numerical quiz 4

What is an integral invariant

F(u) = integral f(u) dv function of atmospheric state u(r,t) dF/dt =0

What are the atmospheric state variables

U(r,t)

How to replace a volume integral

A summation over all discrete modes (grid points) used for the representation of the state variables in the model

How to maintain the long term stability of model solutions.

The preservation of key conservation laws

What are global conservation laws the result of

Local symmetries of the equations.

What’s the key to preserving the conservation laws of the models

Preserving the local symmetries

what is the lagrangian invariant

When a state variable S satisfies equation dS/dt=0

When a state variable is a lagrangian invariant, what is its smooth function

Also lagrangian

What are the two lagrangian invariants in the full primitive equations

potential temp and (ertel) potential vorticity

What creates potential vorticity

Diabetic heating

When hydrostatic balance is in effect, what is hydrostatic balance

Not lagrangian invariant, so need to use isentropic potential vorticity

What is Potential vort simplified to under QG

Geostrophic vorticity, with integral invariant enstrophy

What’s an important invariant that’s non lagrangian

Total energy, with integrand terms of kinetic energy, internal energy, and potential energy

Is conserving local symmetries important

No, less important. Conservation of potential vorticity symmetries are more important

Name two other integral invariants in the energy group

Absolute momentum and angular momentum

What is flux

Flow of S through surface A

What is the local form of conservation of mass

The continuity equation

The flux on two sides of the same wall must have the same magnitude and opposite sign:

Something bruh

NOAA can currently do how many penta flops

10^15

What do numerical schemes do

Discretize the spatial and temporal partial derivatives

When to use spectral transform

Discretize two horizontal directions. Computed on spherical harmonics. Nonlinear terms and physical parameterizations computed on grid

What uses spectral

Euro and GFS

Finite difference schemes

Spatial derivatives approximated by finite differences. Used for horizontal and vertical

What uses finite differences schemes

Idk met offices and WRF

What map preserves angles

Conformal

The _____ is the ratio of the distance between a pair of nearby locations

Map factor

What operational center uses a cube shaped grid in their operational global model

NCEP

Sigma is the ratio of pressure and

Surface pressure

What is sigma at the bottom of the atmosphere

1

What’s the projection point of the northern stereo graphic map projection

South Pole

Replace wind with what

Pseudo wind

In spherical coordinated, positive i is

East

A barotropic model can catch extra tropical cyclogenisis

false

QG barotropic vorticity is extreme reduction of

Divergence equation