easyclimate.physics

Submodules

Functions

get_coriolis_parameter(→ xarray.DataArray | numpy.array)

Calculate the Coriolis parameter at each point.

calc_lat_weight_lin_rood(→ Tuple[numpy.ndarray, ...)

Calculate the latitudes and weights used by the Lin-Rood model.

calc_dewpoint(→ xarray.DataArray)

Calculate the ambient dew point temperature given the vapor pressure.

calc_moist_adiabatic_lapse_rate(→ xarray.DataArray)

Calculate moist adiabatic lapse rate.

calc_mixing_ratio(→ xarray.DataArray)

Calculate the mixing ratio of a gas.

calc_saturation_mixing_ratio(→ xarray.DataArray)

Calculate the saturation mixing ratio of water vapor.

calc_vapor_pressure(→ xarray.DataArray)

Calculate the vapor pressure.

calc_saturation_vapor_pressure(→ xarray.DataArray)

Calculate the saturation water vapor (partial) pressure.

calc_wet_bulb_temperature_iteration(, tolerance, ...)

Calculate wet-bulb potential temperature using iteration.

calc_wet_bulb_potential_temperature_iteration(...)

Calculate wet-bulb potential temperature (\(\theta_w\)).

calc_wet_bulb_potential_temperature_davies_jones2008(...)

Calculate wet-bulb potential temperature using Robert Davies-Jones (2008) approximation.

calc_wet_bulb_temperature_stull2011(→ xarray.DataArray)

Calculate wet-bulb temperature using Stull (2011) empirical formula.

calc_wet_bulb_temperature_sadeghi2013(→ xarray.DataArray)

Calculate wet-bulb temperature using Sadeghi et. al (2011) empirical formula.

calc_equivalent_potential_temperature(→ xarray.DataArray)

Calculate equivalent potential temperature using Bolton (1980) approximation.

calc_equivalent_potential_temperature_davies_jones2009(...)

Calculate equivalent potential temperature using Robert Davies-Jones (2009) approximation.

calc_potential_temperature(→ xarray.DataArray)

Calculate the potential temperature for dry air.

calc_potential_temperature_vertical(→ xarray.DataArray)

Calculate the potential temperature for vertical variables.

calc_virtual_temperature(→ xarray.DataArray)

Calculate virtual temperature.

calc_virtual_temperature_Hobbs2006(→ xarray.DataArray)

Calculate virtual temperature.

calc_lifting_condensation_level_bolton1980(...)

Calculate lifting condensation level using Bolton (1980) approximation.

calc_lifting_condensation_level_Bohren_Albrecht2023(...)

Calculate lifting condensation level using Bohren & Albrecht (2023) approximation.

calc_brunt_vaisala_frequency_atm(→ xarray.DataArray)

Calculation of the Brunt-väisälä frequency for the vertical atmosphere.

calc_static_stability(→ xarray.DataArray)

Calculate the static stability within a vertical profile.

calc_enthalpy(→ xarray.DataArray)

Calculate atmospheric enthalpy from temperature and humidity mixing ratio.

calc_latent_heat_water(→ xarray.DataArray)

Estimate latent heat flux for water: evaporization (condensation), melting (freezing) or sublimation (deposition).

calc_relative_angular_momentum(zonal_wind_speed_data, ...)

Calculate atmospheric relative angular momentum.

transfer_mixing_ratio_2_specific_humidity(...)

Calculate the specific humidity from mixing ratio.

transfer_specific_humidity_2_mixing_ratio(...)

Calculate the mixing ratio from specific humidity.

transfer_dewpoint_2_specific_humidity(→ xarray.DataArray)

Calculate the specific humidity from the dew point temperature and pressure.

transfer_dewpoint_2_mixing_ratio(dewpoint_data, ...)

Calculate the mixing ratio from the dew point temperature and pressure.

transfer_specific_humidity_2_dewpoint(→ xarray.DataArray)

Calculate the dew point temperature from specific humidity and pressure.

transfer_dewpoint_2_relative_humidity(→ xarray.DataArray)

Calculate the relative humidity from dew point temperature.

transfer_mixing_ratio_2_relative_humidity(...)

Calculate the relative humidity from mixing ratio, temperature, and pressure.

transfer_specific_humidity_2_relative_humidity(...)

Calculate the relative humidity from specific humidity, temperature, and pressure.

transfer_relative_humidity_2_dewpoint(→ xarray.DataArray)

Calculate dew point temperature from temperature and relative humidity.

Package Contents

easyclimate.physics.get_coriolis_parameter(lat_data: xarray.DataArray | numpy.array, omega: float = 7.292e-05) → xarray.DataArray | numpy.array

Calculate the Coriolis parameter at each point.

\[f = 2 \Omega \sin(\phi)\]

Parameters

lat_data: xarray.DataArray or numpy.array.

Latitude at each point.

omega: float, default: 7.292e-5 ( \(\mathrm{rad/s}\) ).

The angular speed of the earth.

Returns

Corresponding Coriolis force at each point ( \(\mathrm{s^{-1}}\) ).

xarray.DataArray or numpy.array.

Reference

See also

easyclimate.physics.calc_lat_weight_lin_rood(nlat: int) → Tuple[numpy.ndarray, numpy.ndarray]

Calculate the latitudes and weights used by the Lin-Rood model.

The Lin-Rood model requires a specific distribution of latitudes and corresponding weights for numerical integration on a spherical grid. This function generates these values based on the number of desired latitudes.

Parameters

nlatint

Number of latitudes. Must be at least 2 to define a valid grid (from pole to pole).

Returns

Tuple[ndarray, ndarray]

A tuple containing two numpy arrays: - lat : ndarray

Array of latitudes in degrees, ranging from -90 (South Pole) to 90 (North Pole).

  • weightndarray

    Array of weights corresponding to each latitude, used for numerical integration.

Tip

The weights are computed such that they are suitable for use in the Lin-Rood semi-Lagrangian transport scheme. The latitudes are uniformly spaced between the poles.

