easyclimate.core.eddy

The calculation of transient eddy

Functions

calc_eady_growth_rate(→ xarray.Dataset)

Calculate the maximum Eady growth rate.

calc_apparent_heat_source(→ xarray.DataArray)

Calculate the apparent heat source.

calc_total_diabatic_heating(→ xarray.DataArray)

Calculate the total diabatic heating.

calc_apparent_moisture_sink(→ xarray.DataArray)

Calculate the apparent moisture sink.

calc_Plumb_wave_activity_horizontal_flux(→ xarray.Dataset)

Calculate Plumb wave activity horizontal flux.

calc_TN_wave_activity_horizontal_flux(→ xarray.Dataset)

Calculate TN wave activity horizontal flux.

calc_EP_horizontal_flux(→ xarray.Dataset)

Calculate horizontal Eliassen–Palm Flux.

calc_monthly_rossby_wave_source(→ xarray.DataArray)

Calculate the Rossby wave source following Sardeshmukh and Hoskins (1988).

Module Contents

easyclimate.core.eddy.calc_eady_growth_rate(u_daily_data: xarray.DataArray, z_daily_data: xarray.DataArray, temper_daily_data: xarray.DataArray, vertical_dim: str, vertical_dim_units: Literal['hPa', 'Pa', 'mbar'], lat_dim: str = 'lat') → xarray.Dataset

Calculate the maximum Eady growth rate.

\[\sigma = 0.3098 \frac{f}{N} \frac{\mathrm{d} U}{\mathrm{d} z}\]

Caution

Eady growth rate (EGR) is a non-linear quantity. Hence, calc_eady_growth_rate should NOT be directly applied to monthly means variables. If a monthly climatology of EGR is desired, the EGR values at the high frequency temporal time steps should be calculated; then, use calculate monthly mean.

Parameters

u_daily_data: xarray.DataArray.

The zonal wind daily data.

z_daily_data: xarray.DataArray.

Daily atmospheric geopotential height.

Attention

The unit of z_daily_data should be meters, NOT \(\mathrm{m^2 \cdot s^2}\) which is the unit used in the representation of potential energy.

temper_data: xarray.DataArray.

Daily air temperature.

vertical_dim: str.

Vertical coordinate dimension name.

vertical_dim_units: str.

The unit corresponding to the vertical p-coordinate value. Optional values are hPa, Pa, mbar.

lat_dim: str, default: lat.

Latitude coordinate dimension name. By default extracting is applied over the lat dimension.

Returns

The maximum Eady growth rate (xarray.Dataset).

  • eady_growth_rate: The maximum Eady growth rate.

  • dudz: \(\frac{\mathrm{d} U}{\mathrm{d} z}\)

  • brunt_vaisala_frequency: Brunt-väisälä frequency.

See also

easyclimate.core.eddy.calc_apparent_heat_source(u_data: xarray.DataArray, v_data: xarray.DataArray, omega_data: xarray.DataArray, temper_data: xarray.DataArray, vertical_dim: str, vertical_dim_units: Literal['hPa', 'Pa', 'mbar'], time_units: str, lon_dim='lon', lat_dim='lat', time_dim='time', c_p=1005.7) → xarray.DataArray

Calculate the apparent heat source.

\[Q_1 = C_p \frac{T}{\theta} \left( \frac{\partial \theta}{\partial t} + u \frac{\partial \theta}{\partial x} + v \frac{\partial \theta}{\partial y} + \omega \frac{\partial \theta}{\partial p} \right)\]

Parameters

u_data: xarray.DataArray.

The zonal wind data.

v_data: xarray.DataArray.

The meridional wind data.

omega_data: xarray.DataArray.

The vertical velocity data (\(\frac{\mathrm{d} p}{\mathrm{d} t}\)).

temper_data: xarray.DataArray.

Air temperature.

vertical_dim: str.

Vertical coordinate dimension name.

vertical_dim_units: str.

The unit corresponding to the vertical p-coordinate value. Optional values are hPa, Pa, mbar.

time_units: str.

The unit corresponding to the time dimension value. Optional values are seconds, months, years and so on.

lon_dim: str, default: lon.

Longitude coordinate dimension name. By default extracting is applied over the lon dimension.

lat_dim: str, default: lat.

Latitude coordinate dimension name. By default extracting is applied over the lat dimension.

time_dim: str.

The time coordinate dimension name.

c_p: float, default: 1005.7.

