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Barotropic model experiments

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8.2 Case study: The 2010 Russian blocking case

8.2.3 Barotropic model experiments

Time integration of a numerical model in which a synoptic anticyclone or cyclone upstream of the block is removed is performed to estimate the contribution of the anticy-clone and cyanticy-clone to the block maintenance and to check whether there is asymmetry in the contribution between synoptic anticyclones and cyclones. The model used here is the same equivalent-barotropic quasigeostrophic model as in Section 5.2, which is one of the most simplest models to simulate blocking. Therefore, although the comparison of the simulated blocks with the real ones is difficult in a quantitative sense, the eddy-feedback process, a main part of the block maintenance dynamics, can be simulated to some extent.

The equation is

q

t +J(ψ,q+ f)= −E∇2ψ−νH

(

8− 24 R8 )

2ψ, q= (∇2ψ−γ2ψ+ f).

(8.1)

The variables are the same as in Section 5.2 except that the raw fields of ψ and q are used, but not the anomaly. Also, the right hand side of this equation has only dissipation and no artificial forcing. Values of the arbitrary parameters are determined such that the model relatively well reproduces the amplitude and phase of the real blocking: Ld = 700 km and E = 1/15 day1. νH and the spatial resolution are the same as in Chapter 7 (2.1×1035m8s−1 and T63). The integration period is 4 days. The initial day is denoted as Day 0, then continuing Day 1, Day 2, Day 3, and Day 4.

As the initial value, the streamfunctionψand PVqconstructed from the wind field at 250 hPa are given. Three experiments are performed, in which initial values are different;

i) observational values ofψand qare used (Total-eddy Exp), ii) first, the negative value of highpass-filtered PV with a cutoffperiod of 8 days is subtracted from the original PV in the stormtrack region upstream of the block which is defined as the interior of the closed line, 280E-340E and 40N-70N, and thenψis obtained from the inversion ofq (Hoskins et al. 1985), that is,ψ andq fields without synoptic anticyclones upstream of

the block (No-anti Exp), and iii) same as (ii) but for that the positive value is subtracted, i.e., ψ and q fields without synoptic cyclones (No-cyc Exp). Among three settings, the amplitude of the simulated blocking is compared with each other. Since the PV-inversion technique is used, dynamically balanced initial conditions for wind and PV fields are set. Note that Hakim et al. (1996) show some problems about the PV-inversion in the baroclinic atmosphere for which the averaged PV anomaly over the inverted domain is not zero, corresponding to situations of the initial fields of No-anti and No-cyc Exps.

However, since we use the equivalent barotropic quasigeostrophic model, such problems are avoided, as mentioned in Chapter 7 (Egger 2009; Appendix D).

Time evolution of a PV contour for Total-eddy Exp with the initial date of 06 UTC 12 July is compared with that of observations (Fig. 8.9). Comparing these time evolutions, we find that, though detailed patterns do not match, large-scale behaviors such as the phase of the blocking anticyclone and the intrusion of the low-PV air into the blocking, associated with the maintenance dynamics, can be simulated relatively well even on Day 4. Because the model used here has a similar framework of the contour-dynamics model (Nakamura, M. 1994; Peters and Waugh 1996; Nakamura et al. 1997) and the barotropic vorticity model (Nakamura et al. 1997) used in previous studies for investigating dynam-ics of blocking, it is natural to reproduce about 4-day duration of the blocking.

Next, results of No-anti and No-cyc Exps are shown (Fig. 8.10). Figure 8.10a shows the highpass-filtered PV at the initial date is shown. Then, the initial PV distributions for No-anti and No-cyc Exps, in which the highpassed positive PV and negative PV upstream of the block are removed, are presented in Figs. 8.10b and e, respectively. Due to the subtraction of the synoptic anticyclone and cyclone in the stormtrack region, the short-wave ridge and trough over southwest and south of Greenland are removed, respectively.

Note that about one synoptic anticyclone or cyclone is removed in the anti and No-cyc Exp, respectively, although a part of the synoptic antiNo-cyclone existing over the eastern Atlantic is also removed in No-anti Exp.

