The forecast skill horizon Roberto Buizza, Martin Leutbecher, Franco Molteni, Alan Thorpe and Frederic Vitart European Centre for Medium-Range Weather Forecasts WWOSC 2014 (Montreal, Aug 2014) Roberto Buizza et al: The forecast skill horizon 1 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 twoweek goal to one month (Lorenz, 1969) WWOSC 2014 (Montreal, Aug 2014) Roberto Buizza et al: The forecast skill horizon 2 ECMWF
The forecast skill horizon: the view of the 1970s 30 25 20 15 Forecast skill horizon (~2 weeks) FiSH No skill Fc day 5 0 WWOSC 2014 (Montreal, Aug 2014) Roberto Buizza et al: The forecast skill horizon 3 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 4 ECMWF
The ECMWF IFS (2013) and the coupled ocean atm ENS EDA 25 T L 399L137 HRES T L 1279L137 (d0-10) ENS 51 T L 639L62 (d 0-10) T L 319L62 (d10-32) Atmospheric model Atmospheric model Wave model Wave model Ocean model (d0) ORTAS4 5 Real Time Ocean Analysis ~8 hours WWOSC 2014 (Montreal, Aug 2014) Roberto Buizza et al: The forecast skill horizon 5 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 2013 2012 2011 2010.. 1993 28 6 13 20 27 March 51 T639 L91 51 T319 L91 WWOSC 2014 (Montreal, Aug 2014) Roberto Buizza et al: The forecast skill horizon 6 ECMWF
The predictability limit: definition The predictability limit 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 error CLI reference Forecast Forecast steps (days) F WWOSC 2014 (Montreal, Aug 2014) Roberto Buizza et al: The forecast skill horizon 7 ECMWF
<Z500> 180km over NH: local instantaneous skill Results indicate that for local, instantaneous single fc of Z500 over NH is beyond 2 weeks. CLI single fcs FiSH is ~ 22 days! ENS single fcs (control) 2w 17d WWOSC 2014 (Montreal, Aug 2014) Roberto Buizza et al: The forecast skill horizon 8 ECMWF
Let s think ensemble and generalise the problem ENS fcs: bias corrected forecasts are from the ECMWF 51 member ENS, the mediumrange/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 ENS +10d ENS + d? CLI CLI CLI obs obs obs WWOSC 2014 (Montreal, Aug 2014) Roberto Buizza et al: The forecast skill horizon 9 ECMWF
<Z500> 180km over NH: local instantaneous skill The same conclusion can be reached if we think in probabilistic terms. CLI ensemble FiSH is ~ 22 days. ENS probabilistic fcs 2w 17d WWOSC 2014 (Montreal, Aug 2014) Roberto Buizza et al: The forecast skill horizon 10 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 scale rain anomaly 10 100 1000 10000 km 0.1 1 10 100 days WWOSC 2014 (Montreal, Aug 2014) Roberto Buizza et al: The forecast skill horizon 11 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 2 weeks MJO over tropics 3 4 weeks 6months WWOSC 2014 (Montreal, Aug 2014) Roberto Buizza et al: The forecast skill horizon 12 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 13 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 T15 (1500km) H0 T30 (720km) H0 T7 (3000km) 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) 4d T120 (180km) 2d T120 (180km) 8d T120 (180km) WWOSC 2014 (Montreal, Aug 2014) Roberto Buizza et al: The forecast skill horizon 15 ECMWF
<Z500> 180km over NH: instantaneous, <..> 48h and <..> 96h CLI ENS Instantaneous 4 day average 8 day average ENS fc 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 Instantaneous 1 day average 2 day 4 day 8 day 16 day ENS fc WWOSC 2014 (Montreal, Aug 2014) Roberto Buizza et al: The forecast skill horizon 17 ECMWF
<Z500> 180km over SH: instantaneous, <..> 48h and <..> 96h CLI ENS Instantaneous 4 day average 8 day average ENS fc WWOSC 2014 (Montreal, Aug 2014) Roberto Buizza et al: The forecast skill horizon 18 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 19 ECMWF
The forecast skill horizon: results based on ECMWF ENS 30 FiSH depends on the variable, the 4D scale and the area FiSH F(T850 T120,H96 ) 25 F(T850 T120,H24 ) F (T850 T120,H0 ) 20 15 Fc day 5 0 WWOSC 2014 (Montreal, Aug 2014) Roberto Buizza et al: The forecast skill horizon 20 ECMWF
The forecast skill horizon: results based on ECMWF ENS 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. 30 25 20 15 FiSH depends on the variable, the 4D scale and the area 8d (H48) FiSH 2d (H24) Instantaneous (H0) Fc day 5 0 WWOSC 2014 (Montreal, Aug 2014) Roberto Buizza et al: The forecast skill horizon 21 ECMWF
How can we interpret these results? 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 (X S,T S ) (X,T) (X L,T L ) slave free Phenomena wider longer time External forcing (from Hoskins 2012, QJRMS) WWOSC 2014 (Montreal, Aug 2014) Roberto Buizza et al: The forecast skill horizon 22 ECMWF
How can we interpret these results? Predictable signals propagate from the large scales to the smallest scales Errors propagate from the small to the large scales thus reducing the predictive skill WWOSC 2014 (Montreal, Aug 2014) Roberto Buizza et al: The forecast skill horizon 23 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.. An example: blocking over the Euro Atlantic sector (X S,T S ) (X,T) (X L,T L ) fronts Blocking MJO, El Nino convec organiz convec Free smaller scales Solar radiation Greenhouse gases WWOSC 2014 (Montreal, Aug 2014) Roberto Buizza et al: The forecast skill horizon 24 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 25 ECMWF
So.. how long is the FiSH? Z500 over NH <.;.> 180km,192h 1970s <(t)> 180km <.;.> 180km,48h <.;.> 180km,96h FiSH length 2 weeks 3 weeks 4 weeks 5 weeks 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 WWOSC 2014 (Montreal, Aug 2014) Roberto Buizza et al: The forecast skill horizon 26 ECMWF
In other words.. forget the sea gulls.. think FiSH!! 1970s: results based on atmosphere only models suggested that a sea gull wing could affect the weather anywhere after ~ 2 weeks 2010s: results based on more accurate, higher resolution coupled oceanatmosphere models indicate that the limit is well beyond 2 weeks and that the predictability limit has not yet been reached WWOSC 2014 (Montreal, Aug 2014) Roberto Buizza et al: The forecast skill horizon 27 ECMWF