USSA1976#
The U.S. Standard Atmosphere 1976 model.
This package implements the atmosphere thermophysical model provided by the National Aeronautics and Space Administration technical report NASA-TM-X-74335 published in 1976 and entitled U.S. Standard Atmosphere, 1976.
Features#
Run the U.S. Standard Atmosphere 1976 model on your custom altitude grid
- Compute all 14 atmospheric variables of the model as a function of altitude:
air temperature
air pressure
number density (of individual species)
air number density
air density
air molar volume
air pressure scale height
air particles mean speed
air particles mean free path
air particles mean collision frequency
speed of sound in air
air dynamic viscosity
air kinematic viscosity
air thermal conductivity coefficient
Results stored in NetCDF format
Command-line interface
Python interface
Requirements#
Python 3.8+
Installation#
You can install USSA1976 via pip from PyPI:
$ pip install ussa1976
Usage#
For the Command-line interface, please see the Command-line Reference for details.
For the Python interface, refer to the User Guide.
Contributing#
Contributions are very welcome. To learn more, see the Contributor Guide.
License#
Distributed under the terms of the MIT license, USSA1976 is free and open source software.
Issues#
If you encounter any problems, please file an issue along with a detailed description.
Credits#
This project was generated from @cjolowicz’s Hypermodern Python Cookiecutter template.
Usage#
ussa1976#
Compute the U.S. Standard Atmosphere 1976.
ussa1976 [OPTIONS]
Options
- -z, --zstart <zstart>#
Start altitude [m]
- Default:
0.0
- -Z, --zstop <zstop>#
Stop altitude [m]
- Default:
1000000.0
- -n, --znum <znum>#
Number of altitude points
- Default:
1001
- -f, --filename <filename>#
Output file name
- Default:
ussa1976.nc
- --version#
Show the version and exit.
User Guide#
This page presents the Python interface of ussa1976
.
For details on how to use the command-line interface to ussa1976
, refer
to the usage page.
Getting started#
Compute the U.S. Standard Atmosphere 1976 model:
import ussa1976
ds = ussa1976.compute()
The output is a Dataset
object that tabulates the values of
the different atmospheric variables as a function of altitude.
By default, the U.S. Standard Atmosphere 1976 model is computed on a piece-wise linearly spaced altitude mesh, specified in the table below.
Altitude range |
Altitude step |
---|---|
\([0, 11]\) km |
\(50\) m |
\([11, 32]\) km |
\(100\) m |
\([32, 50]\) km |
\(200\) m |
\([50, 100]\) km |
\(500\) m |
\([100, 300]\) km |
\(1000\) m |
\([300, 500]\) km |
\(2000\) m |
\([500, 1000]\) km |
\(5000\) m |
Inspect the output data set#
You can easily access the values of the different computed variables for further manipulation.
For example, pressure values can be accessed with:
ds["p"].values
Please refer to the xarray documentation for more details.
Plot a variable#
Note
The matplotlib library must be installed for plotting.
Plotting variables is made very convenient with xarray.
For example, the code below plots the pressure as a function of altitude:
import matplotlib.pyplot as plt
plt.figure(dpi=100)
ds.p.plot(y="z", xscale="log")
plt.grid()
plt.show()
Please refer to the xarray documentation for more details.
Work with a custom altitude mesh#
You can compute the U.S. Standard Atmosphere 1976 model on any altitude mesh oy your liking as long as the altitude bounds are within \([0, 1000]\) km.
For example, you can compute the model on a regular altitude mesh between 0 kilometer and 100 kilometer with a 1-meter altitude step, with:
import numpy as np
ds = ussa1976.compute(z=np.arange(0.0, 100001.0, 1.0))
Note
Altitude units are meter.
Compute specific variables#
You might not be interested in computing all 14 variables of the U.S. Standard
Atmosphere 1976 model.
You can select only the variables that are relevant for your application using
the variables
parameters.
For example, to compute only the air temperature (t
), air pressure (p
),
air number density (n_tot
) and the species number density (n
), use:
ds = ussa1976.compute(variables=["t", "p", "n_tot", "n"])
The table below indicates what symbol is used for each variable.
