# Copyright (c) 2008,2015,2016 MetPy Developers.
# Distributed under the terms of the BSD 3-Clause License.
# SPDX-License-Identifier: BSD-3-Clause
"""Contains a collection of basic calculations.
These include:
* wind components
* heat index
* windchill
"""
from __future__ import division
import warnings
import numpy as np
from scipy.ndimage import gaussian_filter
from ..constants import G, g, me, omega, Rd, Re
from ..deprecation import deprecated
from ..package_tools import Exporter
from ..units import atleast_1d, check_units, masked_array, units
from ..xarray import preprocess_xarray
exporter = Exporter(globals())
[docs]@exporter.export
@preprocess_xarray
def wind_speed(u, v):
r"""Compute the wind speed from u and v-components.
Parameters
----------
u : array_like
Wind component in the X (East-West) direction
v : array_like
Wind component in the Y (North-South) direction
Returns
-------
wind speed: array_like
The speed of the wind
See Also
--------
wind_components
"""
speed = np.sqrt(u * u + v * v)
return speed
[docs]@exporter.export
@preprocess_xarray
def wind_direction(u, v):
r"""Compute the wind direction from u and v-components.
Parameters
----------
u : array_like
Wind component in the X (East-West) direction
v : array_like
Wind component in the Y (North-South) direction
Returns
-------
direction: `pint.Quantity`
The direction of the wind in interval [0, 360] degrees, specified as the direction from
which it is blowing, with 360 being North.
See Also
--------
wind_components
Notes
-----
In the case of calm winds (where `u` and `v` are zero), this function returns a direction
of 0.
"""
wdir = 90. * units.deg - np.arctan2(-v, -u)
origshape = wdir.shape
wdir = atleast_1d(wdir)
wdir[wdir <= 0] += 360. * units.deg
# Need to be able to handle array-like u and v (with or without units)
# np.any check required for legacy numpy which treats 0-d False boolean index as zero
calm_mask = (np.asarray(u) == 0.) & (np.asarray(v) == 0.)
if np.any(calm_mask):
wdir[calm_mask] = 0. * units.deg
return wdir.reshape(origshape).to('degrees')
[docs]@exporter.export
@preprocess_xarray
def wind_components(speed, wdir):
r"""Calculate the U, V wind vector components from the speed and direction.
Parameters
----------
speed : array_like
The wind speed (magnitude)
wdir : array_like
The wind direction, specified as the direction from which the wind is
blowing, with 360 degrees being North.
Returns
-------
u, v : tuple of array_like
The wind components in the X (East-West) and Y (North-South)
directions, respectively.
See Also
--------
wind_speed
wind_direction
Examples
--------
>>> from metpy.units import units
>>> metpy.calc.wind_components(10. * units('m/s'), 225. * units.deg)
(<Quantity(7.071067811865475, 'meter / second')>,
<Quantity(7.071067811865477, 'meter / second')>)
"""
wdir = _check_radians(wdir, max_radians=4 * np.pi)
u = -speed * np.sin(wdir)
v = -speed * np.cos(wdir)
return u, v
[docs]@exporter.export
@preprocess_xarray
@deprecated('0.9', addendum=' This function has been renamed wind_speed.',
pending=False)
def get_wind_speed(u, v):
"""Wrap wind_speed for deprecated get_wind_speed function."""
return wind_speed(u, v)
get_wind_speed.__doc__ = (wind_speed.__doc__ +
'\n .. deprecated:: 0.9.0\n Function has been renamed to '
'`wind_speed` and will be removed from MetPy in 0.12.0.')
[docs]@exporter.export
@preprocess_xarray
@deprecated('0.9', addendum=' This function has been renamed wind_direction.',
pending=False)
def get_wind_dir(u, v):
"""Wrap wind_direction for deprecated get_wind_dir function."""
return wind_direction(u, v)
get_wind_dir.__doc__ = (wind_direction.__doc__ +
'\n .. deprecated:: 0.9.0\n Function has been renamed to '
'`wind_direction` and will be removed from MetPy in 0.12.0.')
