Lecture 1 ATS 601. Thomas Birner, CSU. ATS 601 Lecture 1

Transcription

1 Lecture 1 ATS 601 Thomas Birner, CSU

2 About your Instructor: Thomas Birner Assistant Professor, joined CSU 10/2008 M.Sc. Physics (Condensed Matter Theory), U of Leipzig, Germany Ph.D. Atmospheric Science (Tropopause Dynamics), U of Munich, Germany Postdoc s at U of Reading, U.K. and U of Toronto, Canada Atmospheric and Climate Dynamics, Dynamics of the Coupled Troposphere / Stratosphere System thomas at atmos.colostate.edu, room 407, phone

3 What is this course about? Fundamentals of geophysical fluid dynamics (GFD) with (slight) emphasis on atmospheric component GFD is concerned with a physical description and an understanding of the underlying mechanisms & causes of atmospheric and oceanic motion Scales of motion: centimeters (molecular diffusion) to 10,000 kilometers (planetary waves); seconds (sound waves) to years (global circulations) Key aspects: rotation & stratification Need to simplify / filter / idealize, guided by empirical knowledge of the system we re studying Understanding these simplified systems turns out to be complicated enough... We re going to concentrate on dry dynamics.

4 Scales of Motion

5 Scales of Motion Oceanic Baroclinic Eddies: ~100 km, several weeks Atmospheric Baroclinic Eddies: ~1,000 km, ~1 week Convective Plumes: ~1 10 km, min hours Convective Organization: ~ km, several hours

6 Differential Heating Top of the Atmosphere Energy Balance Eddies, ~Weather

7 Hadley Circulation G. Hadley (1735): Concerning the Cause of the General Trade Winds W Circulation envisaged by Hadley: giant meridional cell stretching from equator to pole W E W Hadley hypothesized westerly (W) winds at upper levels and in the polar regions at the surface, and easterly (E) winds near the subtropical surface (trade winds) How does Hadley come up with his wind patterns? Do you think they are reasonable? Physically possible?

8 Differentially Heated Annulus Experiment Fultz et al., 1964

9 Differentially Heated Annulus Experiment Fig. 6.1 from Marshall & Plumb

10 Waves can cause a circulation January mechanically (wave) driven, thermally indirect circulations Vallis, Fig

11 Simplification is Key! There s no sense in being precise when you don t even know what you re talking about. John von Neumann Everything should be made as simple as possible, but not simpler. Albert Einstein read The gap between simulation and understanding in climate modeling by I. Held (BAMS, Nov. 2005) (under lecture material)... we need a model hierarchy on which to base our understanding, describing how the dynamics change as key sources of complexity are added or subtracted. R. Reed (1990): The general success of the forecasts in data-rich areas bears witness to the fact that the cyclogenetical process is indeed now well understood at least by the computer!

12 Richardson s Forecasts Richardson's Forecasts ( ) finite difference solution of simplified primitive equations 6 hour forecast by hand took him 6 weeks(!) Lewis F. Richardson Results were a failure: predicted pressure change ~ 150 hpa, actual pressure change ~ 3 hpa Failure represented a significant deterrent to following this numerical approach Why did Richardson's forecasts fail so badly?

13 Richardson s Forecasts Weather prediction by numerical process, Richardson forecast factory: 64,000 (people) computers working on a globe discretized to 200 km cells message passing domain decomposition synchronization

14 Charney and von Neumann s Forecasts John von Neumann Emergence of computer ENIAC at Institute for Advanced Studies Instead of primitive equations, much simpler barotropic vorticity equation was used Jule Charney First forecast 1950: resolution 750km, time-step 1 hour Required 25,000 punch cards 24 h forecast took 24 h Good and bad features but overall was heralded as great success

15 The Challange of Understanding Dynamics Science can be beautiful, amazing, the best way of trying to understand the world. But it is difficult... if an idea fits with common sense, then it is almost certainly scientifically false... The world is just not built on a common-sense basis. Lewis Wolpart (copied from Persson, 2010: Mathematics versus common sense: the problem of how to communicate dynamic meteorology ). A. Persson (2010):... the problem of understanding and communicating dynamic meteorology does not mainly lie in its complicated non-linear mathematics but in its highly counter-intuitive nature. The motions of the atmosphere and oceans are just not built on a common sense basis.

16 Some Notation Vectors: a = (a x, a y, a z ) Three-dimensional velocity: v = (u, v, w), two-dimensional (horizontal) velocity: u = (u, v) partial derivative: t t, x x, etc. Nabla/gradient operator: = ( x, y, z ) d dt refers to the time-derivative of a quantity which is a function of time only D Dt = t + v refers to the material/lagrangian derivative (to be explained later)

17 Rossby Waves

18 Gravity (Buoyancy) Waves

19 Mountain/Lee Waves

20 Math Concepts: - coordinate transformations - vector calculus - solving partial differential equations (wave problems) - scale analysis Physics Concepts: - fundamental conservation laws (mass, energy, angular momentum) - apparent forces (centrifugal, Coriolis) - fundamental balances (hydrostatic, geostrophic) - effects of rotation and stratification - step-wise simplification model hierarchies - scale analysis