# noqa: D100
from __future__ import annotations
from typing import cast
import numpy as np
import xarray as xr
from numba import float32, float64, vectorize # noqa
from xclim.core.units import (
amount2rate,
convert_units_to,
declare_units,
flux2rate,
rate2flux,
units2pint,
)
from xclim.core.utils import Quantified
from xclim.indices.helpers import (
_gather_lat,
_gather_lon,
cosine_of_solar_zenith_angle,
day_lengths,
distance_from_sun,
extraterrestrial_solar_radiation,
solar_declination,
time_correction_for_solar_angle,
wind_speed_height_conversion,
)
__all__ = [
"clausius_clapeyron_scaled_precipitation",
"heat_index",
"humidex",
"longwave_upwelling_radiation_from_net_downwelling",
"mean_radiant_temperature",
"potential_evapotranspiration",
"prsn_to_prsnd",
"prsnd_to_prsn",
"rain_approximation",
"relative_humidity",
"saturation_vapor_pressure",
"sfcwind_2_uas_vas",
"shortwave_upwelling_radiation_from_net_downwelling",
"snd_to_snw",
"snowfall_approximation",
"snw_to_snd",
"specific_humidity",
"specific_humidity_from_dewpoint",
"tas",
"uas_vas_2_sfcwind",
"universal_thermal_climate_index",
"wind_chill_index",
"wind_power_potential",
"wind_profile",
]
[docs]
@declare_units(tas="[temperature]", tdps="[temperature]", hurs="[]")
def humidex(
tas: xr.DataArray,
tdps: xr.DataArray | None = None,
hurs: xr.DataArray | None = None,
) -> xr.DataArray:
r"""Humidex index.
The humidex indicates how hot the air feels to an average person, accounting for the effect of humidity. It
can be loosely interpreted as the equivalent perceived temperature when the air is dry.
Parameters
----------
tas : xarray.DataArray
Air temperature.
tdps : xarray.DataArray, optional
Dewpoint temperature, used to compute the vapour pressure.
hurs : xarray.DataArray, optional
Relative humidity, used as an alternative way to compute the vapour pressure if the dewpoint temperature is not
available.
Returns
-------
xarray.DataArray, [temperature]
The humidex index.
Notes
-----
The humidex is usually computed using hourly observations of dry bulb and dewpoint temperatures. It is computed
using the formula based on :cite:t:`masterton_humidex_1979`:
.. math::
T + {\frac {5}{9}}\left[e - 10\right]
where :math:`T` is the dry bulb air temperature (°C). The term :math:`e` can be computed from the dewpoint
temperature :math:`T_{dewpoint}` in °K:
.. math::
e = 6.112 \times \exp(5417.7530\left({\frac {1}{273.16}}-{\frac {1}{T_{\text{dewpoint}}}}\right)
where the constant 5417.753 reflects the molecular weight of water, latent heat of vaporization,
and the universal gas constant :cite:p:`mekis_observed_2015`. Alternatively, the term :math:`e` can also be computed
from the relative humidity `h` expressed in percent using :cite:t:`sirangelo_combining_2020`:
.. math::
e = \frac{h}{100} \times 6.112 * 10^{7.5 T/(T + 237.7)}.
The humidex *comfort scale* :cite:p:`canada_glossary_2011` can be interpreted as follows:
- 20 to 29 : no discomfort;
- 30 to 39 : some discomfort;
- 40 to 45 : great discomfort, avoid exertion;
- 46 and over : dangerous, possible heat stroke;
Please note that while both the humidex and the heat index are calculated using dew point, the humidex uses
a dew point of 7 °C (45 °F) as a base, whereas the heat index uses a dew point base of 14 °C (57 °F). Further,
the heat index uses heat balance equations which account for many variables other than vapour pressure,
which is used exclusively in the humidex calculation.
References
----------
:cite:cts:`canada_glossary_2011,masterton_humidex_1979,mekis_observed_2015,sirangelo_combining_2020`
"""
if (tdps is None) and (hurs is None):
raise ValueError("At least one of `tdps` or `hurs` must be given.")
# Vapour pressure in hPa
if tdps is not None:
# Convert dewpoint temperature to Kelvins
tdps = convert_units_to(tdps, "kelvin")
e = 6.112 * np.exp(5417.7530 * (1 / 273.16 - 1.0 / tdps))
elif hurs is not None:
# Convert dry bulb temperature to Celsius
tasC = convert_units_to(tas, "celsius")
e = hurs / 100 * 6.112 * 10 ** (7.5 * tasC / (tasC + 237.7))
else:
raise ValueError("Either `tdps` or `hurs` must be provided.")
# Temperature delta due to humidity in delta_degC
h: xr.DataArray = 5 / 9 * (e - 10)
h = h.assign_attrs(units="delta_degree_Celsius")
# Get delta_units for output
du = (1 * units2pint(tas) - 0 * units2pint(tas)).units
h = convert_units_to(h, du)
# Add the delta to the input temperature
out = h + tas
out = out.assign_attrs(units=tas.units)
return out
[docs]
@declare_units(tas="[temperature]", hurs="[]")
def heat_index(tas: xr.DataArray, hurs: xr.DataArray) -> xr.DataArray:
r"""Heat index.
Perceived temperature after relative humidity is taken into account :cite:p:`blazejczyk_comparison_2012`.
The index is only valid for temperatures above 20°C.
Parameters
----------
tas : xr.DataArray
Temperature. The equation assumes an instantaneous value.
hurs : xr.DataArray
Relative humidity. The equation assumes an instantaneous value.
Returns
-------
xr.DataArray, [temperature]
Heat index for moments with temperature above 20°C.
References
----------
:cite:cts:`blazejczyk_comparison_2012`
Notes
-----
While both the humidex and the heat index are calculated using dew point the humidex uses a dew point of 7 °C
(45 °F) as a base, whereas the heat index uses a dew point base of 14 °C (57 °F). Further, the heat index uses
heat balance equations which account for many variables other than vapour pressure, which is used exclusively in the
humidex calculation.
"""
thresh = 20 # degC
t = convert_units_to(tas, "degC")
t = t.where(t > thresh)
r = convert_units_to(hurs, "%")
out = (
-8.78469475556
+ 1.61139411 * t
+ 2.33854883889 * r
- 0.14611605 * t * r
- 0.012308094 * t * t
- 0.0164248277778 * r * r
+ 0.002211732 * t * t * r
+ 0.00072546 * t * r * r
- 0.000003582 * t * t * r * r
)
out = out.assign_attrs(units="degC")
return convert_units_to(out, tas.units)
[docs]
@declare_units(tasmin="[temperature]", tasmax="[temperature]")
def tas(tasmin: xr.DataArray, tasmax: xr.DataArray) -> xr.DataArray:
"""Average temperature from minimum and maximum temperatures.
We assume a symmetrical distribution for the temperature and retrieve the average value as Tg = (Tx + Tn) / 2
Parameters
----------
tasmin : xarray.DataArray
Minimum (daily) temperature
tasmax : xarray.DataArray
Maximum (daily) temperature
Returns
-------
xarray.DataArray
Mean (daily) temperature [same units as tasmin]
Examples
--------
>>> from xclim.indices import tas
>>> tas = tas(tasmin_dataset, tasmax_dataset)
"""
tasmax = convert_units_to(tasmax, tasmin)
tas = (tasmax + tasmin) / 2
tas.attrs["units"] = tasmin.attrs["units"]
return tas
[docs]
@declare_units(uas="[speed]", vas="[speed]", calm_wind_thresh="[speed]")
def uas_vas_2_sfcwind(
uas: xr.DataArray, vas: xr.DataArray, calm_wind_thresh: Quantified = "0.5 m/s"
) -> tuple[xr.DataArray, xr.DataArray]:
"""Wind speed and direction from the eastward and northward wind components.
Computes the magnitude and angle of the wind vector from its northward and eastward components,
following the meteorological convention that sets calm wind to a direction of 0° and northerly wind to 360°.
Parameters
----------
uas : xr.DataArray
Eastward wind velocity
vas : xr.DataArray
Northward wind velocity
calm_wind_thresh : Quantified
The threshold under which winds are considered "calm" and for which the direction
is set to 0. On the Beaufort scale, calm winds are defined as < 0.5 m/s.
Returns
-------
wind : xr.DataArray, [m s-1]
Wind velocity
wind_from_dir : xr.DataArray, [°]
Direction from which the wind blows, following the meteorological convention where
360 stands for North and 0 for calm winds.
Examples
--------
>>> from xclim.indices import uas_vas_2_sfcwind
>>> sfcWind = uas_vas_2_sfcwind(
... uas=uas_dataset, vas=vas_dataset, calm_wind_thresh="0.5 m/s"
... )
Notes
-----
Winds with a velocity less than `calm_wind_thresh` are given a wind direction of 0°,
while stronger northerly winds are set to 360°.
"""
# Converts the wind speed to m s-1
uas = convert_units_to(uas, "m/s")
vas = convert_units_to(vas, "m/s")
wind_thresh = convert_units_to(calm_wind_thresh, "m/s")
# Wind speed is the hypotenuse of "uas" and "vas"
wind = cast(xr.DataArray, np.hypot(uas, vas))
wind = wind.assign_attrs(units="m s-1")
# Calculate the angle
wind_from_dir_math = np.degrees(np.arctan2(vas, uas))
# Convert the angle from the mathematical standard to the meteorological standard
wind_from_dir = (270 - wind_from_dir_math) % 360.0
# According to the meteorological standard, calm winds must have a direction of 0°
# while northerly winds have a direction of 360°
# On the Beaufort scale, calm winds are defined as < 0.5 m/s
wind_from_dir = xr.where(wind_from_dir.round() == 0, 360, wind_from_dir)
wind_from_dir = xr.where(wind < wind_thresh, 0, wind_from_dir)
wind_from_dir.attrs["units"] = "degree"
return wind, wind_from_dir
[docs]
@declare_units(sfcWind="[speed]", sfcWindfromdir="[]")
def sfcwind_2_uas_vas(
sfcWind: xr.DataArray, sfcWindfromdir: xr.DataArray # noqa
) -> tuple[xr.DataArray, xr.DataArray]:
"""Eastward and northward wind components from the wind speed and direction.
Compute the eastward and northward wind components from the wind speed and direction.
Parameters
----------
sfcWind : xr.DataArray
Wind velocity
sfcWindfromdir : xr.DataArray
Direction from which the wind blows, following the meteorological convention
where 360 stands for North.
Returns
-------
uas : xr.DataArray, [m s-1]
Eastward wind velocity.
vas : xr.DataArray, [m s-1]
Northward wind velocity.
