# Copyright (c) 2008,2015,2016,2017,2018,2019 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
"""
import warnings
import numpy as np
from scipy.ndimage import gaussian_filter
from .. import constants as mpconsts
from ..package_tools import Exporter
from ..units import atleast_1d, check_units, masked_array, units
from ..xarray import preprocess_xarray
exporter = Exporter(globals())
# The following variables are constants for a standard atmosphere
t0 = 288. * units.kelvin
p0 = 1013.25 * units.hPa
[docs]@exporter.export
@preprocess_xarray
@check_units('[speed]', '[speed]')
def wind_speed(u, v):
r"""Compute the wind speed from u and v-components.
Parameters
----------
u : `pint.Quantity`
Wind component in the X (East-West) direction
v : `pint.Quantity`
Wind component in the Y (North-South) direction
Returns
-------
wind speed: `pint.Quantity`
The speed of the wind
See Also
--------
wind_components
"""
speed = np.sqrt(u * u + v * v)
return speed
[docs]@exporter.export
@preprocess_xarray
@check_units('[speed]', '[speed]')
def wind_direction(u, v, convention='from'):
r"""Compute the wind direction from u and v-components.
Parameters
----------
u : `pint.Quantity`
Wind component in the X (East-West) direction
v : `pint.Quantity`
Wind component in the Y (North-South) direction
convention : str
Convention to return direction. 'from' returns the direction the wind is coming from
(meteorological convention). 'to' returns the direction the wind is going towards
(oceanographic convention). Default is 'from'.
Returns
-------
direction: `pint.Quantity`
The direction of the wind in interval [0, 360] degrees, with 360 being North, with the
direction defined by the convention kwarg.
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)
# Handle oceanographic convection
if convention == 'to':
wdir -= 180 * units.deg
elif convention not in ('to', 'from'):
raise ValueError('Invalid kwarg for "convention". Valid options are "from" or "to".')
mask = wdir <= 0
if np.any(mask):
wdir[mask] += 360. * units.deg
# avoid unintended modification of `pint.Quantity` by direct use of magnitude
calm_mask = (np.asarray(u.magnitude) == 0.) & (np.asarray(v.magnitude) == 0.)
# np.any check required for legacy numpy which treats 0-d False boolean index as zero
if np.any(calm_mask):
wdir[calm_mask] = 0. * units.deg
return wdir.reshape(origshape).to('degrees')
[docs]@exporter.export
@preprocess_xarray
@check_units('[speed]')
def wind_components(speed, wdir):
r"""Calculate the U, V wind vector components from the speed and direction.
Parameters
----------
speed : `pint.Quantity`
The wind speed (magnitude)
wdir : `pint.Quantity`
The wind direction, specified as the direction from which the wind is
blowing (0-2 pi radians or 0-360 degrees), with 360 degrees being North.
Returns
-------
u, v : tuple of `pint.Quantity`
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(7.07106781, 'meter / second')>, <Quantity(7.07106781, '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
@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]_, which is a
multi-variable least-squares regression of the values obtained in [Steadman1979]_.
Additional conditional corrections are applied to match what the National
Weather Service operationally uses. See Figure 3 of [Anderson2013]_ for a
depiction of this algorithm and further discussion.
Parameters
----------
temperature : `pint.Quantity`
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.
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 masked where the temperature < 80F. Defaults to `True`.
See Also
--------
windchill
"""
temperature = atleast_1d(temperature)
rh = atleast_1d(rh)
# assign units to rh if they currently are not present
if not hasattr(rh, 'units'):
rh = rh * units.dimensionless
delta = temperature.to(units.degF) - 0. * units.degF
rh2 = rh * rh
delta2 = delta * delta
# Simplifed Heat Index -- constants converted for RH in [0, 1]
a = -10.3 * units.degF + 1.1 * delta + 4.7 * units.delta_degF * rh
# More refined Heat Index -- constants converted for RH in [0, 1]
b = (-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)
# Create return heat index
hi = np.full(np.shape(temperature), np.nan) * units.degF
# Retain masked status of temperature with resulting heat index
if hasattr(temperature, 'mask'):
hi = masked_array(hi)
# If T <= 40F, Heat Index is T
sel = (temperature <= 40. * units.degF)
if np.any(sel):
hi[sel] = temperature[sel].to(units.degF)
# If a < 79F and hi is unset, Heat Index is a
sel = (a < 79. * units.degF) & np.isnan(hi)
if np.any(sel):
hi[sel] = a[sel]
# Use b now for anywhere hi has yet to be set
sel = np.isnan(hi)
if np.any(sel):
hi[sel] = b[sel]
# Adjustment for RH <= 13% and 80F <= T <= 112F
sel = ((rh <= 13. * units.percent) & (temperature >= 80. * units.degF)
& (temperature <= 112. * units.degF))
if np.any(sel):
rh15adj = ((13. - rh * 100.) / 4.
