1. The Seasonal Forecast System
at ECMWF
Tim Stockdale
European Centre for Medium-Range Weather Forecasts

2. Contents Seasonal forecasting with coupled GCMs
Why use GCMs?
How we make a forecast
Basic calibration – how, why, and what are the problems?
Model error
Operational forecasts: ECMWF System 3
System design
How good are the El Nino forecasts?
How good are the atmospheric forecasts?
Multi-model systems and forecast interpretation
EUROSIP multi-model system
Meaning of probabilistic forecasts

3. Sources of seasonal predictability
KNOWN TO BE IMPORTANT:
El Nino variability - biggest single signal
Other tropical ocean SST - important, but multifarious
Climate change - especially important in mid-latitudes
Local land surface conditions - e.g. soil moisture in spring
OTHER FACTORS:
Volcanic eruptions - definitely important for large events
Mid-latitude ocean temperatures - still somewhat controversial
Remote soil moisture/ snow cover - not well established
Sea ice anomalies - local effects, but remote??
Dynamic memory of atmosphere - most likely on 1-2 months
Stratospheric influences - various possibilities
Unknown or Unexpected - ???

4. Methods of seasonal forecasting
Empirical forecasting
Use past observational record and statistical methods
Works with reality instead of error-prone numerical models 
Limited number of past cases means that it works best when observed variability is dominated by a single source of predictability 
A non-stationary climate is problematic 
Two-tier forecast systems
First predict SST anomalies (ENSO or global; dynamical or statistical)
Use ensemble of atmosphere GCMs to predict global response
Many people still use regression of a predicted El Nino index on a local variable of interest
Single-tier GCM forecasts
Include comprehensive range of sources of predictability 
Predict joint evolution of SST and atmosphere flow 
Includes indeterminacy of future SST, important for prob. forecasts 
Model errors are an issue! 

5. Step 1: Build a coupled model
IFS (atmosphere)
TL159L62 Cy31r1, deg grid for physics (operational in Sep 2006)
Full set of singular vectors from EPS system to perturb atmosphere initial conditions (more sophisticated than needed …)
Ocean currents coupled to atmosphere boundary layer calculations
HOPE (ocean)
Global ocean model, 1x1 mid-latitude resolution, 0.3 near equator
A lot of work in developing the OI ocean analyses, including analysis of salinity, multivariate bias corrections and use of altimetry.
Coupling
Fully coupled, no flux adjustments, except no physical model of sea-ice

6. Step 2: Make some forecasts
Initialize coupled system (cf Magdalena’s lecture)
Aim is to start system close to reality. Accurate SST is particularly important, plus ocean sub-surface.
Don’t worry too much about “imbalances”
Run an ensemble forecast
Explicitly generate an ensemble on the 1st of each month, with perturbations to represent the uncertainty in the initial conditions; run forecasts for 7 months
Worry about model error later ….

7. Creating the ensemble Wind perturbations SST perturbations
Perfect wind would give a good ocean analysis, but uncertainties are significant. We represent these by adding perturbations to the wind used in the ocean analysis system.
BUT only have 5 member ensemble, and no representation of other sources of uncertainty in ocean analysis (obs error, ..)
SST perturbations
SST uncertainty is not negligible
SST perturbations added to each ensemble member at start of forecast.
BUT perturbations based on analyses that use the same input data
Atmospheric unpredictability
Atmospheric ‘noise’ soon becomes the dominant source of spread in an ensemble forecast. This sets a fundamental limit to forecast quality.
To ensure that noise grows rapidly enough in the first few days, we activate ‘stochastic physics’ and use EPS singular vectors.

8. RMSE and spread in different systems
.. but ensemble spread (dashed lines) is still substantially less than actual forecast error.
Substantial amounts of forecast error are not from the initial conditions.
Rms error of forecasts has been systematically reduced (solid lines) ….

9. Step 3: Remove systematic errors
Model drift is typically comparable to signal
Both SST and atmosphere fields
Forecasts are made relative to past model integrations
Model climate estimated from 25 years of forecasts ( ), all of which use a 11 member ensemble. Thus the climate has 275 members.
Model climate has both a mean and a distribution, allowing us to estimate eg tercile boundaries.
Model climate is a function of start date and forecast lead time.
EXCEPTION: Nino SST indices are bias corrected to absolute values, and anomalies are displayed wrt a climate.
Implicit assumption of linearity
We implicitly assume that a shift in the model forecast relative to the model climate corresponds to the expected shift in a true forecast relative to the true climate, despite differences between model and true climate.
Most of the time, assumption seems to work pretty well. But not always.

