CFSv2 prediction skill of stratospheric temperature anomalies
Qin Zhang • Chul-Su Shin • Huug van den Dool •
Ming Cai
Received: 29 January 2013 / Accepted: 4 August 2013
� Springer-Verlag Berlin Heidelberg 2013
Abstract This study evaluates the prediction skill of
stratospheric temperature anomalies by the Climate Fore-
cast System version 2 (CFSv2) reforecasts for the 12-year
period from January 1, 1999 to December 2010. The goal is
to explore if the CFSv2 forecasts for the stratosphere would
remain skillful beyond the inherent tropospheric predict-
ability time scale of at most 2 weeks. The anomaly cor-
relation between observations and forecasts for
temperature field at 50 hPa (T50) in winter seasons
remains above 0.3 over the polar stratosphere out to a lead
time of 28 days whereas its counterpart in the troposphere
at 500 hPa drops more quickly and falls below the 0.3 level
after 12 days. We further show that the CFSv2 has a high
prediction skill in the stratosphere both in an absolute sense
and in terms of gain over persistence except in the equa-
torial region where the skill would mainly come from
persistence of the quasi-biennial oscillation signal. We
present evidence showing that the CFSv2 forecasts can
capture both timing and amplitude of wave activities in the
extratropical stratosphere at a lead time longer than
30 days. Based on the mass circulation theory, we con-
jecture that as long as the westward tilting of planetary
waves in the stratosphere and their overall amplitude can
be captured, the CFSv2 forecasts is still very skillful in
predicting zonal mean anomalies even though it cannot
predict the exact locations of planetary waves and their
spatial scales. This explains why the CFSv2 has a high skill
for the first EOF mode of T50, the intraseasonal variability
of the annular mode while its skill degrades rapidly for
higher EOF modes associated with stationary waves. This
also explains why the CFSv2’s skill closely follows the
seasonality and its interannual variability of the meridional
mass circulation and stratosphere polar vortex. In particu-
lar, the CFSv2 is capable of predicting mid-winter polar
stratosphere warming events in the Northern Hemisphere
and the timing of the final polar stratosphere warming in
spring in both hemispheres 3–4 weeks in advance.
Keywords Seasonal prediction � CFSv2 model �Stratosphere dynamics � Wave-mean flow interaction
1 Introduction
Verification of weather predictions pre-dates the emer-
gence of numerical weather prediction (NWP) and has
been around for a century at least. Naturally, the early
verification applied only to a few surface weather elements.
Since the introduction of NWP the scope of weather
forecast verification has grown considerably by looking at
gridded fields, both near-surface and aloft, and often over
very large areas. Instead of observations at a few stations
This paper is a contribution to the Topical Collection on Climate
Forecast System Version 2 (CFSv2). CFSv2 is a coupled global
climate model and was implemented by National Centers for
Environmental Prediction (NCEP) in seasonal forecasting operations
in March 2011. This Topical Collection is coordinated by Jin Huang,
Arun Kumar, Jim Kinter and Annarita Mariotti.
Q. Zhang � H. van den Dool
Climate Prediction Center, NCEP/NWS/NOAA,
College Park, MD, USA
C.-S. Shin � M. Cai (&)
Department of Earth, Ocean, and Atmospheric Science,
Florida State University, Tallahassee, FL 32306, USA
e-mail: [email protected]; [email protected]
Present Address:
C.-S. Shin
Center for Ocean-Land-Atmosphere Studies,
George Mason University, Fairfax, VA 22030, USA
123
Clim Dyn
DOI 10.1007/s00382-013-1907-5
one can now verify gridded forecasts against gridded
analyses, with the caveat that such analyses may not be
perfect, especially not where observations used in making
the analysis are sparse. A commonly used metric is the
5-day 500 hPa height anomaly correlation (AC) for the
extra-tropical hemispheres. This measure has been used
widely and progress in weather forecasting has been
measured by it from *1980 to present, and different pre-
diction centers compare their relative performance through
this metric.
Somehow the NWP for the stratosphere has escaped
systematic verification, i.e., there are very few published
papers on the subject. This may be because of the fol-
lowing reasons. First, the interest in the performance in the
stratosphere may have been low, since ‘weather’ as expe-
rienced by humans in some way seems almost absent above
the troposphere. Secondly, there was not much data
assimilation in the stratosphere early on, so the verifying
analysis may have been poor. Thirdly, the resolution in the
stratosphere was low—in fact initially there was only a
stratosphere in models because it did less harm than a
reflecting lid on top of the troposphere.
However, from a physical standpoint the challenge of
predicting fluid motion in the stratosphere is just as inter-
esting as in the troposphere. With increased vertical reso-
lution (Maycock et al. 2011), and much more data to
assimilate (principally from satellites) we can now address
this issue in a systematic way. The word ‘‘systematic’’
refers to including all cases (every day) in the verification,
not just a spectacular sudden warming in some year
(Christiansen 2005) or a rare volcanic eruption event
(Marshall et al. 2009). We perform here a systematic ver-
ification on a traditional weather element, the temperature.
The key question is whether the stratospheric predictability
is longer than the inherent 2-week predictability limit for
the troposphere. If so, what makes the stratosphere more
predictable?
Although not officially documented in the literature, the
conventional wisdom is that stratosphere is more predict-
able because it is more persistent than the troposphere. The
longer persistence time scale of stratospheric anomalies
immediately implies that the lazy man’s forecast of per-
sistence of the initial state easily yields more forecast skill
in the stratosphere than in the troposphere. The higher
persistency of stratospheric anomalies over the extratropics
in winter seasons can be attributed to the lack of fast
moving synoptic scale waves because only quasi-stationary
planetary scale Rossby waves can propagate through a
strong westerly jet (Charney and Drazin 1961). The dom-
inance of the quasi-biennial oscillation (QBO) over equa-
torial stratosphere, resulting from the interactions among
the zonal flow, vertically propagating Kelvin waves and
Rossby-gravity waves (Lindzen and Holton 1968), is the
source of the long persistency in the equatorial strato-
sphere. In addition, as far as radiation is concerned, the
slow Newtonian damping of 30–35 days in the stratosphere
has been suggested to play a role in causing the long per-
sistency of stratospheric anomalies (Kiehl and Solomon
1986; Newman and Rosenfield 1997).
