"""The combination module contains functions of combination PE methods
"""
import pandas
from numpy import exp, newaxis
from .meteo_utils import (
calc_lambda,
calc_press,
calc_psy,
calc_vpc,
calc_ea,
calc_es,
calc_rho,
calc_res_surf,
calc_res_aero,
day_of_year,
)
from .radiation import (
jensen_haise,
turc,
mcguinness_bordne,
hargreaves,
fao_24,
abtew,
makkink,
oudin,
)
from .temperature import blaney_criddle, romanenko, linacre, haude, hamon
from .rad_utils import calc_rad_net
from .utils import clip_zeros, get_index, check_rh, pet_out
# Specific heat of air [MJ kg-1 °C-1]
CP = 1.013 * 10**-3
# Stefan Boltzmann constant - hourly [MJm-2K-4h-1]
STEFAN_BOLTZMANN_HOUR = 2.042 * 10**-10
# Stefan Boltzmann constant - daily [MJm-2K-4d-1]
STEFAN_BOLTZMANN_DAY = 4.903 * 10**-9
[docs]
def penman(
tmean,
wind,
rs=None,
rn=None,
g=0,
tmax=None,
tmin=None,
rhmax=None,
rhmin=None,
rh=None,
pressure=None,
elevation=None,
lat=None,
n=None,
nn=None,
rso=None,
aw=1,
bw=0.537,
a=1.35,
b=-0.35,
ea=None,
albedo=0.23,
kab=None,
as1=0.25,
bs1=0.5,
clip_zero=True,
):
"""Potential evapotranspiration calculated according to
:cite:t:`penman_natural_1948`.
Parameters
----------
tmean: pandas.Series or xarray.DataArray
average day temperature [°C].
wind: float or pandas.Series or xarray.DataArray
mean day wind speed [m/s].
rs: float or pandas.Series or xarray.DataArray, optional
incoming solar radiation [MJ m-2 d-1].
rn: float or pandas.Series or xarray.DataArray, optional
net radiation [MJ m-2 d-1].
g: float or pandas.Series or xarray.DataArray, optional
soil heat flux [MJ m-2 d-1].
tmax: float or pandas.Series or xarray.DataArray, optional
maximum day temperature [°C].
tmin: float or pandas.Series or xarray.DataArray, optional
minimum day temperature [°C].
rhmax: float or pandas.Series or xarray.DataArray, optional
maximum daily relative humidity [%].
rhmin: float or pandas.Series or xarray.DataArray, optional
mainimum daily relative humidity [%].
rh: float or pandas.Series or xarray.DataArray, optional
mean daily relative humidity [%].
pressure: float or pandas.Series or xarray.DataArray, optional
atmospheric pressure [kPa].
elevation: float or xarray.DataArray, optional
the site elevation [m].
lat: float or xarray.DataArray, optional
the site latitude [rad].
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].
rso: float or pandas.Series or xarray.DataArray, optional
clear-sky solar radiation [MJ m-2 day-1].
aw: float, optional
wind coefficient [-].
bw: float, optional
wind coefficient [-].
a: float, optional
empirical coefficient for Net Long-Wave radiation [-].
b: float, optional
empirical coefficient for Net Long-Wave radiation [-].
ea: float or pandas.Series or xarray.DataArray, optional
actual vapor pressure [kPa].
albedo: float, optional
surface albedo [-].
kab: float, optional
coefficient derived from as1, bs1 for estimating clear-sky radiation [degrees].
as1: float, optional
regression constant, expressing the fraction of extraterrestrial reaching the
earth on overcast days (n = 0) [-].
bs1: float, optional
empirical coefficient for extraterrestrial radiation [-].
clip_zero: bool, optional
if True, replace all negative values with 0.
Returns
-------
pandas.Series or xarray.DataArray containing the calculated potential
evapotranspiration [mm d-1].
Examples
--------
>>> et_penman = penman(tmean, wind, rn=rn, rh=rh)
Notes
-----
Following :cite:t:`penman_natural_1948` and :cite:t:`valiantzas_simplified_2006`.