Examples
--------
>>> from xclim.indices import sfcwind_2_uas_vas
>>> uas, vas = sfcwind_2_uas_vas(
... sfcWind=sfcWind_dataset, sfcWindfromdir=sfcWindfromdir_dataset
... )
"""
# Converts the wind speed to m s-1
sfcWind = convert_units_to(sfcWind, "m/s") # noqa
# Converts the wind direction from the meteorological standard to the mathematical standard
wind_from_dir_math = (-sfcWindfromdir + 270) % 360.0
# TODO: This commented part should allow us to resample subdaily wind, but needs to be cleaned up and put elsewhere.
# if resample is not None:
# wind = wind.resample(time=resample).mean(dim='time', keep_attrs=True)
#
# # nb_per_day is the number of values each day. This should be calculated
# wind_from_dir_math_per_day = wind_from_dir_math.reshape((len(wind.time), nb_per_day))
# # Averages the subdaily angles around a circle, i.e. mean([0, 360]) = 0, not 180
# wind_from_dir_math = np.concatenate([[degrees(phase(sum(rect(1, radians(d)) for d in angles) / len(angles)))]
# for angles in wind_from_dir_math_per_day])
uas = sfcWind * np.cos(np.radians(wind_from_dir_math))
vas = sfcWind * np.sin(np.radians(wind_from_dir_math))
uas.attrs["units"] = "m s-1"
vas.attrs["units"] = "m s-1"
return uas, vas
[docs]
@declare_units(tas="[temperature]", ice_thresh="[temperature]")
def saturation_vapor_pressure(
tas: xr.DataArray,
ice_thresh: Quantified | None = None,
method: str = "sonntag90", # noqa
) -> xr.DataArray:
"""Saturation vapour pressure from temperature.
Parameters
----------
tas : xr.DataArray
Temperature array.
ice_thresh : Quantified, optional
Threshold temperature under which to switch to equations in reference to ice instead of water.
If None (default) everything is computed with reference to water.
method : {"goffgratch46", "sonntag90", "tetens30", "wmo08", "its90"}
Which method to use, see notes.
Returns
-------
xarray.DataArray, [Pa]
Saturation vapour pressure.
Notes
-----
In all cases implemented here :math:`log(e_{sat})` is an empirically fitted function (usually a polynomial)
where coefficients can be different when ice is taken as reference instead of water. Available methods are:
- "goffgratch46" or "GG46", based on :cite:t:`goff_low-pressure_1946`, values and equation taken from :cite:t:`vomel_saturation_2016`.
- "sonntag90" or "SO90", taken from :cite:t:`sonntag_important_1990`.
- "tetens30" or "TE30", based on :cite:t:`tetens_uber_1930`, values and equation taken from :cite:t:`vomel_saturation_2016`.
- "wmo08" or "WMO08", taken from :cite:t:`world_meteorological_organization_guide_2008`.
- "its90" or "ITS90", taken from :cite:t:`hardy_its-90_1998`.
Examples
--------
>>> from xclim.indices import saturation_vapor_pressure
>>> rh = saturation_vapor_pressure(
... tas=tas_dataset, ice_thresh="0 degC", method="wmo08"
... )
References
----------
:cite:cts:`goff_low-pressure_1946,hardy_its-90_1998,sonntag_important_1990,tetens_uber_1930,vomel_saturation_2016,world_meteorological_organization_guide_2008`
"""
if ice_thresh is not None:
thresh = convert_units_to(ice_thresh, "K")
else:
thresh = convert_units_to("0 K", "K")
tas = convert_units_to(tas, "K")
ref_is_water = tas > thresh
e_sat: xr.DataArray
if method in ["sonntag90", "SO90"]:
e_sat = xr.where(
ref_is_water,
100
* np.exp( # Where ref_is_water is True, x100 is to convert hPa to Pa
-6096.9385 / tas # type: ignore
+ 16.635794
+ -2.711193e-2 * tas # type: ignore
+ 1.673952e-5 * tas**2
+ 2.433502 * np.log(tas) # numpy's log is ln
),
100
* np.exp( # Where ref_is_water is False (thus ref is ice)
-6024.5282 / tas # type: ignore
+ 24.7219
+ 1.0613868e-2 * tas # type: ignore
+ -1.3198825e-5 * tas**2
+ -0.49382577 * np.log(tas)
),
)
elif method in ["tetens30", "TE30"]:
e_sat = xr.where(
ref_is_water,
610.78 * np.exp(17.269388 * (tas - 273.16) / (tas - 35.86)),
610.78 * np.exp(21.8745584 * (tas - 273.16) / (tas - 7.66)),
)
elif method in ["goffgratch46", "GG46"]:
Tb = 373.16 # Water boiling temp [K]
eb = 101325 # e_sat at Tb [Pa]
Tp = 273.16 # Triple-point temperature [K]
ep = 611.73 # e_sat at Tp [Pa]
e_sat = xr.where(
ref_is_water,
eb
* 10
** (
-7.90298 * ((Tb / tas) - 1) # type: ignore
+ 5.02808 * np.log10(Tb / tas) # type: ignore
+ -1.3817e-7 * (10 ** (11.344 * (1 - tas / Tb)) - 1)
+ 8.1328e-3 * (10 ** (-3.49149 * ((Tb / tas) - 1)) - 1) # type: ignore
),
ep
* 10
** (
-9.09718 * ((Tp / tas) - 1) # type: ignore
+ -3.56654 * np.log10(Tp / tas) # type: ignore
+ 0.876793 * (1 - tas / Tp)
),
)
elif method in ["wmo08", "WMO08"]:
e_sat = xr.where(
ref_is_water,
611.2 * np.exp(17.62 * (tas - 273.16) / (tas - 30.04)),
611.2 * np.exp(22.46 * (tas - 273.16) / (tas - 0.54)),
)
elif method in ["its90", "ITS90"]:
e_sat = xr.where(
ref_is_water,
np.exp(
-2836.5744 / tas**2
+ -6028.076559 / tas
+ 19.54263612
+ -2.737830188e-2 * tas
+ 1.6261698e-5 * tas**2
+ 7.0229056e-10 * tas**3
+ -1.8680009e-13 * tas**4
+ 2.7150305 * np.log(tas)
),
np.exp(
-5866.6426 / tas
+ 22.32870244
+ 1.39387003e-2 * tas
+ -3.4262402e-5 * tas**2
+ 2.7040955e-8 * tas**3
+ 6.7063522e-1 * np.log(tas)
),
)
else:
raise ValueError(
f"Method {method} is not in ['sonntag90', 'tetens30', 'goffgratch46', 'wmo08', 'its90']"
)
e_sat = e_sat.assign_attrs(units="Pa")
return e_sat
[docs]
@declare_units(
tas="[temperature]",
tdps="[temperature]",
huss="[]",
ps="[pressure]",
ice_thresh="[temperature]",
)
def relative_humidity(
tas: xr.DataArray,
tdps: xr.DataArray | None = None,
huss: xr.DataArray | None = None,
ps: xr.DataArray | None = None,
ice_thresh: Quantified | None = None,
method: str = "sonntag90",
invalid_values: str = "clip",
) -> xr.DataArray:
r"""Relative humidity.
Compute relative humidity from temperature and either dewpoint temperature or specific humidity and pressure through
the saturation vapour pressure.
Parameters
----------
tas : xr.DataArray
Temperature array
tdps : xr.DataArray, optional
Dewpoint temperature, if specified, overrides huss and ps.
huss : xr.DataArray, optional
Specific humidity. Must be given if tdps is not given.
ps : xr.DataArray, optional
Air Pressure. Must be given if tdps is not given.
ice_thresh : Quantified, optional
Threshold temperature under which to switch to equations in reference to ice instead of water.
If None (default) everything is computed with reference to water. Does nothing if 'method' is "bohren98".
method : {"bohren98", "goffgratch46", "sonntag90", "tetens30", "wmo08"}
Which method to use, see notes of this function and of :py:func:`saturation_vapor_pressure`.
invalid_values : {"clip", "mask", None}
What to do with values outside the 0-100 range. If "clip" (default), clips everything to 0 - 100,
if "mask", replaces values outside the range by np.nan, and if `None`, does nothing.
Returns
-------
xr.DataArray, [%]
Relative humidity.
Notes
-----
In the following, let :math:`T`, :math:`T_d`, :math:`q` and :math:`p` be the temperature,
the dew point temperature, the specific humidity and the air pressure.
**For the "bohren98" method** : This method does not use the saturation vapour pressure directly,
but rather uses an approximation of the ratio of :math:`\frac{e_{sat}(T_d)}{e_{sat}(T)}`.
With :math:`L` the enthalpy of vaporization of water and :math:`R_w` the gas constant for water vapour,
the relative humidity is computed as:
.. math::
RH = e^{\frac{-L (T - T_d)}{R_wTT_d}}
From :cite:t:`bohren_atmospheric_1998`, formula taken from :cite:t:`lawrence_relationship_2005`.
:math:`L = 2.5\times 10^{-6}` J kg-1, exact for :math:`T = 273.15` K, is used.
**Other methods**: With :math:`w`, :math:`w_{sat}`, :math:`e_{sat}` the mixing ratio,
the saturation mixing ratio and the saturation vapour pressure.
If the dewpoint temperature is given, relative humidity is computed as:
.. math::
RH = 100\frac{e_{sat}(T_d)}{e_{sat}(T)}
Otherwise, the specific humidity and the air pressure must be given so relative humidity can be computed as:
.. math::
RH = 100\frac{w}{w_{sat}}
w = \frac{q}{1-q}
w_{sat} = 0.622\frac{e_{sat}}{P - e_{sat}}
The methods differ by how :math:`e_{sat}` is computed. See the doc of :py:func:`xclim.core.utils.saturation_vapor_pressure`.
Examples
--------
>>> from xclim.indices import relative_humidity
>>> rh = relative_humidity(
... tas=tas_dataset,
... tdps=tdps_dataset,
... huss=huss_dataset,
... ps=ps_dataset,
... ice_thresh="0 degC",
... method="wmo08",
... invalid_values="clip",
... )
References
----------
:cite:cts:`bohren_atmospheric_1998,lawrence_relationship_2005`
"""
hurs: xr.DataArray
if method in ("bohren98", "BA90"):
if tdps is None:
raise ValueError("To use method 'bohren98' (BA98), dewpoint must be given.")
tdps = convert_units_to(tdps, "K")
tas = convert_units_to(tas, "K")
L = 2.501e6
Rw = (461.5,)
hurs = 100 * np.exp(-L * (tas - tdps) / (Rw * tas * tdps)) # type: ignore
elif tdps is not None:
e_sat_dt = saturation_vapor_pressure(
tas=tdps, ice_thresh=ice_thresh, method=method
)
e_sat_t = saturation_vapor_pressure(
tas=tas, ice_thresh=ice_thresh, method=method
)
hurs = 100 * e_sat_dt / e_sat_t # type: ignore
elif huss is not None and ps is not None:
ps = convert_units_to(ps, "Pa")
huss = convert_units_to(huss, "")
tas = convert_units_to(tas, "K")
e_sat = saturation_vapor_pressure(tas=tas, ice_thresh=ice_thresh, method=method)
w = huss / (1 - huss)
w_sat = 0.62198 * e_sat / (ps - e_sat) # type: ignore
hurs = 100 * w / w_sat
else:
raise ValueError("`huss` and `ps` must be provided if `tdps` is not given.")
if invalid_values == "clip":
hurs = hurs.clip(0, 100)
elif invalid_values == "mask":
hurs = hurs.where((hurs <= 100) & (hurs >= 0))
hurs = hurs.assign_attrs(units="%")
return hurs
[docs]
@declare_units(
tas="[temperature]",
hurs="[]",
ps="[pressure]",
ice_thresh="[temperature]",
)
def specific_humidity(
tas: xr.DataArray,
hurs: xr.DataArray,
ps: xr.DataArray,
ice_thresh: Quantified | None = None,
method: str = "sonntag90",
invalid_values: str | None = None,
) -> xr.DataArray:
r"""Specific humidity from temperature, relative humidity and pressure.
