# PyNRLMSISE-00
**Python interface for the NRLMSISE-00 empirical neutral atmosphere model**
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[](https://pypi.org/project/nrlmsise00)
[](https://pypi.org/project/nrlmsise00)
[](https://pypi.org/project/nrlmsise00)
[](https://codecov.io/gh/st-bender/pynrlmsise00)
[](https://coveralls.io/github/st-bender/pynrlmsise00)
[](https://scrutinizer-ci.com/g/st-bender/pynrlmsise00/?branch=master)
This python version of the NRLMSISE00 upper atmosphere model is
based on the C-version of the code, available at <https://www.brodo.de/space/nrlmsise>.
The C code is imported as a `git` submodule from
[git://git.linta.de/~brodo/nrlmsise-00.git](git://git.linta.de/~brodo/nrlmsise-00.git)
(browsable version at: <https://git.linta.de/?p=~brodo/nrlmsise-00.git>).
:warning: This python interface is in the **beta** stage, that is,
it should work but may still have some bugs.
The interface is supposed to be stable but may still change slightly in future versions.
Documentation can be found at <https://pynrlmsise00.readthedocs.io>,
and development happens on github <https://github.com/st-bender/pynrlmsise00>.
**Quote** from <https://ccmc.gsfc.nasa.gov/models/modelinfo.php?model=MSISE>:
“The MSISE model describes the neutral temperature and densities in Earth's atmosphere from ground to thermospheric heights.
The NRLMSIS-00 empirical atmosphere model was developed by Mike Picone, Alan Hedin, and Doug Drob.”
## Install
### Requirements
- `numpy` - required
- `spaceweather` and `xarray` - optional, for the `datatset` sub-package, see below
- `pytest` - optional, for testing
- `sphinx` - optional, to build the documentation
To compile the C source code, additional system header files may be required.
For example on Debian/Ubuntu Linux, the package `libc6-dev` is needed.
### pynrlmsise00
A `pip` package called `nrlmsise00` is available from the
main package repository, and can be installed with:
```sh
$ pip install nrlmsise00
```
In some cases this will install from the source package and the note
above about the additional requirements applies.
As binary package support is limited, pynrlmsise00 can be installed
with [`pip`](https://pip.pypa.io) directly from github
(see <https://pip.pypa.io/en/stable/reference/pip_install/#vcs-support>
and <https://pip.pypa.io/en/stable/reference/pip_install/#git>):
```sh
$ pip install [-e] git+https://github.com/st-bender/pynrlmsise00.git
```
The other option is to use a local clone:
```sh
$ git clone https://github.com/st-bender/pynrlmsise00.git
$ cd pynrlmsise00
$ git submodule init
$ git submodule update
```
and then using `pip` (optionally using `-e`, see
<https://pip.pypa.io/en/stable/reference/pip_install/#install-editable>):
```sh
$ pip install [-e] .
```
or using `setup.py`:
```sh
$ python setup.py install
```
Optionally, test the correct function of the module with
```sh
$ py.test [-v]
```
or even including the [doctests](https://docs.python.org/library/doctest.html)
in this document:
```sh
$ py.test [-v] --doctest-glob='*.md'
```
## Usage
The python module itself is named `nrlmsise00` and is imported as usual:
```python
>>> import nrlmsise00
```
Basic class and method documentation is accessible via `pydoc`:
```sh
$ pydoc nrlmsise00
```
### Python interface
The Python interface functions take `datetime.datetime` objects for
convenience. The local solar time is calculated from that time
and the given location, but it can be set explicitly via the `lst` keyword.
The returned value has the same format as the original C version (see below).
Because of their similarity, `gtd7()` and `gtd7d()` are selected via the
`method` keyword, `gtd7` is the default.
The return values are tuples of two lists containing
the densities (`d[0]`--`d[8]`) and temperatures (`t[0]`, `t[1]`).
