def monthly_mean_daylight_hours(latitude, year=None):
"""
Calculate mean daylight hours for each month of the year for a given latitude.
:param latitude: Latitude [radians]
:param year: Year for the daylight hours are required. The only effect of
*year* is to change the number of days in Feb to 29 if it is a leap year.
If left as the default, None, then a normal (non-leap) year is assumed.
:return: Mean daily daylight hours of each month of a year [hours]
:rtype: List of floats.
"""
# validate the latitude argument
_check_latitude_rad(latitude)
# get the array of days for each month based on whether or not we're in a leap year
if year is None or not calendar.isleap(year):
month_days = _MONTH_DAYS_NONLEAP
else:
month_days = _MONTH_DAYS_LEAP
# allocate an array of daylight hours for each of the 12 months of the year
monthly_mean_dlh = np.zeros((12,))
# keep count of the day of the year
day_of_year = 1
# loop over each calendar month to calculate the daylight hours for the month
for i, days_in_month in enumerate(month_days):
cumulative_daylight_hours = 0.0 # cumulative daylight hours for the month
for _ in range(1, days_in_month + 1):
daily_solar_declination = solar_declination(day_of_year)
daily_sunset_hour_angle = sunset_hour_angle(latitude, daily_solar_declination)
cumulative_daylight_hours += daylight_hours(daily_sunset_hour_angle)
day_of_year += 1
# calculate the mean daylight hours of the month
monthly_mean_dlh[i] = cumulative_daylight_hours / days_in_month
return monthly_mean_dlh
def sunset_hour_angle(latitude, sol_dec):
"""
Calculate sunset hour angle (*Ws*) from latitude and solar
declination.
Based on FAO equation 25 in Allen et al (1998).
:param latitude: Latitude [radians]. Note: *latitude* should be negative
if in the southern hemisphere, positive if in the northern hemisphere.
:param sol_dec: Solar declination [radians]. Can be calculated using ``sol_dec()``.
:return: Sunset hour angle [radians].
:rtype: float
"""
# validate the latitude and solar declination angle arguments
_check_latitude_rad(latitude)
_check_sol_dec_rad(sol_dec)
cos_sha = -math.tan(latitude) * math.tan(sol_dec)
# If tmp is >= 1 there is no sunset, i.e. 24 hours of daylight
# If tmp is <= 1 there is no sunrise, i.e. 24 hours of darkness
# See http://www.itacanet.org/the-sun-as-a-source-of-energy/part-3-calculating-solar-angles/
# Domain of acos is -1 <= x <= 1 radians (this is not mentioned in FAO-56!)
return math.acos(min(max(cos_sha, -1.0), 1.0))