References

See also

easyclimate.physics.calc_dewpoint(vapor_pressure_data: xarray.DataArray, vapor_pressure_data_units: Literal['hPa', 'Pa', 'mbar']) → xarray.DataArray

Calculate the ambient dew point temperature given the vapor pressure.

This function inverts the Bolton (1980) formula for saturation vapor pressure to instead calculate the temperature. This yields the following formula for dewpoint in degrees Celsius, where \(e\) is the ambient vapor pressure in millibars:

\[T = \frac{243.5 \log(e / 6.112)}{17.67 - \log(e / 6.112)}\]

Parameters

vapor_pressure_data: xarray.DataArray.

Water vapor partial pressure.

vapor_pressure_data_units: str.

The unit corresponding to vapor_pressure_data value. Optional values are hPa, Pa.

Returns

The dew point ( \(\\mathrm{degC}\) ).

xarray.DataArray

See also

easyclimate.physics.calc_moist_adiabatic_lapse_rate(pressure_data: xarray.DataArray, temperature_data: xarray.DataArray, pressure_data_units: Literal['hPa', 'Pa', 'mbar'], temperature_data_units: Literal['celsius', 'kelvin', 'fahrenheit']) → xarray.DataArray

Calculate moist adiabatic lapse rate.

Parameters

pressure_data: xarray.DataArray.

The pressure data set.

temperature_data: xarray.DataArray.

Atmospheric temperature.

pressure_data_units: str.

The unit corresponding to pressure_data value. Optional values are hPa, Pa, mbar.

temperature_data_units: str.

The unit corresponding to temperature_data value. Optional values are celsius, kelvin, fahrenheit.

Returns:

dtdpxarray.DataArray ( \(\mathrm{K/hPa}\) ).

Moist adiabatic lapse rate.

easyclimate.physics.calc_mixing_ratio(partial_pressure_data: xarray.DataArray, total_pressure_data: xarray.DataArray, molecular_weight_ratio: float = 0.6219569100577033) → xarray.DataArray

Calculate the mixing ratio of a gas.

This calculates mixing ratio given its partial pressure and the total pressure of the air. There are no required units for the input arrays, other than that they have the same units.

Parameters

partial_pressure_data: xarray.DataArray.

Partial pressure of the constituent gas.

total_pressure_data: xarray.DataArray.

Total air pressure.

molecular_weight_ratiofloat, optional.

The ratio of the molecular weight of the constituent gas to that assumed for air. Defaults to the ratio for water vapor to dry air (\(\epsilon\approx0.622\)).

Note

The units of partial_pressure_data and total_pressure_data should be the same.

Returns

The mixing ratio ( \(\mathrm{g/g}\) ).

xarray.DataArray.

See also

easyclimate.physics.calc_saturation_mixing_ratio(total_pressure_data: xarray.DataArray, temperature_data: xarray.DataArray, temperature_data_units: Literal['celsius', 'kelvin', 'fahrenheit'], total_pressure_data_units: Literal['hPa', 'Pa', 'mbar']) → xarray.DataArray

Calculate the saturation mixing ratio of water vapor.

This calculation is given total atmospheric pressure and air temperature.

Parameters

total_pressure_data: xarray.DataArray.

Total atmospheric pressure.

temperature_data: xarray.DataArray.

Atmospheric temperature.

temperature_data_units: str.

The unit corresponding to temperature_data value. Optional values are celsius, kelvin, fahrenheit.

total_pressure_data_units: str.

The unit corresponding to total_pressure_data value. Optional values are hPa, Pa.

Returns

The saturation mixing ratio ( \(\mathrm{g/g}\) ).

xarray.DataArray.

See also

easyclimate.physics.calc_vapor_pressure(pressure_data: xarray.DataArray, mixing_ratio_data: xarray.DataArray, pressure_data_units: Literal['hPa', 'Pa', 'mbar'] = None, epsilon: float = 0.6219569100577033) → xarray.DataArray

Calculate the vapor pressure.

Parameters

pressure_data: xarray.DataArray.

The pressure data set.

mixing_ratio_data: xarray.DataArray.

The mixing ratio of a gas.

epsilon: float.

The molecular weight ratio, which is molecular weight of the constituent gas to that assumed for air. Defaults to the ratio for water vapor to dry air. (\(\epsilon \approx 0.622\))

pressure_data_units: str.

The unit corresponding to pressure_data value. Optional values are hPa, Pa.

Returns

The water vapor (partial) pressure, units according to pressure_data_units.

xarray.DataArray

See also

easyclimate.physics.calc_saturation_vapor_pressure(temperature_data: xarray.DataArray, temperature_data_units: Literal['celsius', 'kelvin', 'fahrenheit']) → xarray.DataArray

Calculate the saturation water vapor (partial) pressure.

Parameters

temperature_data: xarray.DataArray.

Atmospheric temperature.

temperature_data_units: str.

The unit corresponding to temperature_data value. Optional values are celsius, kelvin, fahrenheit.

Returns

The saturation water vapor (partial) pressure ( \(\mathrm{hPa}\) ).

xarray.DataArray.

See also

easyclimate.physics.calc_wet_bulb_temperature_iteration(temperature_data: xarray.DataArray, relative_humidity_data: xarray.DataArray, pressure_data: xarray.DataArray, temperature_data_units: Literal['celsius', 'kelvin', 'fahrenheit'], relative_humidity_data_units: Literal['%', 'dimensionless'], pressure_data_units: Literal['hPa', 'Pa', 'mbar'], A: float = 0.662 * 10**-3, tolerance: float = 0.01, max_iter: int = 100, method: Literal['easyclimate-backend', 'easyclimate-rust'] = 'easyclimate-rust') → xarray.DataArray

Calculate wet-bulb potential temperature using iteration.

The iterative formula

\[e = e_{tw} - AP(t-t_{w})\]

  • \(e\) is the water vapor pressure

  • \(e_{tw}\) is the saturation water vapor pressure over a pure flat ice surface at wet-bulb temperature \(t_w\) (when the wet-bulb thermometer is frozen, this becomes the saturation vapor pressure over a pure flat ice surface)

  • \(A\) is the psychrometer constant

  • \(P\) is the sea-level pressure

  • \(t\) is the dry-bulb temperature

  • \(t_w\) is the wet-bulb temperature

Parameters

temperature_data: xarray.DataArray.