The output has the same order as the C reference code, in particular:
* `d[0]` - He number density [cm⁻³]
* `d[1]` - O number density [cm⁻³]
* `d[2]` - N2 number density [cm⁻³]
* `d[3]` - O2 number density [cm⁻³]
* `d[4]` - Ar number density [cm⁻³]
* `d[5]` - total mass density [g cm⁻³]) (includes d[8] in `gtd7d()`)
* `d[6]` - H number density [cm⁻³]
* `d[7]` - N number density [cm⁻³]
* `d[8]` - Anomalous oxygen number density [cm⁻³]
* `t[0]` - exospheric temperature [K]
* `t[1]` - temperature at `alt` [K]
The `flags` and `ap_a` value array are set via keywords, but both default
to the standard setting, such that changing them should not be necessary
for most use cases.
For example setting `flag[0]` to `1` changes the output to metres
and kilograms instead of centimetres and grams (`0` is the default).
```python
>>> from datetime import datetime
>>> from nrlmsise00 import msise_model
>>> msise_model(datetime(2009, 6, 21, 8, 3, 20), 400, 60, -70, 150, 150, 4, lst=16)
([666517.690495152, 113880555.97522168, 19982109.255734544, 402276.3585712511, 3557.464994515886, 4.074713532757222e-15, 34753.12399717142, 4095913.2682930017, 26672.73209335869], [1250.5399435607994, 1241.4161300191206])
```
### NumPy interface
A `numpy` compatible *flat* version is available as `msise_flat()`,
it returns a 11-element `numpy.ndarray` with the densities in the
first 9 entries and the temperatures in the last two entries.
That is `ret = numpy.ndarray([d[0], ..., d[8], t[0], t[1]])`.
```python
>>> from datetime import datetime
>>> from nrlmsise00 import msise_flat
>>> msise_flat(datetime(2009, 6, 21, 8, 3, 20), 400, 60, -70, 150, 150, 4)
array([5.65085279e+05, 6.79850175e+07, 1.18819263e+07, 2.37030166e+05,
1.32459684e+03, 2.39947892e-15, 5.32498381e+04, 1.07596246e+06,
2.66727321e+04, 1.10058413e+03, 1.09824872e+03])
```
All arguments can be `numpy.ndarray`s, but must be broadcastable
to a common shape. For example to calculate the values for
three altitudes (200, 300, and 400 km) and two latitude locations
(60 and 70 °N) simultaneously, one can use `numpy.newaxis`
(which is equal to `None`) like this:
```python
>>> from datetime import datetime
>>> import numpy as np
>>> from nrlmsise00 import msise_flat
>>> alts = np.arange(200, 401, 100.) # = [200, 300, 400] [km]
>>> lats = np.arange(60, 71, 10.) # = [60, 70] [°N]
>>> # Using broadcasting, the output will be a 2 x 3 x 11 element array:
>>> msise_flat(datetime(2009, 6, 21, 8, 3, 20), alts[None, :], lats[:, None], -70, 150, 150, 4)
array([[[1.36949418e+06, 1.95229496e+09, 3.83824808e+09, 1.79130515e+08,
4.92145034e+06, 2.40511268e-13, 8.34108685e+04, 1.74317585e+07,
3.45500931e-08, 1.10058413e+03, 9.68827485e+02],
[8.40190601e+05, 3.25739060e+08, 1.82477392e+08, 5.37973134e+06,
6.53609278e+04, 1.75304136e-14, 5.92944463e+04, 4.36516218e+06,
1.03939126e+02, 1.10058413e+03, 1.08356514e+03],
[5.65085279e+05, 6.79850175e+07, 1.18819263e+07, 2.37030166e+05,
1.32459684e+03, 2.39947892e-15, 5.32498381e+04, 1.07596246e+06,
2.66727321e+04, 1.10058413e+03, 1.09824872e+03]],
<BLANKLINE>
[[1.10012225e+06, 1.94725472e+09, 4.08547233e+09, 1.92320077e+08,
6.65460281e+06, 2.52846563e-13, 6.16745965e+04, 2.45012145e+07,
5.21846603e-08, 1.13812434e+03, 1.00132640e+03],
[6.83809952e+05, 3.42643970e+08, 2.13434661e+08, 6.43426889e+06,
1.01162173e+05, 1.95300073e-14, 4.36031132e+04, 6.70490625e+06,
1.59911615e+02, 1.13812434e+03, 1.12084651e+03],
[4.65787225e+05, 7.52160226e+07, 1.51795904e+07, 3.13560147e+05,
2.32541183e+03, 2.76353370e-15, 3.92811827e+04, 1.73321928e+06,
4.12296154e+04, 1.13812434e+03, 1.13580463e+03]]])
```
### Xarray Dataset interface
Output to a 4-D `xarray.Dataset` is supported via the `dataset` submodule
which can be installed with:
```sh
pip install [-U] 'nrlmsise00[dataset]'
```
This module provides a 4-D version `msise_4d()` to broadcast the
1-D inputs for time, altitude, latitude, and longitude.
