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# Copyright (C) 2019 NRL |
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# Author: Angeline Burrell |
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# Disclaimer: This code is under the MIT license, whose details can be found at |
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# the root in the LICENSE file |
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# |
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# -*- coding: utf-8 -*- |
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"""utilities that support the AACGM-V2 C functions. |
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References |
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---------- |
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Laundal, K. M. and A. D. Richmond (2016), Magnetic Coordinate Systems, Space |
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Sci. Rev., doi:10.1007/s11214-016-0275-y. |
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""" |
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from __future__ import division, absolute_import, unicode_literals |
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import datetime as dt |
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import numpy as np |
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import aacgmv2 |
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def gc2gd_lat(gc_lat): |
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"""Convert geocentric latitude to geodetic latitude using WGS84. |
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Parameters |
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----------- |
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gc_lat : (array_like or float) |
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Geocentric latitude in degrees N |
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Returns |
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--------- |
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gd_lat : (same as input) |
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Geodetic latitude in degrees N |
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""" |
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wgs84_e2 = 0.006694379990141317 - 1.0 |
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gd_lat = np.rad2deg(-np.arctan(np.tan(np.deg2rad(gc_lat)) / wgs84_e2)) |
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return gd_lat |
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def subsol(year, doy, utime): |
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"""Finds subsolar geocentric longitude and latitude. |
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Parameters |
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---------- |
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year : (int) |
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Calendar year between 1601 and 2100 |
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doy : (int) |
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Day of year between 1-365/366 |
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utime : (float) |
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Seconds since midnight on the specified day |
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Returns |
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------- |
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sbsllon : (float) |
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Subsolar longitude in degrees E for the given date/time |
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sbsllat : (float) |
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Subsolar latitude in degrees N for the given date/time |
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Raises |
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------ |
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ValueError if year is out of range |
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Notes |
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----- |
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Based on formulas in Astronomical Almanac for the year 1996, p. C24. |
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(U.S. Government Printing Office, 1994). Usable for years 1601-2100, |
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inclusive. According to the Almanac, results are good to at least 0.01 |
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degree latitude and 0.025 degrees longitude between years 1950 and 2050. |
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Accuracy for other years has not been tested. Every day is assumed to have |
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exactly 86400 seconds; thus leap seconds that sometimes occur on December |
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31 are ignored (their effect is below the accuracy threshold of the |
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algorithm). |
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References |
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---------- |
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After Fortran code by A. D. Richmond, NCAR. Translated from IDL |
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by K. Laundal. |
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""" |
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# Convert from 4 digit year to 2 digit year |
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yr2 = year - 2000 |
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if year >= 2101 or year <= 1600: |
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raise ValueError('subsol valid between 1601-2100. Input year is:', year) |
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# Determine if this year is a leap year |
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nleap = np.floor((year - 1601) / 4) |
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nleap = nleap - 99 |
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if year <= 1900: |
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ncent = np.floor((year - 1601) / 100) |
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ncent = 3 - ncent |
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nleap = nleap + ncent |
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# Calculate some of the coefficients needed to deterimine the mean longitude |
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# of the sun and the mean anomaly |
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l_0 = -79.549 + (-0.238699 * (yr2 - 4 * nleap) + 3.08514e-2 * nleap) |
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g_0 = -2.472 + (-0.2558905 * (yr2 - 4 * nleap) - 3.79617e-2 * nleap) |
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# Days (including fraction) since 12 UT on January 1 of IYR2: |
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dfrac = (utime / 86400 - 1.5) + doy |
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# Mean longitude of Sun: |
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l_sun = l_0 + 0.9856474 * dfrac |
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# Mean anomaly: |
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grad = np.radians(g_0 + 0.9856003 * dfrac) |
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# Ecliptic longitude: |
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lmrad = np.radians(l_sun + 1.915 * np.sin(grad) + 0.020 * np.sin(2 * grad)) |
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sinlm = np.sin(lmrad) |
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# Days (including fraction) since 12 UT on January 1 of 2000: |
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epoch_day = dfrac + 365.0 * yr2 + nleap |
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# Obliquity of ecliptic: |
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epsrad = np.radians(23.439 - 4.0e-7 * epoch_day) |
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# Right ascension: |
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alpha = np.degrees(np.arctan2(np.cos(epsrad) * sinlm, np.cos(lmrad))) |
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# Declination, which is the subsolar latitude: |
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sbsllat = np.degrees(np.arcsin(np.sin(epsrad) * sinlm)) |
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# Equation of time (degrees): |
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etdeg = l_sun - alpha |
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etdeg = etdeg - 360.0 * np.round(etdeg / 360.0) |
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# Apparent time (degrees): |
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aptime = utime / 240.0 + etdeg # Earth rotates one degree every 240 s. |
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# Subsolar longitude: |
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sbsllon = 180.0 - aptime |
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sbsllon = sbsllon - 360.0 * np.round(sbsllon / 360.0) |
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return sbsllon, sbsllat |
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def igrf_dipole_axis(date): |
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"""Get Cartesian unit vector pointing at dipole pole in the north, |
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according to IGRF |
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Parameters |
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---------- |
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date : (dt.datetime) |
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Date and time |
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Returns |
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------- |
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m_0: (np.ndarray) |
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Cartesian 3 element unit vector pointing at dipole pole in the north |
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(geocentric coords) |
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Notes |
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----- |
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IGRF coefficients are read from the igrf12coeffs.txt file. It should also |
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work after IGRF updates. The dipole coefficients are interpolated to the |
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date, or extrapolated if date > latest IGRF model |
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""" |
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# get time in years, as float: |
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year = date.year |
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doy = date.timetuple().tm_yday |
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year_days = dt.date(date.year, 12, 31).timetuple().tm_yday |
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year = year + doy / year_days |
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# read the IGRF coefficients |
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with open(aacgmv2.IGRF_COEFFS, 'r') as f_igrf: |
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lines = f_igrf.readlines() |
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years = lines[3].split()[3:][:-1] |
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years = np.array(years, dtype=float) # time array |
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g10 = lines[4].split()[3:] |
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g11 = lines[5].split()[3:] |
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h11 = lines[6].split()[3:] |
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# secular variation coefficients (for extrapolation) |
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g10sv = np.float32(g10[-1]) |
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g11sv = np.float32(g11[-1]) |
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h11sv = np.float32(h11[-1]) |
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# model coefficients: |
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g10 = np.array(g10[:-1], dtype=float) |
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g11 = np.array(g11[:-1], dtype=float) |
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h11 = np.array(h11[:-1], dtype=float) |
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# get the gauss coefficient at given time: |
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if year <= years[-1] and year >= years[0]: |
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# regular interpolation |
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g10 = np.interp(year, years, g10) |
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g11 = np.interp(year, years, g11) |
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h11 = np.interp(year, years, h11) |
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else: |
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# extrapolation |
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dyear = year - years[-1] |
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g10 = g10[-1] + g10sv * dyear |
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g11 = g11[-1] + g11sv * dyear |
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h11 = h11[-1] + h11sv * dyear |
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# calculate pole position |
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B_0 = np.sqrt(g10**2 + g11**2 + h11**2) |
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# Calculate output |
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m_0 = -np.array([g11, h11, g10]) / B_0 |
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return m_0 |
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aburrell /
aacgmv2
