"""The temperature module contains functions of temperature PET methods.
"""
from numpy import exp, pi, asarray, newaxis
from pandas import date_range
from xarray import DataArray
from .meteo_utils import daylight_hours, calc_ea, calc_es, calc_e0
from .utils import get_index, check_lat, clip_zeros, check_rh, pet_out
[docs]
def blaney_criddle(
tmean,
lat,
a=-1.55,
b=0.96,
k=0.65,
wind=None,
rhmin=None,
n=None,
nn=None,
py=None,
method=0,
clip_zero=True,
):
"""Potential evapotranspiration calculated according to
:cite:t:`blaney_determining_1952`.
Parameters
----------
tmean: pandas.Series or xarray.DataArray
average day temperature [°C].
lat: float or xarray.DataArray, optional
the site latitude [rad].
a: float, optional
calibration coefficient for method 0 [-].
b: float, optional
calibration coefficient for method 0 [-].
k: float, optional
calibration coefficient for method 1 [-].
wind: float or pandas.Series or xarray.DataArray, optional
mean day wind speed [m/s].
rhmin: float or pandas.Series or xarray.DataArray, optional
mainimum daily relative humidity [%].
n: float or pandas.Series or xarray.DataArray, optional
actual duration of sunshine [hour].
nn: float or pandas.Series or xarray.DataArray, optional
maximum possible duration of sunshine or daylight hours [hour].
py: float or pandas.Series or xarray.DataArray, optional
percentage of actual day-light hours for the day compared to the
number of day-light hour during the entire year [-].
method: float, optional
0 => Blaney Criddle after :cite:t:`schrodter_hinweise_1985`
1 => Blaney Criddle after :cite:t:`xu_evaluation_2001`
2 => FAO-24 Blaney Criddle after :cite:t:`mcmahon_estimating_2013`.
clip_zero: bool, optional
if True, replace all negative values with 0.
Returns
-------
float or pandas.Series or xarray.DataArray containing the calculated
Potential evapotranspiration [mm d-1].
Examples
--------
>>> pet_blaney_criddle = blaney_criddle(tmean, lat)
Notes
-----
Method = 0; Based on :cite:p:`schrodter_hinweise_1985`.
.. math:: PET=a+b(py(0.46 * T_{mean} + 8.13))
Method = 1; Based on :cite:p:`xu_evaluation_2001`.
.. math:: PET=kpy(0.46 * T_{mean} + 8.13)
Method = 2; Based on :cite:p:`mcmahon_estimating_2013`.
.. math:: PET=k_1+b_{var}(py(0.46*T_{mean} + 8.13))
, where:
.. math:: k1 = (0.0043RH_{min}-\\frac{n}{N}-1.41)
.. math:: bvar =e_0+e1 RH_{min}+e_2 \\frac{n}{N} + e_3 u_2 +
e_4 RH_{min} \\frac{n}{N} + e_5 * RH_{min} * u_2
.. math:: e_0=0.81917, e_1 = -0.0040922, e_2 = 1.0705, e_3 = 0.065649,
e_4 = -0.0059684, e_5 = -0.0005967.
"""
index = get_index(tmean)
if nn is None:
nn = daylight_hours(index, lat)
if py is None:
nn_sum = sum(daylight_hours(date_range("2000-1-1", "2000-12-31"), lat))
py = nn / nn_sum * 100
if isinstance(tmean, DataArray) and len(py.shape) == 1:
py = py[:, None, None]
if method == 0:
pet = a + b * (py * (0.457 * tmean + 8.128))
elif method == 1:
pet = k * py * (0.46 * tmean + 8.13)
elif method == 2:
nn_sum = sum(daylight_hours(date_range("2000-1-1", "2000-12-31"), lat))
py = n / nn_sum * 100
if isinstance(rhmin, DataArray) and len(nn.shape) == 1:
nn = nn[:, None, None]
k1 = 0.0043 * rhmin - n / nn - 1.41
e0, e1, e2, e3, e4, e5 = (
0.81917,
-0.0040922,
1.0705,
0.065649,
-0.0059684,
-0.0005967,
)
bvar = (
e0
+ e1 * rhmin
+ e2 * n / nn
+ e3 * wind
+ e4 * rhmin * n / nn
+ e5 * rhmin * wind
)
pet = k1 + bvar * py * (0.46 * tmean + 8.13)
else:
raise Exception("Method can be either 0, 1 or 2.")
pet = clip_zeros(pet, clip_zero)
return pet_out(tmean, pet, "Blaney_Criddle")
[docs]
def haude(tmean, rh, k=1, clip_zero=True):
"""Potential evapotranspiration calculated according to
:cite:t:`haude_determination_1955`.
