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Natural Flood Storage and Extreme Flood Events Final Report

3 Modelling and gis analysis

3.1 Natural storage and attenuation

The objective of this study was to assess the scope for using 'natural' flood storage within a river system. The focus on 'natural' storage means that we have investigated only areas that would flood naturally (according to model predictions). There is generally greater resistance to flow over the floodplain than in the river channel. Floodplains also provide 'storage' in the form of volumes of water that become disconnected from the main channel flow. The net effect is to attenuate the peak of a flood hydrograph, or 'event', as it passes downstream.

This project aims to quantify the amount (volume or extent) of water that would have to be held back to mitigate against downstream flooding given a specified hydrological event. For example, consider a town where flooding occurs for flows greater than the 100 year flow. If the target is to limit a 200 year event to a 100 year peak flow, then we are interested in the difference between the 100 year and 200 year events.

A conventional way to tackle this problem is to model hydrographs for the two events and to calculate the difference in the volume of water between the larger event and the peak of the smaller event. Graphically, this can be described as 'slicing the top off the larger hydrograph' (see Figure 3-1). Typically, a feasibility study would then involve a search of the upstream floodplain to find areas that may be suitable for impounding water. Embankments can be placed across the river valley in a GIS analysis, and the volume and area of the impoundments calculated from a DEM. This type of analysis would indicate how much storage volume could be found at those locations, which can be compared with the hydrograph analysis. As a final step, the most promising impoundments could be added to a routing model as reservoirs or ponds, allowing their effectiveness to be tested.

Because we are looking at potential 'natural' storage, we have not used this approach (although it would be needed as a follow-up to the type of analysis described here for more detailed scheme design).

3.2 Flood events

We can assign a probability or return period to the flow that causes flooding at a downstream risk location. However, the 'event' that causes this flood cannot be assigned a return period without some ambiguity. This is because there are many possible combinations of rainfall events and antecedent conditions that could generate the same downstream outcome. These different conditions could also involve different durations, storm tracks or multiple peaks that could cause different responses on the floodplain.

Whilst the definition of a T-year flow is reasonably clear, the concept of the 'T-year' event, as it is commonly understood in engineering hydrology in the UK, is based on a relationship between the probabilities of rainfall and peak flood flows derived under strong assumptions about the shape and uniformity of the rainfall profile, antecedent conditions and losses during an event.

There are three approaches that can be used to generate a suitable flood event for analysis of storage or attenuation. The first is continuous simulation of synthetic flow sequences. This is the preferred approach scientifically because it can account for the multiple rainfall and soil moisture histories that can combine to produce a given flood flow. However, it is not yet a standard method in engineering practice and was beyond the scope of this project. The second approach is the event-based 'rainfall-runoff' model described in the Flood Estimation Handbook (FEH, Institute of Hydrology, 1999), which is the standard approach in UK practice. Both continuous simulation and event approaches can be applied as boundary conditions to a model of the river flow.

A third approach is a purely hydrological one in which statistical estimates of peak flows are made a regular intervals along the river network and a standardised hydrograph shape applied to simulate an 'event'. This approach has been adopted for national-scale flood outline modelling in England and Wales because it is relatively generalised and can therefore be applied without needing local data. It does not guarantee hydrologically consistent changes in hydrograph shape or magnitude in a downstream direction (although significant work has been done to enhance the spatial consistency of the statistical estimates, as reported by Morris, 2003).

We have used the event-based approach because it remains the approach most likely to be used in existing models. For the sake of simplicity we have assumed that the flood-producing event is in effect a uniform rainstorm, but that the return period of the flow at the downstream location defines the return period of the 'event'. We can note that this is a simplification and that in nature the return period of the flow generated by this 'event' would vary with location in the catchment.

3.3 Event modelling

We have used two approaches to simulate flood events in this study, namely one-dimensional and two-dimensional models.

3.3.1 One-dimensional models

The simpler approach is one-dimensional (1-D) flow routing, in which event hydrograph inputs, generated using FEH methods, are applied as upstream or lateral boundary conditions on a 1-D model of the river. The routing model then represents the movement of the hydrograph downstream as a flood wave. (The flood is referred to as a 'wave' since its movement downstream is a wave motion; the wave is a disturbance in the flow, representing the passage of the flood peak.)

There are many routing models. The most commonly used are:

• Muskingum or Muskingum-Cunge
• Kinematic wave
• Hydrodynamic modelling (e.g. HEC-RAS, ISIS)

The Muskingum model is often known as hydrological routing, in which flow down the river can be thought of as a series of conceptual stores. The resulting computer model requires only a few conceptual parameters (related to the speed of the flood wave and the degree of attenuation). The kinematic wave and hydrodynamic models can be thought of as hydraulic models that include differing degrees of process detail (see below). The Muskingum-Cunge is a useful routing model that can be shown theoretically to be essentially the same as some forms of hydraulic model.

