# Atmospheric properties (fluids.atmosphere)¶

This module contains models of earth’s atmosphere. Models are emperical and based on extensive research, primarily by NASA.

For reporting bugs, adding feature requests, or submitting pull requests, please use the GitHub issue tracker or contact the author at Caleb.Andrew.Bell@gmail.com.

## Atmospheres¶

class fluids.atmosphere.ATMOSPHERE_1976(Z, dT=0)[source]

Bases: object

US Standard Atmosphere 1976 class, which calculates T, P, rho, v_sonic, mu, k, and g as a function of altitude above sea level. Designed to provide reasonable results up to an elevation of 86,000 m (0.4 Pa). The model is also valid under sea level, to -610 meters.

Parameters: Z : float Elevation, [m] dT : float, optional Temperature difference from standard conditions used in determining the properties of the atmosphere, [K]

Notes

Up to 32 km, the International Standard Atmosphere (ISA) and World Meteorological Organization (WMO) standard atmosphere are identical.

This is a revision of the US 1962 atmosphere.

References

 [1] NOAA, NASA, and USAF. “U.S. Standard Atmosphere, 1976” October 15, 1976. http://ntrs.nasa.gov/search.jsp?R=19770009539.
 [2] “ISO 2533:1975 - Standard Atmosphere.” ISO. http://www.iso.org/iso/catalogue_detail.htm?csnumber=7472.
 [3] Yager, Robert J. “Calculating Atmospheric Conditions (Temperature, Pressure, Air Density, and Speed of Sound) Using C++,” June 2013. http://www.dtic.mil/cgi-bin/GetTRDoc?AD=ADA588839

Examples

>>> five_km = ATMOSPHERE_1976(5000)
>>> five_km.P, five_km.rho, five_km.mu
(54048.28614576141, 0.7364284207799743, 1.628248135362207e-05)
>>> five_km.k, five_km.g, five_km.v_sonic
(0.02273190295142526, 9.791241076982665, 320.5455196704035)

Attributes: T : float Temperature of atmosphere at specified conditions, [K] P : float Pressure of atmosphere at specified conditions, [Pa] rho : float Mass density of atmosphere at specified conditions [kg/m^3] H : float Geopotential height, [m] g : float Acceleration due to gravity, [m/s^2] mu : float Viscosity of atmosphere at specified conditions, [Pa*s] k : float Thermal conductivity of atmosphere at specified conditions, [W/m/K] v_sonic : float Speed of sound of atmosphere at specified conditions, [m/s]

Methods

 density(T, P) Method defined in the US Standard Atmosphere 1976 for calculating density of air as a function of T and P. gravity(Z) Method defined in the US Standard Atmosphere 1976 for calculating the gravitational acceleration above earth as a function of elevation only. pressure_integral(T1, P1, dH) Method to compute an integral of the pressure differential of an elevation difference with a base elevation defined by temperature T1 and pressure P1. sonic_velocity(T) Method defined in the US Standard Atmosphere 1976 for calculating the speed of sound in air as a function of T only. thermal_conductivity(T) Method defined in the US Standard Atmosphere 1976 for calculating thermal conductivity of air as a function of T only. viscosity(T) Method defined in the US Standard Atmosphere 1976 for calculating viscosity of air as a function of T only.
R = 8314.32
static density(T, P)[source]

Method defined in the US Standard Atmosphere 1976 for calculating density of air as a function of T and P. MW is defined as 28.9644 g/mol, and R as 8314.32 J/kmol/K

$\rho_g = \frac{P\cdot MW}{T\cdot R\cdot 1000}$
Parameters: T : float Temperature, [K] P : float Pressure, [Pa] rho : float Mass density, [kg/m^3]
static gravity(Z)[source]

Method defined in the US Standard Atmosphere 1976 for calculating the gravitational acceleration above earth as a function of elevation only.

$g = g_0\left(\frac{r_0}{r_0+Z}\right)^2$
Parameters: Z : float Elevation above sea level, [m] g : float Acceleration due to gravity, [m/s^2]
static pressure_integral(T1, P1, dH)[source]

Method to compute an integral of the pressure differential of an elevation difference with a base elevation defined by temperature T1 and pressure P1. This is similar to subtracting the pressures at two different elevations, except it allows for local conditions (temperature and pressure) to be taken into account. This is useful for e.x. evaluating the pressure difference between the top and bottom of a natural draft cooling tower.

