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Information to Users INFORMATION TO USERS This manuscript has been reproduced trom the microfilm master. UMI films the text directly trom the original or copy submitted. Thus. sorne thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer. The quallty of thl. reproduction is depend.nt upon the quallty of the copy submltted. Broken or indistind print. colored or poor quality illustrations and photographs, print bleedthrough, substandard margins. and improper alignment can adversely affect reprodudion. ln the unlikely avent that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright materia' had to be removed, a note will indicate the deletion. Oversize materials (e.g., maps, drawings, charts) are reproduced by seetioning the original, beginning at the upper left-hand camer and cantinuing tram left to right in equal sedions with small overtaps. ProQuest Information and Leaming 300 North Zeeb Raad, Ann Arbor, MI 48106-1346 USA 800-521-0600 On the Parameterization of • Slantwise Convection in General Circulation Models Liang Ma Department of Atmospheric and Oceanic Sciences McGill University Montreal, Canada August, 2000 Submitted to the faculty of Graduate Studies and Research in partial fu]fillment of the requirements for the degree of Doctor of Philosophy @Liang Ma 2000 i 1 •1 National Libr8Jy ~nation8le 14'1 of canada duc.nada ~uilitionsand AcquilitioM et BibIiographïc ServiceS services bibliOgraphiques _ ".'VllllltgIDn Street _.n.-\\"', a...ON K1A0N4 OI.-ON K1A0N4 c..da c..a The autbor bas granted a non­ L'auteur a accordé une licence non exclusive licence aIloWÎDg the exclusive permettant à la Natioual Library ofCanada ta Bibliothèque natiouale du Canada de reproduce, 10an, distnbute or sen reproduire, prêter, distribuer ou copies oftbis thesis in microform, vendre des copies de cette thèse sous paper or electroDic formats. la forme de microfichel~ de reproduction S1U' papier ou sm' format électronique. The author retains ownership ofthe L'auteur conserve la propriété du copyright inthis thesis. Neitber the droit d'auteur qui protèp cette thèse. thesis nor substantial extracts nom it Ni la thèse ni des extraits substantiels may be printed or otherwise de celle-ci ne doivent atre imprimés reproduced without the author's ou autrement reproduits sans son permission. autorisation. 0-612-70086-0 • Abstract This study is concerned with the effect of slantwise convection in general circulation models (GCl\JIs). The approach is through the development of a slantwise convective parameterization scheme (SCPS) and its implementation into version 11 of the third generation GCM of the Canadian Climate Centre for modelling and analysis (CCCma gcm11). "vVe first study the characteristics of conditional symmetric instability (CSI) in an environment which is also unstable for conditional upright instability (CUI). The results indicate features common to both upright and slantwise convection. This so called slantwise buoyant instability (SBI) possesses two relevant time scales and its horizontal scale can ranges from tens of km up to over one thousand km. \Ve then analyze the 15-year ECMWF re-analysis (ERA) data to compute the global distributions of convective available potential energy (CAPE) and slantwise convective available energy eSCAPE). We show that the potential for CSI and CUI indeed co-exists over most areas around the globe. Based on the results of the theo­ retical study and the data analysis, a parameterization for slantwise convection was • ü developed and implemented into gcml1. It was round that the scheme impacts sig­ • nificantly the simulated general circulation by the development of a direct meridional secondary circulation. The results of the 5-year simulations show that the scheme re­ duces SCAPE and SCAPE residual Ta over the mid-latitudes, leading to a weakening of the thermal wind and the strength of the upper-level jets. The largest improve­ ment in the simulated dimate however lies in the reduced meridional transient eddy transports of heat and zonal momentum. With the inclusion of the scheme, the eddy transports agree much more favorably with the observational analysis. • ili • Résumé Cette étude porte sur les effets de la convection oblique dans les modèles de circulation générale (GCM). L'approche utilisée est la suivante. Un paramétrage de la convection oblique (SCPS) a été développé et implanté dans la version Il du GCM (troisième génération) du Centre Climatique Canadien pour la modélisation et l'analyse (CC­ Cma). Les caractéristiques de l'instabilité conditionnelle symétrique (CSI) ont d'abord été étudiées dans le contexte d'un environement propice au dévelopement de l'instabilité conditionnelle verticale (CUI). Ceci a permis d'identifier certaines car­ actéristiques communes au.x deux types d'instabilité. L'instabilité résultante, qual­ ifiée de convective-oblique, possède deux échelles de temps caractéristiques. De plus, nous avons déterminé que les échelles horizontales typiques associées à cette instabilité varient entre