Jeff Neal 1 , Paul Bates 1 , Caroline Keef 2 , Keith Beven 3 and David Leedal 3

1. Modelling of the 2005 flood event in Carlisle and probabilistic flood risk estimation at confluences Jeff Neal1, Paul Bates1, Caroline Keef2, Keith Beven3and David Leedal3 1School of Geographical Sciences, University Road, University of Bristol, Bristol. BS8 1SS. 2JBA Consulting, South Barn, Broughton Hall, Skipton, N Yorkshire, BD23 3AE, UK. 3Lancaster Environment Centre, Lancaster University, Lancaster, LA1 4YQ, UK.

2. Introduction • A Framework for Assessing Uncertainty in Flood Risk Mapping, Data and Modelling • Carlisle 2005 event data • Overview • Evaluation data errors • Inundation modelling example uncertainties • Channel hydraulics and gauges • Structural complexity • Resolution • Beyond inundation modelling • Probabilistic flood risk at confluences • New numerical scheme • Results

3. Uncertainty Framework • A framework for the discussion and assessment of uncertainty in flood risk mapping between analysts and clients, stakeholders and users • A way to audit uncertainties in each element of the whole systems model

4. 2005 event data

5. 2005 event data

6. 2005 event data

7. Channel hydraulics and gauges

8. 1D/2D model complexity

9. Urban floodplain processes 25 m resolution 10 m resolution 5 m resolution Neal et al., 2009

10. Probabilistic flood risk mapping at confluences Q RP

11. The problem at confluences Q RP ? ? Q Q RP RP

12. The problem at confluences • Model the conditional distribution of a set of variables given that one of these variables exceeds a high threshold. Event simulation with spatial dependence

13. The problem at confluences (uncertainty) • Model the conditional distribution of a set of variables given that one of these variables exceeds a high threshold. Refit to data and run event generator may times to approximate uncertainty

14. Hydraulic modelling

15. i j • A new LISFLOOD-FP formulation • Continuity Equation • Continuity equation relating flow fluxes and change in cell depth • Momentum Equation • Flow between two cells is • calculated using: • Manning’s equation (ATS) hflow j i Representation of flow between cells in LISFLOOD-FP

16. A new LISFLOOD-FP formulation

17. A new LISFLOOD-FP formulation

18. Hydraulic modelling • LISFLOOD-FP hydraulic model (Bates et al., 2010) • 1D diffusive channel model • 2D floodplain model at 10 m resolution • Model calibrated on 2005 flood event (RMSE 0.25 m).

19. Hydraulic modelling • LISFLOOD-FP hydraulic model (Bates et al., 2010) • 1D diffusive channel model • 2D floodplain model at 10 m resolution • Model calibrated on 2005 flood event (RMSE 0.25 m). • Event simulation • 47000 events • Scaled 2005 hydrographs • Event simulation time was 0.1-2 hours • Analysis took 5 days and generated 40 GB of data

20. Run 1 flood frequency • Run 1 of the event generator using all flow data

21. Run 1 flood frequency • The maximum flood outline was a combination of multiple events. • Cannot assume same return period on all tributaries

22. Uncertainty in the 1 in 100 yr flood outline

23. Risk • MasterMap building outlines • Depth damage curve • Calculate damage from each event

24. Conclusions • Flooding at confluences is critical to the basin-wide development of flood hazard and depends on the joint spatial distribution of flows. • Assuming steady state flows over predicted flood hazard for a range of flows and event durations. • The maximum flood outline was a combination of multiple events. • Cannot assume the same return period on all tributaries • Risk assessment using the event data was demonstrated. • Expected damages increase nonlinearly. • As expected a few events caused most of the damage.