the forecast skill horizon - world meteorological organization · wwosc 2014 (montreal, aug 2014)...

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


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)


The forecast skill horizon: the view of the 1970s

30

25

20

15

5

0

Fc day

FiSHNo skill

Forecast skill horizon (~2 weeks)


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?


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


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

…..


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


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!


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


<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


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


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



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’?



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)



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)


<Z500>180km over NH: instantaneous, <..>48h and <..>96h

CLI ENS

ENS fc

Instantaneous

4‐day average

8‐day average


<Z500>180km over NH: instantaneous, <..>48h and <..>96h

CLI ENS

ENS fc

Instantaneous1‐day average2‐day …4‐day …

8‐day …16‐day …


<Z500>180km over SH: instantaneous, <..>48h and <..>96h

CLI ENS

ENS fc

Instantaneous

4‐day average

8‐day average


<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.


The forecast skill horizon: results based on ECMWF ENS

30

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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


The forecast skill horizon: results based on ECMWF ENS

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25

20

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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


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?


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


‐ 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


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.


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


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!!

the forecast skill horizon - world meteorological organization · wwosc 2014 (montreal, aug 2014)...

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