DOC: Discuss Angstrom Kasten TL, set default alpha (#563)

* DOC: add example for Kasten pyrheliometric formula

* closes #302
* add references to Kasten 96 and Molineaux
* discuss using Kasten and calculating broadband AOD usinge Angstrom turbidity model

Signed-off-by: Mark Mikofski <bwana.marko@yahoo.com>

* DOC: update what's new, add refs to Bird & Hulstrom and Angstrom

* DOC: split sentences, replace abbrev. AOD

* use TMY in pvlib/data, lowercase MBARS, use non-specific variable names
* split output from readtmy3 instead of using indexing for clarity

* DOC: fix up ipython example

* DOC: split sentences, revise, add angstrom example

* ENH: set default alpha to 1.14, update what's new

* DOC: use coerce year, use v0.6.0 get_property() for airmass

* DOC: print calculated AOD, move TL calculation after turbidity section

* DOC: wrap long lines, abbrev AOD, be explicit re: fictitious AOD

Author: mikofski

docs/sphinx/source/clearsky.rst

@@ -26,14 +26,12 @@ time series of clear sky data for a location. The :ref:`ineichen` and
 input data. The :ref:`detect_clearsky` subsection demonstrates the use
 of the clear sky detection algorithm.
 
-The :py:func:`~pvlib.atmosphere.bird_hulstrom80_aod_bb`, and
-:py:func:`~pvlib.atmosphere.kasten96_lt` functions are useful for
-calculating inputs to the clear sky functions.
-
 We'll need these imports for the examples below.
 
 .. ipython::
 
+    In [1]: import os
+
     In [1]: import itertools
 
     In [1]: import matplotlib.pyplot as plt
@@ -42,7 +40,7 @@ We'll need these imports for the examples below.
 
     In [1]: import pvlib
 
-    In [1]: from pvlib import clearsky, atmosphere
+    In [1]: from pvlib import clearsky, atmosphere, tmy, solarposition
 
     In [1]: from pvlib.location import Location
 
@@ -118,6 +116,7 @@ The Ineichen and Perez clear sky model parameterizes irradiance in terms
 of the Linke turbidity [Ine02]_. pvlib-python implements this model in
 the :py:func:`pvlib.clearsky.ineichen` function.
 
+
 Turbidity data
 ^^^^^^^^^^^^^^
 
@@ -198,6 +197,62 @@ varies from 300 m to 1500 m.
     @savefig turbidity-yes-interp.png width=6in
     In [1]: plt.ylabel('Linke Turbidity');
 
+The :py:func:`~pvlib.atmosphere.kasten96_lt` function can be used to calculate
+Linke turbidity [Kas96]_ as input to the clear sky Ineichen and Perez function.
+The Kasten formulation requires precipitable water and broadband aerosol
+optical depth (AOD). According to Molineaux, broadband AOD can be approximated
+by a single measurement at 700-nm [Mol98]_. An alternate broadband AOD
+approximation from Bird and Hulstrom combines AOD measured at two
+wavelengths [Bir80]_, and is implemented in
+:py:func:`~pvlib.atmosphere.bird_hulstrom80_aod_bb`.
+
+.. ipython::
+
+    In [1]: pvlib_data = os.path.join(os.path.dirname(pvlib.__file__), 'data')
+
+    In [1]: mbars = 100  # conversion factor from mbars to Pa
+
+    In [1]: tmy_file = os.path.join(pvlib_data, '703165TY.csv')  # TMY file
+
+    In [1]: tmy_data, tmy_header = tmy.readtmy3(tmy_file, coerce_year=1999)  # read TMY data
+
+    In [1]: tl_historic = clearsky.lookup_linke_turbidity(time=tmy_data.index,
+       ...:     latitude=tmy_header['latitude'], longitude=tmy_header['longitude'])
+
+    In [1]: solpos = solarposition.get_solarposition(time=tmy_data.index,
+       ...:     latitude=tmy_header['latitude'], longitude=tmy_header['longitude'],
+       ...:     altitude=tmy_header['altitude'], pressure=tmy_data['Pressure']*mbars,
+       ...:     temperature=tmy_data['DryBulb'])
+
+    In [1]: am_rel = atmosphere.get_relative_airmass(solpos.apparent_zenith)
+
+    In [1]: am_abs = atmosphere.get_absolute_airmass(am_rel, tmy_data['Pressure']*mbars)
+
+    In [1]: airmass = pd.concat([am_rel, am_abs], axis=1).rename(
+       ...:     columns={0: 'airmass_relative', 1: 'airmass_absolute'})
+
+    In [1]: tl_calculated = atmosphere.kasten96_lt(
+       ...:     airmass.airmass_absolute, tmy_data['Pwat'], tmy_data['AOD'])
+
+    In [1]: tl = pd.concat([tl_historic, tl_calculated], axis=1).rename(
+       ...:     columns={0:'Historic', 1:'Calculated'})
+
+    In [1]: tl.index = tmy_data.index.tz_convert(None)  # remove timezone
+
+    In [1]: tl.resample('W').mean().plot();
+
+    In [1]: plt.grid()
+
+    In [1]: plt.title('Comparison of Historic Linke Turbidity Factors vs. \n'
+       ...:     'Kasten Pyrheliometric Formula at {name:s}, {state:s} ({usaf:d}TY)'.format(
+       ...:     name=tmy_header['Name'], state=tmy_header['State'], usaf=tmy_header['USAF']));
+
+    In [1]: plt.ylabel('Linke Turbidity Factor, TL');
+
+    @savefig kasten-tl.png width=10in
+    In [1]: plt.tight_layout()
+
+
 Examples
 ^^^^^^^^
 
@@ -326,11 +381,32 @@ contain one or both of aerosols and precipitable water. Consider data
 from the `ECMWF <https://software.ecmwf.int/wiki/display/WEBAPI/Access+ECMWF+Public+Datasets>`_
 and `SoDa <http://www.soda-pro.com/web-services/radiation/cams-mcclear>`_.
 
