Table Of Content

1 An Introduction To The General Circulation of the Atmosphere David A. Randall Department of Atmospheric Science Colorado State University Spring 2005 i About the Cover This image (actually pieced together from multiple images) was acquired on December 8, 1992, by NASA’s Galileo spacecraft, as it swung by Earth on its way out to Jupiter. It shows a wonderful but physically impossible view of the Southern Hemisphere. A substantial fraction of the image should be in darkness, even though the image depicts a time near the summer solstice of the Southern Hemisphere. This view was created by patching together a mosaic of several images taken by Galileo over a 24-hour period, and remapping them as they would be seen from above the pole. South America, Africa, and Australia are respectively seen at the middle left, upper right, and lower right. Of particular interest are the beautiful cloud patterns associated with extratropical cyclones in the storm track ringing Antarctica. This picture is reminiscent of photos of “dishpan” experiments, in which aspects of the general circulation are simulated in a rotating, differentially heated laboratory tank. ii Announcements Subject: The general circulation of the atmosphere Text: Class notes Course grade: Based entirely on homework, including some projects Schedule: Classes will be missed occasionally. Make-ups will be scheduled. A calendar showing class meetings will be distributed early in the semester, and past experience suggests that not many changes will be made. An Introduction to the General Circulation of the Atmosphere iii Handy Numbers Radius of the Earth 6.37 x 106 m Angular velocity of the Earth’s rotation 7.29 x 10-5 s-1 Latent heat of condensation at 0 °C 2.52 x 106 J kg-1 Globally averaged surface air temperature 288 K Globally averaged precipitable water 25 mm (= 25 kg m-2) Annual mean incident solar radiation 340 W m-2 Global albedo 0.30 Outgoing longwave radiation 240 W m-2 Stefan-Boltzman constant 5.67 x 10-8 W m-2 K-4 Globally averaged precipitation rate 3 mm day-1 c for dry air 1000 J kg-1 K-1 p R for dry air 287 J kg-1 K-1 Globally averaged surface pressure 984 mb Acceleration of Earth’s gravity 9.81 m s-2 Density of air near sea level 1.2 kg m-3 Molecular viscosity of air 1.5 x 10-5 m2 s-1 iv General References (on reserve in ATS Library) Physics of Climate, by J. P. Peixoto and A. H. Oort, American Institute of Physics, 1992. Atmosphere-Ocean Dynamics, by A. E. Gill, International Geophysics Series, Vol. 30, Academic Press,1982. Dynamics in Atmospheric Physics, by R. S. Lindzen, Cambridge University Press, 1990. The Nature and Theory of the General Circulation of the Atmosphere, by E. N. Lorenz, World Meteorological Organization, #218, 1967. Global Atmospheric Circulations, Observations and Theories, by R. Grotjahn, Oxford University Press, 1993. Large-Scale Dynamical Processes in the Atmosphere, edited by B. J. Hoskins and R. P. Pearce, Academic Press, 1983. An Introduction to Dynamic Meteorology, by J. R. Holton, Academic Press, third edition, 1992. Dynamic Meteorology, by A. Eliassen and E. Kleinschmidt Jr., in Handbuch der Physik, Band XLVIII Geophysik II, pp. 1-154, Springer Verlag, 1957. Global Physical Climatology, by D. L. Hartmann, Academic Press, 1994. Introduction to Circulating Atmospheres, by I. N. James, Cambridge University Press, 1994. An Introduction to the General Circulation of the Atmosphere v Preface This is an introductory course on the general circulation of the atmosphere, a subject that is closely tied to atmospheric dynamics. A course on dynamics tends to focus on basic physical concepts and methods for their analysis, however, while a course on the general circulation must focus on what the atmosphere actually does, and why. Graduate-level studies in atmospheric dynamics are essential as preparation for this course, and most students will learn some additional dynamics in the process of taking this course. It is difficult to draw a line between the general circulation and climate. The two subjects appear to be growing closer together, as the roles of heating and dissipation in the general circulation emerge as key issues. Clearly, such topics as monsoons, the hydrologic cycle, and the planetary energy budget can be included under either “climate” or “general circulation,” although perhaps with different slants. Climate is the bigger subject. This course skirts the edges of physical climatology. There is way too much material to cover in one semester, so I have had to make choices. This particular course emphasizes the role of moisture in the workings of the general circulation, and makes frequent use of models as tools to aid understanding. I have also discussed energetics in some detail, and have included a chapter on the general circulation as turbulence, including an extended section on the chaotic nature of the circulation. This is a graduate-level course, and it is an elective. The level of difficulty is set so as to maximize the potential benefit to the strongest students in the class; if they work very hard, they should just barely be able to master the material. It will be worth the effort. This is a beautiful subject. A lot of work is involved in putting together these course notes. For the past several years, Michelle Beckman has very professionally made many additions and corrections to the notes. She also developed and applied the formatting that you see, and combined the many separate documents into a unified “book.” The notes would be much less useful without her contributions. Mark Branson, Don Dazlich, Kelley Wittmeyer, and Mike Kelly have ably assisted in the production of some of the figures. Mike Kelly, Cara-Lyn Lappen Katherine Harris, Stefan Tulich, Anning Cheng, Mike Toy, Kyle Wiens, and vi Cristiana Stan, and Jason Furtado performed beautifully as Teaching Assistants for the course, and both the students and I learned as a result of their efforts. Finally, I am grateful to the students who have taken this course over the years; their questions and suggestions have led to major improvements. David Randall January 19, 2005 10:49 am An Introduction to the General Circulation of the Atmosphere vii About the Cover .....................................................................................................i Announcements ....................................................................................................ii Handy Numbers ...................................................................................................iii General References ...............................................................................................iv Preface ...................................................................................................................v CHAPTER 1 Introduction 1 The nature of the subject .............................................................................................1 A brief overview .........................................................................................................3 Fasten your seatbelts ...................................................................................................8 CHAPTER 2 What makes it go? 9 The Earth’s radiation budget: An “upper boundary condition” on the general circulation ..............................................................................................9 Surface boundary conditions 1....................................................................................6 Energy and moisture budgets of the surface and atmosphere ...................................21 Summary ...................................................................................................................27 Problems ..............................................................................................................28 CHAPTER 3 An overview of the observations 29 Introduction ...............................................................................................................29 The global distribution of atmospheric mass ............................................................32 Zonal wind ................................................................................................................42 Meridional wind ........................................................................................................46 Geopotential height ...................................................................................................50 Vertical velocity and the mean meridional circulation. ............................................54 Angular momentum ..................................................................................................63 Temperature .............................................................................................................69 A view in potential temperature coordinates ............................................................74 The global distribution of water vapor .....................................................................80 Precipitation ..............................................................................................................85 Surface fluxes due to turbulence............................................................................... 89 A quick and superficial introduction to the effects of large-scale eddies on the zonally averaged flow ..............................................................................96 A preliminary interpretation of the observations ....................................................102 Lots of questions .....................................................................................................108 Problems ............................................................................................................109 An Introduction to the General Circulation of the Atmosphere viii CHAPTER 4 Conservation of momentum and energy 111 Introduction .............................................................................................................111 Conservation of momentum on a rotating sphere ...................................................111 Conservation of kinetic energy and potential energy .............................................116 Conservation of thermodynamic energy .................................................................120 Conservation of total energy ...................................................................................122 Static energies .........................................................................................................126 Entropy ....................................................................................................................127 Approximations .......................................................................................................131 The mechanical energy equation in other vertical coordinate systems ...................132 The effects of turbulence ........................................................................................133 Summary .................................................................................................................135 Problems ............................................................................................................136 CHAPTER 5 The mean meridional circulation 145 The observed meridional transports of energy and moisture.................................. 145 A simple theory of the Hadley circulation .............................................................151 Extension to other planetary atmospheres ..............................................................160 Particle trajectories on the sphere: A partial explanation of “bandedness” ..........163 Summary .................................................................................................................169 Problems .................................................................................................................169 CHAPTER 6 An overview of the effects of radiation and convection 171 Convective energy transports ..................................................................................171 Radiative-convective equilibrium ...........................................................................173 The observed vertical structure of the atmosphere, and the mechanisms of vertical energy transport ...............................................................................180 More on moist convection ......................................................................................188 Summary .................................................................................................................203 Problems................................................................................................................. 203 CHAPTER 7 The Energy Cycle 207 Available potential energy ......................................................................................207 The gross static stability ..........................................................................................213 An Introduction to the General Circulation of the Atmosphere