Technical Appendix 2
Geomorphological and modelling
methods
Technical Appendix 2: Geomorphological and modelling methods
Contents
Page
List of Figures
ii
List of Tables
iii
1. Introduction
1
2. Data collection and preparation
1
2.1 Construction of catchment Digital Elevation Models (DEMs)
2.2 Construction of reach DEMs
2.3 Hydrological and climatic data
2.4 Assessment of present-day patterns and recent changes in flood
magnitude and frequency in the study catchments
2.5 Assessment of present-day patterns and recent changes in flood
hazard in the study reaches
2.6 Future climate change scenarios
1
1
4
4
5
5
3. Field-based geomorphological investigations of study reach
landforms and sediment sequences
7
3.1 Geomorphological mapping
3.2 Cartographic analysis of river channel change
3.3 Sediment observations and dating
3.4 Ground penetrating radar and global positioning surveys
7
7
7
8
4 CAESAR-based catchment and reach geomorphological modelling
8
4.1 The CAESAR model
4.2 Flow routing
4.3 Sediment transport
4.4 Sediment layers
4.5 Examples
8
9
10
12
13
5 Model set up
21
5.1 Hydrological calibration
5.2 Structure of model set up
5.3 HEC-GeoRAS modelling
21
25
30
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Technical Appendix 2: Geomorphological and modelling methods
List of Figures
Page
Figure 1:
Outline of the geomorphological modelling approach to flood
hazard assessment
2
Figure 2:
High resolution LIDAR DEM of the River Dee at Bangor-on-Dee
3
Figure 3:
Contour/spot height based DEM of the River Severn study reach
at Welshpool
4
Patterns of change for winter average precipitation in 2080 for
the medium-high emissions scenario, after Hulme et al. (2002).
6
Changes in average winter (left) and summer (right) temperature
and precipitation in respect to the average 1961 to 1990 climate.
After Hulme et al., (2002).
6
Figure 6:
Conceptual structure of the CAESAR model
9
Figure 7:
Routing directions for bedload (a) and suspended sediment load (b) 12
Figure 8:
Sediment layers in CAESAR
13
Figure 9:
Dynamics of the active layer during erosion (a) and deposition (b).
14
Figure 4:
Figure 5:
Figure 10: DEM of the Teifi reach.
14
Figure 11: Flow depths at different discharges in simulation T1. a. 20 m3/s.
b. 100 m3/s. c. 200 m3/s.
16
Figure 12: Flow depths at different discharges in HEC-RAS simulations.
a. 20 m3/s. b. 100 m3/s. c. 200 m3/s.
18
Figure 13: Elevation change (a) and median grain size in the active layer (b)
at the end of simulation T2.
19
Figure 14: Cross-sectional profile of elevation (bottom) and median grain
size (top) across two splays, formed in simulation T2.
20
Figure 15: Mean residuals plotted in m-p space for all flood events
22
Figure 16: Mean residuals plotted in m-p space where the gauge data
discharge is > 10 m3s-1
23
Figure 17: caption pending
24
Figure 18: caption pending
24
Figure 19: Overview of structure of CAESAR model set up for the Upper
Severn
25
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Technical Appendix 2: Geomorphological and modelling methods
Figure 20: Overview of structure of CAESAR model set up for the Severn
at the Roundabout reach
26
Figure 21: Overview of structure of CAESAR model set up for the Teifi at
Tregaron.
26
Figure 22: Overview of structure of CAESAR model set up for the Teifi at
Lampeter
27
Figure 23: Overview of structure of CAESAR model set up for the Dyfi at
Machynlleth
28
Figure 24: Overview of structure of CAESAR model set up for the Dee at
Corwen
29
Figure 25: Overview of structure of CAESAR model set up for the Dee at
Bangor on Dee
29
Figure 26: Schematic of HEC-GeoRAS, illustrating (a) the TIN (Triangular
Irregular Network) DEM that cross sections are extracted from
(b) the structure of the main channel network and location
of cross sections and (c) detail of one of the cross sections.
30
Figure 27: Image of HEC-GeoRAS results for the reach around Bangor on
Dee. The cross sections used by HEC-RAS are clearly
shown running across the floodplain.
31
List of Tables
Page
Table 1:
Values of residuals for a matrix of ‘m’ and ‘p’ values for all floods.
Table 2:
Values of residuals for a matrix of ‘m’ and ‘p’ values for floods
greater than 10 m3s-1.
23
Table 3:
M and P values for catchment simulations
iii
22
25
Technical Appendix 2: Geomorphological and modelling methods
An integrated geomorphological modelling approach to flood
hazard assessment
1.
Introduction
The project was broken down into three main work phases (Figure 1):
(1)
Data collection and preparation (section 2): collection and integration into GIS of
data sets required for modelling studies; provision of baseline data on present–
day flooding and flood hazard at study sites.
(2)
Field–based geomorphological studies (section 3): assessment of past flood
hazard in study reaches based on landform and sediment evidence for river–
floodplain morphological dynamics and variations in flood activity.
(3)
Model–based geomorphological studies (sections 4 and 5): assessment of future
flood hazard based on modelling geomorphological response of study
catchments and reaches to selected environmental change scenarios;
investigation of linkages between environmental change, geomorphological
change, and flood hazard.
2.