It should be pointed out that the strong persistence does
not necessarily imply that a dynamical model would have
to have more prediction skill in both absolute terms and in
reference to persistent forecasts, regardless of that it may or
may not yield more skill than persistent forecasts. For
example, as will be shown later in this paper, the Climate
Forecast System version 2’s (CFSv2) predictions in spring
seasons actually have higher skill in the absolute terms for
polar stratospheric anomalies than that for equatorial
stratospheric anomalies, although the latter has much
longer persistent time scale than the former. In reference to
persistent forecasts, our results will show that CFSv2 pre-
dictions are much more skillful over the extratropical
stratosphere than over the equatorial stratosphere. In this
sense, the prediction skill of a dynamical model is not
always trivially related to the persistency. Furthermore, as
shown in Christiansen (2005) for stratospheric sudden
warming events and later in this paper for everyday cases, a
dynamical model actually has a higher skill in predicting
zonal mean flow anomalies than quasi-stationary wave
anomalies. Therefore, the lack of synoptic-scale waves in
the extratropical stratosphere, which contributes to the
relatively long persistency in the extratropical stratosphere
in comparison with the troposphere below, is not the most
essential factor why a dynamical model would have a
higher skill there. In addition, the longer radiative cooling
time scale in the stratosphere could help to explain why it
would be easier to predict the recovery of stratospheric
polar vortex. However, consideration of persistence cannot
explain why the onset of stratospheric warming events is
quite predictable as will be shown in this paper. This is
because the onset of stratospheric warming events takes
place so rapidly (particularly for a sudden warming event)
that a persistent forecast would not have much skill beyond
1 week. These examples seem to support the conjecture
that if a dynamical model, such as the CFSv2, has good
skill for stratospheric predictions beyond the inherent
2-week predictability limit for the troposphere, it cannot be
just due to the relatively long persistent time scale alone.
Then the question is what makes the stratosphere more
predictable, which is one of the focal points of this paper.
We believe the exercise of verifying stratosphere fore-
casts might also be helpful for improvement of troposphere
forecasts beyond the 2-week predictability limit. Beside the
ENSO signal and its impact on climate variability, the
systematic slow downward propagation of the extratropical
anomalies of both signs in zonal wind and temperature
Q. Zhang et al.
123
from stratosphere into the troposphere (e.g., Baldwin and
Dunkerton 1999, 2001; Zhou et al. 2002; Cai and Ren
2006, 2007; Ren and Cai 2007, 2008) is suggestive of a
recently recognized source of predictability for the tropo-
sphere (Thompson et al. 2002; Baldwin et al. 2003a, b).
Some studies have shown that the predictability length can
be improved since there is one dramatic stratospheric
phenomenon that can occur occasionally during the polar
winter, namely a sudden stratospheric warming (SSW)
(Charlton and Polvani 2007). Major SSW events are
associated with a large (*50 K) and rapid (of order a
week) increase in temperature over the polar cap and a
temporary reversal of the climatological westerly strato-
spheric jet to easterly. It has been suggested that this
improvement depends on the initial day of the forecast
relative to the central date of the SSW (Kurda 2010;
Hornqvist and Kornich 2012). The relationship between the
strong/weak stratospheric polar vortex (or positive/negative
phase in the annular mode in the stratosphere) and the
climate variability at the surface in the winter season may
allow us to use stratospheric information (or forecast
models with well-represented stratospheres) to improve
surface weather forecasts beyond the 2 week limit of
weather prediction models (e.g., Thompson and Wallace
2001; Thompson et al. 2002; Ren and Cai 2007). It is found
that when the North Atlantic Oscillation (NAO) is positive,
pressures are lower than normal over the polar cap but
higher at low latitudes, with stronger westerlies at mid-
latitudes, especially across the Atlantic. Northern Europe
and much of the United States are warmer and wetter than
average, and Southern Europe is drier than average. As
shown in Hardiman et al. (2011), the stratospheric final
warming (the seasonal transition of the stratosphere to
summer-time conditions) can be used to improve predict-
ability of the NAO, mainly in April.
In this study, we focus on how skillful the NCEP Climate
Forecast System (CFSv2) forecasts are for the extratropical
stratosphere temperature anomalies in the extended range
beyond 2 weeks. We also aim to explain why the CFSv2
could have useful prediction skill for stratosphere in the
extended range at which the CFSv2 would have little skill
for the troposphere. The compelling reason to use the
CFSv2 model is the huge hindcast data set that accompanies
this model which allows for systematic verification. The AC
between analysis (observations) and forecasts as a function
of forecast lead time of the NCEP CFSv2 model is exam-
ined in both hemispheres for all seasons.
This paper is organized as follows. The next section
describes the CFSv2 reforecast data and methodology used
in this study. In Sect. 3 we discuss the prediction skill of
the CFSv2 model for the temperature at 50 hPa (T50) and
compare it with the skill for the temperature at 500 hPa
(T500). In Sect. 4, we conduct an EOF analysis for the CFS
reanalysis (CFSR) and evaluate the skill of CFSv2 ref-
orecasts in predicting the dominant modes of the strato-
spheric variability. Section 5 is devoted to a better
understanding of how and why the relative high forecast
skill of the stratosphere temperature anomalies relates to
mass circulation variability in the extratropical strato-
sphere. A summary of the main findings in this study is
presented in Sect. 6.
2 Data and methodology
2.1 Model and reforecast data
The CFSv2 model became operational at NCEP, as suc-
cessor of CFSv1, in March 2011. The atmospheric com-
ponent has T126L64 atmospheric resolution, of which 25
are above 100 hPa and the top at 0.2 hPa. The ocean
component is a Modular Ocean Model, MOM4, which uses
40 levels in the vertical, a zonal resolution of 0.5�, and a
meridional resolution of 0.25� between 10�S and 10�N,
gradually increasing through the tropics until becoming
fixed at 0.5� poleward of 30�S and 30�N. The ocean–
atmosphere coupling is now truly global with an interactive
sea-ice model and the coupling is more frequent than in
CFSv1. Initial states for the integrations are provided by a
coupled Reanalysis at T382L64 resolution (Saha et al.
2010). CFSv2 has, as much as practically possible, con-
sistency between the forecast model and the initial states.
Further details of the model components, the initial states
and some forecast results will be in Saha et al. (2013).
Other aspects of the CFSv2 skill below the tropopause have
already been described (Zhang and Van den Dool 2012).