10. Plots courtesy Paco Doblas-Reyes
Biases (eg JJA 2mT as shown here) are often comparable in magnitude to the anomalies which we seek to predict
ECMWF
Met Office
Météo-France
CFS
Plots courtesy Paco Doblas-Reyes

11. SST bias is a function of lead time and season.
More recent systems have less bias, but it is still large enough to require correcting for.

12. Despite SST bias and other errors, anomalies in the coupled system can be remarkably similar to those obtained using observed (unbiased) SSTs …..

13. … and can also verify well against observations

14. Model errors are still serious …
Models have errors other than mean bias
Eg weak wind and SST variability in system 2
Strong underestimation of MJO activity
Suspected too-weak teleconnections to mid-latitudes
Mean state errors interact with model variability
Nino 4 region is very sensitive (cold tongue/warm pool boundary)
Atlantic variability suppressed if mean state is badly wrong
Our forecast errors are larger than they should be
With respect to internal variability estimates and (occasionally) other prediction systems
Reliability of probabilistic forecasts is not particularly high

15. ENSO forecast quality – Feb. starts only
ECMWF S3, 1 Feb Starts, first 3 months of forecast
Completion of TAO array
Dramatic pre/post TAO contrast is specific to these forecasts. Hypothesis is that model error usually dominates forecasts, but at this particular time of year, for this model and this forecast range, model error has negligible impact on forecasts. In this case, the role of initial condition error becomes visible, and the pre/post TAO era is clearly demarcated. At longer lead times (eg May verification), we start to get forecast errors in the post-TAO era, although June and July SSTs verify almost perfectly in the last 10 years ( ).
The striking behaviour of the forecasts plotted above was first noted using forecasts to and 2007 (the last two points above) continue the pattern of excellent recent forecasts. The forecast from 2008 looks as if it is also going to be nearly perfect, despite the challenging evolution of SST over the last few months.
Note that since the above plot was “selected” from a range of possible plots covering different seasons and lead times, there is likely to be an element of artificial skill. Nonetheless, it is believed that an important part of the apparent error reduction is real.

16. ENSO forecast quality – all start months
Model error partially masks the benefit of improved observations

17. System 3 vs Cycle 33r1
The most recent ECMWF cycles (such as 33r1, shown here) develop a too-strong cold tongue in the West Pacific. This results in a large drop in skill in SST forecasts in Nino 4. This relationship between mean-state error and forecast performance in the Nino-4 region has been seen time and again in different model versions.
The model version used for System 3 has a pretty good balance, but even it is not perfect.

18. Statistical post-processing
Red: statistically corrected System 3 forecast
Improvement is mainly seen in Nino 4, where there are clear indications of anomaly / mean-state interactions, and where state-dependent errors are visible.
(Statistical model is a cross-validated linear regression, based on initial condition SST anomaly and model predicted SST anomaly)
Not used operationally

19. Capturing trends is important. Some are handled well ….

20. … other trends are poorly handled
Global mean T at 50 hPa. The observed cooling at this altitude is mainly driven by trends in ozone, which our model does not include. The volcanic spikes of El Chichon and Pinatubo are also clear in the observed data.

21. Volcanic influence on Eurasian winters?
ECMWF System 3 hindcast
Analysed 2m T anomaly
DJF 82/83
NH winters with large volcanic aerosol in the NH look like tend to look like 82/83 and 91/92, particularly over Eurasia (based on reconstructions back to 1600). Our coupled forecasts get both these winters badly wrong (although for 91/92, the observed SST does better). Shindell et al 2004 (JGR) have modelling results to suggest volcanic aerosol impact is similar to observed pattern.
Even if no volcanoes occur in the future, our estimates of past forecast quality may need to take into account volcanic winters. ECMWF are working on including the relevant aerosol effects (historically, and in the real-time analysis an forecast system).
DJF 91/92

22. Operational seasonal forecasts
Real time forecasts since 1997
“System 1” initially made public as “experimental” in Dec 1997
System 2 started running in August 2001, released in early 2002
System 3 started running in Sept 2006, operational in March 2007
Burst mode ensemble forecast
Initial conditions are valid for 0Z on the 1st of a month
Forecast is created typically on the 11th/12th (SST data is delayed up to 11 days)
Forecast and product release date is 12Z on the 15th.
Range of operational products
Moderately extensive set of graphical products on web
Raw data in MARS
Formal dissemination of real time forecast data

