Stratospheric precursor induces wintertime phase reversal of the “warm Arctic-cold Eurasia” pattern

Domain: chemistry
Published: 2026-02-27
Editorial outcome: major_revision

Abstract
Rapid Arctic warming has reached 2–4 times the global average, contrasting with the cooling trend
in mid-high latitude Eurasia during the 1990s–2010s. A notable phenomenon of this so-called “warm
Arctic-cold Eurasia” (WACE) pattern is its frequent phase reversal between early and late winter seen in
the last decade. As one of the important drivers of climate variability, the role of the stratosphere in WACE
reversal remains unclear. Here, we find that approximately 25 days before WACE reversal, the
morphology of the stratospheric polar vortex over North America-North Atlantic undergoes a transition
between stretching and contraction. Through vertical wave coupling and downward propagation, this
stratospheric transition effectively modulates the key atmospheric circulation responsible for the WACE
reversal. CMIP6 models including complete stratospheric processes can successfully simulate the WACE
reversal induced by the stratospheric precursor, while low-top models fail to capture this linkage. Our
findings deepen the understanding of cold-warm transition events from a stratosphere-troposphere
coupling perspective.

Introduction
The seesaw linkages between Arctic and Eurasian winter temperatures have garnered considerable
attention1-3. Explorations mainly focus on both the long-term trend of “Arctic warming-Eurasia cooling”
and the interannual-decadal variability of the “warm Arctic-cold Eurasia” (WACE) pattern4-5. In the recent
decade, a notable phenomenon of WACE pattern is its frequent phase reversal between early and late
winter6. That is to say, a significant reversal between WACE phase and “cold Arctic-warm Eurasia”
(CAWE) phase occurs in a single winter, and the phase in both early and late winter is pronounced and
persistent (Supplementary Fig. 1). Such phase reversal was observed in seven winters since 2012,
indicating a notable increase in subseasonal variability. The opposite anomalies between early and late
winter cancel each other out on the winter-mean scale, thus presenting a weakened “Arctic warming-
Eurasia cooling” trend6,7. The WACE reversal causes a dramatic change in the meridional gradient of
surface air temperature (SAT) between Arctic and Eurasia8, and substantially enhances the likelihood of
extreme events, including the winter abrupt cold-warm transition in East Asia and the severe spring super
sandstorms in North China9,10. Understanding the physical processes and mechanisms underlying the
WACE reversal is therefore essential for interpreting Arctic-Eurasia climate variability and its
implications for extreme climate.

The formation mechanisms of the WACE pattern have been widely discussed, with more insights
revealed on the interannual-decadal scales. Climate forcing factors, such as the autumn Arctic sea ice
melting11,1, La Niña13, and the Pacific Decadal Oscillation14, can contribute to the WACE pattern through
Rossby wave and stratosphere-troposphere interactions. In the atmospheric internal variability, the
weakened stratospheric polar vortex and the deep Arctic warming are also conducive to the formation of
the WACE pattern15,16. In recent years, increasing attention has been devoted to the phase reversal of
WACE between early and late winter, and its underlying physical mechanisms are being progressively
uncovered. The coordination of the preceding tropical-subtropical sea surface temperature anomalies in
the North Atlantic and Indian Ocean can effectively modulate the reversal between the WACE and CAWE
phase6. In addition, the reversal of Ural blocking anomalies in late December is also a potential factor,
which can affect the upward propagation of planetary-scale waves to promote the contribution of
stratospheric polar vortex to the SAT reversal in Arctic-Eurasia regions17. Previous studies provided
physical explanations for the WACE reversal by focusing on the air-sea interaction and the variations of
tropospheric atmospheric circulations. However, as a key driver of extreme climate, it remains unclear
whether the stratospheric variability can impact the phase reversal of the WACE pattern between early
and late winter.

The stratospheric polar vortex (SPV) is a critical bridge linking the stratospheric variability and the
tropospheric response, and plays a crucial role in climate changes over the mid-high latitudes18,19. The
SPV anomalies can affect the phase of Arctic Oscillation/North Atlantic Oscillation (NAO) through
various mechanisms such as downward propagation of zonal-mean anomalies, vertical wave coupling,
surface amplification20,21, thereby modulating the frequency of tropospheric blockings in the North
Atlantic-Eurasia and the intensity of East Asian winter monsoons22,23. The weakened SPV contributes to
an increasing number of cold air outbreaks in the Northern Hemisphere, especially over northern Eurasia
and eastern America24,25. A stretched SPV, characterized by zonally asymmetric anomalies, can also lead
to cold anomalies over Eurasia through stratosphere-troposphere coupling26,27. The stratosphere exhibits
a longer characteristic timescale compared to the troposphere, thus serving as an important source of
subseasonal-seasonal predictability for the extreme climate28,29. In several winters, the SPV undergoes a
significant phase transition, such as the 1987/1988 winter. The SPV exhibited a prominent transition from
weak to strong, accompanied by an out-of-phase tropospheric zonal wind anomaly between early and late
winter30. This suggests that the changes in the strength or morphology of the SPV have a potential effect
on the SAT reversal in the Arctic-Eurasia region, although this mechanism has not yet been revealed.

Given the close linkages between SPV and troposphere-surface climate variability, we propose
exploring the role of the stratosphere in the WACE reversal. We first examine the characteristics and lead
time of the SPV associated with the WACE reversal, and then investigate the pivotal processes by which
the SPV modulates the phase reversal between WACE and CAWE. The key linkages and processes
proposed are further demonstrated in the large ensemble simulations, and the reasons for the differences
in simulation abilities are discussed.

Results
Linkages between SPV morphology transition and WACE reversal

The WACE pattern is usually expressed by the SAT difference between the Barents–Kara seas (70°–
85°N, 30°–100°E) and Eurasia (40°–60°N, 60°–120°E) after detrending, defined as the WACE index
(the former minus the latter)5,6. The positive WACE represents the WACE phase, while the negative
value represents the CAWE phase. As illustrated by the daily WACE index in the winters of 1979/80–
2023/24, the WACE reversal from early to late winter occurred in 16 winters (see Methods). Among
these, 8 winters experienced a reversal from WACE to CAWE, and 8 winters underwent a reversal from
CAWE to WACE. Most of the reversal points are around January 10th, manifesting as the opposite
WACE between periods December 1st to January 10th (Dec1Jan10, defined as early winter) and January
11th to February 28th (Jan11Feb28, defined as late winter) (Supplementary Fig. 1). The SAT anomalies in
the Arctic and Eurasian centers both show significant cold/warm transition within a single winter and
remain consistent and persistent in each half-winter.

In the composite of these WACE reversal years, a significant feature of stratospheric anomalies is
the transition of the SPV morphology between contraction and stretching over North America-North
Atlantic (Fig. 1a, b). Specifically, when the WACE reverses from the CAWE phase in early winter to
the WACE phase in late winter, the SPV undergoes a variation from contraction to a stretched shape over
North America. The transition time of the SPV morphology is earlier than the WACE reversal, mainly
manifested as an evident transition between November 1st–December 15th (Nov1Dec15) and December
16th–February 10th (Dec16Feb10). During Nov1Dec15, the stratospheric anomalies show a zonal
asymmetry, with negative potential vorticity (PV) anomalies over North America-North Atlantic and
positive anomalies over Eurasia on the 530K isentropic surface (Fig. 1a). However, the PV anomalies
transition to a uniform positive pattern in Dec16Feb10, presenting an enhanced SPV, with its center more
biased towards North America-North Atlantic (Fig. 1b). The SPV changes in these two periods do not
exhibit a completely out-of-phase variation, so the zonal mean stratospheric anomalies cannot capture the
evident features well (Supplementary Fig. 2). In both periods, the contraction and stretching of the SPV
edge relative to the climate state are most significant over North America-North Atlantic, and the local
stratospheric anomalies show significant phase reversal. Therefore, we focus on the linkages between the
SPV morphology transition over North America-North Atlantic and the WACE phase reversal.

The morphology and shifting of SPV are represented by the area-weighted mean of potential vorticity
on the 530K (approximately 44 hPa) over North America-North Atlantic (0–120°W, 60–75°N)31, defined
as the NANA-SPV index. The positive NANA-SPV indicates that the SPV shifts and stretches
toward North America-North Atlantic, while a negative NANA-SPV indicates that the SPV moves
away from and contracts over North America-North Atlantic (Supplementary Fig. 3). When the SAT
pattern changes from CAWE to WACE, the composited NANA-SPV is persistently negative in
Nov1Dec15, then turns to positive in mid-December and maintains until February (Fig. 1c). The SPV
edge determined by 58PVU on the 530K isentropic surface32 also clearly reflects the SPV area over North
America-North Atlantic transits from contraction to expansion (Supplementary Fig. 4). That is to say, a
contracted SPV over North America-North Atlantic in Nov1Dec15 tends to be followed by a CAWE phase
in early winter, and a stretched SPV towards North America-North Atlantic in Dec16Feb10 tends to be
followed by a WACE phase in late winter. Conversely, the SPV morphology transition from stretching to
contracting corresponds to a precursor to the reversal from WACE to CAWE. Both NANA-SPV and
WACE experience significant phase reversal, and the reversal time of NANA-SPV is approximately
25 days prior to that of WACE (Fig. 1c).

The NANA-SPV and WACE processed with a 45-day low-pass filtering can focus more on the
phase changes (Fig. 1c). The filtered variations highlight the pronounced transition of the SPV
morphology over North America-North Atlantic at mid-December, and more clearly reflect the lead-lag
relationship between the NANA-SPV transition and the WACE reversal. The moving t-test of NANA-
SPV and WACE variations can detect the mean-value shift in subsequences (see methods), which also
confirms their phase reversal and corresponding time points in the WACE reversal years (Fig. 1c).

Further analysis on information flow (see methods) shows that the PV anomalies at 530K over North
America-North Atlantic exceed the 95% confidence level for causality (Supplementary Fig. 5), indicating
that the NANA-SPV transition plays a pivotal role in modulating the WACE reversal. During the
longer period from 1950/51 to 2023/24 (25 WACE reversal years), the lead-lag linkages between the
NANA-SPV transition and the WACE reversal still exist (Supplementary Fig. 6). Thus, the SPV
morphology transition over North America-North Atlantic is assumed to be one of the important drivers
for the phase reversal between WACE and CAWE.

The NANA-SPV can effectively capture the variations in SPV morphology and shift over North
America-North Atlantic (Supplementary Fig. 3). Based on the analysis of the daily variation of NANA-
SPV, the years when the SPV morphology over North America-North Atlantic undergoes a transition
are identified. During 1979/80–2023/24, the significant phase transition of NANA-SPV is observed in
18 years (see Methods), including two types: the SPV morphology transition over North America-North
Atlantic from contraction to stretching (9 years) and from stretching to contraction (9 years)
(Supplementary Fig. 7). The transition time of NANA-SPV is predominantly concentrated around
December 15th. This reversal is characterized by stable yet opposite NANA-SPV anomalies between
Nov1Dec15 and Dec16Feb10, and the anomalies in Dec16Feb10 are stronger than that in Nov1Dec15.
Additionally, to assess whether the phenomenon of NANA-SPV phase transition is sensitive to the
selection of the NANA-SPV reversal timing, we perturbed the division dates by a few days around
December 15th and found the results to be consistent. In 12 of the 18 years with NANA-SPV transition,
the WACE reverses from early to late winter (Supplementary Fig. 8), covering up to 75% of the winters
with WACE reversal.

The stratospheric anomalies associated with WACE reversal are deep and barotropic on the vertical
structure, especially over the North America-North Atlantic (Supplementary Fig. 9a). Both during
Nov1Dec15 and Dec16Feb10, the opposite geopotential height anomalies over North America-North
Atlantic can extend from the stratosphere down to the near surface. This phenomenon can also be observed
in the westerly jet surrounding SPV over North America-North Atlantic. The anomalies of geopotential
height and zonal wind in Dec16Feb10 are stronger and last longer than those in Nov1Dec15.
Correspondingly, the WACE in Jan11Feb28, lagging NANA-SPV by about 25 days, is more
prominent and persistent (Fig. 1c), indicating an enhanced impact of NANA-SPV
in Dec16Feb10. The
stratospheric anomalies of geopotential height and the zonal wind over Eurasia are opposite with those
over North America-North Atlantic in Nov1Dec15 (Supplementary Fig. 2). These anomalies can also
extend from the middle stratosphere to the near-surface, indicating the barotropy of the zonal asymmetric
pattern. During the Dec16Feb10 period, the center of the stratospheric signal is more concentrated over
North America-North Atlantic, while it is relatively weak over Eurasia and fails to effectively propagate
downward (Supplementary Fig. 9b). Thus, an important stratospheric precursor associated with the
WACE reversal is the SPV morphology transition over North America-North Atlantic. This raises a
question of how the SPV morphology transition over North America-North Atlantic drives the WACE
pattern to reverse.

Cross-continental physical processes modulated by the SPV

The SPV variations correlate closely with the tropospheric atmosphere through stratosphere-
troposphere coupling processes, thereby affecting the occurrence of extreme weather and climate20. When
a negative NANA-SPV occurs in Nov1Dec15, the SPV morphology is contracted over North America-
North Atlantic. The geopotential height anomalies at 50 hPa form a zonal asymmetrical pattern, with
positive anomalies over North America-North Atlantic and negative anomalies over western Eurasia,
which are consistent with the stratospheric anomalies when WACE reverses (Fig. 2a). We use the Plumb
wave activity fluxes averaged over 60°–70°N as a function of longitude and pressure to investigate the
role of vertical wave coupling21. The Plumb fluxes in the lower stratosphere over North America-North
Atlantic are predominantly upward (Supplementary Fig. 10a), contributing to the enhancement and
persistence of the anomalous stratospheric high pressure over North America-North Atlantic. The upward
and eastward propagating Plumb waves form anomalous downward wave activity flux over Western
Europe, accompanied by the negative geopotential height anomalies that propagate from the stratosphere
to the troposphere (Fig. 3a).

In the troposphere, the positive geopotential height anomaly over North America-North Atlantic and
the negative anomaly over Western Europe form a Rossby wave propagating eastward (Supplementary
Fig. 11a). This is conducive to a notable positive PV anomaly at 315K and anomalously increased static
stability in the Ural Mountains region (Supplementary Fig. 12), thereby suppressing the Ural blocking
activities33 (Fig. 2a). The weakened Ural high can last until mid-January and forms the sustained southerly
winds in the mid-high latitudes of Eurasia (Supplementary Fig. 11c), which hinder the southward transport
of cold air and gather the cold air in the Barents-Kara Seas, thus resulting in a significant CAWE anomaly
during early winter (Fig. 2a, 3c).

When the NANA-SPV transits from negative to positive, the SPV appears to be stretched towards
North America-North Atlantic in Dec16Feb10. The entire Arctic region is covered by an enhanced SPV,
with the center of anomalies biased towards North America-North Atlantic (Fig. 2b). Over North America-
North Atlantic, anomalous downward propagation of the Plumb vertical flux is observed (Fig. 3b,
Supplementary Fig. 10b). The negative geopotential height anomalies and intensified zonal winds
propagate strongly and persistently from the stratosphere to the troposphere (Fig. 3c), contributing to the
formation of a positive NAO phase (Fig. 2b). The Rossby wave train triggered by the stratospheric
atmosphere anomaly is generated in the mid-latitudes of the North Atlantic (Supplementary Fig. 11b, d),
serving as a wave source34. The wave activity flux in the troposphere propagates eastward and causes the
abnormal high pressure over Western Europe and the mid-high latitudes of Eurasia. The persistence of
this Rossby wave makes the Ural High enhanced and sustained in late winter (Fig. 2b). In addition, the
eddy vorticity forcing forms a positive synoptic eddy feedback (see Methods), and further enhances the
tropospheric response35. Under the influence of enhanced SPV, the eddy vorticity forcing in the North
Atlantic is conducive to the maintenance of a positive NAO phase. The divergent eddy vorticity fluxes
over Western Europe and the Ural region generate an anticyclonic forcing (Supplementary Fig. 13), which
strengthens and maintains the Ural blocking in late winter. Driven by the intensified Ural high, a
pronounced WACE phase occurs in late winter that is opposite to that in early winter (Fig. 2b, 3c).

In the real case observed in 1983/84, a typical NANA-SPV transition from negative to positive
occurred, leading to a WACE reversal with a lag of about 25 days (Supplementary Fig. 14). An abnormal
positive pressure center at 50 hPa was located over North America-North Atlantic in Nov1Dec15 of
1983/84, but there was a negative pressure center over Eurasia, representing a contraction of the SPV area
over North America-North Atlantic (Supplementary Fig. 14a). While in Dec16Feb10, the SPV expanded
sharply towards North America-North Atlantic, with a remarkable negative geopotential height anomaly
at 50 hPa (Supplementary Fig. 14b). Affected by the downward influence of the stratospheric anomalies
and the propagation of tropospheric Rossby waves (Supplementary Fig. 15), the Ural high intensity
underwent a significant variation from weakened in early winter to enhanced in late winter, thus causing
a phase reversal from CAWE to WACE (Supplementary Fig. 14c). The stratospheric anomaly in
Dec16Feb10 was stronger than that in the other sub-period, thereby causing a more pronounced response
of Ural high and WACE in late winter. East Asia was affected by the significant WACE phase and
experienced a severe cold wave in January and February of 198436.