.. math:: PET = \\frac{\\frac{\\Delta (R_n-G)}{\\lambda} +
\\gamma (a_w + b_w u_2) (e_s-e_a)}{(\\Delta +\\gamma)}
"""
pressure, gamma, dlt, lambd, ea, es = _lambda_gamma_dlt_ea_es(
elevation, pressure, tmean, tmax, tmin, rhmax, rhmin, rh, ea
)
rn = calc_rad_net(
tmean,
rn,
rs,
lat,
n,
nn,
tmax,
tmin,
rhmax,
rhmin,
rh,
elevation,
rso,
a,
b,
ea,
albedo,
as1,
bs1,
kab,
)
fu = aw + bw * wind
den = dlt + gamma
num1 = dlt * (rn - g) / den / lambd
num2 = gamma * (es - ea) * fu / den
pet = num1 + num2
pet = clip_zeros(pet, clip_zero)
return pet_out(tmean, pet, "Penman")
[docs]
def pm_asce(
tmean,
wind,
rs=None,
rn=None,
g=0,
tmax=None,
tmin=None,
rhmax=None,
rhmin=None,
rh=None,
pressure=None,
elevation=None,
lat=None,
n=None,
nn=None,
rso=None,
a=1.35,
b=-0.35,
cn=900,
cd=0.34,
ea=None,
albedo=0.23,
kab=None,
as1=0.25,
bs1=0.5,
clip_zero=True,
etype="os",
):
"""Potential evapotranspiration calculated according to
:cite:t:`monteith_evaporation_1965`.
Parameters
----------
tmean: pandas.Series or xarray.DataArray
average day temperature [°C].
wind: float or pandas.Series or xarray.DataArray
mean day wind speed [m/s].
rs: float or pandas.Series or xarray.DataArray, optional
incoming solar radiation [MJ m-2 d-1].
rn: float or pandas.Series or xarray.DataArray, optional
net radiation [MJ m-2 d-1].
g: float or pandas.Series or xarray.DataArray, optional
soil heat flux [MJ m-2 d-1].
tmax: float or pandas.Series or xarray.DataArray, optional
maximum day temperature [°C].
tmin: float or pandas.Series or xarray.DataArray, optional
minimum day temperature [°C].
rhmax: float or pandas.Series or xarray.DataArray, optional
maximum daily relative humidity [%].
rhmin: float or pandas.Series or xarray.DataArray, optional
mainimum daily relative humidity [%].
rh: float or pandas.Series or xarray.DataArray, optional
mean daily relative humidity [%].
pressure: float or xarray.DataArray, optional
atmospheric pressure [kPa].
elevation: float or xarray.DataArray, optional
the site elevation [m].
lat: float or xarray.DataArray, optional
the site latitude [rad].
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].
rso: float or pandas.Series or xarray.DataArray, optional
clear-sky solar radiation [MJ m-2 day-1].
a: float, optional
empirical coefficient for Net Long-Wave radiation [-].
b: float, optional
empirical coefficient for Net Long-Wave radiation [-].
cn: float, optional
numerator constant [K mm s3 Mg-1 d-1].
cd: float, optional
denominator constant [s m-1].
ea: pandas.Series or float, optional
actual vapor pressure [kPa].
albedo: float, optional
surface albedo [-].
kab: float, optional
coefficient derived from as1, bs1 for estimating clear-sky radiation [degrees].
as1: float, optional
regression constant, expressing the fraction of extraterrestrial reaching the
earth on overcast days (n = 0) [-].
bs1: float, optional
empirical coefficient for extraterrestrial radiation [-].
clip_zero: bool, optional
if True, replace all negative values with 0.
etype: str, optional
"os" => ASCE-PM method is applied for a reference surfaces representing
clipped grass (a short, smooth crop). "rs" => ASCE-PM method is applied for a
reference surfaces representing alfalfa (a taller, rougher agricultural crop),).
Returns
-------
pandas.Series or xarray.DataArray containing the calculated potential
evapotranspiration [mm d-1].
Examples
--------
>>> et_pm = pm_asce(tmean, wind, rn=rn, rh=rh)
Notes
-----
Following :cite:t:`monteith_evaporation_1965` and :cite:t:`walter_asces_2000`
.. math:: PET = \\frac{\\Delta (R_{n}-G)+ \\rho_a c_p K_{min}
\\frac{e_s-e_a}{r_a}}{\\lambda(\\Delta +\\gamma(1+\\frac{r_s}{r_a}))}
"""
pressure, gamma, dlt, lambd, ea, es = _lambda_gamma_dlt_ea_es(
elevation, pressure, tmean, tmax, tmin, rhmax, rhmin, rh, ea
)
rn = calc_rad_net(
tmean,
rn,
rs,
lat,
n,
nn,
tmax,
tmin,
rhmax,
rhmin,
rh,
elevation,
rso,
a,
b,
ea,
albedo,
as1,
bs1,
kab,
)
if etype == "rs":
cn = 1600
cd = 0.38
den = dlt + gamma * (1 + cd * wind)
num1 = (0.408 * dlt * (rn - g)) / den
num2 = gamma * cn / (tmean + 273) * wind * (es - ea) / den
pet = num1 + num2
pet = clip_zeros(pet, clip_zero)
return pet_out(tmean, pet, "PM_ASCE")
[docs]
def pm(
tmean,
wind,
rs=None,
rn=None,
g=0,
tmax=None,
tmin=None,
rhmax=None,
rhmin=None,
rh=None,
pressure=None,
elevation=None,
lat=None,
n=None,
nn=None,
rso=None,
ea=None,
a=1.35,
b=-0.35,
lai=None,
croph=0.12,
r_l=100,
r_s=None,
ra_method=0,
a_sh=1,
a_s=1,
lai_eff=0,
srs=0.0009,
co2=300,
albedo=0.23,
kab=None,
as1=0.25,
bs1=0.5,
clip_zero=True,
):
"""Potential evapotranspiration calculated according to
:cite:t:`monteith_evaporation_1965`.
