On the Existence of the Predictability Barrier in the 2 Wintertime Stratospheric Polar Vortex: 3 Intercomparison of Two Stratospheric Sudden 4 Warmings in 2009 and 2010 Winters

To compare the predictability of two stratospheric sudden warming (SSW) events occurring in 2009 and 2010, ensemble forecast experiments are conducted using an Atmospheric General Circulation Model (AGCM). It is found that the predictable period of the vortex splitting SSW in 2009 is about 7 days which is much shorter than that of the 33 vortex-displacement SSW in 2010. The latter event is predictable more than 13 days in 34 advance. The ensemble spread in the upper stratosphere for medium-range forecasts is 35 found to be enlarged just prior to the onset of the 2009 SSW event, while no such 36 enlargement is seen for the 2010 SSW event. 37 Stability analysis of the zonally asymmetric basic states specified by the ensemble 38 mean forecast using a nondivergent barotropic vorticity equation reveals that the 39 extremely distorted polar vortex in the upper stratosphere just before the onset of the 40 2009 SSW event is highly unstable to infinitesimal perturbations, whereas there is no 41 such unstable mode with an extremely large growth rate during the 2010 SSW event. In 42 addition, the most unstable mode during the onset of the 2009 SSW event has a similar 43 horizontal structure to the 1 st EOF of the ensemble spread. Thus, it is suggested that a 44 predictability barrier inherent in the upper stratospheric circulation, characterized by the 45 presence of dynamically unstable modes with large growth rates limits the predictable period of the 2009 SSW event.


Introduction
were observed in the stratosphere is highly unstable to infinitesimal perturbations. They 88 attributed a short predictable period of about 7 days for the downward propagating event to 89 the existence of a predictability barrier in the stratosphere associated with the dynamical 90 instability of large growth rates. Moreover, they hypothesized that the obtained unstable 91 mode in the upper stratosphere acts as a precursor for the emergence of the downward 92 propagating planetary waves in the stratosphere. 93 In this paper, we will pursue the role of dynamical instability of stratospheric circulation 94 in limiting the predictability of SSW events. If the stratospheric circulation during the onset 95 phase of an SSW event is highly unstable, we can argue for the existence of a predictability 96 barrier in the stratosphere which limits the predictable period of the SSW. For this purpose, 97 first, the same AGCM used in N16 will be utilized to conduct ensemble forecast experiments  We also reexamine ensemble forecasts starting every day during January 2009, which were 128 used in N16. Daily-mean prediction data on 2.5° by 2.5° horizontal grids with 38 vertical 129 pressure levels with a top at 0.4 hPa computed from 6-hourly model outputs are analyzed.

Non-divergent barotropic vorticity equation on a sphere 131
To examine the dynamical stability of stratospheric circulations, we utilize the following 132 non-divergent barotropic vorticity equation on a sphere linearized about the specified basic 133 flow denoted by the notation overbar ̅ ) as in M17: (1)  corresponding to the vortex displacement SSW event (Fig. 1c).

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The predictability of each SSW event was assessed by the spatial anomaly correlation 162 coefficient (ACC) for 10-hPa geopotential height field poleward of 40°N using a box-and-163 whisker diagram (Fig. 2) . For the 2009 SSW event (Fig. 2a), the ACC of the ensemble mean 164 forecast on day 0 (24 January) becomes larger than 0.6 for forecasts starting after day −9.

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However, the spread among ensemble members is considerably large, and ACCs of some  2b) is larger than 0.6 even for the forecast from day −15 (9 January), but the spread is still 171 large with a couple of members having ACCs less than 0.6. The day 0 spreads also become 172 much smaller in the forecasts after day −13 (11 January). Hence, the predictable period of  and a small growth rate (Fig. 8b).  Fig. 5b of their paper, has a horizontal structure very similar to the most unstable mode obtained in our study (Fig. 9c). In addition, 349 the SV1 has a large amplitude in the upper stratosphere and shows an amplification rate 1 350 of about 1.1 day −1 which is comparable to the maximum growth rate of the unstable mode 351 at 5 hPa (Fig. 8a). These similarities between the most unstable mode and the SV1 also

(A1)
Here, is the phase of the most unstable mode. Note that the square root of the variance 423 at t is also given by , if we ignore the temporal amplification with exp , where is the growth rate. This is because will only increase by a certain constant , where is the imaginary part of the eigenvalue, but the integral range for is 426 independent of t in Eq. (A1).

427
Now, Fig. A1a shows the horizontal distribution of , for the most unstable mode 428 on day −4 (Fig. 9c). The magnitude of , attains its peak at four longitudes along 60°N: unstable mode depending on its phase shown in Fig. 10 is closely related to the predicted 441 variability of the polar vortex among the ensemble members (Fig. 3a).    prediction date (the abscissa) of the forecast starting from 6 to 28 January (the ordinate).

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The radius of the filled circle is proportional to the growth rate, and its color also indicates 658 the range of the growth rate as shown in the legend. The red vertical line represents day