We here study CFSv2 reforecasts of 90-day forecasts
made for each day during 1999–2010. Although about 30
fields of model outputs were archived when these refore-
casts were made, only few of them were saved in both the
troposphere and stratosphere at the daily interval and the
temperature field happens to be one of them. The temper-
atures at 50 and 500 hPa are extracted from the CFSv2
hindcast archive, derived from the daily 00Z forecast from
day 1 through day 90 forecast with 1 day interval. As to the
model bias correction, the anomalies are calculated as
departures from the model climatology, which is estimated
as the annual mean plus the first 4 harmonic modes of the
365 daily values averaged across 12 years. The data used in
our analysis are at the 2.5� by 2.5� latitude longitude spatial
resolution.
2.2 CFSR data as verification of the prediction
To assess the forecast skill we must verify against an
analysis and for this we employ the NCEP/CFS
CFSv2 prediction skill
123
reanalysis (CFSR; Saha et al. 2010). The CFSR is pro-
duced for 1979-present (and ongoing) based on a coupled
atmosphere–ocean–land guess forecast with a much
higher atmospheric horizontal resolution (T382) and
includes direct assimilation of radiance data (Saha et al.
2010). Note that the CFSR provides both initial condi-
tions for the predictions and serves as verification for
1999–2010. For verification the CFSR was regridded to
the 2.5� by 2.5� latitude longitude spatial resolution. Our
skill evaluation is based on verification against anomaly
field of the CFSR analysis, which is defined as the
departure from the CFSR climatology of the same
12 years estimated in the same fashion as that for the
model forecasts.
2.3 EOF analysis
An EOF analysis was performed on the domain 20� to the
pole for the full 30 year CFSR data set to find ‘observed’
components of stratospheric circulation that are potentially
more predictable, as one typically hopes for the leading
EOFs. Because the spatial resolution of the data is high
(10,512 points globally) and the time series quite long
(almost 11,000 time levels), the traditional covariance
matrix approach, i.e., calculating EOF as eigenvectors of
the covariance matrix, is cumbersome in terms of CPU. A
faster method we use here is to calculate the EOFs as
singular vectors of the full resolution data matrix via an
iterative procedure (van den Dool 2011). This method has
been known for some time (Van den Dool et al. 2000), but
it is only recently (Baldwin et al. 2009) that its advantages
on very large data sets have become apparent. The verifi-
cation of EOF modes’ forecasts is done by comparing the
projections of CFSv2 anomalies on these EOF modes with
their counterparts of CFSR anomalies in the 12 years
between 1999 and 2010.
3 Forecast skills of T50 versus T500
The method for evaluating the prediction skill commonly
used is to measure how similar a forecast field is to an
observed (or analyzed) field. In this study, the anomaly
correlation (hereafter AC) is used, which is defined below.
AC ¼P
n F0i � O0i� �
Pn F0i � F0ið Þ
Pn O0i � O0ið Þ
� �1=2
Here F0 and O0 are anomalies of forecast and analysis at
grid point i. The summing in space and time is absorbed
into a single index n. Not shown are the weights that rep-
resent the area occupied by each grid point.
For perfect forecasts, we have AC = 1.0. While always
a bit arbitrary, we use AC = 0.5 as the threshold for
‘‘useful’’ skill, which is consistent with Mean Square Error
(MSE) being equal to the MSE of always forecasting the
climatology. We also consider AC = 0.3 as the cut-off for
‘‘marginally useful’’ skill, a term that is borrowed from the
experience in predictions of upper level (i.e., 500 hPa
height) charts in the 6–10 day range.
Figure 1 shows the AC of the CFSv2 forecast for T50
(solid lines) and T500 (dashed lines) for forecast lead day 1
through day 45 in winter season (DJF) of the Northern
Hemisphere (NH) and austral winter season (JJA) of the
Southern Hemisphere (SH). Given the inherently chaotic
nature of the troposphere, the model does not break through
the 2-week limit in any latitude bands, except temporarily
when the El Nino impact (Anderson and Van den Dool
1994) is strong. In contrast, the forecast scores of the
stratosphere are much higher in general than those in the
troposphere. The lead time of the forecast for the NH
(black solid line) extends from 7 days for the troposphere
to about 15 days (Fig. 1a) for the stratosphere at the 0.5
correlation level and the ‘‘marginally useful’’ forecast skills
(the correlation above 0.3) are maintained to 23 days, twice
as long as that for T500. Note that the skills of the pre-
diction over the high-latitude of the stratosphere (blue solid
line) is the highest of all and the lead time of the marginally
useful skill at high latitudes is the longest, reaching to
28 days. The prediction score for the stratosphere over the
tropics is lower than that in high-latitudes, which is the
opposite to the troposphere where predictable ENSO
impacts on the global climate are seen foremost in low
latitudes. The forecast skills of the SH winter (Fig. 1b)
have similar features as those in NH. Such high skillful
predictions in the polar stratosphere region may supply
useful information about the intra-seasonal climate forecast
in the troposphere because of the relation between the
strong/weak stratospheric polar vortex (or positive/negative
phase in annular mode in stratosphere) and the climate
variability at the surface in winter season (e.g., Thompson
and Wallace 2001; Thompson et al. 2002; Cai 2003), which
may lead to improve the extended range forecast
(8–14 days) and monthly to seasonal outlook in Climate
Prediction Center (CPC) via statistical downscaling.
To demonstrate the seasonality of the CFSv2 forecast
skills, we plot in Fig. 2 the AC of the stratospheric 50 hPa
temperature anomaly averaged for the high-latitude domain
(60�–90�) as a function of the calendar month and forecast
lead time. In NH, the prediction skill for the polar strato-
sphere is higher in the cold half of a year (NDJFMA) than
in the warm half (MJJASO). In cold season, the lead time
of the stratosphere prediction over the Arctic with AC
above 0.5 is about 20 days and the marginal useful pre-
diction skill (AC C 0.3) extends to about 30 days. In warm
season, the polar stratosphere prediction skill drops very
rapidly with the lead time and the prediction loses useful
Q. Zhang et al.
123
skill when the lead time exceeds the 2-week limit. In SH,
the skillful predictions for the polar stratosphere exist
beyond the 2-week limit mainly in the austral spring season
in the months August through November. However, the
longest lead time of useful predictions for polar strato-
sphere is found in SH in September, which is about
45 days.
