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: cai@met.fsu.edu; mcai@fsu.edu

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.

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