Data collection and preparation
2.1
Construction of catchment Digital Elevation Models (DEMs)
Catchment DEMs, used to define the present–day landscape surface in CAESAR
catchment model simulations, were constructed from Ordnance Survey national
elevation data for Wales. Within this data set, Wales is sub–divided into regularly
spaced 50 m grid squares containing mean land surface elevation values accurate to ±
1 m. The elevation data were stored within ARCGIS in GRID file format.
Pre–processing within ARCHYDRO software was necessary to transform the national
elevation data set into CAESAR–compatible catchment DEMs. Raw DEMs of the
catchments upstream from each of the seven study reaches were produced in three
stages: first, whole catchment DEMs were clipped from the national data set; second,
whole catchment DEMs were clipped to upstream entry point of the study reaches; third,
LIDAR (Laser Induced Direction and Ranging) data were integrated to improve
topographic accuracy in valley–floor areas. Three further stages were necessary to
produce hydrologically robust DEMs: first, ‘basins’ that might trap water and sediment
were ‘infilled’; second, a drainage network was defined along lines of steepest gradient;
third, 2 m deep channels were cut out along the drainage network. Finally, for CAESAR
model runs, each catchment hydrological DEM was subdivided into a number of sub–
catchment areas.
2.2
Construction of reach DEMs
Where possible, reach DEMs were based on high–resolution LIDAR elevation data
supplied by the Environment Agency. LIDAR data provide precise valley–floor
elevations (± 0.1 m), resolved on a 2 m grid. It represents the best available topographic
data for Welsh floodplains. LIDAR was available for the Dyfi, Teifi and Dee reaches, but
not for the two reaches in the Severn catchment.
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Technical Appendix 2: Geomorphological and modelling methods
Figure 1: Outline of the geomorphological modelling approach to flood hazard
assessment
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Technical Appendix 2: Geomorphological and modelling methods
Two versions of the LIDAR data are available. Un–filtered data provides a map of both
the natural floodplain surface and any features upon it (Figure 2), including vegetation
(e.g. trees and hedge lines) and structures (e.g. bridges, elevated roads and houses).
This is useful for establishing the relationships between natural and man–made
features, and has been employed here in geomorphological mapping studies (see
Section 3.1 & Technical Appendix 9). Filtered LIDAR data removes raised features,
giving an estimate of the ‘bare ground’ floodplain surface. These data are used in flood
inundation modelling and valley–floor geomorphic model studies (Section 4).
Filtered LiDAR elevation data
2m spatial resolution
N
Flow
Bangor-on-Dee
2km
Figure 2: High resolution LIDAR DEM of the River Dee at Bangor-on-Dee
Owing to the lack of LIDAR data for the upper Severn, a different method was used to
construct reach DEMs for the Caersws and Welshpool. This involved the use of spot
height data (0.1 m interval) and contour data (0.25 m interval), supplied from aerial
photographic analysis by the Environment Agency. In ARCGIS, spot heights and
contours were digitised, combined, and converted into continuous surface elevation
maps in a triangulated irregular network (TIN) format (Figure 3).
Information on channel bathymetry, not available from the LIDAR or digitised data, was
integrated into reach DEMs by the following method. Channel margins were identified
from digital OS LANDLINE feature maps and available surveyed channel cross sections
were cut into the DEM. River bed elevations between survey sites were estimated by
linear interpolation using RASTEREDIT software. For un–surveyed reaches, channel
depth was estimated using well-established and empirically derived hydraulic geometry
relationships.
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Technical Appendix 2: Geomorphological and modelling methods
Figure 3: Contour/spot height based DEM of the River Severn study reach at Welshpool
2.3
Hydrological and climatic data
Gauged river flow data and rain gauge data were supplied for each study catchment by
the Environment Agency. They included daily mean flow records, varying in length
between 34 and 47 years, and peak daily flow records, mostly covering the period since
1990 or 1991. These data sets were used for two purposes in the study: (1) to establish
the present day and recent flood magnitude and frequency characteristics of each river
(section 2.4, Technical Appendix 6); and (2) to calibrate CAESAR catchment models
(section 3.4).
Hourly rain gauge data covering for up to 7 years were available for several locations,
located either within or close to each study catchment. These data were used as the
climate input for CAESAR catchment geomorphic simulations (section 3.4).
2.4
Assessment of present–day patterns and recent changes in flood
magnitude and frequency in the study catchments
Annual maximum flood series, based on water years (October to September), were
derived from a single flow gauge on each river. For the River Dee at Manley Hall, this
series was derived from peak daily flow data covering the period 1970–2003. For the
remaining rivers, however, peak daily flow records beginning after 1990 were deemed
to be too short for meaningful analysis. For these rivers, annual maximum series were
derived from mean daily flow records (the Afon Dyfi at Dyfi Bridge, Afon Teifi at Glanteifi
and River Severn at Abermule), also covering the period 1970–2003.
In order to assess recent changes in flood magnitude and frequency, the four
records were partitioned in time. Based on analysis of the Rivers Severn and Dee
indicating a statistically significant increase in flooding after 1987, each record
partitioned into two 17 year periods, 1970–1986 and 1987–2003. For the Dyfi
4
flow
data
was
flow
Technical Appendix 2: Geomorphological and modelling methods
record, data for 1971–1974 were incomplete and were substituted with data from the
preceding years 1966–1970.
