The NCEP Climate Forecast System

S. Saha^\*^, S. Nadiga^\*^, C. Thiaw^\*^, J. Wang^\*^, W. Wang^\*\*^, Q.
Zhang^\*\*^,

H. M. van den Dool^\*\*^, H.-L. Pan^\*^, S. Moorthi^\*^, D.
Behringer^\*^, D. Stokes^\*^,

G. White^\*^, S. Lord^\*^, W. Ebisuzaki^\*\*^, P. Peng^\*\*^, P.
Xie^\*\*^

Submitted to the J. Climate

**^\*^**Environmental Modeling Center

National Centers for Environmental Prediction

NWS/NOAA/DOC, Washington, D. C.

**^\*\*^**Climate Prediction Center

National Centers for Environmental Prediction

NWS/NOAA/DOC, Washington, D. C.

# Corresponding author address :

Dr. Suranjana Saha, Environmental Modeling Center,

5200 Auth Road, Camp Springs, MD 20746.

E-mail : <Suranjana.Saha@noaa.gov>

**Abstract**

The Climate Forecast System (CFS), the fully coupled
ocean-land-atmosphere dynamical seasonal prediction system that became
operational at NCEP in August 2004, is described and evaluated in this
paper. The CFS provides important advances in operational seasonal
prediction on a number of fronts. For the first time in the history of
U.S. operational seasonal prediction, a dynamical modeling system has
demonstrated a level of skill in forecasting U.S. surface temperature
and precipitation that is comparable to the skill of the statistical
methods used by the NCEP Climate Prediction Center (CPC). This
represents a significant improvement over the previous dynamical
modeling system used at NCEP. Furthermore, the skill provided by the CFS
spatially and temporally complements the skill provided by the
statistical tools. The availability of a dynamical modeling tool with
demonstrated skill should result in overall improvement in the
operational seasonal forecast products produced by CPC.

The atmospheric component of the CFS is a lower resolution version of
the Global Forecast System (GFS) that was the operational global weather
prediction model at NCEP during 2003. The ocean component is the GFDL
Modular Ocean Model version 3 (MOM3). The previous dynamical seasonal
forecast system used at NCEP consisted of the 1998 GFS (a.k.a. MRF) and
the GFDL MOM1 ocean model. In addition to the replacement of the oceanic
and atmospheric components, there are several important improvements
inherent in the new CFS relative to the previous dynamical forecast
system. These include: (i) The atmosphere-ocean coupling spans almost
all of the globe (as opposed to the tropical Pacific only); (ii) The CFS
is a fully coupled modeling system with no flux correction (as opposed
to the previous uncoupled 'tier-2' system, which employed multiple bias
and flux corrections); (iii) A set of fully coupled retrospective
forecasts covering a 24 year period (1981-2004), with 15 forecasts per
calendar month out to nine months into the future, have been produced
with the CFS. In contrast "perfect" (i.e., observed) SST was prescribed
in the production of the retrospective forecasts for the previously
operational dynamical forecast system.

These 24 years of fully coupled retrospective forecasts are of paramount
importance to the proper calibration (bias correction) of subsequent
operational seasonal forecasts. They provide a meaningful à *priori*
estimate of model skill that is critical in determining the utility of
the real-time dynamical forecast in the operational framework. The
retrospective dataset also provides a wealth of information for
researchers to study interactive atmosphere-land-ocean processes.

**Outline of the Paper**

1.  Introduction

2.  Overview of the NCEP Climate Forecast System

3.  Design of the CFS Retrospective Forecasts

4.  CFS Performance Statistics

5.  CFS Diagnostics

6.  Summary and Conclusions

7.  Operational CFS Forecasts and Availability of CFS Data

8.  References

9.  Appendix 1

10. Figure Legends

11. Figures

**1. Introduction**

It is generally assumed that the memory of the geophysical system that
could aid in seasonal climate forecasting resides mainly in the ocean.
The strong El Nino events of 1982/83 and 1997/98 appeared to provide
empirical evidence that, at least in some cases, this is indeed true
(Barnston et al. 1999). It is thus logical for the scientific community
to develop global coupled atmosphere-ocean models to aid in seasonal
forecasting. At the National Centers for Environmental Prediction (NCEP)
in Washington, D. C., coupled ocean-atmosphere models are looked upon as
an extension of existing numerical weather prediction infrastructure.
For this task, one obviously needs numerical models of both the
atmosphere and the ocean, along with their own data assimilation
systems. Global numerical prediction models for weather (and their
attendant data assimilation systems) have matured since about 1980 and
are the tool of choice today for day-to-day global weather forecasting
out to one or two weeks. On the other hand, while numerical prediction
models for the ocean coupled to an atmosphere have existed for a long
time in research mode (Manabe and Bryan 1969), such models had not been
tested in real time forecasting, nor had a data assimilation system been
developed for the ocean until the 1990's. Ji et al. (1995) described the
early data assimilation effort at NCEP (then NMC) for a tropical strip
of the Pacific Ocean using the Modular Ocean Model, version 1(MOM1),
developed at the Geophysical Fluid Dynamical Laboratory (GFDL) in
Princeton, NJ. An ocean reanalysis was performed by Ji et al. (1995) and
Behringer et al. (1998) for the Pacific basin (20°S-20°N) starting from
July 1982 onward. This provided the ocean initial conditions for coupled
forecast experiments, including retrospective forecasts.

The first coupled forecast model at NCEP in the mid-nineties consisted
of an ocean model for the Pacific Ocean, coupled to a coarser resolution
version of the then operational NMC Medium Range Forecast (MRF) model.
The atmospheric model had a spectral triangular truncation of 40 waves
(T40) in the horizontal and 18 sigma levels (L18) in the vertical (Ji et
al. 1994, 1998). In order to avoid very large biases, "anomaly flux
corrections" were applied at the ocean-atmosphere interface. The final
stand alone atmospheric forecasts were made in 'tier-2' mode, in which
the sea surface temperature fields produced during the coupled
integration were used, after more bias correction, as a prescribed time
varying lower boundary condition for an ensemble of Atmospheric General
Circulation Model (AGCM) runs. The 'tier-2' approach and its attendant
flux correction procedure is common to this day. Since the SST outside
the tropical Pacific had to be specified as well, damped persistence
became a common substitute. This early set-up of the coupled model was
known as MRFb9x for the atmospheric component, and CMP12/14 for the
oceanic component. The atmospheric component was upgraded both in
physics and resolution to T62L28 several years later (Kanamitsu et al.
2002B). This upgraded system, known as the Seasonal Forecast Model (SFM)
was operational at NCEP until August 2004.

Very few operational centers have been able to afford the development of
a coupled atmosphere-ocean-land model for real time seasonal prediction.
The European Centre for Medium-Range Weather Forecasts (ECMWF) has been
engaged in this effort along with NCEP. At ECMWF, the first coupled
model (System-1) was developed around 1996 (Stockdale et al. 1998), with
a second update (System-2) in 2003 (Anderson et al. 2003). An evaluation
against empirical models can be found in Van Oldenborgh et al. (2005).
In Europe, a large experiment is underway, called the Development of a
European Multimodel Ensemble system for seasonal to interannual
prediction (DEMETER), in which six different atmospheric models are
coupled to the same ocean model as described in Palmer et al (2005). At
most other centers, such as the International Research Institute for
Climate Prediction (IRI), the 'tier-2' system continues to be used
(Barnston et al. 2003).

The purpose of this paper is to document the new NCEP Climate Forecast
System (CFS), which became operational in August 2004. As part of the
design of the CFS, three major improvements were made to the old
operational coupled forecast system. First, the component models have
been greatly modernized. The ocean model, MOM1, has been replaced by
MOM3, and the atmospheric model, SFM, has been replaced by a coarse
resolution version of the operational (as of 2003) NCEP Global Forecast
System (GFS). Most notably, this change includes an upgrade in vertical
resolution from the old SFM, from 28 to 64 sigma layers. Second, the
ocean-atmosphere coupling is now nearly global (64°N-74°S), instead of
only in the tropical Pacific Ocean, and flux correction is no longer
applied. Thus, the CFS is a fully 'tier-1' forecast system. The coupling
over the global ocean required an important upgrade in the ocean data
assimilation as well (see Behringer et al. 2005). Third, an extensive
set of retrospective forecasts ('hindcasts') was generated to cover a 24
years period (1981-2004), in order to obtain a history of the model.
This history can be used operationally to calibrate and assess the skill
of the real-time forecasts. Hindcast histories that were generated to
assess the skill of all previous tier-2 seasonal forecast systems in use
at NCEP were obtained by prescribing 'perfect' (observed) SST. This
methodology is often assumed to provide an 'upper limit of
predictability.' However, this method did not provide an accurate
estimate of the skill of the tier-2 operational model, which used
predicted, not 'perfect' SST. This methodology is still being practiced
elsewhere to determine the 'skill' of multi model ensembles, etc. In the
current CFS system, the model skill is assessed solely by the use of a
tier-1 retrospective set of forecasts.