* ((17. * units.delta_degF - np.abs(delta - 95. * units.delta_degF))
/ 17. * units.delta_degF) ** 0.5)
hi[sel] = hi[sel] - rh15adj[sel]
# Adjustment for RH > 85% and 80F <= T <= 87F
sel = ((rh > 85. * units.percent) & (temperature >= 80. * units.degF)
& (temperature <= 87. * units.degF))
if np.any(sel):
rh85adj = 0.02 * (rh * 100. - 85.) * (87. * units.delta_degF - delta)
hi[sel] = hi[sel] + rh85adj[sel]
# See if we need to mask any undefined values
if mask_undefined:
mask = np.array(temperature < 80. * units.degF)
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, mask_undefined=True):
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`.
mask_undefined : bool, optional
A flag indicating whether a masked array should be returned with
values where wind chill or heat_index is undefined masked. For wind
chill, these are values where the temperature > 50F or
wind speed <= 3 miles per hour. For heat index, these are values
where the temperature < 80F.
Defaults to `True`.
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)
# NB: mask_defined=True is needed to know where computed values exist
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)
# NB: older numpy.ma.where does not return a masked array
app_temperature = masked_array(
np.ma.where(masked_array(wind_chill_temperature).mask,
heat_index_temperature.to(temperature.units),
wind_chill_temperature.to(temperature.units)
), temperature.units)
# If mask_undefined is False, then set any masked values to the temperature
if not mask_undefined:
app_temperature[app_temperature.mask] = temperature[app_temperature.mask]
# If no values are masked and provided temperature does not have a mask
# we should return a non-masked array
if not np.any(app_temperature.mask) and not hasattr(temperature, 'mask'):
app_temperature = np.array(app_temperature.m) * temperature.units
if is_not_scalar:
return app_temperature
else:
return atleast_1d(app_temperature)[0]
[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 [NOAA1976]_.
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}]
"""
gamma = 6.5 * units('K/km')
return (t0 / gamma) * (1 - (pressure / p0).to('dimensionless')**(
mpconsts.Rd * gamma / mpconsts.g))
[docs]@exporter.export
@preprocess_xarray
@check_units('[length]')
def height_to_geopotential(height):
r"""Compute geopotential for a given height above sea level.
Calculates the geopotential from height above mean sea level using the following formula,
which is derived from the definition of geopotential as given in [Hobbs2006]_ Pg. 69 Eq
3.21, along with an approximation for variation of gravity with altitude:
.. math:: \Phi = \frac{g R_e z}{R_e + z}
(where :math:`\Phi` is geopotential, :math:`z` is height, :math:`R_e` is average Earth
radius, and :math:`g` is standard gravity.)
Parameters
----------
height : `pint.Quantity`
Height above sea level
Returns
-------
`pint.Quantity`
The corresponding geopotential value(s)
Examples
--------
>>> 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. 9805.11102602 19607.14506998 29406.10358006
39201.98800351 48994.79978671 58784.54037509 68571.21121319
78354.81374467 88135.34941224 97912.81965774], 'meter ** 2 / second ** 2')>
Notes
-----
This calculation approximates :math:`g(z)` as
.. math:: g(z) = g_0 \left( \frac{R_e}{R_e + z} \right)^2
where :math:`g_0` is standard gravity. It thereby accounts for the average effects of
centrifugal force on apparent gravity, but neglects latitudinal variations due to
centrifugal force and Earth's eccentricity.
(Prior to MetPy v0.11, this formula instead calculated :math:`g(z)` from Newton's Law of
Gravitation assuming a spherical Earth and no centrifugal force effects.)
See Also
--------
geopotential_to_height
"""
return (mpconsts.g * mpconsts.Re * height) / (mpconsts.Re + height)
[docs]@exporter.export
@preprocess_xarray
def geopotential_to_height(geopot):
r"""Compute height above sea level from a given geopotential.
Calculates the height above mean sea level from geopotential using the following formula,
which is derived from the definition of geopotential as given in [Hobbs2006]_ Pg. 69 Eq
3.21, along with an approximation for variation of gravity with altitude:
.. math:: z = \frac{\Phi R_e}{gR_e - \Phi}
(where :math:`\Phi` is geopotential, :math:`z` is height, :math:`R_e` is average Earth
radius, and :math:`g` is standard gravity.)