Specific humidity is the ratio between the mass of water vapour
and the mass of moist air :cite:p:`world_meteorological_organization_guide_2008`.
Parameters
----------
tas : xr.DataArray
Temperature array
hurs : xr.DataArray
Relative Humidity.
ps : xr.DataArray
Air Pressure.
ice_thresh : Quantified, optional
Threshold temperature under which to switch to equations in reference to ice instead of water.
If None (default) everything is computed with reference to water.
method : {"goffgratch46", "sonntag90", "tetens30", "wmo08"}
Which method to use, see notes of this function and of :py:func:`saturation_vapor_pressure`.
invalid_values : {"clip", "mask", None}
What to do with values larger than the saturation specific humidity and lower than 0.
If "clip" (default), clips everything to 0 - q_sat
if "mask", replaces values outside the range by np.nan,
if None, does nothing.
Returns
-------
xarray.DataArray, [dimensionless]
Specific humidity.
Notes
-----
In the following, let :math:`T`, :math:`hurs` (in %) and :math:`p` be the temperature,
the relative humidity and the air pressure. With :math:`w`, :math:`w_{sat}`, :math:`e_{sat}` the mixing ratio,
the saturation mixing ratio and the saturation vapour pressure, specific humidity :math:`q` is computed as:
.. math::
w_{sat} = 0.622\frac{e_{sat}}{P - e_{sat}}
w = w_{sat} * hurs / 100
q = w / (1 + w)
The methods differ by how :math:`e_{sat}` is computed. See :py:func:`xclim.core.utils.saturation_vapor_pressure`.
If `invalid_values` is not `None`, the saturation specific humidity :math:`q_{sat}` is computed as:
.. math::
q_{sat} = w_{sat} / (1 + w_{sat})
Examples
--------
>>> from xclim.indices import specific_humidity
>>> rh = specific_humidity(
... tas=tas_dataset,
... hurs=hurs_dataset,
... ps=ps_dataset,
... ice_thresh="0 degC",
... method="wmo08",
... invalid_values="mask",
... )
References
----------
:cite:cts:`world_meteorological_organization_guide_2008`
"""
ps = convert_units_to(ps, "Pa")
hurs = convert_units_to(hurs, "")
tas = convert_units_to(tas, "K")
e_sat = saturation_vapor_pressure(tas=tas, ice_thresh=ice_thresh, method=method)
w_sat = 0.62198 * e_sat / (ps - e_sat) # type: ignore
w = w_sat * hurs
q: xr.DataArray = w / (1 + w)
if invalid_values is not None:
q_sat = w_sat / (1 + w_sat)
if invalid_values == "clip":
q = q.clip(0, q_sat)
elif invalid_values == "mask":
q = q.where((q <= q_sat) & (q >= 0))
q = q.assign_attrs(units="")
return q
[docs]
@declare_units(
tdps="[temperature]",
ps="[pressure]",
)
def specific_humidity_from_dewpoint(
tdps: xr.DataArray,
ps: xr.DataArray,
method: str = "sonntag90",
) -> xr.DataArray:
r"""Specific humidity from dewpoint temperature and air pressure.
Specific humidity is the ratio between the mass of water vapour
and the mass of moist air :cite:p:`world_meteorological_organization_guide_2008`.
Parameters
----------
tdps : xr.DataArray
Dewpoint temperature array.
ps : xr.DataArray
Air pressure array.
method : {"goffgratch46", "sonntag90", "tetens30", "wmo08"}
Method to compute the saturation vapour pressure.
Returns
-------
xarray.DataArray, [dimensionless]
Specific humidity.
Notes
-----
If :math:`e` is the water vapour pressure, and :math:`p` the total air pressure, then specific humidity is given by
.. math::
q = m_w e / ( m_a (p - e) + m_w e )
where :math:`m_w` and :math:`m_a` are the molecular weights of water and dry air respectively. This formula is often
written with :math:`ε = m_w / m_a`, which simplifies to :math:`q = ε e / (p - e (1 - ε))`.
Examples
--------
>>> from xclim.indices import specific_humidity_from_dewpoint
>>> rh = specific_humidity_from_dewpoint(
... tdps=tas_dataset,
... ps=ps_dataset,
... method="wmo08",
... )
References
----------
:cite:cts:`world_meteorological_organization_guide_2008`
"""
ε = 0.6219569 # weight of water vs dry air []
e = saturation_vapor_pressure(tas=tdps, method=method) # vapour pressure [Pa]
ps = convert_units_to(ps, "Pa") # total air pressure
q: xr.DataArray = ε * e / (ps - e * (1 - ε))
q = q.assign_attrs(units="")
return q
[docs]
@declare_units(pr="[precipitation]", tas="[temperature]", thresh="[temperature]")
def snowfall_approximation(
pr: xr.DataArray,
tas: xr.DataArray,
thresh: Quantified = "0 degC",
method: str = "binary",
) -> xr.DataArray:
"""Snowfall approximation from total precipitation and temperature.
Solid precipitation estimated from precipitation and temperature according to a given method.
Parameters
----------
pr : xarray.DataArray
Mean daily precipitation flux.
tas : xarray.DataArray, optional
Mean, maximum, or minimum daily temperature.
thresh : Quantified
Freezing point temperature. Non-scalar values are not allowed with method "brown".
method : {"binary", "brown", "auer"}
Which method to use when approximating snowfall from total precipitation. See notes.
Returns
-------
xarray.DataArray, [same units as pr]
Solid precipitation flux.
Notes
-----
The following methods are available to approximate snowfall and are drawn from the
Canadian Land Surface Scheme :cite:p:`verseghy_class_2009,melton_atmosphericvarscalcf90_2019`.
- ``'binary'`` : When the temperature is under the freezing threshold, precipitation
is assumed to be solid. The method is agnostic to the type of temperature used
(mean, maximum or minimum).
- ``'brown'`` : The phase between the freezing threshold goes from solid to liquid linearly
over a range of 2°C over the freezing point.
- ``'auer'`` : The phase between the freezing threshold goes from solid to liquid as a degree six
polynomial over a range of 6°C over the freezing point.
References
----------
:cite:cts:`verseghy_class_2009,melton_atmosphericvarscalcf90_2019`
"""
prsn: xr.DataArray
if method == "binary":
thresh = convert_units_to(thresh, tas)
prsn = pr.where(tas <= thresh, 0)
elif method == "brown":
if not np.isscalar(thresh):
raise ValueError("Non-scalar `thresh` are not allowed with method `brown`.")
# Freezing point + 2C in the native units
thresh_plus_2 = convert_units_to(thresh, "degC") + 2
upper = convert_units_to(f"{thresh_plus_2} degC", tas)
thresh = convert_units_to(thresh, tas)
# Interpolate fraction over temperature (in units of tas)
t = xr.DataArray(
[-np.inf, thresh, upper, np.inf], dims=("tas",), attrs={"units": "degC"}
)
fraction = xr.DataArray([1.0, 1.0, 0.0, 0.0], dims=("tas",), coords={"tas": t})
# Multiply precip by snowfall fraction
prsn = pr * fraction.interp(tas=tas, method="linear")
elif method == "auer":
dtas = convert_units_to(tas, "K") - convert_units_to(thresh, "K")
# Create nodes for the snowfall fraction: -inf, thresh, ..., thresh+6, inf [degC]
t = np.concatenate(
[[-273.15], np.linspace(0, 6, 100, endpoint=False), [6, 1e10]]
)
t = xr.DataArray(t, dims="tas", name="tas", coords={"tas": t})
# The polynomial coefficients, valid between thresh and thresh + 6 (defined in CLASS)
coeffs = xr.DataArray(
[100, 4.6664, -15.038, -1.5089, 2.0399, -0.366, 0.0202],
dims=("degree",),
coords={"degree": range(7)},
)
fraction = xr.polyval(t.tas, coeffs).clip(0, 100) / 100
fraction[0] = 1
fraction[-2:] = 0
# Convert snowfall fraction coordinates to native tas units
prsn = pr * fraction.interp(tas=dtas, method="linear")
else:
raise ValueError(f"Method {method} not one of 'binary', 'brown' or 'auer'.")
prsn = prsn.assign_attrs(units=pr.attrs["units"])
return prsn
[docs]
@declare_units(pr="[precipitation]", tas="[temperature]", thresh="[temperature]")
def rain_approximation(
pr: xr.DataArray,
tas: xr.DataArray,
thresh: Quantified = "0 degC",
method: str = "binary",
) -> xr.DataArray:
"""Rainfall approximation from total precipitation and temperature.
Liquid precipitation estimated from precipitation and temperature according to a given method.
This is a convenience method based on :py:func:`snowfall_approximation`, see the latter for details.
Parameters
----------
pr : xarray.DataArray
Mean daily precipitation flux.
tas : xarray.DataArray, optional
Mean, maximum, or minimum daily temperature.
thresh : Quantified
Freezing point temperature. Non-scalar values are not allowed with method 'brown'.
method : {"binary", "brown", "auer"}
Which method to use when approximating snowfall from total precipitation. See notes.
Returns
-------
xarray.DataArray, [same units as pr]
Liquid precipitation rate.
Notes
-----
This method computes the snowfall approximation and subtracts it from the total
precipitation to estimate the liquid rain precipitation.
See Also
--------
snowfall_approximation
"""
prra: xr.DataArray = pr - snowfall_approximation(
pr, tas, thresh=thresh, method=method
)
prra = prra.assign_attrs(units=pr.attrs["units"])
return prra
[docs]
@declare_units(snd="[length]", snr="[mass]/[volume]", const="[mass]/[volume]")
def snd_to_snw(
snd: xr.DataArray,
snr: Quantified | None = None,
const: Quantified = "312 kg m-3",
out_units: str | None = None,
) -> xr.DataArray:
"""Snow amount from snow depth and density.
