nakametpy.thermo module

nakametpy.thermo.density(pressure, temperature, mixing_ratio, molecular_weight_ratio=0.622)

Calculate density.

This calculation must be given an air parcel’s pressure, temperature, and mixing ratio. The implementation uses the formula outlined in [Hobbs2006] pg.67.

Parameters

• pressure (numpy.ndarray) – Total atmospheric pressure [Pa]

• temperature (numpy.ndarray) – air temperature [K]

• mixing_ratio (numpy.ndarray) – dimensionless mass mixing ratio

• molecular_weight_ratio (numpy.ndarray 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. (\(\varepsilon\approx0.622\)).

Returns

The corresponding density of the parcel

Return type

numpy.ndarray

Note

\[\rho = \frac{p}{R_dT_v}\]

nakametpy.thermo.dewpoint(e)

Calculate the ambient dewpoint given the vapor pressure.

Parameters

e (numpy.ndarray) – Water vapor partial pressure [Pa]

Returns

dewpoint temperature

Return type

numpy.ndarray

See also

dewpoint_from_relative_humidity, saturation_vapor_pressure, vapor_pressure

Note

This function inverts the [Bolton1980] formula for saturation vapor pressure to instead calculate the temperature. This yield the following formula for dewpoint in degrees Celsius:

\[T = \frac{243.5 \log(e / 6.112)}{17.67 - \log(e / 6.112)}\]

nakametpy.thermo.dewpoint_from_relative_humidity(temperature, rh)

Calculate the ambient dewpoint given air temperature and relative humidity.

Parameters

• temperature (numpy.ndarray) – air temperature [K]

• rh (numpy.ndarray) – relative humidity expressed as a ratio in the range 0 < rh <= 1

Returns

The dewpoint temperature

Return type

numpy.ndarray

See also

dewpoint, saturation_vapor_pressure

nakametpy.thermo.dewpoint_from_specific_humidity(pressure, temperature, specific_humidity)

Calculate the dewpoint from specific humidity, temperature, and pressure.

Parameters

• pressure (numpy.ndarray) – Total atmospheric pressure [Pa]

• temperature (numpy.ndarray) – Air temperature [K]

• specific_humidity (numpy.ndarray) – Specific humidity of air

Returns

Dew point temperature

Return type

numpy.ndarray

Changed in version 1.0: Changed signature from (specific_humidity, temperature, pressure)

See also

relative_humidity_from_mixing_ratio, dewpoint_from_relative_humidity

nakametpy.thermo.equivalent_potential_temperature(pressure, temperature, dewpoint)

Calculate equivalent potential temperature.

This calculation must be given an air parcel’s pressure, temperature, and dewpoint. The implementation uses the formula outlined in [Bolton1980]:

First, the LCL temperature is calculated:

\[T_{L}=\frac{1}{\frac{1}{T_{D}-56}+\frac{ln(T_{K}/T_{D})}{800}}+56\]

Which is then used to calculate the potential temperature at the LCL:

\[\theta_{DL}=T_{K}\left(\frac{1000}{p-e}\right)^\kappa \left(\frac{T_{K}}{T_{L}}\right)^{0.28r}\]

Both of these are used to calculate the final equivalent potential temperature:

\[\theta_{E}=\theta_{DL}\exp\left[\left(\frac{3036.}{T_{L}} -1.78\right)\times r(1+0.448r)\right]\]

Parameters

• pressure (numpy.ndarray) – Total atmospheric pressure [Pa]

• temperature (numpy.ndarray) – Temperature of parcel [K]

• dewpoint (numpy.ndarray) – Dewpoint of parcel [K]

Returns

The equivalent potential temperature of the parcel

Return type

numpy.ndarray

Note

[Bolton1980] formula for Theta-e is used, since according to [DaviesJones2009] it is the most accurate non-iterative formulation available.

nakametpy.thermo.exner_function(pressure, reference_pressure=100000)

Calculate the Exner function.

\[\Pi = \left( \frac{p}{p_0} \right)^\kappa\]

This can be used to calculate potential temperature from temperature (and visa-versa), since

\[\Pi = \frac{T}{\theta}\]

Parameters

• pressure (numpy.ndarray) – total atmospheric pressure [Pa]

• reference_pressure (numpy.ndarray, optional) – The reference pressure against which to calculate the Exner function, defaults to metpy.constants.P0

Returns

The value of the Exner function at the given pressure

Return type

numpy.ndarray

See also

potential_temperature, temperature_from_potential_temperature

nakametpy.thermo.k_index_2d(t850, t700, t500, rh850, rh700)

