"""This module contains general-purpose routines for computing
daily-average incoming solar radiation at the top of the atmosphere.
:Example:
Compute the timeseries of insolation at 65N at summer
solstice over the past 5 Myears::
import numpy as np
from climlab.solar.orbital import OrbitalTable
from climlab.solar.insolation import daily_insolation
# array with specified kyears (can be plain numpy or xarray.DataArray)
years = np.linspace(-5000, 0, 5001)
# subset of orbital parameters for specified time
orb = OrbitalTable.interp(kyear=years)
# insolation values for past 5 Myears at 65N at summer solstice (day 172)
S65 = daily_insolation(lat=65, day=172, orb=orb)
# returns an xarray.DataArray object with insolation values in W/m2
.. note::
Ported and modified from MATLAB code daily_insolation.m \n
*Original authors:* \n
Ian Eisenman and Peter Huybers, Harvard University, August 2006
Available online at http://eisenman.ucsd.edu/code/daily_insolation.m
If using calendar days, solar longitude is found using an
approximate solution to the differential equation representing conservation
of angular momentum (Kepler's Second Law). Given the orbital parameters
and solar longitude, daily average insolation is calculated exactly
following :cite:`Berger_1978`. Further references: :cite:`Berger_1991`.
"""
from __future__ import division
import numpy as np
from climlab import constants as const
from numpy import sqrt, deg2rad, rad2deg, sin, cos, tan, arcsin, arccos, pi
import xarray as xr
# suppress warning message generated by arccos here!
oldsettings = np.seterr(invalid='ignore')
[docs]
def daily_insolation(lat, day, orb=const.orb_present, S0=const.S0, day_type=1,
days_per_year=const.days_per_year):
"""Compute daily average insolation given latitude, time of year and orbital parameters.
Orbital parameters can be interpolated to any time in the last 5 Myears with
``climlab.solar.orbital.OrbitalTable`` (see example above).
Longer orbital tables are available with ``climlab.solar.orbital.LongOrbitalTable``
Inputs can be scalar, ``numpy.ndarray``, or ``xarray.DataArray``.
The return value will be ``numpy.ndarray`` if **all** the inputs are ``numpy``.
Otherwise ``xarray.DataArray``.
**Function-call argument** \n
:param array lat: Latitude in degrees (-90 to 90).
:param array day: Indicator of time of year. See argument ``day_type``
for details about format.
:param dict orb: a dictionary with three members (as provided by
``climlab.solar.orbital.OrbitalTable``)
* ``'ecc'`` - eccentricity
* unit: dimensionless
* default value: ``0.017236``
* ``'long_peri'`` - longitude of perihelion (precession angle)
* unit: degrees
* default value: ``281.37``
* ``'obliquity'`` - obliquity angle
* unit: degrees
* default value: ``23.446``
:param float S0: solar constant \n
- unit: :math:`\\textrm{W}/\\textrm{m}^2` \n
- default value: ``1365.2``
:param int day_type: Convention for specifying time of year (+/- 1,2) [optional].
*day_type=1* (default):
day input is calendar day (1-365.24), where day 1
is January first. The calendar is referenced to the
vernal equinox which always occurs at day 80.
*day_type=2:*
day input is solar longitude (0-360 degrees). Solar
longitude is the angle of the Earth's orbit measured from spring
equinox (21 March). Note that calendar days and solar longitude are
not linearly related because, by Kepler's Second Law, Earth's
angular velocity varies according to its distance from the sun.
:raises: :exc:`ValueError`
if day_type is neither 1 nor 2
:returns: Daily average solar radiation in unit
:math:`\\textrm{W}/\\textrm{m}^2`.
Dimensions of output are ``(lat.size, day.size, ecc.size)``
:rtype: array
Code is fully vectorized to handle array input for all arguments. \n
Orbital arguments should all have the same sizes.
This is automatic if computed from
:func:`~climlab.solar.orbital.OrbitalTable.lookup_parameters`
For more information about computation of solar insolation see the
:ref:`Tutorial` chapter.
