The Disclaimers

• The subject to be investigated might be called physical science fiction, where many of the details of physical processes are left out of the description of a basic structure into which the neglected details can be introduced, a few at a time. The challenge is to keep enough of the physics, so that restoring the details does not lead to qualitative changes of results. (Precise definition?: no _ perhaps only a qualitative description of qualitative can be offered.)
  
  Hence, there are many important details that will not be included here.
  
• There will be greek letters and other mathematical symbols here, and for reasons I disapprove of, some purveyors of browsers have stopped allowing the use of symbol fonts (including math and music) in html documents. If that seems inconvenient, don't complain to me.

The Argument
Realistic atmosphere models are necessarily hugh, with a long list of physical processes whose relative importance is different in different parts of the globe (notably, over land and over water). Add to that the necessity of considering a great many parts of the globe (thousands to millions), at and below the surface of the earth and within quite a few layers of the atmosphere (one to a hundred ,say). That much makes it unlikely that one person can keep track of all the details, and it becomes virtually impossible to run a realistic model on a PC. The hope, perhaps never to be realized by me, is to come up with a rough (very rough) numerical model of atmospheric motions that is small enough to run on a PC, so everyone with an interest in climate or weather can have a personal model to modify in any number of different ways. That way, a quantitative sense of the importance of various effects, such as water vapor and latent heat (very important) and greenhouse gases (also very important) can perhaps be investigated by and communicated to a larger audience.

The Plan

• Produce a Perfect Babylonian Model of atmospheric dynamics __ one that has so few of the details that there is hope that a PC can run simulations with computational gridpoints that have separations of the order of 100 km (thanks to the French, a spherical angle of 1° spans very nearly 111 km. - a number worth remembering.),



• provide algorithms for the required numerical analysis,



• provide code (in C) for implementation of the algorithms,



• and maybe even get it all to run (someday).

The Agenda

• A Perfect Babylonian Atmosphere __ a relatively simple one-layer model, but not a nonlinear shallow water approximation __ that would be throwing away the baby (puns intended).


• The thermodynamics of a perfect gas



• The fundamental equations _ nonrotating



• Vertical structure



• The perfect atmosphere



• The perfect Babylonian atmosphere



• The perfect Babylonian atmosphere on a rotating sphere



• Numerical algorithms


• An almost perfect Babylonian grid



• Interpolation on edges



• Algorithms for transport equations: 1-D flow



• Selective grid refinement: 1-D



• Interpolation in patches



• Algorithms for transport equations: 2-D flow



• Selective grid refinement: 2-D



• Perelandra (a digression)
  
  
• The perfect, rotating, Babylonian algorithm



• Implementations in C



• Interpolation on edges
  
  
• Interpolation in patches
  
  
• Structures
  
  
• Predictors (leap-frog)
  
  
• Correctors (semi-Lagrangian)
  
  
• Contour lines
  
  
• The model

The Future (maybe)

• A better lid
  
  
• Water vapor, latent heat and clouds, greenhouse gasses, etc.
  
  
• More layers
  
  
• Oceans
  
  
• Better graphics