Parameters
----------
tmean: float or xarray.DataArray
average day temperature [°C].
wind: float or pandas.Series or xarray.DataArray
mean day wind speed [m/s].
rs: float or pandas.Series or xarray.DataArray, optional
incoming solar radiation [MJ m-2 d-1].
rn: float or pandas.Series or xarray.DataArray, optional
net radiation [MJ m-2 d-1].
g: float or pandas.Series or xarray.DataArray, optional
soil heat flux [MJ m-2 d-1].
tmax: float or pandas.Series or xarray.DataArray, optional
maximum day temperature [°C].
tmin: float or pandas.Series or xarray.DataArray, optional
minimum day temperature [°C].
rhmax: float or pandas.Series or xarray.DataArray, optional
maximum daily relative humidity [%].
rhmin: float or pandas.Series or xarray.DataArray, optional
mainimum daily relative humidity [%].
rh: float or pandas.Series or xarray.DataArray, optional
mean daily relative humidity [%].
pressure: float or xarray.DataArray, optional
atmospheric pressure [kPa].
elevation: float or xarray.DataArray, optional
the site elevation [m].
lat: float or xarray.DataArray, optional
the site latitude [rad].
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].
rso: float or pandas.Series or xarray.DataArray, optional
clear-sky solar radiation [MJ m-2 day-1].
ea: float or pandas.Series or xarray.DataArray, optional
actual vapor pressure [kPa].
a: float, optional
empirical coefficient for Net Long-Wave radiation [-].
b: float, optional
empirical coefficient for Net Long-Wave radiation [-].
lai: float or pandas.Series or xarray.DataArray, optional
leaf area index [-].
croph: float or pandas.Series or xarray.DataArray, optional
crop height [m].
r_l: pandas.Series or float, optional
bulk stomatal resistance [s m-1].
r_s: pandas.Series or float, optional
bulk surface resistance [s m-1].
ra_method: float, optional
0 => ra = 208/wind
1 => ra is calculated based on equation 36 in FAO (1990), ANNEX V.
a_s: float, optional
Fraction of one-sided leaf area covered by stomata (1 if stomata are 1
on one side only, 2 if they are on both sides).
a_sh: float, optional
Fraction of projected area exchanging sensible heat with the air (2).
lai_eff: float, optional
0 => LAI_eff = 0.5 * LAI
1 => LAI_eff = lai / (0.3 * lai + 1.2)
2 => LAI_eff = 0.5 * LAI; (LAI>4=4)
3 => see :cite:t:`zhang_comparison_2008`.
srs: float or pandas.Series or xarray.DataArray, optional
Relative sensitivity of rl to Δ[CO2].
co2: float or pandas.Series or xarray.DataArray, optional
CO2 concentration [ppm].
albedo: float, optional
surface albedo [-].
kab: float, optional
coefficient derived from as1, bs1 for estimating clear-sky radiation [degrees].
as1: float, optional
regression constant, expressing the fraction of extraterrestrial reaching the
earth on overcast days (n = 0) [-].
bs1: float, optional
empirical coefficient for extraterrestrial radiation [-].
clip_zero: bool, optional
if True, replace all negative values with 0.
Returns
-------
pandas.Series or xarray.DataArray containing the calculated potential
evapotranspiration [mm d-1].
Examples
--------
>>> tet_pm = pm(tmean, wind, rn=rn, rh=rh)
Notes
-----
Following :cite:t:`monteith_evaporation_1965`, :cite:t:`allen_crop_1998`,
:cite:t:`zhang_comparison_2008`, :cite:t:`schymanski_leaf-scale_2017` and
:cite:t:`yang_hydrologic_2019`.