Parameters: T1 : float Temperature at the lower elevation condition, [K] P1 : float Pressure at the lower elevation condition, [Pa] dH : float Elevation difference for which to evaluate the pressure difference, [m] delta_P : float Pressure difference between the elevations, [Pa]
static sonic_velocity(T)[source]

Method defined in the US Standard Atmosphere 1976 for calculating the speed of sound in air as a function of T only.

$c = \left(\frac{\gamma R T}{MW}\right)^{0.5}$
Parameters: T : float Temperature, [K] c : float Speed of sound, [m/s]
static thermal_conductivity(T)[source]

Method defined in the US Standard Atmosphere 1976 for calculating thermal conductivity of air as a function of T only.

$k_g = \frac{2.64638\times10^{-3}T^{1.5}} {T + 245.4\cdot 10^{-12./T}}$
Parameters: T : float Temperature, [K] kg : float Thermal conductivity, [W/m/K]
static viscosity(T)[source]

Method defined in the US Standard Atmosphere 1976 for calculating viscosity of air as a function of T only.

$\mu_g = \frac{1.458\times10^{-6}T^{1.5}}{T+110.4}$
Parameters: T : float Temperature, [K] mug : float Viscosity, [Pa*s]
class fluids.atmosphere.ATMOSPHERE_NRLMSISE00(Z, latitude=0, longitude=0, day=0, seconds=0, f107=150.0, f107_avg=150.0, geomagnetic_disturbance_indices=None)[source]

Bases: object

NRLMSISE 00 model for calculating temperature and density of gases in the atmosphere, from ground level to 1000 km, as a function of time of year, longitude and latitude, solar activity and earth’s geomagnetic disturbance.

NRLMSISE stands for the US Naval Research Laboratory Mass Spectrometer and Incoherent Scatter Radar Exosphere model, released in 2001; see [1] for details.

Parameters: Z : float Elevation, [m] latitude : float, optional Latitude, between -90 and 90 [degrees] longitude : float, optional Longitude, between -180 and 180 or 0 and 360, [degrees] day : float, optional Day of year, 0-366 [day] seconds : float, optional Seconds since start of day, in UT1 time; using UTC provides no loss in accuracy [s] f107 : float, optional Daily average 10.7 cm solar flux measurement of the strength of solar emissions on the 100 MHz band centered on 2800 MHz, averaged hourly; in sfu units, which are multiples of 10^-22 W/m^2/Hz; use 150 as a default [10^-22 W/m^2/Hz] f107_avg : float, optional 81-day sfu average; centered on specified day if possible, otherwise use the previous days [10^-22 W/m^2/Hz] geomagnetic_disturbance_indices : list of float, optional List of the 7 following Ap indexes also known as planetary magnetic indexes. Has a negligible effect on the calculation. 4 is the default value often used for each of these values. Average daily Ap. 3-hour average Ap centered on the current time. 3-hour average Ap before the current time. 6-hour average Ap before the current time. 9-hour average Ap before the current time. Average Ap from 12 to 33 hours before the current time, based on eight 3-hour average Ap values. Average Ap from 36 to 57 hours before the current time, based on eight 3-hour average Ap values.

Notes

No full description has been published of this model; it has been defined by its implementation only. It was written in FORTRAN, and is accessible at ftp://hanna.ccmc.gsfc.nasa.gov/pub/modelweb/atmospheric/msis/nrlmsise00/

A C port of the model by Dominik Brodowskihas become popular, and is available on his website: http://www.brodo.de/space/nrlmsise/.

In 2013 Joshua Milas ported the C port to Python. This is an interface to his excellent port. It is a 1000-sloc model, and has been rigorously tested against the C version, and the online calculation tool available at [3] for parametric inputs of latitude, longitude, altitude, time of day and day of year.

This model is based on measurements other than gravity; it does not provide a calculation method for g. It does not provide transport properties.

References

 [1] (1, 2, 3) Picone, J. M., A. E. Hedin, D. P. Drob, and A. C. Aikin. “NRLMSISE-00 Empirical Model of the Atmosphere: Statistical Comparisons and Scientific Issues.” Journal of Geophysical Research: Space Physics 107, no. A12 (December 1, 2002): 1468. doi:10.1029/2002JA009430.
 [2] Tapping, K. F. “The 10.7 Cm Solar Radio Flux (F10.7).” Space Weather 11, no. 7 (July 1, 2013): 394-406. doi:10.1002/swe.20064.
 [3] (1, 2) Natalia Papitashvili. “NRLMSISE-00 Atmosphere Model.” Accessed November 27, 2016. http://ccmc.gsfc.nasa.gov/modelweb/models/nrlmsise00.php.

