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WWOSC 2014 (Montreal, Aug 2014) – Roberto Buizza et al: The forecast skill horizon 1 © ECMWF
Roberto Buizza, Martin Leutbecher, Franco Molteni, Alan Thorpe and Frederic Vitart
European Centre for Medium-Range Weather Forecasts
The forecast skill horizon
WWOSC 2014 (Montreal, Aug 2014) – Roberto Buizza et al: The forecast skill horizon 2 © ECMWF
How long is the forecast skill horizon (FiSH)?
The view so far has been that local, daily values can be predicted only up to about 2 weeks.
‘… the range of predictability (is defined as) the time interval within which the errors in prediction do not exceed some pre‐chosen magnitude …’
‘.. the range of predictability is about 16.8 days ..’
‘.. these results .. offer little hope for those who would extend the two‐week goal to one month … ’
(Lorenz, 1969)
WWOSC 2014 (Montreal, Aug 2014) – Roberto Buizza et al: The forecast skill horizon 3 © ECMWF
The forecast skill horizon: the view of the 1970s
30
25
20
15
5
0
Fc day
FiSHNo skill
Forecast skill horizon (~2 weeks)
WWOSC 2014 (Montreal, Aug 2014) – Roberto Buizza et al: The forecast skill horizon 4 © ECMWF
What’s the point of this work?
We aim to address the following key questions:
1. If we consider local, instantaneous Z500 fcs, how long is the FiSH?
2. Does it make sense to talk very generally about a forecast ‘predictability limit’?
3. Can we develop a unifying framework that allows us to compare in a clear way the skill of forecasts of different variables at different scales and over different regions?
WWOSC 2014 (Montreal, Aug 2014) – Roberto Buizza et al: The forecast skill horizon 5 © ECMWF
The ECMWF IFS (2013) and the coupled ocean‐atm ENS
ORTAS45 Real Time Ocean Analysis ~8 hours
HRESTL1279L137 (d0-10)
ENS51
TL639L62 (d 0-10)TL319L62 (d10-32)
Atmospheric model
Wave model
Ocean model (d0)
Atmospheric model
Wave model
EDA25
TL399L137
WWOSC 2014 (Montreal, Aug 2014) – Roberto Buizza et al: The forecast skill horizon 6 © ECMWF
ENS re‐fc suite to estimate the model‐climate
51m ENS is run twice a week up to 32d.
A 5m ENS is run for the past 20y to estimate the M‐climate (re‐fc suite).
ENS fcs have been bias‐corrected, with bias computed using 500 ENS re‐fcs [5w*(5m*20y)].
A reference 100m climatological ensemble (CLI) has been defined by 32d consecutive analyses (with the same IC as the ENS refc).
20y
51T639L91
51T319L91
2013
5 55 5
5 55 5
5 5
…28 6 13 20 27 March …
2012
5 55 5
5 55 5
5 5
5 55 5
5 55 5
5 5
2011
5 55 5
5 55 5
5 5
2010
1993
…..
WWOSC 2014 (Montreal, Aug 2014) – Roberto Buizza et al: The forecast skill horizon 7 © ECMWF
The predictability limit: definition
The predictabilitylimit is the time when the forecast error crosses a certain threshold.
As threshold, we have used m‐2σ, where m is the average climatological error.
m‐2σ
Forecast
Forecast steps (days)
error
CLI reference
F
WWOSC 2014 (Montreal, Aug 2014) – Roberto Buizza et al: The forecast skill horizon 8 © ECMWF
CLI single fcs
ENS single fcs (control)
2w 17d
<Z500>180km over NH: local instantaneous skill
Results indicate that for local, instantaneous single fc of Z500 over NH is beyond 2‐weeks.
FiSH is ~ 22 days!
WWOSC 2014 (Montreal, Aug 2014) – Roberto Buizza et al: The forecast skill horizon 9 © ECMWF
Let’s think ensemble and generalise the problem
ENS fcs: bias‐corrected forecasts are from the ECMWF 51‐member ENS, the medium‐range/monthly forecasts (32km up do d10, 64km afterwards)
Verification: ERA‐I analyses CLI fcs: 100‐member climatological ensemble defined by ERA‐I 32‐d subsequent
analyses Accuracy metric: Continuous Ranked Probability Score (CRPS) Skill: CRPS(ENS) vs CRPS(CLI) Cases: 141 (2 per week, for 16m from 2/7/12 to 4/11/13)
ENS +5d
CLI CLI CLI
ENS +10dENS + … d?
obs obs obs
WWOSC 2014 (Montreal, Aug 2014) – Roberto Buizza et al: The forecast skill horizon 10 © ECMWF
<Z500>180km over NH: local instantaneous skill
ENS probabilistic fcs
2w 17d
The same conclusion can be reached if we think in probabilistic terms.