Symbol |
Variable name |
---|---|
|
air temperature |
|
air pressure |
|
number density |
|
air number density |
|
air density |
|
air molar volume |
|
air pressure scale height |
|
air particles mean speed |
|
air particles mean free path |
|
air particles mean collision frequency |
|
speed of sound in air |
|
air dynamic viscosity |
|
air kinematic viscosity |
|
air thermal conductivity coefficient |
By default, all 14 variables are computed.
Reference#
constants
#
Constants module.
As much as possible, constants’ names are chosen to be as close as possible to the notations used in [NNU76].
Notes
Constants’ values are evaluated in the following set of units: * length: meter * time: second * mass: kilogram * temperature: kelvin * quantity of matter: mole
Note the following derived units: * 1 Pa = 1 kg * m^-1 * s^-2 * 1 Joule = 1 kg * m^2 * s^-2
- ussa1976.constants.A = {'Ar': 4.487e+20, 'H': 3.305e+21, 'He': 1.7e+21, 'O': 6.986e+20, 'O2': 4.863e+20}#
Thermal diffusion coefficients [m * s^-1].
- ussa1976.constants.ALPHA = {'Ar': 0.0, 'H': -0.25, 'He': -0.4, 'N2': 0.0, 'O': 0.0, 'O2': 0.0}#
Thermal diffusion constants above 86 km [dimensionless].
- ussa1976.constants.AR_7 = 1.3514e+18#
Argon number density at altitude
Z7
[m^-3].
- ussa1976.constants.B = {'Ar': 0.87, 'H': 0.5, 'He': 0.691, 'O': 0.75, 'O2': 0.75}#
Thermal diffusion constants [dimensionless].
- ussa1976.constants.BETA = 1458000.0#
\(\beta\) constant in eq. 51 of [NNU76] [kg * m^-1 * s^-1 * K^-0.5].
- ussa1976.constants.F = {'Ar': 0.00934, 'CH4': 2e-06, 'CO2': 0.000314, 'H2': 5e-07, 'He': 5.24e-06, 'Kr': 1.14e-06, 'N2': 0.78084, 'Ne': 1.818e-05, 'O2': 0.209476, 'Xe': 8.7e-08}#
Sea level volume fractions below 86 km [dimensionless].
- ussa1976.constants.G0 = 9.80665#
Sea level gravity [m / s^-2].
- ussa1976.constants.GAMMA = 1.4#
Ratio of specific heat of air at constant pressure to the specific heat of air at constant volume [dimensionless].
- ussa1976.constants.H: ndarray[Any, dtype[float64]] = array([ 0. , 11000. , 20000. , 32000. , 47000. , 51000. , 71000. , 84852.05])#
Geopotential altitudes of the layers’ boundaries (below 86 km) [m].
- ussa1976.constants.HE_7 = 758170000000000.0#
Helium number density at altitude
Z7
[m^-3].Notes
Assumes typo at page 13.
- ussa1976.constants.H_11 = 80000000000.0#
Hydrogen number density at altitude
Z7
[m^-3].
- ussa1976.constants.K = 1.380622e-23#
Boltzmann constant [J * K^-1].
- ussa1976.constants.K_7 = 120.0#
Eddy diffusion coefficients [m^2 * s^-1].
- ussa1976.constants.LK: ndarray[Any, dtype[float64]] = array([-0.0065, 0. , 0.001 , 0.0028, 0. , -0.0028, -0.002 ])#
Temperature gradients in the seven layers (below 86 km) [K * m^-1].
- ussa1976.constants.LK7 = 0.0#
Temperature gradient in the 8th layer [K * m^-1].
- ussa1976.constants.LK9 = 0.012#
Temperature gradient in the 10th layer [K * m^-1].
- ussa1976.constants.M = {'Ar': 0.039948, 'CH4': 0.01604303, 'CO2': 0.04400995, 'H': 0.00100797, 'H2': 0.00201594, 'He': 0.0040026, 'Kr': 0.0838, 'N2': 0.0280134, 'Ne': 0.020183, 'O': 0.01599939, 'O2': 0.0319988, 'Xe': 0.1313}#
Molar masses of the individual species [kg * mole^-1].