.. math:: PET = \\frac{\\Delta (R_{n}-G)+ \\rho_a c_p K_{min}
\\frac{e_s-e_a}{r_a}}{\\lambda(\\Delta +\\gamma(1+\\frac{r_s}{r_a}))}
, where
.. math:: r_s = f_{co2} * r_l / LAI_{eff}
.. math:: f_{co2} = (1+S_{r_s}*(CO_2-300))
ra_method == 0:
.. math:: r_a = \\frac{208}{u_2}
ra_method == 1:
.. math:: r_a = log(\\frac{(zw - d)}{zom}) *
\\frac{log(\\frac{(zh - d)}{zoh})}{(0.41^2)u_2}
"""
pressure, gamma, dlt, lambd, ea, es = _lambda_gamma_dlt_ea_es(
elevation, pressure, tmean, tmax, tmin, rhmax, rhmin, rh, ea
)
res_a = calc_res_aero(wind, ra_method=ra_method, croph=croph)
res_s = calc_res_surf(
lai=lai, r_s=r_s, r_l=r_l, lai_eff=lai_eff, srs=srs, co2=co2, croph=croph
)
gamma1 = gamma * a_sh / a_s * (1 + res_s / res_a)
rn = calc_rad_net(
tmean,
rn,
rs,
lat,
n,
nn,
tmax,
tmin,
rhmax,
rhmin,
rh,
elevation,
rso,
a,
b,
ea,
albedo,
as1,
bs1,
kab,
)
kmin = 86400 # unit conversion s d-1
rho_a = calc_rho(pressure, tmean, ea)
den = lambd * (dlt + gamma1)
num1 = dlt * (rn - g) / den
num2 = rho_a * CP * kmin * (es - ea) * a_sh / res_a / den
pet = num1 + num2
pet = clip_zeros(pet, clip_zero)
return pet_out(tmean, pet, "Penman_Monteith")
[docs]
def pm_fao56(
tmean,
wind,
rs=None,
rn=None,
g=0,
tmax=None,
tmin=None,
rhmax=None,
rhmin=None,
rh=None,
pressure=None,
elevation=None,
lat=None,
n=None,
nn=None,
rso=None,
a=1.35,
b=-0.35,
ea=None,
albedo=0.23,
kab=None,
as1=0.25,
bs1=0.5,
clip_zero=True,
):
"""Potential evapotranspiration calculated according to
:cite:t:`allen_crop_1998`.
Parameters
----------
tmean: pandas.Series or xarray.DataArray
average day temperature [°C].
wind: float or pandas.Series or xarray.DataArray
mean day wind speed [m/s].
rs: float or pandas.Series or xarray.DataArray, optional
incoming solar radiation [MJ m-2 d-1].
rn: float or pandas.Series or xarray.DataArray, optional
net radiation [MJ m-2 d-1].
g: float or pandas.Series or xarray.DataArray, optional
soil heat flux [MJ m-2 d-1].
tmax: float or pandas.Series or xarray.DataArray, optional
maximum day temperature [°C].
tmin: float or pandas.Series or xarray.DataArray, optional
minimum day temperature [°C].
rhmax: float or pandas.Series or xarray.DataArray, optional
maximum daily relative humidity [%].
rhmin: float or pandas.Series or xarray.DataArray, optional
mainimum daily relative humidity [%].
rh: float or pandas.Series or xarray.DataArray optional
mean daily relative humidity [%].
pressure: float or pandas.Series or xarray.DataArray, optional
atmospheric pressure [kPa].
elevation: float or xarray.DataArray, optional
the site elevation [m].
lat: float or xarray.DataArray, optional
the site latitude [rad].
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].
rso: float or pandas.Series or xarray.DataArray, optional
clear-sky solar radiation [MJ m-2 day-1].
a: float, optional
empirical coefficient for Net Long-Wave radiation [-].
b: float, optional
empirical coefficient for Net Long-Wave radiation [-].
ea: float or pandas.Series or xarray.DataArray, optional
actual vapor pressure [kPa].
albedo: float, optional
surface albedo [-].
kab: float, optional
coefficient derived from as1, bs1 for estimating clear-sky radiation [degrees].
as1: float, optional
regression constant, expressing the fraction of extraterrestrial reaching the
earth on overcast days (n = 0) [-].
bs1: float, optional
empirical coefficient for extraterrestrial radiation [-].
clip_zero: bool, optional
if True, replace all negative values with 0.
Returns
-------
pandas.Series or xarray.DataArray containing the calculated potential
evapotranspiration [mm d-1].
