Comparison study of the polar cold air mass between Northern and Southern Hemispheric winters based on a zonal-mean two-box model

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1 AMOSPHERIC SCIENCE LEERS Atmos. Sci. Let. 16: 7 76 (215) Published online 7 August 214 in Wiley Online Library (wileyonlinelibrary.com) DOI: 1.12/asl2.522 Comparison study of the polar cold air mass between Northern and Southern Hemispheric winters based on a zonal-mean two-box model Yuki Kanno, akamichi Shoji and oshiki Iwasaki Department of Geophysics, Graduate School of Science, ohoku University, Sendai, Japan *Correspondence to: Y. Kanno, Department of Geophysics, Graduate School of Science, ohoku University, A519, Physics A Building, 6-3, Aoba, Aramaki, Aoba-ku, Sendai , Japan. kanno@wind.gp.tohoku.ac.jp Received: 8 May 214 Revised: 15 July 214 Accepted: 16 July 214 Abstract he characteristics of the polar cold air mass (PCAM) below a threshold potential temperature θ are quantitatively compared between two hemispheric winters and analyzed with a zonal-mean two-box model. his model estimates a residence time in a genesis box, a life time in a loss box, and PCAM flux between them. he hemispheric total PCAM amount below θ =28 K in the Northern Hemispheric winter is approximately 4% greater than that in the Southern Hemispheric winter. his difference is attributed to the residence time enhanced due to the land sea distribution and mountain barriers, while the PCAM flux is almost equivalent between the two winters. Keywords: isentropic analysis; polar cold air mass; asymmetry between the two hemispheres 1. Introduction he polar cold air mass (PCAM) in winter hemispheres is one of the most fundamental components of the Earth s atmosphere. It distributes so as to satisfy thermal wind balance with the polar vortex and forms a strong baroclinic zone at midlatitudes. In addition, intermittent outflows of the PCAM cause severe cold events in mid and low latitudes (e.g. Dallavalle and Bosart, 1975; Zhang et al., 1997; Lupo et al., 21; Ashcroft et al., 29; Pezza et al., 21). hus, quantitative analyses of the PCAM are highly desired to understand the dynamical system of winter monsoon. Isentropic coordinates facilitate the definition of the PCAM. In particular, hemispheric total amount of the PCAM below a threshold potential temperature is conserved and its local change is caused only from its horizontal flux divergence under adiabatic processes (Iwasaki et al., 214; hereafter I14). he zonal mean meridional circulation diagnosed with mass-weighted isentropic zonal mean (MIM) has a distinct extratropical direct (ED) circulation in winter hemispheres (ownsend and Johnson, 1985; Iwasaki, 1989, 1992; Juckes et al., 1994), which is mainly driven through wave-mean flow interactions (anaka et al., 24; Iwasaki and Mochizuki, 212). Iwasaki and Mochizuki (212) indicated that the PCAM is generated in the downward branch of the ED circulation and transferred equatorward in midlatitudes. I14 showed the geographical distribution of the PCAM horizontal flux. In the Northern Hemispheric (NH) winter, there are two main climatological PCAM streams, termed the East Asian stream and the North American stream. he former grows over the northern part of the Eurasian continent, flows eastward on the northern side of a high mountain range, turns down southeastward over East Asia, and then disappears over the western North Pacific Ocean. he latter grows over the Arctic Ocean, flows toward the east coast of North America, and then disappears over the North Atlantic Ocean. he behavior of the PCAM is strongly affected by topography. herefore, there is an increasing interest in the comparison between the PCAM behaviors in the two hemispheric winters, because the topography is very different from each other. In this study, we quantitatively compare the total PCAM amount below the threshold potential temperature between the NH and Southern Hemispheric (SH) winters and clarify the reasons for their differences. o this end, a zonal-mean two-box model is proposed to separate the latitudinal region of the PCAM into genesis and loss boxes, and examine a residence time for the former and a life time for the latter. Although the standard threshold potential temperature is set to be 28 K, the sensitivity to the threshold is also examined. 2. Zonal-mean two-box model associated with the PCAM budget he PCAM is defined as the atmosphere below the threshold potential temperature θ. In this analysis, we set θ at 28 K following I14. In MIM analyses, the potential temperature of 28 K is approximately the value at the turning point of the ED circulation from downward to equatorward in the two winters (Figure 1). We also conduct a sensitivity experiment of changing θ to 275 and 285 K. 214 Royal Meteorological Society

