"""
The ``irradiance`` module contains functions for modeling
global horizontal irradiance, direct normal irradiance,
diffuse horizontal irradiance, and total irradiance
under various conditions.
"""
from __future__ import division
import logging
pvl_logger = logging.getLogger('pvlib')
import datetime
import numpy as np
import pandas as pd
from pvlib import tools
from pvlib import solarposition
SURFACE_ALBEDOS = {'urban': 0.18,
'grass': 0.20,
'fresh grass': 0.26,
'soil': 0.17,
'sand': 0.40,
'snow': 0.65,
'fresh snow': 0.75,
'asphalt': 0.12,
'concrete': 0.30,
'aluminum': 0.85,
'copper': 0.74,
'fresh steel': 0.35,
'dirty steel': 0.08}
# would be nice if this took pandas index as well.
# Use try:except of isinstance.
def _scalar_to_datetimeindex(doy_scalar):
"""
Convert a scalar day of year number to a pd.DatetimeIndex.
Parameters
----------
doy_array : int or float
Contains days of the year
Returns
-------
pd.DatetimeIndex
"""
return pd.DatetimeIndex([_doy_to_timestamp(doy_scalar)])
def _array_to_datetimeindex(doy_array):
"""
Convert an array of day of year numbers to a pd.DatetimeIndex.
Parameters
----------
doy_array : Iterable
Contains days of the year
Returns
-------
pd.DatetimeIndex
"""
return pd.DatetimeIndex(list(map(_doy_to_timestamp, doy_array)))
def _doy_to_timestamp(doy, epoch='2013-12-31'):
"""
Convert a numeric day of the year to a pd.Timestamp.
Parameters
----------
doy : int or float.
Numeric day of year.
epoch : pd.Timestamp compatible object.
Date to which to add the day of year to.
Returns
-------
pd.Timestamp
"""
return pd.Timestamp('2013-12-31') + datetime.timedelta(days=float(doy))
[docs]def aoi_projection(surface_tilt, surface_azimuth, solar_zenith, solar_azimuth):
"""
Calculates the dot product of the solar vector and the surface normal.
Input all angles in degrees.
Parameters
==========
surface_tilt : float or Series.
Panel tilt from horizontal.
surface_azimuth : float or Series.
Panel azimuth from north.
solar_zenith : float or Series.
Solar zenith angle.
solar_azimuth : float or Series.
Solar azimuth angle.
Returns
=======
float or Series. Dot product of panel normal and solar angle.
"""
projection = (
tools.cosd(surface_tilt) * tools.cosd(solar_zenith) + tools.sind(surface_tilt) *
tools.sind(solar_zenith) * tools.cosd(solar_azimuth - surface_azimuth))
try:
projection.name = 'aoi_projection'
except AttributeError:
pass
return projection
[docs]def aoi(surface_tilt, surface_azimuth, solar_zenith, solar_azimuth):
"""
Calculates the angle of incidence of the solar vector on a surface.
This is the angle between the solar vector and the surface normal.
Input all angles in degrees.
Parameters
==========
surface_tilt : float or Series.
Panel tilt from horizontal.
surface_azimuth : float or Series.
Panel azimuth from north.
solar_zenith : float or Series.
Solar zenith angle.
solar_azimuth : float or Series.
Solar azimuth angle.
Returns
=======
float or Series. Angle of incidence in degrees.
"""
projection = aoi_projection(surface_tilt, surface_azimuth, solar_zenith, solar_azimuth)
aoi_value = np.rad2deg(np.arccos(projection))
try:
aoi_value.name = 'aoi'
except AttributeError:
pass
return aoi_value
[docs]def poa_horizontal_ratio(surface_tilt, surface_azimuth,
solar_zenith, solar_azimuth):
"""
Calculates the ratio of the beam components of the
plane of array irradiance and the horizontal irradiance.
Input all angles in degrees.
Parameters
==========
surface_tilt : float or Series.
Panel tilt from horizontal.
surface_azimuth : float or Series.
Panel azimuth from north.
solar_zenith : float or Series.
Solar zenith angle.
solar_azimuth : float or Series.
Solar azimuth angle.
Returns
=======
float or Series. Ratio of the plane of array irradiance to the
horizontal plane irradiance
"""
cos_poa_zen = aoi_projection(surface_tilt, surface_azimuth,
solar_zenith, solar_azimuth)
cos_solar_zenith = tools.cosd(solar_zenith)
# ratio of titled and horizontal beam irradiance
ratio = cos_poa_zen / cos_solar_zenith
try:
ratio.name = 'poa_ratio'
except AttributeError:
pass
return ratio
[docs]def beam_component(surface_tilt, surface_azimuth,
solar_zenith, solar_azimuth, dni):
"""
Calculates the beam component of the plane of array irradiance.
Parameters
----------
surface_tilt : float or Series.
Panel tilt from horizontal.
surface_azimuth : float or Series.
Panel azimuth from north.
solar_zenith : float or Series.
Solar zenith angle.
solar_azimuth : float or Series.
Solar azimuth angle.
dni : float or Series
Direct Normal Irradiance
Returns
-------
Series
"""
beam = dni * aoi_projection(surface_tilt, surface_azimuth,
solar_zenith, solar_azimuth)
beam[beam < 0] = 0
return beam
# ToDo: how to best structure this function? wholmgren 2014-11-03
[docs]def total_irrad(surface_tilt, surface_azimuth,
apparent_zenith, azimuth,
dni, ghi, dhi, dni_extra=None, airmass=None,
albedo=.25, surface_type=None,
model='isotropic',
model_perez='allsitescomposite1990', **kwargs):
'''
Determine diffuse irradiance from the sky on a
tilted surface.
.. math::
I_{tot} = I_{beam} + I_{sky} + I_{ground}
Parameters
----------
surface_tilt : float or Series.
Panel tilt from horizontal.
surface_azimuth : float or Series.
Panel azimuth from north.
solar_zenith : float or Series.
Solar zenith angle.
solar_azimuth : float or Series.
Solar azimuth angle.
dni : float or Series
Direct Normal Irradiance
ghi : float or Series
Global horizontal irradiance
dhi : float or Series
Diffuse horizontal irradiance
dni_extra : float or Series
Extraterrestrial direct normal irradiance
airmass : float or Series
Airmass
albedo : float
Surface albedo
surface_type : String
Surface type. See grounddiffuse.
model : String
Irradiance model.
model_perez : String
See perez.
Returns
-------
DataFrame with columns ``'poa_global', 'poa_direct',
'poa_sky_diffuse', 'poa_ground_diffuse'``.
References
----------
[1] Loutzenhiser P.G. et. al. "Empirical validation of models to compute
solar irradiance on inclined surfaces for building energy simulation"
2007, Solar Energy vol. 81. pp. 254-267
'''
pvl_logger.debug('planeofarray.total_irrad()')
solar_zenith = apparent_zenith
solar_azimuth = azimuth
beam = beam_component(surface_tilt, surface_azimuth,
solar_zenith, solar_azimuth, dni)
model = model.lower()
if model == 'isotropic':
sky = isotropic(surface_tilt, dhi)
elif model in ['klucher', 'klutcher']:
sky = klucher(surface_tilt, surface_azimuth, dhi, ghi,
solar_zenith, solar_azimuth)
elif model == 'haydavies':
sky = haydavies(surface_tilt, surface_azimuth, dhi, dni, dni_extra,
solar_zenith, solar_azimuth)
elif model == 'reindl':
sky = reindl(surface_tilt, surface_azimuth, dhi, dni, ghi, dni_extra,
solar_zenith, solar_azimuth)
elif model == 'king':
sky = king(surface_tilt, dhi, ghi, solar_zenith)
elif model == 'perez':
sky = perez(surface_tilt, surface_azimuth, dhi, dni, dni_extra,
solar_zenith, solar_azimuth, airmass,
modelt=model_perez)
else:
raise ValueError('invalid model selection {}'.format(model))
ground = grounddiffuse(surface_tilt, ghi, albedo, surface_type)
diffuse = sky + ground
total = beam + diffuse
all_irrad = pd.DataFrame()
all_irrad['poa_global'] = total
all_irrad['poa_direct'] = beam
all_irrad['poa_diffuse'] = diffuse
all_irrad['poa_sky_diffuse'] = sky
all_irrad['poa_ground_diffuse'] = ground
return all_irrad
# ToDo: keep this or not? wholmgren, 2014-11-03
[docs]def globalinplane(aoi, dni, poa_sky_diffuse, poa_ground_diffuse):
'''
Determine the three components on in-plane irradiance
Combines in-plane irradaince compoents from the chosen diffuse translation,
ground reflection and beam irradiance algorithms into the total in-plane
irradiance.
Parameters
----------
aoi : float or Series
Angle of incidence of solar rays with respect
to the module surface, from :func:`aoi`.
dni : float or Series
Direct normal irradiance (W/m^2), as measured
from a TMY file or calculated with a clearsky model.
poa_sky_diffuse : float or Series
Diffuse irradiance (W/m^2) in the plane of the modules, as
calculated by a diffuse irradiance translation function
poa_ground_diffuse : float or Series
Ground reflected irradiance (W/m^2) in the plane of the modules,
as calculated by an albedo model (eg. :func:`grounddiffuse`)
Returns
-------
DataFrame with the following keys:
* ``poa_global`` : Total in-plane irradiance (W/m^2)
* ``poa_direct`` : Total in-plane beam irradiance (W/m^2)
* ``poa_diffuse`` : Total in-plane diffuse irradiance (W/m^2)
Notes
------
Negative beam irradiation due to aoi :math:`> 90^{\circ}` or AOI
:math:`< 0^{\circ}` is set to zero.
