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Development of a stochastic precipitation nowcast scheme for flood forecasting and warning. Clive Pierce 1 , Alan Seed 2 , Neill Bowler 3 1. Met Office, Joint Centre for Hydro-Meteorological Research, Wallingford, Oxfordshire, UK, OX10 8BB - PowerPoint PPT Presentation
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© Crown copyright 2004 Page 1
Development of a stochastic precipitation nowcast scheme for
flood forecasting and warningClive Pierce1 , Alan Seed2 , Neill Bowler3
1. Met Office, Joint Centre for Hydro-Meteorological Research, Wallingford, Oxfordshire, UK, OX10 8BB
2. Cooperative Research Centre for Catchment Hydrology, Bureau of Meteorology, Melbourne, Australia
3. Met Office, FitzRoy Road, Exeter, Devon, UK, EX1 3PB
© Crown copyright 2004 Page 2
Overview
A stochastic QPN scheme - STEPS Overview of the Short Term Ensemble Prediction System Cascade modelling framework STEPS cascade model Uncertainties in advection & Lagrangian temporal evolution Formulation of STEPS
Towards stochastic fluvial forecasting
Propagating uncertainty in QPNs through a rainfall-run-off model Plans
© Crown copyright 2004 Page 3
Short Term Ensemble Prediction System
Model design Cascade framework (Lovejoy et al., 1996; Seed, 2003) to model dynamic scaling behaviour merging extrapolation nowcasts with NWP forecast
Sources of uncertainty / error diagnosed velocity fields (Bowler et al., 2004) Lagrangian temporal evolution NWP forecast initial state
Forecast evolution blends extrapolation, NWP and noise cascades stochastic noise
replaces extrapolated features beyond their life times introduces features unresolved by NWP
ensemble produced
© Crown copyright 2004 Page 4
Radar based precipitation field 2-D FFT
Bandpass filter per pixel, k=1,8
Inverse transform
Additive cascade
Normalise Xk(t)
Based upon S-PROG cascade - Seed (2003)
STEPS cascade model
njik
n
kji LLjLitXtdBR 2,,..,1,,..,1),()( ,,
1,
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21
kkk LL
)(
)()()(
,,
,,,, t
ttXtY
jik
kjikjik
© Crown copyright 2004 Page 5
Cascade decomposition
256-128 km
128-64 km
64-32 km
32-16 km 16-8 km 4-2 km8-4 km
courtesy of Alan Seed, Bureau of Meteorology, Australia
© Crown copyright 2004 Page 6
Uncertainty in the extrapolation nowcast
Uncertainty in field evolution Modelled in Lagrangian reference frame
Noise replaces extrapolated features beyond predicted life time
k,i,j = temporally independent noise cascade
Uncertainty in advection velocities Add perturbation to velocities
)(60
1)()( lonperturbatil
smoothlnoisy ttvvsmoothft
tvttv
)()()( tvtfttv onperturbatillonperturbati
)()()2()()()()(ˆ,,0,2,1, ,,,,,, ljikkl
nkl
nkl
n ttttttYttttYtttYjikjikjik
analysisn PP
)2()()()()(ˆ,,2,,,1,,, tttYttttYtttY l
ejikkl
ejikkl
ejik
© Crown copyright 2004 Page 7
Formulation of STEPS
A blend of three cascades Extrapolation
Noise
NWP
Weights assigned according to skill of extrapolation and NWP components
Advection velocities blend perturbed velocity, e with NWP diagnosed velocity, m
)()(1)()()( 22 lmle
lele
l ttvttwttvttwttv
)( lek ttY
)( lnk ttY
)( lmk ttY
)()()()()()()(,,,,,,,, ln
lnkl
ml
mkl
el
ekljik ttYttwttYttwttYttwttY
jikjikjik
© Crown copyright 2004 Page 8
STEPS - products
Ensemble members - T+15 minutes
© Crown copyright 2004 Page 9
Probability of precipitation
STEPS - products
© Crown copyright 2004 Page 10
Towards stochastic fluvial flood forecasting and warning
Uncertainty in rainfall input dominates (Moore, 2002)
Ignore errors in rainfall-runoff model
PDF of river flow from PDF of rain accumulation
Underestimates total uncertainty (Krzyztofowicz, 2001) Cost-loss decision making model (Mylne, 2002)
© Crown copyright 2004 Page 11
Flow forecast ensembles
courtesy of Bob Moore, Centre for Ecology and Hydrology, UK
© Crown copyright 2004 Page 12
Plans
STEPS operational trial in the UK and Australia
starts autumn 2005 pdfs of rain accumulation and river flow (PDM – Moore, 1985)
cost-loss model (Mylne, 2002) for pluvial & fluvial flood warning
verification of deterministic and probabilistic forecasts
© Crown copyright 2004 Page 13
Thank you