Examples

>>> atmosphere = ATMOSPHERE_NRLMSISE00(1E3, 45, 45, 150)
>>> atmosphere.T, atmosphere.rho
(285.54408606237405, 1.1019062026405517)

Attributes: rho : float Mass density [kg/m^3] T : float Temperature, [K] P : float Pressure, calculated with ideal gas law [Pa] He_density : float Density of helium atoms [count/m^3] O_density : float Density of monatomic oxygen [count/m^3] N2_density : float Density of nitrogen molecules [count/m^3] O2_density : float Density of oxygen molecules [count/m^3] Ar_density : float Density of Argon atoms [count/m^3] H_density : float Density of hydrogen atoms [count/m^3] N_density : float Density of monatomic nitrogen [count/m^3] O_anomalous_density : float Density of anomalous oxygen; see [1] for details [count/m^3] particle_density : float Total density of molecules [count/m^3] components : list[str] List of species making up the atmosphere [-] zs : list[float] Mole fractions of each molecule in the atmosphere, in order of components [-]
MWs = [28.0134, 31.9988, 39.948, 4.002602, 15.9994, 1.00794, 14.0067]
atrrs = ['N2_density', 'O2_density', 'Ar_density', 'He_density', 'O_density', 'H_density', 'N_density']
components = ['N2', 'O2', 'Ar', 'He', 'O', 'H', 'N']
fluids.atmosphere.airmass(func, angle, H_max=86400.0, R_planet=6371229.0, RI=1.000276)[source]

Calculates mass of air per square meter in the atmosphere using a provided atmospheric model. The lowest air mass is calculated straight up; as the angle is lowered to nearer and nearer the horizon, the air mass increases, and can approach 40x or more the minimum airmass.

$m(\gamma) = \int_0^\infty \rho \left\{1 - \left[1 + 2(\text{RI}-1) (1-\rho/\rho_0)\right] \left[\frac{\cos \gamma}{(1+h/R)}\right]^2\right\}^{-1/2} dH$
Parameters: func : float Function which returns the density of the atmosphere as a function of elevation angle : float Degrees above the horizon (90 = straight up), [degrees] H_max : float, optional Maximum height to compute the integration up to before the contribution of density becomes negligible, [m] R_planet : float, optional The radius of the planet for which the integration is being performed, [m] RI : float, optional The refractive index of the atmosphere (air on earth at 0.7 um as default) assumed a constant, [-] m : float Mass of air per square meter in the atmosphere, [kg/m^2]

Notes

Numerical integration via SciPy’s quad is used to perform the calculation.

References

 [1] Kasten, Fritz, and Andrew T. Young. “Revised Optical Air Mass Tables and Approximation Formula.” Applied Optics 28, no. 22 (November 15, 1989): 4735-38. https://doi.org/10.1364/AO.28.004735.

Examples

>>> airmass(lambda Z : ATMOSPHERE_1976(Z).rho, 90)
10356.127665863998


## Wind Models (requires Fortran compiler!)¶

fluids.atmosphere.hwm93(Z, latitude=0, longitude=0, day=0, seconds=0, f107=150.0, f107_avg=150.0, geomagnetic_disturbance_index=4)[source]

Horizontal Wind Model 1993, for calculating wind velocity in the atmosphere as a function of time of year, longitude and latitude, solar activity and earth’s geomagnetic disturbance.

The model is described across the publications [1], [2], and [3].

Parameters: Z : float Elevation, [m] latitude : float, optional Latitude, between -90 and 90 [degrees] longitude : float, optional Longitude, between -180 and 180 or 0 and 360, [degrees] day : float, optional Day of year, 0-366 [day] seconds : float, optional Seconds since start of day, in UT1 time; using UTC provides no loss in accuracy [s] f107 : float, optional Daily average 10.7 cm solar flux measurement of the strength of solar emissions on the 100 MHz band centered on 2800 MHz, averaged hourly; in sfu units, which are multiples of 10^-22 W/m^2/Hz; use 150 as a default [W/m^2/Hz] f107_avg : float, optional 81-day sfu average; centered on specified day if possible, otherwise use the previous days [W/m^2/Hz] geomagnetic_disturbance_index : float, optional Average daily Ap or also known as planetary magnetic index. v_north : float Wind velocity, meridional (Northward) [m/s] v_east : float Wind velocity, zonal (Eastward) [m/s]

Notes

No full description has been published of this model; it has been defined by its implementation only. It was written in FORTRAN, and is accessible at ftp://hanna.ccmc.gsfc.nasa.gov/pub/modelweb/atmospheric/hwm93/.