It also uses the [`spaceweather`](https://pypi.org/project/spaceweather) package
by default to automatically obtain the geomagnetic and Solar flux indices.
The variable names are set according to the MSIS output.
```python
>>> from datetime import datetime
>>> from nrlmsise00.dataset import msise_4d
>>> alts = np.arange(200, 401, 100.) # = [200, 300, 400] [km]
>>> lats = np.arange(60, 71, 10.) # = [60, 70] [°N]
>>> lons = np.arange(-70., 71., 35.) # = [-70, -35, 0, 35, 70] [°E]
>>> # broadcasting is done internally
>>> ds = msise_4d(datetime(2009, 6, 21, 8, 3, 20), alts, lats, lons)
>>> ds
<xarray.Dataset>
Dimensions: (alt: 3, lat: 2, lon: 5, time: 1)
Coordinates:
* time (time) datetime64[ns] 2009-06-21T08:03:20
* alt (alt) float64 200.0 300.0 400.0
* lat (lat) float64 60.0 70.0
* lon (lon) float64 -70.0 -35.0 0.0 35.0 70.0
Data variables:
He (time, alt, lat, lon) float64 8.597e+05 1.063e+06 ... 4.936e+05
O (time, alt, lat, lon) float64 1.248e+09 1.46e+09 ... 2.635e+07
N2 (time, alt, lat, lon) float64 2.555e+09 2.654e+09 ... 1.667e+06
O2 (time, alt, lat, lon) float64 2.1e+08 2.062e+08 ... 3.471e+04
Ar (time, alt, lat, lon) float64 3.16e+06 3.287e+06 ... 76.55 67.16
rho (time, alt, lat, lon) float64 1.635e-13 1.736e-13 ... 7.984e-16
H (time, alt, lat, lon) float64 3.144e+05 3.02e+05 ... 1.237e+05
N (time, alt, lat, lon) float64 9.095e+06 1.069e+07 ... 6.765e+05
AnomO (time, alt, lat, lon) float64 1.173e-08 1.173e-08 ... 1.101e+04
Texo (time, alt, lat, lon) float64 805.2 823.7 807.1 ... 818.7 821.2
Talt (time, alt, lat, lon) float64 757.9 758.7 766.4 ... 818.7 821.1
lst (time, lon) float64 3.389 5.722 8.056 10.39 12.72
Ap (time) int32 6
f107 (time) float64 66.7
f107a (time) float64 69.0
```
### C model interface
The C submodule directly interfaces the model functions `gtd7()` and `gtd7d()`
by importing `nrlmsise00._nrlmsise00`.
