Auxiliary Material Submission for Paper ... - IARC Research

Auxiliary Material Submission for Paper
2008gl035607
Recent Radical Shifts of Atmospheric Circulations and Rapid Changes in Arctic
Climate System
Xiangdong Zhang
International Arctic Research Center, University of Alaska Fairbanks, 930
Koyukuk Dr., Fairbanks, AK 99775, USA.
Asgeir Sorteberg
Bjerknes Centre for Climate Research, Allegaten 55, 5007 Bergen, Norway.
Jing Zhang
Geophysical Institute, University of Alaska Fairbanks, 903 Koyukuk Dr.,
Fairbanks, AK 99775, USA.
Ruediger Gerdes
Alfred Wegener Institute for Polar and Marine Research, Bussestrasse 24,
Bremerhaven, D-27570, Germany.
Josefino C. Comiso
Cryospheric Science Branch, NASA Goddard Space Flight Center, Greenbelt, MD
20771, USA.
Zhang, X., A. Sorteberg, J. Zhang, R. Gerdes, and J. C. Comiso (2008), Recent
Radical Shifts of Atmospheric Circulations and Rapid Changes in Arctic Climate
System, Geophys. Res. Lett., XX, doi:10.1029/XXXXXXXXXX.
Introduction
The auxiliary material contains one paragraph of the text that describes the
statistical and physical significance of the first EOF/PC patterns of monthly
mean sea level pressure (MSLP), references, three tables, and three figures.
1. 2008gl035607-text01: Statistical and Physical Significance of the First
EOF/PC Patterns
The Empirical Orthogonal Function/Principal Component (EOF/PC) analysis seeks
spatially and temporally coordinated structures to explain maximum variance of
climate variability, and identify centres of maximum variance. However, dataset
size in practice has never been as large as theoretically expected and random
noise may be embedded; therefore the EOF/PC estimate could be subject to

uncertainties caused by sampling errors. It is necessary to evaluate the
robustness of the EOF/PC estimates, or whether the identified leading EOF/PC
pattern is sufficiently distinguished from neighbouring patterns and is well
above noise-level signals. Furthermore, a pattern identified by EOF/PC analysis
does not necessarily represent any physical process. Thus, the physical
significance of such a pattern must be assessed.
The first EOF/PC patterns are significantly distinct from subsequent patterns
throughout all wintertime analysis periods based on an assessment of sampling
errors [North et al., 1982] . To further enhance the robustness of the EOF/PC
estimate, we employ the powerful Monte Carlo simulation approach for additional
significance testing to verify that our EOF/PC estimates are not due to
uncorrelated random noise [Preisendorfer and Mobley, 1988]. The implementation
of the Monte Carlo simulations is achieved by forming surrogate data sets via
scrambling the original data using randomization so that the chronological order
of the original data set is broken, and then repeating the same EOF/PC analysis
for the surrogate data sets as for the original data set. The eignvalue, or
fraction of variance explained by an EOF/PC pattern, is statistically
significant at the 99% level if it is not exceeded by more than 1% of the
corresponding eignvalues or fractions of variance obtained using the scrambled
data sets. This procedure is similar to the significance test in the Singular
Value Decomposition (SVD) analysis of mean sea level pressure (MSLP) and sea
surface temperature (SST) [Wallace et al., 1992].
In detail, we (1) scramble the data set at all spatial grid points to form the
surrogate data set; (2) perform the same Rn-EOF/PC on the scrambled data set as
was performed on the original data set; (3) repeat the above procedure 1000
times with the newly scrambled data set; and (4) compare the eignvalue or
fraction of variance of the original and scrambled data sets.
Table S1 lists the fractions of variance explained by the first EOF/PC patterns
from the original data set and the maximum fractions of variance explained by
the first EOF/PC patterns from the 1000-trial Monte Carlo simulations for the
selected wintertime windows in Figure 1. The comparison indicates that the
former values are much larger than the latter values, suggesting the first
EOF/PC patterns we identified are statistically significant; they are uniquely
determined and cannot be produced by random noise. The comparison also indicates
that the covariance matrix defined by the MSLP anomalies has only one
eigenvector corresponding to its maximum eigenvalue.
Although the statistical significance test can be used as a guide to assess
robustness of the EOF/PC patterns, physical interpretation will augment the
strength of this test and is a final requirement for validating EOF/PC patterns.
The physical significance of the first EOF/PC patterns before 2001 obviously
represents systematic NAO/AO patterns with significant spatial and temporal
coordination. To demonstrate the correspondence between the Arctic Rapid change
Pattern (ARP) and MSLP variability in reality, we chose two 5-month data sets
during which the ARP index was either in its extreme positive phase or negative
phase, during the 2001/02-2005/06 winters, as listed in Table S2. We used the
criterion values of 1.0 sigma for the positive phase and 1.2 sigma for the
negative phase to avoid any discrimination between positive and negative phase
considering downward linear change of the ARP index. We then performed a

