Range Estimations, Coordinate Systems and Projections

pyDARN uses several different measurement and plotting systems to easily allow the user to customise their plots, this page aims to describe their uses:

  • Range Estimation: the estimate of how far the target (echo) is from the radar

  • Coordinate systems: determines the unique position using a set of points, primarily we use geographic and AACGMv2 magnetic coordinate systems for Earth

  • Projections: used primarily on spatial plots (FOV, Fan, Grid...) projection choices allow the user to choose what type of projection the plot appears in (see also Axes Setup)

RangeEstimation

Range Gates: RangeEstimation.RANGE_GATE a rectangle section determined by beam width and set distance for each range (nominally 45 km). RAWACF and FITACF data give their parameter values with respect to range gates. Range gates are a unit-less measure of estimating distance.

Slant Range: RangeEstimation.SLANT_RANGE is a conversion from range gates to km units. Slant range estimates the distance of ionospheric echos from the radar, using the time it takes for the radio wave to travel to the ionosphere and return, assuming the radio wave is travelling at the speed of light. Measured in km.

Half Slant: RangeEstimation.HALF_SLANT is slant range divided by two, measured in km.

Ground Scatter Mapped Range RangeEstimation.GSMR uses echos from ground scatter to adjust slant range coordinates, more information on this algorithm can be found in the GitHub discussion.

Alternate Ground Scatter Mapped Range: RangeEstimation.GSMR_BRISTOW uses echos from ground scatter to adjust slant range coordinates based on Dr. Bill Bristow's paper. Implemented by Dr. Nathaniel Frissell and Francis Tholley from University of Scranton. Measured in km.

Time of Flight: RangeEstimation.TIME_OF_FLIGHT Due to the development of bistatic radar measurements, range estimates of distance cannot be easily used so a time of flight option is alos included. This mode can only be used in range-time plots. Measured in ms.

Note

Slant range is calculated from the value of frang, the distance to the first range gate. In pyDARN, we assume that this value is the distance to the inner edge of the first range gate. We are aware that not all radars use this exact definition, this is outside the remit of pyDARN and should be addressed at a higher level. The value rxrise is also used in the definition of slant range. This is the receiver rise time of the radar, however, due to discussion outside of pyDARN's remit* the value of rxrise is adjusted in FITACF files and may not match the value given in hardware files. Currently, pyDARN has decided to use the values for rxrise given in the hardware files. We will amend or reconsider this approach as and when a solution to the differing values is found. In some plots, the user can change these values to fit their needs.

Coords: Coordinate System

This function is used to determine the position of data in spatial plots: fan, grid and convection map plots. Range time plots now also allow for Coords use. The y-axis can be converted to latitude or longitude using a the coords keyword. E.G. using coords=Coords.GEOGRAPHIC and latlon='lon' in the method call, will convert the chosen range estimate (see above) into geographic longitudes.

Geographic: Coords.GEOGRAPHIC is the standard geographical coordinate system for latitude and longitude (degrees)

AACGM: Coords.AACGM is Altitude Adjusted Corrected Geogmagnetic Coordinates developed by Dr. Simon Shepherd are an extension of corrected geomagnetic (CGM) coordinates that more accurately represent the actual magnetic field. In AACGM coordinates points along a given magnetic field line are given the same coordinates and thus are a better reflection of magnetic conjugacy. pyDARN uses AACGM-V2 from the aacgmv2 python library.

AACGM_MLT: Coords.AACGM_MLT is Coords.AACGM with the geomagnetic longitude converted to magnetic local time.

RangeEstimation methods can be used with a Coords calculation. For example, using Coords.GEOGRAPHIC and RangeEstimation.GSMR together, will give a plot of ionospheric echoes at a distance from the radar calculated in ground scatter mapped range, in geographic coordinates.

Projs: Projections

Spatial plots have three options for projections. See also Axes Setup tutorial.

Polar: Projs.POLAR sets up the axis of the spatial plot in polar coordinates common in studies that show data over the poles.

Geographic: Projs.GEO sets up the axes of the spatial plots in geographic coordinates using Cartopy.

Geomagnetic: Projs.MAG sets up the axes of the spatial plots in geographic coordinates using Cartopy.

Note

The 'look-direction' of the projections may be different for the Southern hemisphere. Polar projections show a view of the south pole as if looking down through the planet from above the north pole, geographic and geomagnetic projections show a view of the south pole as if looking from above the south pole.

Note

Some combinations of Projs/Coords/RangeEstimates are not designed to work. For example, you cannot plot a fan plot using range gates; spatial plots require a value in kilometers. AACGM Coordinates do not plot on Geographic projections. Geographic coordinates are not supported on POLAR or MAG projections. Convection maps only support polar projections for now.

Including a Terminator

Spatial plots have the option to include a terminator called nightshade at a given height in the ionosphere. This functions uses the Cartopy nightshade function. Nightshade is only available using the geographic projection and can be implemented by adding nightshade=250 to the spacial plot call where 250 is the desired height in the ionosphere to be in the Earth's shadow. If you would like to plot your own terminator on any plot, the terminator function will return the anti-sub-solar position and the great circle distance to the terminator in geographic coordinates:

antisolarpsn, arc_length, angle_of_terminator = pydarn.terminator(date, nightshade)

The antisolarpsn is given in geographic degrees lon, lat. The arc_length is in kilometers and the angle_of_terminator is the angle from the subsolar point to the terminator (i.e. is 90 degrees at ground level). The terminator position can be calculated using (lat, lon) = new_coordinate(lat, lon, arc_length, bearing, R=Re) for any bearing from the antisolar position. This can be converted to magnetic coordinates using the AACGMv2 library. Unfortunately, Matplotlib is unable to plot the terminator using fill consistently, hence we leave this option up to the user. An example of this is shown below:

import pydarn
import aacgmv2
import datetime as dt
import matplotlib.pyplot as plt
import numpy as np

# North Winter
pydarn.Fan.plot_fov(66, dt.datetime(2023, 12, 21, 0, 0),
    lowlat= 5, boundary=True, line_color='red', coastline=True)

# Test to plot terminator if ever required - plot line not fill!
# Get antisolar point in geographic coords and radius of terminator
# at given height
date = dt.datetime(2023, 12, 21, 0, 0)
antisolarpsn, arc, ang = pydarn.terminator(date, 250)
# Convert position to magnetic coordinates
mlat, lon_mag, _ =  aacgmv2.convert_latlon(antisolarpsn[1],
                                           antisolarpsn[0],
                                           250, date, method_code='G2A')
# Shift to MLT
shifted_mlts = lon_mag - (aacgmv2.convert_mlt(lon_mag, date) * 15)
shifted_lons = lon_mag - shifted_mlts
mlon = np.radians(shifted_lons)
# Get positions at a distance from new position to plot terminator
lats = []
lons = []
for b in range(-180,180,1):
    (lat, lon) = pydarn.GeneralUtils.new_coordinate(mlat, shifted_lons, arc, b, R=pydarn.Re)
    nlon =np.radians(lon)
    lats.append(lat)
    lons.append(nlon)
lats2 = np.zeros(len(lats))
plt.plot(np.squeeze(lons), np.squeeze(lats), color='b', zorder=2.0,
         linewidth=3.0, linestyle='dashed')

plt.show()