Gumbel frequency analysis was performed on each partitioned annual maximum flood
series in order to estimate the return period of a given event. Flood magnitude–return
period curves were plotted on a probability scale using Weibull plotting positions. A
straight line was fitted to the curves using Origin™, and this was used to estimate the
size of 5, 10, 20, 50 and 100 year floods. See Technical Appendix 6 for a more detailed
analysis and interpretation of the flood frequency and magnitude data.
2.5.
Assessment of present–day patterns and recent changes in flood hazard in
the study reaches
The HEC–GeoRAS software package was used to simulate the extent and limits of
inundation produced by different return period floods according to present–day reach
DEM topography. Present day flood hazard zones were defined as areas lying within
the inundation limits of simulated 100 year (e.g. ‘low’ hazard zone) and 10 year (e.g.
‘high hazard zone) post–1987 flood magnitudes. The HEC–modelled ‘low’ hazard limit
was compared to that of the 100 year flood as defined by the Environment Agency
Indicative Floodplain Map (IFM). Recent changes in flood hazard were assessed by
calculating the different extent of flooding for each of the 5, 10, 20, 50 and 100 year
return period events between the periods 1970–1986 and 1987–2003.
2.6
Future climate change scenarios
An important part of this project is to determine what effect future climate change may
have on river behaviour and in turn future flood hazard. In order to determine this, we
required predictions of changes in future rainfall patterns. At the onset of this project,
the most contemporaneous work, specifically for the UK was the UKCIP02 report
“Climate Change Scenarios for the United Kingdom” (Hulme et al., 2002). This report
used nine different models to simulate future climate patterns under a range of
scenarios, with high, medium and low CO2 emissions. The models all generated slightly
different results, but the general conclusions were that winter precipitation would
increase for all periods with increases up to 2080 ranging from 5 to 15% for low
emissions, to 30% + for medium and high emissions scenarios. This was accompanied
by a decrease in summer precipitation - an increase in the seasonality of precipitation.
These results can be seen in Figures 4 and 5 below.
In light of this report, it was decided to use the following three scenarios for all the future
model runs carried out.
1. Climate 1. No change in present climate
2. Climate 2. 20% increase in magnitude of winter precipitation
3. Climate 3. 20% increase in magnitude of year round precipitation
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Technical Appendix 2: Geomorphological and modelling methods
Figure 4: Patterns of change for winter average precipitation in 2080 for the mediumhigh emissions scenario, after Hulme et al. (2002).
Figure 5: Changes in average winter (left) and summer (right) temperature and
precipitation in respect to the average 1961 to 1990 climate, after Hulme et al., (2002).
6
Technical Appendix 2: Geomorphological and modelling methods
The increases were not as large as those forecast by Hulme et al., (2002); they were
used because the simulations here only span 50 years into the future, as opposed to
80, they are also the values used by the Environment Agency for determining possible
future increases in flood magnitude. The predictions above use the term precipitation
change, which does not refer to whether these changes are in magnitude, frequency or
both. Therefore, for this study, we have interpreted these as changes in rain magnitude,
so for the Climate 3 run, we multiply an existing rain data set by 1.2.
3.
Field–based geomorphological investigations of study reach
landforms and sediment sequences
3.1
Geomorphological mapping
Interpretive geomorphological mapping was carried out in order to identify the
distribution of fluvial features preserved on the floodplain surface within each study
reach. Particular attention was given to mapping the following features: valley floor
margins, modern channel margins, river terrace surfaces, terrace margins,
palaeochannels and tributary alluvial fans, non–fluvial (e.g. glacial) landforms and man–
made structures (e.g. embankments). For the Dyfi (Johnstone, 2004) and Severn study
reaches, landform boundaries were identified during field walk surveys, and mapped
directly onto expanded 1:10,000 scale OS base maps.
Geomorphological mapping of the Dee and Teifi reaches involved two stages. First, the
planimetric position of landforms were identified from available un–filtered LIDAR data,
classified within ARCGIS at height intervals of 0.1 to 1 m. Second, field walk surveys
were carried out in order to ground–truth the LIDAR geomorphological maps, and to
identify any additional (i.e. topographically subtle) features. The successful application
of LIDAR data for mapping Welsh flood study reaches represents an important new
methodology for cost–effective valley geomorphological mapping. A full account of the
LIDAR–based methodology is due for publication in Earth Surface Processes and
Landforms later in 2006 (Jones et al., submitted; see Technical Appendix 9).
3.2
Cartographic analysis of river channel change
Available maps and aerial photographs were used as a source of information regarding
the sequence of channel and floodplain changes which have occurred within each study
reach since the mid– to late–19th century. Channel margins, gravel bars and islands
identified on each map or photograph were all digitised as feature layers using ARCGIS
software. These digitised layers were transformed and scaled onto a common OS grid
coordinate system, facilitating visual and quantitative comparisons by GIS overlay
operations. This enabled time sequence analysis of lateral channel migration rates and
gravel bar dynamics to be carried out.