One may ask why the predictability of the stratosphere is
much higher than that of the troposphere and why the polar
stratosphere is particularly more predictable in winter/
spring season but becomes as unpredictable as the tropo-
sphere beyond the 2-week limit in warm season. We will
attempt to address these questions in the next two sections.
4 Prediction skill of the dominant modes
in the stratosphere
In this section, we wish to examine whether the CFSv2’s
skill in predicting stratospheric anomalies comes from
mainly the dominant modes in the stratosphere. We use the
EOFs of the 30-year daily CFSR analysis dataset to
describe the dominant modes of the stratospheric vari-
ability. Figure 3 shows the resulting first four EOFs in the
CFSR daily T50 dataset. The first EOF describes 23.4 % of
the variance in daily NH T50 data. In the troposphere the
first EOF of daily data explains not even 10 % of the total
variance. The first EOF is essentially an annular mode,
representing an oscillation between stronger and weaker
stratosphere polar vortex, although there is a noticeable
weak zonal asymmetry between the Eurasia and North
America longitude sectors. The second and third modes are
characterized by a wavenumber one structure. They
describe two ways by which a polar vortex can be pushed
away from the pole, namely one from the east Asian/west
Pacific sector (EOF2) and the other from the North
America sector (EOF3). These three modes together
explain 55 % of the variance in daily NH T50 field, indi-
cating far simpler or less chaotic nature in the stratosphere
than in the troposphere. The fourth EOF mode is dominated
by a wavenumber two structure, describing a simultaneous
push from both the Eurasia and North America longitude
sectors of warm temperature anomalies in getting to the
polar stratosphere. However, the EOF4 only explains about
3.2 % of variance in daily NH T50 field. This suggests that
the preferred pathway to the polar stratosphere for warm air
is through either the east Asian/west Pacific sector or the
North America sector. Therefore, the first three EOF modes
shown in Fig. 3 describe 55 % of variance and they toge-
ther are closely associated with the annular mode vari-
ability, stratosphere sudden warming, and an earlier or late
winter to summer transition of the polar stratosphere
circulation.
We next project forecasts onto the spatial patterns of
Fig. 3. The correlations of the predicted and observed
principal component (PC) time series of each of the EOF
mode as a function of forecast lead time are shown in
Fig. 4. One can indeed see that PC1 has exceptionally high
forecast skill, adding another 10 and 20 days of the skill at
the 0.5 and 0.3 level, respectively, to the overall skill
shown in Fig. 1a (or the dashed curve in Fig. 4), implying
the forecasts for the EOF1 by CFSv2 is still useful (at the
0.3 level) at the lead time of 40 days. The skill of pre-
dicting EOF2 and EOF3 is still higher than the average
stratospheric skill till the lead time of 35 days, at which the
average stratospheric skill is already below 0.2. However,
the EOF4 is much more difficult to predict with skill at the
0.5 level only out to 12 days, about 3 days less than the
Fig. 1 Decay of the anomaly correlation (AC) of daily 50 hPa
temperature prediction a in the NH as a function of lead time from 1
to 45 days in boreal winter (DJF) of 1999–2010 and b in the SH as a
function of lead time from 1 to 45 days in austral winter (JJA) of
1999–2010. The geographical domains over which the AC is
calculated are indicated by the color coding of the lines. The dashed
curves are the same but for temperature at 500 hPa
CFSv2 prediction skill
123
average stratospheric skill. The remaining EOF modes,
accounting for 42 % of variance of the daily T50 field, are
characterized by higher wave numbers and they are harder
to predict beyond the 2-week limit. Therefore, remarkable
high prediction skill of T50 in the range longer than the
2-week limit mainly comes from the first three EOF modes,
particularly the first EOF mode. As discussed above, the
first three EOF modes represent mainly the variability
associated with polar vortex oscillation. Therefore, we
conjecture that the CFSv2’s high skill in the stratosphere is
mainly due to its ability in predicting polar stratosphere
anomalies associated with polar vortex oscillation or
annular mode variability. We provide more evidence in
supporting this conjecture in the next section.
5 Latitudinal variation of prediction skill
in the stratosphere
To understand the source(s) of the CFSv2’s high prediction
skill for stratosphere zonal mean temperature anomalies
and its relation with the longer persistency of stratospheric
anomalies, we first plot in Fig. 5 (shadings) the temporal
evolution of the zonal mean of the observed daily T50
anomalies (denoted as [T50]0 hereafter, where [] is the
zonal mean and prime symbol (0) is the temporal deviation
from its climatological annual cycle) derived from daily
CFSR analysis in this 12-year period under consideration.
A large portion of equatorial [T50]0 is associated with the
equatorial stratosphere QBO, namely negative [T50]0
anomalies are found in the easterly phase and positive
[T50]0 anomalies in the westerly phase. In the extratropics
of both hemispheres, [T50]0 has large amplitude primarily
in the cold season. Temperature anomalies over the polar
stratosphere represent either stratosphere (major or minor)
warming events in winter season (both timing and ampli-
tude), or the timing of the annual winter to summer tran-
sition of the polar stratosphere circulation. There is
evidence suggesting a poleward propagation signal prior to
peak temperature anomalies over the polar stratosphere.
The work reported in Cai and Ren (2006, 2007) and Ren
and Cai (2006, 2008) shows that the intra-seasonal vari-
ability of the stratospheric polar vortex in winter season is
intimately related to the poleward propagation of
Fig. 2 a The anomaly correlation (times 100 %) of daily 50 hPa temperature prediction in the polar cap (60�-pole) of the NH as a function of the
lead from 1 to 45 days (abscissa) and calendar month (ordinate) in the period of 1999–2010. b The same as a but for the SH
Q. Zhang et al.
123
stratospheric anomalies along equivalent latitudes parallel
to isentropic PV contours. The upper stratospheric pole-
ward propagation leads the poleward propagation in the
lower stratosphere. As a result, there appears a simulta-
neous downward propagation in the polar stratosphere. The
zonal wind anomalies follow the poleward/downward
propagating temperature anomalies of the opposite sign.