The first two items include several advances in physics and a much
better coupled system, both in multi-decadal free runs (Wang et al.
2005) and in nine month forecasts from many initial conditions.
Specifically, the ENSO simulation and the synoptic tropical activity
(Madden Julian Oscillations, easterly waves, etc.) appear state of the
art in the CFS with 64 vertical levels. The third item, while costly in
terms of computer time and resources, is especially important to the
user of the model in that a robust measure of skill is provided.

The lay-out of the paper is as follows: In sections 2 and 3 we describe
the components of the CFS and the organization of the hindcasts
respectively. In section 4 we discuss the CFS performance for its main
application as a monthly/seasonal forecast tool. In section 5 we present
some diagnostics highlighting strengths and systematic errors in the
CFS. Summary and conclusions are found in Section 6.

**2. Overview of the Climate Forecast System**

The atmospheric component of the CFS is the NCEP atmospheric GFS model,
as of February 2003 (Moorthi et al. 2001). Except for having a coarser
horizontal resolution, it is the same as that used for operational
weather forecasting with no tuning for climate applications. It adopts a
spectral triangular truncation of 62 waves (T62) in the horizontal
(equivalent to nearly a 200 Km Gaussian grid) and a finite differencing
in the vertical with 64 sigma layers. The model top is at 0.2 hPa. This
version of the GFS has been modified from the version of the NCEP model
used for the NCEP/NCAR Reanalysis (Kalnay et al. 1996 ; Kistler et al.
2001), with upgrades in the parameterization of solar radiation transfer
(Hou, 1996 and Hou et al. 2002), boundary layer vertical diffusion (Hong
and Pan 1996), cumulus convection (Hong and Pan 1998), gravity wave drag
(Kim and Arakawa 1995). In addition, the cloud condensate is a
prognostic quantity with a simple cloud microphysics parameterization
(Zhao and Carr 1997, Sundqvist et al. 1989, Moorthi et al. 2001). The
fractional cloud cover used for radiation is diagnostically determined
by the predicted cloud condensate.

The oceanic component is the GFDL Modular Ocean Model V.3 (MOM3)
(Pacanowski and Griffies 1998), which is a finite difference version of
the ocean primitive equations under the assumptions of Boussinesq and
hydrostatic approximations. It uses spherical coordinates in the
horizontal with a staggered Arakawa B grid and the z-coordinate in the
vertical. The ocean surface boundary is computed as an explicit free
surface. The domain is quasi-global extending from 74°S to 64°N. The
zonal resolution is 1°. The meridional resolution is 1/3° between 10°S
and 10°N, gradually increasing through the tropics until becoming fixed
at 1° poleward of 30°S and 30°N. There are 40 layers in the vertical
with 27 layers in the upper 400 m, and the bottom depth is around 4.5
Km. The vertical resolution is 10 m from the surface to the 240-m depth,
gradually increasing to about 511 m in the bottom layer. Vertical mixing
follows the non-local K-profile parameterization of Large et al. (1994).
The horizontal mixing of tracers uses the isoneutral method pioneered by
Gent and McWilliams (1990) (see also Griffies et al. 1998). The
horizontal mixing of momentum uses the nonlinear scheme of Smagorinsky
(1963).

The atmospheric and oceanic components are coupled with no flux
adjustment or correction. The two components exchange daily averaged
quantities, such as heat and momentum fluxes, once a day. Because of the
difference in latitudinal domain, full interaction between atmospheric
and oceanic components is confined to 65°S to 50°N. Poleward of 74°S and
64°N, SSTs needed for the atmospheric model are taken from observed
climatology. Between 74°S and 65°S, and between 64°N and 50°N, SSTs for
the atmospheric component are weighted average of the observed
climatology and the SST from the ocean component of the CFS. The weights
vary linearly with latitude, such that the SSTs at 74°S and 64°N equal
observed climatology and the SSTs from 65°S and 50°N equal values from
the ocean component. Sea ice extent is prescribed from the observed
climatology.

The ocean initial conditions were obtained from the Global Ocean Data
Assimilating System (GODAS) (Behringer, et al. 2005), which was made
operational at NCEP in September 2003. The ocean model used in GODAS is
the same as used in the CFS retrospective forecasts. The ocean data
assimilation system uses the 3-D variational technique of Derber and
Rosati (1989), modified to include vertical variations in the error
covariances (Behringer et al., 1998). The ocean model in GODAS was
forced with weekly fluxes of heat (Q), surface buoyancy fluxes (E-P) and
wind stress vectors (τ) from NCEP Reanalysis-2 (Kanamitsu et al. 2002A).
Also, a relaxation technique (with a relaxation time scale of 90 days)
was used to relax the simulated GODAS sea surface temperatures to
Reynolds SST (Reynolds and Smith 1994), and the sea surface salinity
fields were relaxed to Levitus climatological monthly fields of sea
surface salinity (Levitus et al. 1994). The subsurface temperature data
that were assimilated were obtained from expendable bathythermographs
(XBTs), the tropical atmosphere-ocean (TAO) array of moored buoys, and
the ARGO network of floats. As shown in Maes and Behringer (2000) and Ji
et al. (2000), the subsurface salinity variability strongly influences
the density stratification in the ocean through the formation of
salt-stratified barrier layers, especially in the western and central
equatorial Pacific Ocean. Therefore, a climatological
Temperature-Salinity (T-S) relationship was imposed to correct the
subsurface salinity profiles in the model runs.

For the land surface hydrology the two layer model described in Mahrt
and Pan(1984) is used here.

**3. Design of the CFS Retrospective Forecasts**

The CFS includes a comprehensive set of retrospective runs that are used
to calibrate and evaluate the skill of its forecasts. Each run is a full
nine month integration. The retrospective period covers all 12 calendar
months in the 24 years from 1981 to 2004. Runs are initiated from 15
initial conditions that span each month, amounting to a total of 4320
runs. Since each run is a nine month integration, the CFS was run for an
equivalent of 3240 years! Due to limitations in computer time, only 15
days in the month were used as initial conditions. These initial
conditions were carefully selected to span the evolution of both the
atmosphere and ocean in a continuous fashion.

The atmospheric initial conditions were from the NCEP/DOE Atmospheric
Model Intercomparison Project (AMIP) II Reanalysis (R2) data (Kanamitsu
et al. 2002A), and the ocean initial conditions were from the NCEP
Global Ocean Data Assimilation (GODAS) (Behringer 2005). Each month was
partitioned into 3 segments. The first was centered on the pentad ocean
initial condition of the 11^th^ of the month, i.e. the 5 atmospheric
initial states of 9^th^, 10^th^, 11^th^, 12^th^ and 13^th^ of the month
used the same pentad ocean initial condition of the 11^th^. The second
set of 5 atmospheric initial states of 19^th^, 20^th^, 21^st^, 22^nd^
and 23^rd^ of the month used the same pentad ocean initial condition of
the 21^st^ of the month. The last set of 5 atmospheric initial states
include the second-to-last day of the month, the last day of the month,
and 1^st^, 2^nd^ and 3^rd^ days of the next month used the same pentad
ocean initial condition of the 1^st^ of the next month. These 15 runs
from the retrospective forecasts form the ensemble that is used by
operational forecasters for calibration and skill assessment for the
operational monthly seasonal forecast at NCEP. Note that no
perturbations of the initial conditions are applied for making the
ensemble forecast. The perturbations come automatically by taking
atmospheric states one day apart, but this may not be optimal.

A hypothetical example is the official forecast made by the Climate
Prediction Center (CPC) of NCEP around the 10^th^ of February. February
is then considered to be the month of forecast lead zero, March is the
month of forecast lead one, and so on. Runs originating from initial
conditions after the 3^rd^ of February from the retrospective forecasts
are not considered for calibration of the February forecasts. This is
done because in 'operations' there is a 7-day lag in obtaining the ocean
initial conditions (see Section 7 that explains the design of
operational CFS forecasts). The 15 members in the ensemble thus include
9^th^ - 13^th^ January, 19^th^ - 23^rd^ January, and 30^th^ January -
3^rd^ of February. This method of calibration and subsequent skill
assessment is used throughout this paper in order to replicate the
operational procedures used at NCEP and to provide the most accurate
assessment possible of the CFS skill to the forecasting community.