3.3
Sediment observations and dating
Sub–surface floodplain sediments were investigated to provide information about the
chronological sequence of flood–related deposition. Geomorphological mapping
(section 3.1) and ground penetrating radar (section 3.4) surveys were used to select
sites that were most likely to be underlain by thick vertical sequences of fine–grained
(clay to gravel sized) material, and were therefore suitable for retrieval by a 7.5 cm
diameter, percussion ‘vibra’ corer with a maximum penetration depth of ~7 m. Typically,
such sites occupy areas of low lying terrain most susceptible to flood inundation and
7
Technical Appendix 2: Geomorphological and modelling methods
sedimentation, for example localised bogs or palaeochannel hollows. Where access
permitted, cores were taken from sites on all identified river terrace levels within a
reach. In addition to coring, a small number of exposed river bank sections were
selected for study.
Vertical sediment sequences in cores and river banks were described in terms of
several key characteristics at each depth: grain size, cohesiveness, water content,
sediment bedding, colour and organic matter content. These descriptions formed the
basis for interpretations of past floodplain environments and flooding activity. Material
required for radiocarbon dating – wood, charcoal, leaves and seeds – was sampled.
Where possible, radiocarbon samples were taken from layers where a sedimentary
change indicated a change in flooding activity, such as: (1) an up–sequence change
from coarse channel gravels to fine–grained sediments, relating to the abandonment of
an active channel; (2) an up–sequence switch from fine to coarse deposits, relating to
an increase in flood activity. Radiocarbon samples were analysed and dated at the
Waikato Radiocarbon Dating Laboratory, New Zealand.
3.4. Ground penetrating radar and global positioning surveys
Ground penetrating radar (GPR) surveys were conducted in order to investigate sub–
surface characteristics of the floodplain, such as former land surfaces and channel
morphologies, changes in sediment calibre, and bedding structures. Radar
measurements, relating to the depth to a sub–surface reflector, were taken every 0.5 m
along transects covering an area of interest. Global positioning system (GPS)
measurements were taken simultaneously to obtain land surface elevation data.
4.
CAESAR–based catchment and reach
modelling (published in Van De Wiel et al., in press)
geomorphological
4.1 The CAESAR model
The CAESAR landscape evolution model used here (Coulthard et al., 2000; 2002;
2005) is based on the cellular automaton concept, whereby the continued iteration of a
series of local process-‘rules’ governs the behaviour of the entire system. Although
these rules are relatively simple and straightforward representations of fluvial and
hillslope processes, their combined and repeatedly iterated effect is such that complex
non-linear geomorphological response can be simulated within the model. Both positive
and negative feedbacks between form and process can emerge.
CAESAR can be run in two modes: a catchment mode, with no external in-fluxes other
than rainfall; and a reach mode, with one or more points where sediment and water
enter the system. In both modes the model requires the specification of various spatially
distributed landscape parameters (initial conditions): elevation, roughness, grain sizes
and vegetation cover. The temporal input requirements (forcing conditions) vary
according to the mode in which the simulation is run. In catchment mode, the model
requires rainfall data for the duration of the simulation; in reach mode, it requires
discharges and sediment fluxes for all inflow points. These temporal data are usually
specified at hourly intervals.
8
Technical Appendix 2: Geomorphological and modelling methods
Figure 6: Conceptual structure of the CAESAR model.
Landscape simulation in CAESAR follows a simple structure (Figure 6), whereby
topography drives fluvial and hillslope processes that determine the spatial distribution
of erosion and deposition for a given time step. This alters the topography, which
becomes the starting point for the next time step. The model uses variable length time
steps, depending on the rates of erosion and deposition occurring within the system
(see below). Outputs of the model are elevation and sediment distributions through
space and time, and discharges and sediment fluxes at the outlet(s) through time.
Additional fluxes at specified points in the catchment or reach can be easily obtained.
4.2 Flow routing
Flow is the main driver for the geomorphological processes in alluvial environments.
Although highly accurate solutions for flow depth and flow velocity can be obtained from
traditional computational fluid dynamic approaches, such as finite difference solutions to
either full or depth-averaged Navier-Stokes equations (cf. Lane, 1998), these
techniques are computationally too demanding to be used in landscape evolution
models. Since the flow routing routine affects the entire grid and since it is called every
time step (see Figure 6), a more efficient algorithm for calculating the flow field is
required (Coulthard et al., in Press).
CAESAR uses a “flow-sweeping” algorithm, which calculates a steady-state
approximation to the flow field. The new version of the model has a slightly modified
implementation of the original flow sweeping algorithm to accommodate high-resolution
9
Technical Appendix 2: Geomorphological and modelling methods
grids, where the channel width can easily exceed the grid cell size. Similar to the
original CAESAR model, a multi-sweep scanning procedure is applied, except here one
scan (i.e. one calculation of the flow field) consists of eight sweeps instead of four: two
in each of the four primary directions on the grid. During a sweep, the discharge is
routed to a range of cells in front, identified through a sweep width ω (default ω = 11).
Although smaller values (ω = 3 or ω = 5) are commonly used in low-resolution CA
models (e.g. Murray and Paola, 1994; Coulthard et al., 2001; Thomas and Nicholas,
2002), it was found that, for high-resolution grids, higher values are needed to avoid
unrealistic super-elevation of the water level along outer bank in river bends. Discharge
is distributed to all cells within the ω -range according to differences in water elevation
of the donor cell and bed elevations in the receiving cell. If no eligible receiving cells can
be identified in the sweep direction, i.e. if there is a topographic obstruction, then the
discharge remains in the donor cells to be distributed in subsequent sweeps (in
different directions) during the same scan. Flow depths and flow velocity are calculated
from discharges using Manning’s equation:
(1)
where Q, U and h respectively denote discharge, flow velocity and flow depth, A is the
cross- sectional area of the flow (A = h cw), S is the average downstream slope, and n is
Manning’s coefficient. Depending on the topography, the flow depth and flow velocity
can be calculated more than once during a scan for a given cell, i.e. in different sweeps.
