, commencing
along the western and eastern flanks of the site and later undergoing widespread
overbank spillage in areas with poorly developed levees, whilst elsewhere local
breach flow occurs. During a 1-in-l year flood event up to 3.6 km2 of the flood
plain of the study reach is inundated, including almost all of the study site.
864 D. J. Simm et al.
Fig. 1 (a) Map of the study site near Rewe, (b) locality map of the lower River
Culm, southeast Devon, and (c) plot of the hydraulic model nodes for the study
reach.
The potential application of finite element modelling of flood plain inundation 865
METHODOLOGY
As outlined previously, the 137Cs technique is capable of providing information on the
spatial distribution of average rates of deposition and scour for the past 36 years.
Sediment cores (42 cm2 surface area and a depth of 50 cm) were collected at 51
sampling points using a Cobra percussion corer. The samples from the site were
supplemented by eight samples taken from upstream of the northern channel branch
(E, Fig. 1), upstream of the road crossing the floodplain. Sediment was carefully
removed from the core cylinder and, before bulking the material, a 1.5 cm thick
basal slice was removed from the core to be assayed independently to ensure that the
core had penetrated the full depth of alluvium containing 137Cs. An additional surface
sample, from the topmost 0.5 cm, was also collected at each sampling point. In
addition, following the site prerequisites outlined in Campbell et al. (1988), a core
was obtained from a local undisturbed site above the level of the flood plain to
provide a reference inventory.
Samples were air-dried, in preference to oven drying at 105°C, because of their
high clay content. In order to achieve a consistent packing geometry in the 1500 g
Marinelli pots used for gamma assay, each sample was disaggregated and the
<2 mm fraction was separated by dry sieving. The 137Cs content of the sample was
analysed using a Canberra Series 35 multi-channel analyser linked to a HPGe
detector housed in a 10 cm thick lead shield. Regular monitoring of detector
efficiency and a count time of c. 20 000 s provided a typical analytical measurement
precision of ±6% (2 standard deviations) (Walling & Bradley, 1989). A reference
inventory of 250 mBq g"1 was obtained from the local control site.
By comparing the inventories of the individual cores with the local reference
datum (250 mBq g'1), residuals were obtained representing increased ("excess") and
depleted ("deficit) inventories. These are indicative of the predominance of
deposition and scour respectively over the time period and are shown in Fig. 2(a).
An approximate estimate of the mean annual accumulation rate over the past 35 years
(Fig. 2(b)) was also calculated for each sampling point associated with a positive
residual, by dividing the "excess" inventory by an estimate of the average 137Cs
content of suspended sediment deposited during the period since 1956, adjusted for
decay to the present and the bulk density of the sediment (Walling & Bradley, 1989).
Estimation of the scour rates, indicated by negative residuals, is more problematic
because scour removes some of the atmospheric input. With bulked samples, the
depth distribution of 137Cs, from which the depth of scour is estimated from the
proportion of the inventory remaining, is lost. Thus values of scour can only be
considered as tentative.
The pattern of 137Cs concentrations associated with the surface sediment is shown
in Fig. 2(c). Simulated flood water velocity, depth and flow direction (Fig.3) were
compared with the maps of 137Cs excess and deficit, accumulation rates and surface
137
Cs activity (Fig. 2) in order to assess the relationship between the hydraulic and
sedimentological conditions. Although these data are not temporally compatible (see
discussion), they nevertheless provide a basis for a preliminary appraisal of the
potential of the model for explaining rates and patterns of flood plain sedimentation.
D. J. Simm et al.
Reference baselevel = 250 mBq cm" 2
(b)
Fig. 2 (a) Whole core inventories of 137Cs (mBq cm"2), (b) the estimated vertical
accumulation rates (mm year"1) based on 35 year period, and (c) the distribution of
137
Cs concentrations (mBq g"1) in surface samples for the study site and selected
samples immediately upstream.
The potential application of finite element modelling of flood plain inundation g67
Fig. 3 (a) Floodplain topography and RMA-2 simulated floodplain depth at peak
flow for a 1 year recurrence interval event at the site (after Bates et al., 1992), and
(b) schematic representation of the flow field and water depth information for the
study site (after Bates et al, 1992).
The comparison of the 137Cs data and the model output is subject to two main
qualifications. Firstly, the hydraulic data obtained from the model are only an
approximation because of the inaccuracy of plotting points due to the simplified
channel cross-section and modified planform used in the model (Bates et al, 1992).
Secondly, both the hydraulic and the sedimentation data sets were independently
derived by secondary methods and do not involve any actual "field" measurement.