The NANA-SPV transition is approximately 25 days ahead of the WACE phase reversal (Fig.
1c), which may be related to the time required for the downward transmission of stratospheric signal and
the excitation and propagation of Rossby waves37. This time interval is coordinated with a maximum
suppression of Ural blocking observed around day 24 following the SPV weakening33. The downward
influences of the SPV morphology transition indicate the modulations from the stratospheric variability
on the phase variations of SAT pattern in the Arctic-Eurasian region, deepening the understanding of the
widely concerned cold-warm transition events from a fresh perspective of stratosphere-troposphere
coupling38.

Simulations of the key processes and linkages

To further determine the robustness of the linkages between the variation of SPV morphology over
North America-North Atlantic and the WACE phase reversal, and verify the proposed physical processes,
we performed the analysis using historical simulations of the Coupled Model Intercomparison Project
Phase 6 (CMIP6) from 1950–2014 and the Community Earth System Model large ensemble (CESM-LM)
experiments from 1920–2005 (see methods). The simulations of 21 CMIP6 models and 39 CESM-LE
members, which have daily data and are available for download, are used for analysis. Since the PV
variable is not directly available in simulations, we use the 50 hPa geopotential height to identify the years
with the SPV morphology transition39. The conclusions obtained from the reanalysis using the PV at 530K
and the geopotential height at 50hPa are consistent (see Methods for detailed explanations).

Specifically, the case is selected as the SPV morphology transition over North America-North
Atlantic from contraction to stretching based on these two conditions: (1) the area-weighted mean of
geopotential height anomalies at 50 hPa over North America-North Atlantic transits from positive in
Nov1Dec15 to negative in Dec16Feb10; (2) the geopotential height anomalies in Nov1Dec15 present a
zonal asymmetry over North America-North Atlantic and Eurasia, which is defined as the simulated “Con-
to-Stre NANA-SPV” case (Supplementary Fig. 16a, b). Conversely, the case is defined as the simulated
“Stre-to-Con NANA-SPV” to represent the SPV morphology transition over North America-North
Atlantic from stretching to contraction (Supplementary Fig. 16c, d). In the CMIP6 and CESM-LE
simulations, the SPV morphology transitions over North America-North Atlantic between Nov1Dec15
and Dec16Feb10 occur in 27% and 28% of the years (Fig. 4a), respectively, which are lower than the
observed frequency of NANA-SPV transition (40%).

The WACE reversal represents a significant WACE difference between early and late winter (the
latter minus the former, defined as Diff-WACE). We first verify whether the SPV morphology transition
over North America-North Atlantic can lead to the corresponding Diff-WACE through the model
simulations. In the 200 cases of simulated Con-to-Stre NANA-SPV, the mean Diff-WACE is positive
(Fig. 4a), and the distribution of SAT difference over Arctic-Eurasia exhibits a notable WACE anomaly
(Supplementary Fig. 17a). Among these 200 cases, 72% show a positive Diff-WACE, indicating that the
transition of SPV morphology over North America-North Atlantic from contraction to stretching is
conducive to the reversal towards the WACE phase. In the 176 cases of simulated Stre-to-Con NANA-
SPV, the mean SAT difference in all such years shows a significant CAWE anomaly (Supplementary Fig.
17b). The negative Diff-WACE can be captured in 71% of these years, indicating a tendency and a higher
probability to reverse to CAWE phase (Fig. 4a). The two transition types based on CESM-LE simulations,
which have a larger sample size, also strongly verify that the SPV morphology transition over North
America-North Atlantic facilitates the reversal between WACE and CAWE phase from early to late winter
(Supplementary Fig. 17c, d). However, the responses of Diff-WACE associated with the SPV
morphology transitions over North America-North Atlantic simulated by CMIP6 and CESM-LE are both
weaker than the reanalysis results (Fig. 4a).

However, there is a large spread of simulated Diff-WACE in Con-to-Stre NANA-SPV and Stre-to-
Con NANA-SPV years in different CMIP6 models, and not all models can capture the physical linkages
between the two well. The model top height is revealed to be one of the key factors restricting the model
simulation ability of the stratosphere-troposphere interactions40. We categorize the models into high-top
and low-top groups based on whether their model top level reaches 0.1 hPa, thereby comparing their
simulation capabilities for the SPV morphology transition and its influence on WACE phase reversal. The
high-top and low-top model groups consist of 9 and 12 models, respectively, with the ranges of top level
being 4.5×10-6–0.1 hPa and 0.2–10 hPa, respectively (Supplementary Table 1).

Both the high-top and low-top models can simulate the variations of the geopotential height
anomalies at 50 hPa during Nov1Dec15 and Dec16Feb10 associated with the SPV morphology transition
over North America-North Atlantic (Fig. 4c, d). In the years when the SPV morphology undergoes
transition, the accuracy rates for the sign of the simulated Diff-WACE in the high-top and low-top models
are 76% and 69%. The accuracy rate refers to the proportion of cases in which a positive Diff-WACE is
simulated in Con-to-Stre NANA-SPV cases and a negative Diff-WACE is simulated in Stre-to-Con
NANA-SPV cases. A higher accuracy rate of high-top models indicates that they have a better simulation
ability for the linkage between SPV morphology transitions and WACE phase reversal. Specifically, both
the high-top and low-top models can simulate the WACE response in early winter, but significant
differences exist in simulations of the WACE in late winter (Fig. 4b). The high-top models can more
accurately reproduce the WACE phase reversal, and the opposite WACE between early and late winter
can be clearly distinguished. Especially for the type where the SPV changes from stretching to contraction,
the high-top models effectively simulate the SAT pattern reversing from WACE to CAWE, while the low-
top models cannot capture the phase reversal in late winter.

The discrepancy in simulating the WACE response between the high-top and low-top models may
stem from the differences in their simulation of the stratospheric anomaly intensity in Dec16Feb10. Both
the high-top and low-top models are capable of simulating the weakened Ural high, which is associated
with the downward influence of the stratospheric zonal asymmetry (Supplementary Fig. 18, 19). The
positive geopotential height anomalies over North America-North Atlantic and negative anomalies over
western Eurasia at 50 hPa in Nov1Dec15 lead to the CAWE phase in early winter (Fig. 4c, d). However,
when stratospheric anomalies undergo a phase reversal, the high-top models simulate a stronger intensity
of the geopotential height anomaly at 50 hPa over North America-North Atlantic in Dec16Feb10
compared to that simulated by low-top models (Fig. 4c), with an approximate enhancement of 18%. The
high-top models can better capture the downward propagation intensity of stratospheric anomalies. The
response of the geopotential height anomalies over the North America-North Atlantic region (defined as
NANA) is more significant (Supplementary Fig. 18d), which is more conducive to the formation and
propagation of Rossby waves in the troposphere, ultimately enhancing the Ural High and promoting a
reversal toward the WACE phase in late winter (Fig. 4c, Supplementary Fig. 18f).

In contrast, the low-top models simulate weaker stratospheric signals and their corresponding
downward propagation over North America-North Atlantic in Dec16Feb10, and the response in the
troposphere extends to the western European coast (Fig. 4d, Supplementary Fig. 19d), which is
unfavorable for the establishment of the Ural high in late winter and the formation of the WACE phase
(Supplementary Fig. 19f). The high top-level models, with comprehensive stratospheric representation,
well simulate and verify the physical linkages through which the SPV morphology transition modulates
the WACE reversal between early and late winter through cross-continental process. Models with a
higher top level are more conducive to simulating the stratosphere-troposphere coupling and its impacts
on near-surface extreme climate, further providing key evidence that model design and construction
should be extended to higher levels.

Methods
Data treatment and statistical methods

In this study, we use the ERA5 reanalysis data for analysis52. The linear trend and its long-term
(1979/80–2023/24) mean of all the daily data are removed, which indicates that the seasonal cycle is also
removed. The method of detrending is to first calculate the slope and intercept of the least squares linear
trend line of the original variables during 1979/80–2023/24, and obtain the linear trend term of year(i) as
slope×year(i)+intercept, and then remove the linear trend term from the original variables to obtain the
detrended results.

In this study, the statistical methods such as correlation coefficient, composite analysis, trend analysis,
significance tests, and moving t-test are used53. The type of correlation coefficient used in this study is
Pearson correlation, which measures the linear relationship between two random variables. The linear
trends during the different sub-periods are calculated by the least squares method. A two-sided student’s t-
test is used to test the statistical significance of the composite analysis. The significance of the correlation
and the slope rates of the linear trends during the different sub-periods can be tested by using the
student’s t-test. The 95% confidence level is denoted by p < 0.05. The moving t-test can examine whether
the difference between the means of two sample groups is statistically significant, in order to detect the
abrupt change point. In this study, a sample length of 45 days is adopted, which effectively captures the
phase variation and shift on the subseasonal scale.

The Liang–Kleeman (L-K) information flow analysis is applied to verify the causal relationship
between the NANA-SPV transition and the WACE reversal. The causality is measured by the time
rate of information flowing from one series to the other. In this study, a causal analysis is conducted on
the 30-day time series of the NANA-SPV phase transition process (December 1st to December 30th)
and the WACE reversal process (December 26th to January 25th). These 30 days represent the 15 days
before and 15 days after the reversal point of NANA-SPV and WACE. According to theory, the
maximum likelihood estimation form of the information flow from time series X2 to time series X1 under
the assumption of the linear model is as follows:

(1) 𝑇 = 𝐶11𝐶12𝐶2,𝑑1−𝐶122𝐶1,𝑑1 / 𝐶121𝐶22−𝐶11𝐶122
2→1

where 𝐶 is the sample covariance between 𝑋 and 𝑋 , and 𝐶 is the covariance between 𝑋
𝑖𝑗 𝑖 𝑗 𝑖,𝑑𝑗 𝑖
and {(𝑋 −𝑋 )/𝜕𝑡}, with 𝜕𝑡 representing the time interval. According to the L-K theory, causation
𝑗,𝑛+1 𝑗,𝑛
implies correlation. However, the converse is that correlation does not imply causation. When |𝑇 | >
2→1
0, 𝑋 is a cause of 𝑋 ; and when |𝑇 | = 0, 𝑋 is not a cause of 𝑋 54.
2 1 2→1 2 1

Definitions of the WACE phase reversal and NANA-SPV transition

The WACE phase reversal needs to satisfy two conditions: (1) the WACE in early winter and late
winter is reversed after the removal of the trend and climate mean of 1979/80–2023/24; and (2) the sum
of the standard deviation in early winter and late winter after the standardization of daily WACE in
December 1st to February 28th is < 1.8. The second condition picks out the persistent WACE or CAWE
stage in half-winter. The threshold of 1.8 is selected based on a summary of year-by-year analyses of daily
WACE index that met the first condition, excluding years that primarily exhibited fluctuating variations.
Minor adjustments to this threshold do not affect the feature of WACE phase reversal. In this study, the
early winter and late winter are divided by January 10th, meaning early winter spans from December 1st
to January 10th, and late winter spans from January 11th to February 28th. To verify the reliability of the
WACE reversal years selected by this method, we perturbed the division dates for a few days before and
after January 10th and found the results consistent.

Using the above similar methods to define the NANA-SPV transition, two conditions also need
to be met: (1) the NANA-SPV in periods Nov1Dec15 and Dec16Feb10 is reversed after the removal
of the trend and climate mean of 1979/80–2023/24; and (2) the sum of the standard deviation in periods
Nov1Dec15 and Dec16Feb10 after the standardization of daily NANA-SPV in November 1st to
February 10th is < 1.6. Similarly, the threshold of 1.6 is selected based on a summary of year-by-year
analyses of daily NANA-SPV index that met the first condition, excluding years that primarily
exhibited fluctuating variations. Minor adjustments to this threshold do not affect the conclusions of this
study. In addition, when perturbing the division date (December 15th), the selected NANA-SPV
transition years remained consistent.

By applying the empirical orthogonal function (EOF) analysis over the latitude-time (day) domain
to daily geopotential height anomaly at 50 hPa zonally averaged from 0° to 120°W55, the spatiotemporal
evolution of the NANA-SPV transition is further explained. The combined manifestation of EOF1 and
EOF3 can effectively capture the variation of geopotential height anomaly associated with the NANA-
SPV transition (Supplementary Fig. 20). The presentation of the EOF pattern is robust, which has
undergone sensitivity tests using the additional period 1950/51–1978/79. The specific manifestation is
that the stratospheric anomaly over North America-North Atlantic reverses at around mid-December, and
the anomaly is stronger during the Dec16Feb10 period. The sum of these two mode’s time series in the
NANA-SPV reversal years is generally extreme (Supplementary Fig. 20g), further indicating the
importance of studying such events.

Plumb wave activity flux

We used the 3D Plumb wave activity flux to examine zonal, meridional, and vertical wave
propagation of quasi-stationary waves56.

(2) (𝐹 ,𝐹 ,𝐹) = 𝑝cos𝜑 [𝑣′2 − 1 𝜕(𝑣′Φ′) / 𝑓𝑎cos𝜑 𝜕𝜆 , -𝑢′𝑣′ + 1 𝜕(𝑢′Φ′) / 𝑓𝑎cos𝜑 𝜕𝜆 , 𝑓 [𝑣′𝑇′ − 1 𝜕(𝑇′Φ′) / 𝑓𝑎cos𝜑 𝜕𝜆 ] / { 𝜕𝑇̃/𝜕𝑧+𝜅𝑇̃/𝐻 }]
𝜆 𝜑 𝑧

where 𝜆 is longitude, 𝜑 is latitude, 𝑧 is height, and 𝑝 is pressure. 𝑢 is the zonal wind, 𝑣 is the
meridional wind, 𝑇 is temperature, and Φ is geopotential height. 𝑓 is the Coriolis parameter. 𝑎 is
Earth’s radius. 𝜅 is the specific gas constant of dry air divided by the specific heat of dry air. 𝑇̃ denotes
the domain average of temperature. 𝐻 is the log-pressure scale height. Primes denote the deviations from
zonal means.

Eddy vorticity forcing

The stream function tendency induced by eddy-vorticity fluxes, namely eddy-vorticity forcing (EVF),
can measure the dynamic synoptic eddy feedback onto the low frequency flow57. The EVF can be
expressed as

(3) (∂ψ𝑎 / ∂t) = -Δ-1∇∙[𝑉′𝜁′]𝑎
se

where 𝑉′(𝑢′,𝑣′) and 𝜁′ denote the 2–8-day bandpass filtered zonal wind, meridional wind, and
vorticity, respectively. [ ]𝑎denote the anomaly during Dec16Feb10 period. ∇∙( ) and ∆-1( ) are the
horizontal divergence and the Laplacian inversion operators, respectively. ( ) indicates the tendency
se
induced by synoptic eddy. The positive (negative) EVF can contribute to a positive (negative) tendency
of the stream function, which expresses an anticyclonic (cyclonic) vorticity tendency.

Calculation methods for the contribution of WACE reversal intensity

The intensity of the WACE reversal is denoted as the WACE difference between early and late
winter (defined as Diff-WACE). The NANA-SPV difference between Nov1Dec15 and Dec16Feb10
serves as the intensity of the stratospheric anomalies. The SST anomalies in the tropical Atlantic and
Indian oceans had significant primary impacts on the WACE/CAWE pattern in early and late winter,
respectively6. Their synergistic effect effectively modulates the phase reversal between the WACE and
CAWE. Therefore, the sum of the standardized time series of these two SST factors is used to represent
the tropical-subtropical SST anomaly signals. After standardizing the time series of tropical-subtropical
SST signals and stratospheric signals, a linear regression is performed against Diff-WACE.
The
contribution of stratospheric anomalies to the WACE reversal intensity in a given year is calculated by
multiplying the regression coefficient of the stratospheric anomalies by their standardized anomaly value
in that year58. The average across all WACE reversal years represents the contribution of stratospheric
anomalies. The same method is applied to obtain the contribution of tropical-subtropical SST signals.

CMIP6 and CESM-LE simulations

To verify the strong linkage between NANA-SPV transition and WACE reversal, the Coupled
Model Intercomparison Project Phase 6 (CMIP6)59 historical simulations and the Community Earth
System Model large ensemble (CESM-LE)60 simulations are used to complement the statistical analyses.
Daily surface air temperature and geopotential height on pressure levels from the historical simulations
of 21 available CMIP6 models from 1950 to 2014 and from 39 members of the Community Earth System
Model from 1920–2005 are employed in this study. Similar to the process of observations, the linear
trends during 1950–2014 in the CMIP6 simulations and during 1920–2005 in the CESM-LE simulations
are removed to obtain the daily anomaly.