23. System 3 configuration Real time forecasts:
41 member ensemble forecast to 7 months
SST and atmos. perturbations added to each member
11 member ensemble forecast to 13 months
Designed to give an ‘outlook’ for ENSO
Only once per quarter (Feb, May, Aug and Nov starts)
November starts are actually 14 months (to year end)
Back integrations from (25 years)
11 member ensemble every month
5 members to 13 months once per quarter

24. How many back integrations?
Back integrations dominate total cost of system
System 3: 3300 back integrations (must be in first year)
492 real-time integrations (per year)
Back integrations define model climate
Need both climate mean and the pdf, latter needs large sample
May prefer to use a “recent” period (30 years? Or less??)
System 2 had a 75 member “climate”, System 3 has 275.
Sampling is basically OK
Back integrations provide information on skill
A forecast cannot be used unless we know (or assume) its level of skill
Observations have only 1 member, so large ensembles are much less helpful than large numbers of cases.
Care needed eg to estimate skill of 41 member ensemble based on past performance of 11 member ensemble
For regions of high signal/noise, System 3 gives adequate skill estimates
For regions of low signal/noise (eg <= 0.5), need hundreds of years

25. Example forecast products
A few examples only – see web pages for full details and assessment of skill
Note: Significance values on plots
A lot of variability in seasonal mean values is due to chaos
Ensembles are large enough to test whether any apparent signals are real shifts in the model pdf
We use the w-test, non-parametric, based on the rank distribution
NOT related to past levels of skill

30. Other operational plots for JJA 2009

32. ( … although these are not routinely plotted)
Many other fields are available from the forecast system …
( … although these are not routinely plotted)

33. SST forecast performance
Actual rms errors > model estimate of “perfect model” errors

34. More recent SST forecasts are better ....

36. At longer leads, model spread starts to catch up

40. How good are the forecasts?
Deterministic skill: DJF ACC
Temperature: actual forecasts
Temperature: perfect model

41. How good are the forecasts?
Deterministic skill: DJF ACC
Precip: actual forecasts
Precip: perfect model

42. How good are the forecasts?
Probabilistic skill: Reliability diagrams
Tropical precip < lower tercile, JJA
NH extratrop temp > upper tercile, DJF

43. How good are the forecasts?
Probabilistic skill: Reliability diagrams
Europe: Temp > upper tercile, DJF

44. EUROSIP multi-model ensemble
Three models running at ECMWF:
ECMWF – as described
Met Office – HADCM3 model, Met Office ocean analyses
Meteo-France – Meteo-France model, Mercator ocean analyses
Unified system
Real-time since mid-2005
All data in ECMWF operational archive
Common operational schedule (products released at 12Z on 15th)
Common products
Coordinated development strategy (sort of …)
See “EUROSIP User Guide” on web for details, and also the recent ECMWF Newsletter article (Issue No. 118, Winter 2008/09)

45. Summer 2009 temperature forecast
ECMWF
EUROSIP
(See Antje’s lecture for more on multi-model ensembles ...)

46. Model error and forecast interpretation
Model error is large
It dominates El Nino forecast errors
Mean state and variability errors are very significant
Errors cannot be easily fixed
Products typically account for sampling error only
Don’t take model probabilities as true probabilities
Estimating forecast skill can be difficult
In many cases, data is insufficient to produce sensible estimates
Makes interpretation of forecasts tough
In the end we need trustworthy models
(Multi-model ensembles are small, and only partially span the space of model errors)

47. Calibrated forecasts Frequentist or Bayesian
Sampling uncertainties give rise to frequentist probabilities
Model errors mean our forecast pdfs are wrong. We can try to represent our lack of knowledge as “probabilities” in a Bayesian framework.
Calibration of probabilistic forecasts
Given the model forecast pdf, the past history of forecast pdfs, the past history of observed outcomes, what is the best estimate of the true pdf?
A Bayesian analysis depends on specification of the prior. Mathematically, no single “right” answer.
We hope one day to implement a hierarchical Bayesian analysis, accounting for the major uncertainties and producing some general purpose calibrated probabilistic forecasts.
Handling trends and non-stationarities is an additional challenge

48. Some final comments Plenty of scope for improving model forecasts
Nino SST forecasts still much worse than predictability limits
Model errors still obvious in many cases
Initial conditions probably OK in Pacific for some time, recently improved elsewhere by ARGO
Model output -> user forecast
Calibration and presentation of forecast information
Potential for multi-model ensembles
Timescale for improvements
Optimist: in 10 years, we’ll have much better models, pretty reliable forecasts, confidence in our ability to handle climate variations
Pessimist: in 10 years, modelling will still be a hard problem, and progress will largely be down to improved calibration