- ussa1976.constants.M0 = 0.028964425278793997#
Sea level mean air molar mass [kg * mole^-1].
- ussa1976.constants.N2_7 = 1.129794e+20#
Molecular nitrogen number density at altitude
Z7
[m^-3].
- ussa1976.constants.NA = 6.022169e+23#
Avogadro number [mole^-1].
- ussa1976.constants.O2_7 = 3.030898e+19#
Molecular oxygen number density at altitude
Z7
[m^-3].
- ussa1976.constants.O_7 = 8.6e+16#
Atomic oxygen number density at altitude
Z7
[m^-3].
- ussa1976.constants.P0 = 101325.0#
Pressure at sea level [Pa].
- ussa1976.constants.PHI = 720000000000.0#
Vertical air particles flux [m^2 * s^-1].
- ussa1976.constants.Q1 = {'Ar': 9.434079e-14, 'He': -2.457369e-13, 'O': -5.809644e-13, 'O2': 1.366212e-13}#
Vertical transport constants above 86 km [m^-3].
- ussa1976.constants.Q2 = {'Ar': 0.0, 'He': 0.0, 'O': -3.416248e-12, 'O2': 0.0}#
Vertical transport constants above 86 km [m^-3].
- ussa1976.constants.R = 8.31432#
Universal gas constant [J * K^-1 * mole^-1].
- ussa1976.constants.R0 = 6356766.0#
Effective Earth radius [m].
- ussa1976.constants.SIGMA = 3.65e-10#
Mean effective collision diameter [m].
- ussa1976.constants.T0 = 288.15#
Temperature at sea level [K].
- ussa1976.constants.T10 = 360.0#
Temperature at altitude
Z10
[K].
- ussa1976.constants.T11 = 999.2356#
Temperature at altitude
Z11
[K].
- ussa1976.constants.T7 = 186.8673#
Temperature at altitude
Z7
[K].
- ussa1976.constants.T9 = 240.0#
Temperature at altitude
Z9
[K].
- ussa1976.constants.TINF = 1000.0#
Exospheric temperature [K].
- ussa1976.constants.U1 = {'Ar': 86000.0, 'He': 86000.0, 'O': 56903.11, 'O2': 86000.0}#
Vertical transport constants above 86 km [m].
- ussa1976.constants.U2 = {'O': 97000.0}#
Vertical transport constants above 86 km [m].
- ussa1976.constants.W1 = {'Ar': 8.333333e-14, 'He': 6.666667e-13, 'O': 2.70624e-14, 'O2': 8.333333e-14}#
Vertical transport constants above 86 km [m^-3].
- ussa1976.constants.W2 = {'O': 5.008765e-13}#
Vertical transport constants above 86 km [m^-3].
- ussa1976.constants.Z10 = 120000.0#
Top altitude of the 10th layer [m].
- ussa1976.constants.Z12 = 1000000.0#
Top altitude of the 12nd layer [m].
- ussa1976.constants.Z7 = 86000.0#
Top altitude of the 7th layer [m].
- ussa1976.constants.Z8 = 91000.0#
Top altitude of the 8th layer [m].
- ussa1976.constants.Z9 = 110000.0#
Top altitude of the 9th layer [m].
core
#
U.S. Standard Atmosphere 1976 thermophysical model.
The U.S. Standard Atmosphere 1976 model [NNU76] divides the atmosphere into two altitude regions:
the low-altitude region, from 0 to 86 kilometers
the high-altitude region, from 86 to 1000 kilometers.
A number of computational functions hereafter are specialised for one or
the other altitude region and is valid only in that altitude region, not in
the other.
Their name include a low_altitude
or a high_altitude
part to reflect
that they are valid only in the low altitude region and high altitude region,
respectively.
- ussa1976.core.compute(z=array([0.00e+00, 5.00e+01, 1.00e+02, ..., 9.90e+05, 9.95e+05, 1.00e+06]), variables=None)#
Compute U.S. Standard Atmosphere 1976 data set on specified altitude grid.