It is important to note that the CFS model codes were 'frozen' in June
2003. The running of the entire retrospective forecasts and operational
implementation of the CFS that took nearly a year, were made with these
codes. No changes or tuning for results were made to these codes during
the execution of the forecasts. These forecasts truly represent the
"history" of the operational CFS.

**4. CFS Performance Statistics**

In this section we review the performance of CFS retrospective
forecasts, mainly in terms of skill as measured by the anomaly
correlation (AC) against observations. We refer to the Appendix 1 for
details about definitions, and the adjustments necessary in using the AC
in the context of (i) systematic error correction and (ii)
cross-validation, which has been adhered to in computing the results
that are presented in this paper. In this section we correct for the
overall mean error by subtracting the model climatology from model
forecasts. See details in Appendix.

We focus on , in order, the prediction of SST in the Nino3.4 area
(5S-5N;170W-120W) of the tropical Pacific, SST in mid-latitudes, surface
air temperature, precipitation, 500 hPa geopotential and soil moisture.
In all cases we verify either monthly or seasonal mean values. In most
cases we verify the bias corrected ensemble mean averaged over the 15
ensemble members. In some cases, we also compare to other tools : either
a previous model or some statistical tools that are being used by CPC.
When we quote scores for 1981-2003 this includes verifying data well
into 2004 for the longer lead forecasts starting in 2003.

Fig 1 shows the skill (anomaly correlation) of the Nino3.4 SST forecasts
over the period 1981-2003. Nino3.4 SST is probably the single most
predictable entity. We use here, and in many graphs below, a display of
forecast lead in months (on the Y-axis) versus the [target]{.underline}
or verification month (on the X-axis). Forecasts for December and
January exceed 0.9 in correlation for leads out to 5 months, i.e. these
forecasts were initiated during the previous summer. However, forecasts
for the Northern Hemisphere summer months, most notably for July, are
more difficult, with correlations as low as 0.4 at leads of 7 months.
The sudden drop in skill near April is known as the spring barrier. A
display of forecast lead versus [initial]{.underline} month (not shown)
shows a "return of skill", because the decay of skill with lead time is
interfered with by a strong seasonality of the errors.

CPC has maintained an archive of Nino3.4 SST predictions ***in real
time***. Fig. 2 shows the overall scores as a function of forecast lead
for seasonal Nino3.4 SST prediction by various methods from 1997 to the
present. The correlations shown are evaluated on all cases in the
period. The CFS, the only retrospective method in this display, is shown
by red bars. The other methods are NCEPs previous coupled model and
labeled CMP14, the Canonical Correlation Analysis (CCA) (Barnston and
Ropelewski 1992), Constructed Analogue (CA) (Van den Dool 1994), the
'Markov' method (Xue et al. 2000) and a Consolidation (CON) of all
methods available in real time (Unger et al. 1996). The CFS results, if
achieved in real time, would easily have been competitive with all the
other methods and, in fact, would have been a big improvement over the
CMP14. The main reason CON did worse than the best single method is that
CMP14 scored much lower over 1997 onward than anticipated, based on its
1982-96 evaluation. This illustrates the importance of an evaluation
that will hold up on independent data.

Fig 3 is the same as Fig 1, except that the ensemble mean over 14
members is verified against the one member left out. This procedure
measures [potential predictability]{.underline} under perfect model
assumptions. Although scores for Nino3.4 SST are already very high,
there is a suggestion of large improvements still ahead, especially in
summer.

Ever since Barnston et al. (1994), the standard has been the performance
of Nino 3.4 SST prediction at a lead of 6 months. As an example, for
initial conditions in April, Fig.4 shows, as a time series, the
observations and forecasts (by CFS, CMP-14 and CA) for the following
November. Relative to Fig.2 we note that the CFS not only has an overall
high correlation, but also maintains amplitude in the forecast better
than the other methods .

In Figs 1-3 the variable to be verified was averaged in space to be
consistent with the Nino34 'index'. Below we report traditional skill
estimates as per anomaly correlations, without any space averaging. Keep
in mind that scores for the Nino34 area would drop by 0.05 to 0.1 or so
if the space averaging is not applied.

The CFS is the first NCEP coupled model for the near global oceans.
While the main skill continues to be in the tropical Pacific, we can now
begin to evaluate where we stand, for instance, in the prediction of
mid-latitudes SST. Although much less than Nino3.4, Fig. 5 shows
appreciable skill in SST forecasts for most target months at short leads
in the NH, an area defined as all ocean grid points north of 35°N (no
spatial mean). At longer leads, the skill in the NH pales in comparison
to Nino3.4, and only February and March have a slight measure of skill
out to a few months. We speculate this may well be due to mid-latitude
atmospheric teleconnection patterns related to the tropics, strongest in
February, leaving a mark on the mid-latitude oceans.

Fig. 6 is as Fig 5, but now showing the potential predictability of
mid-latitude SST. Improvement is seen (and can be expected under perfect
model assumptions) for many leads, but fundamentally the mid-latitudes
appear less predictable than the tropical Pacific.

The SST forecasts, except for some marine interests, are not in, and of
themselves, of great practical importance. We now move to weather
elements over land, as well as 500hPa geopotential (Z500) and soil
moisture as an aid in interpreting the practical skill of the CFS. Fig.7
shows the skill of monthly mean (ensemble mean) surface air temperature
at 2 meters above ground (T2m) and precipitation (P) over the
extratropical NH land north of 22.5N. Already at lead 1, these skills
are extremely low, and only in summer for T2m, and winter for
precipitation, is there a suggestion of non-zero correlation (for all
grid points combined). These numbers obviously improve a little when
3-month means are used or specific regions are considered (not shown).

Fig. 8 shows similar displays of skill for monthly mean 500mb height and
soil moisture in the upper 2 meter soil. Skill for 500mb height is quite
low in NH extratropics, and only worth mentioning in the NH winter
months. Notice also the significant error bars on correlations which are
very low for a field with few degrees of freedom, resulting in a noisy
picture.

Fig. 8 also shows very high skill for soil wetness. While this skill
relates mainly to high persistence, it nevertheless conveys information
about the initial condition to the lower atmosphere which is known
several months ahead of time. It appears that the summer skill in T2m is
caused by soil wetness, while the winter skill in P is consistent with
the skill in circulation (Z500). The words 'coupled model' should be
thought of as including the coupling to the soil also. Potential
predictability estimates (not shown) confirm the idea of skill for P in
winter and T2m in summer, although we cannot report anything above 0.35
(domain averaged) in correlation, thus suggesting a low predictability
ceiling.

Figs. 9 and 10 show the spatial distribution of the anomaly correlation
at lead 1 month of the seasonal mean for T2m (Fig.9) and P (Fig.10) over
the United States, averaged over June, July and August (JJA) on the left
and December, January and February (DJF) on the right respectively.
Local correlations less than 0.3, deemed insignificant in CPC operation,
are not contoured. In JJA, the skill is restricted to the Northwest for
both P and T2m, while most of the country has no demonstrable skill. In
DJF, the skill is better, and situated mainly across the south for P,
and in weaker form across both the north and the south for T2m. The DJF
picture of skill would be consistent with ENSO composites, i.e. mainly
from years like 1982/83 and 1997/98. Skill for P in Florida in DJF is
exceedingly high. Fig. 9 and 10 also address the issue of ensemble size.
From top to bottom they show the usage of 5, 10, and 15 members for
making the ensemble mean, respectively. Although the pattern should
stabilize more for 15 members, one can observe that, leaving details
aside, the 5 member ensemble has a similar distribution of skill in
space. This is a demonstration that the CFS has reasonably stable skill.