Since the PV variable is not directly available in simulations, we use the 50 hPa geopotential height
to identify the years with the SPV morphology transition39. In the WACE
reversal year, both the PV at
530K and the geopotential height at 50 hPa over North America-North Atlantic undergo significant phase
reversals (Supplementary Fig. 21). The daily variations of these two indices are basically the same, only
with opposite signs. The reversal time points of these two indices are basically consistent. When the
NANA-SPV transits, the geopotential height anomaly also shows a phase reversal over North America-
North Atlantic between Nov1Dec15 and Dec16Feb10, with a zonal asymmetric pattern in Nov1Dec15
(Supplementary Fig. 2a). Among the 18 years of observed NANA-SPV transition, 17 years exhibit
these characteristics. Therefore, using these definitions to identify the cases of SPV morphology transition
over North America-North Atlantic in the simulation is relatively reasonable and reliable.

In CMIP6 and CESM-LE simulations, the cases are selected as the SPV morphology transition over
North America-North Atlantic from contraction to stretching based on these two conditions: (1) the area-
weighted mean of geopotential height anomalies at 50 hPa over North America-North Atlantic transits
from positive in Nov1Dec15 to negative in Dec16Feb10; (2) the geopotential height anomalies in
Nov1Dec15 present a zonal asymmetry over North America-North Atlantic and Eurasia. Conversely, the
cases represent the SPV morphology transition over North America-North Atlantic from stretching to
contraction. In addition, we explore the simulation capabilities of the CMIP6 models with different top
height. The models are divided into high-top and low-top groups based on whether the model top level
reaches 0.1 hPa. The high-top and low-top model groups consist of 9 and 12 models, respectively, with
the ranges of top level being 4.5×10-6–0.1 hPa and 0.2–10 hPa, respectively.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "Review of “Stratospheric precursor induces wintertime phase reversal of the “Warm Arctic-Cold Eurasia” pattern” by Zhang et al. This study identifies a stratospheric precursor for the phase shift of the “Warm Arctic-Cold Eurasia” (WACE) pattern in winters. Composite analysis suggests that the sign change in stratospheric anomalies over North America precedes the WACE phase shift by about 25 days. Wave diagnostics suggest that the stratospheric variability facilitates the development of circulation and temperature anomalies over Eurasia. Climate models from CMIP6 generally support the observational results. However, this linkage appears to be missing in low-top models. I find the key points interesting, providing fresh perspectives on the role of the stratosphere in winter climate. But as I explain below, I have several major and minor concerns, mainly regarding the interpretation of the results and the clarity of the methods. In addition, it requires careful, thorough proofreading and language editing in both the main text and the supplementary information. General comments In my opinion, framing the stratospheric variation as an intensity change in the stratospheric polar vortex over North America is confusing and potentially misleading. The intensity of the stratospheric polar vortex is widely studied and is commonly described by the strength of its westerly winds, which reflect the polar vortex's overall intensity. The stratospheric anomalies analyzed here appear to be asymmetric, especially in early winter (Figure 1a). The current description of regional polar vortex intensity is confusing and does not connect well with the literature on the polar vortex, especially given that the significant anomalies appear outside of the vortex edge in the plot. In my opinion, in the years of CAWE to WACE, the morphology of the polar vortex undergoes an evident change. It appears to be stretched towards North America from early to late winter, in contrast to the contraction from a stretched shape during WACE to CAWE years. A stretched polar vortex, characterized by zonally asymmetric anomalies in the stratosphere, has been associated with cold anomalies over Eurasia in both observations and climate models (see Fig. 6 in Zou et al., 2023, Fig. 1 in Ding et al., 2023). On a related note, the discussion on the stratosphere’s downward influence requires major revisions. The authors ambiguously describe it as the stratospheric signal propagates downward into the troposphere, potentially confusing the mechanism of a weak polar vortex with a stretched polar vortex or strong stratospheric waves. Following a weak polar vortex, the downward propagation of negative zonal wind anomalies (negative NAM) may be amplified by tropospheric synoptic eddy feedbacks, thereby inducing midlatitude coldness. During polar vortex stretching, vertical wave coupling and planetary wave reflection are likely responsible for the changes in the tropospheric circulation. Given the asymmetry in the stratospheric anomalies reported here, I would suspect a substantial role of vertical wave coupling. The frequencies of WACE reversal and NAPZ should be added to both the results and methods sections. It only mentioned that there are 16 WACE reversals. But I have no idea whether it means 16 CAWE-to-WACE years or 16 WACE-to-CAWE years. Supplementary Fig. 7 may help, but it lacks a clear caption that explains it to readers. The frequency in models should also be documented and compared with observations. Since the authors find the results consistent during 1950–2023, I suggest including a longer record in CMIP6 models and observations than 1979–2014, as larger sample sizes provide better statistical robustness. It is encouraging to see confirmation in CMIP6 models. And I appreciate the comparison between high-top and low-top models. However, the presentation of Fig. 4b is concerning. Fig. 4b claims a linear relationship between model lid height and the strength of WACE reversal by listing models on a linear x-axis. But the actual differences in model lid heights are far from linear (Supplementary Table 1). For example, several models share the same top level. This information has to be properly accounted for in Fig. 4b, or the presentation can be very misleading. This part also needs further development, as currently the differences between high-top and low-top models appear in the troposphere rather than the stratosphere. What aspects of the stratospheric variability are different? Without a physical explanation, the authors may wish to soften their claim on the role of model lid height. Individual comments L21: What is the “warming hole” in mid-high latitude Eurasia? I’m unaware of such an expression. Was it used elsewhere? L22: It feels like an overstatement, as this reversal does not occur every year. L30: The implication statement seems too general. L46: A decreasing trend of temperature variance has been widely studied (e.g., Screen, 2014). Is it in contradiction to the claim of an increase in subseasonal variability here? L67: How does upward wave propagation affect SAT reversals? They also suggest the important role of the stratospheric polar vortex. L77: This is inaccurate. See my general comments. L83: The stratosphere serves as an important source of predictability due to its longer timescale compared to the troposphere (e.g., Domeisen et al., 2020a, 2020b). L90: “highly likely” feels a bit stretched. A brief review on the polar vortex stretching may suit here (see my general comments). Fig. 1: What is the shading in the upper parts of panel c? What are the makers in the lower parts? What represents the 45-day low-passed results in the upper parts? L171: Documentation of the EOF analysis must be included in the methods. However, another question is, why perform this EOF analysis? It feels disconnected from other parts. L187: No documentation of the EOF analysis. The center of the leading EOF over North America does not imply stronger variability there, as other EOF modes exist. A simpler way to show greater variability would be to plot the variance of geopotential height. However, even if North America shows stronger variability, I don’t see why it can explain a stronger correlation with the WACE reversal. L205: It depends on the type of stratospheric variability. Planetary wave reflection can have nearly immediate tropospheric responses. L216: Where shows the PV and static stability? Fig. 2: What are the colored arrows? What is the reason for connecting those anomaly centers? L247: It could use a reference here. Fig. 3: I don’t find Fig. 3 very informative in discussing the physical processes. In my opinion, instead of a case study, the authors should elaborate on the dynamic diagnostics using composites of all events. I suggest replacing Fig. 3 with Supplementary Fig. 10, or a combination of Supplementary Fig. 9 & 10. It would better illustrate stratosphere-troposphere coupling during WACE reversals and may partly answer the question of whether zonal mean dynamics or vertical wave coupling dominates the process. A description of the wave activity flux must be added in the methods. Currently, I have no idea which flux is discussed. L311: What is the accuracy rate? Fig. 4a: Adding results in reanalysis would help to understand the model performance. Statistical tests also should be added to assess the significance of the Diff-WACE in models. The selected events should be compared with climatology or neutral samples where there are not reversals. L330: What is NAPV on 500 hPa? L381: What are the tropical-subtropical SST signals? Please document how the regression is performed. Fig. 5: What are the dotted arrows? Methods: Which reanalysis is used? L460, 471: Why choose the threshold of 1.8 and 1.6 standard deviations? Are the results sensitive to it? L477: The reference seems only unavailable in English. I suggest choosing a more commonly used method to define the polar vortex edge. Supplementary Fig. 10 & 11: What are the yellow arrows? They exaggerate the downward wave flux anomalies in regions where wave flux anomalies can be hardly seen. References Ding, X., Chen, G., Zhang, P., Domeisen, D. I. V., & Orbe, C. (2023). Extreme stratospheric wave activity as harbingers of cold events over North America. Communications Earth & Environment, 4(1), 187. https://doi.org/10.1038/s43247-023-00845-y Domeisen, D. I. V., Butler, A. H., Charlton-Perez, A. J., Ayarzagüena, B., Baldwin, M. P., Dunn-Sigouin, E., et al. (2020a). The Role of the Stratosphere in Subseasonal to Seasonal Prediction: 1. Predictability of the Stratosphere. Journal of Geophysical Research: Atmospheres, 125(2), e2019JD030920. https://doi.org/10.1029/2019JD030920 Domeisen, D. I. V., Butler, A. H., Charlton-Perez, A. J., Ayarzagüena, B., Baldwin, M. P., Dunn-Sigouin, E., et al. (2020b). The Role of the Stratosphere in Subseasonal to Seasonal Prediction: 2. Predictability Arising From Stratosphere-Troposphere Coupling. Journal of Geophysical Research: Atmospheres, 125(2), e2019JD030923. https://doi.org/10.1029/2019JD030923 Screen, J. A. (2014). Arctic amplification decreases temperature variance in northern mid- to high-latitudes. Nature Climate Change, 4(7), 577–582. https://doi.org/10.1038/nclimate2268 Zou, C., Zhang, R., Zhang, P., Wang, L., & Zhang, R. (2023). Contrasting physical mechanisms linking stratospheric polar vortex stretching events to cold Eurasia between autumn and late winter. Climate Dynamics. https://doi.org/10.1007/s00382-023-07030-z", "reviewer_2": "Reply to Reviewer #1: Review of “Stratospheric precursor induces wintertime phase reversal of the “Warm Arctic-Cold Eurasia” pattern” by Zhang et al. This study identifies a stratospheric precursor for the phase shift of the “Warm Arctic-Cold Eurasia” (WACE) pattern in winters. Composite analysis suggests that the sign change in stratospheric anomalies over North America precedes the WACE phase shift by about 25 days. Wave diagnostics suggest that the stratospheric variability facilitates the development of circulation and temperature anomalies over Eurasia. Climate models from CMIP6 generally support the observational results. However, this linkage appears to be missing in low-top models. I find the key points interesting, providing fresh perspectives on the role of the stratosphere in winter climate. But as I explain below, I have several major and minor concerns, mainly regarding the interpretation of the results and the clarity of the methods. In addition, it requires careful, thorough proofreading and language editing in both the main text and the supplementary information. General comments 1. In my opinion, framing the stratospheric variation as an intensity change in the stratospheric polar vortex over North America is confusing and potentially misleading. The intensity of the stratospheric polar vortex is widely studied and is commonly described by the strength of its westerly winds, which reflect the polar vortex's overall intensity. The stratospheric anomalies analyzed here appear to be asymmetric, especially in early winter (Figure 1a). The current description of regional polar vortex intensity is confusing and does not connect well with the literature on the polar vortex, especially given that the significant anomalies appear outside of the vortex edge in the plot. In my opinion, in the years of CAWE to WACE, the morphology of the polar vortex undergoes an evident change. It appears to be stretched towards North America from early to late winter, in contrast to the contraction from a stretched shape during WACE to CAWE years. A stretched polar vortex, characterized by zonally asymmetric anomalies in the stratosphere, has been associated with cold anomalies over Eurasia in both observations and climate models (see Fig. 6 in Zou et al., 2023, Fig. 1 in Ding et al., 2023). Reply: Your comment has corrected our problem in the mixed usage of word when describing the morphology and intensity of polar vortex. We fully agree that the morphology of the polar vortex more accurately describe the stratospheric variation in our study. In the revised manuscript, we newly employed the area-weighted mean of potential vorticity on the 530K isentropic surface over North America to describe the morphology of the polar vortex (defined as NAPV ), and the availability of this index is shown in Supplementary Fig. 3. IPV After changing to the index describing the morphology of the polar vortex, the conclusion is consistent with our previous findings. The specific analysis and explanation are as follows. Supplementary Fig. 3. Features of NAPV transiton. Composites of the potential vorticity on the IPV 530K isentropic surface in (a) November 1st to December 15th and (b) December 16th to February 10th in the NAPV transition years during 1979/80 to 2023/24 (negative to positive NAPV years minus IPV IPV positive to negative NAPV years). The green, red and blue lines represent the composited polar IPV vortex edge in climate mean, negative to positive NAPV years and positive to negative NAPV IPV IPV years, respectively. The white dots indicate that the results are significant above the 95% confidence level. (1) When the SAT pattern undergoes a phase reversal between WACE and CAWE from early and late winter, the significant stratosphere feature is the transition of polar vortex shape over North America between stretching and contraction from November 1st to December 15th (Nov1Dec15) to December 16th to February 10th (Dec16Feb10). The composited stratospheric zonally asymmetric anomalies in WACE reversal years can capture the phase transition (Fig R1a, b). The wave index, which can reflect the zonal asymmetric anomaly, also shows a significant sign reversal between Nov1Dec15 to Dec16Feb10 (Fig R1c). The zonal wind at 60°N, which reflect the polar vortex’s overall intensity, also shows a phase reversal, but the anomaly during Nov1Dec15 period is weak due to the zonal asymmetric anomalies (Fig R1d-f). The phase transitions of stratospheric anomalies are more pronounced and stronger over North America (the red line in Fig R1f), so we mainly still focus on the variations of the polar vortex morphology over North America Fig R1. Composites of the (a) zonal asymmetric anomalies and (b) zonal wind at 50 hPa in November 1st to December 15th and December 16th to February 10th in the WACE reversal years during 1979/80 to 2023/24 (CAWE to WACE years minus WACE to CAWE years), and the daily variation of the wave index, WACE , and the zonal wind at 60N over the Polar (blue) and over the North America (red) . The T white horizontal line indicate that the results are significant above the 95% confidence level. The thicker lines indicate that the results are significant above the 95% confidence level. (2) In the revised manuscript, the area-weighted mean of the potential vorticity on the 530K isentropic surface (approximately 44 hPa) over North America (0–120°W, 60–75°N) is newly defined (NAPV index) to characterize the morphology and shift of the polar IPV vortex (Zhang et al., 2022). The positive NAPV can indicate that the polar vortex IPV stretches over North America, and a negative NAPV represent that the polar vortex IPV contracts over North America (Supplementary Fig. 3). The stratospheric polar vortex edge at 530K in winter is characterized by the 58 PVU (Karami et al., 2025). Therefore, this index can effectively describe the variations in polar vortex morphology over North America. In the years of CAWE reversing to WACE, the NAPV changes from negative in IPV Nov1Dec15 to positive in Dec16Feb10, indicating that the polar vortex transitions from contraction to stretched shape over North America, in contrast to the a negative NAPV from IPV positive during WACE to CAWE years (Fig. 1). The timing of the NAPV transition also IPV precedes the WACE reversal by approximately 25 days, which is consistent with our previous T conclusion. Fig. 1. Linkages between the precursory stratospheric polar vortex and the reversal of “warm Arctic-cold Eurasia”. Composites of the potential vorticity on the 530K isentropic surface in (a) November 1st to December 15th and (b) December 16th to February 10th in the WACE reversal years T during 1979/80 to 2023/24 (CAWE to WACE years minus WACE to CAWE years). The green, red and blue lines represent the composited polar vortex edge in climate mean, CAWE to CAWE years and WACE to CAWE years, respectively. The SPV edge is determined by 58PVU on the 530K isentropic. The white dots indicate that the results are significant above the 95% confidence level. (c) The upper part: Daily variations of the SPV morphology over North America (NAPV ; red solid line) and the IPV WACE pattern (WACE ; black solid line) composited in the WACE reversal years (CAWE to WACE T years minus WACE to CAWE years), and the composited variations after 45-day low passed filtering are represented by the thick lines. The thicker lines indicate that the results are significant above the 95% confidence level. The red shadings represent the Nov1Dec15 and Dec16Feb10 periods associated with NAPV transitions, and the gray shadings represent the early and late winter associated with WACE IPV T reversal. The lower part: 45-day moving t-test of the NAPV and WACE during November to IPV T February in each WACE reversal years (shading) and their means (lines), and the most significant point T are represented by the markers. The linear trend is removed. (3) The years in which the polar vortex morphology over North America exhibits phase transition are reselected based on the NAPV index. There are 18 years undergoes an evident IPV transition, presenting the revered geopotential height anomalies at 50 hPa between Nov1Dec15 to Dec16Feb10. During Nov1Dec15period, a zonally asymmetric pattern between North America and Eurasia is observed, while during Dec16Feb10 period, a consistent anomaly emerges among North America and Eurasia, though the anomaly center and intensity are biased toward North America (Fig. 2a). The above features are highly consistent with the significant stratospheric variations in the WACE reversal years. Fig. 2. Composites of the geopotential height at 50 hPa in Nov1Dec15 and Dec16Feb10 