- ussa1976.core.compute_gravity(z)#
Compute gravity.
- ussa1976.core.compute_high_altitude(data_set, mask=None, inplace=False)#
Compute U.S. Standard Atmosphere 1976 in high-altitude region.
- Parameters:
- Returns:
If
inplace
is True, returns nothing, else returns a copy ofdata_set
.- Return type:
- ussa1976.core.compute_levels_temperature_and_pressure_low_altitude()#
Compute temperature and pressure at low-altitude region’ levels.
- Returns:
Levels temperatures [K] and pressures [Pa].
- Return type:
tuple
ofarrays
- ussa1976.core.compute_low_altitude(data_set, mask=None, inplace=False)#
Compute U.S. Standard Atmosphere 1976 in low-altitude region.
- Parameters:
- Returns:
If
inplace
isTrue
, returns nothing, else returns a copy ofdata_set
.- Return type:
- ussa1976.core.compute_mean_molar_mass_high_altitude(z)#
Compute mean molar mass in high-altitude region.
- ussa1976.core.compute_number_densities_high_altitude(altitudes)#
Compute number density of individual species in high-altitude region.
- Parameters:
altitudes (
ndarray
) – Altitudes [m].- Returns:
Number densities of the individual species and total number density at the given altitudes.
- Return type:
Notes
A uniform altitude grid is generated and used for the computation of the integral as well as for the computation of the number densities of the individual species. This gridded data is then interpolated at the query
altitudes
using a linear interpolation scheme in logarithmic space.
- ussa1976.core.compute_pressure_low_altitude(h, pb, tb)#
Compute pressure in low-altitude region.
- ussa1976.core.compute_pressure_low_altitude_non_zero_gradient(h, hb, pb, tb, lkb)#
Compute pressure in low-altitude non-zero temperature gradient region.
- Parameters:
h (
ndarray
) – Geopotential height [m].hb (
float
) – Geopotential height at the bottom of the layer [m].pb (
float
) – Pressure at the bottom of the layer [Pa].tb (
float
) – Temperature at the bottom of the layer [K].lkb (
float
) – Temperature gradient in the layer [K * m^-1].
- Returns:
Pressure [Pa].
- Return type:
- ussa1976.core.compute_pressure_low_altitude_zero_gradient(h, hb, pb, tb)#
Compute pressure in low-altitude zero temperature gradient region.
- ussa1976.core.compute_temperature_gradient_high_altitude(z)#
Compute temperature gradient in high-altitude region.
- ussa1976.core.compute_temperature_high_altitude(z)#
Compute temperature in high-altitude region.
- ussa1976.core.compute_temperature_low_altitude(h, tb)#
Compute temperature in low-altitude region.
- ussa1976.core.eddy_diffusion_coefficient(z)#
Compute Eddy diffusion coefficient in high-altitude region.
- Parameters:
z (
ndarray
) – Altitude [m].- Returns:
Eddy diffusion coefficient [m^2 * s^-1].
- Return type:
Notes
Valid in the altitude region \(86 \leq z \leq 150\) km.
- ussa1976.core.f_above_115_km(g, t, dt_dz, mi, alpha)#
Evaluate function \(f\) above 115 km altitude.
Evaluate the function \(f\) defined by equation (36) in [NNU76] in the altitude region \(115\) \(\lt z \leq 1000\) km.
- Parameters:
g (
ndarray
) – Gravity at the different altitudes [m * s^-2].t (
ndarray
) – Temperature at the different altitudes [K].dt_dz (
ndarray
) – Temperature gradient at the different altitudes [K * m^-1].mi (
float
) – Species molar masses [kg * mole^-1].alpha (
float
) – Alpha thermal diffusion constant [dimensionless].
- Returns:
Function \(f\) at the different altitudes.
- Return type:
- ussa1976.core.f_below_115_km(g, t, dt_dz, m, mi, alpha, d, k)#
Evaluate function \(f\) below 115 km altitude.
Evaluates the function \(f\) defined by equation (36) in [NNU76] in the altitude region \(86\) km \(\leq z \leq 115\) km.