composite analysis of MSLP for each of the 5-month data sets and took the
difference between them (Figure S1).
The pattern of MSLP differences (positive minus negative) is exactly the same as
the ARP spatial pattern (Figure 1b). This indicates that the ARP truly
represents physics in the real world and accounts for a predominant fraction of
MSLP variability. When we look at the original composite MSLP maps, we can also
observe obvious atmospheric circulation changes. In the positive ARP phase, the
Icelandic low extends far into the Barents Sea, leaving an intensified low
pressure centre there, and the whole body of the Siberian high contracts
southward, compared to the corresponding negative phase. This is strikingly
different from the composite MSLPs associated with the Arctic Oscillation/North
Atlantic Oscillation (AO/NAO). Although the Icelandic low strengthens and the
Siberian high weakens in the positive AO/NAO phase, their main bodies and
centres remain at nearly the same locations. The AO/NAO accordingly cannot
capture changes in spatial patterns of atmospheric circulation. Comparing the
original composite MSLPs provides additional information about the recent
changes in atmospheric circulation from a different angle.
In addition, a recent effort identified three sea-ice-motion-defined MSLP
patterns [Maslanik et al., 2007]; among them, an increased frequency of
occurrence of an across-basin sea-ice motion associated with a MSLP dipole
pattern from 2000-2004 would be partially an ARP manifestation, though it
obviously differs from ARP in spatiotemporal structures and physical
significance. Its MSLP centers are located over northeastern China and the
northeastern Pacific, different from the ARP centers of action (maximum
variance). This is also similar for the 2nd EOF/PC pattern [Skeie, 2000], which
explains much smaller fraction of variance, and mainly depicts local variability
over the Nordic seas when the signal correlated with AO is removed.
References
North, G. R., T. L., Bell, R. F. Cahalan, and F. J. Moeng (1982), Sampling
errors in the estimation of empirical orthogonal functions, Mon. Wea. Rev., 110,
699-706.
Preisendorfer, R. W., and C. D. Mobley (1988), Principal component analysis in
meteorology and oceanography, Elsevier Science Publishers B. V., the
Netherlands, 425p.
Skeie, P. (2000), Meridional flow variability over the Nordic seas in the Arctic
Oscillation framework, Geophys. Res. Lett., 27, 2569-2572.
Wallace, J. M., C. Smith, and C. S. Bretherton (1992), Singular value
decomposition of wintertime sea surface temperature and 500-mb height anomalies,
J. Clim., 5, 561-576.
Figure Captions

Figure S1. MSLP composite for the months with (a) positive and (b) negative ARP
index extremes during 2001/02-2005/06 winters, and (c) their differences
(positive minus negative). The selected months are listed in Table S1.
Figure S2. Amplitude time series or index of (a) ARP, and (b) AO/NAO for
1985/86-2005/06 winters, constructed by projecting the MSLP anomalies onto the
leading spatial patterns in the time windows of 2001/02-2005/06 and 1986/87-
1990/91. Blue: original monthly data; Green: 5-month smoothed monthly data; and
red: linear trend.
Figure S3. The regional geographic divisions for sea-ice area computation.

Table S1 The fractions of variance (%) explained by the first
EOF/PC patterns from the original MSLP anomaly data set and the
maximum of fractions of variance explained by the first EOF/PC
patterns from the 1000-trial Monte Carlo simulations for the
selected wintertime windows in Fig. 1b.
Fraction 1986/87- 1989/90- 1992/93- 1995/96- 1998/99- 2001/02-
of 1990/91 1993/94 1996/97 1999/2000 2002/03 2005/06
Variance
Original 29.0 22.5 26.8 24.1 25.2 21.0
Data
Scrambled 4.9 4.9 5.0 4.8 4.9 4.8
Data

Table S2 Winter months with ARP index extremes for the
composite analysis during 2001/02-2005/06.
Months with Positive ARP Jan. - Mar. 2002; Dec. 2003;
Index Extremes Nov. 2004
Months with Negative ARP Nov. 2001; Nov. 2002; Feb.
Index Extremes 2005; Dec.2005; Jan. 2006

Table S3 Months with ARP index extremes for the composite
analysis for 2007 summer sea-ice minimum. The criterion
values of 0.5 sigma for the positive phase and 1.2 sigma for
the negative phase were chosen to avoid impact of seasonality
between positive and negative phases due to the climatologically
weaker summer than winter MSLP fluctuations.
Months with Positive ARP Sept. 2006; Dec. 2006; Jan.
Index Extremes during 2006- 2007; May 2007; Aug. 2007
2007
Months with Negative ARP Dec. 2002; Feb. 2005; Dec.
Index Extremes during 2001- 2005; Jan. 2006; Apr. 2006
2006

(a) (b) (c)
Figure S1

(a)
(b)
Figure S2

North Atlantic Shelf
Seas (NAAS)
North Pacific Shelf
Seas (NPAS)
Figure S3