Ren and Cai (2007) interpreted such slow propagation of
temperature anomalies of both signs as a result of the
intensity variability of poleward mass transport in the
stratosphere. Specifically, a stronger poleward mass trans-
port leads to warm temperature anomalies over polar
region and vice versa. The arrival of warmer air from low
latitudes by itself means positive temperature anomalies in
high latitudes. The mass accumulation over the polar
stratosphere also implies a descent motion (in isentropic
surface analysis, an increase in mass between two adjacent
isentropic surfaces implies an increase in the pressure level
or a decrease in elevation of the lower isentropic surface).
The adiabatic warming acts to amplified positive temper-
ature anomalies in high latitudes. The reverse can be said
cold temperature anomalies over polar stratosphere result-
ing from a weaker poleward mass transport (in reference to
climatological mean transport). This explains why the
Fig. 3 The spatial patterns of the first four EOF modes of T50 over the domain 20�N-pole calculated from CFSR for the period of 1982–2011 on
a 2.5� by 2.5� lat/lon grid. The explained variance of each EOF mode is given in the heading of the four panels
CFSv2 prediction skill
123
largest [T50]0 is found over the polar stratosphere. The
more pronounced poleward propagation signal in SH is
partially due to the slower propagation there, which on
average is half of the speed as that in NH according to Ren
and Cai (2008). Recall that the poleward propagation in
NH reported in Cai and Ren (2007) is found in an equiv-
alent latitude coordinate defined from the PV contours. It is
expected that the poleward propagation signal is faster in
the geographical latitude coordinate, explaining why the
poleward propagation in NH is less noticeable.
We next show the time mean AC skills of persistent
forecasts of [T]0 as a function of latitude and lead time in
each calendar month over the period of 1999 and 2010
(Fig. 6). The black line in Fig. 6 corresponds to the 0.5
contour line of the correlation, whose lead time is con-
sidered as a conservative estimate of the maximum forecast
lead for useful forecasts. Considering the relatively slowly
varying circulation anomalies in the stratosphere, one may
argue that even a persistence forecast can have a good
prediction skill. A persistent forecast is made by using the
initial condition’s [T]0 as a forecast for a later time.
Although it is definitely not a real forecast, we use per-
sistent forecasts as a benchmark to ascertain that the rela-
tively high skill of CFSv2 forecasts in the stratosphere is
not purely due to the slow variation of stratospheric
anomalies. The dominance of the long lasting QBO signal
makes easy persistent forecasts for [T50]0 in the equatorial
stratosphere. The skill of persistent forecasts degrades
rapidly but not monotonically as latitude increases. The
meridional band structure of persistent forecasts’ skill
reflects the meridional see-saw pattern of [T50]0 with
minimum score centers in the latitudes of frequent occur-
rence of the nodal points of [T50]0 and maximum centers in
the latitudes where large amplitude of [T50]0 tend to take
place. The score of persistent forecasts over the polar area
decreases with the lead time more rapidly than that in mid-
latitudes despite of the fact that the largest anomalies of
[T50] are found in polar area in winter seasons.
Figure 7 shows the counterparts of Fig. 6 predicted by
CFSv2 and Fig. 8 shows the difference between Figs. 7
and 6 with positive values indicating additional skill gain in
predicting [T50]0 by CFSv2. Let us first examine the skill
in predicting the QBO over the equatorial stratosphere.
According to Fig. 7, CFSv2 has little skill in predicting the
very slow QBO signal beyond the lead time 30 days in all
calendar months except in January, February, and March,
in which CFSv2 forecasts are still useful at a lead time of
60 days. However, most of the skill in predicting the QBO
mainly comes from the slowness of the QBO itself because
the CFSv2’s skill has little advantage over the persistent
forecast skill. The return of forecast skill in reference to
persistent forecasts over the tropical stratosphere after
30 days in January through May could result from the
delayed ENSO signal impact on the upper-level atmo-
sphere in the tropics. The absence of additional skill in
predicting the QBO over persistence merely reflects that
the fact that CFSv2 (or any existing operational forecast
models) cannot even simulate the QBO signal. Therefore,
the QBO signal in CFSv2 forecasts comes mainly from
initial conditions, which disappears very rapidly as the lead
time increases because the model does not have the correct
dynamics and physics to hold on to the QBO signal. On the
other hand, persistence as a forecast can keep the QBO
signal intact for a very long lead time. As indicated in
Fig. 6, persistent forecasts for the equatorial [T50]0 are still
correlated with observations at the 0.5 level even at the
lead time of longer than 60 days in the months of June
through December. However, the skill of persistent fore-
casts for the QBO signal degrades quickly in the months of
January through May with the minimum skill in March in
Fig. 4 The anomaly correlation
(times 100 %) of the CFSv2
predictions of the principal
component time series of the
first four T50 EOFs shown in
Fig. 3 as a function of lead time
from 1 to 45 days in boreal
winter (DJF) of 1999–2010
Q. Zhang et al.
123
which the skill of persistent forecasts already degrades to
the 0.5 level at the lead time 30 days. The relatively fast
degrading of persistence forecasts for the QBO signal in
the months of January through May explains the extra skill
of CFSv2 for tropical stratosphere predictions at the longer
lead time over persistent forecasts in these 5 months.
Now let us turn our attention to the NH extratropics.
Between June and September, CFSv2 forecasts have little
skill in predicting [T50]0 over the NH extratropics beyond
week 2. During these 4 months, CFSv2 forecasts over the
NH extratropics are as poor as persistent forecasts. From
October to May, however, CFSv2 forecasts for [T50]0 over
Fig. 5 The zonal mean of daily
T50 anomalies (shading) and
the root mean square of the
wavy portion of daily total T50
field (contours, only contour
line greater than 3 K) derived
from CFSR in the period from
January 1999 to December
2010. The panel shows years
a 1999–2002, b 2003–2006,
c 2007–2010
CFSv2 prediction skill
123
the NH extratropics show remarkable advantage over per-
sistent forecasts. The biggest improvement of the CFSv2
skill over persistence is in the NH polar stratosphere in
these 7 months. Also the center of largest improvement of
CFSv2 forecasts over persistence shifts towards higher
latitude as the forecast lead increases. In December, for
example, CFSv2 forecasts show an extra skill over
persistence in the entire region poleward of 30�N for a lead
time less than 30 days, but at a longer lead time, the gain
over persistence is found only over the polar stratosphere.