2 Comparison study of the polar cold air mass 71 Mass Stream Function [1 1 kg s 1 ] 1 DJF climate 1 JJA climate S 6S 3S EQ 3N 6N 9N 9S 6S 3S EQ 3N 6N 9N Figure 1. Meridional cross sections of MIM s mass stream functions shaded with intervals of 1 1 kg s 1 and potential temperature contoured with intervals of 1 K averaged over DJF and JJA. he 28 K potential temperature lines are shown by bold lines. Zonally averaged topography is shaded with black. Figure 2. Schematic diagram of the zonal-mean two-box model. DP 1 and DP 2 represent the PCAM amounts in the genesis box and in the loss box, respectively. G 1, L 2,andI represent the PCAM genesis rate in the genesis box, the PCAM loss rate in the loss box, and the PCAM flux from the genesis box to the loss box, respectively. θ and φ c represent the threshold potential temperature and the critical latitude, respectively. he blue line indicates the threshold potential temperature plane and black dotted line indicates the critical latitude. he governing equations of the PCAM amount and its horizontal flux are reported by I14. Our approach to formulating the zonal-mean two-box model is based on a simple Lagrangian-mean cold air outbreak perspective; the PCAM grows over high latitudes, outflows equatorward, and then disappears in the subtropics, as suggested by Iwasaki and Mochizuki (212). According to this idea, the zonal-mean two-box model divides the latitudinal region of the PCAM into two boxes. On the climatological mean states, two boxes are a genesis box on the polar side of the maximal latitude of the zonal mean equatorward PCAM flux and a loss box on the equatorial side of it. he PCAM generated by diabatic cooling in the genesis box remains for some time before flowing into the loss box. In the loss box, the PCAM incoming from the genesis box disappears at a certain rate by diabatic heating (Figure 2). he maximal latitude of the equatorward PCAM flux is called a critical latitude φ c. Let us begin with the PCAM conservation relation at each geographical point (Equation (3) in I14): DP t = p s p(θ ) vdp + G ( θ ) (1) where DP( p s p(θ )) is the PCAM amount, v is the horizontal wind vector, p s is the ground surface pressure, p(θ ) is the pressure on θ surface, and G(θ )is the diabatic change rate of the PCAM (downward crossing rate at θ surface). By integrating Equation (1) with respect to longitude and dividing by the gravitational acceleration, we obtain a zonally integrated PCAM conservation equation: 1 g t p s DPa cos φdλ = 1 g φ v cos φdpdλ + 1 p(θ ) g G ( θ ) a cos φdλ (2) where a, g, v, φ, andλ are the radius of the Earth, the gravitational acceleration, meridional wind, latitude, and longitude, respectively. On the right hand side of Equation (2), the first term is the meridional convergence of the zonally integrated PCAM flux and the second term is the diabatic genesis/loss rate of the zonally integrated PCAM. he critical latitude for the genesis/loss boxes is specified, at which meridional convergence of PCAM flux is zero. he PCAM budgets of the genesis and loss boxes are derived by integrating Equation (2) from the North (or 214 Royal Meteorological Society Atmos. Sci. Let. 16: 7 76 (215)

3 72 Y. Kanno,. Shoji and. Iwasaki South) Pole to the critical latitude and from the critical latitude to the Equator, respectively. he equations are as follows: t DP 1 = I + G 1 (3) and t DP 2 = I L 2 (4) where angle brackets denote zonal and meridional integrals of any variable A, and subscripts 1 and 2 denote integrals over the genesis box and loss box, respectively: and A 1 1 g A 2 1 g φ c φ pole φ c Aa 2 cos φdλdφ (5) Aa 2 cos φdλdφ (6) where φ pole is a latitude at the North (or South) Pole. In Equations (3) and (4), L 2 is the PCAM loss rate defined as L 2 G 2 and I is the net PCAM flux from the genesis box to the loss box. I 1 g p s p(θ ) vacos φ dpdλ (7) φ=φc We compute total amounts of each variable for the genesis and loss boxes. Next, let us consider the steady state of the zonal-mean two-box model. Assuming an electrical circuit connects a resistor (resistance R) and a capacitor (capacitance C) to an alternator in parallel, the time constant of this circuit is defined as τ RC = Q/I, where Q is an electric charge in the capacitor and I is an electric current. As Equation (3) is analogous to the equation of the charge in the capacitor, we