```python
>>> from nrlmsise00._nrlmsise00 import gtd7, gtd7d
>>> # using the standard flags
>>> gtd7(2009, 172, 29000, 400, 60, -70, 16, 150, 150, 4)
([666517.690495152, 113880555.97522168, 19982109.255734544, 402276.3585712511, 3557.464994515886, 4.074713532757222e-15, 34753.12399717142, 4095913.2682930017, 26672.73209335869], [1250.5399435607994, 1241.4161300191206])
```
This module also provides "flat" variants of the C functions as `gtd7_flat()`
and `gtd7d_flat()`. For example using `gtd7()` the same way as above:
```python
>>> import numpy as np
>>> from nrlmsise00 import gtd7_flat
>>> alts = np.arange(200, 401, 100.) # = [200, 300, 400] [km]
>>> lats = np.arange(60, 71, 10.) # = [60, 70] [°N]
>>> # Using broadcasting, the output will be a 2 x 3 x 11 element array:
>>> gtd7_flat(2009, 172, 29000, alts[None, :], lats[:, None], -70, 16, 150, 150, 4)
array([[[1.55567936e+06, 2.55949597e+09, 4.00342724e+09, 1.74513806e+08,
6.56916263e+06, 2.64872982e-13, 5.63405578e+04, 4.71893934e+07,
3.45500931e-08, 1.25053994e+03, 1.02704994e+03],
[9.58507714e+05, 4.66979460e+08, 2.31041924e+08, 6.58659651e+06,
1.16566762e+05, 2.38399390e-14, 3.86535595e+04, 1.43755262e+07,
1.03939126e+02, 1.25053994e+03, 1.20645403e+03],
[6.66517690e+05, 1.13880556e+08, 1.99821093e+07, 4.02276359e+05,
3.55746499e+03, 4.07471353e-15, 3.47531240e+04, 4.09591327e+06,
2.66727321e+04, 1.25053994e+03, 1.24141613e+03]],
<BLANKLINE>
[[1.31669842e+06, 2.40644124e+09, 4.21778196e+09, 1.89878716e+08,
8.17662024e+06, 2.71788520e-13, 4.64192484e+04, 5.13265845e+07,
5.21846603e-08, 1.24246351e+03, 1.04698385e+03],
[8.22632403e+05, 4.52803942e+08, 2.53857090e+08, 7.50201654e+06,
1.53431033e+05, 2.46179628e-14, 3.20594861e+04, 1.62651506e+07,
1.59911615e+02, 1.24246351e+03, 1.20963726e+03],
[5.73944168e+05, 1.10836468e+08, 2.19925518e+07, 4.58648922e+05,
4.68600377e+03, 4.10277781e-15, 2.89330169e+04, 4.65636025e+06,
4.12296154e+04, 1.24246351e+03, 1.23665288e+03]]])
```
### Note
All functions require the solar 10.7 cm radio flux and and the geomagnetic Ap
index values to produce correct results.
In particular, according to the C source code:
- f107A: 81 day average of F10.7 flux (centered on the given day of year)
- f107: daily F10.7 flux for previous day
- ap: magnetic index (daily)
The f107 and f107A values used to generate the model correspond
to the 10.7 cm radio flux at the actual distance of the Earth
from the Sun rather than the radio flux at 1 AU.
The following site provides both classes of values (**outdated**):
ftp://ftp.ngdc.noaa.gov/STP/SOLAR_DATA/SOLAR_RADIO/FLUX/
More up-to-date index files can be found at <https://celestrak.com/SpaceData/>,
which are also provided by the
[spaceweather](https://pypi.org/project/spaceweather) package.
f107, f107A, and ap effects are neither large nor well
established below 80 km and these parameters should be set to
150., 150., and 4. respectively.
## License
This python interface is free software: you can redistribute it or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, version 2 (GPLv2), see [local copy](./COPYING.GPLv2)
or [online version](http://www.gnu.org/licenses/gpl-2.0.html).
The [C source code of NRLMSISE-00](https://www.brodo.de/space/nrlmsise)
is in the public domain, see [COPYING.NRLMSISE-00](./COPYING.NRLMSISE-00).