相対湿度、気温(およびリファレンスのための気圧)からK指数を計算する。

Parameters

• pressure (numpy.ndarray) – Pressure level value [Pa]

• temperature (numpy.ndarray) – Air temperature [K]

• rh (numpy.ndarray) – Dimensionless relative humidity

Returns

K Index in Kelvin

Return type

numpy.ndarray

Note

Formula based on that from [George1960]

\[KI = T_{850} - T_{500} + Td_{850} - \left(T_{700} - Td_{700}\right)\]

• \(KI\) is K index

• \(T\) is temperature

• \(Td\) is dew-point temperature

Subscript means its pressure level

nakametpy.thermo.k_index_3d(pressure, temperature, rh)

相対湿度、気温(およびリファレンスのための気圧)からK指数を計算する。

Parameters

• pressure (numpy.ndarray) – Pressure level value [Pa]

• temperature (numpy.ndarray) – Air temperature [K]

• rh (numpy.ndarray) – Dimensionless relative humidity [0<=rh<=1]

Returns

K index

Return type

numpy.ndarray

Note

Formula based on that from [George1960]

\[KI = T_{850} - T_{500} + Td_{850} - \left(T_{700} - Td_{700}\right)\]

• \(KI\) is K index

• \(T\) is temperature

• \(Td\) is dew-point temperature

Subscript means its pressure level

nakametpy.thermo.mixing_ratio(part_press, tot_press, molecular_weight_ratio=0.622)

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

• part_press (numpy.ndarray) – Partial pressure of the constituent gas [Pa]

• tot_press (numpy.ndarray) – Total air pressure Pa

• molecular_weight_ratio (numpy.ndarray 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 (\(\varepsilon\approx0.622\)). 水の分子量と空気の平均の分子量の比=18/28.8

Returns

The (mass) mixing ratio, dimensionless (e.g. Kg/Kg or g/g)

Return type

numpy.ndarray

Note

This function is a straightforward implementation of the equation given in many places, such as [Hobbs1977] pg.73:

\[r = \varepsilon \frac{e}{p - e}\]

See also

saturation_mixing_ratio, vapor_pressure

nakametpy.thermo.mixing_ratio_from_relative_humidity(relative_humidity, temperature, pressure)

Calculate the mixing ratio from relative humidity, temperature, and pressure.

Parameters

• relative_humidity (numpy.ndarray) – Relative Humidity [0<=rh<=1] 相対湿度 値は(0, 1]である必要がある

• temperature (numpy.ndarray) – Air temperature [K] 気温

• pressure (numpy.ndarray) – Total atmospheric pressure [Pa] 全圧

Returns

Dimensionless mixing ratio

Return type

numpy.ndarray

Note

Formula adapted from [Hobbs1977] pg. 74.

\[w = (RH)(w_s)\]

• \(w\) is mixing ratio

• \(RH\) is relative humidity as a unitless ratio

• \(w_s\) is the saturation mixing ratio

See also

relative_humidity_from_mixing_ratio, saturation_mixing_ratio

nakametpy.thermo.mixing_ratio_from_specific_humidity(specific_humidity)

Calculate the mixing ratio from specific humidity.

Parameters

specific_humidity (numpy.ndarray) – Specific humidity of air

Returns

Mixing ratio

Return type

numpy.ndarray

Note

Formula from [Salby1996] pg. 118.

\[w = \frac{q}{1-q}\]

• \(w\) is mixing ratio

• \(q\) is the specific humidity

See also

mixing_ratio, specific_humidity_from_mixing_ratio

nakametpy.thermo.potential_temperature(pressure, temperature)

Calculate the potential temperature.

Uses the Poisson equation to calculation the potential temperature given pressure and temperature.

Parameters

• pressure (numpy.ndarray) – total atmospheric pressure [Pa]

• temperature (numpy.ndarray) – air temperature [K]

Returns

The potential temperature corresponding to the temperature and pressure.

Return type

numpy.ndarray

See also

dry_lapse

Note

Formula:

\[\Theta = T (P_0 / P)^\kappa\]

nakametpy.thermo.relative_humidity_from_dewpoint(temperature, dewpt)

Calculate the relative humidity.

Uses temperature and dewpoint in celsius to calculate relative humidity using the ratio of vapor pressure to saturation vapor pressures.