When this occurs, the highest calculated flow depth is retained.
The flow-sweeping routine described here is similar in concept to the implicit solution
schemes employed in finite difference CFD algorithms, where information (i.e.
discharge) propagates through the system as each grid point is updated. This
propagation of information during an individual time step does not conform to the
cellular automaton concept strictu sensu, where cells are updated simultaneously and
independent of changes in other cells, but was found to be significantly faster than nonpropagating explicit implementations. The two main drawbacks of the flow-sweeping
algorithm in comparison with CFD-approaches are 1) that it does not conserve
momentum, and 2) that it only provides overall flow velocities at each grid point and
does not distinguish between primary and secondary flows.
4.3 Sediment transport
Although flow is the main driver of the model, all morphological changes result from
entrainment, transport and deposition of sediments. CAESAR distinguishes between
several sediment fractions, which are transported either as bed load or as suspended
load, depending on the grain sizes.
Sediment transport is driven by a mixed-size formula, which calculates transport rates,
qi, for each sediment fraction i (Wilcock and Crowe, 2003):
(2)
where, Fi denotes the fractional volume of the i-th sediment in the active layer, U* is the
shear velocity, s is the ratio of sediment to water density, g denotes gravity, and Wi* is
10
Technical Appendix 2: Geomorphological and modelling methods
a complex function that relates the fractional transport rate to the total transport rate
(see Wilcock and Crowe, 2003, using same notation). Although equation 2, and in
particular the expansion of Wi* , was developed for sand/gravel mixtures only, its use is
extrapolated here to include finer non- cohesive sediments (silts). This extrapolation is
untested and may be an invalid simplification. Nonetheless, it is deemed a sufficient
initial approximation in investigative studies, and it is employed here for convenience
rather than accuracy. However, other relations for the entrainment of fine sediments
may be required in more detailed studies.
Rates of transport can be converted in to volumes, Vi, by multiplying with the time step
of the iteration:
(3)
The model uses variable length time steps for each iteration, such that the maximal
calculated rate of entrainment, qmax, results in a maximal allowed elevation change,
ΔZmax (default: ΔZmax = 0.1 Lh) :
(4)
This measure assures that the model operates at high temporal resolution (i.e. subsecond) during periods of intense geomorphological change, and on coarser temporal
resolution (i.e. hourly) during periods of relative stability.
Sediments are transported as either bed load or suspended load, which can be selected
by the user for each of the grain sizes. Bedload is distributed proportional to the local
bed slope:
(5)
where the indices i and k respectively denote the sediment fraction and the direction of
the neighbour, V is volume and S is slope. Only neighbours with lower bed elevations
(i.e. Sk > 0) are considered (Figure 7a). Suspended load, on the other hand, is routed
according flow velocity:
(6)
where, U denotes flow velocity. All neighbouring cells where the bed elevation is lower
than the water elevation in the current cell are considered (Figure 7b). The calculation of
suspended load routing makes the implicit simplification that suspended sediments are
uniformly distributed over the water column at any grid point.
11
Technical Appendix 2: Geomorphological and modelling methods
Figure 7: Routing directions for bedload (a) and suspended sediment load (b).
Deposition of sediments also differs between bed load and suspended load. Each
iteration, all transported bed load material is deposited in the receiving cells (Vi,dep = Vi),
where it can be re-entrained in the next iteration. Deposition of suspended sediments,
however, is derived from fall velocities, Vi, and concentrations, Ki , for each suspended
sediment fraction:
(7)
The remaining volume of suspended load is retained for the next iteration.
Sediment transport in CAESAR is both capacity-limited and detachment-limited. The
primary capacity limitation is the transport equation (equation 2), which defines the
maximal transport rate for each sediment fraction i at every point on the grid. For
suspended sediments, a secondary capacity limitation is employed, such that the total
suspended sediment concentration, does not exceed a maximum capacity after
entrainment (default Kmax= 0.01). Detachment-limitation follows from the restriction that,
for each sediment fraction i, the transported volume, Vi, must be less or equal to the
volume present in the active layer VAL,i.
4.4 Sediment layers
The model allows for sediment heterogeneity and keeps track of several (usually 9)
user-defined grain size fractions. Selective erosion, transport and deposition of these
different fractions will result in spatially variable sediment distributions. Since this
variability is expressed not only in the planform dimensions, but also vertically, it
requires a method of storing sub-surface sediment data. The original version of
CAESAR recorded sediment profiles using a multiple active layer system, where each
layer is fixed relative to the surface elevation. However, this scheme is physically
unrealistic as buried sediments move up and down with topographic changes.
Furthermore, it is computationally cumbersome and occasionally causes numerical
instabilities. Hence, an alternative approach is adopted herein, using one active layer,
multiple buried layers (strata), a base layer and a bedrock layer (Figure 8). In the
current version of the model the bedrock layer is fixed and cannot be eroded. The base
layer comprises the lower part of the buried regolith. It has a variable thickness,
depending on the number of strata overlaying it. The strata cover the upper part of the
12
Technical Appendix 2: Geomorphological and modelling methods
buried regolith. They have a fixed width, Lh (default Lh = 20 cm), and their position is
fixed relative to the bedrock layer. Up to 20 strata can be stored at any cell on the grid.