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"description": "# PyNRLMSISE-00\n\n**Python interface for the NRLMSISE-00 empirical neutral atmosphere model**\n\n[](https://github.com/st-bender/pynrlmsise00/actions/workflows/ci_build_and_test.yml)\n[](https://pynrlmsise00.readthedocs.io/en/latest/?badge=latest)\n[](https://pypi.org/project/nrlmsise00)\n[](https://pypi.org/project/nrlmsise00)\n[](https://pypi.org/project/nrlmsise00)\n[](https://codecov.io/gh/st-bender/pynrlmsise00)\n[](https://coveralls.io/github/st-bender/pynrlmsise00)\n[](https://scrutinizer-ci.com/g/st-bender/pynrlmsise00/?branch=master)\n\nThis python version of the NRLMSISE00 upper atmosphere model is\nbased on the C-version of the code, available at <https://www.brodo.de/space/nrlmsise>.\nThe C code is imported as a `git` submodule from\n[git://git.linta.de/~brodo/nrlmsise-00.git](git://git.linta.de/~brodo/nrlmsise-00.git)\n(browsable version at: <https://git.linta.de/?p=~brodo/nrlmsise-00.git>).\n\n:warning: This python interface is in the **beta** stage, that is,\nit should work but may still have some bugs.\nThe interface is supposed to be stable but may still change slightly in future versions.\n\nDocumentation can be found at <https://pynrlmsise00.readthedocs.io>,\nand development happens on github <https://github.com/st-bender/pynrlmsise00>.\n\n**Quote** from <https://ccmc.gsfc.nasa.gov/models/modelinfo.php?model=MSISE>:\n\n\u201cThe MSISE model describes the neutral temperature and densities in Earth's atmosphere from ground to thermospheric heights.\nThe NRLMSIS-00 empirical atmosphere model was developed by Mike Picone, Alan Hedin, and Doug Drob.\u201d\n\n## Install\n\n### Requirements\n\n- `numpy` - required\n- `spaceweather` and `xarray` - optional, for the `datatset` sub-package, see below\n- `pytest` - optional, for testing\n- `sphinx` - optional, to build the documentation\n\nTo compile the C source code, additional system header files may be required.\nFor example on Debian/Ubuntu Linux, the package `libc6-dev` is needed.\n\n### pynrlmsise00\n\nA `pip` package called `nrlmsise00` is available from the\nmain package repository, and can be installed with:\n```sh\n$ pip install nrlmsise00\n```\nIn some cases this will install from the source package and the note\nabove about the additional requirements applies.\n\nAs binary package support is limited, pynrlmsise00 can be installed\nwith [`pip`](https://pip.pypa.io) directly from github\n(see <https://pip.pypa.io/en/stable/reference/pip_install/#vcs-support>\nand <https://pip.pypa.io/en/stable/reference/pip_install/#git>):\n```sh\n$ pip install [-e] git+https://github.com/st-bender/pynrlmsise00.git\n```\n\nThe other option is to use a local clone:\n```sh\n$ git clone https://github.com/st-bender/pynrlmsise00.git\n$ cd pynrlmsise00\n$ git submodule init\n$ git submodule update\n```\nand then using `pip` (optionally using `-e`, see\n<https://pip.pypa.io/en/stable/reference/pip_install/#install-editable>):\n```sh\n$ pip install [-e] .\n```\n\nor using `setup.py`:\n```sh\n$ python setup.py install\n```\n\nOptionally, test the correct function of the module with\n```sh\n$ py.test [-v]\n```\n\nor even including the [doctests](https://docs.python.org/library/doctest.html)\nin this document:\n```sh\n$ py.test [-v] --doctest-glob='*.md'\n```\n\n## Usage\n\nThe python module itself is named `nrlmsise00` and is imported as usual:\n```python\n>>> import nrlmsise00\n\n```\n\nBasic class and method documentation is accessible via `pydoc`:\n```sh\n$ pydoc nrlmsise00\n```\n\n### Python interface\n\nThe Python interface functions take `datetime.datetime` objects for\nconvenience. The local solar time is calculated from that time\nand the given location, but it can be set explicitly via the `lst` keyword.