River flow can be described by unsteady, 1-D, differential equations (known as the St. Venant equations) that can be solved numerically if the river cross section is known. These can be expressed as

where the first equation is the continuity equation and the second the momentum equation, Q is the cross-sectional average flow rate, A is the wetted area of the cross section, y the depth, x the distance down river, S0 the slope of the river bed, and Sf the friction slope. The last term is a measure of the friction force acting on the flow and is expressed as a slope for convenience. The equation assumes that the baseflow or tributary inflows are equal to q.

The kinematic wave solution is a simplified solution of these equations that assumes the gravitational force is exactly balanced by the friction as it neglects the first three terms - the local acceleration, convective acceleration and the pressure (i.e. the second equation reduces to S0= Sf).

In the diffusion wave model, the pressure term is added to this, meaning that flow can be driven by the water surface slope as well as the bed slope and friction. The dynamic wave model includes all terms. The Muskingum-Cunge method is a solution of a type of diffusion wave equation based on the Muskingum equation. These methods are covered in detail in most river hydraulics text books.

The advantage of using the simpler approaches is that they require less data than a more complex model. In this study, we are aiming to incorporate existing models where available, but cannot assume that detailed data such as river channel and structure surveys are available.

There are three ways in which an existing (or new) 1-D model can be used to assist with the 2-D modelling of the floodplain, as follows

• routing of the flood hydrograph through the river network
• calculation of channel capacity
• conversion of flow to level at the downstream risk location

Routing the flood hydrograph - event definition

A model capable of routing a flood hydrograph (but not necessarily of calculating water levels) is a useful starting point to establish the hydrological event inputs that lead to a prescribed probability of exceeding a given flood flow at the downstream risk location. The steps to be taken are linking flood estimates at key locations (headwaters, lateral inflows, tributaries) and establishing a combination of rainfall intensity, profile and duration that generates a flow of given probability downstream.

Channel capacity

If a model is available that includes river survey data, then this can also be used to estimate the capacity of the channel at each cross section, and hence the rate of flow that should be allowed onto the floodplain. This calculation may be straightforward where there are well-defined bank elevations, or more uncertain if only coarse cross section data exist. An alternative approach is to use LiDAR to set up a river valley cross section, with an assumed standard channel shape. This will not provide as good an estimate of channel capacity as surveyed cross sections, although it may be helpful, especially if banks can be seen clearly in the LiDAR grid.

Establishing flood levels at the downstream location

A hydraulic model covering the downstream risk location will always be useful to provide a rating curve so that the threshold level for flooding can be expressed accurately in terms of flow rate, and hence as an exceedance probability.

3.3.2 2-D floodplain modelling

The second approach used to model flood flows is a 2-D cellular inundation model, JFLOW, which was developed by JBA Consulting as a flood extent modelling tool. It has been tested and validated for large scale automated flood mapping (JBA Consulting, 2003) and also applied successfully at a much more detailed scale in flood mapping studies, to model breaches in defences and also for coastal inundation modelling. It is based on an approach developed by Bates and De Roo (2000).

JFLOW represents the movement of water over the floodplain as a discretised diffusion wave, which means that (a) flow is driven locally by the difference between the water surface slope and frictional resistance over the ground and (b) the calculations are carried out over fixed grid cells on an element-by-element basis. The approach is often referred to as 'raster' modelling because it is designed to take advantage of raster (i.e. gridded) DEM data.

One of the main motivations for this type of modelling approach is the observation that, in many situations, topography is the key control on the routing of floodplain flow, with frictional resistance being the next most important factor. Both of these controls are represented in the 2-D model used here. Other processes, such as momentum exchanges between floodplain and channel flows, are not explicitly included in the modelling, which means that the roughness parameter Manning's n may have to take a value that compensates for neglecting these energy transfer mechanisms, but which also tends to improve efficiency and numerical stability. A value of n = 0.1 was used in this study. The generic approach has been shown to be effective both in modelling the maximum extent of flooding and also the passage of a flood hydrograph when combined with a diffusive wave channel model (Horritt and Bates, 2001, 2002).

Another reason for using JFLOW (or another raster-based model of this type) is that good quality DEM data suitable for floodplain modelling are now available for the whole of Scotland. JFLOW was designed to model the flow of water over the floodplain, and does not currently include a model for flow within the river channel itself, which is regarded as the volume contained within the river banks. This was in part motivated by the needs of large-scale automated flood extent mapping, where the detailed river channel survey data needed to set up a conventional 1-D hydraulic model would be too expensive and time-consuming to collect.

3.4 Model development

For each study catchment, the first step was to estimate peak flow magnitudes for flooding downstream using FEH methods. Only the fluvial flood probabilities were considered, but it is noted that Perth in fact floods from a combination of fluvial and tidal sources.

The main objective of the study was to assess the potential to reduce the downstream effects of a 100 or 200 year event. We have therefore taken the 200 year event as our starting point to define available 'natural' storage areas in each study catchment.

