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# -*- coding: utf-8 -*- |
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"""This module contains helper functions used by :class:`~apexpy.Apex`.""" |
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from __future__ import division, print_function, absolute_import |
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import time |
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import datetime as dt |
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import numpy as np |
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def checklat(lat, name='lat'): |
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"""Makes sure the latitude is inside [-90, 90], clipping close values |
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(tolerance 1e-4). |
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Parameters |
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---------- |
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lat : array-like |
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latitude |
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name : str, optional |
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parameter name to use in the exception message |
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Returns |
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------- |
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lat : ndarray or float |
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Same as input where values just outside the range have been |
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clipped to [-90, 90] |
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Raises |
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------ |
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ValueError |
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if any values are too far outside the range [-90, 90] |
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""" |
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if np.any(np.abs(lat) > 90 + 1e-5): |
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raise ValueError(name + ' must be in [-90, 90]') |
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return np.clip(lat, -90.0, 90.0) |
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def getsinIm(alat): |
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"""Computes sinIm from modified apex latitude. |
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Parameters |
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---------- |
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alat : array-like |
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Modified apex latitude |
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Returns |
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------- |
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sinIm : ndarray or float |
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""" |
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alat = np.float64(alat) |
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return 2 * np.sin(np.radians(alat)) / np.sqrt(4 - 3 |
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* np.cos(np.radians(alat))**2) |
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def getcosIm(alat): |
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"""Computes cosIm from modified apex latitude. |
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Parameters |
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---------- |
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alat : array-like |
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Modified apex latitude |
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Returns |
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------- |
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cosIm : ndarray or float |
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""" |
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alat = np.float64(alat) |
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return np.cos(np.radians(alat)) / np.sqrt(4 - 3 |
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* np.cos(np.radians(alat))**2) |
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def toYearFraction(date): |
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"""Converts :class:`datetime.date` or :class:`datetime.datetime` to decimal |
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year. |
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Parameters |
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---------- |
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date : :class:`datetime.date` or :class:`datetime.datetime` |
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Returns |
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------- |
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year : float |
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Decimal year |
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Notes |
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----- |
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The algorithm is taken from http://stackoverflow.com/a/6451892/2978652 |
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""" |
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def sinceEpoch(date): |
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"""returns seconds since epoch""" |
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return time.mktime(date.timetuple()) |
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year = date.year |
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startOfThisYear = dt.datetime(year=year, month=1, day=1) |
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startOfNextYear = dt.datetime(year=year + 1, month=1, day=1) |
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yearElapsed = sinceEpoch(date) - sinceEpoch(startOfThisYear) |
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yearDuration = sinceEpoch(startOfNextYear) - sinceEpoch(startOfThisYear) |
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fraction = yearElapsed / yearDuration |
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return date.year + fraction |
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def gc2gdlat(gclat): |
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"""Converts geocentric latitude to geodetic latitude using WGS84. |
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Parameters |
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--------- |
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gclat : array-like |
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Geocentric latitude |
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Returns |
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------- |
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gdlat : ndarray or float |
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Geodetic latitude |
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""" |
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WGS84_e2 = 0.006694379990141317 # WGS84 first eccentricity squared |
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return np.rad2deg(-np.arctan(np.tan(np.deg2rad(gclat)) / (WGS84_e2 - 1))) |
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def subsol(datetime): |
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"""Finds subsolar geocentric latitude and longitude. |
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Parameters |
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---------- |
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datetime : :class:`datetime.datetime` or :class:`numpy.ndarray[datetime64]` |
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Date and time in UTC (naive objects are treated as UTC) |
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Returns |
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------- |
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sbsllat : float |
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Latitude of subsolar point |
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sbsllon : float |
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Longitude of subsolar point |
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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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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 to year, day of year and seconds since midnight |
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if isinstance(datetime, dt.datetime): |
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year = np.asanyarray([datetime.year]) |
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doy = np.asanyarray([datetime.timetuple().tm_yday]) |
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ut = np.asanyarray([datetime.hour * 3600 + datetime.minute * 60 |
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+ datetime.second]) |
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elif isinstance(datetime, np.ndarray): |
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# This conversion works for datetime of wrong precision or unit epoch |
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times = datetime.astype('datetime64[s]') |
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year_floor = times.astype('datetime64[Y]') |
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day_floor = times.astype('datetime64[D]') |
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year = year_floor.astype(int) + 1970 |
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doy = (day_floor - year_floor).astype(int) + 1 |
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ut = (times.astype('datetime64[s]') - day_floor).astype(float) |
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else: |
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raise ValueError("input must be datetime.datetime or numpy array") |
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if not (np.all(1601 <= year) and np.all(year <= 2100)): |
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raise ValueError('Year must be in [1601, 2100]') |
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yr = year - 2000 |
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nleap = np.floor((year - 1601.0) / 4.0).astype(int) |
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nleap -= 99 |
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mask_1900 = year <= 1900 |
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if np.any(mask_1900): |
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ncent = np.floor((year[mask_1900] - 1601.0) / 100.0).astype(int) |
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ncent = 3 - ncent |
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nleap[mask_1900] = nleap[mask_1900] + ncent |
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l0 = -79.549 + (-0.238699 * (yr - 4.0 * nleap) + 3.08514e-2 * nleap) |
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g0 = -2.472 + (-0.2558905 * (yr - 4.0 * nleap) - 3.79617e-2 * nleap) |
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# Days (including fraction) since 12 UT on January 1 of IYR: |
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df = (ut / 86400.0 - 1.5) + doy |
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# Mean longitude of Sun: |
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lmean = l0 + 0.9856474 * df |
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# Mean anomaly in radians: |
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grad = np.radians(g0 + 0.9856003 * df) |
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# Ecliptic longitude: |
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lmrad = np.radians(lmean + 1.915 * np.sin(grad) |
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+ 0.020 * np.sin(2.0 * grad)) |
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sinlm = np.sin(lmrad) |
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# Obliquity of ecliptic in radians: |
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epsrad = np.radians(23.439 - 4e-7 * (df + 365 * yr + nleap)) |
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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 also the subsolar latitude: |
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sslat = np.degrees(np.arcsin(np.sin(epsrad) * sinlm)) |
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# Equation of time (degrees): |
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etdeg = lmean - alpha |
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nrot = np.round(etdeg / 360.0) |
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etdeg = etdeg - 360.0 * nrot |
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# Subsolar longitude calculation. Earth rotates one degree every 240 s. |
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sslon = 180.0 - (ut / 240.0 + etdeg) |
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nrot = np.round(sslon / 360.0) |
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sslon = sslon - 360.0 * nrot |
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# Return a single value from the output if the input was a single value |
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if isinstance(datetime, dt.datetime): |
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return sslat[0], sslon[0] |
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return sslat, sslon |
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