- Parameters:
g (
ndarray
) – Gravity values at the different altitudes [m * s^-2].t (
ndarray
) – Temperature values at the different altitudes [K].dt_dz (
ndarray
) – Temperature gradient values at the different altitudes [K * m^-1].m (
ndarray
) – Molar mass [kg * mole^-1].mi (
float
) – Species molar masses [kg * mole^-1].alpha (
float
) – Alpha thermal diffusion constant [dimensionless].d (
ndarray
) – Thermal diffusion coefficient values at the different altitudes [m^2 * s^-1].k (
ndarray
) – Eddy diffusion coefficient values at the different altitudes [m^2 * s^-1].
- Returns:
Function \(f\) at the different altitudes.
- Return type:
- ussa1976.core.init_data_set(z)#
Initialise data set.
- ussa1976.core.log_interp1d(x, y)#
Compute linear interpolation of \(y(x)\) in logarithmic space.
- ussa1976.core.tau_function(z_grid, below_500=True)#
Compute \(\tau\) function.
Compute integral given by equation (40) in [NNU76] at each point of an altitude grid.
- Parameters:
z_grid (
ndarray
) – Altitude grid (values sorted by ascending order) to use for integration [m].below_500 (
bool
, defaultTrue
) –True
if altitudes inz_grid
are lower than 500 km, False otherwise.
- Returns:
Integral evaluations [dimensionless].
- Return type:
Notes
Valid for 150 km \(\leq z \leq\) 500 km.
- ussa1976.core.thermal_diffusion_coefficient(nb, t, a, b)#
Compute thermal diffusion coefficient values in high-altitude region.
- ussa1976.core.thermal_diffusion_term(s, z_grid, g, t, dt_dz, m, d, k)#
Compute thermal diffusion term of given species in high-altitude region.
- Parameters:
s (
str
) – Species.z_grid (
ndarray
) – Altitude grid [m].g (
ndarray
) – Gravity values on the altitude grid [m * s^-2].t (
ndarray
) – Temperature values on the altitude grid [K].dt_dz (
ndarray
) – Temperature gradient values on the altitude grid [K * m^-1].m (
ndarray
) – Values of the mean molar mass on the altitude grid [kg * mole^-1].d (
ndarray
) – Molecular diffusion coefficient values on the altitude grid, for altitudes strictly less than 115 km [m^2 * s^-1].k (
ndarray
) – Eddy diffusion coefficient values on the altitude grid, for altitudes strictly less than 115 km [m^2 * s^-1].
- Returns:
Thermal diffusion term [m^-1].
- Return type:
- ussa1976.core.thermal_diffusion_term_atomic_oxygen(z_grid, g, t, dt_dz, d, k)#
Compute oxygen thermal diffusion term in high-altitude region.
- Parameters:
z_grid (
ndarray
) – Altitude grid [m].g (
ndarray
) – Gravity values on the altitude grid [m * s^-2].t (
ndarray
) – Temperature values on the altitude grid [K].dt_dz (
ndarray
) – Temperature values gradient on the altitude grid [K * m^-1].d (
ndarray
) – Thermal diffusion coefficient on the altitude grid [m^2 * s^-1].k (
ndarray
) – Eddy diffusion coefficient values on the altitude grid [m^2 * s^-1].
- Returns:
Thermal diffusion term [-1].
- Return type:
- ussa1976.core.to_altitude(h)#
Convert geopotential height to (geometric) altitude.
- ussa1976.core.to_geopotential_height(z)#
Convert altitude to geopotential height.
- ussa1976.core.velocity_term(s, z_grid)#
Compute velocity term of a given species in high-altitude region.
- Parameters:
s (
str
) – Species.z_grid (
ndarray
) – Altitude grid [m].
- Returns:
Velocity term [m^-1].
- Return type:
Notes
Not valid for atomic oxygen. See
velocity_term_atomic_oxygen()
.
- ussa1976.core.velocity_term_atomic_oxygen(grid)#
Compute velocity term of atomic oxygen in high-altitude region.
- ussa1976.core.velocity_term_hump(z, q1, q2, u1, u2, w1, w2)#
Compute transport term.