[docs]@exporter.export
@preprocess_xarray
@deprecated('0.9', addendum=' This function has been renamed wind_components.',
pending=False)
def get_wind_components(u, v):
"""Wrap wind_components for deprecated get_wind_components function."""
return wind_components(u, v)
get_wind_components.__doc__ = (wind_components.__doc__ +
'\n .. deprecated:: 0.9.0\n Function has been '
'renamed to `wind_components` and will be removed from MetPy '
'in 0.12.0.')
[docs]@exporter.export
@preprocess_xarray
@check_units(temperature='[temperature]', speed='[speed]')
def windchill(temperature, speed, face_level_winds=False, mask_undefined=True):
r"""Calculate the Wind Chill Temperature Index (WCTI).
Calculates WCTI from the current temperature and wind speed using the formula
outlined by the FCM [FCMR192003]_.
Specifically, these formulas assume that wind speed is measured at
10m. If, instead, the speeds are measured at face level, the winds
need to be multiplied by a factor of 1.5 (this can be done by specifying
`face_level_winds` as `True`.)
Parameters
----------
temperature : `pint.Quantity`
The air temperature
speed : `pint.Quantity`
The wind speed at 10m. If instead the winds are at face level,
`face_level_winds` should be set to `True` and the 1.5 multiplicative
correction will be applied automatically.
face_level_winds : bool, optional
A flag indicating whether the wind speeds were measured at facial
level instead of 10m, thus requiring a correction. Defaults to
`False`.
mask_undefined : bool, optional
A flag indicating whether a masked array should be returned with
values where wind chill is undefined masked. These are values where
the temperature > 50F or wind speed <= 3 miles per hour. Defaults
to `True`.
Returns
-------
`pint.Quantity`
The corresponding Wind Chill Temperature Index value(s)
See Also
--------
heat_index
"""
# Correct for lower height measurement of winds if necessary
if face_level_winds:
# No in-place so that we copy
# noinspection PyAugmentAssignment
speed = speed * 1.5
temp_limit, speed_limit = 10. * units.degC, 3 * units.mph
speed_factor = speed.to('km/hr').magnitude ** 0.16
wcti = units.Quantity((0.6215 + 0.3965 * speed_factor) * temperature.to('degC').magnitude -
11.37 * speed_factor + 13.12, units.degC).to(temperature.units)
# See if we need to mask any undefined values
if mask_undefined:
mask = np.array((temperature > temp_limit) | (speed <= speed_limit))
if mask.any():
wcti = masked_array(wcti, mask=mask)
return wcti
[docs]@exporter.export
@preprocess_xarray
@check_units('[temperature]')
def heat_index(temperature, rh, mask_undefined=True):
r"""Calculate the Heat Index from the current temperature and relative humidity.
The implementation uses the formula outlined in [Rothfusz1990]_. This equation is a
multi-variable least-squares regression of the values obtained in [Steadman1979]_.
Parameters
----------
temperature : `pint.Quantity`
Air temperature
rh : array_like
The relative humidity expressed as a unitless ratio in the range [0, 1].
Can also pass a percentage if proper units are attached.
Returns
-------
`pint.Quantity`
The corresponding Heat Index value(s)
Other Parameters
----------------
mask_undefined : bool, optional
A flag indicating whether a masked array should be returned with
values where heat index is undefined masked. These are values where
the temperature < 80F or relative humidity < 40 percent. Defaults
to `True`.
See Also
--------
windchill
"""
delta = temperature.to(units.degF) - 0. * units.degF
rh2 = rh * rh
delta2 = delta * delta
# Calculate the Heat Index -- constants converted for RH in [0, 1]
hi = (-42.379 * units.degF + 2.04901523 * delta +
1014.333127 * units.delta_degF * rh - 22.475541 * delta * rh -
6.83783e-3 / units.delta_degF * delta2 - 5.481717e2 * units.delta_degF * rh2 +
1.22874e-1 / units.delta_degF * delta2 * rh + 8.5282 * delta * rh2 -
1.99e-2 / units.delta_degF * delta2 * rh2)
# See if we need to mask any undefined values
if mask_undefined:
mask = np.array((temperature < 80. * units.degF) | (rh < 40 * units.percent))
if mask.any():
hi = masked_array(hi, mask=mask)
return hi
[docs]@exporter.export
@preprocess_xarray
@check_units(temperature='[temperature]', speed='[speed]')
def apparent_temperature(temperature, rh, speed, face_level_winds=False):
r"""Calculate the current apparent temperature.
