GFDL’s Coupled Ensemble Data Assimialtion System, 1980-2006 Coupled
Reanalysis and Its Impact on ENSO Forecasts
S. Zhang∗ , A. Rosati, M. J. Harrison, R. Gudgel and W. Stern
Geophysical Fluid Dynamics Laboratory, Princeton, New Jersey(14 February 2008)
ABSTRACT
A coupled data assimilation (CDA) system, consisting of an ensemble filter applied to GFDL’s global fully-coupledclimate model (CM2), has been developed to facilitate the detection and prediction of seasonal-to-multidecadal
climate variability and climate trends. The assimilation provides a self-consistent, temporally-continuous estimateof the coupled model state and its uncertainty, in the form of discrete ensemble members which can be used directly
to initialize probabilistic climate forecasts without initial shocks.
Then 1976-2006 real oceanic observations (XBTs,ARGOs,CTDs,MRBs,OSDs,MBTs and SSTs) and atmospheric (NCAR/NCEP) reanalyses were assimilated into the coupled ensemble system to form 24 member
atmosphere/ocean/land/sea-ice state estimates. This talk focuses on the obtained oceanic reanalysis and its impact
on ENSO forecasts. Hindcast statistics show this ensemble climate state estimate and prediction system improved
ENSO forecast skills dramatically. This happens mainly because the self-consistent ensemble initial conditions fromthis coupled assimilation system make all components of the coupled model stay in a physically-balanced state, which
help model dynamics project the initial signals onto a seasonal-interannual time scale.

1

Description of GFDL’s CDA system

Viewing the evolution of climate states as a continuous stochastic dynamical process, the GFDL’s coupled ensemble data assimilation system (Zhang et al.
2007) directly solves for a temporally-varying joint
probability density function (joint-PDF) of oceanicstates. The filtering assimilation combines the observational PDF and the prior PDF derived fromthe CGCM to produce an analysed PDF (Fig. 1).
In a super-parallelization configuration, the coupledassimilation is a continuous data-incorporation process (Fig. 2), which includes currently the atmospheric and oceanic data assimilation components(Fig. 3). Due to capturing the probabilistic natureof climate evolution, this system has been used tofacilitate the detection (Zhang et al. 2008) and prediction of seasonal-to-multidecadal climate variability and climate trends. This study addresses theestimates and forecasts of the seasonal and interannual variability in the tropical Pacific Ocean.
2*Figure 1: Cartoon of how an ensemble filter updates
the distribution for a scalar variable. The upperleft
reprsents the prior distribution derived from model ensemble integrations starting from the previous assimilation results. The upperright represents an observational
distribution (usually Gaussian). An ensemble filtering
process (lowerleft) combines the observational and priordistributions to form an updated ‘analyzed‘ distribution(lowerright) realized by the ensemble member states that
initialize next ensemble integrations.

DataOceanic observations include the real-time oceanicstates’ samples from available oceanic observing net∗ Corresponding author address: Geophysical Fluid Dynamics Laboratory, PO Box 308, Forrestal Campus, Princeton NJ 08542. USA. Shaoqing.Zhang@noaa.gov

works. They are: XBTs, CTDs, MBTs, MRBs,OSDs, Gridded sea-surface temperatures (SSTs of
the 20th-century and Argo, XBTs, MRBs, Gridded
SSTs of the 21st-century. At this time, the altimetric data have not been used.

model simulated 1.6o C. The variability of El Nino
and Southern Oscillation (ENSO) is completely reconstructed (Fig. 5).

*Figure 2: Flow-chart of the GFDL’s super-parallelized
coupled data assimilation system for 180 PEs case. Generally, this system can be scaled for any ensemble size
and any big enough processing element (PE) number.
But in practice due to efficiency consideration it is currently scaled for running 6, 12, 24 ensemble members.

*Figure 4: The RMS errors of assimilated global (green)
and tropical Pacific (red) SSTs. The corresponding freemodel simulation’s RMS errors are plotted by black-solid(global) and black-dashed (tropical Pacific) as the reference. The arrows denote the subsurface data (in situ
measurements) are throughout the period and SST observations atmospheric data are used starting from 1979
and 1981 respectively.

*Figure 3: Schematic diagram illustrating how theGFDL’s coupled model exchanges fluxes between
model components (black arrows), and constraints ofoceanic/atmospheric observations in this particular climate detection study (red arrows). The dashed green
arrow denotes the radiative forcings in the coupled system, and the dashed means that the radiative forcings
used during assimilation is set as fixed-year (1860).

*
Atmospheric data are the NCEP/NCARreanalysis gridded atmospheric variables including
wind (u,v) and temperature. The specific humidity
is a very sensitive variable for the coupled assimilation, and at this time, is not used for the coupledreanalysis.
3Figure 5: Top: Time series of observed (dashedlines) and analysed (solid lines) domain-averaged SST’s
anomalies in Nino4 (green), Nino3.4 (black) and Nino3(red). Lower 3 panels: Time series of analysed domainaveraged potential temperature anomalies in Nino4(upper-middle), Nino3.4 (lower-middle) and Nino3 (bottom). The contour interval is 0.5o C.

Results of ocean state estmates

The RMS errors of the assimilated SSTs are shownin Fig. 4. The global SST’s errors are reduced by
0.7o C from the model simulated 1.8o C. The tropical
Pacific SST’s errors are reduced by 0.4o C from the4Impact on ENSO forecasts

25 year (82-06) one-year ENSO retrospective forecasts initialized at each month have been done. The

anomaly correlation coefficients (ACC) of forecastedand observed SSTs and normalized RMS errors offorecasted SSTs are shown in Fig. 6 in forecast
leading time and initial time space. Compared tothe forecasts initialized from GFDL’s old 3D-Var
assimilations, the new coupled ensemble assimilation widens the valid forecast area (ACC > 0.6 andthe normalized RMS errors < 1.0) tremendously.
4 individual months were selected to represent theforecast skills in different seasons being shown inFig. 7 and 8. Referred to the persistent forecasts,
the new coupled ensemble assimilation improves theshort (1-4 months) forecast skills dramatically while
extending the valid leading forecast time up to 9months from the 3D-Var’s 3 months.
*Figure 7: Variations of anomaly correlation coefficientsof forecasted and observed Nino3 SSTs, produced by persistent forecast (black), 3D-Var (red), ENSF(blue). The
green line called the perfect model forecast which sets anindividual member as the “truth” and uses the ensemble
mean of the rest of members to forecast the truth.

*Figure 6: Distributions of anomaly correlation coefficients of forecasted and observed SSTs, and the normalized RMS errors of forecasted SSTs in Nino3 produced
by GFDL’s old 3D-Var system (upper) and the new coupled ensemble filter (ENSF) (lower), in forecast leading
time and initial time space. The contour interval is 0.1.

REFERENCES
Zhang, S., M. J. Harrison, A. Rosati and A. T.
Wittenberg, 2007: System design and evaluationof coupled ensemble data assimilation for global
oceanic climate studies. Mon. Wea. Rev., 135,
3541–3564.
Zhang, S., A. Rosati and M. J. Harrison, 2008:
Detection of multi-decadal oceanic variability
within a coupled ensemble data assimilation system. J. of Geophys. Res., in press.

*Figure 8: Variations of normalized RMS errors offorecasted Nino3 SSTs produced by persistent forecast(black), 3D-Var (red), ENSF (blue) and perfect model
forecast (green).