The specific heat at constant pressure of dry air.

Note

specific heat capacity - Glossary of Meteorology

Returns

The apparent heat source (xarray.DataArray).

See also

easyclimate.core.eddy.calc_total_diabatic_heating(u_data: xarray.DataArray, v_data: xarray.DataArray, omega_data: xarray.DataArray, temper_data: xarray.DataArray, vertical_dim: str, vertical_dim_units: Literal['hPa', 'Pa', 'mbar'], time_units: str, lat_dim='lat', lon_dim='lon', time_dim='time', c_p=1005.7) → xarray.DataArray

Calculate the total diabatic heating.

Calculated in exactly the same way as for the apparent heat source.

Parameters

u_data: xarray.DataArray.

The zonal wind data.

v_data: xarray.DataArray.

The meridional wind data.

omega_data: xarray.DataArray.

The vertical velocity data (\(\frac{\mathrm{d} p}{\mathrm{d} t}\)).

temper_data: xarray.DataArray.

Air temperature.

vertical_dim: str.

Vertical coordinate dimension name.

vertical_dim_units: str.

The unit corresponding to the vertical p-coordinate value. Optional values are hPa, Pa, mbar.

time_units: str.

The unit corresponding to the time dimension value. Optional values are seconds, months, years and so on.

lon_dim: str, default: lon.

Longitude coordinate dimension name. By default extracting is applied over the lon dimension.

lat_dim: str, default: lat.

Latitude coordinate dimension name. By default extracting is applied over the lat dimension.

time_dim: str, default: time.

The time coordinate dimension name.

c_p: float, default: 1005.7 (\(\mathrm{J \cdot kg^{-1} \cdot K^{-1}}\)).

The specific heat at constant pressure of dry air.

Note

specific heat capacity - Glossary of Meteorology

Returns

The total diabatic heating (xarray.DataArray).

See also

calc_apparent_heat_source

easyclimate.core.eddy.calc_apparent_moisture_sink(u_data: xarray.DataArray, v_data: xarray.DataArray, omega_data: xarray.DataArray, specific_humidity_data: xarray.DataArray, vertical_dim: str, vertical_dim_units: Literal['hPa', 'Pa', 'mbar'], time_units: str, specific_humidity_data_units: str, lon_dim='lon', lat_dim='lat', time_dim='time', latent_heat_of_condensation=2501000.0) → xarray.DataArray

Calculate the apparent moisture sink.

\[Q_2 = -L \left( \frac{\partial q}{\partial t} + u \frac{\partial q}{\partial x} + v \frac{\partial q}{\partial y} + \omega \frac{\partial q}{\partial p} \right)\]

Parameters

u_data: xarray.DataArray.

The zonal wind data.

v_data: xarray.DataArray.

The meridional wind data.

omega_data: xarray.DataArray.

The vertical velocity data (\(\frac{\mathrm{d} p}{\mathrm{d} t}\)).

specific_humidity_data: xarray.DataArray.

The absolute humidity data.

vertical_dim: str.

Vertical coordinate dimension name.

vertical_dim_units: str.

The unit corresponding to the vertical p-coordinate value. Optional values are hPa, Pa, mbar.

time_units: str.

The unit corresponding to the time dimension value. Optional values are seconds, months, years and so on.

specific_humidity_data_units: str.

The unit corresponding to specific_humidity value. Optional values are kg/kg, g/kg and so on.

lon_dim: str, default: lon.

Longitude coordinate dimension name. By default extracting is applied over the lon dimension.

lat_dim: str, default: lat.

Latitude coordinate dimension name. By default extracting is applied over the lat dimension.

time_dim: str, default: time.

The time coordinate dimension name.

latent_heat_of_condensation: float, default: 2.5008e6 (\(\mathrm{J \cdot kg^{-1}}\)).

Latent heat of condensation of water at 0°C.

Note

Returns

The apparent moisture sink (xarray.DataArray).

See also

easyclimate.core.eddy.calc_Plumb_wave_activity_horizontal_flux(z_prime_data: xarray.DataArray, vertical_dim: str, vertical_dim_units: Literal['hPa', 'Pa', 'mbar'], lon_dim='lon', lat_dim='lat', omega=7.292e-05, g=9.8, R=6370000) → xarray.Dataset

Calculate Plumb wave activity horizontal flux.

Parameters

z_prime_data: xarray.DataArray.

The anormaly of atmospheric geopotential height.

vertical_dim: str.