Compute the transport term given by equation (37) in [NNU76].
- Parameters:
z (
ndarray
) – Altitude [m].q1 (
float
) – Q constant [m^-3].q2 (
float
) – q constant [m^-3].u1 (
float
) – U constant [m].u2 (
float
) – u constant [m].w1 (
float
) – W constant [m^-3].w2 (
float
) – w constant [m^-3].
- Returns:
Transport term [m^-1].
- Return type:
Notes
Valid in the altitude region: 86 km \(\leq z \leq\) 150 km.
- ussa1976.core.velocity_term_no_hump(z, q1, u1, w1)#
Compute transport term.
Compute the transport term given by equation (37) in [NNU76] where the second term is zero.
- Parameters:
z (
ndarray
) – Altitude.q1 (
float
) – Q constant [m^-3].u1 (
float
) – U constant [m].w1 (
float
) – W constant [m^-3].
- Returns:
Transport term [m^-1].
- Return type:
Notes
Valid in the altitude region \(86\) km \(\leq z \leq 150\) km.
ussa1976
#
Command-line interface.
See also
Bibliography#
NASA, NOAA, and USAF. U.S. Standard Atmosphere, 1976. techreport NASA-TM-X-74335, National Aeronautics and Space Administration, 1976. URL: https://ntrs.nasa.gov/search.jsp?R=19770009539 (visited on 2019-10-25).
Contributor Guide#
Thank you for your interest in improving this project. This project is open-source under the MIT license and welcomes contributions in the form of bug reports, feature requests, and pull requests.
Here is a list of important resources for contributors:
How to report a bug#
Report bugs on the Issue Tracker.
When filing an issue, make sure to answer these questions:
Which operating system and Python version are you using?
Which version of this project are you using?
What did you do?
What did you expect to see?
What did you see instead?
The best way to get your bug fixed is to provide a test case, and/or steps to reproduce the issue.
How to request a feature#
Request features on the Issue Tracker.
How to set up your development environment#
You need Python 3.8+ and the following tools:
Install the package with development requirements:
$ poetry install
You can now run an interactive Python session, or the command-line interface:
$ poetry run python
$ poetry run ussa1976
How to test the project#
Run the full test suite:
$ nox
List the available Nox sessions:
$ nox --list-sessions
You can also run a specific Nox session. For example, invoke the unit test suite like this:
$ nox --session=tests
Unit tests are located in the tests
directory,
and are written using the pytest testing framework.
How to submit changes#
Open a pull request to submit changes to this project.
Your pull request needs to meet the following guidelines for acceptance:
The Nox test suite must pass without errors and warnings.
Include unit tests. This project maintains 100% code coverage.
If your changes add functionality, update the documentation accordingly.
Feel free to submit early, though—we can always iterate on this.
To run linting and code formatting checks before commiting your change, you can install pre-commit as a Git hook by running the following command:
$ nox --session=pre-commit -- install
It is recommended to open an issue before starting work on anything. This will allow a chance to talk it over with the owners and validate your approach.
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4. Permanent Ban#
Community Impact: Demonstrating a pattern of violation of community standards, including sustained inappropriate behavior, harassment of an individual, or aggression toward or disparagement of classes of individuals.
Consequence: A permanent ban from any sort of public interaction within the community.
Attribution#
This Code of Conduct is adapted from the Contributor Covenant, version 2.0, available at https://www.contributor-covenant.org/version/2/0/code_of_conduct.html.
Community Impact Guidelines were inspired by Mozilla’s code of conduct enforcement ladder.
For answers to common questions about this code of conduct, see the FAQ at https://www.contributor-covenant.org/faq. Translations are available at https://www.contributor-covenant.org/translations.
MIT License#
Copyright © 2021 Yvan Nollet
Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the “Software”), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
The software is provided “as is”, without warranty of any kind, express or implied, including but not limited to the warranties of merchantability, fitness for a particular purpose and noninfringement. In no event shall the authors or copyright holders be liable for any claim, damages or other liability, whether in an action of contract, tort or otherwise, arising from, out of or in connection with the software or the use or other dealings in the software.