Modelling of the 2005 flood event in Carlisle and probabilistic flood risk

estimation at confluences

Jeff Neal1, Paul Bates1, Caroline Keef2, Keith Beven3 and 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.

• 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

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

2005 event data

2005 event data

2005 event data

Channel hydraulics and gauges

1D/2D model complexity

Urban floodplain processes

Neal et al., 2009

25 m resolution10 m resolution5 m resolution

Probabilistic flood risk mapping at confluences

Q

RP

Q

RP

Q

RP

Q

RP

The problem at confluences

? ?

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

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

Hydraulic modelling

4.0 4.5 5.0 5.5 6.0 6.5 7.0

45

67

89

10

Sheepmount

Model

Empi

rical

2.0 2.2 2.4 2.6 2.8 3.02.

02.

22.

42.

62.

83.

03.

2

Cummersdale

Model

Empi

rical

1.0 1.2 1.4 1.6 1.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

Harraby Green

Model

Empi

rical

3.4 3.6 3.8 4.0 4.2 4.4

3.5

4.0

4.5

5.0

5.5

Linstock

Model

Empi

rical

3.0 3.5 4.0 4.5 5.0

3.0

3.5

4.0

4.5

5.0

5.5

6.0

Great Corby

Model

Empi

rical

2.2 2.4 2.6 2.8 3.0 3.2 3.4

2.5

3.0

3.5

Greenholme

Model

Empi

rical

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)

2

,1,,1,,

xQQQQ

th ji

yjiy

jix

jix

ji

xxzh

nhQ

2135

flow )(

i jhflow

i j

Representation of flow between cells in LISFLOOD-FP

xhqtnghxzhtghq

Qflowflow

flow

3/102 /1

A new LISFLOOD-FP formulation

A new LISFLOOD-FP formulation

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).

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

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

Run 1 flood frequency

• The maximum flood outline was a combination of multiple events.

• Cannot assume same return period on all tributaries

Uncertainty in the 1 in 100 yr flood outline

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

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.