'''
poa_direct = pd.Series(dni * np.cos(np.radians(aoi))).clip_lower(0)
poa_global = poa_direct + poa_sky_diffuse + poa_ground_diffuse
poa_diffuse = poa_sky_diffuse + poa_ground_diffuse
return pd.DataFrame({'poa_global': poa_global,
'poa_direct': poa_direct,
'poa_diffuse': poa_diffuse})
[docs]def grounddiffuse(surface_tilt, ghi, albedo=.25, surface_type=None):
'''
Estimate diffuse irradiance from ground reflections given
irradiance, albedo, and surface tilt
Function to determine the portion of irradiance on a tilted surface due
to ground reflections. Any of the inputs may be DataFrames or scalars.
Parameters
----------
surface_tilt : float or DataFrame
Surface tilt angles in decimal degrees.
SurfTilt must be >=0 and <=180. The tilt angle is defined as
degrees from horizontal (e.g. surface facing up = 0, surface facing
horizon = 90).
ghi : float or DataFrame
Global horizontal irradiance in W/m^2.
albedo : float or DataFrame
Ground reflectance, typically 0.1-0.4 for
surfaces on Earth (land), may increase over snow, ice, etc. May also
be known as the reflection coefficient. Must be >=0 and <=1.
Will be overridden if surface_type is supplied.
surface_type: None or string in
``'urban', 'grass', 'fresh grass', 'snow', 'fresh snow',
'asphalt', 'concrete', 'aluminum', 'copper',
'fresh steel', 'dirty steel'``.
Overrides albedo.
Returns
-------
float or DataFrame
Ground reflected irradiances in W/m^2.
References
----------
[1] Loutzenhiser P.G. et. al. "Empirical validation of models to compute
solar irradiance on inclined surfaces for building energy simulation"
2007, Solar Energy vol. 81. pp. 254-267.
The calculation is the last term of equations 3, 4, 7, 8, 10, 11, and 12.
[2] albedos from:
http://pvpmc.org/modeling-steps/incident-irradiance/plane-of-array-poa-irradiance/calculating-poa-irradiance/poa-ground-reflected/albedo/
and
http://en.wikipedia.org/wiki/Albedo
'''
pvl_logger.debug('diffuse_ground.get_diffuse_ground()')
if surface_type is not None:
albedo = SURFACE_ALBEDOS[surface_type]
pvl_logger.info('surface_type=%s mapped to albedo=%s',
surface_type, albedo)
diffuse_irrad = ghi * albedo * (1 - np.cos(np.radians(surface_tilt))) * 0.5
try:
diffuse_irrad.name = 'diffuse_ground'
except AttributeError:
pass
return diffuse_irrad
[docs]def isotropic(surface_tilt, dhi):
r'''
Determine diffuse irradiance from the sky on a
tilted surface using the isotropic sky model.
.. math::
I_{d} = DHI \frac{1 + \cos\beta}{2}
Hottel and Woertz's model treats the sky as a uniform source of diffuse
irradiance. Thus the diffuse irradiance from the sky (ground reflected
irradiance is not included in this algorithm) on a tilted surface can
be found from the diffuse horizontal irradiance and the tilt angle of
the surface.
Parameters
----------
surface_tilt : float or Series
Surface tilt angle in decimal degrees.
surface_tilt must be >=0 and <=180. The tilt angle is defined as
degrees from horizontal (e.g. surface facing up = 0, surface facing
horizon = 90)
dhi : float or Series
Diffuse horizontal irradiance in W/m^2.
DHI must be >=0.
Returns
-------
float or Series
The diffuse component of the solar radiation on an
arbitrarily tilted surface defined by the isotropic sky model as
given in Loutzenhiser et. al (2007) equation 3.
SkyDiffuse is the diffuse component ONLY and does not include the ground
reflected irradiance or the irradiance due to the beam.
SkyDiffuse is a column vector vector with a number of elements equal to
the input vector(s).
References
----------
[1] Loutzenhiser P.G. et. al. "Empirical validation of models to compute
solar irradiance on inclined surfaces for building energy simulation"
2007, Solar Energy vol. 81. pp. 254-267
[2] Hottel, H.C., Woertz, B.B., 1942. Evaluation of flat-plate solar heat
collector. Trans. ASME 64, 91.
'''
pvl_logger.debug('diffuse_sky.isotropic()')
sky_diffuse = dhi * (1 + tools.cosd(surface_tilt)) * 0.5
return sky_diffuse
[docs]def klucher(surface_tilt, surface_azimuth, dhi, ghi,
solar_zenith, solar_azimuth):
r'''
Determine diffuse irradiance from the sky on a tilted surface
using Klucher's 1979 model
.. math::
I_{d} = DHI \frac{1 + \cos\beta}{2} (1 + F' \sin^3(\beta/2))
(1 + F' \cos^2\theta\sin^3\theta_z)
where
.. math::
F' = 1 - (I_{d0} / GHI)
Klucher's 1979 model determines the diffuse irradiance from the sky
(ground reflected irradiance is not included in this algorithm) on a
tilted surface using the surface tilt angle, surface azimuth angle,
diffuse horizontal irradiance, direct normal irradiance, global
horizontal irradiance, extraterrestrial irradiance, sun zenith angle,
and sun azimuth angle.
Parameters
----------
surface_tilt : float or Series
Surface tilt angles in decimal degrees.
surface_tilt must be >=0 and <=180. The tilt angle is defined as
degrees from horizontal (e.g. surface facing up = 0, surface facing
horizon = 90)
surface_azimuth : float or Series
Surface azimuth angles in decimal degrees.
surface_azimuth must be >=0 and <=360. The Azimuth convention is defined
as degrees east of north (e.g. North = 0, South=180 East = 90,
West = 270).
dhi : float or Series
diffuse horizontal irradiance in W/m^2.
DHI must be >=0.
ghi : float or Series
Global irradiance in W/m^2.
DNI must be >=0.
solar_zenith : float or Series
apparent (refraction-corrected) zenith
angles in decimal degrees.
solar_zenith must be >=0 and <=180.
solar_azimuth : float or Series
Sun azimuth angles in decimal degrees.
solar_azimuth must be >=0 and <=360. The Azimuth convention is defined
as degrees east of north (e.g. North = 0, East = 90, West = 270).
Returns
-------
float or Series.
The diffuse component of the solar radiation on an
arbitrarily tilted surface defined by the Klucher model as given in
Loutzenhiser et. al (2007) equation 4.
SkyDiffuse is the diffuse component ONLY and does not include the ground
reflected irradiance or the irradiance due to the beam.
SkyDiffuse is a column vector vector with a number of elements equal to
the input vector(s).
References
----------
[1] Loutzenhiser P.G. et. al. "Empirical validation of models to compute
solar irradiance on inclined surfaces for building energy simulation"
2007, Solar Energy vol. 81. pp. 254-267
[2] Klucher, T.M., 1979. Evaluation of models to predict insolation on
tilted surfaces. Solar Energy 23 (2), 111-114.
'''
pvl_logger.debug('diffuse_sky.klucher()')
# zenith angle with respect to panel normal.
cos_tt = aoi_projection(surface_tilt, surface_azimuth,
solar_zenith, solar_azimuth)
F = 1 - ((ghi / ghi) ** 2)
try:
# fails with single point input
F.fillna(0, inplace=True)
except AttributeError:
F = 0
term1 = 0.5 * (1 + tools.cosd(surface_tilt))
term2 = 1 + F * (tools.sind(0.5 * surface_tilt) ** 3)
term3 = 1 + F * (cos_tt ** 2) * (tools.sind(solar_zenith) ** 3)
sky_diffuse = dhi * term1 * term2 * term3
return sky_diffuse
[docs]def haydavies(surface_tilt, surface_azimuth, dhi, dni, dni_extra,
solar_zenith=None, solar_azimuth=None, projection_ratio=None):
r'''
Determine diffuse irradiance from the sky on a
tilted surface using Hay & Davies' 1980 model
.. math::
I_{d} = DHI ( A R_b + (1 - A) (\frac{1 + \cos\beta}{2}) )
Hay and Davies' 1980 model determines the diffuse irradiance from the sky
(ground reflected irradiance is not included in this algorithm) on a
tilted surface using the surface tilt angle, surface azimuth angle,
diffuse horizontal irradiance, direct normal irradiance,
extraterrestrial irradiance, sun zenith angle, and sun azimuth angle.
Parameters
----------
surface_tilt : float or Series
Surface tilt angles in decimal degrees.
The tilt angle is defined as
degrees from horizontal (e.g. surface facing up = 0, surface facing
horizon = 90)
surface_azimuth : float or Series
Surface azimuth angles in decimal degrees.
The azimuth convention is defined
as degrees east of north (e.g. North=0, South=180, East=90,
West=270).
dhi : float or Series
Diffuse horizontal irradiance in W/m^2.
dni : float or Series
Direct normal irradiance in W/m^2.
dni_extra : float or Series
Extraterrestrial normal irradiance in W/m^2.
solar_zenith : None, float or Series
Solar apparent (refraction-corrected) zenith
angles in decimal degrees.
