earthkit.meteo.thermo.array.saturation_mixing_ratio_slope

earthkit.meteo.thermo.array.saturation_mixing_ratio_slope(t, p, es=None, es_slope=None, phase='mixed', eps=0.0001)

Compute the slope of saturation mixing ratio with respect to temperature.

Parameters:

  • t (array-like) – Temperature (K)

  • p (array-like) – Pressure (Pa)

  • es (array-like|None, optional) – saturation_vapour_pressure() pre-computed for the given phase (Pa). When specified, it is used in the computation instead of being computed from t and phase using saturation_vapour_pressure().

  • es_slope (array-like|None, optional) – saturation_vapour_pressure_slope() pre-computed for the given phase (Pa/K). When specified, it is used in the computation instead of being computed from t and phase using saturation_vapour_pressure_slope().

  • phase (str, optional) – Define the phase with respect to the computation will be performed. It is either “water”, “ice” or “mixed”. See saturation_vapour_pressure() for details.

  • eps (number) – Where p - es < eps nan is returned.

Returns:

Slope of saturation mixing ratio (\(kg kg^{-1} K^{-1}\))

Return type:

array-like

The computation is based on the following formula:

\[\frac{\partial w_{s}}{\partial t} = \frac{\epsilon p}{(p-e_{s})^{2}} \frac{d e_{s}}{d t}\]

where