def test_datetime_to_decimal_year(source_cal, exp180):
times = xr.DataArray(
date_range(
"2004-01-01", "2004-12-30", freq="D", calendar=source_cal or "default"
),
dims=("time",),
name="time",
)
decy = datetime_to_decimal_year(times, calendar=source_cal)
np.testing.assert_almost_equal(decy[180] - 2004, exp180)
def potential_evapotranspiration(
tasmin: Optional[xr.DataArray] = None,
tasmax: Optional[xr.DataArray] = None,
tas: Optional[xr.DataArray] = None,
method: str = "BR65",
peta: Optional[float] = 0.00516409319477,
petb: Optional[float] = 0.0874972822289,
) -> xr.DataArray:
"""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
Minimum daily temperature.
tasmax : xarray.DataArray
Maximum daily temperature.
tas : xarray.DataArray
Mean daily temperature.
method : {"baierrobertson65", "BR65", "hargreaves85", "HG85", "thornthwaite48", "TW48", "mcguinnessbordne05", "MB05"}
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 [baierrobertson65]_. Requires tasmin and tasmax, daily [D] freq.
- "hargreaves85" or "HG85", based on [hargreaves85]_. Requires tasmin and tasmax, daily [D] freq. (optional: tas can be given in addition of tasmin and tasmax).
- "mcguinnessbordne05" or "MB05", based on [tanguy2018]_. Requires tas, daily [D] freq, with latitudes 'lat'.
- "thornthwaite48" or "TW48", based on [thornthwaite48]_. Requires tasmin and tasmax, monthly [MS] or daily [D] freq. (optional: tas can be given instead of tasmin and tasmax).
The McGuinness-Bordne [McGuinness1972]_ 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]; :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 [Tanguy2018]_.
References
----------
.. [baierrobertson65] Baier, W., & Robertson, G. W. (1965). Estimation of latent evaporation from simple weather observations. Canadian journal of plant science, 45(3), 276-284.
.. [hargreaves85] Hargreaves, G. H., & Samani, Z. A. (1985). Reference crop evapotranspiration from temperature. Applied engineering in agriculture, 1(2), 96-99.
.. [tanguy2018] Tanguy, M., Prudhomme, C., Smith, K., & Hannaford, J. (2018). Historical gridded reconstruction of potential evapotranspiration for the UK. Earth System Science Data, 10(2), 951-968.
.. [McGuinness1972] McGuinness, J. L., & Bordne, E. F. (1972). A comparison of lysimeter-derived potential evapotranspiration with computed values (No. 1452). US Department of Agriculture.
.. [thornthwaite48] Thornthwaite, C. W. (1948). An approach toward a rational classification of climate. Geographical review, 38(1), 55-94.
"""
if method in ["baierrobertson65", "BR65"]:
tasmin = convert_units_to(tasmin, "degF")
tasmax = convert_units_to(tasmax, "degF")
latr = (tasmin.lat * np.pi) / 180
gsc = 0.082 # MJ/m2/min
# julian day fraction
jd_frac = (datetime_to_decimal_year(tasmin.time) % 1) * 2 * np.pi
ds = 0.409 * np.sin(jd_frac - 1.39)
dr = 1 + 0.033 * np.cos(jd_frac)
omega = np.arccos(-np.tan(latr) * np.tan(ds))
re = ((24 * 60 / np.pi) * gsc * dr *
(omega * np.sin(latr) * np.sin(ds) +
np.cos(latr) * np.cos(ds) * np.sin(omega))) # MJ/m2/day
re = re / 4.1864e-2 # cal/cm2/day
# Baier et Robertson(1965) formula
out = 0.094 * (-87.03 + 0.928 * tasmax + 0.933 *
(tasmax - tasmin) + 0.0486 * re)
out = out.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")
latr = (tasmin.lat * np.pi) / 180
gsc = 0.082 # MJ/m2/min
lv = 2.5 # MJ/kg
# julian day fraction
jd_frac = (datetime_to_decimal_year(tasmin.time) % 1) * 2 * np.pi
ds = 0.409 * np.sin(jd_frac - 1.39)
dr = 1 + 0.033 * np.cos(jd_frac)
omega = np.arccos(-np.tan(latr) * np.tan(ds))
ra = ((24 * 60 / np.pi) * gsc * dr *
(omega * np.sin(latr) * np.sin(ds) +
np.cos(latr) * np.cos(ds) * np.sin(omega))) # MJ/m2/day
# Hargreaves and Samani(1985) formula
out = (0.0023 * ra * (tas + 17.8) * (tasmax - tasmin)**0.5) / lv
out = out.clip(0)
elif method in ["mcguinnessbordne05", "MB05"]:
if tas is None:
tasmin = convert_units_to(tasmin, "degC")
tasmax = convert_units_to(tasmax, "degC")
tas = (tasmin + tasmax) / 2
tas.attrs["units"] = "degC"
tas = convert_units_to(tas, "degC")
tasK = convert_units_to(tas, "K")
latr = (tas.lat * np.pi) / 180
jd_frac = (datetime_to_decimal_year(tas.time) % 1) * 2 * np.pi
S = 1367.0 # Set solar constant [W/m2]
ds = 0.409 * np.sin(jd_frac - 1.39) # solar declination ds [radians]
omega = np.arccos(-np.tan(latr) *
np.tan(ds)) # sunset hour angle [radians]
dr = 1.0 + 0.03344 * np.cos(
jd_frac - 0.048869) # Calculate relative distance to sun
ext_rad = (S * 86400 / np.pi * dr *
(omega * np.sin(ds) * np.sin(latr) +
np.sin(omega) * np.cos(ds) * np.cos(latr)))
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
out = 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")
latr = (tas.lat * np.pi) / 180 # rad
start = "-".join([
str(tas.time[0].dt.year.values),
f"{tas.time[0].dt.month.values:02d}",
"01",
])
end = "-".join([
str(tas.time[-1].dt.year.values),
f"{tas.time[-1].dt.month.values:02d}",
str(tas.time[-1].dt.daysinmonth.values),
])
time_v = xr.DataArray(
date_range(start, end, freq="D", calendar="standard"),
dims="time",
name="time",
)
# julian day fraction
jd_frac = (datetime_to_decimal_year(time_v) % 1) * 2 * np.pi
ds = 0.409 * np.sin(jd_frac - 1.39)
omega = np.arccos(-np.tan(latr) * np.tan(ds)) * 180 / np.pi # degrees
# monthly-mean daytime length (multiples of 12 hours)
dl = 2 * omega / (15 * 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
out = 1.6 * dl_m * tas_idy_a # cm/month
out = 10 * out # mm/month
else:
raise NotImplementedError(f"'{method}' method is not implemented.")
out.attrs["units"] = "mm"
return amount2rate(out, out_units="kg m-2 s-1")