Such poleward contraction in the gain of CFSv2 forecasts
over persistence with respect to the lead time reflects the
fact that the maximum CFSv2 skill in the extratropics
gradually shifts poleward from mid-latitudes as the lead
Fig. 5 continued
Q. Zhang et al.
123
time increase (Fig. 7). Such poleward propagation of
CFSv2 skill in predicting [T50]0 is more pronounced in
spring season (i.e., February, March, and April in Fig. 7),
which leads to the maximum gain over persistence in polar
stratosphere at the lead time of around 35 days (Fig. 8).
In the SH extratropics, the CFSv2 also has good skill
beyond week 2 in austral cold season from May through
November, particularly in second half of the austral spring
season (i.e., July, August, September, October, and
November). Compared to the NH extratropics, the CFSv2
skill is noticeably higher at the lead time longer than
30 days. Persistent forecasts for SH extratropical strato-
spheric anomalies, however, have similar poor skill beyond
week 2 as for the NH extratropical stratospheric anomalies.
Fig. 5 continued
CFSv2 prediction skill
123
Therefore, such high skill of CFSv2 at the lead time longer
than 30 days is not due to more persistency in the SH
extratropical stratosphere. The gain of CFSv2 over persis-
tence at a long lead time is more pronounced in SH than in
NH, although it is less pronounced at a short lead time. In
early austral winter (June), CFSv2 forecasts over SH mid-
latitudes degrade very quickly from the initial condition,
but regain usefulness at lead time 50 days. In NH, the
poleward propagation of CFSv2 skill begins at 30�N in
boreal winter months but starts at higher latitude (60�N) in
boreal spring. The poleward propagation of CFSv2 skill in
predicting [T50]0 in SH begins at 30�S in both austral
winter and spring seasons and its speed is much slower
than in NH.
We have verified that CFSv2 has much lower skill for
the wave component of T500 beyond week 2 in both boreal
cold season in the NH extratropics and austral cold season
in SH (not shown here). This is consistent with our finding
presented in the previous section, namely, CFSv2 has little
skill beyond the 2-week limit for higher EOF modes, which
are dominated by waves with wavenumber greater than 1.
We next wish to explore what makes [T]0 over polar
stratosphere more predictable from the perspective of the
meridional mass circulation. Based on the mass circulation
theory, the extratropical poleward mass transport in the
upper atmosphere is done by baroclinically amplifying
waves that tilt westward with height (Townsend and
Johnson 1985; Johnson 1989). Large amplitude of west-
ward titling waves results in a stronger poleward mass
transport in the stratosphere and vice versa. It follows that
as long as CFSv2 can capture the amplitude variability of
these westward titling planetary scale waves even with
large errors in predicting their longitude positions and
some errors in their spatial scale, CFSv2 would still be able
to predict the timing and intensity of the poleward mass
transport.
To validate the conjecture above, we define a latitude-
dependent ‘‘wave_amplitude’’ index from the total T50
Fig. 6 The temporal correlation (times 100 %) of the zonal mean of T50 anomalies between the observation (CFSR) and persistent forecasts in
each month over the period from January 1999 to December 2010 as a function of lead time from 1 to 90 days (abscissa) and latitude (ordinate)
Q. Zhang et al.
123
field (without removing the climatological annual cycle)
according to
Wave amplitudeðy; tÞ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ðT50ðx; y; tÞ � ½T50�ðy; tÞÞ2x
q
where the quantity (T50 - [T50]) is the wavy portion of the
total T50 field at any given time t and location (x, y) and the
overbar with the superscript x denotes the averaging oper-
ator over the entire latitude circle at the latitude y. The
contours in Fig. 5 depict how the ‘‘wave_amplitude’’ index
derived from the daily CFSR analysis vary as a function of
time and latitude for the period from 1999 or 2010. It is seen
that indeed stronger wave activities always proceed large-
amplitude positive [T50]0 anomalies over polar stratosphere
and the later result from stronger poleward mass transport
into the polar stratosphere carried out by former. There are a
few exceptions in which large-amplitude of wave activities
do not lead to large-amplitude positive [T50]0 anomalies,
such as in the austral cold season of 1999 and 2001 over the
Antarctic and in the boreal winter of 2000 over the Arctic.
Perhaps, in these years, the extreme cold polar stratosphere
was caused by other external factors and without strong
poleward mass transport, the polar stratosphere would be
even colder. We have also obtained the counterparts of the
contours shown in Fig. 5 for each lead time of CFSv2
forecasts. Figure 9 shows the ‘‘wave_amplitude’’ index at
60�N as a function of time (abscissa) and forecast lead time
(ordinate: day 0 is the CFSR analysis and day n for n = 1,
2, … 90 corresponds the lead time of day n). It vividly
shows that at most times, the CFSv2 is indeed capable of
predicting both timing and amplitude of wave activities at
least 1 month in advance.
The results presented above clearly demonstrate that
although CFSv2 forecasts already lose most of the skill in
predicting the exact locations of troughs and ridges beyond
week 2, these waves are still present in CFSv2 forecast. As
long as the waves in CFSv2 forecasts have reasonable
amplitude with a similar tilting as observations, their
induced poleward mass transport variability in the strato-
sphere would more or less agree with that in observations
Fig. 7 The same as Fig. 6 but for CFSv2 forecasts
CFSv2 prediction skill
123
(i.e., large-amplitude westward tilting waves would trans-
port more mass poleward and vice versa). This explains
why the CFSv2 has a high skill for the first EOF mode of
T50, the intraseasonal variability of the annular mode
associated with poleward propagation of zonal mean
anomalies, despite that its skill degrades rapidly for higher
EOF modes associated with the wave field. The lack of
wave activities in summer implies a much weaker pole-
ward mass transport into polar stratosphere. As a result,
there is little skill in CFSv2 in predicting [T50]0 in summer
seasons.
According to Cai and Ren (2007), there are typically 1–2
cycles of poleward propagations of stratospheric circulation
anomalies of both signs in NH in a winter season, reflecting
the timing and intensity of the dynamically driven mid-
winter stratospheric polar warming and the spring strato-
spheric polar warming in NH. This explains why the gain of
the CFSv2’s forecasts for the NH polar stratosphere over
persistent forecasts tends to have two distinct peaks during
cold season: one is December and the other is March. The
poleward propagation of stratospheric circulation anomalies
of both signs is much slower in SH. It takes about 110 days
for stratospheric anomalies of one polarity to propagate
from the equator to the Antarctic, which is almost twice as
long as in NH (Ren and Cai 2008). As a result, there is
typically just one cycle of poleward propagations of
stratospheric circulation anomalies of both signs in an
austral winter season, which reflects the timing and inten-
sity of the final polar stratosphere warming in late spring or
early summer of each year in SH. This explains why the
gain of the CFSv2’s forecasts for the SH polar stratosphere
over persistent forecasts becomes pronounced (with the
same amount of gain as the NH case) mainly in later spring
or early summer (i.e., November and December).