\nThe returned value has the same format as the original C version (see below).\nBecause of their similarity, `gtd7()` and `gtd7d()` are selected via the\n`method` keyword, `gtd7` is the default.\n\nThe return values are tuples of two lists containing\nthe densities (`d[0]`--`d[8]`) and temperatures (`t[0]`, `t[1]`).\n\nThe output has the same order as the C reference code, in particular:\n* `d[0]` - He number density [cm\u207b\u00b3]\n* `d[1]` - O number density [cm\u207b\u00b3]\n* `d[2]` - N2 number density [cm\u207b\u00b3]\n* `d[3]` - O2 number density [cm\u207b\u00b3]\n* `d[4]` - Ar number density [cm\u207b\u00b3]\n* `d[5]` - total mass density [g cm\u207b\u00b3]) (includes d[8] in `gtd7d()`)\n* `d[6]` - H number density [cm\u207b\u00b3]\n* `d[7]` - N number density [cm\u207b\u00b3]\n* `d[8]` - Anomalous oxygen number density [cm\u207b\u00b3]\n* `t[0]` - exospheric temperature [K]\n* `t[1]` - temperature at `alt` [K]\n\nThe `flags` and `ap_a` value array are set via keywords, but both default\nto the standard setting, such that changing them should not be necessary\nfor most use cases.\nFor example setting `flag[0]` to `1` changes the output to metres\nand kilograms instead of centimetres and grams (`0` is the default).\n\n```python\n>>> from datetime import datetime\n>>> from nrlmsise00 import msise_model\n>>> msise_model(datetime(2009, 6, 21, 8, 3, 20), 400, 60, -70, 150, 150, 4, lst=16)\n([666517.690495152, 113880555.97522168, 19982109.255734544, 402276.3585712511, 3557.464994515886, 4.074713532757222e-15, 34753.12399717142, 4095913.2682930017, 26672.73209335869], [1250.5399435607994, 1241.4161300191206])\n\n```\n\n### NumPy interface\n\nA `numpy` compatible *flat* version is available as `msise_flat()`,\nit returns a 11-element `numpy.ndarray` with the densities in the\nfirst 9 entries and the temperatures in the last two entries.\nThat is `ret = numpy.ndarray([d[0], ..., d[8], t[0], t[1]])`.\n```python\n>>> from datetime import datetime\n>>> from nrlmsise00 import msise_flat\n>>> msise_flat(datetime(2009, 6, 21, 8, 3, 20), 400, 60, -70, 150, 150, 4)\narray([5.65085279e+05, 6.79850175e+07, 1.18819263e+07, 2.37030166e+05,\n 1.32459684e+03, 2.39947892e-15, 5.32498381e+04, 1.07596246e+06,\n 2.66727321e+04, 1.10058413e+03, 1.09824872e+03])\n\n```\n\nAll arguments can be `numpy.ndarray`s, but must be broadcastable\nto a common shape. For example to calculate the values for\nthree altitudes (200, 300, and 400 km) and two latitude locations\n(60 and 70 \u00b0N) simultaneously, one can use `numpy.newaxis`\n(which is equal to `None`) like this:\n```python\n>>> from datetime import datetime\n>>> import numpy as np\n>>> from nrlmsise00 import msise_flat\n>>> alts = np.arange(200, 401, 100.) # = [200, 300, 400] [km]\n>>> lats = np.arange(60, 71, 10.) # = [60, 70] [\u00b0N]\n>>> # Using broadcasting, the output will be a 2 x 3 x 11 element array:\n>>> msise_flat(datetime(2009, 6, 21, 8, 3, 20), alts[None, :], lats[:, None], -70, 150, 150, 4)\narray([[[1.36949418e+06, 1.95229496e+09, 3.83824808e+09, 1.79130515e+08,\n 