and surface air temperature in early and late winter according to NAPV transition during 1979/80 to 2023/24 IPV (negative to positive NAPV years minus positive to negative NAPV years). IPV IPV During the NAPV phase transition years, the SAT in Arctic and mid-to-high latitude IPV Eurasia shows a phase reversal between WACE and CAWE from early to late winter (Fig. 2), which is consistent with our previous findings. We mainly focus on winters where the stratospheric polar vortex over North America undergoes transition, rather than individual polar vortex or WACE events. The WACE pattern, as an integrated mode, is one of the primary modulation factors for the cold/warm anomalies across the Eurasian continent. Exploring the physical mechanism of the WACE variations is crucial for better understanding and predicting extreme climate events in the mid-low latitudes. Revisions: Lines 104-121: In the composite of these WACE reversal years, a significant feature of T stratospheric anomalies is the transition of the SPV morphology between contraction and stretching over North America (Fig. 1a, b). Specifically, when the WACE reverses from the T CAWE phase in early winter to the WACE phase in late winter, the SPV undergoes a variation from contraction to a stretched shape over North America. The transition time of the SPV morphology is earlier than the WACE reversal, mainly manifested as an evident transition T between November 1st to December 15th (Nov1Dec15) and December 16th to February 10th (Dec16Feb10). During Nov1Dec15, the stratospheric anomalies show a zonal asymmetry, with negative potential vorticity (PV) anomalies over North America and positive anomalies over Eurasia on the 530K isentropic surface (Fig. 1a). While the PV anomalies transit to a uniform positive in Dec16Feb10, presenting an enhanced SPV, but the center is more biased towards North America (Fig. 1b). The SPV changes in these two periods do not exhibit a uniform and consistent out-of-phase variation, so the zonal mean stratospheric anomalies cannot well capture the evident features (Supplementary Fig. 2). In both periods, the contraction and stretching of the SPV edge relative to the climate state are most significant over North America, and the local stratospheric anomalies show significant phase reversal. Therefore, we focus on the linkages between the SPV morphology transition over North America and the WACE T phase reversal. Lines 122-133: The morphology and shifting of SPV are represented by the area-weighted mean of PV on the 530K (approximately 44 hPa) over North America (0–120°W, 60–75°N)31, defined as NAPV . The positive NAPV indicates that the SPV shifts and stretches toward IPV IPV North America, while a negative NAPV indicates that the SPV moves away from and IPV contracts over North America (Supplementary Fig. 3). When the SAT pattern changes from CAWE to WACE, the composited NAPV is persistently negative in Nov1Dec15, then turns IPV to positive in mid-December and maintains until February (Fig. 1c). The SPV edge determined by 58PVU on the 530K isentropic surface32 also clearly reflect the SPV area over North America transits from contraction to expansion (Supplementary Fig. 4). Similarly, the opposite direction from stretching to contracting is corresponded to the reversal from WACE to CAWE. Both NAPV and WACE experience significant phase reversal, and the reversed time of IPV T NAPV is approximately 25 days prior to that of WACE (Fig. 1c). IPV T Lines 166-171: NAPV can effectively captures the variations of SPV morphology and shift IPV over North America (Supplementary Fig. 3). As illustrated by the daily variation of NAPV , IPV the SPV morphology transitions over North America is further confirmed. During 1979/80– 2023/24, the significant phase transition of NAPV is observed in 18 years (see methods), IPV including two types: the SPV morphology transition over North America from contraction to stretching (9 years) and from stretching to contraction (9 years) (Supplementary Fig. 7).、 Related reference: Zhang, C. et al. Impacts of stratospheric polar vortex shift on the East Asian trough. J. Climate 35(17), 5605–5621 (2022). Karami, H., Jacobi, C. & Kumar, A. The morphology of the stratospheric polar vortex under stratospheric aerosol intervention scenarios. Int. J. Climatol. 45(8), e8838 (2025). 2. On a related note, the discussion on the stratosphere’s downward influence requires major revisions. The authors ambiguously describe it as the stratospheric signal propagates downward into the troposphere, potentially confusing the mechanism of a weak polar vortex with a stretched polar vortex or strong stratospheric waves. Following a weak polar vortex, the downward propagation of negative zonal wind anomalies (negative NAM) may be amplified by tropospheric synoptic eddy feedbacks, thereby inducing midlatitude coldness. During polar vortex stretching, vertical wave coupling and planetary wave reflection are likely responsible for the changes in the tropospheric circulation. Given the asymmetry in the stratospheric anomalies reported here, I would suspect a substantial role of vertical wave coupling. Reply: We re-examined and analyzed the physical mechanism of the downward influence of the SPV, focusing on the vertical wave coupling of the stratospheric zonally asymmetry anomalies during the Nov1Dec15, as well as the tropospheric synoptic eddy feedbacks induced by the downward propagation of the polar vortex anomalies during the Dec16Feb10. The specific analysis are as follows. We first use the Plumb wave activity fluxes averaged over 60°–70°N as a function of longitude and pressure to investigate the downward influence of the stratospheric zonally asymmetry anomalies in Nov1Dec15 (Fig. 3a). When the stratospheric anomalies exhibit a positive geopotential height anomaly over North America and negative anomaly over Eurasia, the SPV contracts over North America, and the abnormal ridge extends from the troposphere to stratosphere. The Plumb fluxes in the lower stratosphere over North America are predominantly abnormal upward (Supplementary Fig. 10a), which contribute to the increased geopotential heights over North America (Fig. 3a). The upward and eastward propagating Plumb waves form an abnormal downward wave activity flux over Western Europe, accompanying by the negative geopotential height anomalies that propagate from the stratosphere to troposphere (Fig. 3c). In the troposphere, the positive geopotential height anomaly over North America-North Atlantic and the negative anomaly over Western Europe form an Rossby wave propagating eastward. This favors the formation of significant positive potential vorticity anomalies at 315K and enhances the static stability over the Ural Mountains region (Supplementary Fig. 12), thereby suppressing the Ural high. The weakened Ural high can persist until mid-January, leading to pronounced CAWE anomalies during the early winter (Fig. 3c). Fig. 3. Physical mechanisms of the SPV morphology transition over North America impacting the WACE reversal. Composites of the anomalous geopotential height (shading) and the vertical and zonal components of anomalous Plumb wave activity flux (vector) averaged over 60°–70°N as a function of longitude and pressure in (a) Nov1Dec15 and (b) Dec16Feb10 according to NAPV transition during IPV 1979/80 to 2023/24 (negative to positive NAPV years minus positive to negative NAPV years). IPV IPV The magnitude of the Plumb flux is scaled by (1000/p)1/2. (c) Composites of the daily variations of the pressure-temporal geopotential height (shadings) and zonal wind (contours) along 0–120°W, 60–70°N, and the daily variations of NAPV , Ural blocking (UB) and WACE index. The thicker lines indicate IPV T that the results are significant above the 95% confidence level. The white dots indicate that the results are significant above the 95% confidence level. Supplementary Fig. 10. The vertical component of Plumb wave activity flux at 100 hPa. Composites of the vertical component of Plumb wave activity flux at 100 hPa in (a) November 1st to December 15th and (b) December 1st to January 10th according to NAPV transition during 1979/80 IPV to 2023/24 (negative to positive NAPV minus positive to negative NAPV ). The white dots indicate that the IPV IPV composites are significant above the 95% confidence level. Supplementary Fig. 12. The responses of the tropospheric potential vorticity and static stability in Nov1Dec15. Composites of the (a) potential vorticity at 315K and (b) static stability in November 1st to December 15th according to NAPV transition during 1979/80 to 2023/24 (negative to positive IPV NAPV minus positive to negative NAPV ). The white dots indicate that the composites are IPV IPV significant above the 95% confidence level. During Dec16Feb10 period, the SPV morphology over North America undergo a significant phase transition, and the stratospheric anomalies change from the zonal asymmetric distribution in Nov1Dec15 to a more uniform anomaly pattern. When the NAPV transits IPV from negative to positive, that is, the SPV morphology over North America turns to be stretched toward North America, the entire Arctic region is covered by an enhanced SPV, with the center of anomalies biased towards North America. Over North America, anomalous downward propagation of the Plumb vertical flux is observed (Fig. 3b). The negative geopotential height anomalies and intensified zonal winds propagate strongly and persistently from the stratosphere to the troposphere (Fig. 3c), contributing to the formation of a positive NAO phase. The Rossby wave train triggered by the stratospheric atmosphere anomaly is generated in the mid-latitudes North Atlantic, serving as a wave source. The wave activity flux in troposphere propagates eastward and causes the abnormal high pressure along the coast of Western Europe and over the mid-high latitudes of Eurasia. The persistence of this Rossby wave makes the Ural High enhanced and sustained in the late winter (Supplementary Fig. 11c, d). Furthermore, the streamfunction tendency induced by eddy vorticity fluxes can be expressed as eddy vorticity forcing to measure the dynamical synoptic eddy feedback onto the zonal wind. Under the influence of enhanced SPV, the eddy vorticity forcing in the North Atlantic region is conducive to the enhancement and maintenance of the positive NAO phase. The divergent eddy vorticity fluxes over Western Europe and the Ural region generates an anticyclonic forcing, forming a positive synoptic eddy feedback (Supplementary Fig. 13), which further strengthened the maintenance of the Ural blocking in late winter. Under the influence of this intensified Ural High, a WACE phase occurs in late winter that is opposite to that in early winter (Fig. 3c). Supplementary Fig. 13. The responses of the synoptic eddy vortex in Dec16Feb10. Composites of the eddy vortex forcing (shading), eddy vortex flux (vector) and stream function (contours) in December 16th to February 10th according to NAPV transition during 1979/80 to 2023/24 (negative to positive IPV NAPV minus positive to negative NAPV ). The white oblique line indicate that the composites are IPV IPV significant above the 95% confidence level. Supplementary Fig. 11. The tropospheric atmospheric circulations. Composites of the geopotential height at 500 hPa in (a) November 1st to December 15th, (b) December 1st to January 10th, (c) December 16th to February 10th and (d) January 11th to February 28th according to NAPV transition IPV during 1979/80 to 2023/24 (negative to positive NAPV minus positive to negative NAPV ). The IPV IPV arrows represent the plumb wave activity flux at 500 hPa. The white dots indicate that the composites are significant above the 95% confidence level. Revisions: Lines 200-210: When a negative NAPV occurs in Nov1Dec15, the SPV morphology is IPV contracted over North America. The geopotential height anomalies at 50 hPa form a zonal asymmetrical pattern, with positive anomalies over North America and negative anomalies over Eurasia, which is consistent with the stratospheric anomalies when WACE reversing (Fig. T 2a). We use the Plumb wave activity fluxes averaged over 60°–70°N as a function of longitude and pressure to investigate the role of vertical wave coupling21. The Plumb fluxes in the lower stratosphere over North America are predominantly upward (Supplementary Fig. 10a), contributing to the enhancement and persistent of the anomalous stratospheric high pressure over North America. The upward and eastward propagating Plumb waves form abnormal downward wave activity flux over Western Europe, accompanying by the negative geopotential height anomalies that propagate from the stratosphere to troposphere (Fig. 3a). Lines 224-232: In the troposphere, the positive geopotential height anomaly over North America-North Atlantic and the negative anomaly over Western Europe form a Rossby wave propagating eastward (Supplementary Fig. 11a). This is conducive to a notable positive PV anomaly at 315K and anomalous increased static stability in the Ural Mountains region (Supplementary Fig. 12), thereby suppressing the Ural blocking activities33 (Fig. 2a). The weakened Ural high can last until mid-January and forms the sustained southerly winds in the mid-high latitudes of Eurasia (Supplementary Fig. 11c), which hinder the southward transport of cold air and gather the cold air in the Barents-Kara Sea, thus resulting in a significant CAWE anomaly during early winter (Fig. 2a, 3c). Lines 244-262: When the NAPV transits from negative to positive, the SPV appears to be IPV stretched towards North America from Nov1Dec15 to Dec16Feb10. The entire Arctic region is covered by an enhanced SPV, with the center of anomalies biased towards North America (Fig. 2b). Over North America, anomalous downward propagation of the Plumb vertical flux is observed (Fig. 3b, Supplementary Fig. 10b). The negative geopotential height anomalies and intensified zonal winds propagate strongly and persistently from the stratosphere to the troposphere (Fig. 3c), contributing to the formation of a positive NAO phase (Fig. 2b). The Rossby wave train triggered by the stratospheric atmosphere anomaly is generated in the mid- latitudes North Atlantic (Supplementary Fig. 11b, d), serving as a wave source34. The wave activity flux in troposphere propagates eastward and causes the abnormal high pressure over the Western Europe and the mid-high latitudes of Eurasia. The persistence of this Rossby wave makes the Ural High enhanced and sustained in late winter (Fig. 2b). In addition, the eddy vorticity forcing forms a positive synoptic eddy feedback (see methods), and further enhances the tropospheric response35. Under the influence of enhanced SPV, the eddy vorticity forcing in the North Atlantic is conducive to the maintenance of a positive NAO phase. The divergent eddy vorticity fluxes over Western Europe and the Ural region generates an anticyclonic forcing, (Supplementary Fig. 13), which strengthens and maintains the Ural blocking in late winter. Driven by the intensified Ural high, a pronounced WACE phase occurs in late winter that is opposite to that in early winter (Fig. 2b, 3c). 3. The frequencies of WACE reversal and NAPZ should be added to both the results and methods sections. It only mentioned that there are 16 WACE reversals. But I have no idea whether it means 16 CAWE-to-WACE years or 16 WACE-to-CAWE years. Supplementary Fig. 7 may help, but it lacks a clear caption that explains it to readers. The frequency in models should also be documented and compared with observations. Since the authors find the results consistent during 1950–2023, I suggest including a longer record in CMIP6 models and observations than 1979–2014, as larger sample sizes provide better statistical robustness. Reply: From 1979 to 2023 (45 years), a total of 16 winters showed a WACE phases reversal T between the early and later winter. Among these, 8 winters showed a reversal from CAWE to WACE and 8 years reversed from WACE to CAWE. In terms of NAPV phase IPV transitions between Nov1Dec 15 and Dec16Feb10, 18 years displayed such transitions. Specifically, the polar vortex morphology over North America transitioned from contraction to stretching in 9 years, and from stretching to contraction in another 9 years. We have added these descriptions in the result, method section and related figure captions. In the revised manuscript, the CMIP6 data from 1950 to 2014 are used to simulate and verify the linkages between the SPV morphological transition and the WACE phase reversal, T as well as the associated physical processes. Since the potential vorticity data is not directly available in CMIP6 outputs, we use the geopotential height at 50hPa to identify the years with the SPV morphology transition. Specifically, the definition is based on the following criteria: the geopotential height anomalies at 50 hPa over North America between Nov1Dec 15 and Dec16Feb10 is opposite, and the geopotential height anomalies in Nov1Dec 15 present a zonal asymmetry over North America and Eurasia. We examine that the conclusions based on the reanalysis data obtained by using potential vorticity and geopotential height at 50hPa are consistent, which is also been clarified in the Methods section. Among the 18 years of observed NAPV transition, 17 years exhibit these characteristics. The composite geopotential height IPV anomalies at 50 hPa based on this definition in CMIP6 simulations present stratospheric anomalies consistent with those during NAPV transitions in the reanalysis data IPV (Supplementary Fig. 16). Therefore, using this definition to identify the years of SPV morphology transition over North America in the CMIP6 simulation is relatively reasonable and reliable. During the 1950–2014, among the 21 CMIP6 models, a total of 376 cases show the SPV morphology phase transition over North America between Nov1Dec15 and Dec16Feb10, accounting for 27%, which is lower than the percentage of NAPV IPV transition in the observations (40%). We have added the descriptions in the manuscript regarding the frequency comparison between the model simulations and observations. Supplementary Fig. 16. Simulated geopotential height anomaly at 50 hPa of the SPV morphology transition. Multi-member mean of the simulated geopotential height anomaly at 50 hPa in (a, c) November 1st to December 15th and (b, d) December 16th to February 10th according to simulated Con-to-Stre NAPV years and Stre-to-Con NAPV years based on CMIP6 simulations. The white dots indicate the results significant above the 95% confidence level. Revisions: Lines 94-98: The positive WACE represents the WACE phase, while the negative value T represents the CAWE phase. As illustrated by the daily WACE in the winters during 1979/80– T 2023/24, the WACE reversal from early to late winter occurred in 16 winters (see methods). T Among these, 8 winters experienced a reversal from WACE to CAWE, and 8 winters underwent a reversal from CAWE to WACE. Lines 168-171: During 1979/80–2023/24, the significant phase transition of NAPV is IPV observed in 18 years (see methods), including two types: the SPV morphology transition over North America from contraction to stretching (9 years) and from stretching to contraction (9 years) (Supplementary Fig. 7). Lines 288-306: …… we perform the analysis using historical simulations of the Coupled Model Intercomparison Project Phase 6 (CMIP6) from 1950–2014 and the Community Earth System Model large ensemble (CESM-LM) experiments from 1920–2005 (see methods). The simulations of 21 CMIP6 models and 39 members of the CESM-LE, which have daily data and are available for download, are used to analyze. Since the PV variable is not directly available in simulations, we use the 50hPa geopotential height to identify the years with the SPV morphology transition39. The conclusions obtained from the reanalysis using the PV at 530K and the geopotential height at 50hPa are consistent (detailed explanations see methods). Specifically, the case is selected as the SPV morphology transition over North America from contraction to stretching based on these two conditions: (1) the area-weighted mean of geopotential height anomalies at 50 hPa over North America transits from positive in Nov1Dec15 to negative in Dec16Feb10, (2) the geopotential height anomalies in Nov1Dec 15 present a zonal asymmetry over North America and Eurasia, which is defined as the “simulated Con-to-Stre NAPV” case (Supplementary Fig. 16a, b). Conversely, the case is defined as “simulated Stre-to-Con NAPV” to represent the SPV morphology transition over North America from stretching to contraction (Supplementary Fig. 16c, d). In the CMIP6 and CESM simulations, the SPV morphology transitions over North America between Nov1Dec15 and Dec16Feb10 occur in 27% and 28% of the years (Fig. 4a), respectively, which are lower than the observed frequency of NAPV transition (40%). IPV Lines 561-571: Since the PV variable is not directly available in simulations, we use the 50hPa geopotential height to identify the years with the SPV morphology transition39. In the WACE T reversal year, both the PV at 530K and the geopotential height at 50 hPa over North America undergo significant phase reversals (Supplementary Fig. 21). The daily variations of these two index are basically the same, only with opposite signs. The reversal time points of these two index are basically consistent. When the NAPV transits, the geopotential height anomaly IPV also shows a phase reversal over North America between Nov1Dec15 and Dec16Feb10, with a zonal asymmetric pattern in Nov1Dec15 (Supplementary Fig. 2a). Among the 18 years of observed NAPV transition, 17 years exhibit these characteristics. Therefore, using these IPV definitions to identify the cases of SPV morphology transition over North America in the simulation is relatively reasonable and reliable. 