"""
The ``atmosphere`` module contains methods to calculate relative and
absolute airmass and to determine pressure from altitude or vice versa.
"""
from warnings import warn
import numpy as np
import pandas as pd
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 (Pascals)
Returns
-------
altitude : numeric
Altitude in meters above sea level
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/(kgK)
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 in meters above sea level
Returns
-------
pressure : numeric
Atmospheric pressure (Pascals)
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/(kgK)
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.):
'''
Determine absolute (pressure corrected) airmass from relative
airmass and pressure
Gives the airmass for locations not at sea-level (i.e. not at
standard pressure). The input argument "AMrelative" is the relative
airmass. The input argument "pressure" is the pressure (in Pascals)
at the location of interest and must be greater than 0. The
calculation for absolute airmass is
.. math::
absolute airmass = (relative airmass)*pressure/101325
Parameters
----------
airmass_relative : numeric
The airmass at sea-level.
pressure : numeric, default 101325
The site pressure in Pascal.
Returns
-------
airmass_absolute : numeric
Absolute (pressure corrected) 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'):
'''
Gives the relative (not pressure-corrected) airmass.
Gives the airmass at sea-level when given a sun zenith angle (in
degrees). The ``model`` variable allows selection of different
airmass models (described below). If ``model`` is not included or is
not valid, the default model is 'kastenyoung1989'.
Parameters
----------
zenith : numeric
Zenith angle of the sun in degrees. Note that some models use
the apparent (refraction corrected) zenith angle, and some
models use the true (not refraction-corrected) zenith angle. See
model descriptions to determine which type of zenith angle is
required. Apparent zenith angles must be calculated at sea level.
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' - See reference [3] -
requires apparent sun zenith
* 'gueymard1993' - See reference [4] -
requires apparent sun zenith
* 'young1994' - See reference [5] -
requries true sun zenith
* 'pickering2002' - See reference [6] -
requires apparent sun zenith
Returns
-------
airmass_relative : numeric
Relative airmass at sea level. Will return NaN values for any
zenith angle greater than 90 degrees.
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] 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)))
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::
w = 0.1 H_v \rho_v
using Eq. 2 in [2]_
.. math::
\rho_v = 216.7 R_H e_s /T
:math:`H_v` is the apparant water vapor scale height (km). The
expression for :math:`H_v` is Eq. 4 in [2]_:
.. math::
H_v = 0.4976 + 1.5265*T/273.15 + \exp(13.6897*T/273.15 - 14.9188*(T/273.15)^3)
:math:`\rho_v` is the surface water vapor density (g/m^3). In the
expression :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(22.330 - 49.140*(100/T) - 10.922*(100/T)^2 - 0.39015*T/100)
Parameters
----------
temp_air : numeric
ambient air temperature at the surface (C)
relative_humidity : numeric
relative humidity 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
[docs]def first_solar_spectral_correction(pw, airmass_absolute,
module_type=None, coefficients=None,
min_pw=0.1, max_pw=8):
r"""
Spectral mismatch modifier based on precipitable water and absolute
(pressure corrected) airmass.
Estimates a spectral mismatch modifier M representing the effect on
module short circuit current of variation in the spectral
irradiance. M is estimated from absolute (pressure currected) air
mass, AMa, and precipitable water, Pwat, using the following
function:
.. math::
M = c_1 + c_2*AMa + c_3*Pwat + c_4*AMa^.5
+ c_5*Pwat^.5 + c_6*AMa/Pwat^.5
Default coefficients are determined for several cell types with
known quantum efficiency curves, by using the Simple Model of the
Atmospheric Radiative Transfer of Sunshine (SMARTS) [1]_. Using
SMARTS, spectrums are simulated with all combinations of AMa and
Pwat where:
* 0.5 cm <= Pwat <= 5 cm
* 1.0 <= AMa <= 5.0
* Spectral range is limited to that of CMP11 (280 nm to 2800 nm)
* spectrum simulated on a plane normal to the sun
* All other parameters fixed at G173 standard
From these simulated spectra, M is calculated using the known
quantum efficiency curves. Multiple linear regression is then
applied to fit Eq. 1 to determine the coefficients for each module.
Based on the PVLIB Matlab function ``pvl_FSspeccorr`` by Mitchell
Lee and Alex Panchula, at First Solar, 2016 [2]_.
Parameters
----------
pw : array-like
atmospheric precipitable water (cm).
airmass_absolute : array-like
absolute (pressure corrected) airmass.
min_pw : float, default 0.1
minimum atmospheric precipitable water (cm). A lower pw value will be
automatically set to this minimum value to avoid model divergence.
max_pw : float, default 8
maximum atmospheric precipitable water (cm). If a higher value is
encountered it will be set to np.nan to avoid model divergence.
module_type : None or string, default None
a string specifying a cell type. Can be lower or upper case
letters. Admits values of 'cdte', 'monosi', 'xsi', 'multisi',
'polysi'. If provided, this input selects coefficients for the
following default modules:
* 'cdte' - First Solar Series 4-2 CdTe modules.
* 'monosi', 'xsi' - First Solar TetraSun modules.
* 'multisi', 'polysi' - multi-crystalline silicon modules.
* 'cigs' - anonymous copper indium gallium selenide PV module
* 'asi' - anonymous amorphous silicon PV module
The module used to calculate the spectral correction
coefficients corresponds to the Mult-crystalline silicon
Manufacturer 2 Model C from [3]_. Spectral Response (SR) of CIGS
and a-Si modules used to derive coefficients can be found in [4]_
coefficients : None or array-like, default None
allows for entry of user defined spectral correction
coefficients. Coefficients must be of length 6. Derivation of
coefficients requires use of SMARTS and PV module quantum
efficiency curve. Useful for modeling PV module types which are
not included as defaults, or to fine tune the spectral
correction to a particular mono-Si, multi-Si, or CdTe PV module.