Figs.11 and 12 are similar to Figs. 9 and 10, except that we now compare
the 15- member ensemble mean (left column) to one of CPC's control
statistics, the CCA (Barnston 1994) in the right column. The comparison
is only coarse, since CCA is available for a much longer period
(1942-2002). Fig. 11 is for lead 1 seasonal T2m and Fig. 12 is for
seasonal P forecasts for the four 'official' seasons of March-April-May
(MAM), June-July-August (JJA), September-October-November (SON) and
December-January-February (DJF). We now face these questions: Does the
CFS have skill ? And if so, does it (or CCA for that matter) add any
skill over and above what we know already from other methods ? The
latter is a subtle (difficult) issue when skill is low and especially
when there are many methods. In Figs. 11 and 12 it is encouraging that
CFS and CCA skill do not always occur at the same geographical location,
i.e. they appear complementary. Even when identical skill occurs at the
same spot there is a possibility that the skillful forecasts happen in
different years due to different predictor information being exploited,
such that a combination of CCA and CFS may score higher. If the source
of skill is the same (and it often is) it will be hard to improve upon a
single tool. This topic of consolidation (Van den Dool and Rukhovets
1994 ; Peng et al. 2002) will be the subject of future studies. On the
first question (does CFS have skill?), Figures like Figs 11 and 12
should aid the CPC forecasters. In areas left blank there is no skill.
In areas of correlation \>=0.3 there is evidence of skill in proportion
to the correlation.

The situations most relevant to society are 'extremes', and so we close
this section with a few comments about skill of the forecasts when
extremes were observed (Saha 2004). We define extreme here as anomaly
larger than 2 standard deviations. We then calculate the anomaly
correlation over this small sample of cases (extremes of either sign).
Fig. 13 shows the skill as a function of lead and target month when a
monthly T2m extreme was observed in one of the four quadrants of the US
(defined by 100°W and 40°N). Fig.14 is the same, but now for P. There is
some skill, with correlations numerically higher than in Fig. 7, but
noisier because the sample is smaller. Skill in T2m extremes is mainly
in summer, while skill in P resides mainly in winter, in rough agreement
with full sample results in Fig.7. This analysis is not complete. A more
complete study of extremes is needed, including analysis and
verification of cases where the model forecasts an extreme.

**5. CFS Diagnostics**

In this section we present assorted analyses of model behavior and
errors. The emphasis here is on physical interpretation and a route to
possible model improvements.

**(a) Model Climate Drift**

The model climate drift refers to the evolution with forecast lead time
of the deviation of model climatology from observed climatology. Here
the climatology for a specific season is defined as the average of the
seasonal means over the retrospective period (1982-2004). For the model,
the seasonal means are from the retrospective forecasts for that season.
For observations, the SST is from the optimally interpolated (OI) SST
dataset (Reynolds et al, 2002), the precipitation is from the CPC Merged
Analysis of Precipitation (CMAP) Xie-Arkin dataset (Xie and Arkin 1997),
and the 200hPa height is from the Reanalysis-2 (Kanamitsu et al. 2002A).
(In general we use GODAS for verification and validation, but in section
5(a) the OI-SST is used in favor of GODAS' sea-water temperature at 5
meter depth.)

Fig. 15 exhibits the model climate drift in SST for DJF and JJA seasons
and for 3-month lead and 6-month lead retrospective forecasts
respectively. It is evident that the bias for the DJF season and 3-month
lead (see panel 15b) is quite modest. In most areas of the global oceans
it is less than 0.5^o^C. Stronger bias occurs only in the small areas of
the eastern equatorial Pacific and equatorial Atlantic and along the
coasts (particularly the west coasts) of major continents in middle and
higher latitudes. For the 6-month lead retrospective forecasts (see
panel 15c), the bias gets slightly stronger in the tropical Pacific and
Indian oceans, indicating the tropical oceans drift away more as lead
time increases. For the JJA season, the SST bias in the tropics is
comparable to the DJF season, but in middle and higher latitudes,
particularly in the northern hemisphere, it is much stronger. Warm
biases with magnitude reaching or exceeding 2^o^C are seen across the
North Pacific and North Atlantic in higher latitudes. As lead time
increases from 3-month to 6-month (see panel 15e and 15f), the weak cold
biases in the middle latitudes of Pacific get stronger, but
interestingly, the cold biases in the equatorial Pacific becomes weaker.

Fig. 16 shows the same model climate drift but now for precipitation
rate. Evidently the major biases are in the tropics, no matter what
season or what forecast lead. For the DJF season (panel 16a and 16b),
the biases are characterized by dryness over the equatorial oceans and
in the South Pacific Convergence Zone (SPCZ) area, and wetness along the
flanks of the dry areas. . This corresponds to a north and eastward
shift in the tropical Pacific precipitation. The biases get stronger as
the lead time increases, similar to the situation with SST. For the JJA
season (panel 16c and 16d), the dryness happens mainly in the western
tropical Pacific Ocean and in the eastern Indian Ocean. The wetness
patterns are similar to the DJF season, except in the South Atlantic
Ocean where the errors in JJA are less

Fig. 17 is for the model climate drift in 200 hPa eddy geopotential. As
expected, the major features of the bias are in the extra tropics. For
the DJF season (panel 17a and 17b), the positive bias in the western and
northwestern Pacific and its downstream wave train-like patterns
suggests the geopotential bias in the northern hemisphere is tropically
forced (Peng et al. 2004). For the JJA season (panel 17c and 17d), the
wave train features are still discernable, though less obvious. In the
Atlantic sector and to a lesser degree the Pacific sector, there is
large underestimation of the standing wave pattern causing the flow to
be too zonal.

**(b) SST Bias**

SST climatology has been a concern in climate simulation and prediction
because latent heat anomalies, a major driving force of seasonal
atmospheric circulation anomalies, depend not only on the SST anomalies
but also on the time-mean condition of the ocean surface. Here we focus
on the forecast bias of SST in the tropical Pacific Ocean, the most
important and predictable factor affecting extratropical seasonal
climate. Fig. 18 shows the 2°S-2°N average of SST bias in just the
Pacific Ocean for January, April, July and October 19-23 initial
conditions over the retrospective period of 23 years (1981-2003).
Results from other initial days of each month are similar. There exists
a large cold bias from 150°E to 110°W in target months from July to
January (mainly August to October) in the forecast from January, April,
and July initial conditions. A weaker cold bias is seen in target months
from January to April in the forecast from July, October, and January
initial conditions. Forecasts from all initial months show a warm bias
close to the eastern boundary of the equatorial Pacific in target months
from May to October. The causes in model physics for these SST biases
are not clear. Some preliminary diagnostics indicate that the cold bias
in target months from July to January in the forecast from January,
April, and July initial conditions is probably associated with the
too-strong easterly momentum flux in the central eastern Pacific which
results in cold temperature advection.

Fig. 19 compares forecast time-mean surface momentum flux and
precipitation in June from observational analysis (panel 19a) to that of
the forecast from April initial conditions (panel 19b). The differences
between analysis and forecast are considered to be mainly due to model
physics in the atmospheric component of the CFS because tropical SST
bias in the June forecast from April initial condition is small. It is
seen that the easterly momentum flux errors in the forecast appear to be
associated with the ITCZ precipitation band which is too strong compared
to the observational CMAP analysis. Further diagnostics and additional
experiments are needed to find out which part of the model physics is
responsible for the SST biases.

**(c) Ocean Fields**

In this section, we analyze the most important prognostic variables in
the ocean, the subsurface temperature (T), zonal velocity (U), vertical
velocity (W), and heat content (H), produced by the ocean component of
the CFS. Our analysis focuses on the equatorial Pacific Ocean, the
domain in which the regularly occurring El Nino-Southern Oscillations
(ENSO) is most active. Specifically, we are interested in the faithful
reproduction of the structure of the seasonal thermocline in the
equatorial Pacific and the zonal velocity structure of the upper ocean.
While considerable information can be gleaned from analysis of the
individual members of the 15-member ensemble, we only plot and analyze
ensemble mean fields in this section.

The climatological structure of the temperature field in the equatorial
Pacific Ocean is plotted for the winter (DJF) and summer (JJA) seasons
from GODAS in Fig. 20. The plot shows the warm pool region (\> 28°C) in
the Western Pacific extending to the international date-line in winter
and to 160°W in summer. In winter, the 20°C isotherm, which is usually
considered to be a proxy for the depth of the thermocline (McPhaden et
al. 1998), shoals from approximately 160 m at its deepest point in the
western Pacific (140°E) to 60 m at the eastern Pacific (Nadiga et al.
2004). In the summer, the 20°C isotherm is deeper in the western Pacific
than in winter, but the situation is reversed in the eastern Pacific
with the shallowest depths being less than 50m at the eastern edge of
the basin. In winter, the SST are everywhere warmer than 25°C in the
equatorial Pacific, but the cold tongue region extends further west than
in summer. All these well-known features are well represented in the
GODAS. In the middle and bottom panels in Fig.20 (b and e), the
differences between the retrospective forecasts and GODAS are plotted
for winter (left) and summer (right) seasons. The color bar used in the
middle and bottom panels is different from that used in the top panel,
and runs from --1.5°C to 1.5°C. As shown in Fig. 20, the differences are
small for the most part, and are typically less than 1°C. The greatest
differences can be seen above the seasonal thermocline and in the
barrier layer below the seasonal thermocline, indicating the effect of
errors in vertical mixing in the ocean model. Notice that the
retrospective forecasts are typically colder than GODAS, except in the
region just above and below the 20°C isotherm. While the difference
pattern grows from lead 3 to lead 6 for both winter and summer seasons,
the difference pattern is quite different for winter and summer. We
suspect the difference patterns do not result from inbuilt trends in the
ocean model, but due to errors in ocean-atmosphere coupling in the
retrospective forecasts. In the eastern Pacific, these forecasts are
anomalously cold compared to GODAS, and this is because of too-strong
vertical upwelling in that region.

