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"""
Calculate potential evapotranspiration using the Thornthwaite (1948 method)
:copyright: (c) 2015 by Mark Richards.
:license: BSD 3-Clause, see LICENSE.txt for more details.
References
----------
Thornthwaite CW (1948) An approach toward a rational classification of
climate. Geographical Review, 38, 55-94.
"""
import calendar
from . import fao
from ._check import check_latitude_rad as _check_latitude_rad
_MONTHDAYS = (31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31)
_LEAP_MONTHDAYS = (31, 29, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31)
def thornthwaite(monthly_t, monthly_mean_dlh, year=None):
"""
Estimate monthly potential evapotranspiration (PET) using the
Thornthwaite (1948) method.
Thornthwaite equation:
*PET* = 1.6 (*L*/12) (*N*/30) (10*Ta* / *I*)***a*
where:
* *Ta* is the mean daily air temperature [deg C, if negative use 0] of the
month being calculated
* *N* is the number of days in the month being calculated
* *L* is the mean day length [hours] of the month being calculated
* *a* = (6.75 x 10-7)*I***3 - (7.71 x 10-5)*I***2 + (1.792 x 10-2)*I* + 0.49239
* *I* is a heat index which depends on the 12 monthly mean temperatures and
is calculated as the sum of (*Tai* / 5)**1.514 for each month, where
Tai is the air temperature for each month in the year
:param monthly_t: Iterable containing mean daily air temperature for each
month of the year [deg C].
:param monthly_mean_dlh: Iterable containing mean daily daylight
hours for each month of the year (hours]. These can be calculated
using ``monthly_mean_daylight_hours()``.
:param year: Year for which PET is required. The only effect of year is
to change the number of days in February to 29 if it is a leap year.
If it is left as the default (None), then the year is assumed not to
be a leap year.
:return: Estimated monthly potential evaporation of each month of the year
[mm/month]
:rtype: List of floats
"""
if len(monthly_t) != 12:
raise ValueError(
'monthly_t should be length 12 but is length {0}.'
.format(len(monthly_t)))
if len(monthly_mean_dlh) != 12:
raise ValueError(
'monthly_mean_dlh should be length 12 but is length {0}.'
.format(len(monthly_mean_dlh)))
if year is None or not calendar.isleap(year):
month_days = _MONTHDAYS
else:
month_days = _LEAP_MONTHDAYS
# Negative temperatures should be set to zero
adj_monthly_t = [t * (t >= 0) for t in monthly_t]
# Calculate the heat index (I)
I = 0.0
for Tai in adj_monthly_t:
if Tai / 5.0 > 0.0:
I += (Tai / 5.0) ** 1.514
a = (6.75e-07 * I ** 3) - (7.71e-05 * I ** 2) + (1.792e-02 * I) + 0.49239
pet = []
for Ta, L, N in zip(adj_monthly_t, monthly_mean_dlh, month_days):
# Multiply by 10 to convert cm/month --> mm/month
pet.append(
1.6 * (L / 12.0) * (N / 30.0) * ((10.0 * Ta / I) ** a) * 10.0)
return pet
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.
"""
_check_latitude_rad(latitude)
if year is None or not calendar.isleap(year):
month_days = _MONTHDAYS
else:
month_days = _LEAP_MONTHDAYS
monthly_mean_dlh = []
doy = 1 # Day of the year
for mdays in month_days:
dlh = 0.0 # Cumulative daylight hours for the month
for daynum in range(1, mdays + 1):
sd = fao.sol_dec(doy)
sha = fao.sunset_hour_angle(latitude, sd)
dlh += fao.daylight_hours(sha)
doy += 1
# Calc mean daylight hours of the month
monthly_mean_dlh.append(dlh / mdays)
return monthly_mean_dlh
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