"""
The ``atmosphere`` module contains methods to calculate relative and
absolute airmass and to determine pressure from altitude or vice versa.
"""
import numpy as np
import pandas as pd
import pvlib
from pvlib._deprecation import deprecated
APPARENT_ZENITH_MODELS = ('simple', 'kasten1966', 'kastenyoung1989',
'gueymard1993', 'pickering2002')
TRUE_ZENITH_MODELS = ('youngirvine1967', 'young1994')
AIRMASS_MODELS = APPARENT_ZENITH_MODELS + TRUE_ZENITH_MODELS
[docs]def pres2alt(pressure):
'''
Determine altitude from site pressure.
Parameters
----------
pressure : numeric
Atmospheric pressure. [Pa]
Returns
-------
altitude : numeric
Altitude above sea level. [m]
Notes
------
The following assumptions are made
============================ ================
Parameter Value
============================ ================
Base pressure 101325 Pa
Temperature at zero altitude 288.15 K
Gravitational acceleration 9.80665 m/s^2
Lapse rate -6.5E-3 K/m
Gas constant for air 287.053 J/(kg K)
Relative Humidity 0%
============================ ================
References
-----------
.. [1] "A Quick Derivation relating altitude to air pressure" from
Portland State Aerospace Society, Version 1.03, 12/22/2004.
'''
alt = 44331.5 - 4946.62 * pressure ** (0.190263)
return alt
[docs]def alt2pres(altitude):
'''
Determine site pressure from altitude.
Parameters
----------
altitude : numeric
Altitude above sea level. [m]
Returns
-------
pressure : numeric
Atmospheric pressure. [Pa]
Notes
------
The following assumptions are made
============================ ================
Parameter Value
============================ ================
Base pressure 101325 Pa
Temperature at zero altitude 288.15 K
Gravitational acceleration 9.80665 m/s^2
Lapse rate -6.5E-3 K/m
Gas constant for air 287.053 J/(kg K)
Relative Humidity 0%
============================ ================
References
-----------
.. [1] "A Quick Derivation relating altitude to air pressure" from
Portland State Aerospace Society, Version 1.03, 12/22/2004.
'''
press = 100 * ((44331.514 - altitude) / 11880.516) ** (1 / 0.1902632)
return press
[docs]def get_absolute_airmass(airmass_relative, pressure=101325.):
r'''
Determine absolute (pressure-adjusted) airmass from relative
airmass and pressure.
The calculation for absolute airmass (:math:`AM_a`) is
.. math::
AM_a = AM_r \frac{P}{101325}
where :math:`AM_r` is relative air mass at sea level and :math:`P` is
atmospheric pressure.
Parameters
----------
airmass_relative : numeric
The airmass at sea level. [unitless]
pressure : numeric, default 101325
Atmospheric pressure. [Pa]
Returns
-------
airmass_absolute : numeric
Absolute (pressure-adjusted) airmass
References
----------
.. [1] C. Gueymard, "Critical analysis and performance assessment of
clear sky solar irradiance models using theoretical and measured
data," Solar Energy, vol. 51, pp. 121-138, 1993.
'''
airmass_absolute = airmass_relative * pressure / 101325.
return airmass_absolute
[docs]def get_relative_airmass(zenith, model='kastenyoung1989'):
'''
Calculate relative (not pressure-adjusted) airmass at sea level.
Parameter ``model`` allows selection of different airmass models.
Parameters
----------
zenith : numeric
Zenith angle of the sun. [degrees]
model : string, default 'kastenyoung1989'
Available models include the following:
* 'simple' - secant(apparent zenith angle) -
Note that this gives -Inf at zenith=90
* 'kasten1966' - See reference [1] -
requires apparent sun zenith
* 'youngirvine1967' - See reference [2] -
requires true sun zenith
* 'kastenyoung1989' (default) - See reference [3] -
requires apparent sun zenith
* 'gueymard1993' - See reference [4] -
requires apparent sun zenith
* 'young1994' - See reference [5] -
requires true sun zenith
* 'pickering2002' - See reference [6] -
requires apparent sun zenith
* 'gueymard2003' - See references [7] and [8] -
requires apparent sun zenith
Returns
-------
airmass_relative : numeric
Relative airmass at sea level. Returns NaN values for any
zenith angle greater than 90 degrees. [unitless]
Notes
-----
Some models use apparent (refraction-adjusted) zenith angle while
other models use true (not refraction-adjusted) zenith angle. Apparent
zenith angles should be calculated at sea level.