Planetary waves in the equatorial Pacific Ocean play an important role
in setting the periodicity and duration of ENSO events (Schopf and
Suarez 1988). Thus it is important that the mean zonal velocity in the
retrospective forecasts be examined for any systematic biases when
compared to observations. The climatological zonal velocity in the
equatorial Pacific is plotted in Fig. 21 for winter (upper left panel)
and summer (upper-right panel) seasons for GODAS. The strong eastward
velocities in the undercurrent are shown clearly in both seasons. The
wind-driven westward velocities in the surface layer are stronger in
winter than in summer, while the eastward velocities in the undercurrent
are stronger in summer. The core of the undercurrent tilts upwards and
eastwards, with the largest velocities (approximately 1m s^-1^) being
reached in the core of the undercurrent at around 100 m at 140°W. Zero
zonal velocities are found in regions between the North Equatorial
current (NEC) and the undercurrent and below the undercurrent. In the
warm pool region, strong westward currents are found in summer, possibly
indicating the effect of Rossby waves impinging on the western edge of
the Pacific Basin. In the middle and bottom panels, the differences
between the retrospective forecasts and GODAS are plotted for leads 3
and 6 months. As was found in the temperature differences, we find that
the difference patterns grow with lead time, and these patterns are
quite different for summer and winter seasons. In winter, the largest
differences are found in the undercurrent region, and the forecast
eastward velocities are generally larger than GODAS. In the surface
layers of the eastern Pacific, the wind-driven westward velocities are
much larger than in GODAS, indicating that the surface fluxes are in
error there.

The climatological vertical velocities in the equatorial Pacific Ocean
are plotted in Fig. 22 for the winter (upper left panel) and summer
(upper-right panels) for GODAS. The values shown in the figure are in mm
hour^-1^ . The most important feature shown in the upper panels is the
upwelling in the eastern Pacific. The upwelling velocities are larger in
winter than in summer and reach a maximum of approximately 10 cm
hour^-1^. The negative vertical velocities are largest all through the
water column below the warm pool, indicating the effect of downwelling
Rossby waves. In both seasons, the eastward transport of mass results in
strongly-positive horizontal velocity divergence in the undercurrent
region. This mass transport divergence causes strong upwelling
velocities above the thermocline and strong downwelling velocities below
the thermocline in the

Eastern Pacific. The middle and bottom panels show differences between
GODAS and retrospective forecasts for leads 3 and 6 months for winter
and summer seasons. Unlike the difference plots for temperature and
zonal velocity, the differences here are similar for winter and summer,
indicating that errors in the divergence of surface winds and not errors
in oceanic mixing are the primary cause of these differences. The most
striking and noticeable feature in the middle and bottom panels is the
anomalously large vertical velocities in the entire water column in the
eastern Pacific. In the center of the ocean basin, anomalously large
negative velocities are found. The water that upwells in the eastern
part of the basin is forced westward by the surface wind stress and
sinks in the center of the basin. It should be noted that because the
temperatures in the surface layer in the eastern Pacific are colder in
the forecasts than in GODAS (see Fig. 20), the negative heat advection
due to vertical upwelling is reduced.

The heat content of the upper ocean is an important diagnostic variable
in the context of seasonal weather prediction. The recharge-discharge
oscillator theory (Jin 1997) holds that anomalous buildup of heat
content is a prerequisite for the occurrence of El Nino, and the
equatorial Pacific ocean is purged of excess heat content during the
warm event. The zonally-integrated warm water volume above the 20°C
isotherm has been shown to correlate closely to the Nino 3.4 SST
(McPhaden 2004).

In Fig. 23, the heat content of the upper Pacific Ocean (integrated over
the top 460m) is plotted for the boreal winter (upper-left panel) and
summer (upper-right) seasons.

The plots show the well-known double-gyre structure in the Pacific
Ocean, with the maximum values recorded in the center of the gyres. The
ITCZ located at approximately 10°N demarcates the northern edge of the
south Pacific gyre and the southern edge of the north Pacific gyre, with
approximately 5 degrees in latitude separating the two gyres. It is
clear from the plot that the warm pool region contains more thermal
energy in the boreal winter than in summer. The differences between the
retrospective forecasts and GODAS is plotted in the middle and bottom
panels for leads 3 and 6 months and presents a heartening picture. The
differences between the forecasts and GODAS are typically less than 5 %
in most regions of the Pacific Ocean, and are especially small on the
equator. The difference patterns are similar for winter and summer
seasons and indicate that the largest errors are found in the ITCZ. The
heat content in the forecasts is anomalously warm south of the ITCZ and
cold north of the ITCZ, indicating that errors in the divergence of the
Ekman heat flux are the cause of the heat content errors. In general,
however, Fig. 23 indicates that the forecasts are able to accurately
reproduce the upper ocean heat content in the equatorial Pacific ocean
even for leads of 6 months and beyond. The fidelity of the forecast
upper ocean heat content to the observed values is an important reason
the retrospective forecast system is able to accurately predict ENSO
events as is seen in Figure 24. Here, the heat content anomalies are
computed and plotted for GODAS and for forecasts of leads of one, five
and nine months. The anomalies were smoothed by applying a running
average filter over the signal, with weights one, three and five applied
to months two, one and zero before and after the current month. Fig. 24
clearly shows the three strongest warm ENSO events in the past 23 years
(1982-83, 1987-89 and 1997-98). From the plots, it is clear that the
heat content anomaly was strongest for the 1982-83 and 1997-98 ENSOs in
both GODAS and forecasts. The eastward propagation of the warm anomalies
by downwelling Kelvin waves during the 1982-83, 1987-88, 1991-92,
1997-98 and 2000-02 warm events is accurately reproduced in GODAS and
forecasts. Also, the 1983-84, 1988-89, 1998-99 cold events are
reproduced accurately by the forecasts, and the lead nine month
forecasts faithfully reproduce all the above events with minimal
distortion. One exception is the warming in the eastern Pacific in 1995.
The CFS progressively downgrades the intensity of this warming until it
is no longer seen in the forecast for 9 months.

**(d) Stratosphere**

Although not an item of great practical interest, the forecasts for the
stratosphere are a great challenge scientifically because modeling the
QBO is very difficult. Fig. 25 shows the skill of stratospheric
forecasts from the CFS, by looking at the status of the QBO in the model
as a function of lead time from zero to eight months. While the QBO
phenomenon disappears with an e-folding of close to one year in the CFS,
one can still clearly see it in the eight month forecasts. This appears
to be better than in previous models. Especially near 50 hPa, where
there are many levels in the vertical, the forecasts of the zonal mean
of the zonal wind in the tropics is considerably better than persistence
(which is zero after one quarter period).

**(e) Atmospheric indices**

It is common to report on skill in atmospheric teleconnections patterns.
Even when overall skill is low, the projection onto (observed patterns
of) the North Atlantic Oscillation (NAO) and the Pacific North American
pattern (PNA) may show slightly better skill by virtue of the spatial
averaging implied in calculating the projections. Indeed one can amplify
the scores reported in Fig.8(top) for winter months by filtering the
fields and retaining only NAO and PNA. Fig.26 shows the time series of
NAO and PNA for January and February, lead 1 monthly ensemble mean
forecasts, along with the observations. We find correlations of around
0.4. In other months skill is negligible. This appears consistent with
results by ECMWF (Palmer et al 2005).