The time evolution of No-anti Exp (Figs. 8.10b, c, and d) shows the intrusion of low-PV air into the blocking anticyclone is weaker than that of Total-eddy Exp, especially on

Day 4. This weaker intrusion is thought to be caused by the loss of the PV supply from the removed synoptic anticyclone.

Figures 8.10e, f, and g are the same as Figs. 8.10b, c, and d but for the No-cyc Exp.

Comparing the patterns on Day 4, we can find a slight increase of the northward intrusion of low-PV west of the blocking in cyc Exp relative to anti Exp. Also, in No-cyc Exp, the trough just upstream of the blocking is drifted to the southwest direction on Day4, but not in No-anti Exp. Thus, there are different patterns between No-anti and No-cyc Exps on the same day, which indicates the asymmetry of the influences between the synoptic anticyclone and cyclone. These results are consistent with the SAM.

To obtain more quantitative and generalized results, a key-time composite analysis is performed. Samples to be composited are obtained by changing the initial date, which was fixed in the above experiment. Initial dates are shifted at the 6 hour interval from 00 UTC 10 July to 00 UTC 7 August, and each integrated PV field is composited with the same integrated days (denoted as Day 0, ... , Day 4). Figure 8.11 shows the time evolution of the composited PV fields in Total-eddy Exp and the observation at the same valid dates.

Since key times are almost within the blocking duration period, the composited PV field of the observational data keeps the blocking ridge structure even on Day 4. Compared with this field, the composited field in the model well maintains the amplitude and phase of this ridge, though it is slightly drifted downstream. Thus, it is robust that this model can simulate the maintenance of the blocking to some extent.

The time evolution of the composited PV fields of No-anti and No-cyc Exp are shown in Fig. 8.12. Here, the difference subtracting the result of Total-eddy Exp from that of No-anti or No-cyc Exp is indicated to obviously quantify the effect of a synoptic eddy. In the time evolution of No-anti Exp (Figs. 8.12a, c, e, and g), we can see that the influence of the removed synoptic anticyclone travels downstream. After Day 3, the positive PV response appears at the western blocking ridge (over eastern Europe and western Russia), corresponding to the weakening of the blocking ridge in No-anti Exp. This result further supports the selective absorption of a synoptic anticyclone (Figs. 8.10c and d). Moreover, the PV response of about one synoptic anticyclone locally reaches up to−2.0×105s1,

being equivalent to one-third or a quarter of the amplitude of the blocking ridge. Thus, if 3 or 4 synoptic anticyclones are absorbed to a blocking anticyclone within the damping time scale (∼ 15 day), then the amplitude of the blocking is maintained. Thus, at least in barotropic dynamics, the contribution of synoptic eddies is suggested to be large enough for the maintenance of blocking.

On the other hand, the time evolution of No-cyc Exp (Figs. 8.12b, d, f, and h) shows that the influence of the synoptic cyclone does not reach the blocking ridge but affects the upstream of the ridge, i.e., the trough in Total-eddy Exp. This result implies the asymmetry to synoptic anticyclones, and may be related to the intensification of a large-scale trough (over western Europe) just upstream of a blocking ridge by the interaction with synoptic cyclones.

In this analysis, although the arbitrary values of Ld and E are determined to make the amplitude and phase of the blocking ridge in Total-eddy Exp similar to observations, almost the same results are obtained for different arbitrary values (not shown). Roughly speaking, whenLdbecomes large, the blocking ridge tends to drift downstream, and when Ebecomes large, the ridge tends to decay fast as easily expected. In addition, when the area defined as the stormtrack region is decreased, the response to synoptic anticyclones and cyclones becomes small in amplitude. In particular, when the eastern part of the stormtrack region is cut, the amplitude of the response becomes much smaller.