Atmospheric temperature.

relative_humidity_data: xarray.DataArray.

The relative humidity.

pressure_data: xarray.DataArray.

The pressure data set.

temperature_data_units: str.

The unit corresponding to temperature_data value. Optional values are celsius, kelvin, fahrenheit.

relative_humidity_data_units: str.

The unit corresponding to vapor_pressure_data value. Optional values are %, dimensionless.

pressure_data_units: str.

The unit corresponding to pressure_data value. Optional values are hPa, Pa, mbar.

A: float.

Psychrometer coefficients.

Psychrometer Type and Ventilation Rate

Wet Bulb Unfrozen (10^-3/°C^-1)

Wet Bulb Frozen (10^-3/°C^-1)

Ventilated Psychrometer (2.5 m/s)

0.662

0.584

Spherical Psychrometer (0.4 m/s)

0.857

0.756

Cylindrical Psychrometer (0.4 m/s)

0.815

0.719

Chinese Spherical Psychrometer (0.8 m/s)

0.7949

0.7949
tolerance: float.

Minimum acceptable deviation of the iterated value from the true value.

max_iter: int.

Maximum number of iterations.

method{“easyclimate-backend”,”easyclimate-rust”}

Backend implementation.

Returns

tw: xarray.DataArray ( \(\mathrm{degC}\) )

Wet-bulb temperature

Examples

>>> import xarray as xr
>>> import numpy as np

# Create sample data
>>> temp = xr.DataArray(np.array([20, 25, 30]), dims=['point'])
>>> rh = xr.DataArray(np.array([50, 60, 70]), dims=['point'])
>>> pressure = xr.DataArray(np.array([1000, 950, 900]), dims=['point'])

# Calculate wet-bulb potential temperature
>>> theta_w = calc_wet_bulb_potential_temperature_iteration(
...     temperature_data=temp,
...     relative_humidity_data=rh,
...     pressure_data=pressure,
...     temperature_data_units="celsius",
...     relative_humidity_data_units="%",
...     pressure_data_units="hPa"
... )

# Example with 2D data
>>> temp_2d = xr.DataArray(np.random.rand(10, 10) * 30, dims=['lat', 'lon'])
>>> rh_2d = xr.DataArray(np.random.rand(10, 10) * 100, dims=['lat', 'lon'])
>>> pres_2d = xr.DataArray(np.random.rand(10, 10) * 200 + 800, dims=['lat', 'lon'])
>>> theta_w_2d = calc_wet_bulb_potential_temperature_iteration(
...     temp_2d, rh_2d, pres_2d, "celsius", "%", "hPa"
... )

See also

easyclimate.physics.calc_wet_bulb_potential_temperature_iteration(temperature_data: xarray.DataArray, relative_humidity_data: xarray.DataArray, pressure_data: xarray.DataArray, temperature_data_units: Literal['celsius', 'kelvin', 'fahrenheit', 'degC', 'degK'], relative_humidity_data_units: Literal['%', 'dimensionless'], pressure_data_units: Literal['hPa', 'Pa', 'mbar'], A: float = 0.000662, tolerance: float = 0.01, max_iter: int = 100, method: Literal['easyclimate-backend', 'easyclimate-rust'] = 'easyclimate-rust') → xarray.DataArray

Calculate wet-bulb potential temperature (\(\theta_w\)).

The iterative formula for wet-bulb temperature

\[e = e_{tw} - AP(t-t_{w})\]

  • \(e\) is the water vapor pressure

  • \(e_{tw}\) is the saturation water vapor pressure over a pure flat ice surface at wet-bulb temperature \(t_w\) (when the wet-bulb thermometer is frozen, this becomes the saturation vapor pressure over a pure flat ice surface)

  • \(A\) is the psychrometer constant

  • \(P\) is the sea-level pressure

  • \(t\) is the dry-bulb temperature

  • \(t_w\) is the wet-bulb temperature

Wet-bulb potential temperature (\(\theta_w\)) is defined as the temperature that an air parcel would have if it were first brought to saturation at its ambient pressure (i.e., cooled to the wet-bulb temperature, \(T_w\)), and then brought dry-adiabatically to a reference pressure, conventionally (\(p_0 = 1000 \mathrm{hPa}\)).

This quantity is therefore obtained from two steps:

  • Compute the wet-bulb temperature (\(T_w\)) at the parcel’s pressure (\(p\));

  • Apply the dry-adiabatic (Poisson) transformation from (\(p\)) to (\(p_0\)).

Under this definition, once (\(T_w\)) is known, (\(\theta_w\)) follows directly as

\[\theta_w = (T_w + 273.15) ( \frac{p_0}{p}) ^{\kappa} - 273.15\]

where \(\kappa = \frac{R_d}{c_p} \approx 0.2854\), and \(p_0 = 1000 \mathrm{hPa}\).

This formulation makes clear that the iterative/nonlinear part of the calculation is confined to determining (\(T_w\)); the mapping from (\(T_w\)) to (\(\theta_w\)) is purely algebraic via the dry-adiabatic relation.

Parameters

temperature_data: xarray.DataArray.

Atmospheric temperature.

relative_humidity_data: xarray.DataArray.

The relative humidity.

pressure_data: xarray.DataArray.

The pressure data set.

temperature_data_units: str.

The unit corresponding to temperature_data value. Optional values are celsius, kelvin, fahrenheit.

relative_humidity_data_units: str.

The unit corresponding to vapor_pressure_data value. Optional values are %, dimensionless.

pressure_data_units: str.

The unit corresponding to pressure_data value. Optional values are hPa, Pa, mbar.

A: float.

Psychrometer coefficients.

Psychrometer Type and Ventilation Rate

Wet Bulb Unfrozen (10^-3/°C^-1)

Wet Bulb Frozen (10^-3/°C^-1)

Ventilated Psychrometer (2.5 m/s)

0.662

0.584

Spherical Psychrometer (0.4 m/s)

0.857

0.756

Cylindrical Psychrometer (0.4 m/s)

0.815

0.719

Chinese Spherical Psychrometer (0.8 m/s)

0.7949

0.7949
tolerance: float.