**6. Summary, Conclusions and Discussion.**

In this paper, we describe the new operational NCEP global coupled
ocean-atmosphere model, called the Climate Forecast System or CFS. The
component models are the 2003 NCEP atmospheric global weather prediction
model, called the GFS, but at reduced resolution T62L64, and the GFDL
MOM3 ocean model. The coupling is once a day using daily mean fluxes.
The CFS became operational in August 2004. Apart from the countless
modernizations inherent in replacing the atmospheric and ocean models by
newer versions, the improvements relative to the previous coupled model
include specifically (i) near global atmosphere-ocean coupling (as
opposed to tropical Pacific only), (ii) a fully coupled system with no
flux correction (as opposed to a 'tier-2' system with multiple bias and
flux corrections), and (iii) a comprehensive set of fully coupled
retrospective forecasts covering the period 1981-2004, with 15 forecasts
per calendar month, for forecast leads out to nine months into the
future.

Since the CFS model is used for operational seasonal prediction at CPC,
the 24 year retrospective forecasts, an effort which amounts to an
integration of the system for nearly 3300 years, is of paramount
importance for the proper calibration of subsequent real time
operational forecasts.

The CFS has an acceptably low bias in tropical SST prediction, and a
level of skill in forecasting Nino3.4 SST that is comparable to
statistical methods used operationally at CPC, and is a large
improvement over the previous operational coupled model at NCEP. Skill
in predicting SST in the mid-latitudes (not done before) is much less
than in the tropics, and at longer leads there is some skill only in
winter. Skill for monthly and seasonal mean temperature and
precipitation over NH land, and the US in particular, is modest, but
still comparable to the statistical tools used operationally at CPC and
not unlike a similar model at ECMWF (Van Oldenborgh et al. 2005). Skill
in precipitation is mainly in winter (ENSO related), while skill in
temperature is mainly in summer, when soil moisture anomalies
(initialized by Reanalysis-2, which used observed precipitation during
the analysis procedure) appear helpful. Certainly the notion 'coupled'
model also refers to land-atmosphere interactions.

Model behavior is reported here mainly in terms of biases or climate
drift in global SST, precipitation, 200 hPa geopotential, surface wind
stress, and subsurface oceanic fields. In the tropical Pacific the
climate drift, while small in general, is strongest in
August-September-October, even at very short lead. Some of the
mid-latitude atmospheric biases appear to be forced by tropical
precipitation biases. Oceanic climate drift, relative to the global
ocean data assimilation, from the surface to depths of nearly 500 meters
is discussed for temperature and ocean currents. In most cases, the
atmospheric forcing of the ocean appears to cause climate drift in the
ocean. For instance, too much upwelling in the east Pacific is caused by
overly strong wind stress.

Other validation efforts of the CFS, not shown but described here,
include (a) much improved tropical atmosphere-ocean, (b) reasonable
variability around the model climate, (c) apparent skill in forecasting
vertical shear in the equatorial Atlantic, and (d) the prediction of the
Quasi Biennial Oscillation (QBO). Wang et al (2005) have described the
presence of an active tropical atmosphere in the CFS when using 64
layers (as opposed to 28 levels) in the vertical, and this choice of
vertical levels was essential both for Nino3.4 SST simulation and low
SST biases in the tropics. The variability of many fields has been
studied. The overall standard deviation of monthly mean fields is
reasonable for SST, T2m, and Z500, and the EOF for Z500 appear correct,
at least for the first six (rotated) modes. For variability in
precipitation and soil moisture, the results are not as good. Although
the bias in winds over the equatorial Atlantic Ocean is considerable,
the interannual variation in vertical wind shear in the Main Development
Region (MDR) for tropical hurricanes appears promising, and the CFS
operational forecasts may aid as a new tool in the making of the
operational NOAA hurricane forecast for seasonal hurricane activity for
the US.

The CFS retrospective forecast data lends itself to many studies that
are not just related to seasonal forecasts, and we encourage the readers
to use this data. The availability of data, both the retrospective
forecast data and the real time operational forecast data is discussed
in section 7 and links have been provided.

Seasonal forecasts at NCEP have been released to the public since about
1972. Initially these forecasts were made by old-fashioned subjective
methods. During the 1980's and 90's, several formal statistical tools
were added to the menu that paved the way for the use of more objective
methods in seasonal prediction. In these methods, an estimate of
a-priori skill, based on sufficient cross validation, could be used to
weigh one tool versus another, before combining them into the official
forecast. Adding numerical forecasts that are accompanied by appreciable
a-priori skill is a logical extension of this procedure. These forecasts
may, or may not, have become much better, but we do have a more
representative measure of a-priori skill which is vital for the proper
utility of seasonal forecasts.

**7. Operational Forecasts and Availability of CFS Data**

The initial operational implementation of CFS involved implementation of
three components : Reanalysis 2 (R2) based daily atmospheric data
assimilation, a daily global ocean data assimilation, and a daily nine
month long coupled model integration. The retrospective forecasts with
the coupled model (discussed in the preceding sections) use R2 analysis
based atmospheric initial states and R2 analysis driven assimilated
global ocean states. This required NCEP to make R2 atmospheric analysis
operational because it is needed for both the ocean analysis and as
initial condition for the CFS forecasts. This real time operational
analysis is called Climate Data Assimilation System 2 (CDAS2).

The operational global ocean data assimilation system (GODAS) uses a
28-day data window symmetrically centered around the analysis time. Thus
the analysis date is 14 days behind real time. So if the GODAS analysis
were to be used as the initial condition, then the daily CFS forecasts
would be 14 days behind real time, which would be unacceptable.
Therefore, a new asymmetric GODAS which uses only 21 days of ocean data
and is valid at 7 days prior to real time was developed and implemented.
This asymmetric GODAS uses the previous 28-day symmetric GODAS analysis
as its first guess.

Thus, operationally three analyses are performed daily in real time: the
atmospheric R2 analysis is performed with analysis time which is three
days before real time, the full symmetric GODAS is performed with
analysis time that is 14 days before real time and an asymmetric GODAS
is performed with analysis time seven days before real time. Using this
asymmetric GODAS analysis as the ocean initial state and R2 analysis
valid at that time as the atmospheric state (at 00 UTC), a daily CFS
forecast is made out to 9-10 months lead time. Since the operational CPC
seasonal forecast is issued once a month, this strategy provides at
least a 30 member ensemble of CFS forecasts to be used by the
forecasters.

An additional daily CFS forecast with the same initial oceanic state and
a slightly perturbed atmospheric state (by taking a weighted mean of the
states corresponding to the real time date and a day earlier at 00 UTC)
will soon be operational. With this addition, there will be at least a
60 member ensemble of CFS forecasts per month.

Monthly means of all variables and daily time-series of selected
variables are being archived from these forecasts. The retrospective
forecasts are used to correct the systematic bias from these monthly
means before being used for the seasonal prediction.

The document at the following web link provides the necessary details on
how to access the operational CFS forecast and retrospective
climatological data from the official National Weather Service (NWS)
data site:

<http://www.emc.ncep.noaa.gov/gmb/ssaha/cfs_data/cfs_data.pdf>

A web link provides the necessary details on how to access CFS
retrospective time series data of the 53 most commonly used variables
from an NCEP/EMC anonymous ftp site :

<http://www.emc.ncep.noaa.gov/gmb/ssaha/cfs_data/cfs_data_in_nomad.doc>

**Acknowledgements**

The authors would like to recognize all the scientists and technical
staff of the Global Climate and Weather Modeling Branch of EMC for their
hard work and dedication to the development and implementation of the
GFS. We would also like to express our thanks to the scientists at GFDL
for their work in developing the MOM3 ocean model. We thank Julia Zhu,
Dave Michaud, Brent Gordon and Steve Gilbert from the NCEP Central
Operations (NCO) for the timely implementation of the CFS in August
2004. George VandenBerghe and Carolyn Pasti from IBM are recognized for
their critical support in the smooth running of the CFS retrospective
forecasts and the operational implementation of the CFS on the NCEP IBM
computers. We thank Curtis Marshall, EMC for his help in the editing of
the manuscript and Ake Johansson and Augustin Vintzileos for many
constructive comments. Finally, we thank the NOAA Office of Global
Programs for the funds to obtain extra computing resources, which
enabled us to complete the retrospective forecasts in a timely fashion.