Must supply ``solar_zenith`` and ``solar_azimuth`` or supply
``projection_ratio``.
solar_azimuth : None, float or Series
Solar azimuth angles in decimal degrees.
Must supply ``solar_zenith`` and ``solar_azimuth`` or supply
``projection_ratio``.
projection_ratio : None, float or Series
Ratio of angle of incidence projection to solar zenith
angle projection.
Must supply ``solar_zenith`` and ``solar_azimuth`` or supply
``projection_ratio``.
Returns
--------
sky_diffuse : float or Series
The diffuse component of the solar radiation on an
arbitrarily tilted surface defined by the Perez model as given in
reference [3]. Does not include the
ground reflected irradiance or the irradiance due to the beam.
References
-----------
[1] Loutzenhiser P.G. et. al. "Empirical validation of models to compute
solar irradiance on inclined surfaces for building energy simulation"
2007, Solar Energy vol. 81. pp. 254-267
[2] Hay, J.E., Davies, J.A., 1980. Calculations of the solar radiation
incident on an inclined surface. In: Hay, J.E., Won, T.K. (Eds.), Proc. of
First Canadian Solar Radiation Data Workshop, 59. Ministry of Supply
and Services, Canada.
'''
pvl_logger.debug('diffuse_sky.haydavies()')
# if necessary, calculate ratio of titled and horizontal beam irradiance
if projection_ratio is None:
cos_tt = aoi_projection(surface_tilt, surface_azimuth,
solar_zenith, solar_azimuth)
cos_solar_zenith = tools.cosd(solar_zenith)
Rb = cos_tt / cos_solar_zenith
else:
Rb = projection_ratio
# Anisotropy Index
AI = dni / dni_extra
# these are actually the () and [] sub-terms of the second term of eqn 7
term1 = 1 - AI
term2 = 0.5 * (1 + tools.cosd(surface_tilt))
sky_diffuse = dhi * (AI * Rb + term1 * term2)
sky_diffuse[sky_diffuse < 0] = 0
return sky_diffuse
[docs]def reindl(surface_tilt, surface_azimuth, dhi, dni, ghi, dni_extra,
solar_zenith, solar_azimuth):
r'''
Determine diffuse irradiance from the sky on a
tilted surface using Reindl's 1990 model
.. math::
I_{d} = DHI (A R_b + (1 - A) (\frac{1 + \cos\beta}{2})
(1 + \sqrt{\frac{I_{hb}}{I_h}} \sin^3(\beta/2)) )
Reindl's 1990 model determines the diffuse irradiance from the sky
(ground reflected irradiance is not included in this algorithm) on a
tilted surface using the surface tilt angle, surface azimuth angle,
diffuse horizontal irradiance, direct normal irradiance, global
horizontal irradiance, extraterrestrial irradiance, sun zenith angle,
and sun azimuth angle.
Parameters
----------
surface_tilt : float or Series.
Surface tilt angles in decimal degrees.
The tilt angle is defined as
degrees from horizontal (e.g. surface facing up = 0, surface facing
horizon = 90)
surface_azimuth : float or Series.
Surface azimuth angles in decimal degrees.
The Azimuth convention is defined
as degrees east of north (e.g. North = 0, South=180 East = 90,
West = 270).
dhi : float or Series.
diffuse horizontal irradiance in W/m^2.
dni : float or Series.
direct normal irradiance in W/m^2.
ghi: float or Series.
Global irradiance in W/m^2.
dni_extra : float or Series.
extraterrestrial normal irradiance in W/m^2.
solar_zenith : float or Series.
apparent (refraction-corrected) zenith
angles in decimal degrees.
solar_azimuth : float or Series.
Sun azimuth angles in decimal degrees.
The Azimuth convention is defined
as degrees east of north (e.g. North = 0, East = 90, West = 270).
Returns
-------
poa_sky_diffuse : float or Series.
The diffuse component of the solar radiation on an
arbitrarily tilted surface defined by the Reindl model as given in
Loutzenhiser et. al (2007) equation 8.
SkyDiffuse is the diffuse component ONLY and does not include the
ground reflected irradiance or the irradiance due to the beam.
SkyDiffuse is a column vector vector with a number of elements equal to
the input vector(s).
Notes
-----
The poa_sky_diffuse calculation is generated from the Loutzenhiser et al.
(2007) paper, equation 8. Note that I have removed the beam and ground
reflectance portion of the equation and this generates ONLY the diffuse
radiation from the sky and circumsolar, so the form of the equation
varies slightly from equation 8.
References
----------
[1] Loutzenhiser P.G. et. al. "Empirical validation of models to compute
solar irradiance on inclined surfaces for building energy simulation"
2007, Solar Energy vol. 81. pp. 254-267
[2] Reindl, D.T., Beckmann, W.A., Duffie, J.A., 1990a. Diffuse fraction
correlations. Solar Energy 45(1), 1-7.
[3] Reindl, D.T., Beckmann, W.A., Duffie, J.A., 1990b. Evaluation of hourly
tilted surface radiation models. Solar Energy 45(1), 9-17.
'''
pvl_logger.debug('diffuse_sky.reindl()')
cos_tt = aoi_projection(surface_tilt, surface_azimuth,
solar_zenith, solar_azimuth)
cos_solar_zenith = tools.cosd(solar_zenith)
# ratio of titled and horizontal beam irradiance
Rb = cos_tt / cos_solar_zenith
# Anisotropy Index
AI = dni / dni_extra
# DNI projected onto horizontal
HB = dni * cos_solar_zenith
HB[HB < 0] = 0
# these are actually the () and [] sub-terms of the second term of eqn 8
term1 = 1 - AI
term2 = 0.5 * (1 + tools.cosd(surface_tilt))
term3 = 1 + np.sqrt(HB / ghi) * (tools.sind(0.5 * surface_tilt) ** 3)
sky_diffuse = dhi * (AI * Rb + term1 * term2 * term3)
sky_diffuse[sky_diffuse < 0] = 0
return sky_diffuse
[docs]def king(surface_tilt, dhi, ghi, solar_zenith):
'''
Determine diffuse irradiance from the sky on a tilted surface using the
King model.
King's model determines the diffuse irradiance from the sky
(ground reflected irradiance is not included in this algorithm) on a
tilted surface using the surface tilt angle, diffuse horizontal
irradiance, global horizontal irradiance, and sun zenith angle. Note
that this model is not well documented and has not been published in
any fashion (as of January 2012).
Parameters
----------
surface_tilt : float or Series
Surface tilt angles in decimal degrees.
The tilt angle is defined as
degrees from horizontal (e.g. surface facing up = 0, surface facing
horizon = 90)
dhi : float or Series
Diffuse horizontal irradiance in W/m^2.
ghi : float or Series
Global horizontal irradiance in W/m^2.
solar_zenith : float or Series
Apparent (refraction-corrected) zenith
angles in decimal degrees.
Returns
--------
poa_sky_diffuse : float or Series
The diffuse component of the solar radiation on an
arbitrarily tilted surface as given by a model developed by
David L. King at Sandia National Laboratories.
'''
pvl_logger.debug('diffuse_sky.king()')
sky_diffuse = (dhi * ((1 + tools.cosd(surface_tilt))) / 2 + ghi *
((0.012 * solar_zenith - 0.04)) *
((1 - tools.cosd(surface_tilt))) / 2)
sky_diffuse[sky_diffuse < 0] = 0
return sky_diffuse
[docs]def perez(surface_tilt, surface_azimuth, dhi, dni, dni_extra,
solar_zenith, solar_azimuth, airmass,
modelt='allsitescomposite1990'):
'''
Determine diffuse irradiance from the sky on a tilted surface using one of
the Perez models.
Perez models determine the diffuse irradiance from the sky (ground
reflected irradiance is not included in this algorithm) on a tilted
surface using the surface tilt angle, surface azimuth angle, diffuse
horizontal irradiance, direct normal irradiance, extraterrestrial
irradiance, sun zenith angle, sun azimuth angle, and relative (not
pressure-corrected) airmass. Optionally a selector may be used to use
any of Perez's model coefficient sets.
Parameters
----------
surface_tilt : float or Series
Surface tilt angles in decimal degrees.
surface_tilt must be >=0 and <=180. The tilt angle is defined as
degrees from horizontal (e.g. surface facing up = 0, surface facing
horizon = 90)
surface_azimuth : float or Series
Surface azimuth angles in decimal degrees.
surface_azimuth must be >=0 and <=360. The Azimuth convention is defined
as degrees east of north (e.g. North = 0, South=180 East = 90,
West = 270).
dhi : float or Series
Diffuse horizontal irradiance in W/m^2.
DHI must be >=0.
dni : float or Series
Direct normal irradiance in W/m^2.
DNI must be >=0.
dni_extra : float or Series
Extraterrestrial normal irradiance in W/m^2.
solar_zenith : float or Series
apparent (refraction-corrected) zenith
angles in decimal degrees.
solar_zenith must be >=0 and <=180.
solar_azimuth : float or Series
Sun azimuth angles in decimal degrees.
solar_azimuth must be >=0 and <=360. The Azimuth convention is defined
as degrees east of north (e.g. North = 0, East = 90, West = 270).
airmass : float or Series
relative (not pressure-corrected) airmass
values. If AM is a DataFrame it must be of the same size as all other
DataFrame inputs. AM must be >=0 (careful using the 1/sec(z) model of
AM generation)
model : string (optional, default='allsitescomposite1990')
A string which selects the desired set of Perez
coefficients. If model is not provided as an input, the default,
'1990' will be used.