Examples
--------
>>> et_fao56 = pm_fao56(tmean, wind, rn=rn, rh=rh)
Notes
-----
.. math:: PET = \\frac{0.408 \\Delta (R_{n}-G)+\\gamma \\frac{900}{T+273}
(e_s-e_a) u_2}{\\Delta+\\gamma(1+0.34 u_2)}
"""
if tmean is None:
tmean = (tmax + tmin) / 2
pressure, gamma, dlt, lambd, ea, es = _lambda_gamma_dlt_ea_es(
elevation, pressure, tmean, tmax, tmin, rhmax, rhmin, rh, ea
)
gamma1 = gamma * (1 + 0.34 * wind)
rn = calc_rad_net(
tmean,
rn,
rs,
lat,
n,
nn,
tmax,
tmin,
rhmax,
rhmin,
rh,
elevation,
rso,
a,
b,
ea,
albedo,
as1,
bs1,
kab,
)
den = dlt + gamma1
num1 = (0.408 * dlt * (rn - g)) / den
num2 = (gamma * (es - ea) * 900 * wind / (tmean + 273)) / den
pet = num1 + num2
pet = clip_zeros(pet, clip_zero)
return pet # pet_out(tmean, pet, "PM_FAO_56")
[docs]
def priestley_taylor(
tmean,
rs=None,
rn=None,
g=0,
tmax=None,
tmin=None,
rhmax=None,
rhmin=None,
rh=None,
pressure=None,
elevation=None,
lat=None,
n=None,
nn=None,
rso=None,
a=1.35,
b=-0.35,
alpha=1.26,
albedo=0.23,
kab=None,
as1=0.25,
bs1=0.5,
clip_zero=True,
):
"""Potential evapotranspiration calculated according to
:cite:t:`priestley_assessment_1972`.
Parameters
----------
tmean: pandas.Series or xarray.DataArray
average day temperature [°C].
rs: float or pandas.Series or xarray.DataArray, optional
incoming solar radiation [MJ m-2 d-1].
rn: float or pandas.Series or xarray.DataArray, optional
net radiation [MJ m-2 d-1].
g: float or pandas.Series or xarray.DataArray, optional
soil heat flux [MJ m-2 d-1].
tmax: float or pandas.Series or xarray.DataArray, optional
maximum day temperature [°C].
tmin: float or pandas.Series or xarray.DataArray, optional
minimum day temperature [°C].
rhmax: float or pandas.Series or xarray.DataArray, optional
maximum daily relative humidity [%].
rhmin: float or pandas.Series or xarray.DataArray, optional
mainimum daily relative humidity [%].
rh: float or pandas.Series or xarray.DataArray, optional
mean daily relative humidity [%].
pressure: float or pandas.Series or xarray.DataArray, optional
atmospheric pressure [kPa].
elevation: float or xarray.DataArray, optional
the site elevation [m].
lat: float or xarray.DataArray, optional
the site latitude [rad].
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].
rso: float or pandas.Series or xarray.DataArray, optional
clear-sky solar radiation [MJ m-2 day-1].
a: float, optional
empirical coefficient for Net Long-Wave radiation [-].
b: float, optional
empirical coefficient for Net Long-Wave radiation [-].
alpha: float, optional
calibration coefficient [-].
albedo: float, optional
surface albedo [-].
kab: float, optional
coefficient derived from as1, bs1 for estimating clear-sky radiation [degrees].
as1: float, optional
regression constant, expressing the fraction of extraterrestrial reaching the
earth on overcast days (n = 0) [-].
bs1: float, optional
empirical coefficient for extraterrestrial radiation [-].
clip_zero: bool, optional
if True, replace all negative values with 0.
Returns
-------
pandas.Series or xarray.DataArray containing the calculated pootential
evapotranspiration [mm d-1].
Examples
--------
>>> pt = priestley_taylor(tmean, rn=rn, rh=rh)
Notes
-----
.. math:: PET = \\frac{\\alpha_{PT} \\Delta (R_n-G)}
{\\lambda(\\Delta +\\gamma)}
"""
pressure = calc_press(elevation, pressure)
gamma = calc_psy(pressure)
dlt = calc_vpc(tmean)
lambd = calc_lambda(tmean)
rn = calc_rad_net(
tmean,
rn,
rs,
lat,
n,
nn,
tmax,
tmin,
rhmax,
rhmin,
rh,
elevation,
rso,
a,
b,
None,
albedo,
as1,
bs1,
kab,
)
pet = (alpha * dlt * (rn - g)) / (lambd * (dlt + gamma))
pet = clip_zeros(pet, clip_zero)
return pet_out(tmean, pet, "Priestley_Taylor")
[docs]
def kimberly_penman(
tmean,
wind,
rs=None,
rn=None,
g=0,
tmax=None,
tmin=None,
rhmax=None,
rhmin=None,
rh=None,
pressure=None,
elevation=None,
lat=None,
n=None,
nn=None,
rso=None,
a=1.35,
b=-0.35,
ea=None,
albedo=0.23,
kab=None,
as1=0.25,
bs1=0.5,
clip_zero=True,
):
"""Potential evapotranspiration calculated according to :cite:t:`wright_new_1982`.