FiSH is ~ 22 days.
CLI ensemble
WWOSC 2014 (Montreal, Aug 2014) – Roberto Buizza et al: The forecast skill horizon 11 © ECMWF
Forecast skill depend on the spatial‐temporal scale
Large‐scale, time‐average features are more predictable than instantaneous, grid‐point values, and certain phenomena are known to be predictable weeks and months ahead.
Local, instantaneous wind‐speed
Weekly‐mean,regional
temperature anomaly
Monthly‐mean, continental‐scalerain anomaly
10 100 1000 10000 km0.1 1 10 100 days
WWOSC 2014 (Montreal, Aug 2014) – Roberto Buizza et al: The forecast skill horizon 12 © ECMWF
MJO and NAO
• Few days: the time limit up to which local, instantaneous variables can be predicted
• Few weeks: the time limit up to which large‐scales (NAO, MJO, ..) can be predicted
• Few months: the time limit up to which coupled, very large‐scales (Nino) can be predicted
MJO over tropics
2 weeks
3‐4 weeks
6 months
WWOSC 2014 (Montreal, Aug 2014) – Roberto Buizza et al: The forecast skill horizon 13 © ECMWF
Forecast skill depend on the spatial‐temporal scale
All forecasts represent average values over a space‐time volume: even a instantaneous, local values represents an implicit average.
Large‐scale, t‐average features are more predictable than instantaneous, local values. Unpredictable “noise” can be removed by averaging to isolate the predictable signal.
We have applied the same metric to differently averaged (in 4D) forecasts and asked:a) Does FiSH depend on the spatial‐temporal average (and on the variable)?b) Does it make sense to talk very generally about a forecast ‘predictability limit’?
WWOSC 2014 (Montreal, Aug 2014) – Roberto Buizza et al: The forecast skill horizon 14 © ECMWF
Forecast skill depend on the spatial‐temporal scale
Consider increasingly coarser fields, defined by temporally averaged and spectrally truncated fields:• Spatially: spectrally
truncated from T120 (180km) to T60 (360km), T15, T7, T3
• Temporally: from instantaneous (H0) to 1, 2, 4 and 8 day averages (H24‐H192)
H0 ‐ T120(180km)
H0 ‐ T30(720km)
H0 ‐ T15(1500km)
H0 ‐ T7(3000km)
WWOSC 2014 (Montreal, Aug 2014) – Roberto Buizza et al: The forecast skill horizon 15 © ECMWF
Forecast skill depend on the spatial‐temporal scale
Consider increasingly coarser fields, defined by temporally averaged and spectrally truncated fields:• Spatially: spectrally
truncated from T120 (180km) to T60 (360km), T15, T7, T3
• Temporally: from instantaneous (H0) to 1, 2, 4 and 8 day averages (H24‐H192)
H0 – T120(180km)
2d – T120(180km)
4d – T120(180km)
8d – T120(180km)
WWOSC 2014 (Montreal, Aug 2014) – Roberto Buizza et al: The forecast skill horizon 16 © ECMWF
<Z500>180km over NH: instantaneous, <..>48h and <..>96h
CLI ENS
ENS fc
Instantaneous
4‐day average
8‐day average
WWOSC 2014 (Montreal, Aug 2014) – Roberto Buizza et al: The forecast skill horizon 17 © ECMWF
<Z500>180km over NH: instantaneous, <..>48h and <..>96h
CLI ENS
ENS fc
Instantaneous1‐day average2‐day …4‐day …
8‐day …16‐day …
WWOSC 2014 (Montreal, Aug 2014) – Roberto Buizza et al: The forecast skill horizon 18 © ECMWF
<Z500>180km over SH: instantaneous, <..>48h and <..>96h
CLI ENS
ENS fc
Instantaneous
4‐day average
8‐day average
WWOSC 2014 (Montreal, Aug 2014) – Roberto Buizza et al: The forecast skill horizon 19 © ECMWF
<T850>180km NH, SH & TR: instantaneous, <..>48h and <..>96h
FiSH depends on the variable, the 4D‐scale (i.e. 4D volume where average is taken) and the area where accuracy is computed.