define the time constant of Equations (3) and (4) as a residence time τ 1 ( DP 1 /I) in the genesis box and a life time τ 2 ( DP 2 / L 2 ) in the loss box, respectively. Using these time constants, Equations (3) and (4) are rewritten as t DP 1 = DP 1 + G τ 1 (8) 1 and t DP 2 = I DP 2 (9) τ 2 In a steady state, the PCAM amounts in these boxes are DP 1 = τ 1 G 1 = τ 1 I and DP 2 = τ 2 I (1) Summing up these two equations, the steady state of the hemispheric total PCAM amount DP is written as DP DP 1 + DP 2 = ( τ 1 + τ 2 ) I (11) hus, the steady state of the PCAM amount is expressed in terms of the two time constants and the PCAM flux from the genesis box to the loss box. his study uses the 6-hourly JRA-25/JCDAS reanalysis data (Onogi et al., 27) with a horizontal resolution of We analyze data from December, January, and February (DJF) between the years 198/1981 and 29/21 for the NH winter and June, July, and August (JJA) between 1981 and 21 for the SH winter. Numerical analyses are made of the PCAM amount and its horizontal fluxes. G(θ ) is estimated as a residual of conservation relation of Equation (1) at each grid point. As shown below, the climatological means of their areal integrations almost satisfy the steady state relationship G 1 = I = L 2 inferred from Equations (3) and (4). his suggests that our analysis is not seriously subject to finite difference errors. 3. Results Before dividing the PCAM into two boxes, we compare the latitudinal distribution of the PCAM between the two winters. Figure 3 shows the zonally integrated PCAM amounts, their genesis/loss rates, and their equatorward flux for θ =275, 28, and 285 K. I14 performed a sensitivity experiment with θ =27, 28, and 29 K. he range of θ used in I14 is too large to see the detail, so smaller range is used in this work. he PCAM amount is greater in the NH winter than that in the SH winter (Figure 3). In the zonal mean state, the PCAM is generated over high latitudes and lost over midlatitudes (Figure 3). Zonally integrated loss rates have narrow and sharp peaks due to the strong influence of the SS distributions, as shown below. he latitudinal bands of disappearance are narrower in the SH winter (c) Figure 3. Zonally integrated PCAM amount (1 1 kg m 1 ), genesis/loss rates of the PCAM (1 4 kg m 1 s 1 ), and (c) equatorward component of the PCAM flux (1 1 kg s 1 ). Blue and red lines indicate the NH and SH winter, respectively. Dotted, solid, and broken lines indicate θ = 275, 28, and 285 K, respectively. 214 Royal Meteorological Society Atmos. Sci. Let. 16: 7 76 (215)

4 Comparison study of the polar cold air mass 73 (1 17 kg) (c) (degree) DP DP 1 DP PACM budget based on two box model Blue: NH winter Red: SH winter (1 1 kg s 1 ) (day) (d) 3 φ c τ 1 τ I G 1 L Figure 4. he PCAM budget based on the zonal-mean two-box model. he PCAM amount (1 17 kg). Solid, broken, and dotted lines indicate DP, DP 1,and DP 2, respectively. Genesis, loss, and the PCAM flux between the two boxes (1 1 kg s 1 ). Solid, broken, and dotted lines indicate I, G 1,and L 2, respectively. (c) Critical latitude (degree). (d) Residence time and life time (day). Solid and dotted lines indicate τ 1 and τ 2, respectively. Blue and red lines indicate the NH and SH winters, respectively. than in the NH winter, reflecting the axially symmetrical land sea distribution in the SH. he disappearance regions shift equatorward as θ increases. In the case of θ =28 K, the critical latitudes are approximately 45 N in the NH winter and approximately 5 S in the SH winter. he equatorward PCAM flux at the critical latitude is almost the same in the two winters (Figure 3(c)). he equatorward PCAM flux around 65 S is slightly stronger than in neighboring latitudes. his may be due to the katabatic wind and high frequency cyclones around Antarctica (Pezza et al., 212). Figure 4 shows the PCAM budget based on the zonal-mean two-box model. In the case of θ =28 K, the total PCAM amounts are approximately kg in the NH winter and approximately kg in the SH winter (Figure 4, able S1, Supporting Information). Hence, the total PCAM amount in the NH winter is almost 4% greater than that in the SH winter. In both winters, almost 9% of the PCAM amount is located within the genesis box. In the steady state, the genesis rate in the genesis box and the loss rate in the loss box are equal to the PCAM flux from the genesis box to the loss box ( G 1 = I = L 2 ), as mentioned above. he NH PCAM flux takes the same value of approximately kg s 1 as the SH flux (Figure 4). his is consistent with the fact that the ED circulation diagnosed with MIM in the NH winter is almost as strong as that in the SH winter (Iwasaki, 1992). his result indicates that the meridional heat transport in the extratropics is similar between two winters, although driving waves are somewhat different (anaka et al., 24). he residence time in the genesis box is approximately 24 (15) days in the NH (SH) winter, respectively (Figure 4(d)). he life time in the loss box is 2.2 (2.8) days in the NH (SH) winter, respectively. herefore, from 214 Royal Meteorological Society Atmos. Sci. Let. 16: 7 76 (215)