Vertical coordinate dimension name.

vertical_dim_units: str.

The unit corresponding to the vertical p-coordinate value. Optional values are hPa, Pa, mbar.

lon_dim: str, default: lon.

Longitude coordinate dimension name. By default extracting is applied over the lon dimension.

lat_dim: str, default: lat.

Latitude coordinate dimension name. By default extracting is applied over the lat dimension.

omega: float, default: 7.292e-5.

The angular speed of the earth.

g: float, default: 9.8.

The acceleration of gravity.

R: float, default: 6370000.

Radius of the Earth.

Returns

The Plumb wave activity horizontal flux (xarray.DataArray).

See also

easyclimate.core.eddy.calc_TN_wave_activity_horizontal_flux(z_prime_data: xarray.DataArray | None, u_climatology_data: xarray.DataArray, v_climatology_data: xarray.DataArray, vertical_dim: str, vertical_dim_units: Literal['hPa', 'Pa', 'mbar'], psi_prime_data: xarray.DataArray | None = None, lon_dim: str = 'lon', lat_dim: str = 'lat', time_dim: str = 'time', omega: float = 7.292e-05, g: float = 9.8, R: float = 6371200.0) → xarray.Dataset

Calculate TN wave activity horizontal flux.

\[\begin{split}\mathbf{W_h} = \frac{p\cos\varphi}{2\lvert \mathbf{U_c} \rvert}\begin{pmatrix} \frac{U_c}{R^2 \cos^2 \varphi} \left[ \left( \frac{\partial \psi'}{\partial \lambda} \right)^2 - \psi'\frac{\partial^2 \psi'}{\partial \lambda^2} \right] + \frac{V_c}{R^2 \cos \varphi} \left[ \frac{\partial \psi'}{\partial \lambda} \frac{\partial \psi'}{\partial \varphi} - \psi' \frac{\partial^2 \psi'}{\partial \lambda \partial \varphi} \right] \\ \frac{U_c}{R^2 \cos \varphi} \left[ \frac{\partial \psi'}{\partial \lambda} \frac{\partial \psi'}{\partial \varphi} - \psi' \frac{\partial^2 \psi'}{\partial \lambda \partial \varphi} \right] + \frac{V_c}{R^2} \left[ \left( \frac{\partial \psi'}{\partial \varphi} \right)^2 - \psi'\frac{\partial^2 \psi'}{\partial \varphi^2} \right] \\ \end{pmatrix}\end{split}\]

Parameters

z_prime_data: xarray.DataArray.

The anormaly of atmospheric geopotential height.

Attention

The unit of z_prime_data should be meters, NOT \(\mathrm{m^2 \cdot s^2}\) which is the unit used in the representation of potential energy.

u_climatology_data: xarray.DataArray.

The climatology of zonal wind data.

v_climatology_data: xarray.DataArray.

The climatology of meridional wind data.

vertical_dim: str.

Vertical coordinate dimension name.

vertical_dim_units: str.

The unit corresponding to the vertical p-coordinate value. Optional values are hPa, Pa, mbar.

psi_prime_data: xarray.DataArray.

Perturbation stream function. Geostrophic stream function perturbation calculated from geopotential height anomaly.

lon_dim: str, default: lon.

Longitude coordinate dimension name. By default extracting is applied over the lon dimension.

lat_dim: str, default: lat.

Latitude coordinate dimension name. By default extracting is applied over the lat dimension.

omega: float, default: 7.292e-5.

The angular speed of the earth.

g: float, default: 9.8.

The acceleration of gravity.

R: float, default: 6370000.

Radius of the Earth.

Returns

The TN wave activity horizontal flux (xarray.Dataset).

Reference

See also

easyclimate.core.eddy.calc_EP_horizontal_flux(u_prime_data: xarray.DataArray, v_prime_data: xarray.DataArray, time_dim: str = 'time', lat_dim: str = 'lat') → xarray.Dataset

Calculate horizontal Eliassen–Palm Flux.

Parameters

u_prime_data: xarray.DataArray.

The anormaly of zonal wind data.

v_prime_data: xarray.DataArray.

The anormaly of meridional wind data.

time_dim: str, default: time.

The time coordinate dimension name.

lat_dim: str, default: lat.

Latitude coordinate dimension name. By default extracting is applied over the lat dimension.

Returns

The Eliassen–Palm Flux (xarray.DataArray).