868 D. J. Simm et al.
For instance, there are no available field measurements of flood water depths to
assess the accuracy of the water depths predicted by the model. However, this
approach is still of value because it enables preliminary appraisal of the potential for
using the model for predicting areas of overbank deposition.
RESULTS
The pattern of averaged flood water depths, generated by the RMA-2 computer
model, for a 1-in-l year flood event (>65 m3 s"1) at this site (Bates et al, 1992) has
been compared with the pattern of deposition evidenced by the 137Cs measurements.
An assessment of the factors influencing the pattern of overbank deposition has also
been made. In general, there appears to be a close similarity between the plots of
both 137Cs inventories and concentrations of surface samples (Figs 2(a) and 2(c)) and
that of predicted flood water patterns (Fig. 3(a)). Although the correspondence is not
complete, areas of shallow water depth (Fig. 3(b)) are generally associated with
"excess" inventories, whilst areas with predicted deep flood water and principal flow
lines are associated with low and negative residuals. The spatial distribution of whole
core inventories across the site reveals a central low-lying area associated with
residual inventories of up to approximately -150 mBq cm"2, equating to
approximately 1800 g m"2 year"1 (approximately 2.2 mm year"1) of scour erosion,
which coincides with the zone of deep flood water identified by Bates et al. (1992).
The central area of high water depth is flanked on either side by shallow areas.
Excluding site D, field A has the highest average 137Cs inventory, but also locally
experiences high flood water depths, principally in its southern part and adjacent to
the channel, whilst the central part of this site experiences relatively shallow flood
waters. Field C is also characterised by relatively high 137Cs inventories and shallow
flood water. Vertical accumulation rates of up to 2.2 and 3.9 mm year"1 are found in
these western (A) and eastern (C) compartments respectively. However, there is
considerable variation between the sites due, firstly, to the arbitrary nature of the
classification of sites and, secondly, to the natural variability of deposition. Lower
deposition rates of approximately 0.6 mm year"1 immediately adjacent to the channel
may reflect the potential for scour, as indicated by predicted flow lines. Such
peripheral areas correspond to the major flow paths, parallel to the channel, which
Table 1 Comparison of the different sampling sites.
Field Mean 137Cs inventory Mean 137Cs surface Mean predicted n
(mBq cm"2) ± 1 s.d. concentration water depth
(m Bq g"1) ± 1 s.d. (m) ± 1 s.d.
A 326.37 ± 71.64 24.30 ± 4.81 0.19 ± 0.07 15
B 237.56 ± 57.84 13.55 ±2.14 0.15 ±0.07 14
C 255.92+ 100.18 21.61 ±4.84 0.12 ±0.06 21
D 420 11.50 0.22 1
E 211.63 141.22 24.38 ± 4.47 0.19 ±0.08 8
All 269.23 ± 88.23 20.61 ± 6.02 0.16 ±0.07 59
The potential application of finite element modelling offloodplain inundation g69
circumvent the fringe of the shallow areas. The mean 137Cs inventory and the mean
137
Cs surface concentration for field A are notably higher than for field C, with the
latter having greater variability but the smallest mean water depth (Table 1).
Figure 4(a) displays the relationship between water depth and 137Cs inventory for
the 59 points where cores were collected. When the data are separated into the indi-
vidual fields a general inverse relationship is apparent. Shallow flood water depths
promote increased deposition because of low flow velocities produced by friction,
whilst increased flow velocities are commonly associated with higher flow water
depths (Fig. 3(b)). The data for field C, for instance, illustrate the potential for scour
where higher flood water depths are experienced. The points for field A also display
this inverse relationship, but evidence significantly greater water depths for a given
value of 137Cs inventory than field C. This contrast may be attributable to the high
flood water depths and pondage-induced backwater effects as the channel branches
converge. The high water depths may thus be compensated by stilling of the flood
water promoting increased deposition of 137Cs. Field B is sandwiched between the
points for fields A and C. There is some overlap between fields B and C, mainly
because the area of highest inventories trends NW-SE flanked by areas of generally
°>A
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Field
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it B
A C
o D »JC
o E
0 100 200 300 400 500 600
i37Cs i n v e n t o r y ( m B q c m - 2 )
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f 19 24 29
«7Cs surface concentration (mBq g-1)
Fig. 4 The relationships, and associated trends, of (a) ,37Cs inventories and (b) 137Cs
surface concentrations with water depths predicted by the RMA-2 model.
870 D. J. Simm et al.
lower inventories. Site D, the inside of a meander, undergoes large inundation depths
(Fig. 3(a)) and has a high 137Cs excess residual (Fig. 2(a)) because of depression
storage following flood water recession. Field E shows great variability. Here, the
model predicts high water depths caused by the backwater effects of flood water
already inundating the flood plain from upstream intercepting the northern channel
branch. However, there are also local physical factors which may be responsible for
this situation (see below).
