Local flood forecasting for local flood risk areas Keith Beven, David Leedal, Peter Young and Paul Smith Lancaster Environment Centre

Local flood forecasting NFFS : primarily provides forecasts for gauging stations (some hydrodynamic models that make predictions but of unproven accuracy away from gauging stations) Some moves towards probabilistic forecasts (SC080030) but few models with data assimilation capabilities Warnings based on extrapolations from gauging stations (baseline LOS 2 hr lead time, cannot always be met in small catchments such as Boscastle) Extend lead time using QPF - STEPS (but still high uncertainty) Or provide local forecasts for local flood risk areas?

Rules of Flood Forecasting The Rules 1.The event of greatest interest is the NEXT event when a warning might (or might not) need to be issued. 2.The next event is likely to be different from all previous events (in rainfall pattern; radar anomalies; NWP errors; antecedent conditions; runoff generation; rating curve etc) 3.Allowing for uncertainty means being right more often in terms of bracketing when POD warning thresholds are crossed and allows better assessment of risk of false alarms (NB. this is a GOOD thing in communicating risk).

Rules of Flood Forecasting The Rules 4.Mass balance is not necessarily helpful in forecasting damaging floods Rainfall estimates for the next event will be wrong Rating curve for extreme events will probably be wrong – or at least introduce significant heteroscedasticity into errors Levels are measured; level thresholds used in warning - Why not use levels directly in forecasting?

Local Flood Forecasting Data Based Mechanistic (DBM) Modelling Approach Simple nonlinearity + transfer function model within stochastic data assimilation framework –See Young (Phil Trans Roy Soc Lond, 2002) –Romanowicz et al. (WRR2006, AWR, 2008); –Leedal et al. (FloodRisk2008) –Beven et al. (FloodRisk2008 – emulation of hydraulic models) First implemented for SRPB on River Nith for Dumfries in Scotland (with uncertainty and data assimilation and tidal influences) in 1991 (5 hour natural lag; 6 hour lead time required). State Dependent Nonlinearity in FRMRC1

Predicted Water Level DBM Forecasting Methodology Rainfall to level model Effective Rainfall Nonlinearity Instantaneous Effect Quick Pathway Slow Pathway (“Baseflow”) Effective Rainfall Rainfall Noise Nonlinear Input Transform Linear Transfer Function

Identification of State Dependent Nonlinearity Find first estimate of transfer function Use in inverse mode to identify gains on inputs Rank in order of some state or exogenous variable and filter (level or flow as index of antecedent state) Use resulting non-parametric gains to provide inputs to reidentify transfer function Check for parametric function to represent nonlinearity (power law / RBF / ….) Iterate if necessary

DBM Identification of nonlinearity River Eden (a) Rainfall to Level at Temple Sowerby (b) Rainfall to level at Greenholme (c) Levels to Level at Sheepmount

Adaptive Forecasting Rainfall to level model With data assimilation Effective Rainfall Nonlinearity Instantaneous Effect Quick Pathway Slow Pathway (“Baseflow”) Effective Rainfall Rainfall Predicted Water Level Noise O t Observed Water Level {O t – y t } Update gain g t using weighted innovation gtgt

DBM Forecasting: Data Assimilation Assimilate Observed Data to produce the best deterministic forecast –Start forecasting from ‘best estimate’ of current hydrological states State Space form of DBM model –Kalman Filter –State dependent variances –Optimise variance parameters on f-step ahead forecast (presuming future precipitation known) –Use expected value of predictive distribution as a deterministic forecast.

River Eden Sensor Network Funded by FRMRC2 to (a) Test HD model predictions and (b) Test local flood forecasting Stead McAlpin site

Probabilistic Level Forecasting for Eden- EA Gauges using raingauge inputs

River Eden - January 2005 event Upstream at Appleby Emergency Centre at Carlisle Public response at Carlisle

Probabilistic Level Forecasting for Eden- EA Gauges using reduced network

6 hour ahead forecasts at Sheepmount Aug 2004 Calibration 4 m

Probabilistic Level Forecasting for Eden- EA Gauges using reduced network 7 m 6 hour ahead forecasts at Sheepmount Jan 2005 Prediction

Local Forecasting on the River Caldew Stead McAlpin Factory – flooded in Jan 2005 (almost in 2009 & 2010) River Caldew and installed level sensor

Local Forecasting on the River Caldew Stead McAlpin Factory: Calibration (November 2009) 2hr ahead forecasts for local level with upstream raingauge input

Local Forecasting on the River Caldew Stead McAlpin Factory: Validation (Nov 2010)

Emulating distributed flood inundation predictions Identified nonlinearities for selected sites as a function of input stage

Emulating distributed flood inundation predictions HEC-RAS model v emulated water levels – calibration event

Emulating distributed flood inundation predictions HEC-RAS model v emulated water levels – validation event

Emulating distributed flood inundation predictions HEC-RAS model v emulated water levels reproduction of input-output level hysteresis

Summary The next event will be different so data assimilation should be used wherever possible DBM approach using rainfall-level (or level-level) forecasts based on local level sensor Still requires an input signal – make use of EA gauges? Are there ways of making these local models self- calibrating as soon as river starts to go up and down? Can also be used to emulate hydrodynamic models for forecasting purposes (at least for simple routing) – but cannot be more accurate than original model (unless data assimilation becomes possible….)