Parameters
----------
snd : xr.DataArray
Snow depth.
snr : Quantified, optional
Snow density.
const: Quantified
Constant snow density
`const` is only used if `snr` is None.
out_units: str, optional
Desired units of the snow amount output. If `None`, output units simply follow from `snd * snr`.
Returns
-------
xr.DataArray
Snow amount
Notes
-----
The estimated mean snow density value of 312 kg m-3 is taken from :cite:t:`sturm_swe_2010`.
References
----------
:cite:cts:`sturm_swe_2010`
"""
density = snr if (snr is not None) else const
snw: xr.DataArray = rate2flux(snd, density=density, out_units=out_units).rename(
"snw"
)
# TODO: Leave this operation to rate2flux? Maybe also the variable renaming above?
snw = snw.assign_attrs(standard_name="surface_snow_amount")
return snw
[docs]
@declare_units(snw="[mass]/[area]", snr="[mass]/[volume]", const="[mass]/[volume]")
def snw_to_snd(
snw: xr.DataArray,
snr: Quantified | None = None,
const: Quantified = "312 kg m-3",
out_units: str | None = None,
) -> xr.DataArray:
"""Snow depth from snow amount and density.
Parameters
----------
snw : xr.DataArray
Snow amount.
snr : Quantified, optional
Snow density.
const: Quantified
Constant snow density
`const` is only used if `snr` is None.
out_units: str, optional
Desired units of the snow depth output. If `None`, output units simply follow from `snw / snr`.
Returns
-------
xr.DataArray
Snow depth
Notes
-----
The estimated mean snow density value of 312 kg m-3 is taken from :cite:t:`sturm_swe_2010`.
References
----------
:cite:cts:`sturm_swe_2010`
"""
density = snr if (snr is not None) else const
snd: xr.DataArray = flux2rate(snw, density=density, out_units=out_units).rename(
"snd"
)
snd = snd.assign_attrs(standard_name="surface_snow_thickness")
return snd
[docs]
@declare_units(
prsn="[mass]/[area]/[time]", snr="[mass]/[volume]", const="[mass]/[volume]"
)
def prsn_to_prsnd(
prsn: xr.DataArray,
snr: xr.DataArray | None = None,
const: Quantified = "100 kg m-3",
out_units: str | None = None,
) -> xr.DataArray:
"""Snowfall rate from snowfall flux and density.
Parameters
----------
prsn : xr.DataArray
Snowfall flux.
snr : xr.DataArray, optional
Snow density.
const: Quantified
Constant snow density.
`const` is only used if `snr` is None.
out_units: str, optional
Desired units of the snowfall rate. If `None`, output units simply follow from `snd * snr`.
Returns
-------
xr.DataArray
Snowfall rate.
Notes
-----
The estimated mean snow density value of 100 kg m-3 is taken from
:cite:cts:`frei_snowfall_2018, cbcl_climate_2020`.
References
----------
:cite:cts:`frei_snowfall_2018, cbcl_climate_2020`
"""
density = snr if snr else const
prsnd: xr.DataArray = flux2rate(prsn, density=density, out_units=out_units).rename(
"prsnd"
)
return prsnd
[docs]
@declare_units(prsnd="[length]/[time]", snr="[mass]/[volume]", const="[mass]/[volume]")
def prsnd_to_prsn(
prsnd: xr.DataArray,
snr: xr.DataArray | None = None,
const: Quantified = "100 kg m-3",
out_units: str | None = None,
) -> xr.DataArray:
"""Snowfall flux from snowfall rate and density.
Parameters
----------
prsnd : xr.DataArray
Snowfall rate.
snr : xr.DataArray, optional
Snow density.
const: Quantified
Constant snow density.
`const` is only used if `snr` is None.
out_units: str, optional
Desired units of the snowfall rate. If `None`, output units simply follow from `snd * snr`.
Returns
-------
xr.DataArray
Snowfall flux.
Notes
-----
The estimated mean snow density value of 100 kg m-3 is taken from
:cite:cts:`frei_snowfall_2018, cbcl_climate_2020`.
References
----------
:cite:cts:`frei_snowfall_2018, cbcl_climate_2020`
"""
density = snr if snr else const
prsn: xr.DataArray = rate2flux(prsnd, density=density, out_units=out_units).rename(
"prsn"
)
prsn = prsn.assign_attrs(standard_name="snowfall_flux")
return prsn
[docs]
@declare_units(rls="[radiation]", rlds="[radiation]")
def longwave_upwelling_radiation_from_net_downwelling(
rls: xr.DataArray, rlds: xr.DataArray
) -> xr.DataArray:
"""Calculate upwelling thermal radiation from net thermal radiation and downwelling thermal radiation.
Parameters
----------
rls : xr.DataArray
Surface net thermal radiation.
rlds : xr.DataArray
Surface downwelling thermal radiation.
Returns
-------
xr.DataArray, [same units as rlds]
Surface upwelling thermal radiation (rlus).
"""
rls = convert_units_to(rls, rlds)
rlus: xr.DataArray = rlds - rls
rlus = rlus.assign_attrs(units=rlds.units)
return rlus
[docs]
@declare_units(rss="[radiation]", rsds="[radiation]")
def shortwave_upwelling_radiation_from_net_downwelling(
rss: xr.DataArray, rsds: xr.DataArray
) -> xr.DataArray:
"""Calculate upwelling solar radiation from net solar radiation and downwelling solar radiation.
Parameters
----------
rss : xr.DataArray
Surface net solar radiation.
rsds : xr.DataArray
Surface downwelling solar radiation.
Returns
-------
xr.DataArray, [same units as rsds]
Surface upwelling solar radiation (rsus).
"""
rss = convert_units_to(rss, rsds)
rsus: xr.DataArray = rsds - rss
rsus = rsus.assign_attrs(units=rsds.units)
return rsus
[docs]
@declare_units(
tas="[temperature]",
sfcWind="[speed]",
)
def wind_chill_index(
tas: xr.DataArray,
sfcWind: xr.DataArray,
method: str = "CAN",
mask_invalid: bool = True,
) -> xr.DataArray:
r"""Wind chill index.
The Wind Chill Index is an estimation of how cold the weather feels to the average person.
It is computed from the air temperature and the 10-m wind. As defined by the Environment and Climate Change Canada
(:cite:cts:`mekis_observed_2015`), two equations exist, the conventional one and one for slow winds
(usually < 5 km/h), see Notes.
Parameters
----------
tas : xarray.DataArray
Surface air temperature.
sfcWind : xarray.DataArray
Surface wind speed (10 m).
method : {'CAN', 'US'}
If "CAN" (default), a "slow wind" equation is used where winds are slower than 5 km/h, see Notes.
mask_invalid : bool
Whether to mask values when the inputs are outside their validity range. or not.
If True (default), points where the temperature is above a threshold are masked.
The threshold is 0°C for the canadian method and 50°F for the american one.
With the latter method, points where sfcWind < 3 mph are also masked.
Returns
-------
xarray.DataArray, [degC]
Wind Chill Index.
Notes
-----
Following the calculations of Environment and Climate Change Canada, this function switches from the standardized
index to another one for slow winds. The standard index is the same as used by the National Weather Service of the
USA :cite:p:`us_department_of_commerce_wind_nodate`. Given a temperature at surface :math:`T` (in °C) and 10-m
wind speed :math:`V` (in km/h), the Wind Chill Index :math:`W` (dimensionless) is computed as:
.. math::
W = 13.12 + 0.6125*T - 11.37*V^0.16 + 0.3965*T*V^0.16
Under slow winds (:math:`V < 5` km/h), and using the canadian method, it becomes:
.. math::
W = T + \frac{-1.59 + 0.1345 * T}{5} * V
Both equations are invalid for temperature over 0°C in the canadian method.
The american Wind Chill Temperature index (WCT), as defined by USA's National Weather Service, is computed when
`method='US'`. In that case, the maximal valid temperature is 50°F (10 °C) and minimal wind speed is 3 mph
(4.8 km/h).
For more information, see:
- National Weather Service FAQ: :cite:p:`us_department_of_commerce_wind_nodate`.
- The New Wind Chill Equivalent Temperature Chart: :cite:p:`osczevski_new_2005`.
References
----------
:cite:cts:`mekis_observed_2015,us_department_of_commerce_wind_nodate`
"""
tas = convert_units_to(tas, "degC")
sfcWind = convert_units_to(sfcWind, "km/h")
V = sfcWind**0.16
W: xr.DataArray = 13.12 + 0.6215 * tas - 11.37 * V + 0.3965 * tas * V
if method.upper() == "CAN":
W = xr.where(sfcWind < 5, tas + sfcWind * (-1.59 + 0.1345 * tas) / 5, W)
elif method.upper() != "US":
raise ValueError(f"`method` must be one of 'US' and 'CAN'. Got '{method}'.")
if mask_invalid:
mask = {"CAN": tas <= 0, "US": (sfcWind > 4.828032) & (tas <= 10)}
W = W.where(mask[method.upper()])
W = W.assign_attrs(units="degC")
return W
[docs]
@declare_units(
delta_tas="[temperature]",
pr_baseline="[precipitation]",
)
def clausius_clapeyron_scaled_precipitation(
delta_tas: xr.DataArray,
pr_baseline: xr.DataArray,
cc_scale_factor: float = 1.07,
) -> xr.DataArray:
r"""Scale precipitation according to the Clausius-Clapeyron relation.
Parameters
----------
delta_tas : xarray.DataArray
Difference in temperature between a baseline climatology and another climatology.
pr_baseline : xarray.DataArray
Baseline precipitation to adjust with Clausius-Clapeyron.
cc_scale_factor : float
Clausius Clapeyron scale factor. (default = 1.07).
Returns
-------
xarray.DataArray
Baseline precipitation scaled to other climatology using Clausius-Clapeyron relationship.
Notes
-----
The Clausius-Clapeyron equation for water vapour under typical atmospheric conditions states that the saturation
water vapour pressure :math:`e_s` changes approximately exponentially with temperature
.. math::
\frac{\mathrm{d}e_s(T)}{\mathrm{d}T} \approx 1.07 e_s(T)
This function assumes that precipitation can be scaled by the same factor.
Warnings
--------
Make sure that `delta_tas` is computed over a baseline compatible with `pr_baseline`. So for example,
if `delta_tas` is the climatological difference between a baseline and a future period, then `pr_baseline`
should be precipitations over a period within the same baseline.