The surface concentrations (Fig. 2(c)) primarily reflect the grain size of the
alluvial deposit rather than deposition rate because 137Cs is preferentially associated
with clay and fine silt grade particles. Thus there appears to be a general negative
relationship between water depth and grain size (Fig. 4(b)), with the finest particles
deposited in areas of shallow water depth (fields A and C) whilst the central area
(field B) with relatively deep inundating water exhibits the lowest 137Cs
concentrations and, by inference, the coarsest particles. Deviations from this general
trend may be explained in terms of local factors (see discussion).
In general, the depth of inundating flood waters decreases with distance from the
channel (Fig. 3(a)), with elevated flood water depths, >25 cm, experienced adjacent
to the channel. Whether this is a real feature or an artifact of the simplified
topography used in the model, which excludes the levee, needs to be addressed.
RMA-2 topography along the River Culm is based on OS 1:2500 and 1:25 000 series
height information, supplemented by six surveyed cross-sections, tied into OS bench
marks at bridging points, etc. However, there is a generally weak relationship
between 137Cs inventory and distance from the channel (Walling et al., 1996) which
reflects the variety of modes of inundation and resultant deposition. The RMA-2
model implemented for the River Culm only simulates overbank spillage due to a
simplified topographic specification, whereas passive backponding and breach flow
are also locally important. The flow directions predicted by the RMA-2 model
therefore do not describe the different modes and directions of inundation at different
stages of a flood event.
There are several instances where the predicted water depths and flow pattern
(Fig. 3(b)) show some notable deviations from the pattern of 137Cs inventories
(Fig. 2(b)) and concentrations (Fig. 2(c)). Firstly, assuming that deposition rate is a
reflection of topographic and hydraulic factors, these may be attributed to limitations
of the model (Bates et al, 1992 and see discussion). Secondly, these may be
attributed to local factors producing local irrégularités in deposition.
Important disparities may be caused by the compartmentalization of flow (Simm,
1993) produced by two local features (Fig. 1), the road immediately to the north and
the railway embankment to the west of the site. The road from Columbjohn Bridge
(SX 958 997) to Paddleford Bridge (SX 953 998), flanked by a shallow embankment
and hedgerow, is slightly raised and thus acts as a physical barrier to the downstream
flow of inundating water because it runs tangential to the flood plain downstream
gradient. The inundation directly upstream of the road is fed by laterally displaced
flood water from Columbjohn and further upstream, whilst downstream the flood
water overspills from the channel downstream of either Columbjohn Bridge or
Paddleford Bridge. This obstruction to flow undoubtedly has a significant effect on
The potential application of finite element modelling offloodplain inundation 871
the pattern of overbank deposition. It is commonly accepted that deposition tends to
be increased by the afflux of a barrier to flow. 137Cs inventories from immediately
upstream of the river and the road (field E) are highly variable (with inventories
ranging from 170-270 mBq cm2). Generally, field E records high water depths and
inventory residuals of approximately -50 to -60 mBq cm2 near to the channel. These
deficit residuals are possibly due to scour induced by the lateral displacement of
flood waters westwards towards Paddleford Bridge promoted by a ditch running
parallel to the upstream side of the road and the limited number of culverts and
breaches in the barrier. There are few breaches between each compartment on either
side of the road; water usually spills piecemeal through small gaps in the shallow
embankment along the road. Some small breaches may experience the concentrated
expulsion of water from one compartment to the next, which may result in localised
scour erosion immediately downstream of the exit, for instance in the upstream part
of field B (Fig. 2(a)). Deposition of 137Cs locally occurs immediately downstream of
Paddleford Bridge in the lee of the obstruction (Fig. 2(a)). The caesium
concentration plot (Fig. 2(c)) indicates that coarser material is deposited at this
locality. Deposition may occur locally in the lee of an obstacle, for instance the
wooded area immediately downstream of Columbjohn Bridge, in the northeast corner
of the study site. Both "excess" residuals and high surface concentrations (indicative
of the finest particles) are recorded at this site which undergoes regular flooding.
Thus flood water and, consequently, deposition patterns are influenced by factors
at different scales. It is important to distinguish between, firstly, the effects of
mesoscale factors, such as topography, which determine the inundation sequence and
flood water depths employed in the model, and secondly, local factors which are not
incorporated in the model. These local factors need to be identified, and their
influence assessed, in order to successfully overcome the problems involved in
scaling up from short to longer reaches.
