metpy.calc.thickness_hydrostatic(pressure, temperature, mixing_ratio=None, molecular_weight_ratio=<Quantity(0.62195691, 'dimensionless')>, bottom=None, depth=None)[source]

Calculate the thickness of a layer via the hypsometric equation.

This thickness calculation uses the pressure and temperature profiles (and optionally mixing ratio) via the hypsometric equation with virtual temperature adjustment.

\[Z_2 - Z_1 = -\frac{R_d}{g} \int_{p_1}^{p_2} T_v d\ln p,\]

Which is based off of Equation 3.24 in [Hobbs2006].

This assumes a hydrostatic atmosphere. Layer bottom and depth specified in pressure.

  • pressure (pint.Quantity) – Atmospheric pressure profile

  • temperature (pint.Quantity) – Atmospheric temperature profile

  • mixing_ratio (pint.Quantity, optional) – Profile of dimensionless mass mixing ratio. If none is given, virtual temperature is simply set to be the given temperature.

  • molecular_weight_ratio (pint.Quantity or float, 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. (\(\epsilon\approx0.622\))

  • bottom (pint.Quantity, optional) – The bottom of the layer in pressure. Defaults to the first observation.

  • depth (pint.Quantity, optional) – The depth of the layer in hPa. Defaults to the full profile if bottom is not given, and 100 hPa if bottom is given.


pint.Quantity – The thickness of the layer in meters


Only functions on 1D profiles (not higher-dimension vertical cross sections or grids). Since this function returns scalar values when given a profile, this will return Pint Quantities even when given xarray DataArray profiles.

Changed in version 1.0: Renamed mixing parameter to mixing_ratio