It should be noted that the results here are obtained in a barotropic model. More stud-ies are needed to check whether barotropic models are capable for a quantitative estima-tion of the real block maintenance. For example, in barotropic dynamics, it is unknown whether the contribution of synoptic eddies is overestimated or underestimated. As to the former, we can think that, because in the baroclinic atmosphere synoptic eddies in the lower troposphere have the opposite phase with that in the upper troposphere, flows induced by the lower troposphere tend to suppress those by the upper one, and thus the

‘barotropic’ process tends to be overestimated (Nakamura et al. 1997). On the other hand, as to the latter, synoptic eddies could more grow between the stormtrack region and the blocking ridge, therefore the contribution of synoptic eddies would be underestimated.

The same analysis using a baroclinic model should be taken for quantitative comparison with the observation.

Table 8.1:Same as Table 4.2 but for the event of the 2010 summertime blocking. Here the event names are designated as A-2010a, b, and c. The trajectories for each event are shown in Fig. 8.5.

Event name Date (number of parcels) Date (number of parcels) Displayed date for synoptic anticyclone for synoptic cyclone of the blocking flow A-2010a 7/11/00 (20) 7/11/18 (33) 7/14/00 A-2010b 7/20/06 (15) 7/17/18 (39) 7/22/00

A-2010c 8/1/00 (21) 8/2/00 (37) 8/4/00

(a) (b)

(c) (d)

2: a

(a) (b)

Figure 8.1:(a) Potential temperature-latitude cross section of the climatological zonally averaged standard deviation of highpass-filtered PV with a cutoff period of 8 days (shade, [PVU]) and the unfiltered PV (contour, [PVU]) and (c) pressure-latitude cross sec-tion of climatological zonally averaged potential temperature [K] in summer. (b) and (d): Same as (a) and (c) but in winter. The contour interval in (a) and (b) is 1 PVU between 1 and 10 PVU, while that in (c) and (d) is 10 K between 270 and 370 K.

87

1 1

(a) (b)

1: a

(a) (b)

2: a

Figure 8.2:Climatological standard deviation of the highpass-filtered PV (shade, [PVU]) and un-filtered PV (contour, [PVU]) in (a) summer at the 330 K surface and (b) winter at the 320 K.

(a) (b)

4: b

(a) (b)

(c) (d)

Figure 8.3:Same as Fig. 8.2 but for the standard deviation of the highpass-filtered vorticity (shade, [s−1]) and the unfiltered absolute vorticity (contour, [s−1]). The contour in-terval is 2.0×105s1between 5.0×105and 1.5×104s1. Note that the values at 0E are vanished due to the centered difference scheme.

89

Figure 8.4:Time-mean standard deviation of highpass-filtered PV (shade, [PVU]) and PV (con-tour, [PVU]) fields between 00 UTC 10 July and 00 UTC 10 August at the 330-K surface. The contour interval is 1 PVU between 1 and 6 PVU.

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Figure 8.5:Same as Fig. 4.2 but for the events of (a) A-2010a, (b) A-2010b, and (c) A-2010c at the 330 K surface. Details for each event are described in Table 8.1.

(a) (b)

(c) (d)

4: b

Figure 8.6:Five-day mean PV (blocking PV) and standard deviation of the high-frequency PV component (stormtrack) at 320 K surface. Upper panels show the blocking PV [PVU]

on (a) 12 July and (b) 20 July (contour) with the time-averaged stormtrack (shade, [PVU]) over 5 days before. Bottom ones show the same as (b) but for the composited members which (c) can and (d) cannot predict the blocking ridge.

Figure 8.7:Same as Fig. 8.6c but for each member predicting the blocking ridge.

Figure 8.8:Same as Fig. 8.6c but for each member which cannot predict the blocking ridge.

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Figure 8.9:Time evolution of a PV contour in Total-eddy Exp (shade, [s−1]) or in the observa-tional data (contour, [s1]). Each panel shows the snapshot on (a) Day 0 (06 UTC 12 July), (b) Day 2 (14), (c) Day 3 (15), and (d) Day 4 (16).