References
----------
.. [1] Fritz Kasten. "A New Table and Approximation Formula for the
Relative Optical Air Mass". Technical Report 136, Hanover, N.H.:
U.S. Army Material Command, CRREL.
.. [2] A. T. Young and W. M. Irvine, "Multicolor Photoelectric
Photometry of the Brighter Planets," The Astronomical Journal, vol.
72, pp. 945-950, 1967.
.. [3] Fritz Kasten and Andrew Young. "Revised optical air mass tables
and approximation formula". Applied Optics 28:4735-4738
.. [4] C. Gueymard, "Critical analysis and performance assessment of
clear sky solar irradiance models using theoretical and measured
data," Solar Energy, vol. 51, pp. 121-138, 1993.
.. [5] A. T. Young, "AIR-MASS AND REFRACTION," Applied Optics, vol. 33,
pp. 1108-1110, Feb 1994.
.. [6] Keith A. Pickering. "The Ancient Star Catalog". DIO 12:1, 20,
.. [7] C. Gueymard, "Direct solar transmittance and irradiance
predictions with broadband models. Part I: detailed theoretical
performance assessment". Solar Energy, vol 74, pp. 355-379, 2003.
:doi:`10.1016/S0038-092X(03)00195-6`
.. [8] C. Gueymard (2019). Clear-Sky Radiation Models and Aerosol Effects.
In: Polo, J., Martín-Pomares, L., Sanfilippo, A. (eds) Solar Resources
Mapping. Green Energy and Technology. Springer, Cham.
:doi:`10.1007/978-3-319-97484-2_5`
.. [9] Matthew J. Reno, Clifford W. Hansen and Joshua S. Stein, "Global
Horizontal Irradiance Clear Sky Models: Implementation and Analysis"
Sandia Report, (2012).
'''
# set zenith values greater than 90 to nans
z = np.where(zenith > 90, np.nan, zenith)
zenith_rad = np.radians(z)
model = model.lower()
if 'kastenyoung1989' == model:
am = (1.0 / (np.cos(zenith_rad) +
0.50572*((6.07995 + (90 - z)) ** - 1.6364)))
elif 'kasten1966' == model:
am = 1.0 / (np.cos(zenith_rad) + 0.15*((93.885 - z) ** - 1.253))
elif 'simple' == model:
am = 1.0 / np.cos(zenith_rad)
elif 'pickering2002' == model:
am = (1.0 / (np.sin(np.radians(90 - z +
244.0 / (165 + 47.0 * (90 - z) ** 1.1)))))
elif 'youngirvine1967' == model:
sec_zen = 1.0 / np.cos(zenith_rad)
am = sec_zen * (1 - 0.0012 * (sec_zen * sec_zen - 1))
elif 'young1994' == model:
am = ((1.002432*((np.cos(zenith_rad)) ** 2) +
0.148386*(np.cos(zenith_rad)) + 0.0096467) /
(np.cos(zenith_rad) ** 3 +
0.149864*(np.cos(zenith_rad) ** 2) +
0.0102963*(np.cos(zenith_rad)) + 0.000303978))
elif 'gueymard1993' == model:
am = (1.0 / (np.cos(zenith_rad) +
0.00176759*(z)*((94.37515 - z) ** - 1.21563)))
elif 'gueymard2003' == model:
am = (1.0 / (np.cos(zenith_rad) +
0.48353*(z**0.095846)/(96.741 - z)**1.754))
else:
raise ValueError('%s is not a valid model for relativeairmass', model)
if isinstance(zenith, pd.Series):
am = pd.Series(am, index=zenith.index)
return am
[docs]def gueymard94_pw(temp_air, relative_humidity):
r"""
Calculates precipitable water (cm) from ambient air temperature (C)
and relatively humidity (%) using an empirical model. The
accuracy of this method is approximately 20% for moderate PW (1-3
cm) and less accurate otherwise.
The model was developed by expanding Eq. 1 in [2]_:
.. math::
Pw = 0.1 H_v \rho_v
using Eq. 2 in [2]_
.. math::
\rho_v = 216.7 R_H e_s /T
:math:`Pw` is the precipitable water (cm), :math:`H_v` is the apparent
water vapor scale height (km) and :math:`\rho_v` is the surface water
vapor density (g/m^3). . The expression for :math:`H_v` is Eq. 4 in [2]_:
.. math::
H_v = 0.4976 + 1.5265 \frac{T}{273.15}
+ \exp \left(13.6897 \frac{T}{273.15}
- 14.9188 \left( \frac{T}{273.15} \right)^3 \right)
In the expression for :math:`\rho_v`, :math:`e_s` is the saturation water
vapor pressure (millibar). The expression for :math:`e_s` is Eq. 1 in [3]_
.. math::
e_s = \exp \left(22.330 - 49.140 \frac{100}{T} -
10.922 \left(\frac{100}{T}\right)^2 -
0.39015 \frac{T}{100} \right)
Parameters
----------
temp_air : numeric
ambient air temperature :math:`T` at the surface. [C]
relative_humidity : numeric
relative humidity :math:`R_H` at the surface. [%]
Returns
-------
pw : numeric
precipitable water. [cm]
References
----------
.. [1] W. M. Keogh and A. W. Blakers, Accurate Measurement, Using Natural
Sunlight, of Silicon Solar Cells, Prog. in Photovoltaics: Res.