Parameters
----------
tmean: pandas.Series or xarray.DataArray
average day temperature [°C].
wind: pandas.Series or xarray.DataArray
mean day wind speed [m/s].
rs: pandas.Series or xarray.DataArray, optional
incoming solar radiation [MJ m-2 d-1].
rn: pandas.Series or xarray.DataArray, optional
net radiation [MJ m-2 d-1].
g: pandas.Series or int/xarray.DataArray, optional
soil heat flux [MJ m-2 d-1].
tmax: pandas.Series or xarray.DataArray, optional
maximum day temperature [°C].
tmin: pandas.Series or xarray.DataArray, optional
minimum day temperature [°C].
rhmax: pandas.Series or xarray.DataArray, optional
maximum daily relative humidity [%].
rhmin: pandas.Series or xarray.DataArray, optional
mainimum daily relative humidity [%].
rh: pandas.Series or xarray.DataArray, optional
mean daily relative humidity [%].
pressure: float or xarray.DataArray, optional
atmospheric pressure [kPa].
elevation: float or xarray.DataArray, optional
the site elevation [m].
lat: float or xarray.DataArray, optional
the site latitude [rad].
n: pandas.Series or float, optional
actual duration of sunshine [hour].
nn: pandas.Series or float, optional
maximum possible duration of sunshine or daylight hours [hour].
rso: pandas.Series or float, optional
clear-sky solar radiation [MJ m-2 day-1].
a: float, optional.=
empirical coefficient for Net Long-Wave radiation [-].
b: float, optional
empirical coefficient for Net Long-Wave radiation [-].
ea: float or pandas.Series or xarray.DataArray, optional
actual vapor pressure [kPa].
albedo: float, optional
surface albedo [-].
kab: float, optional
coefficient derived from as1, bs1 for estimating clear-sky radiation [degrees].
as1: float, optional
regression constant, expressing the fraction of extraterrestrial reaching the
earth on overcast days (n = 0) [-].
bs1: float, optional
empirical coefficient for extraterrestrial radiation [-].
clip_zero: bool, optional
if True, replace all negative values with 0..
Returns
-------
pandas.Series or xarray.DataArray containing the calculated potential
evapotranspiration [mm d-1].
Notes
-----
Following :cite:t:`oudin_which_2005`.
.. math:: PET = \\frac{\\Delta (R_n-G)+ \\gamma (e_s-e_a) w}
{\\lambda(\\Delta +\\gamma)}
.. math:: w = u_2 * (0.4 + 0.14 * exp(-(\\frac{J_D-173}{58})^2)) +
(0.605 + 0.345 * exp(-(\\frac{J_D-243}{80})^2))
"""
pressure, gamma, dlt, lambd, ea, es = _lambda_gamma_dlt_ea_es(
elevation, pressure, tmean, tmax, tmin, rhmax, rhmin, rh, ea
)
rn = calc_rad_net(
tmean,
rn,
rs,
lat,
n,
nn,
tmax,
tmin,
rhmax,
rhmin,
rh,
elevation,
rso,
a,
b,
ea,
albedo,
as1,
bs1,
kab,
)
tindex = get_index(tmean)
j = day_of_year(tindex)
if len(wind.shape) == 3:
j = j[:, newaxis, newaxis]
w = wind * (
0.4
+ 0.14 * exp(-(((j - 173) / 58) ** 2))
+ (0.605 + 0.345 * exp((j - 243) / 80) ** 2)
)
den = lambd * (dlt + gamma)
num1 = dlt * (rn - g) / den
num2 = gamma * (es - ea) * w / den
pet = num1 + num2
pet = clip_zeros(pet, clip_zero)
return pet_out(tmean, pet, "Kimberly_Penman")
[docs]
def thom_oliver(
tmean,
wind,
rs=None,
rn=None,
g=0,
tmax=None,
tmin=None,
rhmax=None,
rhmin=None,
rh=None,
pressure=None,
elevation=None,
lat=None,
n=None,
nn=None,
rso=None,
aw=2.6,
bw=0.536,
a=1.35,
b=-0.35,
lai=None,
croph=0.12,
r_l=100,
r_s=None,
ra_method=0,
lai_eff=0,
srs=0.0009,
co2=300,
ea=None,
albedo=0.23,
kab=None,
as1=0.25,
bs1=0.5,
clip_zero=True,
):
"""Potential evapotranspiration calculated according to :cite:t:`thom_penmans_1977`.