DISCUSSION
The physical restrictions and limitations of the RMA-2 model and the method
adopted for assessing the model now need to be considered. These include, first, the
attributes of the model itself (for instance, the mathematical model, numerical
solution scheme, etc.) which are site-independent, and, secondly, attributes of the
discretization and parameterization (resolution, topography inclusion, etc.) which are
site-specific. A critique of the numerical limitations and practicalities of the model
can be found in Bates et al. (1992). In this study there are also some assumptions and
limitations concerning both the modelling procedure and the field techniques which
need to be considered.
The most important limitation is the temporal incompatibility of the 137Cs and
water depth data sets. The 137Cs inventories represent accumulation over a period of
c. 35 years, whilst the surface concentrations are principally a reflection of particle
size over the past few years. However, the model output represents only a single
flood event. Consequently, the data sets are not strictly compatible. Instead they are
872 D. J. Simm et al.
used to provide a preliminary appraisal of the potential of the model to predict
patterns of deposition. This, however, has important implications for modelling
purposes. Use of the RMA-2 model has, to date, been restricted to individual
inundation events (e.g. Baird & Anderson, 1992; Bates et al. 1992). However, in
order to interpret fully 137Cs inventories in relation to hydraulic data it is necessary to
model a representative range of storm magnitudes and their sequence over a period
of c. 35 years (within the temporal resolution of the 137Cs technique) and to derive
resultant averages.
Furthermore, the discharge range of the model is presently restricted to larger
flood events (greater than 1-in-l year recurrence interval). This is a problem at both
small and high flood discharges. The modelling of small events, permitted by the
detailed study site approach favoured by Nicholas & Walling (1995), is limited in the
RMA-2 model of Bates et al. (1992) by the number of nodes along the lower Culm
floodplain. The RMA-2 model becomes increasingly effective and accurate with
increasing discharge, up to approximately 100 m3 s1, because at higher flows
momentum exchange effects between the main channel and the floodplain will be
relatively less intense (Rajaratnam & Ahmadi, 1981) and the channel will begin to
behave more as a single unit. However, beyond this threshold, accuracy becomes
problematic because inundation beyond the railway embankment occurs causing, for
instance, the bisection of the western part of the flood plain at this site (Fig. 1). A
large ditch runs parallel to the railway embankment which may enable the western
side of the embankment to be occasionally inundated, fed by culverts and ditches
(Fig. 1). However, when flooded, deeper water is caused by compartmentalization,
trapped by the road and the embankment. Exit from this "compartment" is limited to
a small culvert beneath the road, immediately west of Paddleford Bridge. Barriers to
flow produce compartments of flood water on a variety of scales. This ranges from
large-scale features such as railway embankments crossing the flood plain to smaller-
scale features, such as raised road surfaces and accompanying hedge banks,
vegetation (hedgerows, trees, etc.) and fences (Simm, 1993). Compartments become
operative during large events and at different stage levels, which has important
implications for modelling purposes.
The necessity to model a representative range of flood events has further
important implications for deposition. The highest deposition rates appear to be
associated with local small-magnitude flooding (by passive backponding via ditches
and breaches) (Simm, 1993) and there is also a general increase in deposition
associated with higher discharges due to significant retention pondage, although
scour remobilization caused by transient currents may be operative at the highest
discharges. Thus the level of detail with which the mesh can predict the spatial and
temporal variability of flood water inundation becomes significant. A representative
range of flood events therefore needs to be modelled to allow comparison with the
caesium inventories, and the flow velocities and water depths of the flood waters to
be averaged at each node in order to become compatible with the l37Cs data.
One of the main problems in scaling-up from detailed to large-scales is the
resolution of the mesh and its ability to model different modes of flooding. The
relative roles of flood water flow through breaches and ditches, overbank spillage
The potential application of finite element modelling of flood plain inundation 873
and retention pondage, which become operative at different stages during the
inundation sequence and also at different discharges (and thus flood water inundation
extents), must be addressed. This is important for the spatial distribution and rates of
deposition during individual flood events. Detailed site studies (e.g. Walling et al.,
1996) may achieve greater success in representing topographic-driven effects despite
a simplified hydraulic representation. In contrast, advective transfer of flood waters
during overbank spillage can be used in conjunction with simplified topography.
The simplification of the channel planform on the southern branch of the channel
has proved necessary because of the physical restrictions of the mesh in terms of its
ability to model tight bends (Bates et al, 1992). Furthermore, attempts to model
such a large-scale study reach as involved here unavoidably result in simplification of
the flood plain topography. The simplification of the channel and levee is discussed
by Bates et al. (1992) but there is a lack of detailed microtopographic form because
of a limited number of nodes, only about three or four (Fig. 1(c)), across the flood
plain (i.e. not connected with the channel form).