All possible model selections are:
* '1990'
* 'allsitescomposite1990' (same as '1990')
* 'allsitescomposite1988'
* 'sandiacomposite1988'
* 'usacomposite1988'
* 'france1988'
* 'phoenix1988'
* 'elmonte1988'
* 'osage1988'
* 'albuquerque1988'
* 'capecanaveral1988'
* 'albany1988'
Returns
--------
float or Series
The diffuse component of the solar radiation on an
arbitrarily tilted surface defined by the Perez model as given in
reference [3].
SkyDiffuse is the diffuse component ONLY and does not include the
ground reflected irradiance or the irradiance due to the beam.
References
----------
[1] Loutzenhiser P.G. et. al. "Empirical validation of models to compute
solar irradiance on inclined surfaces for building energy simulation"
2007, Solar Energy vol. 81. pp. 254-267
[2] Perez, R., Seals, R., Ineichen, P., Stewart, R., Menicucci, D., 1987.
A new simplified version of the Perez diffuse irradiance model for tilted
surfaces. Solar Energy 39(3), 221-232.
[3] Perez, R., Ineichen, P., Seals, R., Michalsky, J., Stewart, R., 1990.
Modeling daylight availability and irradiance components from direct
and global irradiance. Solar Energy 44 (5), 271-289.
[4] Perez, R. et. al 1988. "The Development and Verification of the
Perez Diffuse Radiation Model". SAND88-7030
'''
pvl_logger.debug('diffuse_sky.perez()')
kappa = 1.041 # for solar_zenith in radians
z = np.radians(solar_zenith) # convert to radians
# epsilon is the sky's "clearness"
eps = ((dhi + dni) / dhi + kappa * (z ** 3)) / (1 + kappa * (z ** 3))
# Perez et al define clearness bins according to the following rules.
# 1 = overcast ... 8 = clear
# (these names really only make sense for small zenith angles, but...)
# these values will eventually be used as indicies for coeffecient look ups
ebin = eps.copy()
ebin[(eps < 1.065)] = 1
ebin[(eps >= 1.065) & (eps < 1.23)] = 2
ebin[(eps >= 1.23) & (eps < 1.5)] = 3
ebin[(eps >= 1.5) & (eps < 1.95)] = 4
ebin[(eps >= 1.95) & (eps < 2.8)] = 5
ebin[(eps >= 2.8) & (eps < 4.5)] = 6
ebin[(eps >= 4.5) & (eps < 6.2)] = 7
ebin[eps >= 6.2] = 8
ebin = ebin - 1 # correct for 0 indexing in coeffecient lookup
# remove night time values
ebin = ebin.dropna().astype(int)
# This is added because in cases where the sun is below the horizon
# (var.solar_zenith > 90) but there is still diffuse horizontal light
# (var.DHI>0), it is possible that the airmass (var.AM) could be NaN, which
# messes up later calculations. Instead, if the sun is down, and there is
# still var.DHI, we set the airmass to the airmass value on the horizon
# (approximately 37-38).
# var.AM(var.solar_zenith >=90 & var.DHI >0) = 37;
# var.DNI_ET[var.DNI_ET==0] = .00000001 #very hacky, fix this
# delta is the sky's "brightness"
delta = dhi * airmass / dni_extra
# keep only valid times
delta = delta[ebin.index]
z = z[ebin.index]
# The various possible sets of Perez coefficients are contained
# in a subfunction to clean up the code.
F1c, F2c = _get_perez_coefficients(modelt)
F1 = F1c[ebin, 0] + F1c[ebin, 1] * delta + F1c[ebin, 2] * z
F1[F1 < 0] = 0
F1 = F1.astype(float)
F2 = F2c[ebin, 0] + F2c[ebin, 1] * delta + F2c[ebin, 2] * z
F2[F2 < 0] = 0
F2 = F2.astype(float)
A = aoi_projection(surface_tilt, surface_azimuth,
solar_zenith, solar_azimuth)
A[A < 0] = 0
B = tools.cosd(solar_zenith)
B[B < tools.cosd(85)] = tools.cosd(85)
# Calculate Diffuse POA from sky dome
term1 = 0.5 * (1 - F1) * (1 + tools.cosd(surface_tilt))
term2 = F1 * A[ebin.index] / B[ebin.index]
term3 = F2 * tools.sind(surface_tilt)
sky_diffuse = dhi[ebin.index] * (term1 + term2 + term3)
sky_diffuse[sky_diffuse < 0] = 0
return sky_diffuse
def _get_perez_coefficients(perezmodelt):
'''
Find coefficients for the Perez model
Parameters
----------
perezmodelt : string (optional, default='allsitescomposite1990')
a character string which selects the desired set of Perez
coefficients. If model is not provided as an input, the default,
'1990' will be used.
All possible model selections are:
* '1990'
* 'allsitescomposite1990' (same as '1990')
* 'allsitescomposite1988'
* 'sandiacomposite1988'
* 'usacomposite1988'
* 'france1988'
* 'phoenix1988'
* 'elmonte1988'
* 'osage1988'
* 'albuquerque1988'
* 'capecanaveral1988'
* 'albany1988'
Returns
--------
F1coeffs : array
F1 coefficients for the Perez model
F2coeffs : array
F2 coefficients for the Perez model
References
----------
[1] Loutzenhiser P.G. et. al. "Empirical validation of models to compute
solar irradiance on inclined surfaces for building energy simulation"
2007, Solar Energy vol. 81. pp. 254-267
[2] Perez, R., Seals, R., Ineichen, P., Stewart, R., Menicucci, D., 1987.
A new simplified version of the Perez diffuse irradiance model for tilted
surfaces. Solar Energy 39(3), 221-232.
[3] Perez, R., Ineichen, P., Seals, R., Michalsky, J., Stewart, R., 1990.
Modeling daylight availability and irradiance components from direct
and global irradiance. Solar Energy 44 (5), 271-289.
[4] Perez, R. et. al 1988. "The Development and Verification of the
Perez Diffuse Radiation Model". SAND88-7030
'''
coeffdict = {
'allsitescomposite1990': [
[-0.0080, 0.5880, -0.0620, -0.0600, 0.0720, -0.0220],
[0.1300, 0.6830, -0.1510, -0.0190, 0.0660, -0.0290],
[0.3300, 0.4870, -0.2210, 0.0550, -0.0640, -0.0260],
[0.5680, 0.1870, -0.2950, 0.1090, -0.1520, -0.0140],
[0.8730, -0.3920, -0.3620, 0.2260, -0.4620, 0.0010],
[1.1320, -1.2370, -0.4120, 0.2880, -0.8230, 0.0560],
[1.0600, -1.6000, -0.3590, 0.2640, -1.1270, 0.1310],
[0.6780, -0.3270, -0.2500, 0.1560, -1.3770, 0.2510]],
'allsitescomposite1988': [
[-0.0180, 0.7050, -0.071, -0.0580, 0.1020, -0.0260],
[0.1910, 0.6450, -0.1710, 0.0120, 0.0090, -0.0270],
[0.4400, 0.3780, -0.2560, 0.0870, -0.1040, -0.0250],
[0.7560, -0.1210, -0.3460, 0.1790, -0.3210, -0.0080],
[0.9960, -0.6450, -0.4050, 0.2600, -0.5900, 0.0170],
[1.0980, -1.2900, -0.3930, 0.2690, -0.8320, 0.0750],
[0.9730, -1.1350, -0.3780, 0.1240, -0.2580, 0.1490],
[0.6890, -0.4120, -0.2730, 0.1990, -1.6750, 0.2370]],
'sandiacomposite1988': [
[-0.1960, 1.0840, -0.0060, -0.1140, 0.1800, -0.0190],
[0.2360, 0.5190, -0.1800, -0.0110, 0.0200, -0.0380],
[0.4540, 0.3210, -0.2550, 0.0720, -0.0980, -0.0460],
[0.8660, -0.3810, -0.3750, 0.2030, -0.4030, -0.0490],
[1.0260, -0.7110, -0.4260, 0.2730, -0.6020, -0.0610],
[0.9780, -0.9860, -0.3500, 0.2800, -0.9150, -0.0240],
[0.7480, -0.9130, -0.2360, 0.1730, -1.0450, 0.0650],
[0.3180, -0.7570, 0.1030, 0.0620, -1.6980, 0.2360]],
'usacomposite1988': [
[-0.0340, 0.6710, -0.0590, -0.0590, 0.0860, -0.0280],