and Appl. 2004, vol 12, pp. 1-19 (:doi:`10.1002/pip.517`)
.. [2] C. Gueymard, Analysis of Monthly Average Atmospheric Precipitable
Water and Turbidity in Canada and Northern United States,
Solar Energy vol 53(1), pp. 57-71, 1994.
.. [3] C. Gueymard, Assessment of the Accuracy and Computing Speed of
simplified saturation vapor equations using a new reference
dataset, J. of Applied Meteorology 1993, vol. 32(7), pp.
1294-1300.
"""
T = temp_air + 273.15 # Convert to Kelvin # noqa: N806
RH = relative_humidity # noqa: N806
theta = T / 273.15
# Eq. 1 from Keogh and Blakers
pw = (
0.1 *
(0.4976 + 1.5265*theta + np.exp(13.6897*theta - 14.9188*(theta)**3)) *
(216.7*RH/(100*T)*np.exp(22.330 - 49.140*(100/T) -
10.922*(100/T)**2 - 0.39015*T/100)))
pw = np.maximum(pw, 0.1)
return pw
first_solar_spectral_correction = deprecated(
since='0.10.0',
alternative='pvlib.spectrum.spectral_factor_firstsolar'
)(pvlib.spectrum.spectral_factor_firstsolar)
[docs]def bird_hulstrom80_aod_bb(aod380, aod500):
"""
Approximate broadband aerosol optical depth.
Bird and Hulstrom developed a correlation for broadband aerosol optical
depth (AOD) using two wavelengths, 380 nm and 500 nm.
Parameters
----------
aod380 : numeric
AOD measured at 380 nm. [unitless]
aod500 : numeric
AOD measured at 500 nm. [unitless]
Returns
-------
aod_bb : numeric
Broadband AOD. [unitless]
See also
--------
pvlib.atmosphere.kasten96_lt
References
----------
.. [1] Bird and Hulstrom, "Direct Insolation Models" (1980)
`SERI/TR-335-344 <http://www.nrel.gov/docs/legosti/old/344.pdf>`_
.. [2] R. E. Bird and R. L. Hulstrom, "Review, Evaluation, and Improvement
of Direct Irradiance Models", Journal of Solar Energy Engineering
103(3), pp. 182-192 (1981)
:doi:`10.1115/1.3266239`
"""
# approximate broadband AOD using (Bird-Hulstrom 1980)
return 0.27583 * aod380 + 0.35 * aod500
[docs]def kasten96_lt(airmass_absolute, precipitable_water, aod_bb):
"""
Calculate Linke turbidity using Kasten pyrheliometric formula.
Note that broadband aerosol optical depth (AOD) can be approximated by AOD
measured at 700 nm according to Molineaux [4] . Bird and Hulstrom offer an
alternate approximation using AOD measured at 380 nm and 500 nm.
Based on original implementation by Armel Oumbe.
.. warning::
These calculations are only valid for airmass less than 5 and
precipitable water less than 5 cm.