See also

easyclimate.core.eddy.calc_monthly_rossby_wave_source(u_data: xarray.DataArray, v_data: xarray.DataArray, u_climatology_data: xarray.DataArray, v_climatology_data: xarray.DataArray, lat_dim: str = 'lat', omega: float = 7.292e-05, R: float = 6371200.0) → xarray.DataArray

Calculate the Rossby wave source following Sardeshmukh and Hoskins (1988).

The Rossby wave source (RWS) represents the forcing term for stationary Rossby waves and is widely used to diagnose atmospheric teleconnections. It is decomposed into five terms representing different physical mechanisms:

\[S' = -\nabla \cdot (\mathbf{v}_\chi \zeta)' = \text{term1a} + \text{term1b} + \text{term2a} + \text{term2b} + \text{term3} + \text{term4} + \text{term5}\]

where:

  • term1a: \(-\bar{\zeta} \nabla \cdot \mathbf{v}'_\chi\) (stretching of climatological vorticity by divergent wind anomalies)

  • Term1b: \(-f \nabla \cdot \mathbf{v'_\chi}\) (Stretching of planetary vorticity by anomalous divergence)

  • term2a: \(-\mathbf{v}'_\chi \cdot \nabla\bar{\zeta}\) (advection of climatological vorticity by divergent wind anomalies)

  • term2b: \(-\beta v'_\chi\) (planetary vorticity advection, where \(\beta = \partial f/\partial y\))

  • term3: \(-\zeta' \nabla \cdot \bar{\mathbf{v}}_\chi\) (stretching of vorticity anomalies by climatological divergent wind)

  • term4: \(-\bar{\mathbf{v}}_\chi \cdot \nabla\zeta'\) (advection of vorticity anomalies by climatological divergent wind)

  • term5: \(-\nabla \cdot (\mathbf{v}'_\chi \zeta')\) (nonlinear term: divergence of transient vorticity flux)

where \(\mathbf{v}_\chi = (u_\chi, v_\chi)\) is the divergent (irrotational) wind component, \(\zeta\) is relative vorticity, overbar denotes climatology, and prime denotes anomaly.

Note

  • Anomalies are computed as deviations from the monthly climatology.

  • The planetary term (term6) represents the beta effect, which is important for Rossby wave propagation, especially in the tropics and subtropics.

  • Terms 1, 2, and 6 typically dominate the Rossby wave source.

  • Positive RWS indicates a cyclonic wave source; negative indicates anticyclonic.

Parameters

u_dataxarray.DataArray (\(\mathrm{m/s}\))

Zonal wind component. Must contain a ‘time’ dimension with monthly or higher frequency data. Expected dimensions: (time, lat, lon) or (time, level, lat, lon).

v_dataxarray.DataArray (\(\mathrm{m/s}\))

Meridional wind component. Must have the same dimensions as u_data.

u_climatology_dataxarray.DataArray (\(\mathrm{m/s}\))

Monthly climatology of zonal wind. Expected dimensions: (time, lat, lon) or (time, level, lat, lon), where time/month ranges from 1 to 12.

v_climatology_dataxarray.DataArray (\(\mathrm{m/s}\))

Monthly climatology of meridional wind. Must have the same dimensions as u_climatology_data.

Returns

resultxarray.Dataset

Dataset containing the Rossby wave source and its five decomposed terms:

  • RWS: Total Rossby wave source (sum of all terms)

  • term1a: Vorticity stretching by anomalous divergence

  • term1b: Stretching of planetary vorticity by anomalous divergence

  • term2a: Vorticity advection by anomalous divergent wind

  • term2b: Planetary vorticity advection (beta effect)

  • term3: Anomalous vorticity stretching by climatological divergence

  • term4: Anomalous vorticity advection by climatological divergent wind

  • term5: Nonlinear transient eddy term

All variables have units of \(\mathrm{s^{-2}}\) and retain the spatial/temporal dimensions of the input data.

See also

Examples

>>> # Calculate monthly climatology
>>> u_clim = u.groupby('time.month').mean('time')
>>> v_clim = v.groupby('time.month').mean('time')
>>>
>>> # Compute Rossby wave source
>>> rws_result = calc_rossby_wave_source(u, v, u_clim, v_clim)
>>>
>>> # Visualize the dominant terms
>>> rws_result['RWS'].sel(time='2015-12').plot()
>>> (rws_result['term1'] + rws_result['term2']).sel(time='2015-12').plot()