[0.2550, 0.4740, -0.1910, 0.0180, -0.0140, -0.0330],
[0.4270, 0.3490, -0.2450, 0.0930, -0.1210, -0.0390],
[0.7560, -0.2130, -0.3280, 0.1750, -0.3040, -0.0270],
[1.0200, -0.8570, -0.3850, 0.2800, -0.6380, -0.0190],
[1.0500, -1.3440, -0.3480, 0.2800, -0.8930, 0.0370],
[0.9740, -1.5070, -0.3700, 0.1540, -0.5680, 0.1090],
[0.7440, -1.8170, -0.2560, 0.2460, -2.6180, 0.2300]],
'france1988': [
[0.0130, 0.7640, -0.1000, -0.0580, 0.1270, -0.0230],
[0.0950, 0.9200, -0.1520, 0, 0.0510, -0.0200],
[0.4640, 0.4210, -0.2800, 0.0640, -0.0510, -0.0020],
[0.7590, -0.0090, -0.3730, 0.2010, -0.3820, 0.0100],
[0.9760, -0.4000, -0.4360, 0.2710, -0.6380, 0.0510],
[1.1760, -1.2540, -0.4620, 0.2950, -0.9750, 0.1290],
[1.1060, -1.5630, -0.3980, 0.3010, -1.4420, 0.2120],
[0.9340, -1.5010, -0.2710, 0.4200, -2.9170, 0.2490]],
'phoenix1988': [
[-0.0030, 0.7280, -0.0970, -0.0750, 0.1420, -0.0430],
[0.2790, 0.3540, -0.1760, 0.0300, -0.0550, -0.0540],
[0.4690, 0.1680, -0.2460, 0.0480, -0.0420, -0.0570],
[0.8560, -0.5190, -0.3400, 0.1760, -0.3800, -0.0310],
[0.9410, -0.6250, -0.3910, 0.1880, -0.3600, -0.0490],
[1.0560, -1.1340, -0.4100, 0.2810, -0.7940, -0.0650],
[0.9010, -2.1390, -0.2690, 0.1180, -0.6650, 0.0460],
[0.1070, 0.4810, 0.1430, -0.1110, -0.1370, 0.2340]],
'elmonte1988': [
[0.0270, 0.7010, -0.1190, -0.0580, 0.1070, -0.0600],
[0.1810, 0.6710, -0.1780, -0.0790, 0.1940, -0.0350],
[0.4760, 0.4070, -0.2880, 0.0540, -0.0320, -0.0550],
[0.8750, -0.2180, -0.4030, 0.1870, -0.3090, -0.0610],
[1.1660, -1.0140, -0.4540, 0.2110, -0.4100, -0.0440],
[1.1430, -2.0640, -0.2910, 0.0970, -0.3190, 0.0530],
[1.0940, -2.6320, -0.2590, 0.0290, -0.4220, 0.1470],
[0.1550, 1.7230, 0.1630, -0.1310, -0.0190, 0.2770]],
'osage1988': [
[-0.3530, 1.4740, 0.0570, -0.1750, 0.3120, 0.0090],
[0.3630, 0.2180, -0.2120, 0.0190, -0.0340, -0.0590],
[-0.0310, 1.2620, -0.0840, -0.0820, 0.2310, -0.0170],
[0.6910, 0.0390, -0.2950, 0.0910, -0.1310, -0.0350],
[1.1820, -1.3500, -0.3210, 0.4080, -0.9850, -0.0880],
[0.7640, 0.0190, -0.2030, 0.2170, -0.2940, -0.1030],
[0.2190, 1.4120, 0.2440, 0.4710, -2.9880, 0.0340],
[3.5780, 22.2310, -10.7450, 2.4260, 4.8920, -5.6870]],
'albuquerque1988': [
[0.0340, 0.5010, -0.0940, -0.0630, 0.1060, -0.0440],
[0.2290, 0.4670, -0.1560, -0.0050, -0.0190, -0.0230],
[0.4860, 0.2410, -0.2530, 0.0530, -0.0640, -0.0220],
[0.8740, -0.3930, -0.3970, 0.1810, -0.3270, -0.0370],
[1.1930, -1.2960, -0.5010, 0.2810, -0.6560, -0.0450],
[1.0560, -1.7580, -0.3740, 0.2260, -0.7590, 0.0340],
[0.9010, -4.7830, -0.1090, 0.0630, -0.9700, 0.1960],
[0.8510, -7.0550, -0.0530, 0.0600, -2.8330, 0.3300]],
'capecanaveral1988': [
[0.0750, 0.5330, -0.1240, -0.0670, 0.0420, -0.0200],
[0.2950, 0.4970, -0.2180, -0.0080, 0.0030, -0.0290],
[0.5140, 0.0810, -0.2610, 0.0750, -0.1600, -0.0290],
[0.7470, -0.3290, -0.3250, 0.1810, -0.4160, -0.0300],
[0.9010, -0.8830, -0.2970, 0.1780, -0.4890, 0.0080],
[0.5910, -0.0440, -0.1160, 0.2350, -0.9990, 0.0980],
[0.5370, -2.4020, 0.3200, 0.1690, -1.9710, 0.3100],
[-0.8050, 4.5460, 1.0720, -0.2580, -0.9500, 0.7530]],
'albany1988': [
[0.0120, 0.5540, -0.0760, -0.0520, 0.0840, -0.0290],
[0.2670, 0.4370, -0.1940, 0.0160, 0.0220, -0.0360],
[0.4200, 0.3360, -0.2370, 0.0740, -0.0520, -0.0320],
[0.6380, -0.0010, -0.2810, 0.1380, -0.1890, -0.0120],
[1.0190, -1.0270, -0.3420, 0.2710, -0.6280, 0.0140],
[1.1490, -1.9400, -0.3310, 0.3220, -1.0970, 0.0800],
[1.4340, -3.9940, -0.4920, 0.4530, -2.3760, 0.1170],
[1.0070, -2.2920, -0.4820, 0.3900, -3.3680, 0.2290]], }
array = np.array(coeffdict[perezmodelt])
F1coeffs = array.T[0:3].T
F2coeffs = array.T[3:7].T
return F1coeffs, F2coeffs
[docs]def disc(ghi, zenith, times, pressure=101325):
'''
Estimate Direct Normal Irradiance from Global Horizontal Irradiance
using the DISC model.
The DISC algorithm converts global horizontal irradiance to direct
normal irradiance through empirical relationships between the global
and direct clearness indices.
Parameters
----------
ghi : Series
Global horizontal irradiance in W/m^2.
solar_zenith : Series
True (not refraction - corrected) solar zenith
angles in decimal degrees.
times : DatetimeIndex
pressure : float or Series
Site pressure in Pascal.
Returns
-------
DataFrame with the following keys:
* ``dni``: The modeled direct normal irradiance
in W/m^2 provided by the
Direct Insolation Simulation Code (DISC) model.
* ``kt``: Ratio of global to extraterrestrial
irradiance on a horizontal plane.
* ``airmass``: Airmass
References
----------
[1] Maxwell, E. L., "A Quasi-Physical Model for Converting Hourly
Global Horizontal to Direct Normal Insolation", Technical
Report No. SERI/TR-215-3087, Golden, CO: Solar Energy Research
Institute, 1987.
[2] J.W. "Fourier series representation of the position of the sun".
Found at:
http://www.mail-archive.com/sundial@uni-koeln.de/msg01050.html on
January 12, 2012
See Also
--------
atmosphere.alt2pres
dirint
'''
pvl_logger.debug('clearsky.disc')
temp = pd.DataFrame(index=times, columns=['A','B','C'], dtype=float)
doy = times.dayofyear
DayAngle = 2. * np.pi*(doy - 1) / 365
re = (1.00011 + 0.034221*np.cos(DayAngle) + 0.00128*np.sin(DayAngle)
+ 0.000719*np.cos(2.*DayAngle) + 7.7e-05*np.sin(2.*DayAngle) )
I0 = re * 1370.
I0h = I0 * np.cos(np.radians(zenith))
Ztemp = zenith.copy()
Ztemp[zenith > 87] = np.NaN
AM = 1.0 / ( np.cos(np.radians(Ztemp)) + 0.15*( (93.885 - Ztemp)**(-1.253) ) ) * (pressure / 101325)
Kt = ghi / I0h
Kt[Kt < 0] = 0
Kt[Kt > 2] = np.NaN
temp.A[Kt > 0.6] = -5.743 + 21.77*(Kt[Kt > 0.6]) - 27.49*(Kt[Kt > 0.6] ** 2) + 11.56*(Kt[Kt > 0.6] ** 3)
temp.B[Kt > 0.6] = 41.4 - 118.5*(Kt[Kt > 0.6]) + 66.05*(Kt[Kt > 0.6] ** 2) + 31.9*(Kt[Kt > 0.6] ** 3)
temp.C[Kt > 0.6] = -47.01 + 184.2*(Kt[Kt > 0.6]) - 222.0 * Kt[Kt > 0.6] ** 2 + 73.81*(Kt[Kt > 0.6] ** 3)
temp.A[Kt <= 0.6] = 0.512 - 1.56*(Kt[Kt <= 0.6]) + 2.286*(Kt[Kt <= 0.6] ** 2) - 2.222*(Kt[Kt <= 0.6] ** 3)
temp.B[Kt <= 0.6] = 0.37 + 0.962*(Kt[Kt <= 0.6])
temp.C[Kt <= 0.6] = -0.28 + 0.932*(Kt[Kt <= 0.6]) - 2.048*(Kt[Kt <= 0.6] ** 2)
delKn = temp.A + temp.B * np.exp(temp.C*AM)
Knc = 0.866 - 0.122*(AM) + 0.0121*(AM ** 2) - 0.000653*(AM ** 3) + 1.4e-05*(AM ** 4)
Kn = Knc - delKn
dni = Kn * I0
dni[zenith > 87] = np.NaN
dni[(ghi < 0) | (dni < 0)] = 0
dfout = pd.DataFrame({'dni':dni})
dfout['kt'] = Kt
dfout['airmass'] = AM
return dfout
[docs]def dirint(ghi, zenith, times, pressure=101325, use_delta_kt_prime=True,
temp_dew=None):
"""
Determine DNI from GHI using the DIRINT modification
of the DISC model.