Calculates the current apparent temperature based on the wind chill or heat index
as appropriate for the current conditions. Follows [NWS10201]_.
Parameters
----------
temperature : `pint.Quantity`
The air temperature
rh : `pint.Quantity`
The relative humidity expressed as a unitless ratio in the range [0, 1].
Can also pass a percentage if proper units are attached.
speed : `pint.Quantity`
The wind speed at 10m. If instead the winds are at face level,
`face_level_winds` should be set to `True` and the 1.5 multiplicative
correction will be applied automatically.
face_level_winds : bool, optional
A flag indicating whether the wind speeds were measured at facial
level instead of 10m, thus requiring a correction. Defaults to
`False`.
Returns
-------
`pint.Quantity`
The corresponding apparent temperature value(s)
See Also
--------
heat_index, windchill
"""
is_not_scalar = isinstance(temperature.m, (list, tuple, np.ndarray))
temperature = atleast_1d(temperature)
rh = atleast_1d(rh)
speed = atleast_1d(speed)
wind_chill_temperature = windchill(temperature, speed, face_level_winds=face_level_winds,
mask_undefined=True).to(temperature.units)
heat_index_temperature = heat_index(temperature, rh,
mask_undefined=True).to(temperature.units)
# Combine the heat index and wind chill arrays (no point has a value in both)
app_temperature = np.ma.where(masked_array(wind_chill_temperature).mask,
heat_index_temperature,
wind_chill_temperature)
if is_not_scalar:
# Fill in missing areas where neither wind chill or heat index are applicable with the
# ambient temperature.
app_temperature[app_temperature.mask] = temperature[app_temperature.mask]
return np.array(app_temperature) * temperature.units
else:
if app_temperature.mask:
app_temperature = temperature.m
return atleast_1d(app_temperature)[0] * temperature.units
[docs]@exporter.export
@preprocess_xarray
@check_units('[pressure]')
def pressure_to_height_std(pressure):
r"""Convert pressure data to heights using the U.S. standard atmosphere.
The implementation uses the formula outlined in [Hobbs1977]_ pg.60-61.
Parameters
----------
pressure : `pint.Quantity`
Atmospheric pressure
Returns
-------
`pint.Quantity`
The corresponding height value(s)
Notes
-----
.. math:: Z = \frac{T_0}{\Gamma}[1-\frac{p}{p_0}^\frac{R\Gamma}{g}]
"""
t0 = 288. * units.kelvin
gamma = 6.5 * units('K/km')
p0 = 1013.25 * units.mbar
return (t0 / gamma) * (1 - (pressure / p0).to('dimensionless')**(Rd * gamma / g))
[docs]@exporter.export
@preprocess_xarray
@check_units('[length]')
def height_to_geopotential(height):
r"""Compute geopotential for a given height.
Parameters
----------
height : `pint.Quantity`
Height above sea level (array_like)
Returns
-------
`pint.Quantity`
The corresponding geopotential value(s)
Examples
--------
>>> from metpy.constants import g, G, me, Re
>>> import metpy.calc
>>> from metpy.units import units
>>> height = np.linspace(0,10000, num = 11) * units.m
>>> geopot = metpy.calc.height_to_geopotential(height)
>>> geopot
<Quantity([ 0. 9817.46806283 19631.85526579 29443.16305888
39251.39289118 49056.54621087 58858.62446525 68657.62910064
78453.56156253 88246.42329545 98036.21574306], 'meter ** 2 / second ** 2')>
Notes
-----
Derived from definition of geopotential in [Hobbs2006]_ pg.14 Eq.1.8.
"""
# Calculate geopotential
geopot = G * me * ((1 / Re) - (1 / (Re + height)))
return geopot
[docs]@exporter.export
@preprocess_xarray
def geopotential_to_height(geopot):
r"""Compute height from a given geopotential.
