ch3: Barotropic model

Question 1

In Barotropic model atmosphere, some of the following conditions exist throughout the motion:

Answer 1

• coincidence of pressure and temperature surfaces;
• absence of vertical wind shear;
• absence of vertical motions;
• absence of horizontal velocity divergence; and
• conservation of the vertical component of absolute vorticity

Question 2

Barotropic models are usually divided into two classes:

Answer 2

• the nondivergent barotropic model and
• the divergent barotropic model (also called the shallow‐water equations).

Question 3

The simple nondivergent barotropic model is based on

Answer 3

the barotropic vorticity equation.

Question 4

The Barotropic (Nondivergent ) Model

Answer 4

• This model is based on an assumption that the absolute vorticity is conserved, which applies to a barotropic atmosphere or at the level of non divergence.
• The barotropic models have shown their usefulness for tropical wind prediction especially at those levels where the divergence is small.

Question 5

The barotropic vorticity equation describes

Answer 5

the evolution of a homogeneous (constant density), non‐divergent, incompressible flow, in which the absolute vorticity is conserved following the motion:

Question 6

The barotropic model is obtained from

Answer 6

the barotropic vorticity equation

Question 7

the barotropic vorticity equation

Answer 7

Question 8

the jacobian can be defined in three equivalent ways

Answer 8

Question 9

It turns out that none of the above finite difference analogs for the Jacobian conserves

Answer 9

both kinetic energy and mean square vorticity over the model domain.

They are, therefore, not suitable for use in the model

Question 10

t turns out that none of the above finite difference analogs for the Jacobian conserves both kinetic energy and mean square vorticity over the model domain.

 They are, therefore, not suitable for use in the model
However, Arakawa has shown that

Answer 10

the linear combination as shown below conserves them.

Question 11

Let us write expressions for J1, J2 and J3 using a 9‐point stencil as shown in Fig.

Answer 11

Question 12

Time Derivatives

Answer 12

• The Leap‐frog time differencing scheme can be used in this model.
• that is, a forward difference for the first time step and then a central difference for the next time steps:

Question 13

Implementation of the Model

Answer 13

Question 14

Assumptions and Simplification