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Fig. 5: 0000 UTC 5 May 1998, on the 330-K isentropic surface, shadings represent (a) vertical velocity ( ), (b) relative humidity, (c) divergence ( ), (d) based on Eq. (7) (hours), and (e) with diabatic effect based on Eq. (10) (hours). The contours in each panel stand for potential vorticity (with a contour interval of 0.5 PVU starting at 0.5 PVU). The bold solid line is the 1.5-PVU contour, which represents the dynamic tropopause. (f) Apparent heat source vertical profile calculated for the blue rectangle in (c). Fig. 4: (a-c) Daily TOMS images of total ozone in the Southern Hemisphere. (From Bowman and Mangus 1993) (d-f) Filamentation time, potential vorticity, and wind vectors on the 550-K isentropic surface. 4. Frontogenesis The frontogenetical function diagnosis for a synoptic mei-yu front is proposed by Chen et al. (2007). Here we compare the filamentation time diagnosis with the deformation part of the frontogenetical function (FG3) for the mei- yu front. The results, shown in Fig. 3, suggest the filamentation time diagnosis matches well with the frontogenesis area depicted by FG3 function. Since the filamentation time diagnosis contains the effect of convergence and vorticity, it may be the reason why there is more filamentation zones than FG3 diagnosis. Filamentation Time Diagnosis Yu-Ming Tsai * and Hung-Chi Kuo Department of Atmospheric Sciences, National Taiwan University * Corresponding author e-mail: D95229003@ntu.edu.tw 姓 名：蔡禹明 系 所：大氣科學研究所 學 號： D95229003 指導老師：郭鴻基 教授 此論文發表期刊： Monthly Weather Review 致謝：感謝郭老師和 Prof. Wayne Schubert 樹立的典範和指導，外婆、父母的教導和 養育，小娜的陪伴，以及與我一路同行的 大家 。感謝天主。 The filamentation time in spherical coordinates on an isentropic surface has been derived and used as a diagnostic tool to analyze both midlatitude and tropical trough thinning processes, wave breaking of Antarctic polar vortex, and mei-yu frontogenesis events. The modified filamentation time formula which includes the diabatic heating effect is derived and illustrated with a midlatitude event. From the mei-yu frontogenesis study, the results suggest filamentation time diagnosis matches well with the deformation part of the frontogenetical function. The results show that the filamentation time diagnostic on isentropic potential vorticity maps can serve as a useful aid in the analysis and prediction of observed banded synoptic flows. Abstract A common phenomenon in mesoscale and synoptic scale atmospheric flows is the production of banded or filamentary structures in the potential vorticity (PV) field on isentropic surfaces. Rozoff et al. (2006) defined a local parameter called the "filamentation time," which is the e-folding time for growth rate of the vorticity gradient. The purpose of the present study is to generalize the filamentation time diagnostic of Rozoff et al. (2006) from two-dimensional, nondivergent, vorticity dynamics in Cartesian coordinates to three-dimensional, divergent, potential vorticity dynamics in spherical/isentropic coordinates, and then to apply this diagnostic tool to observed synoptic scale flows. 1. Introduction 2. Theoretical concepts Following the derivation in Tsai et al. (2010), inviscid, adiabatic, quasi-static flow in the atmosphere obeys the material conservation relation: where is the material derivative. being the longitude, being the latitude, and with the partial derivatives taken on the isentropic surface. We now define the isentropic divergence on the sphere as the isentropic relative vorticity as and the isentropic stretching and shearing deformation as and. (1) (2) (3) (4) (5) (6) To understand the evolution of the PV gradient, we differentiate (1) with respect to and. For the strain dominated regions, we can define the filamentation time as the e-folding time of the PV gradient evolution: Strain dominated regions can also be referred to as filamentation zones. For the examples presented in the following, the surface analyzed is an isentropic surface. The reanalysis data used here are from the ECMWF. (7) 2010 理學院院長獎博士論文 3. Trough thinning in the midlatitudes and the tropics 5. Wave breaking of Antarctic polar vortex 6. Diabatic heating effect 8. Bibliography The first example is a strong baroclinic event near the European continent (Fig. 1). Region B is in an elongated trough at lower latitudes. There is cross-PV-contour flow behind the trough and more parallel-PV-contour flow ahead in region B. This is the trough thinning regions according to Thorncroft et al. (1993). These analyses demonstrate that it is useful to combine the cross-PV-contour flow analysis on isentropic surfaces with the filamentation time analysis. [1] Bowman, K. P., and N. J. Mangus, 1993: Observations of deformation and mixing of the total ozone field in the Antarctic polar vortex. J. Atmos. Sci., 50, 2915-2921. [2] Chen, G. T.-J., C.-C. Wang, and A.