The active layer represents the exposed part of the regolith. It has a variable thickness,
between 25 % and 150 % of the stratum thickness (i.e. 5 cm to 30 cm, using the default
Lh value). Erosion removes sediment and causes the active layer thickness to
decrease. If the thickness becomes less than 0.25 Lh, then the upper stratum is
incorporated in the active layer to form a new, thicker active layer (Figure 9a).
Conversely, deposition adds material to the active layer, causing it to grow. If the active
layer becomes greater than 1.5 Lh a new stratum is created, leaving a thinner active
layer (Figure 9b). During deposition, the lowest stratum may become incorporated in the
base layer, if too many (i.e. > 20) strata have been created for the cell.
4.5 Examples
To illustrate the model, two simulations were carried out on a 4.2 km reach of the river
Teifi, near Lampeter, Wales (Figure 10) The Teifi is a meandering river (sinuosity = 2.0)
with irregular meander loops. Several paleochannels exist on the floodplain, mainly on
the north of the channel. On the southern side, a large alluvial fan covers part of the
floodplain and is gradually being eroded by the migrating river channel. Although
LiDAR’s vertical resolution is small enough to resolve paleochannels on the floodplain, it
is unsuitable for defining the channel bed, since it records the water surface elevations
rather than the bed topography. Hence, an artificial channel bed was introduced by
lowering the DEM by 2 metres for channel cells.
Figure 8: Sediment layers in CAESAR.
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Technical Appendix 2: Geomorphological and modelling methods
Figure 9: Dynamics of the active layer during erosion (a) and deposition (b). n denotes
the initial number of buried layers. n* and n” denote the new number of buried layers;
n* = n-1 and n” = n+1.
Figure 10: DEM of the Teifi reach. Note that the DEM is rotated such that the flow is
from left to right.
14
Technical Appendix 2: Geomorphological and modelling methods
As the main purpose of these simulations is to illustrate the different aspects of the
CAESAR model, the numerical setup of the simulations was chosen to accelerate the
development of particular morphological features in the landscape, rather than reflecting
natural conditions at the site (Table 1). Simulation T1 was designed to illustrate the flow
routing abilities of the model for in-channel and overbank flow conditions and does not
incorporate sediment movement. Simulation T2, which was designed to illustrate
overbank deposition, incorporates frequent flooding – alternating 24 hours of in-channel
flow (20m3/s) with 24 hours of overbank flow (200 m 3/s). Clearly, these unrealistic
simulation configurations impose severe restrictions on the quantitative interpretation of
the results. However, we consider that these simulations provide sufficient information
to perform a preliminary qualitative evaluation of the model’s abilities and limitations.
In simulation T1, three different discharges are run across the DEM. Low-discharge
flows are contained within the channel banks (Figure 11a), while high-discharge flows
inundate the floodplain (Figures 11b and 11c). Overbank flooding is more extensive on
the northern side of the channel in this reach of the Teifi, due to the raised terrain of the
alluvial fan to the south. Floodplain topography also controls the pattern and depth of
inundation, with paleochannels and other low lying areas more likely to be flooded.
Although these results may appear trivial, they represent notable improvements for
cellular automaton flow algorithms – particularly, the ability to route flow through a highresolution meandering channel (see Coulthard et al., In Press).
Figure 12 shows the inundation patterns predicted by a 1-dimensional model (HEC-RAS
v3.1; US Army Corps of Engineers, 2003). Although the broad patterns of inundation
are similar in both models, i.e. in-channel flow at 20 m3s-1 and partial flooding at 100
m3s-1 and 200 m3s-1, there are some notable differences as well, particularly in the
spatial occurrence of the flooding. These differences can be attributed to several
factors. First, the channel morphology is slightly different in the two models. Due to a
conversion from a raster DEM to TIN (HEC-RAS requires a TIN), the channel is
narrower in the HEC-RAS simulations (Figure 12 - 1). Second, floodplain inundation
might spread from a limited number of spill points, particularly for near bankfull flow
conditions. Due to cross-sectional spacing, these spill points might not be picked out by
HECRAS (Figure 12 - 2). Finally, CAESAR applies local routing of discharges at every
point on the DEM. HEC-RAS, on the other hand, routes flow from cross-section to
cross-section. As a result, predicted inundation pattern can change rapidly from one
cross-section to another (Figures 12 - 3 and 12 - 4).
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Technical Appendix 2: Geomorphological and modelling methods
Figure 11: Flow depths at different discharges in simulation T1. a. 20 m3s-1.
b. 100 m3s-1. c. 200 m3s-1. Flow is from left to right.