"""
# Get difference in temperature. Time-invariant baseline temperature (from above) is broadcast.
delta_tas = convert_units_to(delta_tas, "delta_degreeC")
# Calculate scaled precipitation.
pr_out: xr.DataArray = pr_baseline * (cc_scale_factor**delta_tas)
pr_out = pr_out.assign_attrs(units=pr_baseline.attrs["units"])
return pr_out
def _get_D_from_M(time): # noqa: N802
start = time[0].dt.strftime("%Y-%m-01").item()
yrmn = time[-1].dt.strftime("%Y-%m").item()
end = f"{yrmn}-{time[-1].dt.daysinmonth.item()}"
return xr.DataArray(
xr.date_range(
start,
end,
freq="D",
calendar=time.dt.calendar,
use_cftime=(time.dtype == "O"),
),
dims="time",
name="time",
)
[docs]
@declare_units(
tasmin="[temperature]",
tasmax="[temperature]",
tas="[temperature]",
lat="[]",
hurs="[]",
rsds="[radiation]",
rsus="[radiation]",
rlds="[radiation]",
rlus="[radiation]",
sfcWind="[speed]",
pr="[precipitation]",
)
def potential_evapotranspiration(
tasmin: xr.DataArray | None = None,
tasmax: xr.DataArray | None = None,
tas: xr.DataArray | None = None,
lat: xr.DataArray | None = None,
hurs: xr.DataArray | None = None,
rsds: xr.DataArray | None = None,
rsus: xr.DataArray | None = None,
rlds: xr.DataArray | None = None,
rlus: xr.DataArray | None = None,
sfcWind: xr.DataArray | None = None,
pr: xr.DataArray | None = None,
method: str = "BR65",
peta: float = 0.00516409319477,
petb: float = 0.0874972822289,
) -> xr.DataArray:
r"""Potential evapotranspiration.
The potential for water evaporation from soil and transpiration by plants if the water supply is sufficient,
according to a given method.
Parameters
----------
tasmin : xarray.DataArray, optional
Minimum daily temperature.
tasmax : xarray.DataArray, optional
Maximum daily temperature.
tas : xarray.DataArray, optional
Mean daily temperature.
lat : xarray.DataArray, optional
Latitude. If not given, it is sought on tasmin or tas using cf-xarray accessors.
hurs : xarray.DataArray, optional
Relative humidity.
rsds : xarray.DataArray, optional
Surface Downwelling Shortwave Radiation
rsus : xarray.DataArray, optional
Surface Upwelling Shortwave Radiation
rlds : xarray.DataArray, optional
Surface Downwelling Longwave Radiation
rlus : xarray.DataArray, optional
Surface Upwelling Longwave Radiation
sfcWind : xarray.DataArray, optional
Surface wind velocity (at 10 m)
pr : xarray.DataArray
Mean daily precipitation flux.
method : {"baierrobertson65", "BR65", "hargreaves85", "HG85", "thornthwaite48", "TW48", "mcguinnessbordne05", "MB05", "allen98", "FAO_PM98", "droogersallen02", "DA02"}
Which method to use, see notes.
peta : float
Used only with method MB05 as :math:`a` for calculation of PET, see Notes section.
Default value resulted from calibration of PET over the UK.
petb : float
Used only with method MB05 as :math:`b` for calculation of PET, see Notes section.
Default value resulted from calibration of PET over the UK.
Returns
-------
xarray.DataArray
Notes
-----
Available methods are:
- "baierrobertson65" or "BR65", based on :cite:t:`baier_estimation_1965`.
Requires tasmin and tasmax, daily [D] freq.
- "hargreaves85" or "HG85", based on :cite:t:`george_h_hargreaves_reference_1985`.
Requires tasmin and tasmax, daily [D] freq. (optional: tas can be given in addition of tasmin and tasmax).
- "mcguinnessbordne05" or "MB05", based on :cite:t:`tanguy_historical_2018`.
Requires tas, daily [D] freq, with latitudes 'lat'.
- "thornthwaite48" or "TW48", based on :cite:t:`thornthwaite_approach_1948`.
Requires tasmin and tasmax, monthly [MS] or daily [D] freq.
(optional: tas can be given instead of tasmin and tasmax).
- "allen98" or "FAO_PM98", based on :cite:t:`allen_crop_1998`. Modification of Penman-Monteith method.
Requires tasmin and tasmax, relative humidity, radiation flux and wind speed (10 m wind will be converted to 2 m).
- "droogersallen02" or "DA02", based on :cite:t:`droogers2002`.
Requires tasmin, tasmax and precipitation, monthly [MS] or daily [D] freq. (optional: tas can be given in addition of tasmin and tasmax).
The McGuinness-Bordne :cite:p:`mcguinness_comparison_1972` equation is:
.. math::
PET[mm day^{-1}] = a * \frac{S_0}{\lambda}T_a + b *\frsc{S_0}{\lambda}
where :math:`a` and :math:`b` are empirical parameters; :math:`S_0` is the extraterrestrial radiation [MJ m-2 day-1],
assuming a solar constant of 1367 W m-2; :math:`\\lambda` is the latent heat of vaporisation [MJ kg-1]
and :math:`T_a` is the air temperature [°C]. The equation was originally derived for the USA,
with :math:`a=0.0147` and :math:`b=0.07353`. The default parameters used here are calibrated for the UK,
using the method described in :cite:t:`tanguy_historical_2018`.
Methods "BR65", "HG85", "MB05" and "DA02" use an approximation of the extraterrestrial radiation.
See :py:func:`~xclim.indices._helpers.extraterrestrial_solar_radiation`.
References
----------
:cite:cts:`baier_estimation_1965,george_h_hargreaves_reference_1985,tanguy_historical_2018,thornthwaite_approach_1948,mcguinness_comparison_1972,allen_crop_1998,droogers2002`
""" # noqa: E501
# ^ Ignoring "line too long" as it comes from un-splittable constructs
if lat is None:
_lat = _gather_lat(tasmin if tas is None else tas)
else:
_lat = lat
pet: xr.DataArray
if method in ["baierrobertson65", "BR65"]:
_tasmin = convert_units_to(tasmin, "degF")
_tasmax = convert_units_to(tasmax, "degF")
re = extraterrestrial_solar_radiation(
_tasmin.time, _lat, chunks=_tasmin.chunksizes
)
re = convert_units_to(re, "cal cm-2 day-1")
# Baier et Robertson(1965) formula
pet = 0.094 * (
-87.03 + 0.928 * _tasmax + 0.933 * (_tasmax - _tasmin) + 0.0486 * re
)
pet = pet.clip(0)
elif method in ["hargreaves85", "HG85"]:
_tasmin = convert_units_to(tasmin, "degC")
_tasmax = convert_units_to(tasmax, "degC")
if tas is None:
_tas = (_tasmin + _tasmax) / 2
else:
_tas = convert_units_to(tas, "degC")
ra = extraterrestrial_solar_radiation(
_tasmin.time, _lat, chunks=_tasmin.chunksizes
)
ra = convert_units_to(ra, "MJ m-2 d-1")
# Is used to convert the radiation to evaporation equivalents in mm (kg/MJ)
ra = ra * 0.408
# Hargreaves and Samani (1985) formula
pet = 0.0023 * ra * (_tas + 17.8) * (_tasmax - _tasmin) ** 0.5
pet = pet.clip(0)
elif method in ["droogersallen02", "DA02"]:
_tasmin = convert_units_to(tasmin, "degC")
_tasmax = convert_units_to(tasmax, "degC")
_pr = convert_units_to(pr, "mm/month", context="hydro")
if tas is None:
_tas = (_tasmin + _tasmax) / 2
else:
_tas = convert_units_to(tas, "degC")
_tasmin = _tasmin.resample(time="MS").mean()
_tasmax = _tasmax.resample(time="MS").mean()
_tas = _tas.resample(time="MS").mean()
_pr = _pr.resample(time="MS").mean()
# Monthly accumulated radiation
time_d = _get_D_from_M(_tasmin.time)
ra = extraterrestrial_solar_radiation(time_d, _lat)
ra = convert_units_to(ra, "MJ m-2 d-1")
ra = ra.resample(time="MS").sum()
# Is used to convert the radiation to evaporation equivalents in mm (kg/MJ)
ra = ra * 0.408
tr = _tasmax - _tasmin
tr = tr.where(tr > 0, 0)
# Droogers and Allen (2002) formula
ab = tr - 0.0123 * _pr
pet = 0.0013 * ra * (_tas + 17.0) * ab**0.76
pet = xr.where(np.isnan(ab**0.76), 0, pet)
pet = pet.clip(0) # mm/month
elif method in ["mcguinnessbordne05", "MB05"]:
if tas is None:
_tasmin = convert_units_to(tasmin, "degC")
_tasmax = convert_units_to(tasmax, "degC")
_tas: xr.DataArray = (_tasmin + _tasmax) / 2
_tas = _tas.assign_attrs(units="degC")
else:
_tas = convert_units_to(tas, "degC")
tasK = convert_units_to(_tas, "K")
ext_rad = extraterrestrial_solar_radiation(
_tas.time, _lat, solar_constant="1367 W m-2", chunks=_tas.chunksizes
)
latentH = 4185.5 * (751.78 - 0.5655 * tasK)
radDIVlat = ext_rad / latentH
# parameters from calibration provided by Dr Maliko Tanguy @ CEH
# (calibrated for PET over the UK)
a = peta
b = petb
pet = radDIVlat * a * _tas + radDIVlat * b
elif method in ["thornthwaite48", "TW48"]:
if tas is None:
_tasmin = convert_units_to(tasmin, "degC")
_tasmax = convert_units_to(tasmax, "degC")
_tas = (_tasmin + _tasmax) / 2
else:
_tas = convert_units_to(tas, "degC")
_tas = _tas.clip(0)
_tas = _tas.resample(time="MS").mean(dim="time")
# Thornthwaite measures half-days
time_d = _get_D_from_M(_tas.time)
dl = day_lengths(time_d, _lat) / 12
dl_m = dl.resample(time="MS").mean(dim="time")
# annual heat index
id_m = (_tas / 5) ** 1.514
id_y = id_m.resample(time="YS").sum(dim="time")
tas_idy_a = []
for base_time, indexes in _tas.resample(time="YS").groups.items():
tas_y = _tas.isel(time=indexes)
id_v = id_y.sel(time=base_time)
a = 6.75e-7 * id_v**3 - 7.71e-5 * id_v**2 + 0.01791 * id_v + 0.49239
frac = (10 * tas_y / id_v) ** a
tas_idy_a.append(frac)
tas_idy_a = xr.concat(tas_idy_a, dim="time")
# Thornthwaite(1948) formula
pet = 1.6 * dl_m * tas_idy_a # cm/month
pet = 10 * pet # mm/month
elif method in ["allen98", "FAO_PM98"]:
_tasmax = convert_units_to(tasmax, "degC")
_tasmin = convert_units_to(tasmin, "degC")
if sfcWind is None:
raise ValueError("Wind speed is required for Allen98 method.")