-H. Wang, 2007: A case study of subtropical frontogenesis during a blocking event. Mon. Wea. Rev., 135, 2588- 2609. [3] Rozoff, C. M., W. H. Schubert, and B. D. McNoldy, 2006: Rapid filamentation zones in intense tropical cyclones. J. Atmos. Sci., 63, 325-340. [4] Rozoff, C. M., J. P. Kossin, W. H. Schubert, and P. J. Mulero, 2009: Internal control of hurricane intensity variability: The dual nature of potential vorticity mixing. J. Atmos. Sci., 66, 133-147. [5] Thorncroft, C. D., B. J. Hoskins, and M. E. McIntyre, 1993: Two paradigms of baroclinic-wave life-cycle behaviour. Q. J. R. Meteorol. Soc., 119, 17-55. [6] Tsai, Y.-M., H.-C. Kuo, and W. H. Schubert, 2010: Filamentation time diagnosis of thinning troughs and cutoff lows. Mon. Wea. Rev. (in press), doi: 10.1175/2010MWR3102.1. [7] Yanai, M., S. Esbensen, and J.-H. Chu, 1973: Determination of bulk properties of tropical cloud clusters from large-scale heat and moisture budgets. J. Atmos. Sci., 30, 611-627. The second example presented here is a TUTT event over the Atlantic Ocean during June 2005. In the example presented here, a low latitude cutoff low (a so-called TUTT cell) also formed. Fig. 2 depicts the evolution of this event on the 360-K isentropic surface. The above two examples indicate that the filamentation time in the tropical event is generally longer than in the midlatitude events, which have stronger baroclinicity. For scale analysis, our results suggest that neglecting curvature terms for simplicity is acceptable if the event is not too close to the pole, but retaining the isentropic divergence term is helpful for increased accuracy. In this Section, we focus on the dynamical process of the wave breaking of the Antarctic polar vortex, which will cause band like structure accompany with low ozone air transports into low latitude (Fig. 4). The data is from the Japanese 25-year Reanalysis Project (JRA-25) with a grid spacing 2.5° in both directions. Comparing with the TOMS observations (Fig. 4a-c, from Bowman and Mangus 1993), a very clear consistency between the low ozone area (black) and the trough is found. It is because the trough induces the meridional movements of the air, and the low concentration ozone is been carried as a passive tracer. Fig. 1: Filamentation time (h; shading), PV (black contours, with 1, 2, 4, 6, and 8 PVU), and wind vectors on the 310-K isentropic surface at (a) 0000 UTC 28 Jan 1990, (b) 1200 UTC 28 Jan 1990, (c) 0000 UTC 29 Jan 1990, and (d) 1200 UTC 29 Jan 1990. In the unshaded areas, the flow is either vorticity dominated or has a filamentation time that is negative or longer than 4 h. Fig. 2: Filamentation time (h; shading), PV (black contours, with a contour interval of 1 PVU starting at 2 PVU), and wind vectors on the 360-K isentropic surface. The filamentation time with diabatic heating effect is derived as follows. Generalizing Eq. (1) to, and define. In order to gain the analytic solutions, we ignore the effect caused by the spatial difference of the diabatic heating and get the filamentation time formula is calculated by, where is the apparent heat source proposed by Yanai et al. (1973). The area labeled "A" in Fig. 5 is a convective area on the 330-K isentropic surface. From Fig. 5a-c, the convection is occurred near A with diabatic heating effect, which generates additional filamentation zones in Fig. 5e. Fig. 5f shows the apparent heat source profile for the blue triangle in Fig. 5c. The results suggest that filamentation time with diabatic heating could capture additional local filamentation zone caused by the local convection, but for the whole cutoff process, the diabatic effect seems to play secondary role in this event. (8) (9) (10) 7. Forced barotropic simulation Fig. 6: The vorticity ( ) and filamentation time (hours) for Exp. A and Exp. B, respectively. In (b, d), the contours (0.1, 0.5, 1, 4, and 8) represent the vorticity field. A spectral f-plane barotropic simulation with a "logistically limited" forcing (Rozoff et al. 2009) is used to study the interaction between the core vortex with a weaker forced convection through the filamentation time diagnosis. Rayleigh friction and diffusion are included in the simulation. We perform two experiments, Exp. A with the core vortex, Exp. B with the core vortex. The outer forced vortex has the maximum vorticity. In these two experiments, the forcing rate is set to take 6 hours to achieve the maximum vorticity. As shown in Fig. 6, the steady state for Exp. A is merge, and concentric pattern for Exp. B. This set of experiment designed for the forced vorticity located at hours in Exp. A, and hours in Exp. B, so the forced convection could survive in Exp. A but suppressed by the filamentation effect in Exp. B. Fig. 3: The 925-hPa frontogenetical function from deformation (FG3; ; red contours). Shadings represent 315-K isentropic surface filamentation time. 動力與模擬實驗室 D YNAMICS & M ODELING L AB. A B VorticityFilamentation Time 2010 Science College Dean Award Ph.D. Dissertation

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