Parameters
----------
geopotential : `pint.Quantity`
Geopotential (array_like)
Returns
-------
`pint.Quantity`
The corresponding height value(s)
Examples
--------
>>> from metpy.constants import g, G, me, Re
>>> import metpy.calc
>>> from metpy.units import units
>>> height = np.linspace(0,10000, num = 11) * units.m
>>> geopot = metpy.calc.height_to_geopotential(height)
>>> geopot
<Quantity([ 0. 9817.46806283 19631.85526579 29443.16305888
39251.39289118 49056.54621087 58858.62446525 68657.62910064
78453.56156253 88246.42329545 98036.21574306], 'meter ** 2 / second ** 2')>
>>> height = metpy.calc.geopotential_to_height(geopot)
>>> height
<Quantity([ 0. 1000. 2000. 3000. 4000. 5000. 6000. 7000. 8000.
9000. 10000.], 'meter')>
Notes
-----
Derived from definition of geopotential in [Hobbs2006]_ pg.14 Eq.1.8.
"""
# Calculate geopotential
height = (((1 / Re) - (geopot / (G * me))) ** -1) - Re
return height
[docs]@exporter.export
@preprocess_xarray
@check_units('[length]')
def height_to_pressure_std(height):
r"""Convert height data to pressures using the U.S. standard atmosphere.
The implementation inverts the formula outlined in [Hobbs1977]_ pg.60-61.
Parameters
----------
height : `pint.Quantity`
Atmospheric height
Returns
-------
`pint.Quantity`
The corresponding pressure value(s)
Notes
-----
.. math:: p = p_0 e^{\frac{g}{R \Gamma} \text{ln}(1-\frac{Z \Gamma}{T_0})}
"""
t0 = 288. * units.kelvin
gamma = 6.5 * units('K/km')
p0 = 1013.25 * units.mbar
return p0 * (1 - (gamma / t0) * height) ** (g / (Rd * gamma))
[docs]@exporter.export
@preprocess_xarray
def coriolis_parameter(latitude):
r"""Calculate the coriolis parameter at each point.
The implementation uses the formula outlined in [Hobbs1977]_ pg.370-371.
Parameters
----------
latitude : array_like
Latitude at each point
Returns
-------
`pint.Quantity`
The corresponding coriolis force at each point
"""
latitude = _check_radians(latitude, max_radians=np.pi / 2)
return (2. * omega * np.sin(latitude)).to('1/s')
[docs]@exporter.export
@preprocess_xarray
@check_units('[pressure]', '[length]')
def add_height_to_pressure(pressure, height):
r"""Calculate the pressure at a certain height above another pressure level.
This assumes a standard atmosphere.
Parameters
----------
pressure : `pint.Quantity`
Pressure level
height : `pint.Quantity`
Height above a pressure level
Returns
-------
`pint.Quantity`
The corresponding pressure value for the height above the pressure level
See Also
--------
pressure_to_height_std, height_to_pressure_std, add_pressure_to_height
"""
pressure_level_height = pressure_to_height_std(pressure)
return height_to_pressure_std(pressure_level_height + height)
[docs]@exporter.export
@preprocess_xarray
@check_units('[length]', '[pressure]')
def add_pressure_to_height(height, pressure):
r"""Calculate the height at a certain pressure above another height.
This assumes a standard atmosphere.
Parameters
----------
height : `pint.Quantity`
Height level
pressure : `pint.Quantity`
Pressure above height level
Returns
-------
`pint.Quantity`
The corresponding height value for the pressure above the height level
See Also
--------
pressure_to_height_std, height_to_pressure_std, add_height_to_pressure
"""
pressure_at_height = height_to_pressure_std(height)
return pressure_to_height_std(pressure_at_height - pressure)
[docs]@exporter.export
@preprocess_xarray
@check_units('[dimensionless]', '[pressure]', '[pressure]')
def sigma_to_pressure(sigma, psfc, ptop):
r"""Calculate pressure from sigma values.
Parameters
----------
sigma : ndarray
The sigma levels to be converted to pressure levels.
psfc : `pint.Quantity`
The surface pressure value.
ptop : `pint.Quantity`
The pressure value at the top of the model domain.
Returns
-------
`pint.Quantity`
The pressure values at the given sigma levels.
Notes
-----
Sigma definition adapted from [Philips1957]_.