For the White Cart catchment, the existing White Cart Millennium study investigated options to reduce a 200 year flood event so that the downstream flow was limited to the current 5 year flow. We have therefore adopted the 5 year flood flow as the 'threshold' flow. In addition, we have modelled the 100 year flow to compare against the 200 year event, as this is one of the project objectives.

For the South Esk, the recent Brechin flood study considered storage options to reduce a 200 year event to the current 100 year downstream flow. We have therefore modelled these two events only. For the Tay, there is no obvious equivalent 'threshold' downstream flow. However, past flooding on the Tay has caused agricultural damages. There are some embankments in the lower Tay that are thought to offer around a 5 year standard of protection. We have adopted this value as a target downstream peak flow in at Ballathie gauging station, in addition to the 100 year event.

A routing model was set up for each of the study catchments. This was calibrated such that the modelled peak flows agreed (at least to a close approximation) with the FEH flood peak estimates or the corresponding return period.

The downstream hydrographs for the larger events were then compared with the peak flow for the 'threshold' event, and the volume that would have to be stored was calculated using the simple approach illustrated in Figure 3-1. For the Clyde, a volume frequency analysis was used instead, as described in Section 8). These figures can be considered as minimum required volumes of flood storage (strictly speaking assumed to exist immediately upstream of the risk location).

As noted in Section 1, this study is concerned with 'natural' flood attenuation, which is interpreted to refer to areas contributing to flood attenuation that appear under existing conditions for a larger event. We would therefore consider the difference between, for example, the extents of the current 200 year and 100 year floods to represent potential 'natural' storage that could be used to mitigate the 100 year flood and restrict downstream flows to those of the current 5 year return period flood.

The starting point for the analysis was therefore to simulate the extents of flooding for each of the flood. This was done using JFLOW as a flood extent modelling tool for flows greater than bankfull. Inflows were taken from the 1-D routing models. For the White Cart, where existing model data were available, we estimated the bankfull flow using the channel cross sections. For the other catchments, we approximated bankfull flow as QMED, estimated using FEH methods. For the experimental work in this study, we have aggregated the DEM up to a 50m scale to improve model run times over the large areas to be modelled. Initial results suggested that this coarser grid did not introduce significant inaccuracies at the catchment scale.

The resulting flood outlines were saved as tables in MapInfo GIS format and can be plotted in map form. However, at the catchment scale the differences in extents are not always visually large. It is therefore useful to summarise the results by computing and plotting the area of inundation as a function of distance upstream from the risk location. We have then calculated the differences between the areas of the larger and smaller events to represent the 'natural' area in which water could be held back to mitigate the larger event. The graphs show the cumulative areas available for 'natural' storage as a function of distance upstream from the 'risk location'. The areas are marginal areas between the 200 year and 100 year events, where available (that is, they represent potential 'additional' natural storage during an event of return period ²1 in 100 years). Steep sections of the graphs indicate locations along the river where there are large differences between the inundation extents for the two return periods. These locations may therefore offer the greatest potential to hold water back during the larger event within the 'natural' flood extent.

3.5 Scope for utilising the natural floodplain

To fully realise the 'natural' flood attenuation in practice would of course require interventions to impound water in order to store the difference in volume identified from the hydrograph analysis.

To permit a general, catchment-scale analysis, it has been necessary to adopt only very simple methods for analysing the potential to store the required volume within the river system. We have made the simplest possible assumption that the volume required at the downstream location can be divided by the modelled flooded area to give a notional average storage depth. In each case study, we have calculated the required average storage depth using both the total extent of the 200 year flood, and also the marginal extent between the 100 year and 200 year outlines.

The figures give an indication of the average depth to which water would have to be stored to utilise the natural floodplain for the events specified above. Based on these figures and the distribution of floodplain extent (expressed with respect to distance upstream), we have calculated the average depth of water that would be required on the floodplain to achieve the required volume of storage.

The required depth is of course large close to the downstream limit since only a small area is available for storage immediately upstream of the limit. As the available area increases with distance upstream, so the required average depth falls. The depth curves have been truncated at 15.0m, which is taken as a pragmatic maximum storage depth.

The depth-distance curves can be used as a broad guide to the feasibility of using the natural flood extent to provide the storage needed to reduce a 100 year event to the 5 year flow downstream. In general, storage is most effective if it is located immediately upstream of the flood risk location. If the average storage depth falls to a practically-attainable value within a few kilometres of the downstream location, then there may be scope to use land in the natural 200 year extent to provide the required storage.

It is clear that these average depths depend critically on the area assumed to be available as 'natural floodplain'. In this case, we have used simulations of a 200 year flood extent. It would be useful to repeat the analysis using a much larger extent from a more extreme event, say for a 1000-year flood.

A second issue is that the concept of an average depth ignores the role of topography in determining where storage might be best located. This is much more difficult to address because it requires the assumption of a water surface, which would depend on the exact location(s) and height(s) of one or more flood banks. Options for building flood banks require location-specific investigations, and cannot be assessed using the type of generalised analysis presented here.

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