DECLINATION_SPENCER
This function computes solar declination, the angle between the Earth-sun line and the equatorial plane, from day-of-year values using the Spencer (1971) Fourier approximation.
Declination is a core geometric input for solar zenith, azimuth, sunrise/sunset timing, and plane-of-array irradiance models.
In solar-geometry notation, declination enters relationships such as:
\cos(\theta_z) = \sin(\phi)\sin(\delta) + \cos(\phi)\cos(\delta)\cos(h)
where \theta_z is solar zenith, \phi is latitude, \delta is declination, and h is hour angle.
Excel Usage
=DECLINATION_SPENCER(dayofyear)dayofyear(list[list], required): Day of the year (1 to 366).
Returns (list[list]): 2D list of declination angles (radians), or an error string.
Example 1: Declination at summer solstice
Inputs:
| dayofyear |
|---|
| 172 |
Excel formula:
=DECLINATION_SPENCER({172})Expected output:
0.409315
Example 2: Declination near March equinox
Inputs:
| dayofyear |
|---|
| 80 |
Excel formula:
=DECLINATION_SPENCER({80})Expected output:
-0.00115059
Example 3: Declination near December solstice
Inputs:
| dayofyear |
|---|
| 355 |
Excel formula:
=DECLINATION_SPENCER({355})Expected output:
-0.408754
Example 4: Scalar day-of-year input
Inputs:
| dayofyear |
|---|
| 1 |
Excel formula:
=DECLINATION_SPENCER(1)Expected output:
-0.402449
Python Code
Show Code
import pandas as pd
import numpy as np
from pvlib.solarposition import declination_spencer71 as result_func
def declination_spencer(dayofyear):
"""
Compute the solar declination angle using Spencer's (1971) formula.
See: https://pvlib-python.readthedocs.io/en/stable/reference/generated/pvlib.solarposition.declination_spencer71.html
This example function is provided as-is without any representation of accuracy.
Args:
dayofyear (list[list]): Day of the year (1 to 366).
Returns:
list[list]: 2D list of declination angles (radians), or an error string.
"""
try:
def flatten_num(data):
if not isinstance(data, list): return [float(data)]
flat = []
for row in data:
row = row if isinstance(row, list) else [row]
for val in row:
if val == "": flat.append(float('nan'))
else: flat.append(float(val))
return flat
doy_list = flatten_num(dayofyear)
if len(doy_list) == 0:
return "Error: input array cannot be empty"
res = result_func(np.array(doy_list))
return [[float(v) if not pd.isna(v) else ""] for v in res]
except Exception as e:
return f"Error: {str(e)}"