Minimum acceptable deviation of the iterated value from the true value.

max_iter: int.

Maximum number of iterations.

method{“easyclimate-backend”,”easyclimate-rust”}

Backend implementation.

Notes

\(\theta_w\) is obtained by first computing the wet-bulb temperature (Tw) and then reducing it dry-adiabatically to 1000 hPa.

easyclimate.physics.calc_wet_bulb_potential_temperature_davies_jones2008(pressure_data: xarray.DataArray, temperature_data: xarray.DataArray, dewpoint_data: xarray.DataArray, pressure_data_units: Literal['hPa', 'Pa', 'mbar'], temperature_data_units: Literal['celsius', 'kelvin', 'fahrenheit'], dewpoint_data_units: Literal['celsius', 'kelvin', 'fahrenheit']) → xarray.DataArray

Calculate wet-bulb potential temperature using Robert Davies-Jones (2008) approximation.

Parameters

pressure_data: xarray.DataArray.

The pressure data set.

temperature_data: xarray.DataArray.

Atmospheric temperature.

dewpoint_data: xarray.DataArray.

The dewpoint temperature.

pressure_data_units: str.

The unit corresponding to pressure_data value. Optional values are hPa, Pa, mbar.

temperature_data_units: str.

The unit corresponding to temperature_data value. Optional values are celsius, kelvin, fahrenheit.

dewpoint_data_units: str.

The unit corresponding to dewpoint_data value. Optional values are celsius, kelvin, fahrenheit.

Returns

tw: xarray.DataArray ( \(\mathrm{K}\) )

Wet-bulb temperature

See also

  • Davies-Jones, R. (2008). An Efficient and Accurate Method for Computing the Wet-Bulb Temperature along Pseudoadiabats. Monthly Weather Review, 136(7), 2764-2785. https://doi.org/10.1175/2007MWR2224.1

  • Knox, J. A., Nevius, D. S., & Knox, P. N. (2017). Two Simple and Accurate Approximations for Wet-Bulb Temperature in Moist Conditions, with Forecasting Applications. Bulletin of the American Meteorological Society, 98(9), 1897-1906. https://doi.org/10.1175/BAMS-D-16-0246.1

Example(s) related to the function

Wet-bulb Temperature

Wet-bulb Temperature
easyclimate.physics.calc_wet_bulb_temperature_stull2011(temperature_data: xarray.DataArray, relative_humidity_data: xarray.DataArray, temperature_data_units: Literal['celsius', 'kelvin', 'fahrenheit'], relative_humidity_data_units: Literal['%', 'dimensionless']) → xarray.DataArray

Calculate wet-bulb temperature using Stull (2011) empirical formula.

\[T_{w} =T\operatorname{atan}[0.151977(\mathrm{RH} \% +8.313659)^{1/2}]+\operatorname{atan}(T+\mathrm{RH}\%)-\operatorname{atan}(\mathrm{RH} \% -1.676331) +0.00391838(\mathrm{RH}\%)^{3/2}\operatorname{atan}(0.023101\mathrm{RH}\%)-4.686035.\]

Tip

This methodology was not valid for ambient conditions with low values of \(T_a\) (dry-bulb temperature; i.e., <10°C), and/or with low values of RH (5% < RH < 10%). The Stull methodology was also only valid at sea level.

Parameters

temperature_data: xarray.DataArray.

Atmospheric temperature.

relative_humidity_data: xarray.DataArray.

The relative humidity.

temperature_data_units: str.

The unit corresponding to temperature_data value. Optional values are celsius, kelvin, fahrenheit.

relative_humidity_data_units: str.

The unit corresponding to vapor_pressure_data value. Optional values are %, dimensionless.

Returns

tw: xarray.DataArray ( \(\mathrm{K}\) )

Wet-bulb temperature

See also

Example(s) related to the function

Wet-bulb Temperature

Wet-bulb Temperature
easyclimate.physics.calc_wet_bulb_temperature_sadeghi2013(temperature_data: xarray.DataArray, height_data: xarray.DataArray, relative_humidity_data: xarray.DataArray, temperature_data_units: Literal['celsius', 'kelvin', 'fahrenheit'], height_data_units: Literal['m', 'km'], relative_humidity_data_units: Literal['%', 'dimensionless']) → xarray.DataArray

Calculate wet-bulb temperature using Sadeghi et. al (2011) empirical formula.

Parameters

temperature_data: xarray.DataArray.

Atmospheric temperature.

height_data: xarray.DataArray.

The elevation.

relative_humidity_data: xarray.DataArray.

The relative humidity.

temperature_data_units: str.

The unit corresponding to temperature_data value. Optional values are celsius, kelvin, fahrenheit.

height_data_units: str.

The unit corresponding to height_data value. Optional values are m, km.

relative_humidity_data_units: str.

The unit corresponding to vapor_pressure_data value. Optional values are %, dimensionless.

Returns

tw: xarray.DataArray ( \(\mathrm{degC}\) )

Wet-bulb temperature

See also

  • Sadeghi, S., Peters, T. R., Cobos, D. R., Loescher, H. W., & Campbell, C. S. (2013). Direct Calculation of Thermodynamic Wet-Bulb Temperature as a Function of Pressure and Elevation. Journal of Atmospheric and Oceanic Technology, 30(8), 1757-1765. https://doi.org/10.1175/JTECH-D-12-00191.1

Example(s) related to the function

Wet-bulb Temperature

Wet-bulb Temperature
easyclimate.physics.calc_equivalent_potential_temperature(pressure_data: xarray.DataArray, temperature_data: xarray.DataArray, dewpoint_data: xarray.DataArray, pressure_data_units: Literal['hPa', 'Pa'], temperature_data_units: Literal['celsius', 'kelvin', 'fahrenheit'], dewpoint_data_units: Literal['celsius', 'kelvin', 'fahrenheit']) → xarray.DataArray

Calculate equivalent potential temperature using Bolton (1980) approximation.