4. It is encouraging to see confirmation in CMIP6 models. And I appreciate the comparison between high-top and low-top models. However, the presentation of Fig. 4b is concerning. Fig. 4b claims a linear relationship between model lid height and the strength of WACE reversal by listing models on a linear x-axis. But the actual differences in model lid heights are far from linear (Supplementary Table 1). For example, several models share the same top level. This information has to be properly accounted for in Fig. 4b, or the presentation can be very misleading. This part also needs further development, as currently the differences between high-top and low-top models appear in the troposphere rather than the stratosphere. What aspects of the stratospheric variability are different? Without a physical explanation, the authors may wish to soften their claim on the role of model lid height. Reply: It is indeed inappropriate to describe the relationship between the model top level and the simulation ability as linear in Fig 4b. What we intend to express is that the high top-level model has a better simulation ability for the linkage between SPV morphology transition and WACE phase reversal, while the low top-level model has a weaker simulation ability. In the revised manuscript, we categorize the models into high-top and low-top groups based on whether the model top level reaches 0.1 hPa, thereby comparing their simulation capabilities for the SPV morphology transition and its influence on WACE phase reversal. The high-top and low-top model group consist of 9 and 12 models, respectively, with the ranges of the top level being 4.5×10-6–0.01hPa and 0.2–10hPa, respectively. Both the high-top and low-top models can simulate the SPV morphological transition over North America, with the simulated frequencies of 27.5% and 26.1% respectively, showing no significant difference. In the years when the SPV morphology undergoes phase transition, the correct simulation rates for the sign of the Diff-WACE in the high-top and low-top models are 76% and 69%, T respectively, indicating that the high-top model has a stronger simulation ability for the linkage between SPV morphology transitions and WACE phase reversal. Specifically, both the high-top and low-top model can simulate the WACE response in early winter, but significant T differences exist in simulations of the WACE reversal in late winter. The high-top models T can more accurately simulate the WACE phase reversal in late winter, and the intensity T of simulated WACE is stronger (Fig. 4b). Especially for the type where the SPV changes T from stretching to contraction, the high-top models effectively simulate the SAT pattern reversing from WACE to CAWE, while the low-top model cannot capture the phase reversal in late winter. We find that this difference may stem from the simulation difference of the stratospheric anomalies intensity in Dec16Feb10 between the high-top and low-top models (Fig. 4c, d). The high-top models simulate a stronger intensity of the geopotential height anomalies at 50 hPa over North America in Dec16Feb10 period compared to low-top models, with an approximate enhancement of 18%. Therefore, the high-top models can better capture the downward propagation of stratospheric anomalies over the North America-North Atlantic region, which is more conducive to the formation and propagation of Rossby wave in the troposphere, ultimately leading to the opposite-phase response of the Ural high in late winter compared to the early winter (Fig. 4c). In contrast, the low-top models simulate weaker downward propagation of stratospheric signals during Dec16Feb10 period, with the response in troposphere extending to the western European coast, which is not conducive to the establishment of the Ural high in late winter (Fig. 4d). In the revised manuscript, we have modified the simulation analysis of the influence of SPV morphology transition on WACE phase in the high-top and low-top models, and added the above possible explanations for the differences between the two model groups. Fig. 4. Verifications of the physical linkages in simulations. (a) Multi-member mean and the probability distribution of the simulated Diff-WACE in the simulated Con-to-Stre NAPV years (red) T and Stre-to-Con NAPV years (blue) based on CMIP6 simulations and CESM-LE simulations. The boxplots show the 25th and 75th percentiles and the mean. The hollow triangles represent the reanalysis results. (b) The simulated WACE in early and late winter in the simulated Con-to-Stre NAPV years T (red) and Stre-to-Con NAPV years (blue) based on the High-top and Low-top CMIP6 models. The boxplots show the 25th and 75th percentiles and the mean. (c, d) Composites of the pressure-temporal geopotential height along 0–120°W, 60–75°N, and the daily variation of the NA , UB and WACE Z500 T according to the simulated SPV morphology transition (Con-to-Stre NAPV years minus Stre-to-Con NAPV years) that selected from the High-top and Low-top CMIP6 models. The white dots and the thicker lines indicate that the results are significant above the 95% confidence level. Revisions: Lines 336-380: However, there is a large spread of simulated Diff-WACE in Con-to-Stre T NAPV and Stre-to-Con NAPV years in different CMIP6 models, and not all models can well capture the physical linkages between the two. The height of top-level is revealed to be one of the key factors restricting the model simulation ability of the stratosphere-troposphere interactions40. We categorize the models into high-top and low-top groups based on whether the model top level reaches 0.1 hPa, thereby comparing their simulation capabilities for the SPV morphology transition and its influence on WACE phase reversal. The high-top and low- top model group consist of 9 and 12 models, respectively, with the ranges of top level being 4.5×10-6–0.1hPa and 0.2–10hPa, respectively (Supplementary Table 1). Both the high-top and low-top models can simulate the variations of the geopotential height anomalies at 50 hPa during Nov1Dec15 and Dec16Feb10 associated with the SPV morphology transition over North America (Fig. 4c, d). In the years when the SPV morphology undergoes transition, the accuracy rates for the sign of the simulated Diff-WACE in the high- T top and low-top models are 76% and 69%. The accuracy rate refers to the proportion of cases in which a positive Diff-WACE is simulated in Con-to-Stre NAPV cases and a negative Diff- T WACE is simulated in Stre-to-Con NAPV cases. A higher accuracy rate of high-top models T indicates that the they have a better simulation ability for the linkage between SPV morphology transitions and WACE phase reversal. Specifically, both the high-top and low-top model can T simulate the WACE response in early winter, but significant differences exist in simulations T of the WACE in late winter (Fig. 4b). The high-top models can more accurately reproduce the T WACE phase reversal, and the opposite WACE between early and late winter can be clearly T T distinguished. Especially for the type where the SPV changes from stretching to contraction, the high-top models effectively simulate the SAT pattern reversing from WACE to CAWE, while the low-top model cannot capture the phase reversal in late winter. The discrepancy in simulating the WACE response between the high-top and low-top T models may stem from the differences in their simulation of the stratospheric anomalies intensity in Dec16Feb10. Both the high-top and low-top models are capable of simulating the weakened Ural high, which is associated with the downward influence of the stratospheric zonally asymmetry (Supplementary Fig. 18, 19). The positive geopotential height anomalies over North America and negative anomalies over Eurasia at 50 hPa in Nov1Dec15 lead to the CAWE phase in early winter (Fig. 4c, d). However, when stratospheric anomalies undergo a phase reversal, the high-top models simulate a stronger intensity of the geopotential height anomaly at 50 hPa over North America in Dec16Feb10 compared to that simulated by low-top models (Fig. 4c), with an approximate enhancement of 18%. The high-top models can better capture the downward propagation intensity of stratospheric anomalies. The response of the geopotential height anomalies over the North America-North Atlantic region (defined as NA ) is more significant (Supplementary Fig. 18d), which is more conducive to the Z500 formation and propagation of Rossby wave in the troposphere, ultimately enhancing the Ural High and promoting a reversal toward to WACE phase in late winter (Fig. 4c, Supplementary Fig. 18f). In contrast, the low-top models simulate weaker stratospheric signals and the corresponding downward propagation over North America in Dec16Feb10, and the response in troposphere extends to the western European coast (Fig. 4d, Supplementary Fig. 19d), which is unfavorable for the establishment of the Ural high in late winter and the formation of the WACE phase (Supplementary Fig. 19f). Individual comments L21: What is the “warming hole” in mid-high latitude Eurasia? I’m unaware of such an expression. Was it used elsewhere? Reply: The “warming hole” refers to the phenomenon where, under the background of global warming, the SAT in mid-high latitudes of Eurasia do not show a warming trend, and even a cooling trend occurred during the 1990s-2010s, thus forming a “warming hole”. This expression has appeared in a few articles (Gong et al., 2025; Sun et al., 2022), but it may not be conducive to understanding. Therefore, we have revised “warming hole” to “cooling trend during the 1990s-2010s”. Related reference: Gong H et al., 2025. Teleconnection from Arctic warming suppresses long-term warming in central Eurasia. Science Advance, 11, eadq9461. Sun C et al., 2022. CMIP6 model simulation of concurrent continental warming holes in Eurasia and North America since 1990 and their relation to the Indo-Pacific SST warming. Global and Planetary Change, 213, 103824. Revisions: Lines 20-21: Rapid Arctic warming has reached 2–4 times the global average, contrasting with the cooling trend in mid-high latitude Eurasia during the 1990s–2010s. L22: It feels like an overstatement, as this reversal does not occur every year. Reply: Our description here is not precise enough, and we have revised it to “frequent phase reversal between early and late winter in recent decade”. Revisions: Lines 21-23: A notable phenomenon of “warm Arctic-cold Eurasia” (WACE) pattern is its frequent phase reversal between early and late winter in recent decade. L30: The implication statement seems too general. Reply: We have rephrased the implication statement. Revisions: Lines 30-32: Our findings deepen the understanding of the widely concerned cold-warm transition events from a fresh perspective of stratosphere-troposphere coupling. L46: A decreasing trend of temperature variance has been widely studied (e.g., Screen, 2014). Is it in contradiction to the claim of an increase in subseasonal variability here? Reply: This statement is not contradictory. In our previous work, we carefully analyzed the relationship between the WACE phase reversal and the winter-mean “Arctic warming-Eurasia cooling” trend (Yin et al., 2023). Through ERA5 data and CMIP6 historical and SSP585 simulations, we find that the frequent WACE phase reversal occurs simultaneously with a decreasing “Arctic warming-Eurasia cooling” trend. That is to say, the frequent WACE phase reversal after 2012 lead to an increase in the subseasonal variability, but at the same time, the opposite anomalies in early and late winter cancel each other out, resulting in a reduced anomaly in the winter-mean scale anomalies. We have added this explanation in the manuscript. Related reference: Yin, Z. C. et al. Subseasonal variability and the “Arctic warming-Eurasia cooling” trend. Sci. Bull. 68 (5), 528–535 (2023). Revisions: Lines 42-43: The opposite anomalies between early and late winter cancel each other out on the winter-mean scale, thus presenting a decreasing trend of surface air temperature (SAT)7. L67: How does upward wave propagation affect SAT reversals? They also suggest the important role of the stratospheric polar vortex. Reply: The research by Xu et al. revealed that the reversal of Ural blocking in late December can modulate upward propagation of planetary wave 1, leading to a weakening of the stratospheric polar vortex, which subsequently promoted the contribution of stratospheric polar vortex to the reversal of surface air temperature anomalies over the Arctic–Eurasian region in late winter. This mechanism primarily emphasizes the troposphere–stratosphere pathway initiated by tropospheric fluctuations. We have rewritten this sentence to make the information clearer. Revisions: Lines 59-62: In addition, the reversal of Ural blocking anomalies in late December is also a potential factor, which can affect the upward propagation of planetary-scale waves to promote the contribution of stratospheric polar vortex to the SAT reversal in Arctic-Eurasia regions17. L77: This is inaccurate. See my general comments. Reply: We have revised this description. Revisions: Lines 69-71: The SPV anomalies can affect the phase of Arctic Oscillation/North Atlantic Oscillation (NAO) through various mechanisms such as downward propagation of zonal-mean anomalies, vertical wave coupling, surface amplification20,21, L83: The stratosphere serves as an important source of predictability due to its longer timescale compared to the troposphere (e.g., Domeisen et al., 2020a, 2020b). Reply: We have revised this sentence. Revisions: Lines 76-78: The stratosphere exhibits longer characteristic timescale compared to the troposphere, thus serving as an important source of subseasonal-seasonal predictability for the extreme climate28,29. L90: “highly likely” feels a bit stretched. A brief review on the polar vortex stretching may suit here (see my general comments). Reply: We have added a brief review on the impact of the stretched polar vortex on SAT anomalies in Eurasia. Revisions: Lines 75-83: A stretched SPV, characterized by zonally asymmetric anomalies, also can lead to cold anomalies over Eurasia through stratosphere-troposphere coupling26.27. …… These suggest that the changes in the strength or morphology of the SPV have a potential effect on the SAT reversal in Arctic-Eurasia region, although this mechanism has not yet been revealed at present. Fig. 1: What is the shading in the upper parts of panel c? What are the makers in the lower parts? What represents the 45-day low-passed results in the upper parts? Reply: The red shadings represent the two periods of the SPV morphology transitions, namely Nov1Dec15 and Dec16Feb10. The black shadings indicate the early winter and late winter periods associated with the WACE phase reversal. The use of shading provides a more intuitive visualization of the variations of SPV and WACE at different time periods. The markers denote the lowest points identified by the moving t-test, offering a clearer indication of the most significant timing of the SPV morphology transition and the WACE phase reversal. The thick red and black solid lines in the upper parts of panel c represent results after applying a 45-day low-pass filter, while the thin solid lines show the unfiltered results. All previously unclear or missing information mentioned above has now been supplemented and revised in the figure captions. Revisions: Lines 142-155: (c) The upper part: Daily variations of the SPV morphology over North America (NAPV ; red solid line) and the WACE pattern (WACE ; black solid line) composited in the WACE IPV T reversal years (CAWE to WACE years minus WACE to CAWE years), and the composited variations after 45-day low passed filtering are represented by the thick lines. The thicker lines indicate that the results are significant above the 95% confidence level. The red shadings represent the Nov1Dec15 and Dec16Feb10 periods associated with NAPV transitions, and the gray shadings represent the early IPV and late winter associated with WACE reversal. The lower part: 45-day moving t-test of the NAPV and T IPV WACE during November to February in each WACE reversal years (shading) and their means T T (lines), and the most significant point are represented by the markers. L171: Documentation of the EOF analysis must be included in the methods. However, another question is, why perform this EOF analysis? It feels disconnected from other parts. Reply: We performed this EOF analysis to demonstrate that the phase transition of stratospheric geopotential height anomalies over North America is a real and observable phenomenon, which can be explained by the time-varying leading EOF mode. However, placing this explanation in the main text indeed felt somewhat abrupt. We have streamlined this content and moved it to the method section that defines SPV morphology transition. We have also added the documentation of the EOF analysis in the methods section. Revisions： Lines 503-513: By applying the empirical orthogonal function (EOF) analysis in the latitude- time (day) domain to daily geopotential height anomaly at 50 hPa zonally averaged from 0° to 120°W55, the spatiotemporal evolution of the NAPV transition is further explained. The IPV combined manifestation of the EOF1 and EOF3 can effectively captures the variation of geopotential height anomaly associated with the NAPV transition (Supplementary Fig. 20). IPV The presentation of the EOF pattern is robust, which is undergone sensitivity tests using the additional period 1950/51–1978/79 (figure not shown). The specific manifestation is that the stratospheric anomaly over North America reverses at around mid-December, and the anomaly is stronger during the Dec16Feb10 period. The sum of these two mode’s time series in the NAPV reversal years is generally extreme (Supplementary Fig. 20g), further indicating the IPV importance of studying such events. L187: No documentation of the EOF analysis. The center of the leading EOF over North America does not imply stronger variability there, as other EOF modes exist. A simpler way to show greater variability would be to plot the variance of geopotential height. However, even if North America shows stronger variability, I don’t see why it can explain a stronger correlation with the WACE reversal. Reply: Our explanation is indeed inadequate and has been removed. Regarding why the correlation between stratospheric anomalies over North America and WACE reversal is stronger, we primarily attribute it to the fact that during the Dec16Feb10 period, the center of stratospheric signals is more concentrated over North America, and a complete downward propagation process occurs over the North America–North Atlantic region. This downward propagation is not observed over Eurasia. However, we have not provided a clear explanation for why stratospheric anomalies are more pronounced over North America and have acknowledged this limitation in the discussion. Revisions: Lines 393-396: However, the verification using the CMIP6 and CESM-LE experiments is a qualitative simulation, and the sensitivity experiments are needed to directly control the intensity and distribution of stratospheric anomalies. Such experiments may further clarify why stratospheric changes over North America exhibit a stronger correlation with WACE reversal. T L205: It depends on the type of stratospheric variability. Planetary wave reflection can have nearly immediate tropospheric responses. Reply： The expression of this sentence is not precise. We have rewritten it. Revisions: Lines 198-200: The SPV variations correlate closely with the tropospheric atmosphere through stratosphere–troposphere coupling processes, thereby affecting the occurrence of extreme weather and climate20. L216: Where shows the PV and static stability? Reply: We have supplemented the figure of the PV at 315K and static stability at 300 hPa as Supplementary Fig.12. This figure shows that when the SPV contracts over North America during Nov1Dec15, a significant PV anomaly and abnormally enhanced static stability occurred in the Ural Mountains region, thereby weakening the Ural High in early winter. Revisions： Supplementary Fig. 12. The responses of the tropospheric potential vorticity and static stability in Nov1Dec15. Composites of the (a) potential vorticity at 315K and (b) static stability in November 1st to December 15th according to NAPV transition during 1979/80 to 2023/24 (negative to positive IPV NAPV minus positive to negative NAPV ). The white dots indicate that the composites are IPV IPV significant above the 95% confidence level. Fig. 2: What are the colored arrows? What is the reason for connecting those anomaly centers? Reply: These arrows indicate the propagation of the plumb waves at 500 hPa during the Nov1Dec15 and Dec16Feb10 periods, as depicted in the Supplementary Fig.11. We added this description to the figure capture. Revisions: Lines 220-221: The cyan arrows represent the propagation of the plumb wave at the 500 hPa in Nov1Dec15 and Dec16Feb10. L247: It could use a reference here. Reply: We have rephrased this sentence added the related reference. Revisions: Lines 281-284: The downward influence of the SPV morphology transition reveal the modulations from the stratospheric variability on the extreme SAT, deepening the understanding of the widely concerned cold-warm transition events from a fresh perspective of stratosphere-troposphere coupling38. 