Source code for pvlib.atmosphere

"""
The ``atmosphere`` module contains methods to calculate relative and
absolute airmass, determine pressure from altitude or vice versa, and wind
speed at different heights.
"""

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)
# Values of the Hellmann exponent HELLMANN_SURFACE_EXPONENTS = { 'unstable_air_above_open_water_surface': 0.06, 'neutral_air_above_open_water_surface': 0.10, 'stable_air_above_open_water_surface': 0.27, 'unstable_air_above_flat_open_coast': 0.11, 'neutral_air_above_flat_open_coast': 0.16, 'stable_air_above_flat_open_coast': 0.40, 'unstable_air_above_human_inhabited_areas': 0.27, 'neutral_air_above_human_inhabited_areas': 0.34, 'stable_air_above_human_inhabited_areas': 0.60, }
[docs] def windspeed_powerlaw(wind_speed_reference, height_reference, height_desired, exponent=None, surface_type=None): r""" Estimate wind speed for different heights. The model is based on the power law equation by Hellmann [1]_ [2]_. Parameters ---------- wind_speed_reference : numeric Measured wind speed. [m/s] height_reference : float The height above ground at which the wind speed is measured. [m] height_desired : float The height above ground at which the wind speed will be estimated. [m] exponent : float, optional Exponent based on the surface type. [unitless] surface_type : string, optional If supplied, overrides ``exponent``. Can be one of the following (see [1]_): * ``'unstable_air_above_open_water_surface'`` * ``'neutral_air_above_open_water_surface'`` * ``'stable_air_above_open_water_surface'`` * ``'unstable_air_above_flat_open_coast'`` * ``'neutral_air_above_flat_open_coast'`` * ``'stable_air_above_flat_open_coast'`` * ``'unstable_air_above_human_inhabited_areas'`` * ``'neutral_air_above_human_inhabited_areas'`` * ``'stable_air_above_human_inhabited_areas'`` Returns ------- wind_speed : numeric Adjusted wind speed for the desired height. [m/s] Raises ------ ValueError If neither of ``exponent`` nor a ``surface_type`` is given. If both ``exponent`` and a ``surface_type`` is given. These parameters are mutually exclusive. KeyError If the specified ``surface_type`` is invalid. Notes ----- Module temperature functions often require wind speeds at a height of 10 m and not the wind speed at the module height. For example, the following temperature functions require the input wind speed to be 10 m: :py:func:`~pvlib.temperature.sapm_cell`, and :py:func:`~pvlib.temperature.sapm_module` whereas the :py:func:`~pvlib.temperature.fuentes` model requires wind speed at 9.144 m. Additionally, the heat loss coefficients of some models have been developed for wind speed measurements at 10 m (e.g., :py:func:`~pvlib.temperature.pvsyst_cell`, :py:func:`~pvlib.temperature.faiman`, and :py:func:`~pvlib.temperature.faiman_rad`). The equation for calculating the wind speed at a height of :math:`h` is given by the following power law equation [1]_ [2]_: .. math:: :label: wind speed WS_{h} = WS_{ref} \cdot \left( \frac{h}{h_{ref}} \right)^a where :math:`h` [m] is the height at which we would like to calculate the wind speed, :math:`h_{ref}` [m] is the reference height at which the wind speed is known, and :math:`WS_{h}` [m/s] and :math:`WS_{ref}` [m/s] are the corresponding wind speeds at these heights. The exponent :math:`a` [unitless] depends on the surface type. Some values found in the literature [1]_ for :math:`a` are: .. table:: Values for the Hellmann-exponent +-----------+--------------------+------------------+------------------+ | Stability | Open water surface | Flat, open coast | Cities, villages | +===========+====================+==================+==================+ | Unstable | 0.06 | 0.10 | 0.27 | +-----------+--------------------+------------------+------------------+ | Neutral | 0.11 | 0.16 | 0.40 | +-----------+--------------------+------------------+------------------+ | Stable | 0.27 | 0.34 | 0.60 | +-----------+--------------------+------------------+------------------+ In a report by Sandia [3]_, the equation was experimentally tested for a height of 30 ft (:math:`h_{ref} = 9.144` [m]) at their test site in Albuquerque for a period of six weeks where a coefficient of :math:`a = 0.219` was calculated. It should be noted that the equation returns a value of NaN if the reference heights or wind speed are negative. References ---------- .. [1] Kaltschmitt M., Streicher W., Wiese A. (2007). "Renewable Energy: Technology, Economics and Environment." Springer, :doi:`10.1007/3-540-70949-5`. .. [2] Hellmann G. (1915). "Über die Bewegung der Luft in den untersten Schichten der Atmosphäre." Meteorologische Zeitschrift, 32 .. [3] Menicucci D.F., Hall I.J. (1985). "Estimating wind speed as a function of height above ground: An analysis of data obtained at the southwest residential experiment station, Las Cruses, New Mexico." SAND84-2530, Sandia National Laboratories. Accessed at: https://web.archive.org/web/20230418202422/https://www2.jpl.nasa.gov/adv_tech/photovol/2016CTR/SNL%20-%20Est%20Wind%20Speed%20vs%20Height_1985.pdf """ # noqa:E501 if surface_type is not None and exponent is None: # use the Hellmann exponent from dictionary exponent = HELLMANN_SURFACE_EXPONENTS[surface_type] elif surface_type is None and exponent is not None: # use the provided exponent pass else: raise ValueError( "Either a 'surface_type' or an 'exponent' parameter must be given") wind_speed = wind_speed_reference * ( (height_desired / height_reference) ** exponent) # if wind speed is negative or complex return NaN wind_speed = np.where(np.iscomplex(wind_speed) | (wind_speed < 0), np.nan, wind_speed) if isinstance(wind_speed_reference, pd.Series): wind_speed = pd.Series(wind_speed, index=wind_speed_reference.index) return wind_speed