Parameters

pressure_data: xarray.DataArray.

The pressure data set.

temperature_data: xarray.DataArray.

Atmospheric temperature.

dewpoint_data: xarray.DataArray.

The dew point temperature.

pressure_data_units: str.

The unit corresponding to pressure_data value. Optional values are hPa, Pa.

temperature_data_units: str.

The unit corresponding to temperature_data value. Optional values are celsius, kelvin, fahrenheit.

dewpoint_data_units: str.

The unit corresponding to dewpoint_data value. Optional values are celsius, kelvin, fahrenheit.

Returns

Equivalent potential temperature ( \(\mathrm{K}\) ).

xarray.DataArray.

See also

easyclimate.physics.calc_equivalent_potential_temperature_davies_jones2009(pressure_data: xarray.DataArray, temperature_data: xarray.DataArray, dewpoint_data: xarray.DataArray, pressure_data_units: Literal['hPa', 'Pa'], temperature_data_units: Literal['celsius', 'kelvin', 'fahrenheit'], dewpoint_data_units: Literal['celsius', 'kelvin', 'fahrenheit']) → xarray.DataArray

Calculate equivalent potential temperature using Robert Davies-Jones (2009) approximation.

Parameters

pressure_data: xarray.DataArray.

The pressure data set.

temperature_data: xarray.DataArray.

Atmospheric temperature.

dewpoint_data: xarray.DataArray.

The dew point temperature.

pressure_data_units: str.

The unit corresponding to pressure_data value. Optional values are hPa, Pa.

temperature_data_units: str.

The unit corresponding to temperature_data value. Optional values are celsius, kelvin, fahrenheit.

dewpoint_data_units: str.

The unit corresponding to dewpoint_data value. Optional values are celsius, kelvin, fahrenheit.

Returns

Equivalent potential temperature ( \(\mathrm{K}\) ).

xarray.DataArray.

See also

easyclimate.physics.calc_potential_temperature(temper_data: xarray.DataArray, pressure_data: xarray.DataArray, pressure_data_units: Literal['hPa', 'Pa', 'mbar'], kappa: float = 287 / 1005.7) → xarray.DataArray

Calculate the potential temperature for dry air.

Uses the Poisson equation to calculation the potential temperature given pressure and temperature.

\[\theta = T \left( \frac{p_0}{p} \right) ^\kappa\]

Parameters

temper_data: xarray.DataArray.

Air temperature.

pressure_data: xarray.DataArray.

The pressure data set.

pressure_data_units: str.

The unit corresponding to pressure_data value. Optional values are hPa, Pa.

kappa: float, default: 287/1005.7.

Poisson constant \(\kappa\).

Note

Poisson constant - Glossary of Meteorology

Returns

Potential temperature, units according to temper_data.

xarray.DataArray.

Reference

See also

easyclimate.physics.calc_potential_temperature_vertical(temper_data: xarray.DataArray, vertical_dim: str, vertical_dim_units: Literal['hPa', 'Pa', 'mbar'], kappa: float = 287 / 1005.7) → xarray.DataArray

Calculate the potential temperature for vertical variables.

Uses the Poisson equation to calculation the potential temperature given pressure and temperature.

\[\theta = T \left( \frac{p_0}{p} \right) ^\kappa\]

Parameters

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.

kappa: float, default: 287/1005.7.

Poisson constant \(\kappa\).

Note

Poisson constant - Glossary of Meteorology

Returns

Potential temperature, units according to temper_data.

xarray.DataArray.

Reference

See also

easyclimate.physics.calc_virtual_temperature(temper_data: xarray.DataArray, specific_humidity_data: xarray.DataArray, specific_humidity_data_units: Literal['kg/kg', 'g/g', 'g/kg'], epsilon: float = 0.608) → xarray.DataArray

Calculate virtual temperature.

The virtual temperature (\(T_v\)) is the temperature at which dry air would have the same density as the moist air, at a given pressure. In other words, two air samples with the same virtual temperature have the same density, regardless of their actual temperature or relative humidity. The virtual temperature is always greater than the absolute air temperature.

\[T_v = T(1+ \epsilon q)\]

where \(\epsilon = 0.608\) when the mixing ratio (specific humidity) \(q\) is expressed in \(\mathrm{g \cdot g^{-1}}\).

Parameters

temper_data: xarray.DataArray.

Air temperature.

specific_humidity_data: xarray.DataArray.

The absolute humidity data.

specific_humidity_data_units: str.

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

epsilon: float.

A constant.

Returns

The virtual temperature, units according to temper_data.

xarray.DataArray.

Reference

See also

easyclimate.physics.calc_virtual_temperature_Hobbs2006(temper_data: xarray.DataArray, specific_humidity_data: xarray.DataArray, specific_humidity_data_units: Literal['kg/kg', 'g/g', 'g/kg'], epsilon: float = 0.6219569100577033) → xarray.DataArray

Calculate virtual temperature.

The virtual temperature (\(T_v\)) is the temperature at which dry air would have the same density as the moist air, at a given pressure. In other words, two air samples with the same virtual temperature have the same density, regardless of their actual temperature or relative humidity. The virtual temperature is always greater than the absolute air temperature.

This calculation must be given an air parcel’s temperature and mixing ratio. The implementation uses the formula outlined in [Hobbs2006] pg.67 & 80.

\[T_v = T \frac{\text{q} + \epsilon}{\epsilon\,(1 + \text{q})}\]

where \(\epsilon \approx 0.622\) when the mixing ratio (specific humidity) \(q\) is expressed in \(\mathrm{g \ g^{-1}}\).

Parameters

temper_data: xarray.DataArray.

Air temperature.

specific_humidity_data: xarray.DataArray.

The absolute humidity data.

specific_humidity_data_units: str.

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

epsilon: float.

The molecular weight ratio, which is molecular weight of the constituent gas to that assumed for air. Defaults to the ratio for water vapor to dry air. (\(\epsilon \approx 0.622\))

Returns

The virtual temperature, units according to temper_data.

xarray.DataArray.