5 74 Y. Kanno,. Shoji and. Iwasaki (c) (d) Figure 5. Geographical distributions of (a and b) the PCAM amount (hpa) and its flux (hpa m s 1 ) and (c and d) genesis/loss rates of the PCAM (hpa day 1 ). (a and c) NH winter, (b and d) SH winter. Contour lines indicate the topography with interval of 5 m. Equation (11), the difference in the PCAM amount between the two winters is attributed primarily to the residence time in the genesis box. he reasoning of the residence time difference will be discussed in the next section. he dependence on θ is also examined. he PCAM amount is greater in the NH winter than in the SH winter commonly for θ =275, 28, and 285 K cases, although the difference in the PCAM amount decreases with increasing θ from 28 to 285 K. One of the reasons for the reduction of the PCAM difference is that the difference in the critical latitude vanishes for θ =285 K. Absolute values of the genesis rates in the genesis box, the loss rates in the loss box, and the PCAM fluxes from the genesis box to the loss box also increase with θ, but are almost equivalent between two winters (Figure 4). herefore, the importance of the residence time for the PCAM amount is independent of θ. For more insights into the difference in the PCAM between the two winters, we compare the geographical distributions of the PCAM amount with its horizontal flux and its genesis/loss rates in the NH and SH winters. In the NH winter, the PCAM amount increases with latitude and elongates from the Far East to North America (I14; Figure 5). In the SH winter, the distribution of the PCAM amount is more axisymmetric (Figure 5). his difference may result from differences in the stationary ultra-long wave activity in the two hemispheric winters. Near the edge of Antarctica, the PCAM flux is intense due to the katabatic wind and high frequency cyclones, as mentioned above. he genesis regions of the PCAM in the NH winter are located over land and sea ice in high latitudes (I14; Figure 5(c)), whereas in 214 Royal Meteorological Society Atmos. Sci. Let. 16: 7 76 (215)

6 Comparison study of the polar cold air mass 75 the SH winter, they are located over Antarctica, sea ice, and even over the ocean adjacent to the sea ice (Figure 5(d)). he disappearance regions in the NH winter are located over the western North Pacific Ocean and the western North Atlantic Ocean (Figure 5(c)). In contrast, the disappearance regions in the SH winter are annularly distributed over the Southern Ocean (Figure 5(d)), where air sea interaction is intense (Simmonds and King, 24). his annular distribution is related to the Southern Annular Mode (hompson and Wallace, 2; hompson and Solomon, 22). Strong disappearance regions of the western North Pacific Ocean, the western North Atlantic Ocean, and the South Indian Ocean correspond to the storm track regions (Wallace et al., 1988; Hoskins and Valdes, 199; renberth, 1991). his suggests that baroclinic waves play an important role in the disappearance of the PCAM. Note that the noisy distribution structures of the genesis and disappearance near the coastal lines of Antarctica may be subject to numerical errors associated with the steep topography of this area. 4. Discussions Why is the residence time in the genesis box of the NH winter longer than that of the SH winter? By the analogy with an electrical circuit considered in Section 2, the time constant is written as a product of the capacitance and the resistance. he capacitance of the PCAM corresponds to an area of the genesis regions, polar side of the critical latitude. he critical latitude of the PCAM below θ =28 K is approximately 45 Ninthe NH winter and approximately 5 S in the SH winter (Figure 4(c)), so that the area of the genesis box in the NH winter is approximately 25% larger than that in the SH winter. he lower critical latitude in the NH winter makes the PCAM capacity larger and then, makes the residence time longer. he larger area of the genesis box in the NH winter may be related to the land sea distribution, because the