else:
# wind speed at two meters
wa2 = wind_speed_height_conversion(sfcWind, h_source="10 m", h_target="2 m")
wa2 = convert_units_to(wa2, "m s-1")
with xr.set_options(keep_attrs=True):
# mean temperature [degC]
tas_m = (_tasmax + _tasmin) / 2
# mean saturation vapour pressure [kPa]
es = (1 / 2) * (
saturation_vapor_pressure(_tasmax) + saturation_vapor_pressure(_tasmin)
)
es = convert_units_to(es, "kPa")
# mean actual vapour pressure [kPa]
ea = hurs * es
# slope of saturation vapour pressure curve [kPa degC-1]
delta = 4098 * es / (tas_m + 237.3) ** 2
# net radiation
Rn = convert_units_to(rsds - rsus - (rlus - rlds), "MJ m-2 d-1")
G = 0 # Daily soil heat flux density [MJ m-2 d-1]
P = 101.325 # Atmospheric pressure [kPa]
gamma = 0.665e-03 * P # psychrometric const = C_p*P/(eps*lam) [kPa degC-1]
# Penman-Monteith formula with reference grass:
# height = 0.12m, surface resistance = 70 s m-1, albedo = 0.23
# Surface resistance implies a ``moderately dry soil surface resulting from
# about a weekly irrigation frequency''
pet = (
0.408 * delta * (Rn - G)
+ gamma * (900 / (tas_m + 273)) * wa2 * (es - ea)
) / (delta + gamma * (1 + 0.34 * wa2))
else:
raise NotImplementedError(f"'{method}' method is not implemented.")
pet = pet.assign_attrs(units="mm")
rate = amount2rate(pet, out_units="mm/d")
out: xr.DataArray = convert_units_to(rate, "kg m-2 s-1", context="hydro")
return out
@vectorize(
# [
# float64(float64, float64, float64, float64),
# float32(float32, float32, float32, float32),
# ],
)
def _utci(tas, sfcWind, dt, wvp):
"""Return the empirical polynomial function for UTCI. See :py:func:`universal_thermal_climate_index`."""
# Taken directly from the original Fortran code by Peter Bröde.
# http://www.utci.org/public/UTCI%20Program%20Code/UTCI_a002.f90
# tas -> Ta (surface temperature, °C)
# sfcWind -> va (surface wind speed, m/s)
# dt -> D_Tmrt (tas - t_mrt, K)
# wvp -> Pa (water vapour partial pressure, kPa)
return (
tas
+ 6.07562052e-1
+ -2.27712343e-2 * tas
+ 8.06470249e-4 * tas * tas
+ -1.54271372e-4 * tas * tas * tas
+ -3.24651735e-6 * tas * tas * tas * tas
+ 7.32602852e-8 * tas * tas * tas * tas * tas
+ 1.35959073e-9 * tas * tas * tas * tas * tas * tas
+ -2.25836520e0 * sfcWind
+ 8.80326035e-2 * tas * sfcWind
+ 2.16844454e-3 * tas * tas * sfcWind
+ -1.53347087e-5 * tas * tas * tas * sfcWind
+ -5.72983704e-7 * tas * tas * tas * tas * sfcWind
+ -2.55090145e-9 * tas * tas * tas * tas * tas * sfcWind
+ -7.51269505e-1 * sfcWind * sfcWind
+ -4.08350271e-3 * tas * sfcWind * sfcWind
+ -5.21670675e-5 * tas * tas * sfcWind * sfcWind
+ 1.94544667e-6 * tas * tas * tas * sfcWind * sfcWind
+ 1.14099531e-8 * tas * tas * tas * tas * sfcWind * sfcWind
+ 1.58137256e-1 * sfcWind * sfcWind * sfcWind
+ -6.57263143e-5 * tas * sfcWind * sfcWind * sfcWind
+ 2.22697524e-7 * tas * tas * sfcWind * sfcWind * sfcWind
+ -4.16117031e-8 * tas * tas * tas * sfcWind * sfcWind * sfcWind
+ -1.27762753e-2 * sfcWind * sfcWind * sfcWind * sfcWind
+ 9.66891875e-6 * tas * sfcWind * sfcWind * sfcWind * sfcWind
+ 2.52785852e-9 * tas * tas * sfcWind * sfcWind * sfcWind * sfcWind
+ 4.56306672e-4 * sfcWind * sfcWind * sfcWind * sfcWind * sfcWind
+ -1.74202546e-7 * tas * sfcWind * sfcWind * sfcWind * sfcWind * sfcWind
+ -5.91491269e-6 * sfcWind * sfcWind * sfcWind * sfcWind * sfcWind * sfcWind
+ 3.98374029e-1 * dt
+ 1.83945314e-4 * tas * dt
+ -1.73754510e-4 * tas * tas * dt
+ -7.60781159e-7 * tas * tas * tas * dt
+ 3.77830287e-8 * tas * tas * tas * tas * dt
+ 5.43079673e-10 * tas * tas * tas * tas * tas * dt
+ -2.00518269e-2 * sfcWind * dt
+ 8.92859837e-4 * tas * sfcWind * dt
+ 3.45433048e-6 * tas * tas * sfcWind * dt
+ -3.77925774e-7 * tas * tas * tas * sfcWind * dt
+ -1.69699377e-9 * tas * tas * tas * tas * sfcWind * dt
+ 1.69992415e-4 * sfcWind * sfcWind * dt
+ -4.99204314e-5 * tas * sfcWind * sfcWind * dt
+ 2.47417178e-7 * tas * tas * sfcWind * sfcWind * dt
+ 1.07596466e-8 * tas * tas * tas * sfcWind * sfcWind * dt
+ 8.49242932e-5 * sfcWind * sfcWind * sfcWind * dt
+ 1.35191328e-6 * tas * sfcWind * sfcWind * sfcWind * dt
+ -6.21531254e-9 * tas * tas * sfcWind * sfcWind * sfcWind * dt
+ -4.99410301e-6 * sfcWind * sfcWind * sfcWind * sfcWind * dt
+ -1.89489258e-8 * tas * sfcWind * sfcWind * sfcWind * sfcWind * dt
+ 8.15300114e-8 * sfcWind * sfcWind * sfcWind * sfcWind * sfcWind * dt
+ 7.55043090e-4 * dt * dt
+ -5.65095215e-5 * tas * dt * dt
+ -4.52166564e-7 * tas * tas * dt * dt
+ 2.46688878e-8 * tas * tas * tas * dt * dt
+ 2.42674348e-10 * tas * tas * tas * tas * dt * dt
+ 1.54547250e-4 * sfcWind * dt * dt
+ 5.24110970e-6 * tas * sfcWind * dt * dt
+ -8.75874982e-8 * tas * tas * sfcWind * dt * dt
+ -1.50743064e-9 * tas * tas * tas * sfcWind * dt * dt
+ -1.56236307e-5 * sfcWind * sfcWind * dt * dt
+ -1.33895614e-7 * tas * sfcWind * sfcWind * dt * dt
+ 2.49709824e-9 * tas * tas * sfcWind * sfcWind * dt * dt
+ 6.51711721e-7 * sfcWind * sfcWind * sfcWind * dt * dt
+ 1.94960053e-9 * tas * sfcWind * sfcWind * sfcWind * dt * dt
+ -1.00361113e-8 * sfcWind * sfcWind * sfcWind * sfcWind * dt * dt
+ -1.21206673e-5 * dt * dt * dt
+ -2.18203660e-7 * tas * dt * dt * dt
+ 7.51269482e-9 * tas * tas * dt * dt * dt
+ 9.79063848e-11 * tas * tas * tas * dt * dt * dt
+ 1.25006734e-6 * sfcWind * dt * dt * dt
+ -1.81584736e-9 * tas * sfcWind * dt * dt * dt
+ -3.52197671e-10 * tas * tas * sfcWind * dt * dt * dt
+ -3.36514630e-8 * sfcWind * sfcWind * dt * dt * dt
+ 1.35908359e-10 * tas * sfcWind * sfcWind * dt * dt * dt
+ 4.17032620e-10 * sfcWind * sfcWind * sfcWind * dt * dt * dt
+ -1.30369025e-9 * dt * dt * dt * dt
+ 4.13908461e-10 * tas * dt * dt * dt * dt
+ 9.22652254e-12 * tas * tas * dt * dt * dt * dt
+ -5.08220384e-9 * sfcWind * dt * dt * dt * dt
+ -2.24730961e-11 * tas * sfcWind * dt * dt * dt * dt
+ 1.17139133e-10 * sfcWind * sfcWind * dt * dt * dt * dt
+ 6.62154879e-10 * dt * dt * dt * dt * dt
+ 4.03863260e-13 * tas * dt * dt * dt * dt * dt
+ 1.95087203e-12 * sfcWind * dt * dt * dt * dt * dt
+ -4.73602469e-12 * dt * dt * dt * dt * dt * dt
+ 5.12733497e0 * wvp
+ -3.12788561e-1 * tas * wvp
+ -1.96701861e-2 * tas * tas * wvp
+ 9.99690870e-4 * tas * tas * tas * wvp
+ 9.51738512e-6 * tas * tas * tas * tas * wvp
+ -4.66426341e-7 * tas * tas * tas * tas * tas * wvp
+ 5.48050612e-1 * sfcWind * wvp
+ -3.30552823e-3 * tas * sfcWind * wvp
+ -1.64119440e-3 * tas * tas * sfcWind * wvp
+ -5.16670694e-6 * tas * tas * tas * sfcWind * wvp
+ 9.52692432e-7 * tas * tas * tas * tas * sfcWind * wvp
+ -4.29223622e-2 * sfcWind * sfcWind * wvp
+ 5.00845667e-3 * tas * sfcWind * sfcWind * wvp
+ 1.00601257e-6 * tas * tas * sfcWind * sfcWind * wvp
+ -1.81748644e-6 * tas * tas * tas * sfcWind * sfcWind * wvp
+ -1.25813502e-3 * sfcWind * sfcWind * sfcWind * wvp
+ -1.79330391e-4 * tas * sfcWind * sfcWind * sfcWind * wvp
+ 2.34994441e-6 * tas * tas * sfcWind * sfcWind * sfcWind * wvp
+ 1.29735808e-4 * sfcWind * sfcWind * sfcWind * sfcWind * wvp
+ 1.29064870e-6 * tas * sfcWind * sfcWind * sfcWind * sfcWind * wvp
+ -2.28558686e-6 * sfcWind * sfcWind * sfcWind * sfcWind * sfcWind * wvp
+ -3.69476348e-2 * dt * wvp
+ 1.62325322e-3 * tas * dt * wvp
+ -3.14279680e-5 * tas * tas * dt * wvp
+ 2.59835559e-6 * tas * tas * tas * dt * wvp
+ -4.77136523e-8 * tas * tas * tas * tas * dt * wvp
+ 8.64203390e-3 * sfcWind * dt * wvp
+ -6.87405181e-4 * tas * sfcWind * dt * wvp