Reference

See also

easyclimate.physics.calc_lifting_condensation_level_bolton1980(temperature_data: xarray.DataArray, relative_humidity_data: xarray.DataArray, temperature_data_units: Literal['celsius', 'kelvin', 'fahrenheit'], relative_humidity_data_units: Literal['%', 'dimensionless']) → xarray.DataArray

Calculate lifting condensation level using Bolton (1980) approximation.

\[T_L = \frac{1}{\frac{1}{T_K - 55} - \frac{\ln (U/100)}{2840}} + 55\]

Parameters

temperature_data: xarray.DataArray.

Atmospheric temperature.

relative_humidity_data: xarray.DataArray.

The relative humidity.

temperature_data_units: str.

The unit corresponding to temperature_data value. Optional values are celsius, kelvin, fahrenheit.

relative_humidity_data_units: str.

The unit corresponding to vapor_pressure_data value. Optional values are %, dimensionless.

Returns

The lifting condensation level ( \(\mathrm{K}\) ).

xarray.DataArray.

See also

easyclimate.physics.calc_lifting_condensation_level_Bohren_Albrecht2023(pressure_data: xarray.DataArray, temperature_data: xarray.DataArray, dewpoint_data: xarray.DataArray, pressure_data_units: Literal['hPa', 'Pa', 'mbar'], temperature_data_units: Literal['celsius', 'kelvin', 'fahrenheit'], dewpoint_data_units: Literal['celsius', 'kelvin', 'fahrenheit']) → xarray.Dataset

Calculate lifting condensation level using Bohren & Albrecht (2023) approximation.

According to formulation (6.32) in Bohren & Albrecht (2023),

\[T_{LCL}=\frac{1-AT_d}{1/T_d + B\ln(T/T_d)-A}\]

Where

\[A=-\left(\frac{c_{pv}-c_{pw}}{l_r}-\frac{c_{pd}}{\epsilon l_v}\right),\quad B=\frac{c_{pd}}{\epsilon l_v}\]

and

\[l_v=l_{vr} - (c_{pv}-c_{pw})T_r, \quad l_v(T_d)=l_r+(c_{pd} - c_{pw}) T_d\]

Parameters

pressure_data: xarray.DataArray.

The pressure data set.

temperature_data: xarray.DataArray.

Atmospheric temperature.

dewpoint_data: xarray.DataArray.

The dewpoint temperature.

pressure_data_units: str.

The unit corresponding to pressure_data value. Optional values are hPa, Pa, mbar.

temperature_data_units: str.

The unit corresponding to temperature_data value. Optional values are celsius, kelvin, fahrenheit.

dewpoint_data_units: str.

The unit corresponding to dewpoint_data value. Optional values are celsius, kelvin, fahrenheit.

Returns

The lifting condensation level (xarray.Dataset)

  • p_lcl: lifting condensation level pressure ( \(\mathrm{hPa}\) ).

  • t_lcl: lifting condensation level temperature ( \(\mathrm{K}\) ).

See also

Bohren, C. F., and B. A. Albrecht, 2023: Atmospheric Thermodynamics Second Edition. Oxford University Press, 579 pp. Website: http://gen.lib.rus.ec/book/index.php?md5=AA3B25841BE3AEBA2628EF9961F58C52

easyclimate.physics.calc_brunt_vaisala_frequency_atm(potential_temperature_data: xarray.DataArray, z_data: xarray.DataArray, vertical_dim: str, g: float = 9.8) → xarray.DataArray

Calculation of the Brunt-väisälä frequency for the vertical atmosphere.

\[N = \left( \frac{g}{\theta} \frac{\mathrm{d}\theta}{\mathrm{d}z} \right)^\frac{1}{2}\]

Parameters

potential_temperature_data: xarray.DataArray.

Vertical atmospheric potential temperature.

z_data: xarray.DataArray ( \(\mathrm{m}\) ).

Vertical atmospheric geopotential height.

Attention

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

vertical_dim: str.

Vertical coordinate dimension name.

g: float, default: 9.8.

The acceleration of gravity.

Returns

Brunt-väisälä frequency, units according to potential_temperature_data \(^{1/2}\).

xarray.DataArray

Reference

See also

easyclimate.physics.calc_static_stability(temper_data: xarray.DataArray, vertical_dim: str, vertical_dim_units: Literal['hPa', 'Pa', 'mbar']) → xarray.DataArray

Calculate the static stability within a vertical profile.

\[\sigma = - T \frac{\partial \ln \theta}{\partial p}\]

Parameters

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.

Returns

Static stability, units according to temper_data_units^2 vertical_dim_units^-1.

xarray.DataArray.

Reference

  • Howard B. Bluestein. (1992). Synoptic-Dynamic Meteorology in Midlatitudes: Principles of Kinematics and Dynamics, Vol. 1

See also

easyclimate.physics.calc_enthalpy(temperature_data: xarray.DataArray, mixing_ratio_data: xarray.DataArray, temperature_data_units: Literal['celsius', 'kelvin', 'fahrenheit'], mixing_ratio_data_units: Literal['kg/kg', 'g/g', 'g/kg']) → xarray.DataArray

Calculate atmospheric enthalpy from temperature and humidity mixing ratio.

Enthalpy is a thermodynamic quantity equivalent to the internal energy plus the energy the system exerts on its surroundings. The enthalpy is a constant pressure function. As such, it includes the work term for expansion against the atmosphere.

\[T \cdot (1.01 + 0.00189 \cdot W) + 2.5 \cdot W\]

where the unit of \(T\) (atmospheric temperature) is degC, and \(W\) (mixing ratio) is g/kg.

Parameters

temperature_data: xarray.DataArray.

Atmospheric temperature.

mixing_ratio_data: xarray.DataArray.

The mixing ratio of a gas.

temperature_data_units: str.

The unit corresponding to temperature_data value. Optional values are celsius, kelvin, fahrenheit.

mixing_ratio_data_units: str.

The unit corresponding to mixing_ratio_data value. Optional values are \(\mathrm{kg/kg}\), \(\mathrm{g/g}\), \(\mathrm{g/kg}\) and so on.