38. Kretschmer, M. et al. The different stratospheric influence on cold-extremes in Eurasia and North America. npj Clim. Atmo. Sci. 1, 44 (2018). Fig. 3: I don’t find Fig. 3 very informative in discussing the physical processes. In my opinion, instead of a case study, the authors should elaborate on the dynamic diagnostics using composites of all events. I suggest replacing Fig. 3 with Supplementary Fig. 10, or a combination of Supplementary Fig. 9 & 10. It would better illustrate stratosphere-troposphere coupling during WACE reversals and may partly answer the question of whether zonal mean dynamics or vertical wave coupling dominates the process. A description of the wave activity flux must be added in the methods. Currently, I have no idea which flux is discussed. Reply: We have redrawn the Fig. 3 and included this case analysis in the Supplementary Fig.14. The revised Fig. 3 presents the dynamic diagnostic analysis of all NAPV transition. It IPV mainly indicates the time-varying signals from the stratosphere to the troposphere over North America during NAPV transition, as well as the WACE phase reversal between early and IPV T late winter caused by the stratospheric changes through the Ural high. In Fig. 3a, b, the vertical components of the plumb wave and geopotential height anomalies of longitude and pressure during the Nov1Dec15 and Dec16Feb10 periods are presented. All relevant analyses have been revised in the manuscript. In this study, the plumb wave activity flux is used, and we have added it in the method section. Revisions： Fig. 3. Physical mechanisms of the SPV morphology transition over North America impacting the WACE reversal. Composites of the anomalous geopotential height (shading) and the vertical and zonal components of anomalous Plumb wave activity flux (vector) averaged over 60°–70°N as a function of longitude and pressure in (a) Nov1Dec15 and (b) Dec16Feb10 according to NAPV transition during IPV 1979/80 to 2023/24 (negative to positive NAPV years minus positive to negative NAPV years). IPV IPV The magnitude of the Plumb flux is scaled by (1000/p)1/2. (c) Composites of the daily variations of the pressure-temporal geopotential height (shadings) and zonal wind (contours) along 0–120°W, 60–70°N, and the daily variations of NAPV , Ural blocking (UB) and WACE index. The thicker lines indicate IPV T that the results are significant above the 95% confidence level. The white dots indicate that the results are significant above the 95% confidence level. L311: What is the accuracy rate? Reply: The accuracy rate refers to the ratio at which the sign of Diff-WACE is correctly T simulated in the years of SPV morphology transition. Based on our analysis, when the SPV morphology over North America changes from contraction to stretching, it can cause the SAT pattern reversing from CAWE to WACE, that is, the sign of Diff-WACE is positive. In T the opposite direction of SPV morphology transition, the sign of Diff-WACE is negative. T We have added the explanation of the accuracy rate in the manuscript. Revisions: Lines 349-351: The accuracy rate refers to the proportion of cases in which a positive Diff- WACE is simulated in Con-to-Stre NAPV cases and a negative Diff-WACE is simulated in T T Stre-to-Con NAPV cases. Fig. 4a: Adding results in reanalysis would help to understand the model performance. Statistical tests also should be added to assess the significance of the Diff-WACE in models. The selected events should be compared with climatology or neutral samples where there are not reversals. Reply: We have added the Diff-WACE of reanalysis in the Fig. 4a and represented them with T hollow triangles. In the Supplementary Fig.17, we present the spatial distribution of SAT difference between early and late winter in two types of SPV morphology transition, and represent the significance test of it compared with climatology. The results show that, compared with the climatology, the SAT differences in the Arctic and Eurasia between the early and late winter caused by SPV morphology transition are significant. Revisions: Lines 333-335: However, the responses of Diff-WACE associated with the SPV morphology T transitions over North America simulated by CMIP6 and CESM-LE are both weaker than the reanalysis results (Fig. 4a). Fig4. (a) Multi-member mean and the probability distribution of the simulated Diff-WACE in the T simulated Con-to-Stre NAPV years (red) and Stre-to-Con NAPV years (blue) based on CMIP6 simulations and CESM-LE simulations. The boxplots show the 25th and 75th percentiles and the mean. The hollow triangles represent the reanalysis results. Supplementary Fig. 17. Simulated WACE difference between early and late winter. Multi- T member mean of the simulated SAT difference between early and late winter under the Con-to-Stre NAPV years and Stre-to-Con NAPV years based on (a, b) CMIP6 and (c, d) CESM-LE simulations. The white dots indicate the results significant above the 95% confidence level relative to the climate mean SAT difference between early and late winter. L330: What is NAPV on 500 hPa? Reply: It refers to the geopotential height anomalies over North American-Atlantic region in the troposphere, which is caused by the stratospheric signals downward-propagation during Dec16Feb10. We have redefined it as NA , and added its definition in the manuscript. Z500 Revisions: Lines 369-372: The high-top models can better capture the downward propagation intensity of stratospheric anomalies. The response of the geopotential height anomalies over the North America-North Atlantic region (defined as NA ) is more significant (Supplementary Fig. Z500 18d), …… L381: What are the tropical-subtropical SST signals? Please document how the regression is performed. Reply: The tropical-subtropical SST signals are the Nov-Dec SST anomalies of the North Atlantic and Jul-Aug SST anomalies of the Indian Ocean, which are revealed to impact the WACE phase reversal in our previous work (Yin et al, 2023). The SST anomalies in the tropical North Atlantic and Indian oceans had significant primary impacts on the WACE/CAWE pattern in early and late winter, respectively. Their coordination work to effectively modulate the phase reversal between the WACE and CAWE. Therefore, the sum of the standardized time series of these two SST factors is used to represent the tropical-subtropical SST signals anomaly. The NAPV difference between Nov1Dec15 and Dec16Feb10 serves as the stratospheric IPV anomalies. The intensity of the WACE reversal is denoted the WACE difference between T T early and late winter (defined as Diff-WACE ). T After standardizing the time series of tropical-subtropical SST signals and stratospheric signals, a linear regression is performed against Diff-WACE . The contribution of T stratospheric anomalies to the WACE reversal intensity in a given year is calculated by T multiplying the regression coefficient of the stratospheric anomalies by their standardized anomaly value in that year. The average across all WACE reversal years represents the T contribution of stratospheric anomalies. The same method is applied to obtain the contribution of tropical-subtropical SST signals. This calculation approach follows the methodology used in studies such as Zhang et al. (2024). We have added the calculation method for these contributions in the methods section. Revisions: Lines 536-550: Calculation method for the contribution of WACE reversal intensity T The intensity of the WACE reversal is denoted the WACE difference between early and T T late winter (defined as Diff-WACE ). The NAPV difference between Nov1Dec15 and T IPV Dec16Feb10 serves as the intensity of the stratospheric anomalies. The SST anomalies in the tropical Atlantic and Indian oceans had significant primary impacts on the WACE/CAWE pattern in early and late winter, respectively6. Their coordination work to effectively modulate the phase reversal between the WACE and CAWE. Therefore, the sum of the standardized time series of these two SST factors is used to represent the tropical-subtropical SST signals anomaly. After standardizing the time series of tropical-subtropical SST signals and stratospheric signals, a linear regression is performed against Diff-WACE . The contribution of stratospheric T anomalies to the WACE reversal intensity in a given year is calculated by T multiplying the regression coefficient of the stratospheric anomalies by their standardized anomaly value in that year58. The average across all WACE reversal years represents the contribution of T stratospheric anomalies. The same method is applied to obtain the contribution of tropical-subtropical SST signals. 58. Zhang, R. et al. A stratospheric precursor of East Asian summer droughts and floods. Nat. Commun. 15, 247 (2024). Fig. 5: What are the dotted arrows? Reply: The dotted arrow indicates the evolution of stratospheric anomalies, that is, the process where positive geopotential height anomalies gradually weaken while an enhanced SPV gradually develop. We have added the explanation of this dotted arrow in the figure caption. Revisions: Line 428: The dotted arrow indicates the evolution of stratospheric anomalies. Methods: Which reanalysis is used? Reply： In the revised manuscript, we have used ERA5 daily reanalysis data for analysis. We have added this description in the method section. Revisions: Line 449: In this study, we use the ERA5 reanalysis data for analysis. L460, 471: Why choose the threshold of 1.8 and 1.6 standard deviations? Are the results sensitive to it? Reply: This threshold is set to screen out the relatively stable and continuous phase transitions of WACE and NAPV . For the WACE phase reversal, based on the daily WACE analysis of T IPV T T the 20 winter selected by the first criterion, 4 of these years do not exhibit a stable and persistent WACE or CAWE phase in early or late winter, instead showing fluctuating variations (Fig. R2, 3). A common feature of these four years is that the sum of the standard deviations of WACE in early winter and late winter exceeds 1.8. Therefore, this study adopts T this threshold as the second criterion for defining the WACE phase reversal. T Fig R2. The variation of WACE in early and late winter. The blue and red solid dots represent the T WACE to CAWE years and CAWE to WACE years, respectively, and the hollow dots represent the 4 years removed. Fig R3. The daily variation of WACE in the 4 years removed. T Adjusting this threshold to 1.9 has no significant impact on the feature of WACE T reversal (Fig R4). Fig R4. Composites of latitude-temporal SAT along 30-100°E in the WACE reversal years (CAWE to T WACE years minus WACE to CAWE years) using the threshold of 1.9. The selection of a 1.6 standard deviation threshold for NAPV transition follows the IPV same rationale. Based on the daily NAPV analysis of the 26 years exhibiting opposite phase IPV between Nov1Dece15 and Dec16Feb10, 8 of these years do not show stable and persistent NAPV , instead displaying fluctuating variations (Fig. R5, 6). A common characteristic IPV of these 8 years is that the sum of their standard deviations exceeds 1.6. Fig R5. The variation of NAPV in Nov1Dec15 and Dec16Fen10. The blue and red solid dots IPV represent the positive to negative NAPV transition years and the negative to positive NAPV IPV IPV transition years, respectively, and the hollow dots represent the 8 years removed. Fig R6. The daily variation of NAPV in the 8 years removed. IPV Adjusting this threshold to 1.7 has no significant impact on the response of SAT anomalies caused by NAPV transitions (Fig. R7). Minor adjustments to these two IPV threshold do not affect the conclusions of this study. We have added the above explanation in the method section. Fig R7. The SAT response in early and late winter to NAPV transition using the threshold of 1.7. IPV Revisions: Lines 486-489: The threshold of 1.8 is selected based on a summary of year-by-year analyses of daily WACE index that met the first condition, excluding years that primarily exhibited T fluctuating variations. Minor adjustments to this threshold do not affect the feature of WACE T phase reversal. Lines 498-501: Similarly, the threshold of 1.6 is selected based on a summary of year-by-year analyses of daily NAPV index that met the first condition, excluding years that primarily IPV exhibited fluctuating variations. Minor adjustments to this threshold do not affect the affect the conclusions of this study. L477: The reference seems only unavailable in English. I suggest choosing a more commonly used method to define the polar vortex edge. Reply: In the revised manuscript, we redefined the polar vortex edge based on isentropic potential vortices. The research of Karami et al. (2025) showed that the stratospheric polar vortex edge at 530K in winter can be characterized by the 58 PVU in winter. Based on this, we redrew the changes in the polar vortex edge in the Nov1Dec15 and Dec16Feb10 associated with the WACE reversal. T Revisions: Lines 128-130: The SPV edge determined by 58PVU on the 530K isentropic surface32 also clearly reflect the SPV area over North America transits from contraction to expansion 32. Karami, H., Jacobi, C. & Kumar, A. The morphology of the stratospheric polar vortex under stratospheric aerosol intervention scenarios. Int. J. Climatol. 45(8), e8838 (2025). Supplementary Fig. 10 & 11: What are the yellow arrows? They exaggerate the downward wave flux anomalies in regions where wave flux anomalies can be hardly seen. Reply: In the revised manuscript, the vertical wave flux is scaled by (1000/p)1/2, and removed these yellow arrows. Revisions: Line 239: The magnitude of the Plumb flux is scaled by (1000/p)1/2. Reply to Reviewer #2: Review of Zhang et al.: “Stratospheric precursor induces wintertime phase reversal of the “Warm Arctic-Cold Eurasia” pattern” In the present study, Zhang et al. investigate the relationship between stratospheric polar vortex variability over North America and the phase reversals of the so-called Warm Arctic-Cold Eurasia (WACE) pattern during boreal winter. Rather than individual polar vortex or WACE events, the authors focus on winters where the stratospheric polar vortex over North America transitions from a negative geopotential height anomaly to a positive anomaly (or vice versa). This transition over time is then linked to a corresponding transition of the WACE pattern at the surface, with a lag of a few weeks. In a set of supplementary analyses, based on wave activity flux diagnostics, the authors argue that Rossby waves propagate downward from the stratosphere to the troposphere, thereby modulating the strength of the Ural blocking and the associated surface temperature anomalies over Eurasia. The relationship is further explored in climate models from CMIP6, where the authors find that models with a higher model top tend to better capture the observed relationship. The study addresses a quite specific topic, focusing on phase reversals of the WACE pattern, as opposed to individual events. The long timescales involved are interesting, as the coupled stratosphere-troposphere evolution is assessed over an entire winter, making it relevant for (sub) seasonal prediction. The quality of the figure presentation is generally very good. Furthermore, clear efforts have been made to provide a comprehensive analysis including various diagnostics, fields, and models. However, the overall clarity of the presentation needs substantial improvement. The manuscript is fairly dense, and I found it sometimes difficult to follow the analyses. In particular, the event definitions for the composites need to be described more clearly. Furthermore, the manuscript would benefit from careful language editing. In several places, the phrasing is unclear enough to make it difficult to follow the authors’ intended meaning. I have some more general comments, followed by a list of more specific comments. Reply: We have made clearer phrasing and careful revising for the language expression of the article. The previously unclear methods and definitions have all been added in the main text and the methods section. To address the issue of article density, we have used shorter sentences and more concise paragraphs to express our content, thereby enhancing readability. 