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Technical Appendix 2: Geomorphological and modelling methods
Simulation T2 shows that erosion and deposition of sediments, according to equations
2-7, not only alters the topography of the reach (Figure 13a), but also affects the
sediment distribution, both in-channel and on the floodplain (Figure 13b). Under the
conditions of simulation T2, the channel is incising for most of its length (Figure 13a),
although there are two smaller sections of in-channel deposition: one at the upper end
of the reach, and one at the final bend near the lower end of the reach. Additionally, at
the end of the simulation most of the channel bed consists of coarser sediments (Figure
13b). This suggests that most of the in-channel incision results from the selective
entrainment of finer sediments. Hence, the model reproduces the processes leading to
bed armouring. The deposition at the upper end of the reach, consisting of both fine and
coarse sediments (Figure 13), is a boundary condition effect, reflecting the system’s
response to a large influx of sediments at the inlet. The second in-channel deposition
area consists mainly of coarse bed load material (Figure 13), and is probably due to the
sudden lateral constriction of the channel where the channel narrows from 50 m width to
10 m width over a short distance. Although this channel narrowing is coupled with a
slope increase in the initial topography, the flow through the narrower channel is not
able to evacuate all the coarse material delivered by the converging upstream sediment
fluxes caused by a step in the channel bed topography at the apex of the second to last
meander bend. This step is an artefact of the LiDAR data and the channel definition.
However, here CAESAR incises immediately upstream of the step, and deposits coarse
material downstream of the step, effectively smoothing the bed perturbation. The fine
sediments which are entrained from the channel bed are either washed out of the
system, or are deposited on the floodplain during the overbank floods. This leads to the
formation of both levees and splays (Figure 13a). There are other areas of subtle
overbank deposition – for example in palaeo-channels – but these are not revealed due
to the shading scheme used in Figure 13. A cross-section profile through two opposite
splays clearly shows that the depositional features consists of fine sediments, while the
erosion of the channel results in bed armouring (Figure 14). All of these results are
consistent with those that would be expected from a natural stream, and demonstrate
how the combination of flow routing, erosion and deposition with several grain size
fractions, active layers and suspended sediment all combine to produce incision,
deposition, splays and levees. Furthermore, Figures 13 and 14 demonstrate how grain
size patterns in bed armouring and the deposition of overbank fines as levees reflect the
trends found in real rivers.
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Technical Appendix 2: Geomorphological and modelling methods
Figure 12: Flow depths at different discharges in HEC-RAS simulations. a. 20 m3s-1. b.
100 m3s-1. c. 200 m3s-1. See main text for explanation of highlighted areas (1-4). Flow is
from left to right.
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Technical Appendix 2: Geomorphological and modelling methods
Figure 13: Elevation change (a) and median grain size in the active layer (b) at the end
of simulation T2. Flow is from left to right. Cross-section a-a' is shown in Figure 14.
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Technical Appendix 2: Geomorphological and modelling methods
Figure 14: Cross-sectional profile of elevation (bottom) and median grain size (top)
across two splays, formed in simulation T2. Location of the cross-section is shown in
Figure 13.
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Technical Appendix 2: Geomorphological and modelling methods
5 Model set up
5.1 Hydrological calibration
For all the modelled catchments, the hydrological model needed to be calibrated, so
that simulated runoff for a given rainfall event, matched that measured in the field. This
step is important, as the magnitude of a flood will not only determine the area inundated
by flood waters, but also the volume and timing of sediment generated by the flood.
CAESAR was first calibrated to present–day conditions by assessing the ‘goodness of
fit’ between modelled and observed (i.e. gauged) flood peaks over a 1 year calibration
period. In CAESAR, river flow volume at a given time is controlled largely by rainfall
intensity, but peak flood magnitude is also controlled by the rate of water table
fluctuation – represented by a factor termed the ‘m’ value in the hydrological model.
Following the method successfully piloted for Welsh catchments in a previous study
(Coulthard and Jones, 2002), calibration involved running each model according to
different combinations of factored rainfall intensity and ‘m’ value, until simulated flood
discharges converged with the gauged flood record. A more detailed description of the
procedure is described below.
For each CAESAR catchment, the following procedure was followed, but here we
illustrate the process with the Alwen catchment, part of the Upper Dee. An hourly rainfall
record (Bala) was used as model input, and the erosion and deposition components of
the model disabled to speed up run times. The output was converted to mean daily flow,
and each day's mean flow was subtracted from the corresponding mean daily flow at
the Druid gauge, and the magnitude of the residual was found. The residuals were
averaged for the first three years (i.e. for the first repeat period), and plotted in 3d with
the corresponding m and p values as shown below.
Comparing the mean residuals for days where discharge exceeded 10 m3s-1 for the
gauge data with mean residuals calculated over all days shows little difference in the
position of the minimum (p=0.8, m= 0.015 and p=0.7, m=0.015 respectively) (Tables 1
and 2; Figures 15 and 16).
Figures 17 and 18 compare the two m-p minima: m=0.015 p=0.7 for all discharge
values, and m=0.015 p=0.8 for all discharge values >10 m3s-1. The two graphs show the
two periods of greatest discharge during the first repeat rainfall cycle of the both runs,
compared with the Druid gauge record.
On the basis of the above runs the final values chosen were m= 0.015 and p=0.7.
Despite m=0.015 p=0.8 giving the lowest mean residual for flow >10 m3s-1, p=0.7 gave
the best fit for the two largest peaks, and so was considered the best fit.
Where there were sufficient data, this procedure was carried out for all the modeled
catchments. Table 3 details the m and p values determined by this calibration scheme.
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Technical Appendix 2: Geomorphological and modelling methods
Table 1: Values of residuals for a matrix of ‘m’ and ‘p’ values for all floods.