4.92145034e+06, 2.40511268e-13, 8.34108685e+04, 1.74317585e+07,\n 3.45500931e-08, 1.10058413e+03, 9.68827485e+02],\n [8.40190601e+05, 3.25739060e+08, 1.82477392e+08, 5.37973134e+06,\n 6.53609278e+04, 1.75304136e-14, 5.92944463e+04, 4.36516218e+06,\n 1.03939126e+02, 1.10058413e+03, 1.08356514e+03],\n [5.65085279e+05, 6.79850175e+07, 1.18819263e+07, 2.37030166e+05,\n 1.32459684e+03, 2.39947892e-15, 5.32498381e+04, 1.07596246e+06,\n 2.66727321e+04, 1.10058413e+03, 1.09824872e+03]],\n<BLANKLINE>\n [[1.10012225e+06, 1.94725472e+09, 4.08547233e+09, 1.92320077e+08,\n 6.65460281e+06, 2.52846563e-13, 6.16745965e+04, 2.45012145e+07,\n 5.21846603e-08, 1.13812434e+03, 1.00132640e+03],\n [6.83809952e+05, 3.42643970e+08, 2.13434661e+08, 6.43426889e+06,\n 1.01162173e+05, 1.95300073e-14, 4.36031132e+04, 6.70490625e+06,\n 1.59911615e+02, 1.13812434e+03, 1.12084651e+03],\n [4.65787225e+05, 7.52160226e+07, 1.51795904e+07, 3.13560147e+05,\n 2.32541183e+03, 2.76353370e-15, 3.92811827e+04, 1.73321928e+06,\n 4.12296154e+04, 1.13812434e+03, 1.13580463e+03]]])\n\n```\n\n### Xarray Dataset interface\n\nOutput to a 4-D `xarray.Dataset` is supported via the `dataset` submodule\nwhich can be installed with:\n```sh\npip install [-U] 'nrlmsise00[dataset]'\n```\n\nThis module provides a 4-D version `msise_4d()` to broadcast the\n1-D inputs for time, altitude, latitude, and longitude.\nIt also uses the [`spaceweather`](https://pypi.org/project/spaceweather) package\nby default to automatically obtain the geomagnetic and Solar flux indices.\nThe variable names are set according to the MSIS output.\n```python\n>>> from datetime import datetime\n>>> from nrlmsise00.dataset import msise_4d\n>>> alts = np.arange(200, 401, 100.) # = [200, 300, 400] [km]\n>>> lats = np.arange(60, 71, 10.) # = [60, 70] [\u00b0N]\n>>> lons = np.arange(-70., 71., 35.) # = [-70, -35, 0, 35, 70] [\u00b0E]\n>>> # broadcasting is done internally\n>>> ds = msise_4d(datetime(2009, 6, 21, 8, 3, 20), alts, lats, lons)\n>>> ds\n<xarray.Dataset>\nDimensions: (alt: 3, lat: 2, lon: 5, time: 1)\nCoordinates:\n * time (time) datetime64[ns] 2009-06-21T08:03:20\n * alt (alt) float64 200.0 300.0 400.0\n * lat (lat) float64 60.0 70.0\n * lon (lon) float64 -70.0 -35.0 0.0 35.0 70.0\nData variables:\n He (time, alt, lat, lon) float64 8.597e+05 1.063e+06 ... 4.936e+05\n O (time, alt, lat, lon) float64 1.248e+09 1.46e+09 ... 2.635e+07\n N2 (time, alt, lat, lon) float64 2.555e+09 2.654e+09 ... 1.667e+06\n O2 (time, alt, lat, lon) float64 2.1e+08 2.062e+08 ... 3.471e+04\n Ar (time, alt, lat, lon) float64 3.16e+06 3.287e+06 ... 76.55 67.16\n rho (time, alt, lat, lon) float64 1.635e-13 1.736e-13 ... 7.984e-16\n H (time, alt, lat, lon) float64 3.144e+05 3.02e+05 ... 1.237e+05\n N (time, alt, lat, lon) float64 9.095e+06 1.069e+07 ... 6.765e+05\n AnomO (time, alt, lat, lon) float64 1.173e-08 1.173e-08 ... 1.101e+04\n Texo (time, alt, lat, lon) float64 805.2 823.7 807.1 ... 818.7 821.2\n Talt (time, alt, lat, lon) float64 757.9 758.7 766.4 ... 818.7 821.1\n lst (time, lon) float64 3.389 5.722 8.056 10.39 12.72\n Ap (time) int32 6\n f107 (time) float64 66.7\n f107a (time) float64 69.0\n\n```\n\n### C model interface\n\nThe C submodule directly interfaces the model functions `gtd7()` and `gtd7d()`\nby importing `nrlmsise00._nrlmsise00`.