WWOSC 2014 (Montreal, Aug 2014) – Roberto Buizza et al: The forecast skill horizon 20 © ECMWF
The forecast skill horizon: results based on ECMWF ENS
30
25
20
15
5
0
F (T850T120,H0)
F(T850T120,H24)
F(T850T120,H96)
FiSH depends on the variable, the 4D‐scale and the area
Fc day
FiSH
WWOSC 2014 (Montreal, Aug 2014) – Roberto Buizza et al: The forecast skill horizon 21 © ECMWF
The forecast skill horizon: results based on ECMWF ENS
30
25
20
15
5
0
FiSH
Fc day
FiSH is shown here for: Variables: Z500, T850 and T200 Time‐averages: 0, 2‐days and 8 days Truncation: T120 Areas: NH, SH and TR
Values are well beyond 2 weeks even for instantaneous, local forecasts.
8d (H48)2d (H24)
Instantaneous (H0)
FiSH depends on the variable, the 4D‐scale and the area
WWOSC 2014 (Montreal, Aug 2014) – Roberto Buizza et al: The forecast skill horizon 22 © ECMWF
Suppose that we have a good system that can simulate all scales relevant to predict phenomena with a scale (X,T), and initialise them properly. The skill of the phenomena depends on the competition between:• Errors propagating from the smaller scales, i.e. noise destroying the signal, and• Predictive signal propagating from the wider, longer‐range scales
Phenomenaslave
External forcing
free
widerlonger‐time
(XS,TS) (X,T) (XL,TL)
(from Hoskins 2012, QJRMS)
How can we interpret these results?
WWOSC 2014 (Montreal, Aug 2014) – Roberto Buizza et al: The forecast skill horizon 23 © ECMWF
How can we interpret these results?
Errors propagate from the small to the large scales thus reducing the predictive skill
Predictable signals propagate from the large scales to the smallest scales
WWOSC 2014 (Montreal, Aug 2014) – Roberto Buizza et al: The forecast skill horizon 24 © ECMWF
‐ The MJO can affect extra‐tropical, low‐frequency phenomena such as blocking‐ Diurnal tropical convection influences organized convection and the MJO‐ The MJO propagates interacting with El Nino‐ El Nino and the MJO are affected by variations in solar radiation and greenhouse gases‐ Blocking influences and is influenced by synoptic scales, fronts‐ …..
Blocking
fronts
Solar radiationGreenhouse gases
organizconvec
MJO, El Nino
convec
(XS,TS) (X,T) (XL,TL)
Free smallerscales
An example: blocking over the Euro‐Atlantic sector
WWOSC 2014 (Montreal, Aug 2014) – Roberto Buizza et al: The forecast skill horizon 25 © ECMWF
Where is the forecast skill horizon?
Lorenz (1969): ‘… one flap of a sea gull’s wing would forever change the future course of the weather .. Such a change would be realized within about 17 days ..’
We showed that there is not a unique definition of predictability and that the Forecast Skill Horizon, say the FiSH length, depends on the forecast field (scale, variable, region).The forecast skill horizon is well beyond 2 weeks even for local, instantaneous fields, thus confirming results published in literature that certain phenomena (MJO, NAO, blocking, ..) can be predicted beyond 2 weeks using a unifying, coherent framework.
WWOSC 2014 (Montreal, Aug 2014) – Roberto Buizza et al: The forecast skill horizon 26 © ECMWF
So .. how long is the FiSH?
• Reduced initial errors• More complete models (coupling to land and ocean)• Better models (improved moist processes, ..)• New methods (ensembles, ..)• Understanding of sources of predictability• Scale analysis
2 weeks 3 weeks 4 weeks 5 weeks
1970s<(t)>180km
<.;.>180km,48h
<.;.>180km,96h
<.;.>180km,192h
Z500 over NH
FiSH length
WWOSC 2014 (Montreal, Aug 2014) – Roberto Buizza et al: The forecast skill horizon 27 © ECMWF
In other words .. 1970s: results based on atmosphere‐only models suggested that a sea‐gull wing could affect the weather anywhere after ~ 2 weeks2010s: results based on more accurate, higher resolution coupled ocean‐atmosphere models indicate that the limit is well beyond 2 weeks and that the predictability limit has not yet been reached
forget the sea‐gulls .. think FiSH!!