Predicting rainfall using ensemble forecasts
Nigel Roberts
Met Office @ Reading
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MOGREPS-UK
Convection-permitting 2.2 km ensemble now running routinely
Embedded within MOGREPS-R ensemble members (18 km)
36-hour forecasts
12 members
Every 6 hours
Downscaling – 18km initial
conditions
No high-resolution initial
perturbations or ‘forecast error’
perturbations to start with
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Olympics
showcase
Probability
of heavy
rain
Must have a convectionpermitting model to do this
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Convective-scale ensembles
(e.g. MOGREPS-UK)
Where to begin ?
Are 12 members enough ?
How do we use it ?
How do we know how good it is ?
How can it be improved ?
Science and development ?
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SplitShort
forecasts
into range
threeweather
scalesforecasting
to medium
1 year
12-km
forecasts
Predictable scales (large synoptic) – no need for an ensemble
Uncertain scales (mesoscale) – ensemble needed
Noise (individual showers) – neighbourhood processing with ensemble
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Small uncertainty at large scales = large uncertainty
at small scales
Low
5% error at 1000 km = 100% error at 50 km
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LBC driven uncertainties
COPS IOP 8b at 12 UTC on July 27th 2007
Kirsty Hanley et al (2011) QJ
PVU. Solid: six strongest convection members.
Dashed: six weakest convection members (dashed)
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Convective-scale ensemble
How many members do we need?
How many times do you need to throw a die for every number to come up - six?
N
E = 6/6 + 6/5 + 6/4 + 6/3 + 6/2 + 6/1 = ~ 15 times
E= N ∑ 1/ i
i=1
If 5x5km flood-producing storm is equally likely anywhere within 50 km square
(not unrealistic).
How many members to give a non-zero probability everywhere?
Answer ~ 520 members (assumes perfect model and tessellation)
Or
~ 2350 members if tessellate on 2.5 km grid
We only have 12 members !!
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1%
chance
Reinvigorate your ensemble by giving it
more members
Use ‘Neighbourhood processing’ – it works like magic
What happens at a particular model grid square is equally
likely to occur at nearby grid squares
This can be used to produce probabilities of occurrence.
If 7 grid squares within a 5x5 grid-square ‘neighbourhood’
around a particular grid square have rain, the probability of
rain at that central grid square is 7/25.
A 9x9 neighbourhood x 12 members = 972 members
This is the neighbourhood 1000 deluxe ensemble
Not independent members – justifiable for unpredictable scales
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Constructing a probability forecast
Insufficient ensemble size
leaves gaps
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Constructing a probability forecast
Probability of rain in period
around the time of interest
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Flooding near Aberystwyth 9th June 2012
MOGREPS-UK probabilities at points ~32 km neighbourhoood
Very predictable
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Flooding near Aberystwyth 9th June 2012
MOGREPS-UK probabilities within 20 km ~32 km neighbourhood
Very predictable
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Adaptive neighbourhood:
Effect of ensemble size and resolution change
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Short Term Ensemble
Prediction System
• Scale decomposed radar
extrapolation + high res NWP
precipitation forecast
• Injects noise with space-time pdf
from radar and high resolution
NWP
• Errors modelled:
Radar observation errors
Extrapolation velocities
Lagrangian evolution of
extrapolated radar
NWP forecasts
Control
Courtesy of Clive Pierce (Met Office)
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STEPS ensemble of surface precipitation rate
– 0300 UTC 17 November 2010
What do we want from a good ensemble ?
When the weather forecast is iffy we want plausible alternatives to know
what might happen instead
When the weather forecast is less iffy we should get less radical
plausible alternatives
In other words we want a good skill-spread relationship
This has traditionally been measured at the gridscale or observation
points (just like deterministic forecast verification).
Is that helpful?
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Spatial skill-spread using the FSS
99th percentile, hourly accumulations
Less spread
More skill
noise
Spread, skill
Large scale
error
Produced by Seonaid Dey, provided courtesy of Giovanni Leoncini
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Hybrid Data assimilation
Courtesy of Neill Bowler (Met Office)
Standard 3D-Var
Standard 4D-Var
Pure ensemble 3D-Var
50/50 hybrid 3D-Var
u response to a single u observation
at centre of window
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Became operational in Summer 2011
Dec 2010
June 2011
Verification vs. obs
What do we do about an imperfect model?
(Poor representation, biases and incorrect error growth)
1. Ignore it (errors grow quicker at high resolution Lorenz 1969)
2. Detect and correct/reduce (Thorwald) (some errors are not correctable)
3. Post process away (e.g. statistical downscaling) (only some errors)
4. Represent in ensemble somehow (e.g. stochastic representation of energy
upscale from unresolved processes or uncertainties in physical processes)
ECMWF – improvements in skill and spread
Jury out on tweaking physical parameters as in climate models
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Physics perturbations compared to uncertainty through
boundaries
Taken from Gebardht et al, Atmos. Res. 2011
2.8 km model
CR = N(GP all ) / N(GP >=1)
CR = Correspondence ratio
Number of pixels all members agree
have rain divided by pixel with rain in at
least one member
Lower CR = more spread
Very low rainfall threshold
(Consistent with Vie et al 2011, MWR)
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Physics vs. boundaries
Seonaid Dey and Giovanni Leoncini
FSS for precipitation hourly accumulations
FSS
• Values 0-1
• 1 = ‘perfect match’
Time after start
0 = ‘totally different’
• Contours every 0.1,
colours black at 0.0
to red at 1.0
• Graupel / convection
scheme / timestep
had little effect at
reliable scales
gridlengths
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Ensemble comparison of microphysics schemes
Taken from Clark et al, Jan 2012 BAMS
Composite frequencies of observed rainfall greater than 0.50-in. relative to
grid-points forecasting rainfall greater than 0.50-in. at forecast hour 30 from
SSEF members using (a) Thompson, (b) WSM6, (c) WDM6, and (d)
Morrison microphysics parameterizations. The boldface dot in each panel
marks the center of the composite domain and the location of the
observation.
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Further research
Where do errors / uncertainties grow and why
Ensemble data assimilation (at convective and larger scales)
Applying perturbations to convective-scale forecasts
Relationship between scales
How to verify convection-permitting ensembles
How to post process and present
Understanding the output
Direct coupling to hydrological models
Domain size, ensemble size and resolution
Blending ensembles and seamless prediction
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That’s it
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