Parameters
----------
tmean: pandas.Series or xarray.DataArray
temperature at 2pm or maximum dailty temperature [°C].
rh: float or pandas.Series or xarray.DataArray
average relative humidity at 2pm [%].
k: float, optional
calibration coefficient [-].
clip_zero: bool, optional
if True, replace all negative values with 0.
Returns
-------
float or pandas.Series or xarray.DataArray containing the calculated potential
evapotranspiration [mm d-1].
Examples
--------
>>> pet_haude = haude(tmean, rh)
Notes
-----
Following :cite:t:`haude_determination_1955` and :cite:t:`schiff_berechnung_1975`.
.. math:: PET = k * f * (e_s-e_a)
"""
e0 = calc_e0(tmean)
ea = check_rh(rh) * e0 / 100
# Haude coefficients from :cite:t:`schiff_berechnung_1975`
fk = [0.27, 0.27, 0.28, 0.39, 0.39, 0.37, 0.35, 0.33, 0.31, 0.29, 0.27, 0.27]
index = get_index(tmean)
fk1 = asarray([fk[x - 1] for x in index.month])
if len(tmean.shape) > 1:
f = fk1[:, newaxis, newaxis] * (tmean / tmean)
else:
f = fk1
pet = k * f * (e0 - ea) * 10 # kPa to hPa
pet = clip_zeros(pet, clip_zero)
return pet_out(tmean, pet, "Haude")
[docs]
def hamon(
tmean,
lat,
k=1,
c=13.97,
cc=218.527,
n=None,
tmax=None,
tmin=None,
method=0,
clip_zero=True,
):
"""Potential evapotranspiration calculated according to
:cite:t:`hamon_estimating_1963`.
Parameters
----------
tmean: pandas.Series or xarray.DataArray
average day temperature [°C].
lat: float or xarray.DataArray
the site latitude [rad].
k: float, optional
calibration coefficient if method = 0 [-].
c: float, optional
c is a constant for calculation in mm per day if method = 1.
cc: float, optional
calibration coefficient if method = 2 [-].
n: float or pandas.Series or xarray.DataArray, optional
actual duration of sunshine [hour].
tmax: float or pandas.Series or xarray.DataArray
maximum day temperature [°C].
tmin: float or pandas.Series or xarray.DataArray
minimum day temperature [°C].
method: float, optional
0 => Hamon after :cite:t:`oudin_which_2005`
1 => Hamon after equation 7 in :cite:t:`ansorge_performance_2019`
2 => Hamon after equation 12 in :cite:t:`ansorge_performance_2019`.
3 => Hamon after equation 12 in :cite:t:`rosenberry_comparison_2004`.
clip_zero: bool, optional
if True, replace all negative values with 0.
Returns
-------
float or pandas.Series or xarray.DataArray containing the calculated potential
evapotranspiration [mm d-1].
Examples
--------
>>> pet_hamon = hamon(tmean, lat)
Notes
-----
Method = 0; Based on cite:t:`oudin_which_2005`.
.. math:: PET = k(\\frac{DL}{12})^2 exp(\\frac{T_{mean}}{16})
Method = 1; Based on equation 7 in cite:t:`ansorge_performance_2019`.
.. math:: PET = c(\\frac{DL}{12})^2 pt
where
.. math:: pt = 4.95 \\frac{exp(0.062T_{mean})}{16}
Method = 2; Based on equation 12 in cite:t:`ansorge_performance_2019`.
.. math:: PET = cc\\frac{DL}{12} \\frac{1}{T_{mean} + 273.3}
exp(\\frac{17.27T_{mean}}{T_{mean} + 273.3})
Method = 3; Based on cite:t:`rosenberry_comparison_2004`.
