thickness_hydrostatic#

metpy.calc.thickness_hydrostatic(pressure, temperature, mixing_ratio=None, molecular_weight_ratio=0.6219569100577033, 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.

Parameters:
• 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.

Returns:

pint.Quantity – The thickness of the layer in meters

Examples

>>> import metpy.calc as mpcalc
>>> from metpy.units import units
>>> temperature = [278, 275, 270] * units.kelvin
>>> pressure = [950, 925, 900] * units.millibar
>>> mpcalc.thickness_hydrostatic(pressure, temperature)
<Quantity(434.376889, 'meter')>

>>> bottom, depth = 950 * units.millibar, 25 * units.millibar
>>> mpcalc.thickness_hydrostatic(pressure, temperature, bottom=bottom, depth=depth)
<Quantity(215.835404, 'meter')>


To include the mixing ratio in the calculation:

>>> r = [0.005, 0.006, 0.002] * units.dimensionless
>>> mpcalc.thickness_hydrostatic(pressure, temperature, mixing_ratio=r,
...                              bottom=bottom, depth=depth)
<Quantity(216.552623, 'meter')>


Compute the 1000-500 hPa Thickness

>>> # pressure
>>> p = [1008., 1000., 950., 900., 850., 800., 750., 700., 650., 600.,
...      550., 500., 450., 400., 350., 300., 250., 200.,
...      175., 150., 125., 100., 80., 70., 60., 50.,
...      40., 30., 25., 20.] * units.hPa
>>> # temperature
>>> T = [29.3, 28.1, 23.5, 20.9, 18.4, 15.9, 13.1, 10.1, 6.7, 3.1,
...      -0.5, -4.5, -9.0, -14.8, -21.5, -29.7, -40.0, -52.4,
...      -59.2, -66.5, -74.1, -78.5, -76.0, -71.6, -66.7, -61.3,
...      -56.3, -51.7, -50.7, -47.5] * units.degC
>>> # specify a layer
>>> layer = (p <= 1000 * units.hPa) & (p >= 500 * units.hPa)
>>> # compute the hydrostatic thickness
>>> mpcalc.thickness_hydrostatic(p[layer], T[layer])
<Quantity(5755.94719, 'meter')>


Notes

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

Examples using metpy.calc.thickness_hydrostatic#

Advanced Sounding Plot with Complex Layout

Advanced Sounding Plot with Complex Layout

Hydrostatic Thickness

Hydrostatic Thickness

Sounding Calculation Examples

Sounding Calculation Examples