1. In my view, the analysis lacks a more explicit consideration of the polar vortex strength itself. The authors focus primarily on geopotential height anomalies at 50 hPa over North America; however, stratospheric variability is inherently large-scale, dominated by changes in the zonal-mean flow with superimposed planetary wave structures. Anomalies over North America may capture part of this variability, but it is not clear that they are the most relevant metric for diagnosing stratosphere troposphere coupling. Including a basic polar vortex strength index– for example, the mean zonal wind anomaly at 60N, 10hPa or the area-averaged geopotential height anomaly– would help establish whether the localized anomalies indeed add explanatory power beyond what a zonal mean or planetary-wave index already provides. This would also clarify whether the so-called “phase shift” over North America represents a distinct dynamical feature or rather the regional manifestation of a zonal-mean (or wave-1) anomaly. Testing whether the overall vortex strength anomaly explains part of the surface temperature evolution over Eurasia would further strengthen the argument. At minimum, a short discussion of this point would help readers understand how the chosen metric relates to the large-scale stratospheric variability that drives the WACE pattern. Reply: The basic polar vortex strength index also shows a phase reversal between Nov1Dec15 and Dec16Feb10 when the WACE pattern reversing. But the anomaly during the Nov1Dec15 period is very weak due to a zonal asymmetric pattern. Furthermore, the anomaly center of the polar vortex during the Dec16Feb10 period is biased towards North America. The phase reversal of stratospheric anomaly occurs more significantly over North America, so the local index over North America can more clearly show the significant variations of the key feature in our study. In addition, the previous description of the “weak/strong polar vortex over North America” is indeed confusing. What we are truly focused is the morphology transition of polar vortex between contraction and stretching over North America. In the revised manuscript, we newly employed the area-weighted mean of potential vorticity on the 530K isentropic surface over North America to describe the morphology of the polar vortex (defined as NAPV ), and IPV the availability of this index is shown in Supplementary Fig. 3. After changing to the index describing the morphology of the polar vortex, the conclusion is consistent with our previous findings. The specific analysis and explanation are as follows. Supplementary Fig. 3. Features of NAPV transiton. Composites of the potential vorticity on the IPV 530K isentropic surface in (a) November 1st to December 15th and (b) December 16th to February 10th in the NAPV transition years during 1979/80 to 2023/24 (negative to positive NAPV years minus IPV IPV positive to negative NAPV years). The green, red and blue lines represent the composited polar IPV vortex edge in climate mean, negative to positive NAPV years and positive to negative NAPV IPV IPV years, respectively. The white dots indicate that the results are significant above the 95% confidence level. (1) When the SAT pattern reverse from a CAWE phase in early winter to a WACE phase in late winter, the zonal wind at 60°N at 10 hPa during Nov 1–Dec 15 period shows a pronounced negative anomaly over North America but a positive anomaly over Eurasia, presenting a zonal asymmetry (Supplementary Fig. 1a). As a result, the mean zonal wind at 60°N appears only as a weak negative anomaly. During Dec 16–Feb 10 period, the zonal wind at 60°N at 10 hPa displays a consistently significant enhancement, but the center of the maximum anomalies and the significant areas are more biased toward North America. The area-averaged geopotential height anomalies over the entire polar also shows the consistent changes mentioned above (Supplementary Fig. 1b). Supplementary Fig. 1. Linkages between the stratopheric polar vortex strength itself and the reversal of “warm Arctic-cold Eurasia”. Composites of the (a) geopotential height and (b) zonal wind at 50 hPa in November 1st to December 15th and December 16th to February 10th in the WACE reversal years during 1979/80 to 2023/24 (CAWE to WACE years minus WACE to CAWE years), and the daily variation of the geopotential height at 60N-90N and zonal wind at 60N over the Polar (blue) and North America (red). The white horizontal line indicate that the results are significant above the 95% confidence level. The thicker lines indicate that the results are significant above the 95% confidence level. The basic polar vortex index shows a reversal from a weak negative anomaly in Nov1Dec15 to a significant positive anomaly in the Dec16Feb10 period. This out-of-phase variation mainly occurs over North America, which is a significant manifestation of the zonal mean anomaly. Therefore, we focus on local stratospheric anomalies over North America, which more clearly capture the key feature of the stratospheric anomaly phase transition. We have added this analysis into the manuscript to explain why we concentrate on the local changes over North America. (2) Our previous description, that is, the phase transition between the strong and weak polar vortex over North America, is indeed inappropriate and potentially confusing. In the revised manuscript, we modify this description to the polar vortex morphology transitions between contraction and stretching over North America from Nov1Dec15 to Dec 16Feb10 (Fig. 1). The area-weighted mean of the potential vorticity on the 530K isentropic surface (approximately 44 hPa) over North America (0–120°W, 60–75°N) is newly defined (NAPV IPV index) to characterize the morphology and shift of the polar vortex. The positive NAPV can IPV indicate that the polar vortex stretches over North America, and a negative NAPV IPV represent that the polar vortex contracts over North America (Supplementary Fig. 6). The stratospheric polar vortex edge at 530K in winter is characterized by the 58 PVU (Karami et al., 2025). Therefore, this index can effectively describe the variations in polar vortex morphology over North America. Fig. 1. Linkages between the precursory stratospheric polar vortex and the reversal of “warm Arctic-cold Eurasia”. Composites of the potential vorticity on the 530K isentropic surface in (a) November 1st to December 15th and (b) December 16th to February 10th in the WACE reversal years T during 1979/80 to 2023/24 (CAWE to WACE years minus WACE to CAWE years). The green, red and blue lines represent the composited polar vortex edge in climate mean, CAWE to CAWE years and WACE to CAWE years, respectively. The SPV edge is determined by 58PVU on the 530K isentropic. The white dots indicate that the results are significant above the 95% confidence level. (c) The upper part: Daily variations of the SPV morphology over North America (NAPV ; red solid line) and the IPV WACE pattern (WACE ; black solid line) composited in the WACE reversal years (CAWE to WACE T years minus WACE to CAWE years), and the composited variations after 45-day low passed filtering are represented by the thick lines. The thicker lines indicate that the results are significant above the 95% confidence level. The red shadings represent the Nov1Dec15 and Dec16Feb10 periods associated with NAPV transitions, and the gray shadings represent the early and late winter associated with WACE IPV T reversal. The lower part: 45-day moving t-test of the NAPV and WACE during November to IPV T February in each WACE reversal years (shading) and their means (lines), and the most significant point T are represented by the markers. The linear trend is removed. The years in which the polar vortex morphology over North America exhibits phase transition are reselected based on the NAPV index. During these years, the SAT in Arctic IPV and mid-to-high latitude Eurasia shows a significatt phase reversal between WACE and CAWE from early to late winter (Fig. 2). The timing of the NAPV transition precedes the WACE IPV T reversal by approximately 25 days, which is consistent with our previous conclusion. Fig. 2. Composites of the SAT in early and late winter according to NAPV transition during 1979/80 IPV to 2023/24 (negative to positive NAPV years minus positive to negative NAPV years). The white IPV IPV dots in the bottom panels indicate that the results are significant above the 95% confidence level. (3) We also preliminarily test the linkage between the phase transition of overall polar vortex strength anomaly and the SAT reversal over the Arctic–mid-high latitude Eurasia. The results show that when the polar vortex transits from overall weak to strong, the SAT responses in Arctic-Eurasia all exhibits warm anomalies with limited intensity and significance (Fig. R1). The WACE phase can emerge in late winter, but the intensity is relatively weak compared with the WACE response in Fig. 2b. Thus, the phase transition of the polar vortex strength anomaly can partially explain the WACE pattern, but it cannot clearly correspond to the WACE phase reversal between early and late winter. Fig R1. The SAT response in early and late winter under the years with phase transition of overall polar vortex strength anomaly. Revisions： Lines 104-121：In the composite of these WACE reversal years, a significant feature of T stratospheric anomalies is the transition of the SPV morphology between contraction and stretching over North America (Fig. 1a, b). Specifically, when the WACE reverses from the T CAWE phase in early winter to the WACE phase in late winter, the SPV undergoes a variation from contraction to a stretched shape over North America. The transition time of the SPV morphology is earlier than the WACE reversal, mainly manifested as an evident transition T between November 1st to December 15th (Nov1Dec15) and December 16th to February 10th (Dec16Feb10). During Nov1Dec15, the stratospheric anomalies show a zonal asymmetry, with negative potential vorticity (PV) anomalies over North America and positive anomalies over Eurasia on the 530K isentropic surface (Fig. 1a). While the PV anomalies transit to a uniform positive in Dec16Feb10, presenting an enhanced SPV, but the center is more biased towards North America (Fig. 1b). The SPV changes in these two periods do not exhibit a uniform and consistent out-of-phase variation, so the zonal mean stratospheric anomalies cannot well capture the evident features (Supplementary Fig. 2). In both periods, the contraction and stretching of the SPV edge relative to the climate state are most significant over North America, and the local stratospheric anomalies show significant phase reversal. Therefore, we focus on the linkages between the SPV morphology transition over North America and the WACE T phase reversal. 2. On a related note, I wonder whether the apparent phase reversal of the WACE pattern could be related to the lagged surface response to the stratospheric precursor. Specifically, do events characterized by negative SPV intensity over North America (Fig. 1c, top) tend to be followed, after several weeks, by negative WACE index anomalies (Fig. 1c, middle), and vice versa for positive SPV intensity events? If so, conditioning on WACE phase reversals might effectively be selecting the lagged response to the stratospheric signal, rather than an independent mode of variability. While this interpretation would not necessarily contradict the authors’ conclusions, it would be useful to clarify and discuss this point. Reply： In fact, numerous studies have revealed that the WACE pattern is an independent mode that is enhanced under the background of global warming (Fig. R2; Mori et al., 2014; Jin et al., 2020). This pattern can be identified in the second EOF mode of the winter SAT over the Arctic-northern Eurasia region, indicating that it is a dominant mode. The formation mechanism of the WACE pattern is complex, including the atmospheric response to changes in Arctic Sea ice and tropical-subtropical SST (Mori et al., 2019; Matsumura et al., 2019), as well as the internal atmospheric dynamics (Blackport et al., 2022; Ku et al., 2025) Fig. R2. The second EOF pattern of the winter SAT over the Arctic-northern Eurasia region (extracting from Mori et al., (2014)) From 1979 to 2023, there were a total of 16 years of WACE phase reversals. In these 16 years, the stratospheric precursor could be found in 12 of them, which indicates that the physical mechanism of the WACE phase reversals is extremely complex and is not solely influenced by the stratosphere. Previous studies have revealed that the WACE phase reversal can be influenced by the reversal of the tropospheric Ural high in late December (Xu et al., 2022), which can be associated with the differences of the impact of autumn Arctic sea ice on the climate in early and late winter (Lü et al., 2019). The coordination of the SST anomalies in the tropical North Atlantic and Indian oceans also can modulate the WACE phase reversal (Yin et al., 2023). In this study, we proposed that the changes in stratospheric anomalies over North America is also an important driver for the WACE phase reversal between early and late winter. We have clarified this point in the manuscript. Related reference: Mori, M., et al. Robust Arctic sea-ice influence on the frequent Eurasian cold winters in past decades. Nat. Geosci. 7, 869–873 (2014). Ku, H.-Y., et al. Unraveling the Warm Arctic–Cold Eurasia Pattern: Interplay of Arctic Amplification and Internal Variability in Shaping Midlatitude Weather. J. Climate, 38, 4975–4987 (2025). Blackport, R., et al. Minimal influence of reduced Arctic sea ice on coincident cold winters in mid-latitudes. Nat. Clim. Change 9, 697–704 (2019). Jin, C., et al. “Warm Arctic–cold Siberia” as an internal mode instigated by North Atlantic warming. Geophys. Res. Lett. 47, L086248 (2020). Matsumura, S. & Kosaka, Y. Arctic–E. Arctic–Eurasian climate linkage induced by tropical ocean variability. Nat. Commun. 10, 3441 (2019). Mori, M., et al. A reconciled estimate of the influence of Arctic sea-ice loss on recent Eurasian cooling. Nat. Clim. Change, 9, 123–219 (2019). Xu, X. et al. The role of mid-latitude westerly jet in the impacts of November Ural blocking on early-winter warmer Arctic-colder Eurasia pattern. Geophys. Res. Lett. 49, e2022GL099096 (2022). Lü, Z. et al. Impacts of the autumn Arctic sea ice on the intraseasonal reversal of the winter Siberian High. Adv. Atmos. Sci., 36(2): 173–188 (2019). Yin, Z. C. et al. Subseasonal variability and the “Arctic warming-Eurasia cooling” trend. Sci. Bull. 68 (5), 528–535 (2023). Revisions: Lines 163-165: Thus, the SPV morphology transitions over North America is assumed to be one of the important driver for the phase reversal between WACE and CAWE from early and late winter. Lines 177-179: In 12 of the 18 years with NAPV transition, the WACE reverses from early IPV T to late winter (Supplementary Fig. 8), covering up to 75% of the winters with WACE reversal. 3. I wonder about the implications for seasonal prediction. The current analysis defines events based on characteristics of the entire winter season, which may limit the predictive potential of the relationship. Could the authors assess (or at least discuss) whether, based on their findings, information from the first half of winter has skill in predicting the WACE pattern or surface temperature anomalies in the second half of winter? Reply： As we pointed out in the response to the comment 2, there are many climate factors influencing the formation of WACE pattern and its phase reversal, not just the stratosphere. For this reason, we did not construct a comprehensive prediction model for the variation of WACE in the previous version. Based on your hint, we attempted to quantify the improvement in predicting the WACE pattern by incorporating the observed stratospheric signals into the European Centre for Medium-Range Weather Forecasts (EC) results. After adding the stratospheric prediction signal, the prediction results have indeed improved significantly, which also confirms the importance of this new stratospheric signal that we have discovered. The correlation coefficients between predicted and observed WACE index increase from 0.39 to 0.52 for early winter and from 0.31 to 0.50 for late winter during 1979–2023. To truly predict the subseasonal to seasonal variations of the WACE pattern, it is necessary to comprehensively consider multiple signals, including the stratosphere and tropical sea surface temperatures. The following are the specific details. (1) Our findings indicate that the phase transition of stratospheric anomalies over North America between Nov1Dec15 and Dec16Feb10 can induce a phase reversal of the WACE pattern between early winter (Dec1Jan10) and late winter (Jan11Feb28). The prediction information from the stratosphere based on our findings is that the daily evolution of stratospheric signals from November 1st to February 10th can provide the predictive information for the variation of WACE phase and intensity in winter (December 1st– February 28th). The reversal point of the stratospheric precursor leads that of WACE by approximately 25 days, corresponding to a predictive time scale of about 25 days. (2) Based on the daily SAT predictions from the European Centre for Medium-Range Weather Forecasts (EC), we incorporate the stratospheric precursor signals into the EC forecast to examine whether our findings can improve the subseasonal-to-seasonal perdition skill of winter SAT over the Arctic and the mid-high latitude Eurasia. Specifically, a multiple linear regression correction is applied at each grid using the PV anomaly over North America (NAPV ) averaged in the preceding 20–25 days as predictors. The SAT in early winter IPV predicted by the EC forecast is released in November, while for late winter, the predicted SAT released in December are used. For example, by using the mean NAPV index from IPV November 1st–5th and the SAT forecast for December 1st from the EC model released in November, an improved SAT prediction for December 1st is obtained through a multiple linear regression. The improved SAT prediction for December 2nd to January 10th are adjusted analogously. For SAT prediction in late winter (January 11–February 28), the EC forecast data released in December are used, and the method of incorporating the stratospheric predictive signal remains the same. After incorporating the stratospheric signal, the predictive skill for SAT over the Arctic and the mid-high latitude Eurasia region shows improvement in both early and late winter (Fig. R3). The averaged correlation coefficient between predictions and observations in early winter on each grid increases from 0.56 to 0.60 for Arctic, and from 0.1 to 0.35 for Eurasia. For late winter, the correlation coefficients between predictions and observations increases from 0.52 to 0.57 for the Arctic and from 0.1 to 0.37 for Eurasia. The predictive performance for the WACE index during 1979–2023 also improved. The correlation coefficients between T predicted and observed WACET increased from 0.39 to 0.52 for early winter and from 0.31 to 0.50 for late winter. This improvement indicates that the changes in stratospheric anomalies provide effective prediction information, and confirms the importance of this new stratospheric signal that we proposed. Fig. R3. Comparison of the grid-by-grid prediction performance of the EC models results in original and improved models, with shadings representing the CC between predictions and OBS from 1981 to 2023: (a, c) Early winter, (b, d) Late winter. The black and white indicate regions significant at the 95% and 99% level, respectively. 4. I appreciate the comprehensive set of 15 supplementary figures to support the analysis. However, navigating between the main text and the supplementary figures can make it somewhat difficult to follow the argument. While I understand the constraints imposed by the journal’s figure limits and I do not wish to insist on changes, the authors may wish to reconsider whether this current separation best serves the clarity of presentation. Reply: We have expressed the core content primarily in the main Figures, which present the main linkages between WACE reversal and stratospheric anomalies (Figure1), the elaboration of the physical mechanisms (Figures 2 and 3), the simulation of the main connections and physical processes by the CMIP6 model (Figure4), and a summary schematic diagram (Figure 5). The supplementary figures provide more detailed support for the content above. While navigating between main text and the supplementary figures does somewhat disrupt reading continuity, it is difficult to avoid. In the revised manuscript, we have provided a concentrated description of key points and minimized the need to navigate between main text and supplementary figures. 