Parameters
----------
geopotential : `pint.Quantity`
Geopotential
Returns
-------
`pint.Quantity`
The corresponding value(s) of height above sea level
Examples
--------
>>> 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. 9805.11102602 19607.14506998 29406.10358006
39201.98800351 48994.79978671 58784.54037509 68571.21121319
78354.81374467 88135.34941224 97912.81965774], '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
-----
This calculation approximates :math:`g(z)` as
.. math:: g(z) = g_0 \left( \frac{R_e}{R_e + z} \right)^2
where :math:`g_0` is standard gravity. It thereby accounts for the average effects of
centrifugal force on apparent gravity, but neglects latitudinal variations due to
centrifugal force and Earth's eccentricity.
(Prior to MetPy v0.11, this formula instead calculated :math:`g(z)` from Newton's Law of
Gravitation assuming a spherical Earth and no centrifugal force effects.)
See Also
--------
height_to_geopotential
"""
return (geopot * mpconsts.Re) / (mpconsts.g * mpconsts.Re - geopot)
[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 [NOAA1976]_.
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})}
"""
gamma = 6.5 * units('K/km')
return p0 * (1 - (gamma / t0) * height) ** (mpconsts.g / (mpconsts.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. * mpconsts.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 [NOAA1976]_.
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 [NOAA1976]_.
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
@units.wraps('=A', ('=A', None))
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
return gaussian_filter(scalar_grid, sgma_seq, truncate=2 * np.sqrt(2))
[docs]@exporter.export
@preprocess_xarray
@units.wraps('=A', ('=A', None, None))
def smooth_n_point(scalar_grid, n=5, passes=1):
"""Filter with normal distribution of weights.
Parameters
----------
scalar_grid : array-like or `pint.Quantity`
Some 2D scalar grid to be smoothed.
n: int
The number of points to use in smoothing, only valid inputs
are 5 and 9. Defaults to 5.
passes : int
The number of times to apply the filter to the grid. Defaults to 1.
Returns
-------
array-like or `pint.Quantity`
The filtered 2D scalar grid.
Notes
-----
This function is a close replication of the GEMPAK function SM5S
and SM9S depending on the choice of the number of points to use
for smoothing. This function can be applied multiple times to
create a more smoothed field and will only smooth the interior
points, leaving the end points with their original values. If a
masked value or NaN values exists in the array, it will propagate
to any point that uses that particular grid point in the smoothing
calculation. Applying the smoothing function multiple times will
propagate NaNs further throughout the domain.
"""
if n == 9:
p = 0.25
q = 0.125
r = 0.0625
elif n == 5:
p = 0.5
q = 0.125
r = 0.0
else:
raise ValueError('The number of points to use in the smoothing '
'calculation must be either 5 or 9.')
smooth_grid = scalar_grid[:].copy()
for _i in range(passes):
smooth_grid[1:-1, 1:-1] = (p * smooth_grid[1:-1, 1:-1]
+ q * (smooth_grid[2:, 1:-1] + smooth_grid[1:-1, 2:]
+ smooth_grid[:-2, 1:-1] + smooth_grid[1:-1, :-2])
+ r * (smooth_grid[2:, 2:] + smooth_grid[2:, :-2] +
+ smooth_grid[:-2, 2:] + smooth_grid[:-2, :-2]))
return smooth_grid
[docs]@exporter.export
@preprocess_xarray
@check_units('[pressure]', '[length]')
def altimeter_to_station_pressure(altimeter_value, height):
r"""Convert the altimeter measurement to station pressure.
This function is useful for working with METARs since they do not provide
altimeter values, but not sea-level pressure or station pressure.
The following definitions of altimeter setting and station pressure
are taken from [Smithsonian1951]_ Altimeter setting is the
pressure value to which an aircraft altimeter scale is set so that it will
indicate the altitude above mean sea-level of an aircraft on the ground at the
location for which the value is determined. It assumes a standard atmosphere [NOAA1976]_.
Station pressure is the atmospheric pressure at the designated station elevation.
Finding the station pressure can be helpful for calculating sea-level pressure
or other parameters.
Parameters
----------
altimeter_value : `pint.Quantity`
The altimeter setting value as defined by the METAR or other observation,
which can be measured in either inches of mercury (in. Hg) or millibars (mb)
height: `pint.Quantity`
Elevation of the station measuring pressure.
