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.

pressure: numpy.ndarray

Total atmospheric pressure [Pa]

temperature: numpy.ndarray

air temperature [K]

mixing_rationumpy.ndarray

dimensionless mass mixing ratio

molecular_weight_rationumpy.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. (\(\varepsilon\approx0.622\)).

numpy.ndarray

The corresponding density of the parcel

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

nakametpy.thermo.dewpoint(e)

Calculate the ambient dewpoint given the vapor pressure.

enumpy.ndarray

Water vapor partial pressure [Pa]

numpy.ndarray

dewpoint temperature

dewpoint_from_relative_humidity, saturation_vapor_pressure, vapor_pressure

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.

temperaturenumpy.ndarray

air temperature [K]

rhnumpy.ndarray

relative humidity expressed as a ratio in the range 0 < rh <= 1

numpy.ndarray

The dewpoint temperature

dewpoint, saturation_vapor_pressure

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

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

pressure: numpy.ndarray

Total atmospheric pressure [Pa]

temperature: numpy.ndarray

Air temperature [K]

specific_humidity: numpy.ndarray

Specific humidity of air

numpy.ndarray

Dew point temperature

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

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:

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

pressure: numpy.ndarray

Total atmospheric pressure [Pa]

temperature: numpy.ndarray

Temperature of parcel [K]

dewpoint: numpy.ndarray

Dewpoint of parcel [K]

numpy.ndarray

The equivalent potential temperature of the parcel

[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

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

pressurenumpy.ndarray

total atmospheric pressure [Pa]

reference_pressurenumpy.ndarray, optional

The reference pressure against which to calculate the Exner function, defaults to metpy.constants.P0

numpy.ndarray

The value of the Exner function at the given pressure

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.

pressure: numpy.ndarray

Pressure level value [Pa]

temperature: numpy.ndarray

Air temperature [K]

rh: numpy.ndarray

Dimensionless relative humidity

numpy.ndarray

K Index in Kelvin

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.

pressure: numpy.ndarray

Pressure level value [Pa]

temperature: numpy.ndarray

Air temperature [K]

rh: numpy.ndarray

Dimensionless relative humidity [0<=rh<=1]

numpy.ndarray

K index

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.

part_pressnumpy.ndarray

Partial pressure of the constituent gas [Pa]

tot_pressnumpy.ndarray

Total air pressure Pa

molecular_weight_rationumpy.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

numpy.ndarray

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

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

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

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.

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

numpy.ndarray

Dimensionless mixing ratio

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

relative_humidity_from_mixing_ratio, saturation_mixing_ratio

nakametpy.thermo.mixing_ratio_from_specific_humidity(specific_humidity)

Calculate the mixing ratio from specific humidity.

specific_humidity: numpy.ndarray

Specific humidity of air

numpy.ndarray

Mixing ratio

Formula from [Salby1996] pg. 118.

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

• \(w\) is mixing ratio

• \(q\) is the specific humidity

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.

pressurenumpy.ndarray

total atmospheric pressure [Pa]

temperaturenumpy.ndarray

air temperature [K]

numpy.ndarray

The potential temperature corresponding to the temperature and pressure.

dry_lapse

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.

temperaturenumpy.ndarray

air temperature [K]

dewpointnumpy.ndarray

dewpoint temperature [K]

numpy.ndarray

relative humidity

saturation_vapor_pressure

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

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

pressure: numpy.ndarray

Total atmospheric pressure [Pa]

temperature: numpy.ndarray

Air temperature [K]

mixing_ratio: numpy.ndarray

Dimensionless mass mixing ratio

numpy.ndarray

Relative humidity

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

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.

pressure: numpy.ndarray

Total atmospheric pressure [Pa]

temperature: numpy.ndarray

Air temperature [K]

specific_humidity: numpy.ndarray

Specific humidity of air

numpy.ndarray

Relative humidity

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

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.

tot_press: numpy.ndarray

Total atmospheric pressure [Pa]

temperature: numpy.ndarray

air temperature [K]

numpy.ndarray

The saturation mixing ratio, dimensionless

nakametpy.thermo.saturation_vapor_pressure(temperature)

Calculate the saturation water vapor (partial) pressure.

temperaturenumpy.ndarray

air temperature [K]

numpy.ndarray

The saturation water vapor (partial) pressure

vapor_pressure, dewpoint

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.

mixing_ratio: numpy.ndarray

mixing ratio

numpy.ndarray

Specific humidity

Formula from [Salby1996] pg. 118.

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

• \(w\) is mixing ratio

• \(q\) is the specific humidity

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.

temperature: numpy.ndarray

air temperature [K]

mixing_rationumpy.ndarray

dimensionless mass mixing ratio

molecular_weight_rationumpy.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. (\(\varepsilon\approx0.622\)).

numpy.ndarray

The corresponding virtual temperature of the parcel

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