Parameters
----------
tmean: pandas.Series
average day temperature [°C].
wind: pandas.Series
mean day wind speed [m/s].
rs: pandas.Series, optional
incoming solar radiation [MJ m-2 d-1].
rn: pandas.Series, optional
net radiation [MJ m-2 d-1].
g: pandas.Series or int, optional
soil heat flux [MJ m-2 d-1].
tmax: pandas.Series, optional
maximum day temperature [°C].
tmin: pandas.Series, optional
minimum day temperature [°C].
rhmax: pandas.Series, optional
maximum daily relative humidity [%].
rhmin: pandas.Series, optional
mainimum daily relative humidity [%].
rh: pandas.Series, optional
mean daily relative humidity [%].
pressure: float, optional
atmospheric pressure [kPa].
elevation: float, optional
the site elevation [m].
lat: float, optional
the site latitude [rad].
n: pandas.Series or float, optional
actual duration of sunshine [hour].
nn: pandas.Series or float, optional
maximum possible duration of sunshine or daylight hours [hour].
rso: pandas.Series or float, optional
clear-sky solar radiation [MJ m-2 day-1].
aw: float, optional
wind coefficient [-].
bw: float, optional
wind coefficient [-].
a: float, optional
empirical coefficient for Net Long-Wave radiation [-].
b: float, optional
empirical coefficient for Net Long-Wave radiation [-].
lai: pandas.Series or float, optional
leaf area index [-].
croph: pandas.Series or float, optional
crop height [m].
r_l: pandas.Series or float, optional
bulk stomatal resistance [s m-1].
r_s: pandas.Series or float, optional
bulk surface resistance [s m-1].
ra_method: float, optional
1 => ra = 208/wind
2 => ra is calculated based on equation 36 in FAO (1990), ANNEX V.
lai_eff: float, optional
0 => LAI_eff = 0.5 * LAI
1 => LAI_eff = lai / (0.3 * lai + 1.2)
2 => LAI_eff = 0.5 * LAI; (LAI>4=4)
3 => see :cite:t:`zhang_comparison_2008`.
srs: float, optional
Relative sensitivity of rl to Δ[CO2].
co2: float
CO2 concentration [ppm].
ea: float or pandas.Series or xarray.DataArray, optional
actual vapor pressure [kPa].
albedo: float, optional
surface albedo [-].
kab: float, optional
coefficient derived from as1, bs1 for estimating clear-sky radiation [degrees].
as1: float, optional
regression constant, expressing the fraction of extraterrestrial reaching the
earth on overcast days (n = 0) [-].
bs1: float, optional
empirical coefficient for extraterrestrial radiation [-].
clip_zero: bool, optional
if True, replace all negative values with 0.
Returns
-------
pandas.Series or xarray.DataArray containing the calculated potential
evapotranspiration [mm d-1].
Notes
-----
Following :cite:t:`oudin_which_2005`.
.. math:: PET = \\frac{\\Delta (R_{n}-G)+ 2.5 \\gamma (e_s-e_a) w}
{\\lambda(\\Delta +\\gamma(1+\\frac{r_s}{r_a}))}
.. math:: w=2.6(1+0.53u_2)
"""
pressure, gamma, dlt, lambd, ea, es = _lambda_gamma_dlt_ea_es(
elevation, pressure, tmean, tmax, tmin, rhmax, rhmin, rh, ea
)
res_a = calc_res_aero(wind, ra_method=ra_method, croph=croph)
res_s = calc_res_surf(
lai=lai, r_s=r_s, r_l=r_l, lai_eff=lai_eff, srs=srs, co2=co2, croph=croph
)
gamma1 = gamma * (1 + res_s / res_a)
rn = calc_rad_net(
tmean,
rn,
rs,
lat,
n,
nn,
tmax,
tmin,
rhmax,
rhmin,
rh,
elevation,
rso,
a,
b,
ea,
albedo,
as1,
bs1,
kab,
)
w = aw * (1 + bw * wind)
den = lambd * (dlt + gamma1)
num1 = dlt * (rn - g) / den
num2 = 2.5 * gamma * (es - ea) * w / den
pet = num1 + num2
pet = clip_zeros(pet, clip_zero)
return pet_out(tmean, pet, "Thom_Oliver")
[docs]
def calculate_all(
tmean, wind, rs, elevation, lat, tmax, tmin, rh=None, rhmax=None, rhmin=None
):
"""Potential evapotranspiration estimated based on all available methods.