Parameters

• temperature (numpy.ndarray) – air temperature [K]

• dewpoint (numpy.ndarray) – dewpoint temperature [K]

Returns

relative humidity

Return type

numpy.ndarray

See also

saturation_vapor_pressure

nakametpy.thermo.relative_humidity_from_mixing_ratio(pressure, temperature, mixing_ratio)

Calculate the relative humidity from mixing ratio, temperature, and pressure.

Parameters

• pressure (numpy.ndarray) – Total atmospheric pressure [Pa]

• temperature (numpy.ndarray) – Air temperature [K]

• mixing_ratio (numpy.ndarray) – Dimensionless mass mixing ratio

Returns

Relative humidity

Return type

numpy.ndarray

Note

Formula based on that from [Hobbs1977] pg. 74.

\[RH = \frac{w}{w_s}\]

• \(relative_humidity\) is relative humidity as a unitless ratio

• \(w\) is mixing ratio

• \(w_s\) is the saturation mixing ratio

See also

mixing_ratio_from_relative_humidity, saturation_mixing_ratio

nakametpy.thermo.relative_humidity_from_specific_humidity(pressure, temperature, specific_humidity)

Calculate the relative humidity from specific humidity, temperature, and pressure.

Parameters

• pressure (numpy.ndarray) – Total atmospheric pressure [Pa]

• temperature (numpy.ndarray) – Air temperature [K]

• specific_humidity (numpy.ndarray) – Specific humidity of air

Returns

Relative humidity

Return type

numpy.ndarray

Note

Formula based on that from [Hobbs1977] pg. 74. and [Salby1996] pg. 118.

\[RH = \frac{q}{(1-q)w_s}\]

• \(relative_humidity\) is relative humidity as a unitless ratio

• \(q\) is specific humidity

• \(w_s\) is the saturation mixing ratio

See also

relative_humidity_from_mixing_ratio

nakametpy.thermo.saturation_mixing_ratio(tot_press, temperature)

Calculate the saturation mixing ratio of water vapor.

This calculation is given total pressure and the temperature. The implementation uses the formula outlined in [Hobbs1977] pg.73.

Parameters

• tot_press (numpy.ndarray) – Total atmospheric pressure [Pa]

• temperature (numpy.ndarray) – air temperature [K]

Returns

The saturation mixing ratio, dimensionless

Return type

numpy.ndarray

nakametpy.thermo.saturation_vapor_pressure(temperature)

Calculate the saturation water vapor (partial) pressure.

Parameters

temperature (numpy.ndarray) – air temperature [K]

Returns

The saturation water vapor (partial) pressure

Return type

numpy.ndarray

See also

vapor_pressure, dewpoint

Note

Instead of temperature, dewpoint may be used in order to calculate the actual (ambient) water vapor (partial) pressure.

The formula used is that from [Bolton1980] for T in degrees Celsius:

\[6.112 e^\frac{17.67T}{T + 243.5}\]

下記の式は既にケルビンに直してある

nakametpy.thermo.showalter_stability_index(t850, t500, p850, p500)

500hPaにおける気温から850 hPaから500 hPaに断熱変化させた際の気温を引いた指数。 この計算では乾燥断熱減率のみを考慮しているため、湿潤断熱変化も含めたSSIを 求める方法が必要である。

\[SSI = T_{500} - T_{850\rightarrow 500}^*\]

nakametpy.thermo.specific_humidity_from_mixing_ratio(mixing_ratio)

Calculate the specific humidity from the mixing ratio.

Parameters

mixing_ratio (numpy.ndarray) – mixing ratio

Returns

Specific humidity

Return type

numpy.ndarray

Note

Formula from [Salby1996] pg. 118.

\[q = \frac{w}{1+w}\]

• \(w\) is mixing ratio

• \(q\) is the specific humidity

See also

mixing_ratio, mixing_ratio_from_specific_humidity

nakametpy.thermo.virtual_temperature(temperature, mixing_ratio, molecular_weight_ratio=0.622)

Calculate virtual temperature.

This calculation must be given an air parcel’s temperature and mixing ratio. The implementation uses the formula outlined in [Hobbs2006] pg.80.

Parameters

• temperature (numpy.ndarray) – air temperature [K]

• mixing_ratio (numpy.ndarray) – dimensionless mass mixing ratio

• molecular_weight_ratio (numpy.ndarray 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. (\(\varepsilon\approx0.622\)).

Returns

The corresponding virtual temperature of the parcel

Return type

numpy.ndarray

Note

\[T_v = T \frac{\text{w} + \varepsilon}{\varepsilon\,(1 + \text{w})}\]