"""
phi, day, ecc, long_peri, obliquity, input_is_xarray, _ignored = _standardize_inputs(lat, day, orb)
# lambda_long (solar longitude) is the angular distance along Earth's orbit
# measured from spring equinox (21 March)
if day_type==1: # calendar days
lambda_long = deg2rad(solar_longitude(day, orb, days_per_year))
elif day_type==2: #solar longitude (1-360) is specified in input, no need to convert days to longitude
lambda_long = deg2rad(day)
else:
raise ValueError('Invalid day_type.')
# Compute declination angle of the sun
delta = arcsin(sin(obliquity) * sin(lambda_long))
# Compute Ho, the hour angle at sunrise / sunset
# Check for no sunrise or no sunset: Berger 1978 eqn (8),(9)
Ho = xr.where( abs(delta)-pi/2+abs(phi) < 0., # there is sunset/sunrise
arccos(-tan(phi)*tan(delta)),
# otherwise figure out if it's all night or all day
xr.where(phi*delta>0., pi, 0.) )
# this is not really the daily average cosine of the zenith angle...
# it's the integral from sunrise to sunset of that quantity...
coszen = Ho*sin(phi)*sin(delta) + cos(phi)*cos(delta)*sin(Ho)
# Compute daily average insolation
Fsw = _compute_insolation_Berger(S0, ecc, lambda_long, long_peri, coszen)
if input_is_xarray:
return Fsw
else:
# Dimensional ordering consistent with previous numpy code
return Fsw.transpose().values
def _compute_insolation_Berger(S0, ecc, lambda_long, long_peri, coszen):
# Compute insolation: Berger 1978 eq (10)
return S0/pi*coszen*(1+ecc*cos(lambda_long - long_peri))**2 / (1-ecc**2)**2
[docs]
def instant_insolation(lat, day, lon=0., orb=const.orb_present, S0=const.S0,
days_per_year=const.days_per_year):
"""Compute instantaneous insolation given latitude, longitude, time of year and orbital parameters.
Orbital parameters can be interpolated to any time in the last 5 Myears with
``climlab.solar.orbital.OrbitalTable`` (see example above).
Longer orbital tables are available with ``climlab.solar.orbital.LongOrbitalTable``
Inputs can be scalar, ``numpy.ndarray``, or ``xarray.DataArray``.
The return value will be ``numpy.ndarray`` if **all** the inputs are ``numpy``.
Otherwise ``xarray.DataArray``.
**Function-call argument** \n
:param array lat: Latitude in degrees (-90 to 90).
:param array day: Indicator of time of year. Format is calendar day (1-365.24), where day 1
is January first. The calendar is referenced to the
vernal equinox which always occurs at day 80.
:param array lon: Longitude in degrees (0 to 360), optional. Defaults to zero.
:param dict orb: a dictionary with three members (as provided by
``climlab.solar.orbital.OrbitalTable``)
* ``'ecc'`` - eccentricity
* unit: dimensionless
* default value: ``0.017236``
* ``'long_peri'`` - longitude of perihelion (precession angle)
* unit: degrees
* default value: ``281.37``
* ``'obliquity'`` - obliquity angle
* unit: degrees
* default value: ``23.446``
:param float S0: solar constant \n
- unit: :math:`\\textrm{W}/\\textrm{m}^2` \n
- default value: ``1365.2``
:returns: Daily average solar radiation in unit
:math:`\\textrm{W}/\\textrm{m}^2`.
Dimensions of output are ``(lat.size, day.size, ecc.size)``
:rtype: array
Code is fully vectorized to handle array input for all arguments. \n
Orbital arguments should all have the same sizes.
This is automatic if computed from
:func:`~climlab.solar.orbital.OrbitalTable.lookup_parameters`
For more information about computation of solar insolation see the
:ref:`Tutorial` chapter.
"""
phi, day, ecc, long_peri, obliquity, input_is_xarray, lam = _standardize_inputs(lat, day, orb, lon)
# lambda_long (solar longitude) is the angular distance along Earth's orbit
# measured from spring equinox (21 March)
lambda_long = deg2rad(solar_longitude(day, orb, days_per_year))
# Compute declination angle of the sun
delta = arcsin(sin(obliquity) * sin(lambda_long))