6 Summary
We here report an extensive verification study of the
stratosphere prediction skill of CFSv2 reforecasts. The
Fig. 8 The same as Fig. 7 but for the difference of the results shown in Fig. 7 and those derived from persistent forecasts in Fig. 6. Only the
positive values are shaded
Q. Zhang et al.
123
main objectives are to explore if the CFSv2 forecasts for
the stratosphere would remain skillful beyond the inherent
tropospheric predictability time scale of at most 2 weeks
and to understand where the stratospheric predictability of
the CFSv2 forecasts comes from when its prediction for the
tropospheric anomalies becomes unskillful.
We confirm that the AC between reanalyses and fore-
casts for temperature field at 50 hPa (T50) in winter
seasons in both hemispheres remains above 0.3 throughout
the first 30 days of forecasts whereas its counterpart in the
troposphere at 500 hPa drops very quickly and below the
0.3 benchmark at the lead time of 12 days. Therefore, the
stratosphere prediction of the CFSv2 remains skillful well
beyond the 2-week limit of the predictability in the tro-
posphere. The highest score in the stratosphere, both in an
absolute sense and in terms of gain over persistence, is in
Fig. 9 The root mean square of
the wavy portion of daily total
T50 field at 60�N derived from
CFSR for the lead time zero and
CFSv2 for the lead time
between day 1 and day 90
(ordinate) in the period from
January 1999 to December 2010
(abscissa). The panel shows
years a 1999–2002,
b 2003–2006, c 2007–2010
CFSv2 prediction skill
123
cold seasons over high-latitudes, in the months of
NDJFMA in the Northern Hemisphere (NH) and MJJASO
in the Southern Hemisphere (SH). In the equatorial region,
the CFSv2, which does not reproduce well the QBO on its
own, has high skill in predicting [T50] anomalies mainly
due to the long persistency of the initial stratospheric QBO
signal.
To understand where the high prediction skill in the high
latitude stratosphere comes from, we evaluate the skill of
the dominant variability modes in the stratosphere. The first
EOF mode of T50 anomalies in NH represents the annular
mode variability, explaining 23 % of daily variance of
T500. The CFSv2 prediction for this mode remains very
skillful with the AC above 0.5 and 0.3 out to 24 and
Fig. 9 continued
Q. Zhang et al.
123
38 days, respectively. The second and third EOF modes are
dominated by a wavenumber one structure, representing
two ways of warm air to get into the polar stratosphere: one
from the east Asian/west Pacific sector and the other from
the North America sector. In comparison with the annular
mode, the CFSv2’s prediction for these two modes is
noticeably less skillful with the AC score dropping below
0.5 and 0.3 out to 17 and 24 days. The CFSv2’s prediction
skill for the higher EOF modes of T50, which are domi-
nated by higher wave numbers and account for about 45 %
daily variance of T50, becomes as poor as that in the tro-
posphere with no useful information beyond the 2-week
limit.
We have verified that the CFSv2 can capture both tim-
ing and amplitude of wave activities although it may have
large errors in predicting their longitude positions and
Fig. 9 continued
CFSv2 prediction skill
123
spatial scales. This makes it possible that the CFSv2 would
still be able to predict the timing and intensity of the
poleward mass transport carried out by the waves. In other
words, although CFSv2 forecasts already lose most of the
skill in predicting the exact locations of troughs and ridges
beyond week 2, these waves are still present in CFSv2
forecast. As long as the waves in CFSv2 forecasts have
reasonable amplitude with a similar tilting as observations,
their induced poleward mass transport variability in the
stratosphere would more or less agree with that in obser-
vations (i.e., large-amplitude westward tilting waves would
transport more mass poleward and vice versa). This
explains why the CFSv2 has a high skill for the first EOF
mode of T50, the intraseasonal variability of the annular
mode associated with poleward propagation of zonal mean
anomalies, despite that its skill degrades rapidly for higher
EOF modes associated with stationary waves.
According to Cai and Ren (2007), there are typically
1–2 cycles of poleward propagations of stratospheric cir-
culation anomalies of both signs in NH in a winter season,
reflecting the timing and intensity of the dynamically dri-
ven mid-winter stratospheric polar warming and the spring
stratospheric polar warming in NH. This explains why the
gain of the CFSv2’s forecasts for the NH polar stratosphere
over persistent forecasts tends to have two distinct peaks
during cold season: one is December and the other is
March. The poleward propagation of stratospheric circu-
lation anomalies of both signs is much slower in SH. It
takes about 110 days for stratospheric anomalies of one
polarity to propagate from the equator to the Antarctic,
which is almost twice as long as in NH (Ren and Cai 2008).
As a result, there is typically just one cycle of poleward
propagations of stratospheric circulation anomalies of both
signs in an austral winter season, which reflects the timing
and intensity of the final polar stratosphere warming in late
spring or early summer of each year in SH. This explains
why the gain of the CFSv2’s forecasts for the SH polar
stratosphere over persistent forecasts becomes pronounced
(with the same amount of gain as the NH case) mainly
in later spring or early summer (i.e., November and
December).
In summary, we conclude that the CFSv2 is capable of
predicting mid-winter polar stratosphere sudden warming
events in the Northern Hemisphere and the timing of the
final warming polar stratosphere warming in both hemi-
spheres 3–4 weeks in advance. We may thus have reached
the point where one may ask questions about the impact of
a well predicted stratosphere on the prediction skill in the
troposphere, especially in the extended range.
Acknowledgments Ming Cai and Chul-Su Shin are supported in
part by research grants from the NOAA CPO/CPPA program
(NA10OAR4310168) and National Science Foundation (ATM-
0833001). The authors are grateful for the informative and con-
structive comments from Shuntai Zhou and two anonymous reviewers
on the early version of this paper.