Returns

Atmospheric enthalpy ( \(\mathrm{kJ/kg}\) ).

xarray.DataArray.

See also

easyclimate.physics.calc_latent_heat_water(temperature_data, temperature_data_units: Literal['celsius', 'kelvin', 'fahrenheit'], latent_heat_type: Literal['evaporation_condensation', 'melting_freezing', 'sublimation_deposition']) → xarray.DataArray

Estimate latent heat flux for water: evaporization (condensation), melting (freezing) or sublimation (deposition).

Tip

This function returns the latent heat of

  • evaporation/condensation

  • melting/freezing

  • sublimation/deposition

for water. The latent heatis a function of temperature t. The formulas are polynomial approximations to the values in Table 92, p. 343 of the Smithsonian Meteorological Tables, Sixth Revised Edition, 1963 by Roland List. The approximations were developed by Eric Smith at Colorado State University.

  • Source: Thomas W. Schlatter and Donald V. Baker: PROFS Program Office, NOAA Environmental Research Laboratories, Boulder, Colorado.

Parameters

temperature_data: xarray.DataArray.

Atmospheric temperature.

temperature_data_units: str.

The unit corresponding to temperature_data value. Optional values are celsius, kelvin, fahrenheit.

latent_heat_type: str.

The type of latent heat to estimate. Optional values are evaporation_condensation, melting_freezing, sublimation_deposition.

Returns

Latent heat flux for water ( \(\mathrm{J/kg}\) ).

xarray.DataArray.

See also

easyclimate.physics.calc_relative_angular_momentum(zonal_wind_speed_data: xarray.DataArray, vertical_dim: str, vertical_dim_units: Literal['hPa', 'Pa', 'mbar'], lon_dim: str = 'lon', lat_dim: str = 'lat', weights=None)

Calculate atmospheric relative angular momentum.

Parameters

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

Zonal wind component with the least similar dimensions (vertical_dim, lon_dim, lat_dim)

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.

weightsxarray.DataArray, optional

Weights for each latitude, same dimension as lat. If None, computed as \(\cos(lat)*\mathrm{d}lat\) with the values of latitude spacing.

Returns

aamxarray.DataArray ( \(\mathrm{kg} \cdot \mathrm{m^2/s}\) )

Atmospheric angular momentum.

See also

easyclimate.physics.transfer_mixing_ratio_2_specific_humidity(mixing_ratio_data: xarray.DataArray, mixing_ratio_data_units: Literal['kg/kg', 'g/g', 'g/kg']) → xarray.DataArray

Calculate the specific humidity from mixing ratio.

Parameters

mixing_ratio_data: xarray.DataArray.

The mixing ratio of a gas.

mixing_ratio_data_units: str.

The unit corresponding to mixing_ratio_data value. Optional values are \(\mathrm{kg/kg}\), \(\mathrm{g/g}\), \(\mathrm{g/kg}\) and so on.

Returns

The specific humidity, dimensionless (e.g. \(\mathrm{kg/kg}\), \(\mathrm{g/g}\)).

xarray.DataArray.

See also

easyclimate.physics.transfer_specific_humidity_2_mixing_ratio(specific_humidity_data: xarray.DataArray, specific_humidity_data_units: Literal['kg/kg', 'g/g', 'g/kg']) → xarray.DataArray

Calculate the mixing ratio from specific humidity.

Parameters

specific_humidity_data: xarray.DataArray.

The Specific humidity of air.

specific_humidity_data_units: str.

The unit corresponding to specific_humidity value. Optional values are \(\mathrm{kg/kg}\), \(\mathrm{g/g}\), \(\mathrm{g/kg}\) and so on.

Returns

The mixing ratio, dimensionless (e.g. \(\mathrm{kg/kg}\), \(\mathrm{g/g}\)).

xarray.DataArray.

See also

easyclimate.physics.transfer_dewpoint_2_specific_humidity(dewpoint_data: xarray.DataArray, pressure_data: xarray.DataArray, dewpoint_data_units: Literal['celsius', 'kelvin', 'fahrenheit'], pressure_data_units: Literal['hPa', 'Pa', 'mbar']) → xarray.DataArray

Calculate the specific humidity from the dew point temperature and pressure.

Parameters

dewpoint_data: xarray.DataArray.

The dew point temperature.

pressure_data: xarray.DataArray.

The pressure data set.

dewpoint_data_units: str.

The unit corresponding to dewpoint_data value. Optional values are celsius, kelvin, fahrenheit.

pressure_data_units: str.

The unit corresponding to pressure_data value. Optional values are hPa, Pa.

Returns

The specific humidity, dimensionless (e.g. \(\mathrm{kg/kg}\), \(\mathrm{g/g}\)).

xarray.DataArray.

See also

easyclimate.physics.transfer_dewpoint_2_mixing_ratio(dewpoint_data: xarray.DataArray, pressure_data: xarray.DataArray, dewpoint_data_units: Literal['celsius', 'kelvin', 'fahrenheit'], pressure_data_units: Literal['hPa', 'Pa', 'mbar'])

Calculate the mixing ratio from the dew point temperature and pressure.

Parameters

dewpoint_data: xarray.DataArray.

The dew point temperature.

pressure_data: xarray.DataArray.

The pressure data set.

dewpoint_data_units: str.

The unit corresponding to dewpoint_data value. Optional values are celsius, kelvin, fahrenheit.

pressure_data_units: str.

The unit corresponding to pressure_data value. Optional values are hPa, Pa.

Returns

The mixing ratio, dimensionless (e.g. \(\mathrm{kg/kg}\), \(\mathrm{g/g}\)).

xarray.DataArray.

easyclimate.physics.transfer_specific_humidity_2_dewpoint(specific_humidity_data: xarray.DataArray, pressure_data: xarray.DataArray, specific_humidity_data_units: Literal['kg/kg', 'g/g', 'g/kg'], pressure_data_units: Literal['hPa', 'Pa', 'mbar'], epsilon: float = 0.6219569100577033) → xarray.DataArray

Calculate the dew point temperature from specific humidity and pressure.