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**Appendix : Anomaly Correlation, Systematic Error Correction and Cross
Validation.**

The anomaly correlation is defined as:

Number range CHAPTER  X'~for~ (s, t) X'~obs~ (s, t) / nst

AC =
\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\--
(1)

\[ X'~for~ (s,t) X'~for~ (s,t) / nst .  X'~obs~ (s,t) X'~obs~ (s,t)
/ nst \] ^½^

where, for a given lead and forecast target month/season, the summation
is both over time (generally 23 cases (years)), space (e.g. the grid
points north of 35^o^N ; cosine weighting (not shown) is used in that
case), and potentially even a third summation over ensemble members. nst
is the number of space-time points. The primed quantities X' (X can be
any variable, or ensemble mean of a variable) are defined as X' = X --
C~obs~ where C~obs~ is the observed climatology. In the traditional
definition of AC, the same observed climatology C~obs~ is removed from
both forecast X~for~ and observation X~obs~. Thus, the climatology could
refer to any set of (previous 30) years (like 1971-2000) over which the
climatology is traditionally calculated. In many modern studies it may
seem natural, at first, to remove the model climatology C~mdl~, if
available, from X~for~ , i.e X'~for~ = X~for~ - C~mdl.~ This approach
can also be written X'~for~ = X~for~ - C\*~obs~ -- (C~mdl~ -- C\*~obs~ )
by adding and subtracting the term C\*~obs\ ,~ which is an observed
climatology computed over the same set of years as the model climatology
. The expression in parentheses is the systematic error correction, as
evaluated over common years (here 1981-2003 or 1982-2004 for longer lead
forecasts starting beyond May). One might say that subtracting the model
climatology from X~for~ ,instead of the observed climatology, is an
implicit correction for the systematic error. If we use common years
(e.g.1981-2003) for the observed and model climatology in equation (1)
i.e. C\*~obs~ = C~obs~ , then the interpretation of equation (1) is
simplified and using X'~for~ = X~for~ - C~mdl~ and X'~obs~ = X~obs~ -
C\*~obs~ in equation (1) amounts to a verification of systematic error
corrected forecasts. In general, however, C\*~obs~ ≠ C~obs~ and thus the
systematic error corrected X'~for~ in equation (1) should be kept as
X'~for~ = X~for~ - C~obs~ -- (C~mdl~ -- C\*~obs~ ). Furthermore, because
of the implied systematic error correction, one needs to do a proper
cross-validation, i.e. not use information about the year to be verified
in the determination of the systematic error correction (which would
amount to 'cheating'). This creates some complication in programming
equation (1). The summation in time requires an 'outer loop', where each
year is withheld in turn. Thus, the computation of X'~for~ (t) = X~for~
(t) - C~obs~ -- (C~mdl~ -- C\*~obs~ ) and X'~obs~ (t) = X~obs~ (t) -
C~obs~ for specific time 't' requires an adjusted C~mdl~ and C\*~obs~
(and possibly C~obs~ ) such that the year 't' is not part of the various
climatologies that are being computed. This cross validation is
important for all verification of retrospective forecasts using anomaly
correlation, rms-error and other skill measures.

**Figure Legends**

Fig.1 Anomaly correlation (%) of CFS ensemble mean forecasts of the
monthly mean Nino3.4 SST over the period 1981-2003, as a function of
target month and lead (in months). Nino3.4 is defined as the spatial
mean SST over 5^o^S-5^o^N and 170^o^W-120^o^W. Example, the anomaly
correlation for a lead 3 forecast for March (made from 15 initial
conditions beginning Nov 9^th^ and ending Dec 3^rd^) is 0.81. Keep in
mind that the spatial averaging increases the correlation relative to
the traditional verification at grid points in the domain.

Fig.2 Anomaly correlation (%) by various methods of the seasonal mean
Nino3.4 SST as a function of lead (in months). The results are
accumulated for all seasons in the (target) period DJF 1997/98 to DJF
2003/04. Except for CFS, all forecasts were archived in real time at
CPC. CMP14 is the previous coupled model, CCA is canonical correlation
analysis, CA is constructed analogue, CON is a consolidation (a weighted
mean), and MARKOV is an autoregressive method (see text for references).

Fig.3 As Fig. 1 but now a 'verification' of the ensemble mean CFS (N-1
members) verified against the remaining single member. This is a
predictability estimate under perfect model assumptions . Note the much
reduced spring barrier.

Fig.4 Time series 1981-2003 of Nino3.4 SST (degree C) in November.
Observations in the top panel and 6 month lead forecasts by CFS, CA and
CMP14. The anomaly correlation over the period is shown in the legend of
each figure. Note that CFS has better amplitude than CA and CMP14. The
forecasts should be considered retrospective in the years before the
respective methods became operational, i.e. before 2003 for CFS, and
before about 1997 for CA and CMP14.

Fig.5 As Fig.1 but now SST grid points in Northern Hemisphere
mid-latitudes (\>=35^o^N). No spatial averaging of SST is done here.

Fig.6 As Fig.3 but now potential predictability for SST in the NH
(\>=35^o^N).

Fig.7 Anomaly correlation (in %) of ensemble mean CFS forecasts as a
function of lead and target month for monthly mean temperature (top) and
precipitation (bottom) over land in the NH (\>=22.5^o^N).

Fig. 8 The same as Fig.7, but now 500 hPa geopotential (top) and soil
moisture (upper 2m). Soil moisture is over land (\>=22.5^o^N) while 500
hPa geopotential is taken north of 35^o^N.

Fig 9 Spatial distribution of retrospective forecast skill (anomaly
correlation in %) over the United States for lead 1 seasonal mean JJA
temperature (left panel) and DJF temperature (right panel). From top to
bottom, the number of members in the CFS ensemble mean increases from 5
to 15. Values less than 0.3 (deemed insignificant) are not shown. The
period is 1981-2003

Fig. 10 As Fig.9, but now for precipitation.

Fig.11 Left column: Spatial distribution of retrospective ensemble mean
CFS forecast skill (anomaly correlation in %) for lead 1 seasonal mean
temperature over the United States. The target seasons are, from top to
bottom, MAM, JJA, SON and DJF. The CFS (left) is compared to CCA, in the
right column. Note that CCA is based on a longer period, 1948-2003.
Correlation less than 0.3 are not shown.

Fig. 12 The same as Fig.11, but now precipitation.

Fig. 13 Anomaly correlation (in %) of ensemble mean CFS forecasts as a
function of lead and target month for monthly mean temperature over four
quadrants of the United States (using 100^o^W and 40^o^N to define
quadrants), evaluated only over those instances during 1981-2003 when an
anomaly larger than 2 standard deviation occurred in the observations
(anywhere in the quadrant). The much reduced sample size (relative to
Fig.7 and 8), causes noisy patterns.

Fig. 14 The same as Fig. 13, but now precipitation.

Fig.15. Observed climatology and the CFS model climate drift for SST.
The climatology is defined over the period of 1982-2004. The climate
drift is obtained by subtracting the observed climatology from the model
forecast climatology. Left panels are for the winter season (DJF) and
right panels are for the summer season (JJA). The top panels are the
observed climatology. The middle and lower panels are the model climate
drift for the 3-month lead and the 6-month lead, respectively. Unit is
^o^C

Fig.16. Same as Fig.15 but for precipitation rate. Unit is mm/day

Fig. 17. Same as Fig.15 but for 200hPa geopotential height. Unit is
meter.

Fig. 18. Climate drift (Bias) of 2^o^S-2^o^N average SSTs in the Pacific
for forecast from initial conditions of (a) January, (b) April, (c)
July, and (d) October. Contours are drawn at 0.5 K interval. Negative
values are shaded.

Fig. 19. Precipitation rate (color shadings) and surface momentum flux
(vectors) of June from (a) R2/CMAP, and (b) forecast from April initial
condition. Contours are the amplitude of surface momentum flux (0.1 N
m^-2^). Precipitation rate is shaded at 1, 2, 4, 8, 16, and 20 mm
day^-1^.

Fig. 20: The climatology of GODAS subsurface temperature in a
depth-longitude cross section along the Equator in the Pacific and mean
difference between the forecasts and GODAS in degrees Celsius. The
figures on the left are for boreal winter (DJF), while the figures on
the right are for boreal summer (JJA). The top panels show the
climatology of subsurface temperature from GODAS. Note that a different
scale is used for the color bar in the top panel.

Fig. 21: As Fig. 20 but now zonal velocity in cm/s.

Fig. 22: As Fig. 20, but now vertical velocity in mm/hour.

Fig. 23: As Fig. 20, but now a latitude/longitude representation of the
upper ocean heat content in 10^7^ J m^-2^.

Fig. 24 Longitude-time plots of heat content anomalies along the equator
in the Pacific from GODAS and CFS retrospective predictions. The
climatology was computed for the period: 1982-2003. Unit is 10^7^ J
m^-2^.