Note that the parameters for modules with very similar QE should
be similar, in most cases limiting the need for module specific
coefficients.
Returns
-------
modifier: array-like
spectral mismatch factor (unitless) which is can be multiplied
with broadband irradiance reaching a module's cells to estimate
effective irradiance, i.e., the irradiance that is converted to
electrical current.
References
----------
.. [1] Gueymard, Christian. SMARTS2: a simple model of the atmospheric
radiative transfer of sunshine: algorithms and performance
assessment. Cocoa, FL: Florida Solar Energy Center, 1995.
.. [2] Lee, Mitchell, and Panchula, Alex. "Spectral Correction for
Photovoltaic Module Performance Based on Air Mass and Precipitable
Water." IEEE Photovoltaic Specialists Conference, Portland, 2016
.. [3] Marion, William F., et al. User's Manual for Data for Validating
Models for PV Module Performance. National Renewable Energy
Laboratory, 2014. http://www.nrel.gov/docs/fy14osti/61610.pdf
.. [4] Schweiger, M. and Hermann, W, Influence of Spectral Effects
on Energy Yield of Different PV Modules: Comparison of Pwat and
MMF Approach, TUV Rheinland Energy GmbH report 21237296.003,
January 2017
"""
# --- Screen Input Data ---
# *** Pwat ***
# Replace Pwat Values below 0.1 cm with 0.1 cm to prevent model from
# diverging"
pw = np.atleast_1d(pw)
pw = pw.astype('float64')
if np.min(pw) < min_pw:
pw = np.maximum(pw, min_pw)
warn('Exceptionally low pw values replaced with {0} cm to prevent '
'model divergence'.format(min_pw))
# Warn user about Pwat data that is exceptionally high
if np.max(pw) > max_pw:
pw[pw > max_pw] = np.nan
warn('Exceptionally high pw values replaced by np.nan: '
'check input data.')
# *** AMa ***
# Replace Extremely High AM with AM 10 to prevent model divergence
# AM > 10 will only occur very close to sunset
if np.max(airmass_absolute) > 10:
airmass_absolute = np.minimum(airmass_absolute, 10)
# Warn user about AMa data that is exceptionally low
if np.min(airmass_absolute) < 0.58:
warn('Exceptionally low air mass: ' +
'model not intended for extra-terrestrial use')
# pvl_absoluteairmass(1,pvl_alt2pres(4340)) = 0.58 Elevation of
# Mina Pirquita, Argentian = 4340 m. Highest elevation city with
# population over 50,000.
_coefficients = {}
_coefficients['cdte'] = (
0.86273, -0.038948, -0.012506, 0.098871, 0.084658, -0.0042948)
_coefficients['monosi'] = (
0.85914, -0.020880, -0.0058853, 0.12029, 0.026814, -0.0017810)
_coefficients['xsi'] = _coefficients['monosi']
_coefficients['polysi'] = (
0.84090, -0.027539, -0.0079224, 0.13570, 0.038024, -0.0021218)
_coefficients['multisi'] = _coefficients['polysi']
_coefficients['cigs'] = (
0.85252, -0.022314, -0.0047216, 0.13666, 0.013342, -0.0008945)
_coefficients['asi'] = (
1.12094, -0.047620, -0.0083627, -0.10443, 0.098382, -0.0033818)
if module_type is not None and coefficients is None:
coefficients = _coefficients[module_type.lower()]
elif module_type is None and coefficients is not None:
pass
elif module_type is None and coefficients is None:
raise TypeError('No valid input provided, both module_type and ' +
'coefficients are None')
else:
raise TypeError('Cannot resolve input, must supply only one of ' +
'module_type and coefficients')
# Evaluate Spectral Shift
coeff = coefficients
ama = airmass_absolute
modifier = (
coeff[0] + coeff[1]*ama + coeff[2]*pw + coeff[3]*np.sqrt(ama) +
coeff[4]*np.sqrt(pw) + coeff[5]*ama/np.sqrt(pw))
return modifier
[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
aod500 : numeric
AOD measured at 500 nm
Returns
-------
aod_bb : numeric
broadband AOD
See also
--------
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 factor 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 air mass less than 5 atm and
precipitable water less than 5 cm.
Parameters
----------
airmass_absolute : numeric
airmass, pressure corrected in atmospheres
precipitable_water : numeric
precipitable water or total column water vapor in centimeters
aod_bb : numeric
broadband AOD
Returns
-------
lt : numeric
Linke turbidity
See also
--------
bird_hulstrom80_aod_bb
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 known wavelength
lambda0 : numeric
wavelength in nanometers corresponding to ``aod0``
alpha : numeric, default 1.14
Angstrom :math:`\alpha` exponent corresponding to ``aod0``
lambda1 : numeric, default 700
desired wavelength in nanometers
Returns
-------
aod1 : numeric
AOD at desired wavelength, ``lambda1``
See also
--------
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
first aerosol optical depth
lambda1 : numeric
wavelength in nanometers corresponding to ``aod1``
aod2 : numeric
second aerosol optical depth
lambda2 : numeric
wavelength in nanometers corresponding to ``aod2``
Returns
-------
alpha : numeric
Angstrom :math:`\alpha` exponent for AOD in ``(lambda1, lambda2)``
See also
--------
angstrom_aod_at_lambda
"""
return - np.log(aod1 / aod2) / np.log(lambda1 / lambda2)