However, the mesh resolution of all models, including detailed small-scale sites,
can only provide general depositional trends. Recent field studies (Lambert, 1986;
Walling et al., 1992; Simm, 1993) have shown that overbank deposition may be
spatially variable even over decimetres and is strongly related to the micro-
topography and vegetation cover of the flood plain. Overbank deposition is very site-
specific, and thus generalizations depend on microtopography, the mode of
inundation, and hydrological and sedimentological parameters (Lambert, 1986;
Simm, 1993). The majority of models are still in their infancy in relation to their
capability to model effectively real flood plains. In particular, most models, regard-
less of the level of topographical detail, remain limited in their ability to
accommodate complex patterns of overbank flood water behaviour (such as overbank
spillage, breach flow and passive backponding), complex topography (occurrence of
secondary flow routes, such as ditches and internal breaches) and retention pondage
of flood waters (Lewin & Hughes, 1980), and the role of vegetation in modifying
flows (Pasche & Rouvé, 1985).
In terms of the limitations and assumptions of the field techniques, consideration
of the spatial density of cores is important because 137Cs variations are often highly
localised. Areas of high deposition or scour are often enlarged by interpolation
procedure because of a coarse sampling grid of cores and the mapping algorithm (i.e.
constant gradients between two points, rather than taking topography into
consideration). Additional problems with the caesium technique include particle size
and organic matter selectivity in the sorption of the radiocaesium. However, the good
correlation of caesium (whole-core) inventories with (surface) concentrations
reinforces the decision to use caesium studies to test the output of the model.
CONCLUSIONS
The detailed study of this site illustrates significant similarities between the spatial
flood water depths simulated by the RMA-2 model and the patterns of overbank
874 D. J. Simm et al.
deposition derived by the caesium technique. Such ground-truthing provides a
general appraisal of the present state of realism in the model. A general inverse
relationship between the deposition of 137Cs and the predicted flood water depths has
been demonstrated for particular fields. Evidently, even a large-scale mesh may
provide valuable results in the prediction of spatial patterns of deposition and,
potentially, the particle size of sediment deposited. This potential will be further
realised with a denser mesh (if numerical stability allows). Water depths, especially
if coupled with velocity vectors, could also be used to predict the calibre of the
sediment deposited. However, the use of water depths to predict areas of high and
low deposition must be treated cautiously because topography and other site
characteristics, in particular vegetation and obstructions to flow, are important
(Simm, 1993).
The way forward from this intermediate stage of "ground-truthing" is to address
the issues of mesh resolution. Further "field verification" is required, in particular of
inundation extent, water depths and flow directions. However, it is necessary to
either run a representative sequence of flood events to provide data which are
temporally compatible with the caesium inventories or, alternatively, individual flood
events could be studied using a sampling grid of flood plain sediment traps (Lambert,
1986; Simm, 1993), which permit investigations of overbank deposition for
individual flood inundation events as the deposited material can be retrieved after
each flood.
The RMA-2 model is able to establish general relationships of flood water depth
and velocities, from which general patterns of overbank deposition can be deduced,
but its detailed operation (for instance, the mode of flooding simulated,
compartmentalization, etc.) do not bear close examination and such aspects of
modelling are currently being researched. Ultimately, it may be possible to develop a
dynamic coupled hydraulic and sediment transport model with mesh sizes as low as
0.5 m and with time-steps of the order of a few seconds rather than 30 min. Such a
combined model would enable assessment of the importance of the relative timing of
the discharge and suspended sediment peaks. This relationship dictates the relative
availability of sediment being routed onto the flood plain during the period of
inundation. The RMA-2 model is still under development and, at present, has
limitations. However, this paper has highlighted some of the potential problems to be
addressed in the process of scaling from small, detailed study sites to long reaches,
and the RMA-2 model, in the light of this study, is in a phase of further development
and modification.
Acknowledgements The authors gratefully acknowledge the support of NERC in
providing a research grant to M. G. Anderson, D. E. Walling and P. D. Bates
(GR3/8633) and a postgraduate studentship to D. J. Simm (GT4/89/AAPS/23) for
work on flood plain sedimentation. Thanks go to the technical and cartographic staff
in the Department of Geography at the University of Exeter: Mr T. Bacon,
Mr A. Bartram, Mr A. Ames and Mr J. Grapes. Special thanks also go to
Gwen Thomas for the French translation.
The potential application of finite element modelling of flood plain inundation 875
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ReceivedD. Ongley, 37-45.accepted 11 April 1997