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Figure 8.10:(a) Snapshot of the highpass-filtered PV (shade, [s1]) and unfiltered PV (contour, [s1]) at 06 UTC 12 July (Day 0). (b-g) Same as Fig. 8.9 but for in No-anti and in No-cyc Exps (shade) on (b and e) Day 0, (c and f) Day 3, and (d and g) Day 4, respectively.

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Figure 8.11:Time evolutions of the composited PV fields in Total-eddy Exp (shade, [s−1]) and the observational data (contour, [s1]). Snapshots on (a) Day 0, (b) Day 2, (c) Day 3, and (d) Day 4 are shown.

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Figure 8.12:Same as Fig. 8.11 but for the composited PV field in (a, c, e, g) No-anti or (b, d, f, h) No-cyc Exp with that in Total-eddy Exp subtracted (shades, [s1]) and the composited PV in Total-eddy Exp (contour, [s1]). Snapshots on (a and b) Day 0, (c and d) Day 2, (e and f) Day 3, and (g and h) Day 4 are shown.

Chapter 9

Conclusions and remarks

About the block maintenance, we investigated the interaction mechanism between blocking and synoptic eddies (high-frequency transients). Then, the Selective Absorption Mechanism (SAM) in which a blocking anticyclone selectively attracts and absorbs syn-optic anticyclones and reinforces its duration was proposed. The SAM is a new block maintenance mechanism based on the vortex-vortex interaction.

The SAM is one of the eddy-feedback mechanisms. In this sense, it is the same as the Eddy Straining Mechanism (ESM). However, the SAM takes into account the vortex-vortex interaction explicitly, which differs from the ESM. The essence of the SAM is the eddy absorption, but not the straining. Furthermore, this mechanism focuses the nature of PV as not only a conservative property but also the ‘vortex.’ Also in this sense, it demarcates other eddy-feedback mechanisms.

From the formulation of the ESM, it was clarified that the ESM does not include the asymmetry between synoptic anticyclones and cyclones, that is, the vortex-vortex interac-tion, which is essential for the SAM. We considered this asymmetry, investigating whether the SAM works in real or realistic blocking maintenance through the case study and nu-merical experiments. In the case study, different behaviors between synoptic anticyclones and cyclones around blocks were found by tracking parcels originating from them. Ten blocking episodes supported that synoptic anticyclones are absorbed into the blocking an-ticyclones, while synoptic cyclones are repelled by them with drifting downstream or are attracted by blocking cyclones. In numerical experiments, we checked blocking duration using an equivalent-barotropic quasigeostrophic PV equation model. Two models on a

β-plane and a sphere were used. The absorption of synoptic anticyclones/cyclones into the blocking anticyclone/cyclone was seen independently of the meridional shift of storm-tracks (at least 1000 km on theβ-plane or 10 on the sphere) and of sizes and amplitudes of synoptic eddies. We thus concluded that the SAM can work robustly irrespective of various situations.

Some applications of the SAM were also introduced in Chapters 7 and 8. A budget analysis to quantify the SAM was developed and quantitative results of the SAM for the block maintenance was obtained. This analysis also proposes a new approach to quantify the interaction of binary vortices.

Finally, the SAM was applied to the block occurring in 2010 summer over west-ern Russia. Through the trajectory analysis, an analysis of ensemble forecast data, and barotropic experiments, it was found that the SAM actually contributes to the maintenance of this blocking. Also, this result supports the application of the SAM to summertime blocking in general.

Hereafter, we mention remarks about this thesis. The essence of the SAM is the PV-thinking and the vortex-vortex interaction. The latter especially would be the basis for many aspects of the blocking dynamics. Some possible applications and implications are noted as follows:

• The SAM would work with, not only synoptic eddies, but also ‘Rossby eddies’ with the low-frequency time scale, since it can work even when the size or magnitude of eddies becomes large. Nakamura et al. (1997) showed that the dynamics of blocking is different between the Atlantic and Pacific blocking in terms of relative contributions of the high-frequency (synoptic eddy) and low-frequency (Rossby wave) dynamics. Then, it is worth investigating the effectiveness of the SAM in the low-frequency one.

