plot_diffuse_PAR_Spitters_relationship.py

"""
Calculating daily diffuse PAR using Spitter's relationship
==========================================================

This example demonstrates how to calculate the diffuse photosynthetically
active radiation (PAR) from diffuse fraction of broadband insolation.
"""

# %%
# The photosynthetically active radiation (PAR) is a key metric in quantifying
# the photosynthesis process of plants. As with broadband irradiance, PAR can
# be divided into direct and diffuse components. The diffuse fraction of PAR
# with respect to the total PAR is important in agrivoltaic systems, where
# crops are grown under solar panels. The diffuse fraction of PAR can be
# calculated using the Spitter's relationship [1]_ implemented in
# :py:func:`~pvlib.irradiance.diffuse_par_spitters`.
# This model requires the average daily solar zenith angle and the
# daily fraction of the broadband insolation that is diffuse as inputs.
#
# .. note::
#    Understanding the distinction between the broadband insolation and the PAR
#    is a key concept. Broadband insolation is the total amount of solar
#    energy that gets to a surface, often used in PV applications, while PAR
#    is a measurement of a narrower spectrum of wavelengths that are involved
#    in photosynthesis. See section on *Photosynthetically Active insolation*
#    in pp. 222-223 of [1]_.
#
# References
# ----------
# .. [1] C. J. T. Spitters, H. A. J. M. Toussaint, and J. Goudriaan,
#    'Separating the diffuse and direct component of global radiation and its
#    implications for modeling canopy photosynthesis Part I. Components of
#    incoming radiation', Agricultural and Forest Meteorology, vol. 38,
#    no. 1, pp. 217-229, Oct. 1986, :doi:`10.1016/0168-1923(86)90060-2`.
#
# Read some example data
# ^^^^^^^^^^^^^^^^^^^^^^
# Let's read some weather data from a TMY3 file and calculate the solar
# position.

import pvlib
import pandas as pd
import matplotlib.pyplot as plt
from matplotlib.dates import AutoDateLocator, ConciseDateFormatter
from pathlib import Path

# Datafile found in the pvlib distribution
DATA_FILE = Path(pvlib.__path__[0]).joinpath("data", "723170TYA.CSV")

tmy, metadata = pvlib.iotools.read_tmy3(
    DATA_FILE, coerce_year=2002, map_variables=True
)
tmy = tmy.filter(
    ["ghi", "dhi", "dni", "pressure", "temp_air"]
)  # remaining columns are not needed
tmy = tmy["2002-09-06":"2002-09-21"]  # select some days

solar_position = pvlib.solarposition.get_solarposition(
    # TMY timestamp is at end of hour, so shift to center of interval
    tmy.index.shift(freq="-30min"),
    latitude=metadata["latitude"],
    longitude=metadata["longitude"],
    altitude=metadata["altitude"],
    pressure=tmy["pressure"] * 100,  # convert from millibar to Pa
    temperature=tmy["temp_air"],
)
solar_position.index = tmy.index  # reset index to end of the hour

# %%
# Calculate daily values
# ^^^^^^^^^^^^^^^^^^^^^^
# The daily average solar zenith angle and the daily diffuse fraction of
# broadband insolation are calculated as follows:

daily_solar_zenith = solar_position["zenith"].resample("D").mean()
# integration over the day with a time step of 1 hour
daily_tmy = tmy[["ghi", "dhi"]].resample("D").sum() * 1
daily_tmy["diffuse_fraction"] = daily_tmy["dhi"] / daily_tmy["ghi"]

# %%
# Calculate Photosynthetically Active Radiation
# ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
# The total PAR can be approximated as 0.50 times the broadband horizontal
# insolation (integral of GHI) for an average solar elevation higher that 10°.
# See section on *Photosynthetically Active Radiation* in pp. 222-223 of [1]_.

par = pd.DataFrame({"total": 0.50 * daily_tmy["ghi"]}, index=daily_tmy.index)
if daily_solar_zenith.min() < 10:
    raise ValueError(
        "The total PAR can't be assumed to be half the broadband insolation "
        + "for average zenith angles lower than 10°."
    )

# Calculate broadband insolation diffuse fraction, input of the Spitter's model
daily_tmy["diffuse_fraction"] = daily_tmy["dhi"] / daily_tmy["ghi"]

# Calculate diffuse PAR fraction using Spitter's relationship
par["diffuse_fraction"] = pvlib.irradiance.diffuse_par_spitters(
    solar_position["zenith"], daily_tmy["diffuse_fraction"]
)

# Finally, calculate the diffuse PAR
par["diffuse"] = par["total"] * par["diffuse_fraction"]

# %%
# Plot the results
# ^^^^^^^^^^^^^^^^
# Insolation on left axis, diffuse fraction on right axis

fig, ax_l = plt.subplots(figsize=(12, 6))
ax_l.set(
    xlabel="Time",
    ylabel="Daily insolation $[Wh/m^2/day]$",
    title="Diffuse PAR using Spitter's relationship",
)
ax_l.xaxis.set_major_formatter(
    ConciseDateFormatter(AutoDateLocator(), tz=daily_tmy.index.tz)
)
ax_l.plot(
    daily_tmy.index,
    daily_tmy["ghi"],
    label="Broadband: total",
    color="deepskyblue",
)
ax_l.plot(
    daily_tmy.index,
    daily_tmy["dhi"],
    label="Broadband: diffuse",
    color="skyblue",
    linestyle="-.",
)
ax_l.plot(daily_tmy.index, par["total"], label="PAR: total", color="orangered")
ax_l.plot(
    daily_tmy.index,
    par["diffuse"],
    label="PAR: diffuse",
    color="coral",
    linestyle="-.",
)
ax_l.grid()
ax_l.legend(loc="upper left")

ax_r = ax_l.twinx()
ax_r.set(ylabel="Diffuse fraction")
ax_r.plot(
    daily_tmy.index,
    daily_tmy["diffuse_fraction"],
    label="Broadband diffuse fraction",
    color="plum",
    linestyle=":",
)
ax_r.plot(
    daily_tmy.index,
    par["diffuse_fraction"],
    label="PAR diffuse fraction",
    color="chocolate",
    linestyle=":",
)
ax_r.legend(loc="upper right")

plt.show()