easyclimate.physics.moisture

Submodules

Functions

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.

Package Contents

easyclimate.physics.moisture.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.moisture.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.moisture.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.moisture.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.moisture.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.moisture.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.moisture.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.moisture.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.moisture.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.moisture.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.moisture.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