+ -9.13863872e-6 * tas * tas * sfcWind * dt * wvp
+ 5.15916806e-7 * tas * tas * tas * sfcWind * dt * wvp
+ -3.59217476e-5 * sfcWind * sfcWind * dt * wvp
+ 3.28696511e-5 * tas * sfcWind * sfcWind * dt * wvp
+ -7.10542454e-7 * tas * tas * sfcWind * sfcWind * dt * wvp
+ -1.24382300e-5 * sfcWind * sfcWind * sfcWind * dt * wvp
+ -7.38584400e-9 * tas * sfcWind * sfcWind * sfcWind * dt * wvp
+ 2.20609296e-7 * sfcWind * sfcWind * sfcWind * sfcWind * dt * wvp
+ -7.32469180e-4 * dt * dt * wvp
+ -1.87381964e-5 * tas * dt * dt * wvp
+ 4.80925239e-6 * tas * tas * dt * dt * wvp
+ -8.75492040e-8 * tas * tas * tas * dt * dt * wvp
+ 2.77862930e-5 * sfcWind * dt * dt * wvp
+ -5.06004592e-6 * tas * sfcWind * dt * dt * wvp
+ 1.14325367e-7 * tas * tas * sfcWind * dt * dt * wvp
+ 2.53016723e-6 * sfcWind * sfcWind * dt * dt * wvp
+ -1.72857035e-8 * tas * sfcWind * sfcWind * dt * dt * wvp
+ -3.95079398e-8 * sfcWind * sfcWind * sfcWind * dt * dt * wvp
+ -3.59413173e-7 * dt * dt * dt * wvp
+ 7.04388046e-7 * tas * dt * dt * dt * wvp
+ -1.89309167e-8 * tas * tas * dt * dt * dt * wvp
+ -4.79768731e-7 * sfcWind * dt * dt * dt * wvp
+ 7.96079978e-9 * tas * sfcWind * dt * dt * dt * wvp
+ 1.62897058e-9 * sfcWind * sfcWind * dt * dt * dt * wvp
+ 3.94367674e-8 * dt * dt * dt * dt * wvp
+ -1.18566247e-9 * tas * dt * dt * dt * dt * wvp
+ 3.34678041e-10 * sfcWind * dt * dt * dt * dt * wvp
+ -1.15606447e-10 * dt * dt * dt * dt * dt * wvp
+ -2.80626406e0 * wvp * wvp
+ 5.48712484e-1 * tas * wvp * wvp
+ -3.99428410e-3 * tas * tas * wvp * wvp
+ -9.54009191e-4 * tas * tas * tas * wvp * wvp
+ 1.93090978e-5 * tas * tas * tas * tas * wvp * wvp
+ -3.08806365e-1 * sfcWind * wvp * wvp
+ 1.16952364e-2 * tas * sfcWind * wvp * wvp
+ 4.95271903e-4 * tas * tas * sfcWind * wvp * wvp
+ -1.90710882e-5 * tas * tas * tas * sfcWind * wvp * wvp
+ 2.10787756e-3 * sfcWind * sfcWind * wvp * wvp
+ -6.98445738e-4 * tas * sfcWind * sfcWind * wvp * wvp
+ 2.30109073e-5 * tas * tas * sfcWind * sfcWind * wvp * wvp
+ 4.17856590e-4 * sfcWind * sfcWind * sfcWind * wvp * wvp
+ -1.27043871e-5 * tas * sfcWind * sfcWind * sfcWind * wvp * wvp
+ -3.04620472e-6 * sfcWind * sfcWind * sfcWind * sfcWind * wvp * wvp
+ 5.14507424e-2 * dt * wvp * wvp
+ -4.32510997e-3 * tas * dt * wvp * wvp
+ 8.99281156e-5 * tas * tas * dt * wvp * wvp
+ -7.14663943e-7 * tas * tas * tas * dt * wvp * wvp
+ -2.66016305e-4 * sfcWind * dt * wvp * wvp
+ 2.63789586e-4 * tas * sfcWind * dt * wvp * wvp
+ -7.01199003e-6 * tas * tas * sfcWind * dt * wvp * wvp
+ -1.06823306e-4 * sfcWind * sfcWind * dt * wvp * wvp
+ 3.61341136e-6 * tas * sfcWind * sfcWind * dt * wvp * wvp
+ 2.29748967e-7 * sfcWind * sfcWind * sfcWind * dt * wvp * wvp
+ 3.04788893e-4 * dt * dt * wvp * wvp
+ -6.42070836e-5 * tas * dt * dt * wvp * wvp
+ 1.16257971e-6 * tas * tas * dt * dt * wvp * wvp
+ 7.68023384e-6 * sfcWind * dt * dt * wvp * wvp
+ -5.47446896e-7 * tas * sfcWind * dt * dt * wvp * wvp
+ -3.59937910e-8 * sfcWind * sfcWind * dt * dt * wvp * wvp
+ -4.36497725e-6 * dt * dt * dt * wvp * wvp
+ 1.68737969e-7 * tas * dt * dt * dt * wvp * wvp
+ 2.67489271e-8 * sfcWind * dt * dt * dt * wvp * wvp
+ 3.23926897e-9 * dt * dt * dt * dt * wvp * wvp
+ -3.53874123e-2 * wvp * wvp * wvp
+ -2.21201190e-1 * tas * wvp * wvp * wvp
+ 1.55126038e-2 * tas * tas * wvp * wvp * wvp
+ -2.63917279e-4 * tas * tas * tas * wvp * wvp * wvp
+ 4.53433455e-2 * sfcWind * wvp * wvp * wvp
+ -4.32943862e-3 * tas * sfcWind * wvp * wvp * wvp
+ 1.45389826e-4 * tas * tas * sfcWind * wvp * wvp * wvp
+ 2.17508610e-4 * sfcWind * sfcWind * wvp * wvp * wvp
+ -6.66724702e-5 * tas * sfcWind * sfcWind * wvp * wvp * wvp
+ 3.33217140e-5 * sfcWind * sfcWind * sfcWind * wvp * wvp * wvp
+ -2.26921615e-3 * dt * wvp * wvp * wvp
+ 3.80261982e-4 * tas * dt * wvp * wvp * wvp
+ -5.45314314e-9 * tas * tas * dt * wvp * wvp * wvp
+ -7.96355448e-4 * sfcWind * dt * wvp * wvp * wvp
+ 2.53458034e-5 * tas * sfcWind * dt * wvp * wvp * wvp
+ -6.31223658e-6 * sfcWind * sfcWind * dt * wvp * wvp * wvp
+ 3.02122035e-4 * dt * dt * wvp * wvp * wvp
+ -4.77403547e-6 * tas * dt * dt * wvp * wvp * wvp
+ 1.73825715e-6 * sfcWind * dt * dt * wvp * wvp * wvp
+ -4.09087898e-7 * dt * dt * dt * wvp * wvp * wvp
+ 6.14155345e-1 * wvp * wvp * wvp * wvp
+ -6.16755931e-2 * tas * wvp * wvp * wvp * wvp
+ 1.33374846e-3 * tas * tas * wvp * wvp * wvp * wvp
+ 3.55375387e-3 * sfcWind * wvp * wvp * wvp * wvp
+ -5.13027851e-4 * tas * sfcWind * wvp * wvp * wvp * wvp
+ 1.02449757e-4 * sfcWind * sfcWind * wvp * wvp * wvp * wvp
+ -1.48526421e-3 * dt * wvp * wvp * wvp * wvp
+ -4.11469183e-5 * tas * dt * wvp * wvp * wvp * wvp
+ -6.80434415e-6 * sfcWind * dt * wvp * wvp * wvp * wvp
+ -9.77675906e-6 * dt * dt * wvp * wvp * wvp * wvp
+ 8.82773108e-2 * wvp * wvp * wvp * wvp * wvp
+ -3.01859306e-3 * tas * wvp * wvp * wvp * wvp * wvp
+ 1.04452989e-3 * sfcWind * wvp * wvp * wvp * wvp * wvp
+ 2.47090539e-4 * dt * wvp * wvp * wvp * wvp * wvp
+ 1.48348065e-3 * wvp * wvp * wvp * wvp * wvp * wvp
)
[docs]
@declare_units(
tas="[temperature]",
hurs="[]",
sfcWind="[speed]",
mrt="[temperature]",
rsds="[radiation]",
rsus="[radiation]",
rlds="[radiation]",
rlus="[radiation]",
)
def universal_thermal_climate_index(
tas: xr.DataArray,
hurs: xr.DataArray,
sfcWind: xr.DataArray,
mrt: xr.DataArray | None = None,
rsds: xr.DataArray | None = None,
rsus: xr.DataArray | None = None,
rlds: xr.DataArray | None = None,
rlus: xr.DataArray | None = None,
stat: str = "sunlit",
mask_invalid: bool = True,
wind_cap_min: bool = False,
) -> xr.DataArray:
r"""Universal thermal climate index (UTCI).
The UTCI is the equivalent temperature for the environment derived from a
reference environment and is used to evaluate heat stress in outdoor spaces.
Parameters
----------
tas : xarray.DataArray
Mean temperature
hurs : xarray.DataArray
Relative Humidity
sfcWind : xarray.DataArray
Wind velocity
mrt: xarray.DataArray, optional
Mean radiant temperature
rsds : xr.DataArray, optional
Surface Downwelling Shortwave Radiation
This is necessary if mrt is not None.
rsus : xr.DataArray, optional
Surface Upwelling Shortwave Radiation
This is necessary if mrt is not None.
rlds : xr.DataArray, optional
Surface Downwelling Longwave Radiation
This is necessary if mrt is not None.
rlus : xr.DataArray, optional
Surface Upwelling Longwave Radiation
This is necessary if mrt is not None.
stat : {'instant', 'sunlit'}
Which statistic to apply. If "instant", the instantaneous cosine
of the solar zenith angle is calculated. If "sunlit", the cosine of the
solar zenith angle is calculated during the sunlit period of each interval.
This is necessary if mrt is not None.
mask_invalid: bool
If True (default), UTCI values are NaN where any of the inputs are outside
their validity ranges : -50°C < tas < 50°C, -30°C < tas - mrt < 30°C
and 0.5 m/s < sfcWind < 17.0 m/s.
wind_cap_min: bool
If True, wind velocities are capped to a minimum of 0.5 m/s following
:cite:t:`brode_utci_2012` usage guidalines. This ensures UTCI calculation
for low winds. Default value False.
Returns
-------
xarray.DataArray
Universal Thermal Climate Index.
Notes
-----
The calculation uses water vapour partial pressure, which is derived from relative
humidity and saturation vapour pressure computed according to the ITS-90 equation.
This code was inspired by the `pythermalcomfort` and `thermofeel` packages.