Implements the modified DISC model known as "DIRINT" introduced in [1].
DIRINT predicts direct normal irradiance (DNI) from measured global
horizontal irradiance (GHI). DIRINT improves upon the DISC model by
using time-series GHI data and dew point temperature information. The
effectiveness of the DIRINT model improves with each piece of
information provided.
Parameters
----------
ghi : pd.Series
Global horizontal irradiance in W/m^2.
zenith : pd.Series
True (not refraction-corrected) zenith
angles in decimal degrees. If Z is a vector it must be of the
same size as all other vector inputs. Z must be >=0 and <=180.
times : DatetimeIndex
pressure : float or pd.Series
The site pressure in Pascal.
Pressure may be measured or an average pressure may be
calculated from site altitude.
use_delta_kt_prime : bool
Indicates if the user would like to
utilize the time-series nature of the GHI measurements. A value of ``False``
will not use the time-series improvements, any other numeric value
will use time-series improvements. It is recommended that time-series
data only be used if the time between measured data points is less
than 1.5 hours. If none of the input arguments are
vectors, then time-series improvements are not used (because it's not
a time-series).
temp_dew : None, float, or pd.Series
Surface dew point temperatures, in degrees C.
Values of temp_dew may be numeric or NaN. Any
single time period point with a DewPtTemp=NaN does not have dew point
improvements applied. If DewPtTemp is not provided, then dew point
improvements are not applied.
Returns
-------
dni : pd.Series.
The modeled direct normal irradiance in W/m^2 provided by the
DIRINT model.
References
----------
[1] Perez, R., P. Ineichen, E. Maxwell, R. Seals and A. Zelenka, (1992).
"Dynamic Global-to-Direct Irradiance Conversion Models". ASHRAE
Transactions-Research Series, pp. 354-369
[2] Maxwell, E. L., "A Quasi-Physical Model for Converting Hourly
Global Horizontal to Direct Normal Insolation", Technical
Report No. SERI/TR-215-3087, Golden, CO: Solar Energy Research
Institute, 1987.
DIRINT model requires time series data (ie. one of the inputs must be a
vector of length >2.
"""
pvl_logger.debug('clearsky.dirint')
disc_out = disc(ghi, zenith, times)
kt = disc_out['kt']
# Absolute Airmass, per the DISC model
# Note that we calculate the AM pressure correction slightly differently
# than Perez. He uses altitude, we use pressure (which we calculate
# slightly differently)
airmass = (1./(tools.cosd(zenith) + 0.15*((93.885-zenith)**(-1.253))) *
pressure/101325)
coeffs = _get_dirint_coeffs()
kt_prime = kt / (1.031 * np.exp(-1.4/(0.9+9.4/airmass)) + 0.1)
kt_prime[kt_prime > 0.82] = 0.82 # From SRRL code. consider np.NaN
kt_prime.fillna(0, inplace=True)
pvl_logger.debug('kt_prime:\n%s', kt_prime)
# wholmgren:
# the use_delta_kt_prime statement is a port of the MATLAB code.
# I am confused by the abs() in the delta_kt_prime calculation.
# It is not the absolute value of the central difference.
if use_delta_kt_prime:
delta_kt_prime = 0.5*( (kt_prime - kt_prime.shift(1)).abs()
.add(
(kt_prime - kt_prime.shift(-1)).abs(),
fill_value=0))
else:
delta_kt_prime = pd.Series(-1, index=times)
if temp_dew is not None:
w = pd.Series(np.exp(0.07 * temp_dew - 0.075), index=times)
else:
w = pd.Series(-1, index=times)
# @wholmgren: the following bin assignments use MATLAB's 1-indexing.
# Later, we'll subtract 1 to conform to Python's 0-indexing.
# Create kt_prime bins
kt_prime_bin = pd.Series(index=times)
kt_prime_bin[(kt_prime>=0) & (kt_prime<0.24)] = 1
kt_prime_bin[(kt_prime>=0.24) & (kt_prime<0.4)] = 2
kt_prime_bin[(kt_prime>=0.4) & (kt_prime<0.56)] = 3
kt_prime_bin[(kt_prime>=0.56) & (kt_prime<0.7)] = 4
kt_prime_bin[(kt_prime>=0.7) & (kt_prime<0.8)] = 5
kt_prime_bin[(kt_prime>=0.8) & (kt_prime<=1)] = 6
pvl_logger.debug('kt_prime_bin:\n%s', kt_prime_bin)
# Create zenith angle bins
zenith_bin = pd.Series(index=times)
zenith_bin[(zenith>=0) & (zenith<25)] = 1
zenith_bin[(zenith>=25) & (zenith<40)] = 2
zenith_bin[(zenith>=40) & (zenith<55)] = 3
zenith_bin[(zenith>=55) & (zenith<70)] = 4
zenith_bin[(zenith>=70) & (zenith<80)] = 5
zenith_bin[(zenith>=80)] = 6
pvl_logger.debug('zenith_bin:\n%s', zenith_bin)
# Create the bins for w based on dew point temperature
w_bin = pd.Series(index=times)
w_bin[(w>=0) & (w<1)] = 1
w_bin[(w>=1) & (w<2)] = 2
w_bin[(w>=2) & (w<3)] = 3
w_bin[(w>=3)] = 4
w_bin[(w == -1)] = 5
pvl_logger.debug('w_bin:\n%s', w_bin)
# Create delta_kt_prime binning.
delta_kt_prime_bin = pd.Series(index=times)
delta_kt_prime_bin[(delta_kt_prime>=0) & (delta_kt_prime<0.015)] = 1
delta_kt_prime_bin[(delta_kt_prime>=0.015) & (delta_kt_prime<0.035)] = 2
delta_kt_prime_bin[(delta_kt_prime>=0.035) & (delta_kt_prime<0.07)] = 3
delta_kt_prime_bin[(delta_kt_prime>=0.07) & (delta_kt_prime<0.15)] = 4
delta_kt_prime_bin[(delta_kt_prime>=0.15) & (delta_kt_prime<0.3)] = 5
delta_kt_prime_bin[(delta_kt_prime>=0.3) & (delta_kt_prime<=1)] = 6
delta_kt_prime_bin[delta_kt_prime == -1] = 7
pvl_logger.debug('delta_kt_prime_bin:\n%s', delta_kt_prime_bin)
# subtract 1 to account for difference between MATLAB-style bin
# assignment and Python-style array lookup.
dirint_coeffs = coeffs[kt_prime_bin-1, zenith_bin-1,
delta_kt_prime_bin-1, w_bin-1]
dni = disc_out['dni'] * dirint_coeffs
dni.name = 'dni'
return dni
def _get_dirint_coeffs():
"""
A place to stash the dirint coefficients.
Returns
-------
np.array with shape ``(6, 6, 7, 5)``.
Ordering is ``[kt_prime_bin, zenith_bin, delta_kt_prime_bin, w_bin]``
"""