5. In addition, it would be helpful to clarify the motivation for including the climate model analysis. Is the goal primarily to test the robustness of the observed relationship in an ensemble framework, or to evaluate how well models reproduce the observed coupling mechanisms? A brief statement on this would help readers understand how to interpret the comparison. Reply： We use the CMIP6 and CESM model simulation primarily to further assess the robustness of the linkage between the SPV morphology transition over North America and the WACE phase reversal, as well as to verify the associated physical processes. During the analysis, we find the differences in simulation capability between high-top and low-top models for the above relationship. This finding also implies the necessity of developing high-top models. We have added a statement in the manuscript regarding the use of climate model data to indicate our purpose. Revisions： Lines 286-290: To further determine the robustness of the linkages between the variation of SPV morphology over North America and the WACE phase reversal, and verify the proposed T physical processes, we perform the analysis using historical simulations of the Coupled Model Intercomparison Project Phase 6 (CMIP6) from 1950–2014 and the Community Earth System Model large ensemble (CESM-LM) experiments from 1920–2005 (see methods). Specific comments: • Line 68: abbreviation not defined Reply: We have added the definition of SAT. Revision: Lines42-43: The opposite anomalies between early and late winter cancel each other out on the winter-mean scale, thus presenting a decreasing trend of surface air temperature (SAT) • Lines 76-77: I suggest not overstating the role of wave reflection as the sole mechanism for stratospheric-troposphere coupling [see Baldwin et al.] Reply: We have revised this description. Revisions: Lines 69-71: The SPV anomalies can affect the phase of Arctic Oscillation/North Atlantic Oscillation (NAO) through various mechanisms such as downward propagation of zonal-mean anomalies, vertical wave coupling, surface amplification20,21, • Lines 100-102: Is the seasonal cycle also removed? If yes, is the raw gridpoint temperature data de-seasonalized or is it the index itself? Reply: In this study, the linear trend and its long-term (1979/80–2023/24) mean of all the daily data are removed, which implies that the seasonal cycle is also removed. Consequently, both the indices such as WACE and NAPV and the composite spatial distributions of SAT and T IPV stratospheric PV are based on the deseasonalized data. We have clarified this data processing method in the Methods section. Revisions： Lines 449-451: The linear trend and its long-term (1979/80–2023/24) mean of all the daily data are removed, which indicates that the seasonal cycle is also removed. • Lines 104-108, related to lines 458-459: please clarify how exactly the events are defined, in particular, the standard deviation criterion Reply: The WACE reversal need to satisfy two conditions: (1) the WACE in early winter and T T late winter is reversed after the removal of the trend and climate mean of 1979/80–2023/24; and (2) the sum of the standard deviation in early winter and late winter after the standardization of daily WACE in December 1st to February 28th is < 1.8. The threshold of 1.8 is set to screen T out the relatively stable and continuous phase transitions of WACE . Based on the daily T WACE analysis of the 20 winter selected by the first criterion, 4 of these years do not exhibit T a stable and persistent WACE or CAWE phase in early or late winter, instead showing fluctuating variations (Fig. R4, 5). A common feature of these four years is that the sum of the standard deviations of WACE in early winter and late winter exceeds 1.8. Therefore, this T study adopts this threshold as the second criterion for defining the WACE phase reversal. T Fig. R4. The variation of WACE in early and late winter. The blue and red solid dots represent the T WACE to CAWE years and CAWE to WACE years, respectively, and the hollow dots represent the 4 years removed. Fig. R5. The daily variation of WACE in the 4 years removed. T Minor adjustments to this threshold (such as 1.9) has no impact on the feature of WACE phase reversal (Fig R6). We have added the above explanation in the method section. Fig. R6. Composites of latitude-temporal SAT along 30-100°E in the WACE reversal years (CAWE to T WACE years minus WACE to CAWE years) using the threshold of 1.9. Revisions: Lines : The threshold of 1.8 is selected based on a summary of year-by-year analyses of daily WACE index that met the first condition, excluding years that primarily exhibited T fluctuating variations. Minor adjustments to this threshold do not affect the feature of WACE phase T reversal. • Lines 170ff.: Are the EOF patterns robust across different time periods? A corresponding sensitivity test would be useful, for example, by using the additional period 1950/51- 1978/79. Cutting a few days off the beginning and end of the analysis period and re-computing the EOFs could also be a useful robustness check. Reply: This EOF pattern is also robust during the 1950-1978 period (Fig. R7a-c). Furthermore, after cutting the beginning days of 11.1-11.10 and the ending days of 2.19-2.28 during 1979- 2023 period, we re-computed the EOF, and the presented main EOF mode remains unchanged (Fig. R7d-f). The above-mentioned sensitivity test indicates that the decomposition of this EOF pattern is robust. Combing the comments of the two reviewers, we have moved this content to the method section that defines SPV morphology transition, in order to enhance the logical coherence of the article. Fig. R7. The first three EOF mode of geopotential height at 50 hPa over 0°–120°W over temporal variations during 1950-1978 and during 1979-2023 but cutting a few days. Revision: Lines 508-509: The presentation of the EOF pattern is robust, which is undergone sensitivity tests using the additional period 1950/51–1978/79 (figure not shown). • Line 178: Do I understand correctly that the choice of the sign of the EOF patterns is important here to make the sum of PC1 and PC3 meaningful? Reply: The results of EOF need to be combined with the sign of spatial distribution and time series, that is, should be the product of spatial mode sigh and time series sign. In our current presentation, the signs of the spatial pattern and the time series are aligned. The positive time series of the each mode represents the anomaly distribution shown in the Supplementary Fig. 20. When PC1 + PC3 is positive, it indicates that the polar vortex morphology transitions from contraction to stretching over North America. • Lines 180-182: Using the EOF analysis based on 1979-2024, as presented, and projecting the data from 1950-1978 onto these patterns could be a useful robustness check– what is the explanatory power of PC1 + PC3 for the WACE phase reversal in that earlier period? Reply: During the 1950-1978 period, the explanatory power of PC1+PC3 for the WACE reversal is also effective. During the 10 years of WACE reversal, the stratospheric changes presented by PC1+PC3 in 9 years are all consistent with our conclusion (Fig. R8). In the 6 years with WACE reversing CAWE, the PC1+PC3 are negative except one year, indicating that the stratospheric geopotential height anomaly over North America changes from negative to positive, and the polar vortex morphology transitions from stretching to contraction over North America. In the 4 years with CAWE reversing WACE, the PC1+PC3 are all positive. Fig. R8. The first and third EOF mode of geopotential height at 50 hPa over 0°–120°W over temporal variations during 1950-1978, and the sum of the standardized times series of EOF1 and EOF3. The red and blue dots represent years with SAT phase reversal from CAWE to WACE and from WACE to CAWE, respectively. • Line 188: NAPZ note subscript Reply: As we have changed the index describing stratospheric anomalies, the NAPVZ has been deleted here. • Line 197f.: While the net surface response to the stratospheric precursor is indeed small in terms of area-averaged geopotential height anomalies, the region could still experience temperature anomalies if it lies near the center of a dipole pattern, where horizontal geopotential height gradients change. Reply: The stratospheric geopotential height anomalies between the mid-high latitude and mid- low latitude of Eurasia form a horizontal geopotential height gradient change. However, during the downward propagation of stratospheric signals, the center of the polar vortex shifts more towards North America and contracts over Eurasia. In the middle troposphere, the mid-high latitudes of Eurasia are all covered by an abnormal high pressure, and no significant geopotential height gradient has been formed (Fig. 2b). • Lines 289f.: The distribution in Fig. 4a seems to cover also positive values– how is that compatible with the statement that all such winters experience a positive ens. mean WACET response? Reply: The expression of this sentence is not sufficiently clear. What we intended to indicate is that the mean Diff-WACE in all such SPV phase transition is positive, not that every T individual case can be simulated with a positive Diff-WACE . We have rewritten this sentence. T Revisions： Lines 322-325: In the 200 cases of simulated Con-to-Stre NAPV, the mean Diff-WACE is T positive (Fig. 4a), and the distribution of SAT difference over Arctic-Eurasia exhibits a notable WACE anomaly (Supplementary Fig. 17a). Among these 200 cases, 72% show a positive Diff- WACE , …… T • Line 325: How is the accuracy rate computed and how should it be interpreted? Reply: The accuracy rate refers to the ratio at which the sign of Diff-WACE is correctly T simulated in the years of SPV morphology transition. Based on our analysis, when the SPV morphology over North America changes from contraction to stretching, it can cause the SAT pattern reversing from CAWE to WACE, that is, the sign of Diff-WACE is positive. In T the opposite direction of SPV morphology transition, the sign of Diff-WACE is negative. T We have added the explanation of the accuracy rate in the manuscript. Revisions： Lines 349-351: The accuracy rate refers to the proportion of cases in which a positive Diff- WACE is simulated in Con-to-Stre NAPV cases and a negative Diff-WACE is simulated in T T Stre-to-Con NAPV cases. • Lines 333f: What is the model top range in these categories? Reply: In the revised manuscript, we categorize the models into high-top and low-top groups based on whether the model top level reaches 0.1 hPa, thereby comparing their simulation capabilities for the SPV morphology transition and its influence on WACE phase reversal. The high-top and low-top model group consist of 9 and 12 models, respectively, with the ranges of the top level being 4.5×10-6–0.01hPa and 0.2–10hPa, respectively. We have added this in the text. Revisions: Lines 340-344: We categorize the models into high-top and low-top groups based on whether the model top level reaches 0.1 hPa, thereby comparing their simulation capabilities for the SPV morphology transition and its influence on WACE phase reversal. The high-top and low- top model group consist of 9 and 12 models, respectively, with the ranges of top level being 4.5×10-6–0.1hPa and 0.2–10hPa, respectively (Supplementary Table 1). Reply to Reviewer #2: This is my second review of the manuscript by Zhang et al., which investigates the relationship between stratospheric polar vortex variability over North America and the phase reversals of the Warm Arctic-Cold Eurasia (WACE) pattern during boreal winter. My main comments have largely been addressed in this revision. In particular, I appreciate the differentiation between overall vortex strength and vortex morphology. The additional analyses presented in the response to my previous comments were mostly convincing. I believe one of my previous comments may not have been sufficiently clear and may have been misinterpreted, so I would like to clarify it here. [...] On a related note, I wonder whether the apparent phase reversal of the WACE pattern could be related to the lagged surface response to the stratospheric precursor. Specifically, do events characterized by negative SPV intensity over North America (Fig. 1c, top) tend to be followed, after several weeks, by negative WACE index anomalies (Fig. 1c, middle), and vice versa for positive SPV intensity events? [...] With this comment, I did not intend to question the existence of the WACE mode itself. Rather, I was wondering whether the phase reversals of the WACE pattern (i.e., transitions from positive to negative WACE index values, or vice versa) could be explained as a lagged surface response to the stratospheric precursor. Perhaps this is already what the authors have in mind, but I wanted to ensure that this point is clearly articulated. In this context, could Fig. 1 be interpreted as follows? A contracted polar vortex, which is more circular, centered closer to the pole, and displaced away from North America, tends to be followed after a few weeks by a negative WACE index anomaly (CAWE). Conversely, a stretched polar vortex that is elongated over North America tends to be followed by a positive WACE index anomaly (WACE). Given that Fig. 1c conditions on “CAWE-to WACE years” minus “WACE-to-CAWE years,” the expected stratospheric precursor signal would then be a transition from a contracted vortex (as a precursor to CAWE) to a stretched vortex (as a precursor to WACE), which appears consistent with the figure. Is this a fair interpretation of the results? Reply: Thank you very much for explaining this comment again. Our research results also indicate that the phase reversal of the WACE pattern can be explained as a lagged surface response to the stratospheric precursor. The interpretation of Figure 1 is consistent with your understanding. The Figures 1a, b present the changes in polar vortex morphology during “CAWE-to-WACE years” and “WACE-to-CAWE years”, which are represented by the pink and blue lines, respectively. When the SAT pattern reverses from CAWE to WACE, the stratospheric precursor signal shows that the SPV morphology transits from contraction to stretching (the pink line). Conversely, when the SAT pattern reverses from WACE to CAWE, the SPV morphology transits from stretching to contraction (the blue line). That is to say, a contracted (stretched) SPV over North America-North Atlantic in Nov1Dec15 tends to be followed by a CAWE (WACE) phase in early winter, and a stretched (contracted) SPV in Dec16Feb10 tends to be followed by a WACE (CAWE) phase in late winter. The SPV morphology transition occurs approximately 25 days prior to the reversal of WACE. We have further clarified this conclusion in the text. Fig. 1. Composites of the potential vorticity on the 530K isentropic surface in (a) November 1st to December 15th and (b) December 16th to February 10th in the WACE reversal years T (CAWE to WACE years minus WACE to CAWE years). The green, pink and blue lines represent the composited polar vortex edge in climate mean, CAWE to CAWE years and WACE to CAWE years, respectively. The SPV edge is determined by 58PVU on the 530K isentropic. The white dots indicate that the results are significant above the 95% confidence level. Revisions: Lines 133-138: That is to say, a contracted SPV over North America-North Atlantic in Nov1Dec15 tends to be followed by a CAWE phase in early winter, and a stretched SPV towards North America-North Atlantic in Dec16Feb10 tends to be followed by a WACE phase in late winter. Conversely, the SPV morphology transition from stretching to contracting corresponds to a precursor to the reversal from WACE to CAWE. Finally, in my opinion, a thorough language edit would further enhance the clarity and readability of the manuscript. I provide a few specific comments below, but I recommend a more comprehensive review of the text. Reply: We have made detailed responses and revisions to the specific comments. Please refer to the following text for the details. We have also carefully and thoroughly revised and edited the language of the manuscript. Minor comments: • Fig. 1c top: clarify in the figure what index is used to measure the morphology Reply: The SPV morphology are measured by the area-weighted mean of potential vorticity on the 530K over North America-North Atlantic, defined as the NANA-SPV index. We have IPV added this information in the Figure. Revisions: • l. 23 As one of important drivers → one of the important drivers • l. 98. reversal points is → reversal points are • l. 278 the downward transmitting → downward transmission Reply: We have corrected these errors and conducted a comprehensive review and revision of the language throughout the manuscript. Revisions: Line 23: As one of the important drivers of climate variability, … Line 101: Most of the reversal points are around January 10th, … Line 293: … for the downward transmission of stratospheric signal…", "reviewer_3": "Reply to Reviewer #1:\nReview of “Stratospheric precursor induces wintertime phase reversal of the “Warm Arctic-\nCold Eurasia” pattern” by Zhang et al.\nThis study identifies a stratospheric precursor for the phase shift of the “Warm Arctic-Cold\nEurasia” (WACE) pattern in winters. Composite analysis suggests that the sign change in\nstratospheric anomalies over North America precedes the WACE phase shift by about 25 days.\nWave diagnostics suggest that the stratospheric variability facilitates the development of\ncirculation and temperature anomalies over Eurasia. Climate models from CMIP6 generally\nsupport the observational results. However"}, "author_response": "This is my second review of the manuscript by Zhang et al., which investigates the relationship between stratospheric polar vortex variability over North America and the phase reversals of the Warm Arctic-Cold Eurasia (WACE) pattern during boreal winter. My main comments have largely been addressed in this revision. In particular, I appreciate the differentiation between overall vortex strength and vortex morphology. The additional analyses presented in the response to my previous comments were mostly convincing. I believe one of my previous comments may not have been sufficiently clear and may have been misinterpreted, so I would like to clarify it here. [...] On a related note, I wonder whether the apparent phase reversal of the WACE pattern could be related to the lagged surface response to the stratospheric precursor. Specifically, do events characterized by negative SPV intensity over North America (Fig. 1c, top) tend to be followed, after several weeks, by negative WACE index anomalies (Fig. 1c, middle), and vice versa for positive SPV intensity events? [...] With this comment, I did not intend to question the existence of the WACE mode itself. Rather, I was wondering whether the phase reversals of the WACE pattern (i.e., transitions from positive to negative WACE index values, or vice versa) could be explained as a lagged surface response to the stratospheric precursor. Perhaps this is already what the authors have in mind, but I wanted to ensure that this point is clearly articulated. In this context, could Fig. 1 be interpreted as follows? A contracted polar vortex, which is more circular, centered closer to the pole, and displaced away from North America, tends to be followed after a few weeks by a negative WACE index anomaly (CAWE). Conversely, a stretched polar vortex that is elongated over North America tends to be followed by a positive WACE index anomaly (WACE). Given that Fig. 1c conditions on “CAWE-to-WACE years” minus “WACE-to-CAWE years,” the expected stratospheric precursor signal would then be a transition from a contracted vortex (as a precursor to CAWE) to a stretched vortex (as a precursor to WACE), which appears consistent with the figure. Is this a fair interpretation of the results? Finally, in my opinion, a thorough language edit would further enhance the clarity and readability of the manuscript. I provide a few specific comments below, but I recommend a more comprehensive review of the text. Minor comments: • Fig. 1c top: clarify in the figure what index is used to measure the morphology • l. 23 As one of important drivers → one of the important drivers • l. 98. reversal points is → reversal points are • l. 278 the downward transmitting → downward transmission"}]

Decision letter