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

2. 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 Introduction

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

7. Channel hydraulics and gauges

8. 1D/2D model complexity

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

10. Probabilistic flood risk mapping at confluences Q RP

11. Q Q Q The problem at confluences ??

12. Set Δ of m gauges. Each is a random variable X at location i Marginal distributions at each location Yi Conditional distribution, spatial dependence Simulate events over time t (e.g. 100 years) when y at Yi is greater than u Sample from data at gauges Δ (Block bootstrapping) 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. Set Δ of m gauges. Each is a random variable X at location i Marginal distributions at each location Yi Conditional distribution (spatial dependence) Simulate events over time t (e.g. 100 years) when y at Yi is greater than u Sample from data at gauges Δ (Block bootstrapping) 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. 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) ij h flow i j Representation of flow between cells in LISFLOOD-FP

16. 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.