\n```python\n>>> from nrlmsise00._nrlmsise00 import gtd7, gtd7d\n>>> # using the standard flags\n>>> gtd7(2009, 172, 29000, 400, 60, -70, 16, 150, 150, 4)\n([666517.690495152, 113880555.97522168, 19982109.255734544, 402276.3585712511, 3557.464994515886, 4.074713532757222e-15, 34753.12399717142, 4095913.2682930017, 26672.73209335869], [1250.5399435607994, 1241.4161300191206])\n\n```\n\nThis module also provides \"flat\" variants of the C functions as `gtd7_flat()`\nand `gtd7d_flat()`. For example using `gtd7()` the same way as above:\n```python\n>>> import numpy as np\n>>> from nrlmsise00 import gtd7_flat\n>>> alts = np.arange(200, 401, 100.) # = [200, 300, 400] [km]\n>>> lats = np.arange(60, 71, 10.) # = [60, 70] [\u00b0N]\n>>> # Using broadcasting, the output will be a 2 x 3 x 11 element array:\n>>> gtd7_flat(2009, 172, 29000, alts[None, :], lats[:, None], -70, 16, 150, 150, 4)\narray([[[1.55567936e+06, 2.55949597e+09, 4.00342724e+09, 1.74513806e+08,\n 6.56916263e+06, 2.64872982e-13, 5.63405578e+04, 4.71893934e+07,\n 3.45500931e-08, 1.25053994e+03, 1.02704994e+03],\n [9.58507714e+05, 4.66979460e+08, 2.31041924e+08, 6.58659651e+06,\n 1.16566762e+05, 2.38399390e-14, 3.86535595e+04, 1.43755262e+07,\n 1.03939126e+02, 1.25053994e+03, 1.20645403e+03],\n [6.66517690e+05, 1.13880556e+08, 1.99821093e+07, 4.02276359e+05,\n 3.55746499e+03, 4.07471353e-15, 3.47531240e+04, 4.09591327e+06,\n 2.66727321e+04, 1.25053994e+03, 1.24141613e+03]],\n<BLANKLINE>\n [[1.31669842e+06, 2.40644124e+09, 4.21778196e+09, 1.89878716e+08,\n 8.17662024e+06, 2.71788520e-13, 4.64192484e+04, 5.13265845e+07,\n 5.21846603e-08, 1.24246351e+03, 1.04698385e+03],\n [8.22632403e+05, 4.52803942e+08, 2.53857090e+08, 7.50201654e+06,\n 1.53431033e+05, 2.46179628e-14, 3.20594861e+04, 1.62651506e+07,\n 1.59911615e+02, 1.24246351e+03, 1.20963726e+03],\n [5.73944168e+05, 1.10836468e+08, 2.19925518e+07, 4.58648922e+05,\n 4.68600377e+03, 4.10277781e-15, 2.89330169e+04, 4.65636025e+06,\n 4.12296154e+04, 1.24246351e+03, 1.23665288e+03]]])\n\n```\n\n### Note\n\nAll functions require the solar 10.7\u202fcm radio flux and and the geomagnetic Ap\nindex values to produce correct results.\nIn particular, according to the C source code:\n\n- f107A: 81 day average of F10.7 flux (centered on the given day of year)\n- f107: daily F10.7 flux for previous day\n- ap: magnetic index (daily)\n\nThe f107 and f107A values used to generate the model correspond\nto the 10.7\u202fcm radio flux at the actual distance of the Earth\nfrom the Sun rather than the radio flux at 1\u202fAU.\nThe following site provides both classes of values (**outdated**):\nftp://ftp.ngdc.noaa.gov/STP/SOLAR_DATA/SOLAR_RADIO/FLUX/\n\nMore up-to-date index files can be found at <https://celestrak.com/SpaceData/>,\nwhich are also provided by the\n[spaceweather](https://pypi.org/project/spaceweather) package.\n\nf107, f107A, and ap effects are neither large nor well\nestablished below 80\u202fkm and these parameters should be set to\n150., 150., and 4. respectively.\n\n## License\n\nThis python interface is free software: you can redistribute it or modify\nit under the terms of the GNU General Public License as published by\nthe Free Software Foundation, version 2 (GPLv2), see [local copy](./COPYING.GPLv2)\nor [online version](http://www.gnu.org/licenses/gpl-2.0.html).\n\nThe [C source code of NRLMSISE-00](https://www.brodo.de/space/nrlmsise)\nis in the public domain, see [COPYING.NRLMSISE-00](./COPYING.NRLMSISE-00).\n\n\n",
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