Returns
-------
`pint.Quantity`
The station pressure in hPa or in. Hg, which can be used to calculate sea-level
pressure
See Also
--------
altimeter_to_sea_level_pressure
Notes
-----
This function is implemented using the following equations from the
Smithsonian Handbook (1951) p. 269
Equation 1:
.. math:: A_{mb} = (p_{mb} - 0.3)F
Equation 3:
.. math:: F = \left [1 + \left(\frac{p_{0}^n a}{T_{0}} \right)
\frac{H_{b}}{p_{1}^n} \right ] ^ \frac{1}{n}
Where
:math:`p_{0}` = standard sea-level pressure = 1013.25 mb
:math:`p_{1} = p_{mb} - 0.3` when :math:`p_{0} = 1013.25 mb`
gamma = lapse rate in [NOAA1976]_ standard atmosphere below the isothermal layer
:math:`6.5^{\circ}C. km.^{-1}`
:math:`t_{0}` = standard sea-level temperature 288 K
:math:`H_{b} =` station elevation in meters (elevation for which station
pressure is given)
:math:`n = \frac{a R_{d}}{g} = 0.190284` where :math:`R_{d}` is the gas
constant for dry air
And solving for :math:`p_{mb}` results in the equation below, which is used to
calculate station pressure :math:`(p_{mb})`
.. math:: p_{mb} = \left [A_{mb} ^ n - \left (\frac{p_{0} a H_{b}}{T_0}
\right) \right] ^ \frac{1}{n} + 0.3
"""
# Gamma Value for this case
gamma = 0.0065 * units('K/m')
# N-Value
n = (mpconsts.Rd * gamma / mpconsts.g).to_base_units()
return ((altimeter_value ** n
- ((p0.to(altimeter_value.units) ** n * gamma * height) / t0)) ** (1 / n)
+ 0.3 * units.hPa)
[docs]@exporter.export
@preprocess_xarray
@check_units('[pressure]', '[length]', '[temperature]')
def altimeter_to_sea_level_pressure(altimeter_value, height, temperature):
r"""Convert the altimeter setting to sea-level pressure.
This function is useful for working with METARs since most provide
altimeter values, but not sea-level pressure, which is often plotted
on surface maps. The following definitions of altimeter setting, station pressure, and
sea-level pressure are taken from [Smithsonian1951]_
Altimeter setting is the pressure value to which an aircraft altimeter scale
is set so that it will indicate the altitude above mean sea-level of an aircraft
on the ground at the location for which the value is determined. It assumes a standard
atmosphere. Station pressure is the atmospheric pressure at the designated station
elevation. Sea-level pressure is a pressure value obtained by the theoretical reduction
of barometric pressure to sea level. It is assumed that atmosphere extends to sea level
below the station and that the properties of the atmosphere are related to conditions
observed at the station. This value is recorded by some surface observation stations,
but not all. If the value is recorded, it can be found in the remarks section. Finding
the sea-level pressure is helpful for plotting purposes and different calculations.
Parameters
----------
altimeter_value : 'pint.Quantity'
The altimeter setting value is defined by the METAR or other observation,
with units of inches of mercury (in Hg) or millibars (hPa)
height : 'pint.Quantity'
Elevation of the station measuring pressure. Often times measured in meters
temperature : 'pint.Quantity'
Temperature at the station
Returns
-------
'pint.Quantity'
The sea-level pressure in hPa and makes pressure values easier to compare
between different stations
See Also
--------
altimeter_to_station_pressure
Notes
-----
This function is implemented using the following equations from Wallace and Hobbs (1977)
Equation 2.29:
.. math::
\Delta z = Z_{2} - Z_{1}
= \frac{R_{d} \bar T_{v}}{g_0}ln\left(\frac{p_{1}}{p_{2}}\right)
= \bar H ln \left (\frac {p_{1}}{p_{2}} \right)
Equation 2.31:
.. math::
p_{0} = p_{g}exp \left(\frac{Z_{g}}{\bar H} \right) \\
= p_{g}exp \left(\frac{g_{0}Z_{g}}{R_{d}\bar T_{v}} \right)
Then by substituting :math:`Delta_{Z}` for :math:`Z_{g}` in Equation 2.31:
.. math:: p_{sea_level} = p_{station} exp\left(\frac{\Delta z}{H}\right)
where :math:`Delta_{Z}` is the elevation in meters and :math:`H = \frac{R_{d}T}{g}`
"""
# Calculate the station pressure using function altimeter_to_station_pressure()
psfc = altimeter_to_station_pressure(altimeter_value, height)
# Calculate the scale height
h = mpconsts.Rd * temperature / mpconsts.g
return psfc * np.exp(height / h)
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