Filters

This module contains the functions associated with filters needed for numerical stability.

SWAMPE.filters.diffusion(Ximn, sigma)

Applies the diffusion filter described in Gelb and Gleeson (eq. 12).

Parameters:

• Ximn (list) – the spectral coefficient data to be filtered

• sigma (float) – the hyperviscosity coefficient

Return newXimn:

filtered spectral coefficient

Return type:

array of float

SWAMPE.filters.modal_splitting(Xidataslice, alpha)

Applies the modal splitting filter from Hack and Jacob (1992).

Parameters:

• Xidata (list) – data array to be filtered

• alpha (float) – filter coefficient

Return newxi:

filtered data slice

Return type:

array of float

SWAMPE.filters.sigma(M, N, K4, a, dt)

Computes the coefficient for the fourth degree diffusion filter described in Gelb and Gleeson (eq. 12) for vorticity and divergence.

Parameters

param M:

spectral dimension

type M:

int

param N:

highest degree of associated Legendre polynomials

type N:

int

param K4:

hyperviscosity coefficient

type K4:

float

param a:

planetary radius, m

type a:

float

param dt:

time step,s

type dt:

float

Returns

return sigma:

coefficient for the diffusion filter for geopotential

rtype:

array of float

SWAMPE.filters.sigma6(M, N, K4, a, dt)

Computes the coefficient for the sixth degree diffusion filter for vorticity and divergence.

Parameters:

• M (int) – spectral dimension

• N (int) – highest degree of associated Legendre polynomials

• K4 (float64) – hyperviscosity coefficient

• a (float64) – planetary radius, m

• dt (float64) – time step,s

Return sigma:

coefficient for the diffusion filter for geopotential

Return type:

array of float64

SWAMPE.filters.sigma6Phi(M, N, K4, a, dt)

Computes the coefficient for the fourth degree diffusion Filter described in Gelb and Gleeson (eq. 12) for geopotential.

Parameters:

• M (int) – spectral dimension

• N (int) – highest degree of associated Legendre polynomials

• K4 (float) – hyperviscosity coefficient

• a (float) – planetary radius, m

• dt (float) – time step,s

Return sigma:

coefficient for the diffusion filter for geopotential

Return type:

array of float

SWAMPE.filters.sigmaPhi(M, N, K4, a, dt)

Computes the coefficient for the fourth degree diffusion Filter described in Gelb and Gleeson (eq. 12) for geopotential.

Parameters:

• M (int) – spectral dimension

• N (int) – highest degree of associated Legendre polynomials

• K4 (float) – hyperviscosity coefficient

• a (float) – planetary radius, m

• dt (float) – time step,s

Return sigma:

coefficient for the diffusion filter for geopotential

Return type:

array of float