Parameters

specific_humidity_data: xarray.DataArray.

The absolute humidity data.

pressure_data: xarray.DataArray.

The pressure data set.

specific_humidity_data_units: str.

The unit corresponding to specific_humidity value. Optional values are \(\mathrm{kg/kg}\), \(\mathrm{g/g}\), \(\mathrm{g/kg}\) and so on.

pressure_data_units: str.

The unit corresponding to pressure_data value. Optional values are hPa, Pa.

epsilon: float.

The molecular weight ratio, which is molecular weight of the constituent gas to that assumed for air. Defaults to the ratio for water vapor to dry air. (\(\epsilon \approx 0.622\))

Returns

The dew point temperature ( \(\mathrm{degC}\) ).

xarray.DataArray.

See also

easyclimate.physics.transfer_dewpoint_2_relative_humidity(temperature_data: xarray.DataArray, dewpoint_data: xarray.DataArray, temperature_data_units: Literal['celsius', 'kelvin', 'fahrenheit'], dewpoint_data_units: Literal['celsius', 'kelvin', 'fahrenheit']) → xarray.DataArray

Calculate the relative humidity from dew point temperature.

Uses temperature and dew point temperature to calculate relative humidity as the ratio of vapor pressure to saturation vapor pressures.

Parameters

temperature_data: xarray.DataArray.

Atmospheric temperature.

dewpoint_data: xarray.DataArray.

The dew point temperature.

temperature_data_units: str.

The unit corresponding to temperature_data value. Optional values are celsius, kelvin, fahrenheit.

dewpoint_data_units: str.

The unit corresponding to dewpoint_data value. Optional values are celsius, kelvin, fahrenheit.

Returns

The relative humidity, dimensionless.

xarray.DataArray.

See also

easyclimate.physics.transfer_mixing_ratio_2_relative_humidity(pressure_data: xarray.DataArray, temperature_data: xarray.DataArray, mixing_ratio_data: xarray.DataArray, pressure_data_units: Literal['hPa', 'Pa', 'mbar'], temperature_data_units: Literal['celsius', 'kelvin', 'fahrenheit'], mixing_ratio_data_units: Literal['kg/kg', 'g/g', 'g/kg'], epsilon: float = 0.6219569100577033) → xarray.DataArray

Calculate the relative humidity from mixing ratio, temperature, and pressure.

Parameters

pressure_data: xarray.DataArray.

The pressure data set.

temperature_data: xarray.DataArray.

Atmospheric temperature.

mixing_ratio_data: xarray.DataArray.

The mixing ratio of a gas.

pressure_data_units: str.

The unit corresponding to pressure_data value. Optional values are hPa, Pa.

temperature_data_units: str.

The unit corresponding to temperature_data value. Optional values are celsius, kelvin, fahrenheit.

mixing_ratio_data_units: str.

The unit corresponding to mixing_ratio_data value. Optional values are \(\mathrm{kg/kg}\), \(\mathrm{g/g}\), \(\mathrm{g/kg}\) and so on.

epsilon: float.

The molecular weight ratio, which is molecular weight of the constituent gas to that assumed for air. Defaults to the ratio for water vapor to dry air. (\(\epsilon \approx 0.622\))

Returns

The relative humidity, dimensionless.

xarray.DataArray.

See also

easyclimate.physics.transfer_specific_humidity_2_relative_humidity(pressure_data: xarray.DataArray, temperature_data: xarray.DataArray, specific_humidity_data: xarray.DataArray, pressure_data_units: Literal['hPa', 'Pa', 'mbar'], temperature_data_units: Literal['celsius', 'kelvin', 'fahrenheit'], specific_humidity_data_units: Literal['kg/kg', 'g/g', 'g/kg']) → xarray.DataArray

Calculate the relative humidity from specific humidity, temperature, and pressure.

Parameters

pressure_data: xarray.DataArray.

The pressure data set.

temperature_data: xarray.DataArray.

Atmospheric temperature.

specific_humidity_data: xarray.DataArray.

The absolute humidity data.

pressure_data_units: str.

The unit corresponding to pressure_data value. Optional values are hPa, Pa.

temperature_data_units: str.

The unit corresponding to temperature_data value. Optional values are celsius, kelvin, fahrenheit.

specific_humidity_data_units: str.

The unit corresponding to specific_humidity value. Optional values are \(\mathrm{kg/kg}\), \(\mathrm{g/g}\), \(\mathrm{g/kg}\) and so on.

Returns

The relative humidity, dimensionless.

xarray.DataArray.

See also

easyclimate.physics.transfer_relative_humidity_2_dewpoint(relative_humidity_data: xarray.DataArray, temperature_data: xarray.DataArray, relative_humidity_data_units: Literal['%', 'dimensionless'], temperature_data_units: Literal['celsius', 'kelvin', 'fahrenheit']) → xarray.DataArray

Calculate dew point temperature from temperature and relative humidity.

The dew point temperature given temperature and relative humidity using the equations from John Dutton’s “Ceaseless Wind” (pp 273-274). Missing values are ignored.

The dew point temperature \(T_d\) (in Kelvin) is calculated from temperature \(T\) and relative humidity \(RH\) using the formula:

\[T_d = \frac{T \cdot L}{L - T \cdot \ln(RH/100)}, \quad \text{where} \quad L = \frac{597.3 - 0.57(T - 273.0)}{GCX} \quad \text{and} \quad GCX = \frac{461.5}{4186}.\]

Parameters

relative_humidity_data: xarray.DataArray.

The relative humidity.

temperature_data: xarray.DataArray.

Atmospheric temperature.

relative_humidity_data_units: str.

The unit corresponding to vapor_pressure_data value. Optional values are %, dimensionless.

temperature_data_units: str.

The unit corresponding to temperature_data value. Optional values are celsius, kelvin, fahrenheit.

Returns

dewpointxarray.DataArray ( \(\mathrm{K}\) )

Dew point temperature.

Reference

See also

https://www.ncl.ucar.edu/Document/Functions/Built-in/dewtemp_trh.shtml