F2PY auto-compilation support is not yet currently supported. To compile this file, run the following command in a shell after navigating to $FLUIDSPATH/fluids/optional/. This should generate the file hwm93.so in that directory. f2py -c hwm93.pyf hwm93.for –f77flags=”-std=legacy” If the module is not compiled, an import error will be raised. References  [1] (1, 2) Hedin, A. E., N. W. Spencer, and T. L. Killeen. “Empirical Global Model of Upper Thermosphere Winds Based on Atmosphere and Dynamics Explorer Satellite Data.” Journal of Geophysical Research: Space Physics 93, no. A9 (September 1, 1988): 9959-78. doi:10.1029/JA093iA09p09959.  [2] (1, 2) Hedin, A. E., M. A. Biondi, R. G. Burnside, G. Hernandez, R. M. Johnson, T. L. Killeen, C. Mazaudier, et al. “Revised Global Model of Thermosphere Winds Using Satellite and Ground-Based Observations.” Journal of Geophysical Research: Space Physics 96, no. A5 (May 1, 1991): 7657-88. doi:10.1029/91JA00251.  [3] (1, 2) Hedin, A. E., E. L. Fleming, A. H. Manson, F. J. Schmidlin, S. K. Avery, R. R. Clark, S. J. Franke, et al. “Empirical Wind Model for the Upper, Middle and Lower Atmosphere.” Journal of Atmospheric and Terrestrial Physics 58, no. 13 (September 1996): 1421-47. doi:10.1016/0021-9169(95)00122-0. Examples >>> hwm93(5E5, 45, 50, 365) (-73.00312042236328, 0.1485661268234253)  fluids.atmosphere.hwm14(Z, latitude=0, longitude=0, day=0, seconds=0, geomagnetic_disturbance_index=4)[source] Horizontal Wind Model 2014, for calculating wind velocity in the atmosphere as a function of time of year, longitude and latitude, and earth’s geomagnetic disturbance. The model is described in [1]. The model no longer accounts for solar flux. Parameters: Z : float Elevation, [m] latitude : float, optional Latitude, between -90 and 90 [degrees] longitude : float, optional Longitude, between -180 and 180 or 0 and 360, [degrees] day : float, optional Day of year, 0-366 [day] seconds : float, optional Seconds since start of day, in UT1 time; using UTC provides no loss in accuracy [s] geomagnetic_disturbance_index : float, optional Average daily Ap or also known as planetary magnetic index. v_north : float Wind velocity, meridional (Northward) [m/s] v_east : float Wind velocity, zonal (Eastward) [m/s] Notes No full description has been published of this model; it has been defined by its implementation only. It was written in FORTRAN, and is accessible at http://onlinelibrary.wiley.com/store/10.1002/2014EA000089/asset/supinfo/ess224-sup-0002-supinfo.tgz?v=1&s=2a957ba70b7cf9dd0612d9430076297c3634ea75. F2PY auto-compilation support is not yet currently supported. To compile this file, run the following command in a shell after navigating to$FLUIDSPATH/fluids/optional/. This should generate the file hwm14.so in that directory.

f2py -c hwm14.pyf hwm14.f90

The fortran .pyf signature file is included with this project, but it can also be re-created with the command:

f2py -m hwm14 -h hwm14.pyf hwm14.f90

If the module is not compiled, an import error will be raised.

No patches were necessary to either the generated pyf or hwm14.f90 file, as the authors of [1] have made it F2PY compatible.

Developed using 73 million data points taken by 44 instruments over 60 years.

References

 [1] (1, 2, 3) Drob, Douglas P., John T. Emmert, John W. Meriwether, Jonathan J. Makela, Eelco Doornbos, Mark Conde, Gonzalo Hernandez, et al. “An Update to the Horizontal Wind Model (HWM): The Quiet Time Thermosphere.” Earth and Space Science 2, no. 7 (July 1, 2015): 2014EA000089. doi:10.1002/2014EA000089.

Examples

>>> hwm14(5E5, 45, 50, 365)
(-38.64341354370117, 12.871272087097168)