# np.fmod(day, 1.0) finds the "fractional" time of day with a range of [0,1)
# where 0 is midnight, and 0.9999... is 23:59. lon/360 converts longitude
# to time since moving along the longitude axis produces the same effect as
# changing time while keeping longitude the same. the fractional time and
# fractional longitude are added together since they now both represent
# longitude/time of day. This lets us calculate the local solar time (in
# "fractional" units) and then convert to hour angle. The -0.5 is included
# in order to assert that noon occurs when the sun is overhead (so h=0 at
# LST=0.5 aka time=noon).
LST = np.fmod((np.fmod(day, 1.0) + (lam/(2*pi))), 1.0)
# hour angle in rad
h = (LST - 0.5) * 2*pi
# instantaneous cosine of solar zenith angle
coszen = (sin(phi)*sin(delta) + cos(phi)*cos(delta)*cos(h)) * pi
# Compute insolation
Fsw = _compute_insolation_Berger(S0, ecc, lambda_long, long_peri, coszen)
# assert |h|<=Ho, i.e. it is day time (same as checking Fsw >= 0)
Fsw = np.maximum(Fsw, 0.0)
if input_is_xarray:
return Fsw
else:
# Dimensional ordering consistent with previous numpy code
return Fsw.transpose().values
[docs]
def solar_longitude(day, orb=const.orb_present, days_per_year=const.days_per_year):
"""Estimates solar longitude from calendar day.
Method is using an approximation from :cite:`Berger_1978` section 3
(lambda = 0 at spring equinox).
**Function-call arguments** \n
:param array day: Indicator of time of year.
:param dict orb: a dictionary with three members (as provided by
:class:`~climlab.solar.orbital.OrbitalTable`)
* ``'ecc'`` - eccentricity
* unit: dimensionless
* default value: ``0.017236``
* ``'long_peri'`` - longitude of perihelion
(precession angle)
* unit: degrees
* default value: ``281.37``
* ``'obliquity'`` - obliquity angle
* unit: degrees
* default value: ``23.446``
:param float days_per_year: number of days in a year (optional)
(default: 365.2422)
Reads the length of the year from
:mod:`~climlab.utils.constants` if available.
:returns: solar longitude ``lambda_long`` in degrees
in dimension``( day.size, ecc.size )``
:rtype: array
Works for both scalar and vector orbital parameters.
"""
ecc = orb['ecc']
long_peri_rad = deg2rad( orb['long_peri'])
delta_lambda = (day - 80.) * 2*pi/days_per_year
beta = sqrt(1 - ecc**2)
lambda_long_m = -2*((ecc/2 + (ecc**3)/8 ) * (1+beta) * sin(-long_peri_rad) -
(ecc**2)/4 * (1/2 + beta) * sin(-2*long_peri_rad) + (ecc**3)/8 *
(1/3 + beta) * sin(-3*long_peri_rad)) + delta_lambda
lambda_long = ( lambda_long_m + (2*ecc - (ecc**3)/4)*sin(lambda_long_m - long_peri_rad) +
(5/4)*(ecc**2) * sin(2*(lambda_long_m - long_peri_rad)) + (13/12)*(ecc**3)
* sin(3*(lambda_long_m - long_peri_rad)) )
return rad2deg(lambda_long)
def _standardize_inputs(lat, day, orb, lon=None):
# Inputs can be scalar, numpy vector, or xarray.DataArray.
# If numpy, convert to xarray so that it will broadcast correctly
lat_is_xarray = True
day_is_xarray = True
lon_is_xarray = True
if type(lat) is np.ndarray:
lat_is_xarray = False
lat = xr.DataArray(lat, coords=[lat], dims=['lat'])
if type(day) is np.ndarray:
day_is_xarray = False
day = xr.DataArray(day, coords=[day], dims=['day'])
ecc = orb['ecc']
long_peri = deg2rad(orb['long_peri'])
obliquity = deg2rad(orb['obliquity'])
# Convert latitude (and all other angles) to radians
phi = deg2rad(lat)
input_is_xarray = lat_is_xarray or day_is_xarray
if lon is not None:
if type(lon) is np.ndarray:
lon_is_xarray = False
lon = xr.DataArray(lon, coords=[lon], dims=['lon'])
input_is_xarray = input_is_xarray or lon_is_xarray
lam = deg2rad(lon)
return phi, day, ecc, long_peri, obliquity, input_is_xarray, lam
else:
return phi, day, ecc, long_peri, obliquity, input_is_xarray, lon