Parameters
----------
airmass_absolute : numeric
Pressure-adjusted airmass. [unitless]
precipitable_water : numeric
Precipitable water. [cm]
aod_bb : numeric
broadband AOD. [unitless]
Returns
-------
lt : numeric
Linke turbidity. [unitless]
See also
--------
pvlib.atmosphere.bird_hulstrom80_aod_bb
pvlib.atmosphere.angstrom_aod_at_lambda
References
----------
.. [1] F. Linke, "Transmissions-Koeffizient und Trubungsfaktor", Beitrage
zur Physik der Atmosphare, Vol 10, pp. 91-103 (1922)
.. [2] F. Kasten, "A simple parameterization of the pyrheliometric formula
for determining the Linke turbidity factor", Meteorologische Rundschau
33, pp. 124-127 (1980)
.. [3] Kasten, "The Linke turbidity factor based on improved values of the
integral Rayleigh optical thickness", Solar Energy, Vol. 56, No. 3,
pp. 239-244 (1996)
:doi:`10.1016/0038-092X(95)00114-7`
.. [4] B. Molineaux, P. Ineichen, N. O'Neill, "Equivalence of
pyrheliometric and monochromatic aerosol optical depths at a single key
wavelength", Applied Optics Vol. 37, issue 10, 7008-7018 (1998)
:doi:`10.1364/AO.37.007008`
.. [5] P. Ineichen, "Conversion function between the Linke turbidity and
the atmospheric water vapor and aerosol content", Solar Energy 82,
pp. 1095-1097 (2008)
:doi:`10.1016/j.solener.2008.04.010`
.. [6] P. Ineichen and R. Perez, "A new airmass independent formulation for
the Linke Turbidity coefficient", Solar Energy, Vol. 73, no. 3,
pp. 151-157 (2002)
:doi:`10.1016/S0038-092X(02)00045-2`
"""
# "From numerically integrated spectral simulations done with Modtran
# (Berk, 1989), Molineaux (1998) obtained for the broadband optical depth
# of a clean and dry atmospshere (fictitious atmosphere that comprises only
# the effects of Rayleigh scattering and absorption by the atmosphere gases
# other than the water vapor) the following expression"
# - P. Ineichen (2008)
delta_cda = -0.101 + 0.235 * airmass_absolute ** (-0.16)
# "and the broadband water vapor optical depth where pwat is the integrated
# precipitable water vapor content of the atmosphere expressed in cm and am
# the optical air mass. The precision of these fits is better than 1% when
# compared with Modtran simulations in the range 1 < am < 5 and
# 0 < pwat < 5 cm at sea level" - P. Ineichen (2008)
delta_w = 0.112 * airmass_absolute ** (-0.55) * precipitable_water ** 0.34
# broadband AOD
delta_a = aod_bb
# "Then using the Kasten pyrheliometric formula (1980, 1996), the Linke
# turbidity at am = 2 can be written. The extension of the Linke turbidity
# coefficient to other values of air mass was published by Ineichen and
# Perez (2002)" - P. Ineichen (2008)
lt = -(9.4 + 0.9 * airmass_absolute) * np.log(
np.exp(-airmass_absolute * (delta_cda + delta_w + delta_a))
) / airmass_absolute
# filter out of extrapolated values
return lt
[docs]def angstrom_aod_at_lambda(aod0, lambda0, alpha=1.14, lambda1=700.0):
r"""
Get AOD at specified wavelength using Angstrom turbidity model.
Parameters
----------
aod0 : numeric
Aerosol optical depth (AOD) measured at wavelength ``lambda0``.
[unitless]
lambda0 : numeric
Wavelength corresponding to ``aod0``. [nm]
alpha : numeric, default 1.14
Angstrom :math:`\alpha` exponent corresponding to ``aod0``. [unitless]
lambda1 : numeric, default 700
Desired wavelength. [nm]
Returns
-------
aod1 : numeric
AOD at desired wavelength ``lambda1``. [unitless]
See also
--------
pvlib.atmosphere.angstrom_alpha
References
----------
.. [1] Anders Angstrom, "On the Atmospheric Transmission of Sun Radiation
and On Dust in the Air", Geografiska Annaler Vol. 11, pp. 156-166 (1929)
JSTOR
:doi:`10.2307/519399`
.. [2] Anders Angstrom, "Techniques of Determining the Turbidity of the
Atmosphere", Tellus 13:2, pp. 214-223 (1961) Taylor & Francis
:doi:`10.3402/tellusa.v13i2.9493` and Co-Action Publishing
:doi:`10.1111/j.2153-3490.1961.tb00078.x`
"""
return aod0 * ((lambda1 / lambda0) ** (-alpha))
[docs]def angstrom_alpha(aod1, lambda1, aod2, lambda2):
r"""
Calculate Angstrom alpha exponent.
Parameters
----------
aod1 : numeric
Aerosol optical depth at wavelength ``lambda1``. [unitless]
lambda1 : numeric
Wavelength corresponding to ``aod1``. [nm]
aod2 : numeric
Aerosol optical depth at wavelength ``lambda2``. [unitless]
lambda2 : numeric
Wavelength corresponding to ``aod2``. [nm]
Returns
-------
alpha : numeric
Angstrom :math:`\alpha` exponent for wavelength in
``(lambda1, lambda2)``. [unitless]
See also
--------
pvlib.atmosphere.angstrom_aod_at_lambda
"""
return - np.log(aod1 / aod2) / np.log(lambda1 / lambda2)