Notes
-----
See: http://www.utci.org/utcineu/utcineu.php
References
----------
:cite:cts:`brode_utci_2009,brode_utci_2012,blazejczyk_introduction_2013`
"""
e_sat = saturation_vapor_pressure(tas=tas, method="its90")
tas = convert_units_to(tas, "degC")
sfcWind = convert_units_to(sfcWind, "m/s")
if wind_cap_min:
sfcWind = sfcWind.clip(0.5, None)
if mrt is None:
mrt = mean_radiant_temperature(
rsds=rsds, rsus=rsus, rlds=rlds, rlus=rlus, stat=stat
)
mrt = convert_units_to(mrt, "degC")
delta = mrt - tas
pa = convert_units_to(e_sat, "kPa") * convert_units_to(hurs, "1")
utci: xr.DataArray = xr.apply_ufunc(
_utci,
tas,
sfcWind,
delta,
pa,
input_core_dims=[[], [], [], []],
dask="parallelized",
output_dtypes=[tas.dtype],
)
utci = utci.assign_attrs({"units": "degC"})
if mask_invalid:
utci = utci.where(
(-50.0 < tas)
& (tas < 50.0)
& (-30 < delta)
& (delta < 30)
& (0.5 <= sfcWind)
& (sfcWind < 17.0)
)
return utci
def _fdir_ratio(
dates: xr.DataArray,
csza: xr.DataArray,
rsds: xr.DataArray,
) -> xr.DataArray:
r"""Return ratio of direct solar radiation.
The ratio of direct solar radiation is the fraction of the total horizontal solar irradiance
due to the direct beam of the sun.
Parameters
----------
dates : xr.DataArray
Series of dates and time of day
csza : xr.DataArray
Cosine of the solar zenith angle during the sunlit period of each interval or at an instant
rsds : xr.DataArray
Surface Downwelling Shortwave Radiation
Returns
-------
xarray.DataArray, [dimensionless]
Ratio of direct solar radiation
Notes
-----
This code was inspired by the `PyWBGT` package.
References
----------
:cite:cts:`liljegren_modeling_2008,kong_explicit_2022`
"""
d = distance_from_sun(dates)
s_star = rsds * ((1367 * csza * (d ** (-2))) ** (-1))
s_star = xr.where(s_star > 0.85, 0.85, s_star)
fdir_ratio = np.exp(3 - 1.34 * s_star - 1.65 * (s_star ** (-1)))
fdir_ratio = xr.where(fdir_ratio > 0.9, 0.9, fdir_ratio)
return xr.where(
(fdir_ratio <= 0) | (csza <= np.cos(89.5 / 180 * np.pi)) | (rsds <= 0),
0,
fdir_ratio,
)
[docs]
@declare_units(
rsds="[radiation]", rsus="[radiation]", rlds="[radiation]", rlus="[radiation]"
)
def mean_radiant_temperature(
rsds: xr.DataArray,
rsus: xr.DataArray,
rlds: xr.DataArray,
rlus: xr.DataArray,
stat: str = "sunlit",
) -> xr.DataArray:
r"""Mean radiant temperature.
The mean radiant temperature is the incidence of radiation on the body from all directions.
Parameters
----------
rsds : xr.DataArray
Surface Downwelling Shortwave Radiation
rsus : xr.DataArray
Surface Upwelling Shortwave Radiation
rlds : xr.DataArray
Surface Downwelling Longwave Radiation
rlus : xr.DataArray
Surface Upwelling Longwave Radiation
stat : {'instant', 'sunlit'}
Which statistic to apply. If "instant", the instantaneous cosine
of the solar zenith angle is calculated. If "sunlit", the cosine of the
solar zenith angle is calculated during the sunlit period of each interval.
Returns
-------
xarray.DataArray, [K]
Mean radiant temperature
Warnings
--------
There are some issues in the calculation of mrt in polar regions.
Notes
-----
This code was inspired by the `thermofeel` package :cite:p:`brimicombe_thermofeel_2021`.
References
----------
:cite:cts:`di_napoli_mean_2020`
"""
rsds = convert_units_to(rsds, "W m-2")
rsus = convert_units_to(rsus, "W m-2")
rlds = convert_units_to(rlds, "W m-2")
rlus = convert_units_to(rlus, "W m-2")
dates = rsds.time
lat = _gather_lat(rsds)
lon = _gather_lon(rsds)
dec = solar_declination(dates)
if stat == "sunlit":
csza = cosine_of_solar_zenith_angle(
dates,
dec,
lat,
lon=lon,
stat="average",
sunlit=True,
chunks=rsds.chunksizes,
)
elif stat == "instant":
tc = time_correction_for_solar_angle(dates)
csza = cosine_of_solar_zenith_angle(
dates,
dec,
lat,
lon=lon,
time_correction=tc,
stat="instant",
chunks=rsds.chunksizes,
)
else:
raise NotImplementedError(
"Argument 'stat' must be one of 'instant' or 'sunlit'."
)
fdir_ratio = _fdir_ratio(dates, csza, rsds)
rsds_direct = fdir_ratio * rsds
rsds_diffuse = rsds - rsds_direct
gamma = np.arcsin(csza)
fp = 0.308 * np.cos(gamma * 0.988 - (gamma**2 / 50000))
i_star = xr.where(csza > 0.001, rsds_direct / csza, 0)
mrt = cast(
xr.DataArray,
np.power(
(
(1 / 5.67e-8) # Stefan-Boltzmann constant
* (
0.5 * rlds
+ 0.5 * rlus
+ (0.7 / 0.97) * (0.5 * rsds_diffuse + 0.5 * rsus + fp * i_star)
)
),
0.25,
),
)
mrt = mrt.assign_attrs({"units": "K"})
return mrt
[docs]
@declare_units(wind_speed="[speed]", h="[length]", h_r="[length]")
def wind_profile(
wind_speed: xr.DataArray,
h: Quantified,
h_r: Quantified,
method: str = "power_law",
**kwds,
):
r"""Wind speed at a given height estimated from the wind speed at a reference height.
Estimate the wind speed based on a power law profile relating wind speed to height above the surface.
Parameters
----------
wind_speed : xarray.DataArray
Wind speed at the reference height.
h : Quantified
Height at which to compute the wind speed.
h_r : Quantified
Reference height.
method : {"power_law"}
Method to use. Currently only "power_law" is implemented.
kwds : dict
Additional keyword arguments to pass to the method. For power_law, this is alpha, which takes a default value
of 1/7, but is highly variable based on topography, surface cover and atmospheric stability.
Notes
-----
The power law profile is given by
.. math::
v = v_r \left( \frac{h}{h_r} \right)^{\alpha},
where :math:`v_r` is the wind speed at the reference height, :math:`h` is the height at which the wind speed is
desired, and :math:`h_r` is the reference height.
"""
# Convert units to meters
h = convert_units_to(h, "m")
h_r = convert_units_to(h_r, "m")
if method == "power_law":
alpha = kwds.pop("alpha", 1 / 7)
out: xr.DataArray = wind_speed * (h / h_r) ** alpha
out = out.assign_attrs(units=wind_speed.attrs["units"])
return out
else:
raise NotImplementedError(f"Method {method} not implemented.")
[docs]
@declare_units(
wind_speed="[speed]",
air_density="[air_density]",
cut_in="[speed]",
rated="[speed]",
cut_out="[speed]",
)
def wind_power_potential(
wind_speed: xr.DataArray,
air_density: xr.DataArray | None = None,
cut_in: Quantified = "3.5 m/s",
rated: Quantified = "13 m/s",
cut_out: Quantified = "25 m/s",
) -> xr.DataArray:
r"""Wind power potential estimated from an idealized wind power production factor.
The actual power production of a wind farm can be estimated by multiplying its nominal (nameplate) capacity by the
wind power potential, which depends on wind speed at the hub height, the turbine specifications and air density.
Parameters
----------
wind_speed : xarray.DataArray
Wind speed at the hub height. Use the `wind_profile` function to estimate from the surface wind speed.
air_density: xarray.DataArray
Air density at the hub height. Defaults to 1.225 kg/m³.
This is worth changing if applying in cold or mountainous regions with non-standard air density.
cut_in : Quantified
Cut-in wind speed. Default is 3.5 m/s.
rated : Quantified
Rated wind speed. Default is 13 m/s.
cut_out : Quantified
Cut-out wind speed. Default is 25 m/s.
Returns
-------
xr.DataArray
The power production factor. Multiply by the nominal capacity to get the actual power production.
See Also
--------
wind_profile : Estimate wind speed at the hub height from the surface wind speed.
Notes
-----
This estimate of wind power production is based on an idealized power curve with four wind regimes specified
by the cut-in wind speed (:math:`u_i`), the rated speed (:math:`u_r`) and the cut-out speed (:math:`u_o`).
Power production is zero for wind speeds below the cut-in speed, increases cubically between the cut-in
and rated speed, is constant between the rated and cut-out speed, and is zero for wind speeds above the cut-out
speed to avoid damage to the turbine :cite:p:`tobin_2018`:
.. math::
\begin{cases}
0, & v < u_i \\
(v^3 - u_i^3) / (u_r^3 - u_i^3), & u_i ≤ v < u_r \\
1, & u_r ≤ v < u_o \\
0, & v ≥ u_o
\end{cases}
For non-standard air density (:math:`\rho`), the wind speed is scaled using
:math:`v_n = v \left( \frac{\rho}{\rho_0} \right)^{1/3}`.
The temporal resolution of wind time series has a significant influence on the results: mean daily wind
speeds yield lower values than hourly wind speeds. Note however that percent changes in the wind power potential
climate projections are similar across resolutions :cite:p:`chen_2020`.
To compute the power production, multiply the power production factor by the nominal
turbine capacity (e.g. 100), set the units attribute (e.g. "MW"), resample and sum with
`xclim.indices.generic.select_resample_op(power, op="sum", freq="D")`, then convert to
the desired units (e.g. "MWh") using `xclim.core.units.convert_units_to`.
References
----------
:cite:cts:`chen_2020,tobin_2018`.
"""
# Convert units
cut_in = convert_units_to(cut_in, wind_speed)
rated = convert_units_to(rated, wind_speed)
cut_out = convert_units_to(cut_out, wind_speed)
# Correct wind speed for air density
if air_density is not None:
default_air_density = convert_units_to("1.225 kg/m^3", air_density)
f = (air_density / default_air_density) ** (1 / 3)
else:
f = 1
v = wind_speed * f
out: xr.DataArray = xr.apply_ufunc(_wind_power_factor, v, cut_in, rated, cut_out)
out = out.assign_attrs(units="")
return out
@vectorize
def _wind_power_factor(v, cut_in, rated, cut_out):
"""Wind power factor function"""
if v < cut_in:
return 0.0
if v < rated:
return (v**3 - cut_in**3) / (rated**3 - cut_in**3)
if v < cut_out:
return 1.0
return 0.0