PCAM is generated over land in relatively lower latitudes. In the NH winter, high mountain ranges in the Eurasian continent block the PCAM from moving equatorward (I14), so that the PCAM is dammed on the northern side of the mountains (Murakami and Nakamura, 1983). After leaving from the genesis box, the PCAM disappears mainly over the North Pacific Ocean and North Atlantic Ocean in the subtropics. hus, the equatorward pathways of the PCAM toward the loss box are limited to East Asia and the east coast of North America. hese limited pathways may act as a strong resistance for the PCAM flux. herefore, the residence time in the genesis box becomes longer in the NH winter. On the other hand, in the SH winter, the PCAM directly slides down the Antarctic Plateau and continuously moves equatorward over the ocean (Murphy and Simmonds, 1993; Perrin and Simmonds, 1995). In addition, strong traveling baroclinic wave activities over the Southern Ocean play an important role for transporting the PCAM to the subtropics. In addition to the area of the PCAM genesis region, the land sea distribution and topography in midlatitudes make difference in the residence time, which is responsible for the difference in the PCAM in two hemispheric winters. 5. Concluding remarks he difference between the PCAM below the threshold potential temperature θ for the two winters is quantitatively investigated by means of a simple zonal-mean two-box model. his model separates the latitudinal region of the PCAM into a genesis box on the polar side of the maximal latitude of the zonal mean equatorward PCAM flux and a loss box on the equatorial side of it. At the steady state, both the genesis and loss rates of the PCAM become equivalent to its flux from the genesis box to the loss box. herefore, the hemispheric total PCAM amount can be written as DP = (τ 1 + τ 2 )I. In the case of θ = 28 K, the total PCAM amount in the NH winter is almost 4% greater than that in the SH winter. he PCAM fluxes from the genesis box to the loss box, in contrast, have almost the same value for both winters independent of θ. his result makes our analysis with zonal-mean two-box model effective. he residence t imes τ 1 in the genesis box are approximately 24 (15) days in the NH (SH) winter, respectively. he life times τ 2 in the loss box are much shorter than the residence times in the genesis box. hus, the difference in the PCAM between the two winters is attributed to the residence time in the genesis box. he difference in the residence time results from the difference in (1) the critical latitude, (2) mountain ranges blocking the equatorward PCAM flow, (3) the land sea distribution limiting the PCAM disappearance. he land sea distribution and topography are considered to be responsible for the difference in the PCAM amount. In the NH, the effect of the topography on the climatological PCAM streams is already stated in I14. Our results suggest that the topography also affects the hemispheric total PCAM amount through the extension of the residence time. here is not so strong stationary PCAM stream in the SH as is found in the NH. In the SH, cold air outbreaks may occur in various longitudinal regions when synoptic conditions are favorable (Simmonds and Richter, 2; Simmonds and Rashid, 21). hus, cold air outbreaks in the SH have zonally broader influence on midlatitude than that in the NH winter (Garreaud, 21). Further study of hemispheric influence of cold air outbreak in the SH is beneficial for understanding the climate system. he zonal-mean two-box model proposed in this study is applicable to the analysis of temporal variations in various time scales, such as daily, intraseasonal, seasonal, and interannual variations. In this work, we 214 Royal Meteorological Society Atmos. Sci. Let. 16: 7 76 (215)

7 76 Y. Kanno,. Shoji and. Iwasaki noticed that the residence time is a valuable parameter to understand the total amount of the PCAM. emporal variations of the residence time may be closely related to the hemispheric scale charge and discharge of the PCAM amount. Further study of the variability of PCAM is expected to explore the dynamical system of winter monsoon. Acknowledgements he authors would like to express their sincere thanks to anonymous reviewers for their constructive comments. his study is supported in part by the Japanese Ministry of Education, Culture, Sports, Science and echnology through a Grant-in-Aid for Scientific Research in Innovative AREAS #225 and Research Program on Climate Change Adaptation (RECCA). 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