• The effectiveness or contribution of the SAM in the baroclinic atmosphere should be investigated. Some previous studies show, especially for the formation, the im-portance of the baroclinicity upstream of blocks. Croci-Maspoli and Davies (2009) show the importance of the Sea Surface Temperature (SST) distribution over the

At-lantic for a block formation. This distribution may affect the blocking downstream through the baroclinic process. Also, very recently, H¨akkinen et al. (2011) have argued that the Atlantic blocking is strongly correlated with variability of the North Atlantic SST in the decadal time scale. The effect of baroclinicity cannot be esti-mated in barotropic models; therefore the extension of this study to the baroclinic atmosphere is needed.

• The way of how blocking is maintained might be classified into two categories according to the amplitude of blocking; one is that a massive and much low-PV anticyclone stays in almost a same region without large fluctuations of amplitude (for example, P-2003 in Chapter 4), and the other is a relatively weak low-PV anti-cyclone in a fixed region, through which lower-PV cutoffanticyclones or filaments with the synoptic scale repeatedly pass. In this case, of course, the amplitude shows large fluctuations (A-2003 or Fig. 11 in Hoskins et al. 1985). These two categories are related to (i) and (ii) in Chapter 4. Thus, the difference of them is thought to de-pend on the strength of the vortex-vortex interaction via amplitudes of maintained blocking anticyclones (Chapters 4 and 5). In the former, since the vortex-vortex interaction is strong, synoptic anticyclones absorbed by blocking anticyclones keep to be strongly trapped within it. On the other hand, in the latter, synoptic ones at-tracted by blocking anticyclones keep located at the north side of it and are drifted downstream. Therefore, these differences may cause differences in the momen-tum and mass transports from middle to polar latitudes or downstream influences of blocking. Moreover, those two categories may be related to the PV response in Chapter 7; the response of the large-amplitude blocks shows similar patterns with the composited one, while that of the small-amplitude blocks does not.

• The vortex-vortex interaction also may be important for the blocking formation.

This is associated with some studies that a climatological stationary ridge can trig-ger the formation of blocking. For example, Luo (2005) demonstrates in his numer-ical model that blocking can be formed on a stationary ridge generated by forcing mimicking the large-scale topography of the Northern Hemisphere with a

wave-maker of synoptic eddies upstream of the ridge. To this formation, the mechanism of the vortex-vortex interaction could be adopted. This is because it can be thought that a stationary ridge can collaborate with anticyclones generated by large-scale dynamics such as a local resonance near the ridge and incoming Rossby waves from upstream, to form a PV minimum region with a blocking scale. Then, this region may become an ‘anchor’ for gathering synoptic anticyclones, promoting the vortex-vortex interaction of anticyclones.

The SAM may be applied to, more generally, other large-scale phenomena in mid-and high-latitudes, where the PV-thinking is a powerful tool for analyses. They are per-sistent anomalies with larger spatial and temporal scales than those of blocking such as the stationary lows (e.g., the Aleutian and Icelandic lows) and low-frequency variabilities (e.g., the NAO and PNA). They have large-scale PV anomalies in geographically-fixed positions and many sources of synoptic and/or Rossby eddies around them. Because vari-abilities of their PV anomalies change the large-scale jet strength and/or horizontal shear, the PV anomalies affect behaviors of synoptic waves via their preferred routes or breaking processes (e.g., Rivi`ere and Orlanski 2007). It can be thought that, if such wave break-ing, i.e., the PV mixing repeatedly occurs within a persistent anomaly, a PV extremum region might be formed with the anomaly scale. Thus, the interaction between these large-scale phenomena with PV extrema and synoptic eddies through the absorbing or repelling mechanism of the vortex-vortex interaction may be important for the dynamics of persis-tent anomalies. Applications of the SAM to other phenomena should be investigated in future studies.

In this study, the importance of the SAM for the blocking maintenance has been con-firmed. However, quantitative estimations of this mechanism on the real blocking main-tenance, especially in the baroclinic atmosphere, are not mentioned nor considered here.