Mean residuals
M values
P values
0.5
0.6
0.7
0.8
0.9
1
1.2
1.4
0.005
3.670
3.304
3.541
4.201
5.243
0.01
5.040
3.372
3.246
3.680
4.253
4.866
6.357
8.906
0.015
5.130
4.667
3.069
3.380
4.184
4.730
6.281
0.02
5.200
4.931
3.414
3.592
4.047
4.641
6.149
0.025
5.288
5.083
4.254
3.550
7.587
Figure15: Mean residuals plotted in m-p space for all flood events
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Technical Appendix 2: Geomorphological and modelling methods
Table 2: Values of residuals for a matrix of ‘m’ and ‘p’ values for floods greater than 10
m3s-1.
For daily mean discharge > 10 m3s-1, mean residuals
P values
M values
0.5
0.6
0.7
0.8
0.9
1
1.2
1.4
0.005
9.615
7.930
8.375
10.239 12.885
0.01
15.258
8.933
8.126
8.517
10.228 11.946 16.148 24.896
0.015
15.636 13.672
7.882
7.759
9.360
10.283 15.083
0.02
15.790 14.863
9.296
7.970
8.940
9.840
0.025
16.062 15.239 11.689
7.967
13.837 18.588
Figure 16: Mean residuals plotted in m-p space where the gauge data discharge is > 10
m3s-1
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Technical Appendix 2: Geomorphological and modelling methods
Figure 17: caption pending
Figure 18: caption pending
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Technical Appendix 2: Geomorphological and modelling methods
Table 3: M and P values for catchment simulations
Catchment
M values
P values
Dee
0.015
0.7
Dyfi
0.014
1.1
Severn
0.015
1.0
Teifi
0.02
0.45
5.2 Structure of model set up
As previously described, CAESAR can run in both catchment and reach modes. Figures
19 to 25 indicate the structure of how each set of simulations were constructed. They
show the reach, where flood risk was calculated and the contributing catchments. These
range from simple systems such as the Teifi, where there was only one contributing
catchment, to the Severn, where 13 simulations were required to create the input data
for but one reach simulation. Figure 19 includes a flow diagram that describes how the
catchment and reach runs work together.
Figure 19: Overview of structure of CAESAR model set up for the Upper Severn
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Technical Appendix 2: Geomorphological and modelling methods
Figure 20: Overview of structure of CAESAR model set up for the Severn at the
Roundabout reach
Figure 21: Overview of structure of CAESAR model set up for the Teifi at Tregaron.
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Technical Appendix 2: Geomorphological and modelling methods
Figure 22: Overview of structure of CAESAR model set up for the Teifi at Lampeter
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Technical Appendix 2: Geomorphological and modelling methods
Figure 23: Overview of structure of CAESAR model set up for the Dyfi at Machynlleth
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Technical Appendix 2: Geomorphological and modelling methods
Figure 24: Overview of structure of CAESAR model set up for the Dee at Corwen
Figure 25: Overview of structure of CAESAR model set up for the Dee at Bangor on
Dee
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Technical Appendix 2: Geomorphological and modelling methods
5.3 HEC-GeoRAS modelling
Whilst CAESAR can simulate the areas of a floodplain that are inundated with water
during flood events, the ‘standard’ method used by the Environment Agency and other
consultancies to model flood inundation is a 1 dimensional approach, using models
such as ISIS or HEC-GeoRAS. In order to give the results from this study more
relevance, we use HEC-GeoRAS to model flood inundation areas on the topographies
generated by the CAESAR model. A brief description of the operation of HEC-GeoRAS
is provided below.
Figure 26: Schematic of HEC-GeoRAS, illustrating (a) the TIN (Triangular Irregular
Network) DEM that cross sections are extracted from (b) the structure of the main
channel network and location of cross sections and (c) detail of one of the cross
sections.
HEC-RAS is a 1 dimensional hydraulic model working on the step backwater approach
developed by the US Army’s engineering corps. It operates by dividing the channel
network up into a series of linked cross sections (see Figure 26). Water depths are then
calculated for given discharges at each cross section based on the slope between the
water surface at a given cross section and the section immediately downstream – hence
the name step back water. HEC-GeoRAS is a version of the model that is integrated
within the GIS package ARCVIEW 3.2. Within the GIS, cross sections are determined,
and the elevations for each point along a cross section are calculated from a DEM of
the modelled surface. These points are then exported into HEC-RAS where the water
surface elevations are modelled. HEC-GeoRAS then exports this data back into the
GIS, where outlines of inundated areas and flow depths are determined by subtracting
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Technical Appendix 2: Geomorphological and modelling methods
the water surface elevation from the original elevation of the DEM. These can then be
displayed on top of the DEM providing extents of flood inundation as shown in Figure
27.
Figure 27: Image of HEC-GeoRAS results for the reach around Bangor on Dee. The
cross sections used by HEC-RAS are clearly shown running across the floodplain.
HEC-GeoRAS does have some limitations. It is one dimensional, so only simulates flow
occurring at the cross sections. Therefore it does not account for any heterogeneities or
changes between cross sections and also does not simulate any secondary circulation
or flow effects. Therefore, it can provide a slightly inaccurate picture of overbank
inundation extents and depths. However, it is simple to use, relatively well tested and is
worthwhile using in this study to allow direct comparison to methods used by the
Environment Agency.
31