easyclimate.physics.moisture.wet_bulb

Wet-bulb Temperature

Functions

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.

Module Contents

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