chapter 3 summery

Question 1

In barotropic model atmosphere some conditions exist throughout the motion

Answer 1

• Coincidence of pressure and temperature surfaces
• Absence of
  
  • Vertical wind shear
  • Vertical motions
  • Horizontal velocity divergence
• Conservation of the vertical component of absolute vorticity

Question 2

Classes of barotropic models:

Answer 2

• Non divergent barotropic model
  
  • Simple non divergent barotropic model is based on the barotropic vorticity eqn
• Divergent barotropic model (shallow-water equations)

Question 3

The barotropic (non-divergent) model assumptions:

Answer 3

• Absolute vorticity is conserved

Question 4

The barotropic (non-divergent) model applies to

Answer 4

• Barotropic atmosphere or
• Level of non divergence

Question 5

The barotropic (non-divergent) models are useful for:

Answer 5

• Tropical wind predictions
  
  • Especially at levels where div. is small

Question 6

Barotropic vorticity equation describes:

Answer 6

• The evolution of a
  
  • Homogeneous (constant density)
  • Non divergent
  • Incompressible flow
• In which absolute vorticity is conserved following the motion

Question 7

Barotropic model is obtained from:

Answer 7

• The barotropic vorticity equation

Question 8

Finite difference analogs for the Jacobian do not conserve:

Answer 8

• Do not conserve:
  
  • Kinetic energy
  • Mean square vorticity over the model domain

Not suitable for use in model

Question 9

Arakawa:

Answer 9

• Show that the linear combination of FD analogs for the Jacobian conserve both
  
  • Kinetic energy
  • Mean square vorticity over the model domain

Question 10

What time derivative can be used in the barotropic model? How?

Answer 10

• The leap-frog time differencing scheme
• Two steps:
  
  • Forward D then
  • Central D

Question 11

Assumptions and simplifications for the shallow water model:

Answer 11

• we have a layer of fluid with constant density
• (under hydrostatic assumptions) there is no vertical variation of the PGF if density is constant

Question 12

What does the assumptions and simplifications for the shallow water model mean?

Answer 12

If initially the horizontal velocities are independent of height they will remain so during all times

Question 13

What term doesn’t appear in the shallow water equations?

Answer 13

The vertical advection terms

Question 14

Shallow water equations contain

Answer 14

• Slow moving Rossby waves
• High-frequency gravity waves

Question 15

Requirements of handling high frequency gravity waves:

Answer 15

• Shorter time steps
  
  • As demanded by CFL criterion
    
    • Computationally expensive

Question 16

How to overcome the demanding requirements of handling high frequency gravity waves?

Answer 16

• Apply implicit time integration scheme
  
  • Permits relatively longer time steps

Note that:

• Nonlinear part of the equation is dealt with explicitly
• Linear part of the equation is dealt with implicitly (known as: semi-implicit time-integration scheme)

Question 17

Helmholtz equation:

Answer 17

• One equation and one unknown.
• Can be solved using relaxation techniques