.. math:: p = \sigma * (p_{sfc} - p_{top}) + p_{top}
* :math:`p` is pressure at a given `\sigma` level
* :math:`\sigma` is non-dimensional, scaled pressure
* :math:`p_{sfc}` is pressure at the surface or model floor
* :math:`p_{top}` is pressure at the top of the model domain
"""
if np.any(sigma < 0) or np.any(sigma > 1):
raise ValueError('Sigma values should be bounded by 0 and 1')
if psfc.magnitude < 0 or ptop.magnitude < 0:
raise ValueError('Pressure input should be non-negative')
return sigma * (psfc - ptop) + ptop
[docs]@exporter.export
@preprocess_xarray
def smooth_gaussian(scalar_grid, n):
"""Filter with normal distribution of weights.
Parameters
----------
scalar_grid : `pint.Quantity`
Some n-dimensional scalar grid. If more than two axes, smoothing
is only done across the last two.
n : int
Degree of filtering
Returns
-------
`pint.Quantity`
The filtered 2D scalar grid
Notes
-----
This function is a close replication of the GEMPAK function GWFS,
but is not identical. The following notes are incorporated from
the GEMPAK source code:
This function smoothes a scalar grid using a moving average
low-pass filter whose weights are determined by the normal
(Gaussian) probability distribution function for two dimensions.
The weight given to any grid point within the area covered by the
moving average for a target grid point is proportional to
EXP [ -( D ** 2 ) ],
where D is the distance from that point to the target point divided
by the standard deviation of the normal distribution. The value of
the standard deviation is determined by the degree of filtering
requested. The degree of filtering is specified by an integer.
This integer is the number of grid increments from crest to crest
of the wave for which the theoretical response is 1/e = .3679. If
the grid increment is called delta_x, and the value of this integer
is represented by N, then the theoretical filter response function
value for the N * delta_x wave will be 1/e. The actual response
function will be greater than the theoretical value.
The larger N is, the more severe the filtering will be, because the
response function for all wavelengths shorter than N * delta_x
will be less than 1/e. Furthermore, as N is increased, the slope
of the filter response function becomes more shallow; so, the
response at all wavelengths decreases, but the amount of decrease
lessens with increasing wavelength. (The theoretical response
function can be obtained easily--it is the Fourier transform of the
weight function described above.)
The area of the patch covered by the moving average varies with N.
As N gets bigger, the smoothing gets stronger, and weight values
farther from the target grid point are larger because the standard
deviation of the normal distribution is bigger. Thus, increasing
N has the effect of expanding the moving average window as well as
changing the values of weights. The patch is a square covering all
points whose weight values are within two standard deviations of the
mean of the two dimensional normal distribution.
The key difference between GEMPAK's GWFS and this function is that,
in GEMPAK, the leftover weight values representing the fringe of the
distribution are applied to the target grid point. In this
function, the leftover weights are not used.
When this function is invoked, the first argument is the grid to be
smoothed, the second is the value of N as described above:
GWFS ( S, N )
where N > 1. If N <= 1, N = 2 is assumed. For example, if N = 4,
then the 4 delta x wave length is passed with approximate response
1/e.
"""
# Compute standard deviation in a manner consistent with GEMPAK
n = int(round(n))
if n < 2:
n = 2
sgma = n / (2 * np.pi)
# Construct sigma sequence so smoothing occurs only in horizontal direction
nax = len(scalar_grid.shape)
# Assume the last two axes represent the horizontal directions
sgma_seq = [sgma if i > nax - 3 else 0 for i in range(nax)]
# Compute smoothed field and reattach units
res = gaussian_filter(scalar_grid, sgma_seq, truncate=2 * np.sqrt(2))
if hasattr(scalar_grid, 'units'):
res = res * scalar_grid.units
return res
def _check_radians(value, max_radians=2 * np.pi):
"""Input validation of values that could be in degrees instead of radians.
Parameters
----------
value : `pint.Quantity`
The input value to check.
max_radians : float
Maximum absolute value of radians before warning.
Returns
-------
`pint.Quantity`
The input value
"""
try:
value = value.to('radians').m
except AttributeError:
pass
if np.greater(np.nanmax(np.abs(value)), max_radians):
warnings.warn('Input over {} radians. '
'Ensure proper units are given.'.format(max_radians))
return value