GLOW2D

This package builds off of the GLobal airglOW model. The GLOW model is evaluated on an altitude grid at a location. For non-zenith observation geometries, the model requires evaluation at multiple points along the line of sight. The glow2d library wraps the ncarglow.no_precipitation() function to generate the output on a 2D grid in a geocentric (GEO) coordinate system and in a local (ZA, R) coordinate system.

Principle

GLOW model is evaluated at one geolocation (latitude, longitude) at a given time. Assuming spherical geometry, for a given bearing, the GLOW model can be evaluated at different geolocations at a given time in a geocentric coordinate system $(R, \theta, \phi)$ . The local polar coordinate system, defined at the starting location as $(r, \zeta, \phi)$ , is related to the geocentric coordinate system through the equations: $r = \sqrt{(R\cos{\theta} - R_0)^2 + R^2\sin^2{\theta}}, \\ \zeta = \arctan{\frac{R\sin\theta}{R\cos\theta - R_0}},\\ \phi = \phi$ $R_0$ is the distance to the origin of the local polar coordinate system from the center of the earth.

Fig. 1: Geometry of observation

A volume element in the $(R, \theta, \phi)$ coordinate system is related to a volume element in the $(r, \zeta, \phi)$ coordinate system through the following equation: $dR d\theta d\phi = \left|J_{Rr}\right| dr d\zeta d\phi,$ where $\left|J_{Rr}\right|$ is the determinant $\left|\begin{array}{cc} \frac{\partial r}{\partial R} & \frac{\partial r}{\partial \theta} \\ \frac{\partial \zeta}{\partial R} & \frac{\partial \zeta}{\partial \theta} \end{array}\right| = \frac{R}{r^3}\left(R^2 + R_0^2 - 2 R R_0 \cos{\theta}\right).$ The determinant is evaluated at a position $(R, \theta, \phi)$ . Note, that the determinant does not depend on $\phi$ , i.e. the geometry is azimuthally symmetric, and $r$ is known given $R, \theta$ .

GLOW model is executed in the $R, \theta~(,~\phi)$ coordinate system on a uniform grid. The non-linearity of the coordinate transformation from $R, \theta~(,~\phi)$ to $r, \zeta~(,~\phi)$ results in a non-uniform grid in $r, \zeta$ coordinates for points in $R, \theta$ coordinates. An interpolation is performed to an uniform grid in $r, \zeta$ coordinates, followed by a normalization by $\left|J_{Rr}\right|$ for density outputs, such as the volume emission rate.

The emission reaching a detector of area $A$ , subtending a solid angle $d\zeta d\phi$ is, then, $IER(\zeta) = A \int_0^\phi \int_0^\infty \int_{\zeta - \delta\zeta}^{\zeta + \delta\zeta} \frac{VER(r, \zeta)}{4\pi r^2}r^2 dr d\zeta d\phi.$ Note, since the volume emission rate is isotropic, the number of photons incident from one point in the sky onto the detector is given by $A\frac{VER(r, \zeta)}{4\pi r^2}$ .

Installation

Directly using pip:

$ pip install glow2d

Indirectly by git clone:

$ git clone https://github.com/sunipkm/glow2d && cd glow2d
$ pip install .

Dependencies

The following non-trivial dependencies are present:

This code uses glowpython package to run the GLOW model. geomagdata is used to get the $F_{10.7}$ and $A_p$ indices from the new data source.

Usage

For example:

from datetime import datetime
from glow2d import glow2d_polar as grc

time = datetime(2022, 2, 15, 20, 0, 0).astimezone('UTC') # 20:00 hours local in UTC
lat, lon = 42.64981361744372, -71.31681056737486 # location of observation
bearing = 40 # 40 deg northeast, refer to geopy.GreatCircleDistance().destination() for more info.

iono_loc, iono_geo = grc.polar_model(time, lat, lon, bearing, full_output=True) # generate output in local and GEO coordinates

The iono_loc dataset is:

<xarray.Dataset>
Dimensions:     (za: 200, r: 500, wavelength: 15, energy: 100)
Coordinates:
  * za          (za) float64 1.571 1.563 1.555 1.547 ... 0.01579 0.007893 0.0
  * r           (r) float64 0.0 7.391 14.78 ... 3.673e+03 3.681e+03 3.688e+03
  * wavelength  (wavelength) <U21 '3371' '4278' '5200' ... '1356' '1493' '1304'
  * energy      (energy) float64 0.2 0.8 1.2 1.8 2.2 ... 457.3 480.7 505.4 531.3
Data variables: (12/18)
    Tn          (za, r) float64 0.0 0.0 0.0 0.0 0.0 0.0 ... 0.0 0.0 0.0 0.0 0.0
    O           (za, r) float64 0.0 0.0 0.0 0.0 0.0 0.0 ... 0.0 0.0 0.0 0.0 0.0
    N2          (za, r) float64 0.0 0.0 0.0 0.0 0.0 0.0 ... 0.0 0.0 0.0 0.0 0.0
    O2          (za, r) float64 0.0 0.0 0.0 0.0 0.0 0.0 ... 0.0 0.0 0.0 0.0 0.0
    NO          (za, r) float64 0.0 0.0 0.0 0.0 0.0 0.0 ... 0.0 0.0 0.0 0.0 0.0
    NeIn        (za, r) float64 0.0 0.0 0.0 0.0 0.0 0.0 ... 0.0 0.0 0.0 0.0 0.0
    ...          ...
    pedersen    (za, r) float64 0.0 0.0 0.0 0.0 0.0 0.0 ... 0.0 0.0 0.0 0.0 0.0
    hall        (za, r) float64 0.0 0.0 0.0 0.0 0.0 0.0 ... 0.0 0.0 0.0 0.0 0.0
    Te          (za, r) float64 0.0 0.0 0.0 0.0 0.0 0.0 ... 0.0 0.0 0.0 0.0 0.0
    Ti          (za, r) float64 0.0 0.0 0.0 0.0 0.0 0.0 ... 0.0 0.0 0.0 0.0 0.0
    ver         (za, r, wavelength) float64 0.0 0.0 0.0 0.0 ... 0.0 0.0 0.0 0.0
    precip      (r, energy) float64 0.0 0.0 0.0 0.0 0.0 ... 0.0 0.0 0.0 0.0 0.0
Attributes:
    geomag_params:                       Ap     Kp   f107 resolution       f1...
    time:           2022-02-15T11:00:00+00:00
    glatlon:        (42.64981361744372, -71.31681056737486)

The iono_geo dataset is:

name="__codelineno-4-1" href="#__codelineno-4-1"><xarray.Dataset> class="n">Dimensions: (angle: 100, alt_km: 250, wavelength: 15, state: 12, energy: 100) class="n">Coordinates: * alt_km (alt_km) float64 60.0 60.6 61.2 61.8 ... 953.4 957.9 962.4 * wavelength (wavelength) <U21 '3371' '4278' '5200' ... '1493' '1304' * state (state) <U6 'O+(2P)' 'O+(2D)' 'O+(4S)' ... 'O(1S)' 'O(1D)' * energy (energy) float64 0.2 0.8 1.2 1.8 ... 457.3 480.7 505.4 531.3 * angle (angle) float64 0.0 0.005323 0.01065 ... 0.5163 0.5217 0.527 lat (angle) float64 42.65 42.88 43.12 ... 60.15 60.25 60.34 lon (angle) float64 -71.32 -71.05 -70.78 ... -31.7 -31.12 -30.53 class="n">Data variables: (12/21) Tn (angle, alt_km) float64 237.0 236.0 235.0 ... 815.0 815.0 O (angle, alt_km) float64 0.0 0.0 0.0 ... 1.2e+03 1.11e+03 N2 (angle, alt_km) float64 4.49e+15 4.17e+15 ... 0.0102 0.00893 O2 (angle, alt_km) float64 1.2e+15 1.12e+15 ... 1.9e-05 NO (angle, alt_km) float64 7.81e+07 7.81e+07 ... 5.92e-08 NeIn (angle, alt_km) float64 100.0 100.0 ... 2.35e+04 2.34e+04 ... ... Ti (angle, alt_km) float64 236.9 235.9 ... 2.715e+03 2.726e+03 ver (angle, alt_km, wavelength) float64 0.0 0.0 0.0 ... 0.0 0.0 production (angle, alt_km, state) float64 0.0 nan nan ... 0.0 0.0 0.0 loss (angle, alt_km, state) float64 nan nan nan ... 0.0 1.1 0.01 precip (angle, energy) float64 0.0 0.0 0.0 0.0 ... 0.0 0.0 0.0 0.0 excitedDensity (angle, alt_km, state) float64 nan nan nan ... 0.0 0.0 0.01 class="o">... class="n">Attributes: geomag_params: Ap Kp f107 resolution f1... time: 2022-02-15T11:00:00+00:00 glatlon: (42.64981361744372, -71.31681056737486)

All angles are in radians, and distances in km. Due to the nature of the coordinate transformation, local coordinate outputs do not contain any NaN values.