-Aerosol optical depth is a function of wavelength, and the Simplified
-Solis model requires AOD at 700 nm. Models exist to convert AOD between
-different wavelengths, as well as convert Linke turbidity to AOD and PW
-[Ine08con]_, [Ine16]_.
+Aerosol optical depth (AOD) is a function of wavelength, and the Simplified
+Solis model requires AOD at 700 nm.
+:py:func:`~pvlib.atmosphere.angstrom_aod_at_lambda` is useful for converting
+AOD between different wavelengths using the Angstrom turbidity model. The
+Angstrom exponent, :math:`\alpha`, can be calculated from AOD at two
+wavelengths with :py:func:`~pvlib.atmosphere.angstrom_alpha`.
+[Ine08con]_, [Ine16]_, [Ang61]_.
+
+.. ipython::
+
+    In [1]: aod1240nm = 1.2  # fictitious AOD measured at 1240-nm
+
+    In [1]: aod550nm = 3.1  # fictitious AOD measured at 550-nm
 
+    In [1]: alpha_exponent = atmosphere.angstrom_alpha(aod1240nm, 1240, aod550nm, 550)
+
+    In [1]: aod700nm = atmosphere.angstrom_aod_at_lambda(aod1240nm, 1240, alpha_exponent, 700)
+
+    In [1]: aod380nm = atmosphere.angstrom_aod_at_lambda(aod550nm, 550, alpha_exponent, 380)
+
+    In [1]: aod500nm = atmosphere.angstrom_aod_at_lambda(aod550nm, 550, alpha_exponent, 500)
+
+    In [1]: aod_bb = atmosphere.bird_hulstrom80_aod_bb(aod380nm, aod500nm)
+
+    In [1]: print('compare AOD at 700-nm = {:g}, to estimated broadband AOD = {:g}, '
+       ...:     'with alpha = {:g}'.format(aod700nm, aod_bb, alpha_exponent))
 
 Examples
 ^^^^^^^^
@@ -617,3 +693,17 @@ References
 .. [Ren16] Reno, M.J. and C.W. Hansen, "Identification of periods of clear
    sky irradiance in time series of GHI measurements" Renewable Energy,
    v90, p. 520-531, 2016.
+
+.. [Mol98] B. Molineaux, P. Ineichen, and N. O’Neill, “Equivalence of
+   pyrheliometric and monochromatic aerosol optical depths at a single key
+   wavelength.,” Appl. Opt., vol. 37, no. 30, pp. 7008–18, Oct. 1998.
+
+.. [Kas96] F. Kasten, “The linke turbidity factor based on improved values
+   of the integral Rayleigh optical thickness,” Sol. Energy, vol. 56, no. 3,
+   pp. 239–244, Mar. 1996.
+
+.. [Bir80] R. E. Bird and R. L. Hulstrom, “Direct Insolation Models,”
+   1980.
+
+.. [Ang61] A. ÅNGSTRÖM, “Techniques of Determinig the Turbidity of the
+   Atmosphere,” Tellus A, vol. 13, no. 2, pp. 214–223, 1961.

docs/sphinx/source/whatsnew/v0.6.0.rst

@@ -107,6 +107,7 @@ Enhancements
 * Add irradiance.clearness_index_zenith_independent function. (:issue:`396`)
 * Add checking for consistency between module_parameters and dc_model. (:issue:`417`)
 * Add DC model methods desoto and pvsyst to ModelChain (:issue:`487`)
+* Set default alpha to 1.14 in :func:`~pvlib.atmosphere.angstrom_aod_at_lambda` (:issue:`563`)
 
 
 Bug fixes
@@ -152,6 +153,8 @@ Documentation
   top-level "Intro Examples" page.
 * Copy pvlib documentation's "Getting support" section to README.md.
 * Add PVSystem documentation page. (:issue:`514`, :issue:`319`)
+* Add example of Kasten Linke Turbidity calculation, discuss broadband AOD and
+  Angstrom Turbidity Model. (:issue:`302`)
 
 
 Testing

pvlib/atmosphere.py

@@ -621,7 +621,7 @@ def kasten96_lt(airmass_absolute, precipitable_water, aod_bb):
     return lt
 
 
-def angstrom_aod_at_lambda(aod0, lambda0, alpha, lambda1=700.0):
+def angstrom_aod_at_lambda(aod0, lambda0, alpha=1.14, lambda1=700.0):
     r"""
     Get AOD at specified wavelength using Angstrom turbidity model.
 
@@ -631,7 +631,7 @@ def angstrom_aod_at_lambda(aod0, lambda0, alpha, lambda1=700.0):
         aerosol optical depth (AOD) measured at known wavelength
     lambda0 : numeric
         wavelength in nanometers corresponding to ``aod0``
-    alpha : numeric
+    alpha : numeric, default 1.14
         Angstrom :math:`\alpha` exponent corresponding to ``aod0``
     lambda1 : numeric, default 700
         desired wavelength in nanometers