# To allow for maximum copy/paste from the MATLAB 1-indexed code,
# we create and assign values to an oversized array.
# Then, we return the [1:, 1:, :, :] slice.
coeffs = np.zeros((7,7,7,5))
coeffs[1,1,:,:] = [
[0.385230, 0.385230, 0.385230, 0.462880, 0.317440],
[0.338390, 0.338390, 0.221270, 0.316730, 0.503650],
[0.235680, 0.235680, 0.241280, 0.157830, 0.269440],
[0.830130, 0.830130, 0.171970, 0.841070, 0.457370],
[0.548010, 0.548010, 0.478000, 0.966880, 1.036370],
[0.548010, 0.548010, 1.000000, 3.012370, 1.976540],
[0.582690, 0.582690, 0.229720, 0.892710, 0.569950 ]]
coeffs[1,2,:,:] = [
[0.131280, 0.131280, 0.385460, 0.511070, 0.127940],
[0.223710, 0.223710, 0.193560, 0.304560, 0.193940],
[0.229970, 0.229970, 0.275020, 0.312730, 0.244610],
[0.090100, 0.184580, 0.260500, 0.687480, 0.579440],
[0.131530, 0.131530, 0.370190, 1.380350, 1.052270],
[1.116250, 1.116250, 0.928030, 3.525490, 2.316920],
[0.090100, 0.237000, 0.300040, 0.812470, 0.664970 ]]
coeffs[1,3,:,:] = [
[0.587510, 0.130000, 0.400000, 0.537210, 0.832490],
[0.306210, 0.129830, 0.204460, 0.500000, 0.681640],
[0.224020, 0.260620, 0.334080, 0.501040, 0.350470],
[0.421540, 0.753970, 0.750660, 3.706840, 0.983790],
[0.706680, 0.373530, 1.245670, 0.864860, 1.992630],
[4.864400, 0.117390, 0.265180, 0.359180, 3.310820],
[0.392080, 0.493290, 0.651560, 1.932780, 0.898730 ]]
coeffs[1,4,:,:] = [
[0.126970, 0.126970, 0.126970, 0.126970, 0.126970],
[0.810820, 0.810820, 0.810820, 0.810820, 0.810820],
[3.241680, 2.500000, 2.291440, 2.291440, 2.291440],
[4.000000, 3.000000, 2.000000, 0.975430, 1.965570],
[12.494170, 12.494170, 8.000000, 5.083520, 8.792390],
[21.744240, 21.744240, 21.744240, 21.744240, 21.744240],
[3.241680, 12.494170, 1.620760, 1.375250, 2.331620 ]]
coeffs[1,5,:,:] = [
[0.126970, 0.126970, 0.126970, 0.126970, 0.126970],
[0.810820, 0.810820, 0.810820, 0.810820, 0.810820],
[3.241680, 2.500000, 2.291440, 2.291440, 2.291440],
[4.000000, 3.000000, 2.000000, 0.975430, 1.965570],
[12.494170, 12.494170, 8.000000, 5.083520, 8.792390],
[21.744240, 21.744240, 21.744240, 21.744240, 21.744240],
[3.241680, 12.494170, 1.620760, 1.375250, 2.331620 ]]
coeffs[1,6,:,:] = [
[0.126970, 0.126970, 0.126970, 0.126970, 0.126970],
[0.810820, 0.810820, 0.810820, 0.810820, 0.810820],
[3.241680, 2.500000, 2.291440, 2.291440, 2.291440],
[4.000000, 3.000000, 2.000000, 0.975430, 1.965570],
[12.494170, 12.494170, 8.000000, 5.083520, 8.792390],
[21.744240, 21.744240, 21.744240, 21.744240, 21.744240],
[3.241680, 12.494170, 1.620760, 1.375250, 2.331620 ]]
coeffs[2,1,:,:] = [
[0.337440, 0.337440, 0.969110, 1.097190, 1.116080],
[0.337440, 0.337440, 0.969110, 1.116030, 0.623900],
[0.337440, 0.337440, 1.530590, 1.024420, 0.908480],
[0.584040, 0.584040, 0.847250, 0.914940, 1.289300],
[0.337440, 0.337440, 0.310240, 1.435020, 1.852830],
[0.337440, 0.337440, 1.015010, 1.097190, 2.117230],
[0.337440, 0.337440, 0.969110, 1.145730, 1.476400 ]]
coeffs[2,2,:,:] = [
[0.300000, 0.300000, 0.700000, 1.100000, 0.796940],
[0.219870, 0.219870, 0.526530, 0.809610, 0.649300],
[0.386650, 0.386650, 0.119320, 0.576120, 0.685460],
[0.746730, 0.399830, 0.470970, 0.986530, 0.785370],
[0.575420, 0.936700, 1.649200, 1.495840, 1.335590],
[1.319670, 4.002570, 1.276390, 2.644550, 2.518670],
[0.665190, 0.678910, 1.012360, 1.199940, 0.986580 ]]
coeffs[2,3,:,:] = [
[0.378870, 0.974060, 0.500000, 0.491880, 0.665290],
[0.105210, 0.263470, 0.407040, 0.553460, 0.582590],
[0.312900, 0.345240, 1.144180, 0.854790, 0.612280],
[0.119070, 0.365120, 0.560520, 0.793720, 0.802600],
[0.781610, 0.837390, 1.270420, 1.537980, 1.292950],
[1.152290, 1.152290, 1.492080, 1.245370, 2.177100],
[0.424660, 0.529550, 0.966910, 1.033460, 0.958730 ]]
coeffs[2,4,:,:] = [
[0.310590, 0.714410, 0.252450, 0.500000, 0.607600],
[0.975190, 0.363420, 0.500000, 0.400000, 0.502800],
[0.175580, 0.196250, 0.476360, 1.072470, 0.490510],
[0.719280, 0.698620, 0.657770, 1.190840, 0.681110],
[0.426240, 1.464840, 0.678550, 1.157730, 0.978430],
[2.501120, 1.789130, 1.387090, 2.394180, 2.394180],
[0.491640, 0.677610, 0.685610, 1.082400, 0.735410 ]]
coeffs[2,5,:,:] = [
[0.597000, 0.500000, 0.300000, 0.310050, 0.413510],
[0.314790, 0.336310, 0.400000, 0.400000, 0.442460],
[0.166510, 0.460440, 0.552570, 1.000000, 0.461610],
[0.401020, 0.559110, 0.403630, 1.016710, 0.671490],
[0.400360, 0.750830, 0.842640, 1.802600, 1.023830],
[3.315300, 1.510380, 2.443650, 1.638820, 2.133990],
[0.530790, 0.745850, 0.693050, 1.458040, 0.804500 ]]
coeffs[2,6,:,:] = [
[0.597000, 0.500000, 0.300000, 0.310050, 0.800920],
[0.314790, 0.336310, 0.400000, 0.400000, 0.237040],
[0.166510, 0.460440, 0.552570, 1.000000, 0.581990],
[0.401020, 0.559110, 0.403630, 1.016710, 0.898570],
[0.400360, 0.750830, 0.842640, 1.802600, 3.400390],
[3.315300, 1.510380, 2.443650, 1.638820, 2.508780],
[0.204340, 1.157740, 2.003080, 2.622080, 1.409380 ]]
coeffs[3,1,:,:] = [
[1.242210, 1.242210, 1.242210, 1.242210, 1.242210],
[0.056980, 0.056980, 0.656990, 0.656990, 0.925160],
[0.089090, 0.089090, 1.040430, 1.232480, 1.205300],
[1.053850, 1.053850, 1.399690, 1.084640, 1.233340],
[1.151540, 1.151540, 1.118290, 1.531640, 1.411840],
[1.494980, 1.494980, 1.700000, 1.800810, 1.671600],
[1.018450, 1.018450, 1.153600, 1.321890, 1.294670 ]]
coeffs[3,2,:,:] = [
[0.700000, 0.700000, 1.023460, 0.700000, 0.945830],
[0.886300, 0.886300, 1.333620, 0.800000, 1.066620],
[0.902180, 0.902180, 0.954330, 1.126690, 1.097310],
[1.095300, 1.075060, 1.176490, 1.139470, 1.096110],
[1.201660, 1.201660, 1.438200, 1.256280, 1.198060],
[1.525850, 1.525850, 1.869160, 1.985410, 1.911590],
[1.288220, 1.082810, 1.286370, 1.166170, 1.119330 ]]
coeffs[3,3,:,:] = [
[0.600000, 1.029910, 0.859890, 0.550000, 0.813600],
[0.604450, 1.029910, 0.859890, 0.656700, 0.928840],
[0.455850, 0.750580, 0.804930, 0.823000, 0.911000],
[0.526580, 0.932310, 0.908620, 0.983520, 0.988090],
[1.036110, 1.100690, 0.848380, 1.035270, 1.042380],
[1.048440, 1.652720, 0.900000, 2.350410, 1.082950],
[0.817410, 0.976160, 0.861300, 0.974780, 1.004580 ]]
coeffs[3,4,:,:] = [
[0.782110, 0.564280, 0.600000, 0.600000, 0.665740],
[0.894480, 0.680730, 0.541990, 0.800000, 0.669140],
[0.487460, 0.818950, 0.841830, 0.872540, 0.709040],
[0.709310, 0.872780, 0.908480, 0.953290, 0.844350],
[0.863920, 0.947770, 0.876220, 1.078750, 0.936910],
[1.280350, 0.866720, 0.769790, 1.078750, 0.975130],
[0.725420, 0.869970, 0.868810, 0.951190, 0.829220 ]]
coeffs[3,5,:,:] = [
[0.791750, 0.654040, 0.483170, 0.409000, 0.597180],
[0.566140, 0.948990, 0.971820, 0.653570, 0.718550],
[0.648710, 0.637730, 0.870510, 0.860600, 0.694300],
[0.637630, 0.767610, 0.925670, 0.990310, 0.847670],
[0.736380, 0.946060, 1.117590, 1.029340, 0.947020],
[1.180970, 0.850000, 1.050000, 0.950000, 0.888580],
[0.700560, 0.801440, 0.961970, 0.906140, 0.823880 ]]
coeffs[3,6,:,:] = [
[0.500000, 0.500000, 0.586770, 0.470550, 0.629790],
[0.500000, 0.500000, 1.056220, 1.260140, 0.658140],
[0.500000, 0.500000, 0.631830, 0.842620, 0.582780],
[0.554710, 0.734730, 0.985820, 0.915640, 0.898260],
[0.712510, 1.205990, 0.909510, 1.078260, 0.885610],
