Moist Potential Vorticity Generation in Extratropical Cyclones Zuohao
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Moist Potential Vorticity Generation in Extratropical Cyclones bv Zuohao Cao A thesis submitted in conformity with the requirements for the Degree o f Doctor o f Philosophy in the Department o f Physics o f the University o f Toronto © Copyright by Zuohao Cao 1995 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission For my parents Mr. Jie Cao and Mrs. Sujuan Vang Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Moist Potential Vorticity Generation in Extratropical Cyclones Zuohao Cao, Ph.D. 1995 Department of Physics, University of Toronto Abstract The mechanism o f moist potential vorticity (M PV) generation in a three- dimensional moist adiabatic and frictionless flow is investigated. It is found that MPV generation is governed by baroclinic vectors and moisture gradients. Negative (positive) M PV can be generated in the region where baroclinic vectors have a component along (against) the direction o f moisture gradients. Numerical simulations of extratropical cyclones with different moisture distributions show that at the different stages of cvclogenesis, negative MPV usually appears in the warm sector near the north part o f the cold front, the bent-back warm front, the warm core and the cold front. The effects o f the Boussinesq approximation on the distribution of vorticity and M PV are examined. The Boussinesq approximation neglects several components o f the ^olenoidal term in the vorticity equation. As a result, it underestimates the thermally direct circulations in the cold front and the bent-back warm front by 25% to 30%. This effect is more pronounced when latent heat release is taken into account. Consequently, the influence o f the Boussinesq approximation on the MPV field is very significant. Evidence o f the presence o f conditional symmetric instability in the negative MPV region of the extratropical cyclone is also presented. i Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Acknowledgments Many individuals, who deserve special recognition, made the direct and indirect contribution to this thesis. I would like to express my thanks to Professor Man-Ru Cho. my supervisor, for his insights, encouragement, understanding and guidance, to Professors G. YV. K. Moore and T. G. Shepherd for serving in my supervisory committee, and to Professors M. K. Yau (the external examiner) and R. List for their interest in this research. Thanks are due to Professor D.-L. Zhang for providing the basic code of PSU/NCAR three-dimensional hydrostatic mesoscale model. I am indebted to Dr. M. Medley for many enjoyable and helpful discussions on numerical methods. Thanks also go to my colleagues in the department of physics for their assistance and discussions, especially Dr. John Koshyk. M urray Mackay and Paul Kushner. I am grateful to my wife. Shu Chen, for her love and support, and my lovely son. Eric Yixiao Cao, for his moral support. The specially important people are my parents. Mr. Jie Cao and Mrs. Sujuan Yang. Their encouragement and support will be remembered for ever. My financial support by the department of physics of University of Toronto through various fellowships and by Professor Han-Ru Cho from his research grant is highly appreciated. This research was supported by the NSERC and AES o f Canada. ii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Contents Abstract i Acknowledgments ii 1. INTRODUCTION I 1.1 Extratropical cyclones 1 1.2 Dry and moist potential vorticity 3 1.3 Objectives and organization o f the thesis 8 2. GOVERNING EQUATION AND GENERATION OF MOIST POTENTIAL VORTICITY 10 2 1 Governing equation o f moist potential vorticity 10 2.2 Formulation for the baroclinic generation o f moist potential vorticity 1 - 3. N U M E R IC A L M O D E L 16 3.1 Model equations 16 3.2 Initial conditions 19 3.3 Experiment design 24 3.3.1 Control experiment 24 3.3.2 Sensitivity experiments 27 4. GENERATION OF MOIST POTENTIAL VORTICITY IN EXTRATROPICAL CYCLONES 30 4.1 The control experiment 30 iii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4.1.1 Life cycle o f the extratropical cyclones and MPV distribution 30 4 I 2 Baroclinic generation o f MPV 37 4 .1 3 Effects o f horizontal diffusion and rainwater evaporation 44 4.2 Sensitivity study 47 4.3 Summary 67 5. BOUSSINESQ APPROXIMATION AND ITS IMPLICATIONS 70 5.1 Vorticity dynamics 70 5.2 Moist potential vorticity dynamics 79 5.3 Summary 81 6. CONDITIONAL SYMMETRIC INSTABILITY (CSI) IN EXTRATROPICAL CYCLONES 82 6. 