For example, Haines (1989) shows that the duration of blocking modeled by a modon solution becomes shorter in a baroclinic model than that in a barotropic one. Then, in the next, quantitative studies of the SAM in the baroclinic atmosphere should be introduced.

Acknowledgments

I am sincerely appreciated to my supervisor, Professor Hisanori Itoh, for his kind sup-port and essential advise to my study over 6 years. Not only this study but also my present attitude to research and knowledge for the atmospheric science could not be accom-plished without him. I also would like to thank Hitoshi Mukougawa, Hisashi Nakamura, Masahide Kimoto, Atsushi Kubokawa, Saburo Miyahara, Toshihiko Hirooka, Kensuke Nakajima, Osamu Morita, Tetsuya Kawano, David G. Andrews, Hung-Chi Kuo, Hiroshi L. Tanaka, Mototaka Nakamura, Masahiro Watanabe, Masato Mori, Koutarou Takaya, Kazuaki Nishii, Yu Kosaka, Mio Matsueda, Olivia Martius, Takahiro Iwayama, Kunihiko Kodera, Yuhji Kuroda, Hiroshi Niino, Keita Iga, Yoshinobu Wakata, Yoshihisa Matsuda, Norihiko Sugimoto, Wataru Yanase, Ryohei Kato, Ken-ichi Shimose, Eigo Tochimoto, Ying-Wen Chen, Takenari Kinoshita, Hiroki Yamamoto, and Takatoshi Sakazaki for stim-ulating discussions and helpful comments. I am especially grateful to Prof. Kubokawa for generous help for solving the modon solutions in this thesis. I am also grateful to Dr.

Kensuke Nakajima for his attention on some techniques for PV-inversion. Dr. Masato Mori and Mr. Ryohei Kato kindly gave me a lot of advice in various situations for me through my PhD student course. In this context, I also thank the GFD dennou club (http://www.gfd-dennou.org/index.html.en), an organization for education and research of the geophysical fluid dynamics (GFD), which has provided many educational workshops for the GFD and research tools to us.

I thank the staffs at Department of Earth and Planetary Sciences in Kyushu Univer-sity who gave (and are giving) me a lot of knowledge for science. I especially would like to thank Drs. Hisanori Itoh, Saburo Miyahara, Toshihiko Hirooka, Osamu Morita, Yasunobu Miyoshi, Kensuke Nakajima, and Tetsuya Kawano who kindly have taught the

Atmospheric Sciences to me since my undergraduate years. I also thank the Front Re-searcher Developing Program (FRDP), an educational program for graduate students at Graduate School of Sciences in Kyushu University, which provided many chances to learn various interdisciplinary approaches for research to me.

I also thank my older and younger students in our and neighbor laboratories for their advise and warm friendship to me. In particular, I thank Ms. Hanae Matsuo who gave me many aspects to my study.

Thanks are also due to my mother, Kumiko Yamazaki, for her mental and financial support to me. I also thank my sister, Yuko Yamazaki, who helped me draw some schematic pictures in this thesis and designed web pages of our laboratory (http://

weather.geo.kyushu-u.ac.jp/).

I have been supported by a grant from the Research Fellowship of the Japan Society for the Promotion of Science for Young Scientists. On many procedures related above, I am grateful to Ms. Midori Mizoguchi who helped my tasks.

The dataset used in this study is provided by the cooperative research project of the JRA-25 long-term reanalysis by the Japan Meteorological Agency and the Central Research Institute of Electric Power Industry. The ensemble data in Chapter 8 is ob-tained from the TIGGE ECMWF portal website (http://tigge-portal.ecmwf.int/

d/tigge/) and how to use it could be learned by courtesy of Dr. Mio Matuseda. An original code for the trajectory analysis is kindly shown by Dr. Ken-ichi Shimose to me.

The SPMODEL (Takehiro et al. 2006) is used for the channel model. The figures were produced by GFD-DENNOU Libraries, GrADs, and MjoGraph.

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