[1.899260, 1.559710, 1.000000, 1.150000, 1.120390],
[0.653880, 0.793120, 0.903320, 0.944070, 0.796130 ]]
coeffs[4,1,:,:] = [
[1.000000, 1.000000, 1.050000, 1.170380, 1.178090],
[0.960580, 0.960580, 1.059530, 1.179030, 1.131690],
[0.871470, 0.871470, 0.995860, 1.141910, 1.114600],
[1.201590, 1.201590, 0.993610, 1.109380, 1.126320],
[1.065010, 1.065010, 0.828660, 0.939970, 1.017930],
[1.065010, 1.065010, 0.623690, 1.119620, 1.132260],
[1.071570, 1.071570, 0.958070, 1.114130, 1.127110 ]]
coeffs[4,2,:,:] = [
[0.950000, 0.973390, 0.852520, 1.092200, 1.096590],
[0.804120, 0.913870, 0.980990, 1.094580, 1.042420],
[0.737540, 0.935970, 0.999940, 1.056490, 1.050060],
[1.032980, 1.034540, 0.968460, 1.032080, 1.015780],
[0.900000, 0.977210, 0.945960, 1.008840, 0.969960],
[0.600000, 0.750000, 0.750000, 0.844710, 0.899100],
[0.926800, 0.965030, 0.968520, 1.044910, 1.032310 ]]
coeffs[4,3,:,:] = [
[0.850000, 1.029710, 0.961100, 1.055670, 1.009700],
[0.818530, 0.960010, 0.996450, 1.081970, 1.036470],
[0.765380, 0.953500, 0.948260, 1.052110, 1.000140],
[0.775610, 0.909610, 0.927800, 0.987800, 0.952100],
[1.000990, 0.881880, 0.875950, 0.949100, 0.893690],
[0.902370, 0.875960, 0.807990, 0.942410, 0.917920],
[0.856580, 0.928270, 0.946820, 1.032260, 0.972990 ]]
coeffs[4,4,:,:] = [
[0.750000, 0.857930, 0.983800, 1.056540, 0.980240],
[0.750000, 0.987010, 1.013730, 1.133780, 1.038250],
[0.800000, 0.947380, 1.012380, 1.091270, 0.999840],
[0.800000, 0.914550, 0.908570, 0.999190, 0.915230],
[0.778540, 0.800590, 0.799070, 0.902180, 0.851560],
[0.680190, 0.317410, 0.507680, 0.388910, 0.646710],
[0.794920, 0.912780, 0.960830, 1.057110, 0.947950 ]]
coeffs[4,5,:,:] = [
[0.750000, 0.833890, 0.867530, 1.059890, 0.932840],
[0.979700, 0.971470, 0.995510, 1.068490, 1.030150],
[0.858850, 0.987920, 1.043220, 1.108700, 1.044900],
[0.802400, 0.955110, 0.911660, 1.045070, 0.944470],
[0.884890, 0.766210, 0.885390, 0.859070, 0.818190],
[0.615680, 0.700000, 0.850000, 0.624620, 0.669300],
[0.835570, 0.946150, 0.977090, 1.049350, 0.979970 ]]
coeffs[4,6,:,:] = [
[0.689220, 0.809600, 0.900000, 0.789500, 0.853990],
[0.854660, 0.852840, 0.938200, 0.923110, 0.955010],
[0.938600, 0.932980, 1.010390, 1.043950, 1.041640],
[0.843620, 0.981300, 0.951590, 0.946100, 0.966330],
[0.694740, 0.814690, 0.572650, 0.400000, 0.726830],
[0.211370, 0.671780, 0.416340, 0.297290, 0.498050],
[0.843540, 0.882330, 0.911760, 0.898420, 0.960210 ]]
coeffs[5,1,:,:] = [
[1.054880, 1.075210, 1.068460, 1.153370, 1.069220],
[1.000000, 1.062220, 1.013470, 1.088170, 1.046200],
[0.885090, 0.993530, 0.942590, 1.054990, 1.012740],
[0.920000, 0.950000, 0.978720, 1.020280, 0.984440],
[0.850000, 0.908500, 0.839940, 0.985570, 0.962180],
[0.800000, 0.800000, 0.810080, 0.950000, 0.961550],
[1.038590, 1.063200, 1.034440, 1.112780, 1.037800 ]]
coeffs[5,2,:,:] = [
[1.017610, 1.028360, 1.058960, 1.133180, 1.045620],
[0.920000, 0.998970, 1.033590, 1.089030, 1.022060],
[0.912370, 0.949930, 0.979770, 1.020420, 0.981770],
[0.847160, 0.935300, 0.930540, 0.955050, 0.946560],
[0.880260, 0.867110, 0.874130, 0.972650, 0.883420],
[0.627150, 0.627150, 0.700000, 0.774070, 0.845130],
[0.973700, 1.006240, 1.026190, 1.071960, 1.017240 ]]
coeffs[5,3,:,:] = [
[1.028710, 1.017570, 1.025900, 1.081790, 1.024240],
[0.924980, 0.985500, 1.014100, 1.092210, 0.999610],
[0.828570, 0.934920, 0.994950, 1.024590, 0.949710],
[0.900810, 0.901330, 0.928830, 0.979570, 0.913100],
[0.761030, 0.845150, 0.805360, 0.936790, 0.853460],
[0.626400, 0.546750, 0.730500, 0.850000, 0.689050],
[0.957630, 0.985480, 0.991790, 1.050220, 0.987900 ]]
coeffs[5,4,:,:] = [
[0.992730, 0.993880, 1.017150, 1.059120, 1.017450],
[0.975610, 0.987160, 1.026820, 1.075440, 1.007250],
[0.871090, 0.933190, 0.974690, 0.979840, 0.952730],
[0.828750, 0.868090, 0.834920, 0.905510, 0.871530],
[0.781540, 0.782470, 0.767910, 0.764140, 0.795890],
[0.743460, 0.693390, 0.514870, 0.630150, 0.715660],
[0.934760, 0.957870, 0.959640, 0.972510, 0.981640 ]]
coeffs[5,5,:,:] = [
[0.965840, 0.941240, 0.987100, 1.022540, 1.011160],
[0.988630, 0.994770, 0.976590, 0.950000, 1.034840],
[0.958200, 1.018080, 0.974480, 0.920000, 0.989870],
[0.811720, 0.869090, 0.812020, 0.850000, 0.821050],
[0.682030, 0.679480, 0.632450, 0.746580, 0.738550],
[0.668290, 0.445860, 0.500000, 0.678920, 0.696510],
[0.926940, 0.953350, 0.959050, 0.876210, 0.991490 ]]
coeffs[5,6,:,:] = [
[0.948940, 0.997760, 0.850000, 0.826520, 0.998470],
[1.017860, 0.970000, 0.850000, 0.700000, 0.988560],
[1.000000, 0.950000, 0.850000, 0.606240, 0.947260],
[1.000000, 0.746140, 0.751740, 0.598390, 0.725230],
[0.922210, 0.500000, 0.376800, 0.517110, 0.548630],
[0.500000, 0.450000, 0.429970, 0.404490, 0.539940],
[0.960430, 0.881630, 0.775640, 0.596350, 0.937680 ]]
coeffs[6,1,:,:] = [
[1.030000, 1.040000, 1.000000, 1.000000, 1.049510],
[1.050000, 0.990000, 0.990000, 0.950000, 0.996530],
[1.050000, 0.990000, 0.990000, 0.820000, 0.971940],
[1.050000, 0.790000, 0.880000, 0.820000, 0.951840],
[1.000000, 0.530000, 0.440000, 0.710000, 0.928730],
[0.540000, 0.470000, 0.500000, 0.550000, 0.773950],
[1.038270, 0.920180, 0.910930, 0.821140, 1.034560 ]]
coeffs[6,2,:,:] = [
[1.041020, 0.997520, 0.961600, 1.000000, 1.035780],
[0.948030, 0.980000, 0.900000, 0.950360, 0.977460],
[0.950000, 0.977250, 0.869270, 0.800000, 0.951680],
[0.951870, 0.850000, 0.748770, 0.700000, 0.883850],
[0.900000, 0.823190, 0.727450, 0.600000, 0.839870],
[0.850000, 0.805020, 0.692310, 0.500000, 0.788410],
[1.010090, 0.895270, 0.773030, 0.816280, 1.011680 ]]
coeffs[6,3,:,:] = [
[1.022450, 1.004600, 0.983650, 1.000000, 1.032940],
[0.943960, 0.999240, 0.983920, 0.905990, 0.978150],
[0.936240, 0.946480, 0.850000, 0.850000, 0.930320],
[0.816420, 0.885000, 0.644950, 0.817650, 0.865310],
[0.742960, 0.765690, 0.561520, 0.700000, 0.827140],
[0.643870, 0.596710, 0.474460, 0.600000, 0.651200],
[0.971740, 0.940560, 0.714880, 0.864380, 1.001650 ]]
coeffs[6,4,:,:] = [
[0.995260, 0.977010, 1.000000, 1.000000, 1.035250],
[0.939810, 0.975250, 0.939980, 0.950000, 0.982550],
[0.876870, 0.879440, 0.850000, 0.900000, 0.917810],
[0.873480, 0.873450, 0.751470, 0.850000, 0.863040],
[0.761470, 0.702360, 0.638770, 0.750000, 0.783120],
[0.734080, 0.650000, 0.600000, 0.650000, 0.715660],
[0.942160, 0.919100, 0.770340, 0.731170, 0.995180 ]]
coeffs[6,5,:,:] = [
[0.952560, 0.916780, 0.920000, 0.900000, 1.005880],
[0.928620, 0.994420, 0.900000, 0.900000, 0.983720],
[0.913070, 0.850000, 0.850000, 0.800000, 0.924280],
[0.868090, 0.807170, 0.823550, 0.600000, 0.844520],
[0.769570, 0.719870, 0.650000, 0.550000, 0.733500],
[0.580250, 0.650000, 0.600000, 0.500000, 0.628850],
[0.904770, 0.852650, 0.708370, 0.493730, 0.949030 ]]
coeffs[6,6,:,:] = [
[0.911970, 0.800000, 0.800000, 0.800000, 0.956320],
[0.912620, 0.682610, 0.750000, 0.700000, 0.950110],
[0.653450, 0.659330, 0.700000, 0.600000, 0.856110],
[0.648440, 0.600000, 0.641120, 0.500000, 0.695780],
[0.570000, 0.550000, 0.598800, 0.400000, 0.560150],
[0.475230, 0.500000, 0.518640, 0.339970, 0.520230],
[0.743440, 0.592190, 0.603060, 0.316930, 0.794390 ]]
return coeffs[1:,1:,:,:]