Where next for research in to simplified surface water flood modelling?

The Environment Agency has recently completed research looking at rainfall runoff assumption within national scale surface water flood mapping in England and Wales. In particular, the research focussed on the use of a single drainage rate parameter (x mm/hr) to represent the water removed by sub-surface drainage system. The research project developed a method for varying the drainage rate from the national default using local knowledge. We concluded that this approach was valid for the current generation of national scale flood maps. However, we also identified that there is very little scope to develop the approach further. Instead we suggest that new methods need to be developed to support future improvements to national scale surface water flood mapping.


Introduction
In England there are 3 million properties at risk from surface water flooding (Environment Agency 2014).By comparison, there are 2.4 million properties at risk of flooding from rivers and the sea.Future projections for climate change, urban creep and population growth all mean that surface water flood risk is only going to get worse.
So it is crucial that risk management authorities and local communities have a method for understanding the level of surface water flood risk that they face.In England and Wales, the Updated Flood Map for Surface Water (uFMfSW) has been published.It provides flood depth and velocity information, at 2 metre resolution for a range of flood probabilities and storm durations.It aims to give a broad understanding of flood risk in an area rather than accurate property level risk assessments.

Drainage rates as a model simplification
Creating a map with national coverage requires the underlying model to be simplified so that the model can built and run within a reasonable time.Simplification is also necessary when data is unavailable or cannot be collated cost effectively.For example, in England and Wales, there is no national dataset of drainage assets.In fact, model simplification is desirable for many reasons besides national flood mapping.It allows models to be run for real time purposes such as flood forecasting and enables models to be run multiple times to better understand model uncertainty or the impact of flood management options.
The main simplification used in the uFMfSW is to parameterise the drainage network.So, we assume that a fixed 12 mm per hour of rainfall is removed by the drainage network.The volume of rainfall that remains is used as the starting condition for a 2d hydraulic model run that resolves the full shallow water equation.

Problems with drainage rates
The use of a drainage rate succeeds in simplifying the model, but it creates several problems of its own.-The national default of 12 mm per hour does not reflect local differences in the drainage network.This means that, some areas are overestimating drainage and others are underestimating.It also means that we can't show the effect that a change in drainage would make.
-The rainfall is removed only during model set up instead of during model run time.This is unlikely to be an issue when the same drainage rate is used everywhere, but could become important when water flows from an area with one drainage rate to an area with a different drainage rate.
-Related to the point above, the drainage rate is assumed to be constant throughout the storm event.In reality, the drainage system can remove more water at the beginning of the event than it can at end because at the beginning of the event the pipes are empty.
-The drainage rate removes water permanently from the system.This means that it doesn't reproduce the way that real sewers have storage capacity that fills up during an event.It also means that water doesn't emerge elsewhere in the model domain in the way that sewers behave when they surcharge.-Finally, the drainage rate is not a physical characteristic that could be measured or verified.Instead it is more of a calibration parameter similar to, say, Manning's n.This makes it difficult to parameterise with confidence.

Aim for this research project
This piece of research aimed to tackle the first problem described in the list above: the fact that our current default value of 12mm per hour does not represent local differences in the drainage network.

Method
We attempted two different approaches to tackle this problem: an empirical approach and a statistical approach.

Empirical approach
The empirical approach used case studies from six sites.The sites were Market Harborough (a market town in Leicestershire), Ellenbrook (a district of Ipswich, Suffolk), Stirchley (a district south of south of Birmingham city centre) and Liverpool (three areas in central Liverpool).
For each site we re-ran the flood models using a drainage rate of 6mm per hour and 18 mm per hour.By comparing these outlines (and the original 12mm per hour model run) against detailed local models we could see which of the three drainage rates most closely resembled the detailed model.
So that we could identify the right drainage rate, we performed both a visual comparison of the outputs, as well as looking at key metrics such as number of properties at risk.
Finally, we compared the six case studies to see if we could identify trends that could be used to predict the true drainage rate in other sites.The relationships that we looked at were: building density, impervious area, sewer diameter, sewer density, manhole density, sewer gradient and the distribution of pipe sizes within the catchment.

Statistical approach
The national estimate of drainage rate used in the uFMfSW (12mm per hour) is obtained using a drainage system capacity equation, based on a modified form of the rational method.The single national estimate was created by using a Monte Carlo analysis across the range of possible input values.
The drainage system capacity equation takes into account the percentage runoff; critical storm duration; level of service of the drainage system; and the depth, duration and frequency parameters of typical rainfall events.The full approach is described in Horritt et al (2009).
For this approach we used the same Monte Carlo analysis but changed the input parameters, narrowing down the range of possible values using local knowledge about the catchment.
We compared predicted drainage rates against the drainage rates identified for three of the case studies used in the empirical method.We also used a further case study in Greater Manchester where the local authority had previously provided their estimate of the local drainage rate.

Results
The drainage rates that gave results closest to the detailed local model are provided below:

Results from the empirical approach
The drainage rates identified from local models were compared against seven different characteristics of the case study sites.The seven characteristics were: 1. Building density 2. Impervious area 3. Average sewer diameter 4. Sewer density 5. Manhole density 6.Average sewer gradient 7. cumulative pipe frequency The results are provided below, however, no strong relationships emerged from the results.

Results from the statistical approach
The statistical approach identified the following drainage rates for each case study.

Greater Manchester 16
Table 2. Drainage rate for each case study site as estimated by the statistical method.
These results can be compared to drainage rates extracted from local data, provided below.Most of these case studies focussed on improving the current estimate for the drainage rate.So we would hope that the estimate from the statistical approach is closer to the local data than the default national rate (12 mm/hr) is.

Area
The Ellenbrook case study was different in that it explored the impact of improving the level of service of the drainage system.We don't know what the drainage rate should be for the improved system but it should be higher than the default national rate.

Market Harborough
The input data used to estimate the drainage rate for Market Harborough is provided below.Local knowledge was used for storm duration and rainfall parameters.

Input Parameter
Min  The Monte Carlo analysis gave results with a mode much higher than the national default.This results matched exactly the data extracted from the local model.

Ellenbrook
The input data used to explore the impact of improving the drainage system in Ellenbrook is provided below.Local knowledge was used for rainfall parameters.The Monte Carlo analysis gave results with a mode slightly higher than the national default.This shows that the direction of change is as expected however further work would be needed to identify if the magnitude of change was correct.

Stirchley
The input data used to estimate the drainage rate for Stirchley is provided below.Local knowledge was used for the rainfall parameters only.The Monte Carlo analysis gave results with a mode slightly lower than the national default.This shows that te statistical method is an improvement on national default but it could be closer to the estimate from a local model of (6 mm/hr).

Figure 8 .
Figure 8. Calculated drainage rate for Market Harborough.

Table 1 .
Drainage rate for each case study site that makes the national model most closely resemble the detailed local model.

Table 3 .
Reference drainage rate for each case study site for comparison against the outputs from the statistical method.
FLOODrisk 2016 -3 rd European Conference on Flood Risk Management

Table 4 .
Input data for Market Harborough.Changes from the national defaults are highlighted with *

Table 5 .
Input data for Ellenbrook.Changes from the national defaults are highlighted with *

Table 6 .
Input data for Stirchley.Changes from the national defaults are highlighted with *