Fig. 25: Anomaly correlation of Zonal mean zonal wind anomaly at the
equator as a function of pressure level (above 100 hPa) versus forecast
lead time (in months).

Fig. 26 An evaluation of skill in the NAO and PNA index for January and
February at lead 1. The forecast values (ensemble mean) are multiplied
by 2.5 for the purpose showing realistic magnitude in the anomalies.

.

![](media/image1.png){width="6.0in" height="4.583333333333333in"}

Fig. 1 Anomaly correlation (%) of CFS ensemble mean forecasts of the
monthly mean NINO3.4 SST over the period 1981-2003, as a function of
target month and lead (in months). Nino3.4 is defined as the spatial
mean SST over 5^o^S-5^o^N and 170^o^W-120^o^W. Example, the anomaly
correlation for a lead 3 forecast for March (made from 15 initial
conditions beginning Nov 9^th^ and ending Dec 3^rd^) is 0.81. Keep in
mind that the spatial averaging increases the correlation relative to
the traditional verification at grid points in the domain.

![](media/image2.png){width="6.75in" height="5.2034722222222225in"}

Fig. 2 Anomaly correlation (%) by various methods of the seasonal mean
Nino3.4 SST as a function of lead (in months). The results are
accumulated for all seasons in the (target) period DJF 1997/98 to DJF
2003/04. Except for CFS, all forecasts were archived in real time at
CPC. CMP14 is the previous coupled model, CCA is canonical correlation
analysis, CA is constructed analogue, CON is a consolidation (a weighted
mean), and MARKOV is an autoregressive method (see text for references).

![](media/image3.png){width="6.0in" height="4.583333333333333in"}

Fig. 3 As in Fig. 1 but now a "verification" of the ensemble mean CFS
(N-1 members) verified against the remaining single member. This is a
predictability estimate under perfect model assumptions . Note the much
reduced spring barrier.

![](media/image4.png){width="5.729166666666667in" height="7.5in"}

Fig. 4 Time series of Nino3.4 SST (^o^C) in November. Observations in
the top panel and 6 month lead forecasts by CFS, CA and CMP14. The
anomaly correlation over the period is shown in the legend of each
figure. Note that CFS has better amplitude than CA and CMP14. The
forecasts should be considered retrospective in the years before the
respective methods became operational, i.e. before 2003 for CFS, and
before about 1997 for CA and CMP14.

![](media/image5.png){width="6.0in" height="4.583333333333333in"}

Fig. 5 As in Fig.1 but now SST grid points in NH mid-latitudes
(\>=35^o^N). No spatial averaging of SST is done here.

![](media/image6.png){width="6.0in" height="4.583333333333333in"}

Fig. 6 As in Fig.3 but now potential predictability for SST in the NH
(\>=35^o^N).

![](media/image7.png){width="5.75in"
height="3.75in"}![](media/image8.png){width="5.583333333333333in"
height="3.482638888888889in"}

Fig. 7: Anomaly correlation (in %) of ensemble mean CFS forecasts as a
function of lead and target month for monthly mean temperature (top) and
precipitation (bottom) over land in the NH (\>=22.5^o^N).

![](media/image9.png){width="5.377083333333333in"
height="3.3743055555555554in"}![](media/image10.png){width="5.5in"
height="3.626388888888889in"}

Fig. 8 As in Fig.7, but now 500mb height (top) and soil moisture (upper
2m). Soil moisture is over land (\>=22.5^o^N) while 500mb height is
taken north of 35^o^N.

![](media/image11.png){width="5.729166666666667in" height="7.5in"}

Fig. 9 Spatial distribution of retrospective forecast skill (anomaly
correlation in %) over the United States for lead 1 seasonal mean JJA
temperature (left panel) and DJF temperature (right panel). From top to
bottom, the number of members in the CFS ensemble mean increases from 5
to 15. Values less than 0.3 (deemed insignificant) are not shown. The
period is 1981-2003.

![](media/image12.png){width="5.729166666666667in" height="7.5in"}

Fig. 10 As in Fig.9, but now for Precipitation.

![](media/image13.png){width="5.729166666666667in" height="7.5in"}

Fig. 11 Left column: Spatial distribution of retrospective ensemble mean
CFS forecast skill (anomaly correlation in %) for lead 1 seasonal mean
temperature over the United States. The target seasons are, from top to
bottom, MAM, JJA, SON and DJF. The CFS (left) is compared to CCA, in the
right column. Note that CCA is based on a longer period, 1948-2003.
Correlation less than 0.3 are not shown.

![](media/image14.png){width="5.729166666666667in" height="7.5in"}

Fig. 12 As in Fig.11, but now for precipitation.

![](media/image15.png){width="6.666666666666667in"
height="5.092361111111111in"}

Fig.13 Anomaly correlation (%) of ensemble mean CFS forecasts as a
function of lead and target month for monthly mean temperature over four
quadrants of the United States (using 100^o^W and 40^o^N to define
quadrants), evaluated only over those instances during 1981-2003 when an
anomaly larger than 2 standard deviation occurred in the observations
(anywhere in the quadrant). The much reduced sample size (relative to
Fig.7 and 8), causes noisier patterns.

![](media/image16.png){width="7.083333333333333in"
height="5.411111111111111in"}

Fig. 14 As in Fig. 13, but now for precipitation.

![](media/image17.wmf){width="5.997916666666667in"
height="4.866666666666666in"}

Fig.15. Observed climatology and the CFS model climate drift for SST.
The climatology is defined over the period of 1982-2004. The climate
drift is obtained by subtracting the observed climatology from the model
forecast climatology. Left panels are for the winter season (DJF) and
right panels are for the summer season (JJA). The top panels are the
observed climatology. The middle and lower panels are the model climate
drift for the 3-month lead and the 6-month lead, respectively. Unit is
^o^C.

![](media/image18.wmf){width="5.992361111111111in"
height="4.830555555555556in"}

Fig.16. As in Fig.15 but for precipitation rate. Unit is mm day^-1^.

![](media/image19.wmf){width="5.989583333333333in" height="4.85625in"}

Fig. 17. As in Fig.15 but for 200hPa geopotential height. Unit is
meters.

![](media/image20.wmf){width="6.458333333333333in"
height="4.247916666666667in"}

Fig. 18. Climate drift (Bias) of 2^o^S-2^o^N average SSTs in the Pacific
for forecast from initial conditions of (a) January, (b) April, (c)
July, and (d) October. Contours are drawn at 0.5 K interval. Negative
values are shaded.

![](media/image21.wmf){width="4.647222222222222in"
height="4.955555555555556in"}

Fig. 19. Precipitation rate (color shadings) and surface momentum flux
(vectors) of June from (a) R2/CMAP, and (b) forecast from April initial
condition. Contours are the amplitude of surface momentum flux (0.1 N
m^-2^). Precipitation rate is shaded at 1, 2, 4, 8, 16, and 20 mm
day^-1^.

![](media/image22.png){width="6.0in" height="6.0in"}

Fig. 20: The climatology of GODAS subsurface temperature in a
depth-longitude cross section along the Equator in the Pacific and mean
difference between the forecasts and GODAS in degrees Celsius. The
figures on the left are for boreal winter (DJF), while the figures on
the right are for boreal summer (JJA). The top panels show the
climatology of subsurface temperature from GODAS. Note that a different
scale is used for the color bar in the top panel.

![](media/image23.png){width="6.0in" height="6.0in"}

Fig. 21: As in Fig. 20 but now for zonal velocity in cm s^-1^.

![](media/image24.png){width="6.0in" height="6.0in"}

Fig. 22: As in Fig. 20, but now for vertical velocity in mm hour^-1^ .

![](media/image25.png){width="6.0in" height="6.0in"}

Fig. 23: As in Fig. 20, but now a latitudinal/longitudinal
representation for the upper ocean heat content in 10^7^ J m^-2^.

![](media/image26.png){width="6.0in" height="6.0in"}

Fig. 24: Longitude-time plots of heat content anomalies along the
equator in the Pacific from GODAS and CFS retrospective predictions. The
climatology was computed for the period: 1982-2003. Unit is 10^7^ J
m^-2^.

![](media/image27.png){width="5.125in" height="3.915277777777778in"}

Fig. 25: Anomaly correlation of Zonal mean zonal wind anomaly at the
equator as a function of pressure level (above 100 hPa) versus forecast
lead time (in months).

![](media/image28.png){width="3.70748031496063in"
height="5.9992125984251965in"}![](media/image29.png){width="3.7098425196850395in"
height="5.9992125984251965in"}