Parameters
----------
tmean: pandas.Series or xarray.DataArray
average day temperature [°C].
wind: float or pandas.Series or xarray.DataArray
mean day wind speed [m/s].
rs: float or pandas.Series or xarray.DataArray
incoming solar radiation [MJ m-2 d-1].
elevation: float or xarray.DataArray
the site elevation [m].
lat: float or xarray.DataArray
the site latitude [rad].
tmax: float or pandas.Series or xarray.DataArray
maximum day temperature [°C].
tmin: float or pandas.Series or xarray.DataArray
minimum day temperature [°C].
rh: float or pandas.Series or xarray.DataArray
mean daily relative humidity [%].
rhmax: pandas.Series, optional
maximum daily relative humidity [%].
rhmin: pandas.Series, optional
minimum daily relative humidity [%].
Returns
-------
pandas.DataFrame containing the calculated Potential evapotranspiration
Examples
--------
>>> pe_all = calculate_all(tmean, wind, rs, elevation, lat, tmax=tmax,
tmin=tmin, rh=rh)
"""
pe_df = pandas.DataFrame()
pe_df["Penman"] = penman(
tmean,
wind,
rs=rs,
elevation=elevation,
lat=lat,
tmax=tmax,
tmin=tmin,
rh=rh,
rhmax=rhmax,
rhmin=rhmin,
)
pe_df["FAO-56"] = pm_fao56(
tmean,
wind,
rs=rs,
elevation=elevation,
lat=lat,
tmax=tmax,
tmin=tmin,
rh=rh,
rhmax=rhmax,
rhmin=rhmin,
)
pe_df["Priestley-Taylor"] = priestley_taylor(
tmean,
rs=rs,
elevation=elevation,
lat=lat,
tmax=tmax,
tmin=tmin,
rh=rh,
rhmax=rhmax,
rhmin=rhmin,
)
pe_df["Kimberly-Penman"] = kimberly_penman(
tmean,
wind,
rs=rs,
elevation=elevation,
lat=lat,
tmax=tmax,
tmin=tmin,
rh=rh,
rhmax=rhmax,
rhmin=rhmin,
)
pe_df["Thom-Oliver"] = thom_oliver(
tmean,
wind,
rs=rs,
elevation=elevation,
lat=lat,
tmax=tmax,
tmin=tmin,
rh=rh,
rhmax=rhmax,
rhmin=rhmin,
)
pe_df["Blaney-Criddle"] = blaney_criddle(tmean, lat)
pe_df["Hamon"] = hamon(tmean, lat=lat, method=1)
pe_df["Romanenko"] = romanenko(
tmean, rh=rh, tmax=tmax, tmin=tmin, rhmax=rhmax, rhmin=rhmin
)
pe_df["Linacre"] = linacre(tmean, elevation, lat, tmax=tmax, tmin=tmin)
pe_df["Haude"] = haude(tmax, rh)
pe_df["Turc"] = turc(tmean, rs, rh)
pe_df["Jensen-Haise"] = jensen_haise(tmean, rs=rs)
pe_df["Mcguinness-Bordne"] = mcguinness_bordne(tmean, lat=lat)
pe_df["Hargreaves"] = hargreaves(tmean, tmax, tmin, lat)
pe_df["FAO-24"] = fao_24(tmean, wind, rs=rs, rh=rh, elevation=elevation)
pe_df["Abtew"] = abtew(tmean, rs)
pe_df["Makkink"] = makkink(tmean, rs, elevation=elevation)
pe_df["Oudin"] = oudin(tmean, lat=lat)
return pe_df
def _lambda_gamma_dlt_ea_es(
velevation, vpressure, vtmean, vtmax, vtmin, vrhmax, vrhmin, vrh, vea
):
"""Just ot avoid duplicated rows."""
vpressure = calc_press(velevation, vpressure)
gamma = calc_psy(vpressure)
dlt = calc_vpc(vtmean)
lambd = calc_lambda(vtmean)
ea = calc_ea(
tmean=vtmean,
tmax=vtmax,
tmin=vtmin,
rhmax=check_rh(vrhmax),
rhmin=check_rh(vrhmin),
rh=check_rh(vrh),
ea=vea,
)
es = calc_es(tmean=vtmean, tmax=vtmax, tmin=vtmin)
return vpressure, gamma, dlt, lambd, ea, es