References
Anderson JL, van den Dool HM (1994) Skill and return of skill in
dynamic extended-range forecasts. Mon Weather Rev-USA
122:507–516
Baldwin MP, Dunkerton TJ (1999) Propagation of the Arctic
Oscillation from the stratosphere to the troposphere. J Geophys
Res 104:30937–30946
Baldwin MP, Dunkerton TJ (2001) Stratospheric harbingers of
anomalous weather regimes. Science 294:581–584
Baldwin MP, Thompson DWJ, Shuckburgh EF, Norton WA, Gillett NP
(2003a) Weather from the Stratosphere? Science 301:317–319
Baldwin MP, Stephenson DB, Thompson DWJ, Dunkerton TJ,
Charlton AJ, O’Neill A (2003b) Stratospheric memory and
extended-range weather forecasts. Science 301:636–640
Baldwin MP, Stephenson DB, Jolliffe IT (2009) Spatial weighting
and iterative projection methods for EOFs. J Clim 22:234–243
Cai M (2003) Potential vorticity intrusion index and climate
variability of surface temperature. Geophys Res Lett 30:1119.
doi:10.1029/2002GL015926
Cai M, Ren R-C (2006) 40–70 day meridional propagation of global
circulation anomalies. Geophys Res Lett 33:L06818. doi:10.
1029/2005GL025024
Cai M, Ren R-C (2007) Meridional and downward propagation of
atmospheric circulation anomalies. Part I: Northern Hemisphere
cold season variability. J Atmos Sci 64:1880–1901
Charlton AJ, Polvani LM (2007) A new look at stratospheric sudden
warmings. Part I: climatology and modeling benchmarks. J Clim
20:449–469. doi:10.1175/JCLI3996.1
Charney JG, Drazin PG (1961) Propagation of planetary-scale
disturbances from the lower into the upper atmosphere. J Geo-
phys Res 66:83–109
Christiansen B (2005) Downward propagation and statistical forecast
of the near-surface weather. J Geophys Res 110:D14104. doi:10.
1029/2004JD005431
Hardiman SC, Butchart N, Charlton-Perez AJ, Shaw TA, Akiyoshi H,
Baumgaertner A, Bekki S, Braesicke P, Chipperfield M, Dameris
M, Garcia RR, Michou M, Pawson S, Rozanov E, Shibata K
(2011) Improved predictability of the troposphere using strato-
spheric final warmings. J Geophys Res 116:D18113. doi:10.
1029/2011JD015914
Hornqvist E, Kornich H (2012) Tropospheric predictability around
stratospheric warming events examined with an idealized
forecast ensemble. EGU General Assembly 2012, held 22–27
April, 2012 in Vienna, Austria, p 12093
Johnson DR (1989) The forcing and maintenance of global monsoonal
circulations: an isentropic analysis. Adv Geophys 31:43–316
Kiehl JT, Solomon S (1986) On the radiative balance of the
stratosphere. J Atmos Sci 43:1525–1534
Kurda Y (2010) High initial-time sensitivity of medium-range
forecasting observed for a stratospheric sudden warming.
Geophys Res Lett 37:L16804. doi:10.1029/2010GL044119
Lindzen RS, Holton JR (1968) A theory of the quasi-biennial
oscillation. J Atmos Sci 25:1095–1107
Marshall AG, Scaife AA, Ineson S (2009) Enhanced seasonal
prediction of European winter warming following volcanic
eruptions. J Clim 22:6168–6180. doi:10.1175/2009JCLI3145.1
Q. Zhang et al.
123
Maycock AC, Keeley SPE, Charlton-Perez AJ, Doblas-Reyes FJ
(2011) Stratospheric circulation in seasonal forecasting models:
implications for seasonal prediction. Clim Dyn 36(1–2):309–
321. doi:10.1007/s00382-009-0665-x
Newman PA, Rosenfield JE (1997) Stratospheric thermal damping
times. Geophys Res Lett 24:433–436
Ren R-C, Cai M (2006) Polar vortex oscillation viewed in an
isentropic potential vorticity coordinate. Adv Atmos Sci
23:884–900
Ren R-C, Cai M (2007) Meridional and vertical out-of-phase
relationships of temperature anomalies associated with the
NAM variability. Geophys Res Lett 34:L07704. doi:10.1029/
2006GL028729
Ren R-C, Cai M (2008) Meridional and downward propagation of
atmospheric circulation anomalies. Part II: Southern Hemisphere
cold season variability. J Atmos Sci 65:2343–2359
Saha S et al (2010) The NCEP climate forecast system reanalysis.
Bull Am Meteorol Soc 91:1015–1057. doi:10.1175/2010BAMS
3001.1
Saha S, Moorthi S, Wu X, Wang J, Nadiga S, Tripp P, Behringer D,
Hou Y-T, Chuang H, Iredell M, Ek M, Meng J, Yang R, van den
Dool H, Zhang Q, Wang W, Chen M (2013) The NCEP climate
forecast system version 2. Submitted to J Clim
Thompson DWJ, Wallace JM (2001) Regional climate impacts of the
Northern Hemisphere annular mode. Science 293:85–89
Thompson DWJ, Baldwin MP, Wallace JM (2002) Stratospheric
connection to Northern Hemisphere wintertime weather: impli-
cations for prediction. J Clim 15:1421–1428
Townsend RD, Johnson DR (1985) A diagnostic study of the
isentropic zonally averaged mass circulation during the first
GARP global experiment. J Atmos Sci 42:1565–1579. doi:10.
1175/1520-0469(1985)042\1565:ADSOTI[2.0.CO;2
Van den Dool H (2011) An iterative projection method to calculate
EOFs successively without use of the covariance matrix. In: 36th
NOAA annual climate diagnostics and prediction workshop fort
worth, TX, 3–6 October 2011. http://www.nws.noaa.gov/ost/
climate/STIP/36CDPW/36cdpw-vandendool.pdf
Van den Dool H, Saha S, Johansson A (2000) Empirical orthogonal
teleconnections. J Clim 13:1421–1435
Zhang Q, van den Dool H (2012) Relative merit of model
improvement versus availability of retrospective forecasts: the
case of Climate Forecast System MJO prediction. Weather
Forecast 27:1045–1051
Zhou S, Miller AJ, Wang J, Angell JK (2002) Downward-propagating
temperature anomalies in the preconditioned polar stratosphere.
J Clim 15:781–792
CFSv2 prediction skill
123