pyshqg.core.dissipation module

Submodule dedicated to dissipation processes.

class pyshqg.core.dissipation.QGEkmanDissipation(backend, spectral_transformations, orography, tau, weight_land_sea_mask, weight_orography, orography_scale)

Bases: object

Class for the Ekman dissipation processes.

The Ekman dissipation term is defined as…

backend

The backend.

Type:

pyshqg.backend.Backend object

mu

Friction coefficient $mu$ defined on the grid.

Type:

backend array, shape (Nlat, Nlon)

dmu_dphi

Gradient of $mu$ with respect to longitude ($phi$).

Type:

backend array, shape (Nlat, Nlon)

dmu_dtheta

Gradient of $mu$ with respect to latitude ($theta$).

Type:

backend array, shape (Nlat, Nlon)

__init__(backend, spectral_transformations, orography, tau, weight_land_sea_mask, weight_orography, orography_scale)

Constructor for the Ekman dissipation.

First, the orography object is used to pre-compute the friction coefficient $mu$ in the grid. Then, the spectral_transformations object is used to pre-compute the spatial gradients of $mu$ in the grid.

Parameters:

• backend (pyshqg.backend.Backend object) – The backend.

• spectral_transformations (pyshqg.core.spectral_transformations.SpectralTransformations) – The object encapsulating the spectral transformations.

• orography (pyshqg.preprocessing.orography.Orography) – The object encapsulating the orography in the grid.

• tau (float) – The parameter $tau$ of the friction coefficient $mu$.

• weight_land_sea_mask (float) – The weight of the land/sea mask contribution in $mu$.

• weight_orography (float) – The weight of the orography contribution in $mu$.

• orography_scale (float) – The vertical length scale for the orography in $mu$.

compute_ekman_dissipation(zeta, dpsi_dtheta, dpsi_dphi)

Computes the Ekman dissipation term in the QG model tendencies.

The Ekman dissipation term is computed in the grid, at the lowest level (indexed by -1). The output is padded with zeros to get a contribution for all levels.

Parameters:

• zeta (backend array, shape (..., Nlat, Nlon)) – The drag $zeta$ in grid space.

• dpsi_dtheta (backend array, shape (..., Nlevel, Nlat, Nlon)) – The gradient of the stream function $psi$ with respect to latitude ($theta$) in grid space.

• dpsi_dphi (backend array, shape (..., Nlevel, Nlat, Nlon)) – The gradient of the stream function $psi$ with respect to longitude ($phi$) in grid space.

Returns:

ekman – The Ekman dissipation term in the grid.

Return type:

backend array, shape (…, Nlevel, Nlat, Nlon)

class pyshqg.core.dissipation.QGSelectiveDissipation(backend, spectral_transformations, tau)

Bases: object

Class for the selective dissipation processes.

The selective dissipation term is defined as…

backend

The backend.

Type:

pyshqg.backend.Backend object

spectrum

Eignen spectrum in spectral space, with respect to l (the first spectral index), of the selective dissipation.

Type:

backend array, shape (T+1,)

__init__(backend, spectral_transformations, tau)

Constructor for the selective dissipation.

The Eigen spectrum of the Laplacian operator, defined in the spectral_transformations object is used to pre-compute the Eigen spectrum of the selective dissipation.

Parameters:

• backend (pyshqg.backend.Backend object) – The backend.

• spectral_transformations (pyshqg.core.spectral_transformations.SpectralTransformations) – The object encapsulating the spectral transformations.

• tau (float) – The parameter $tau$ of the selective dissipation.

compute_selective_dissipation(spec_total_q)

Computes the selective dissipation term in the QG model tendencies.

The selective dissipation term is computed in spectral space, using the Eigen spectrum.

Parameters:

spec_total_q (backend array, shape (..., Nlevel, 2, T+1, T+1)) – The total vorticity in spectral space $hat{q}^{mathsf{t}}$.

Returns:

selective – The selective dissipation term in spectral space.

Return type:

backend array, shape (…, Nlevel, 2, T+1, T+1)

class pyshqg.core.dissipation.QGThermalDissipation(backend, vertical_parametrisation, tau)

Bases: object

Class for the thermal dissipation processes.

The thermal dissipation term is defined as…

backend

The backend.

Type:

pyshqg.backend.Backend object

thermal_coupling

Vertical coupling matrix for the thermal dissipation.

Type:

backend array, shape (Nlevel, Nlevel)

__init__(backend, vertical_parametrisation, tau)

Constructor for the thermal dissipation.

The vertical coupling matrix is pre-computed using the vertical_parametrisation object.

Parameters:

• backend (pyshqg.backend.Backend object) – The backend.

• vertical_parametrisation (pyshqg.preprocessing.vertical_parametrisation.VerticalParametrisation) – The object encapsulating the vertical parametrisation.

• tau (float) – The parameter $tau$ of the thermal dissipation.

compute_thermal_dissipation(spec_psi)

Computes the thermal dissipation term in the QG model tendencies.

The thermal dissipation term is computed in spectral space, using a coupling matrix between vertical levels.

Parameters:

spec_psi (backend array, shape (..., Nlevel, 2, T+1, T+1)) – The stream function in spectral space $hat{psi}$.

Returns:

thermal – The thermal dissipation term in spectral space.

Return type:

backend array, shape (…, Nlevel, 2, T+1, T+1)

class pyshqg.core.dissipation.QGDissipation(ekman: pyshqg.core.dissipation.QGEkmanDissipation, selective: pyshqg.core.dissipation.QGSelectiveDissipation, thermal: pyshqg.core.dissipation.QGThermalDissipation)

Bases: object

Container class for all dissipation processes.

Parameters:

• ekman (pyshqg.core.dissipation.QGEkmanDissipation) – The Ekman dissipation object.

• selective (pyshqg.core.dissipation.QGSelectiveDissipation) – The selective dissipation object.

• thermal (pyshqg.core.dissipation.QGThermalDissipation) – The thermal dissipation object.

ekman: pyshqg.core.dissipation.QGEkmanDissipation

selective: pyshqg.core.dissipation.QGSelectiveDissipation

thermal: pyshqg.core.dissipation.QGThermalDissipation