.. math:: PET = 14 * (n / 12) ** 2 * (216.7 * e_s * 10 /
(T_{mean} + 273.3)) / 100
"""
index = get_index(tmean)
# Use transpose to work with lat either as int or xarray.DataArray
dl = daylight_hours(index, lat)
if len(dl.shape) < len(tmean.shape):
dl = tmean / tmean * dl[:, newaxis, newaxis]
if method == 0:
pet = k * (dl / 12) ** 2 * exp(tmean / 16)
elif method == 1:
# saturated water content after Xu and Singh (2001)
pt = 4.95 * exp(0.062 * tmean) / 100
pet = c * (dl / 12) ** 2 * pt
elif method == 2:
pet = (
cc
* (dl / 12)
* 1
/ (tmean + 273.3)
* exp((17.26939 * tmean) / (tmean + 273.3))
)
elif method == 3:
es = calc_es(tmean, tmax, tmin)
pet = k * 14 * (n / 12) ** 2 * (216.7 * es * 10 / (tmean + 273.3)) / 100
else:
raise Exception("method can be either 0, 1, 2 or 3.")
pet = clip_zeros(pet, clip_zero)
return pet_out(tmean, pet, "Hamon")
[docs]
def romanenko(
tmean, rh, k=4.5, rhmax=None, rhmin=None, tmax=None, tmin=None, clip_zero=True
):
"""Potential evapotranspiration calculated according to
:cite:t:`romanenko_computation_1961`.
Parameters
----------
tmean: float or pandas.Series or xarray.DataArray
average day temperature [°C].
rh: float or pandas.Series or xarray.DataArray
mean daily relative humidity [%].
k: float, optional
calibration coefficient [-].
tmax: float or pandas.Series or xarray.DataArray
maximum day temperature [°C].
tmin: float or pandas.Series or xarray.DataArray
minimum day temperature [°C].
rhmax: pandas.Series, optional
maximum daily relative humidity [%].
rhmin: pandas.Series, optional
mainimum daily relative humidity [%].
clip_zero: bool, optional
if True, replace all negative values with 0.
Returns
-------
float or pandas.Series or xarray.DataArray containing the calculated potential
evapotranspiration [mm d-1].
Examples
--------
>>> pet_romanenko = romanenko(tmean, rh)
Notes
-----
Based on equation 11 in :cite:p:`xu_evaluation_2001`.
.. math:: PET=k(1 + (\\frac{T_{mean}}{25})^2 (1 - \\frac{e_a}{e_s})
"""
ea = calc_ea(
tmean=tmean,
tmax=tmax,
tmin=tmin,
rhmax=check_rh(rhmax),
rhmin=check_rh(rhmin),
rh=check_rh(rh),
)
es = calc_es(tmean=tmean, tmax=tmax, tmin=tmin)
pet = k * (1 + tmean / 25) ** 2 * (1 - ea / es)
pet = clip_zeros(pet, clip_zero)
return pet_out(tmean, pet, "Romanenko")
[docs]
def linacre(tmean, elevation, lat, tdew=None, tmax=None, tmin=None, clip_zero=True):
"""Potential evapotranspiration calculated according to
:cite:t:`linacre_simple_1977`.
Parameters
----------
tmean: pandas.Series or array_like
average day temperature [°C].
elevation: array_like
the site elevation [m].
lat: array_like, optional
the site latitude [°].
tdew: pandas.Series or array_like, optional
mean dew-point temperature [°C].
tmax: pandas.Series or array_like, optional
maximum day temperature [°C].
tmin: pandas.Series or array_like, optional
minimum day temperature [°C].
clip_zero: bool, optional
if True, replace all negative values with 0.
Returns
-------
pandas.Series or array_like containing the calculated potential
evapotranspiration [mm d-1].
Examples
--------
>>> pet_linacre = linacre(tmean, elevation, lat)
Notes
-----
Based on equation 5 in :cite:p:`xu_evaluation_2001`.
.. math:: PET = \\frac{\\frac{500 T_m}{(100-lat)}+15 (T_a-T_d)}{80-T_a}
"""
if tdew is None and tmax is None and tmin is None:
raise Exception("Please provide either Tdew or Tmax and Tmin!")
lat = check_lat(lat)
lat_deg = lat / pi * 180
if tdew is None:
tmax, tmin = tmax.values, tmin.values
tdew = 0.52 * tmin + 0.6 * tmax - 0.009 * tmax**2 - 2
tm = tmean + 0.006 * elevation
pet = (500 * tm / (100 - lat_deg) + 15 * (tmean - tdew)) / (80 - tmean)
pet = clip_zeros(pet, clip_zero)
return pet_out(tmean, pet, "Linacre")