quelques dizaines et plus d'un millier de kilomètres. Les données provenant des ré-analyses de l'ECMWF ont été utilisées pour calculer la distribution de l'énergie convective potentielle disponible (CAPE) et de l'énergie convective oblique potentielle (SCAPE) sur la planète. Nous avons demontré qu'en général, le CSI et le CUI co-existent. En se basant sur une étude théorique ainsi que • iv sur l'analyse de données, un paramétrage de la convection oblique a été développé • et mis en application dans le GCMIL Nous avons demontré que ce paramétrage a comme effet le développement d'une circulation méridienne directe, laquelle représente un impact significatif sur la circulation générale simulée. Une série de simulations de cinq ans a démontré que ce paramétrage a pour effet de réduire, aux latitudes moyennes, le SCAPE ainsi que son résidu, rs' Ceci a pour effet de diminuer la force des courants-jets et du vent thermique. Par contre, la réduction du transport de la chaleur et de la quantité de mouvement zonale, par les tourbillons meridionau..'"< transitoires, constitue l'amélioration du climat simulé la plus significative. Ainsi, avec ce nouveau schéma, le transport par les tourbillons est mieu..x modélisé tel que demontré par une comparaison avec des observations. • v • Statement of originality The original aspects of this thesis are as follows: 1) An investigation of the instability in a 2D baroclinic flow with an unstable stratification using a two-layer parcel model. 2) An analysis of the global distribution of CAPE and SCAPE using ECMWF re-analysis and the finding that the conditions for upright convection and slantwise convection generally co-exist in the atmosphere. 3) Oevelopment of a 20 parameterization scheme for slantwise buoyant instability (SBI). 4) Oevelopment of a simplified ID version of the slantwise convective parameter­ ization scheme and its implementation in version Il of the third generation CCCma GCM. 5) Sensitivity tests and 5 year simulations using the scheme leading to the findings that the scheme a) reduces SCAPE and SCAPE residual over the mid-latitudes. b) significantly weakens the poleward transient eddy transports of temperature and zonal momentum over the mid- and higher latitudes. • vi c) decreases the zonally averaged temperature gradient and high level jets over • the midlatitudes. d) generates a direct secondary meridional circulation. • vii • Acknowledgments First of al1, 1 sincerely thank my supervisor Professor M. K. Yau. His advice and suggestions help me to choose the research project. Over the years in my doctor­ ate program, he has been giving me countless and continuous encouragement and instruction. Without his support and guidance, 1 would never have completed my thesis work. 1 would also like to thank Dr. N. A. ~IcFarlane ofthe Canadian Climate Centre for modelling and analysis (CCCma) for kindly introducing to me the CCCma GCM and allowing me to use their computing facilities. Discussion with him greatly encouraged me to continue my reseach. 1 am indebted to ail the people at CCCma who gave me help and advice during and after my visit to implement my scheme into the CCCma GCM. Special appreciation goes to Richard Harvey, Fouad ~Iajaess, Dr. Damin Liu, Dr. Jiangnan Li, and Dr. Jian Sheng. 1 will oever forget the lectures and instructions 1 received from professors in the Department of Atmospheric and Oceanic Sciences. 1 would aIso like to thank my office mates Dr. Ning Bao, Dr. Nagarajan Batrinath, Stephen Dery, Dr. Yubao Liu, Dr. Zhaomin Wang, Dr. F. Kong, and Yongsheng Chen. 1 was inspired from the • viii many useful discussions with them and received valuable help in model programming, • figure plotting, and thesis typesetting. 1 also thank Dr. Paul Vaillancourt for the translation of the thesis abtract ioto French. The finandaI support from grants awarded to Professor lVI. K. Yau are gratefully acknowledged. Finally, 1 would like ta thank my family, my wife Ye.xu Li for her support, my aider son Fan for his understanding, and my little son ~lichel for the joy he gives me, although he knows nothing about what 1 have been doing. • ix • Contents List of Tables xiii List of Figures xiv 1 Introduction 1 1.1 Motivation. 1 1.2 Review of the theory for symmetric instability 5 1.2.1 Critenon for conditional symmetric instability . .. 5 1.2.2 Charactenstic scales 9 1.2.3 Other characteristics Il 2 Slantwise Buoyant Instability 13 2.1 A 2-dimensional two-Iayer Lagrangian model .. 13 2.2 Governing equations 14 2.3 Analytical solutions . 20 2.3.1 Solution for the lower layer (z < hd ... 20 2.3.2 Solution for the upper layer (z > hd 23 • x 2.4 Numerical results ........................... .. 24 • 3 Climatology of CAPE and SCAPE from ECMWF Re-Analysis 34 3.1 Calculation of CAPE and SCAPE ....... 35 3.2 The data and the thermodynamic process ..... 39 3.3 The global distribution of CAPE and SCAPE 40 3.4 Distributions of CAPE/SCAPE and precipitation 43 4 A Generalized Moist Convective Adjustment Scheme 53 4.1 Formulation .
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