1 The criteria o f CSI used in this study 83 6.2 The scheme for taking two-dimensional cross sections o f equivalent potential temperature and absolute momentum 84 6.3 CSI in extratropical cyclones 86 6.3.1 Evidence o f CSI in extratropical cyclones 86 6.3.2 Possible roles o f CSI in extratropical cyclones 92 6.3 .3 Effects of moisture distribution on CSI in extratropical cyclones 102 6.4 Summary 115 7. CONCLUSIONS AND SUGGESTIONS FOR FUTURE RESEARCH 116 iv Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. APPENDIX A THE ESTIMATION OF FUNCTION A 119 APPENDIX B LIST OF SYMBOLS 120 REFERENCES 123 V Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1 Chapter 1 INTRODUCTION 1.1 Extratropical cyclones Extratropical cyclones have been recognized as an important class o f systems in weather forecasting for at least 150 years because they frequently occur in the mid latitudes. An example o f a marine extratropical cyclone is shown in Fig. 1.1. Many theories have been developed to aid in the understanding o f cyclone behavior and structure. In the 19th century, the thermal theory o f cyclones based on Espv’s work claimed that the decrease o f the surface pressure in storms is essentially related to the release o f latent heat in the ascending air near the storm center. The ever-increasing knowledge o f dynamical processes gave birth to the polar front theory (Bjerknes and Solberg 1922). According to the polar front theory, the cyclone forms as a result o f an instability o f the polar front, a surface o f discontinuity separating tropical and polar air masses. After the debates on the relative importance o f dynamic and thermodynamic processes in extratropical storms in the 1920s. the dynamic processes associated with low-level fronts and existence o f a strong upper-level current were realized as important elements for the development of cyclones. However, the importance o f latent heat release from boundary layer and free atmosphere was not ruled out. Another remarkable achievement o f cvclogenesis theory was baroclinic instability theory introduced by Chamey (1947) and Eady (1949). This theory emphasizes the instability o f the broad baroclinic westerlies rather than the frontal discontinuities. The baroclinic theory' successfully predicts the structure o f the incipient waves, realistic growth rates o f their development and their characteristic wavelengths. The success o f the baroclinic theory and the failure o f earlier works on frontal instability Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. v rffii^s: Fig. 1.1 Visible images of a storm occurred in the western Pacific Ocean at (a) 2100 UTC 10 April 1992, (b) 1800 UTC 11 April 1992, and (c) 2000 UTC 12 April 1992. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (Solberg 1928; Kotschin 1932; Bjerknes and Godske 1936) result in general acceptance o f baroclinic instability as the fundamental cause o f cvclogenesis. These classical studies o f cyciogenesis by Charney (1947) and Eadv (1949) can also be described from potential vorticity point of view (e.g., Chamev and Stem 1962). Because in the middle latitudes precipitation is mainly caused by extratropical cyclones, especially those associated with explosive deepening, the extratropical cyclones have received much attention in recent years (e.g., Houze and Hobbs 1982). Although precipitation processes cover temporal scales from 10'*s to I CPs and spatial scales from meso-y (2-20 km in horizontal dimension) tc meso-a (200-2.000 km), most precipitation in extratropical cyclones is organized at meso-p jcale (20-200 km) in the form o f rainbands. According to Houze et al. (1976). Hobbs (1978) and Matejka et al. (1980), the principal rainbands in mid-latitude cyclones are classified into six types ( see Fig. 1.2). Several theories have been proposed to explain the formation o f these rainbands (see Table 1.1 for details). Table 1.1 suggests that conditional symmetric instability is one o f the successful candidates to elucidate the formation o f some rainbands in cyclones. The observational studies by Bennetts and Ryder (1984), and Parsons and Hobbs (1983) also show that the theory o f conditional symmetric instability can explain many o f the observed features o f the warm-sector and wide cold-frontal rainbands. Because the value o f (moist) potential vorticity is critical for the appearance o f (conditional) symmetric instability, the importance o f (moist) potential vorticity is emphasized in the literature. Further discussions and implications o f (moist) potential vorticity w ill be given in the next section. 1.2 Dry and moist potential vorticity Although the importance of potential vorticity (PV) thinking has been recognized only relatively recently, the application of this concept to the study of extratropical cyclones can be traced back to Rossbv's work (Rossby 1940). As he Reproduced with permission of the copyright owner.