# Copyright (c) 2017 MetPy Developers.
# Distributed under the terms of the BSD 3-Clause License.
# SPDX-License-Identifier: BSD-3-Clause
"""Contains calculation of various derived indices."""
import numpy as np
from .thermo import mixing_ratio, saturation_vapor_pressure
from .tools import get_layer
from .. import constants as mpconsts
from ..package_tools import Exporter
from ..units import atleast_1d, check_units, concatenate, units
from ..xarray import preprocess_xarray
exporter = Exporter(globals())
[docs]@exporter.export
@preprocess_xarray
@check_units('[temperature]', '[pressure]', '[pressure]')
def precipitable_water(dewpt, pressure, bottom=None, top=None):
r"""Calculate precipitable water through the depth of a sounding.
Formula used is:
.. math:: -\frac{1}{\rho_l g} \int\limits_{p_\text{bottom}}^{p_\text{top}} r dp
from [Salby1996]_, p. 28.
Parameters
----------
dewpt : `pint.Quantity`
Atmospheric dewpoint profile
pressure : `pint.Quantity`
Atmospheric pressure profile
bottom: `pint.Quantity`, optional
Bottom of the layer, specified in pressure. Defaults to None (highest pressure).
top: `pint.Quantity`, optional
The top of the layer, specified in pressure. Defaults to None (lowest pressure).
Returns
-------
`pint.Quantity`
The precipitable water in the layer
"""
# Sort pressure and dewpoint to be in decreasing pressure order (increasing height)
sort_inds = np.argsort(pressure)[::-1]
pressure = pressure[sort_inds]
dewpt = dewpt[sort_inds]
if top is None:
top = np.nanmin(pressure) * pressure.units
if bottom is None:
bottom = np.nanmax(pressure) * pressure.units
pres_layer, dewpt_layer = get_layer(pressure, dewpt, bottom=bottom, depth=bottom - top)
w = mixing_ratio(saturation_vapor_pressure(dewpt_layer), pres_layer)
# Since pressure is in decreasing order, pw will be the opposite sign of that expected.
pw = -1. * (np.trapz(w.magnitude, pres_layer.magnitude) * (w.units * pres_layer.units)
/ (mpconsts.g * mpconsts.rho_l))
return pw.to('millimeters')
[docs]@exporter.export
@preprocess_xarray
@check_units('[pressure]')
def mean_pressure_weighted(pressure, *args, **kwargs):
r"""Calculate pressure-weighted mean of an arbitrary variable through a layer.
Layer top and bottom specified in height or pressure.
Parameters
----------
pressure : `pint.Quantity`
Atmospheric pressure profile
*args : `pint.Quantity`
Parameters for which the pressure-weighted mean is to be calculated.
heights : `pint.Quantity`, optional
Heights from sounding. Standard atmosphere heights assumed (if needed)
if no heights are given.
bottom: `pint.Quantity`, optional
The bottom of the layer in either the provided height coordinate
or in pressure. Don't provide in meters AGL unless the provided
height coordinate is meters AGL. Default is the first observation,
assumed to be the surface.
depth: `pint.Quantity`, optional
The depth of the layer in meters or hPa.
Returns
-------
`pint.Quantity`
u_mean: u-component of layer mean wind.
`pint.Quantity`
v_mean: v-component of layer mean wind.
"""
heights = kwargs.pop('heights', None)
bottom = kwargs.pop('bottom', None)
depth = kwargs.pop('depth', None)
ret = [] # Returned variable means in layer
layer_arg = get_layer(pressure, *args, heights=heights,
bottom=bottom, depth=depth)
layer_p = layer_arg[0]
layer_arg = layer_arg[1:]
# Taking the integral of the weights (pressure) to feed into the weighting
# function. Said integral works out to this function:
pres_int = 0.5 * (layer_p[-1].magnitude**2 - layer_p[0].magnitude**2)
for i, datavar in enumerate(args):
arg_mean = np.trapz(layer_arg[i] * layer_p, x=layer_p) / pres_int
ret.append(arg_mean * datavar.units)
return ret
[docs]@exporter.export
@preprocess_xarray
@check_units('[pressure]', '[speed]', '[speed]', '[length]')
def bunkers_storm_motion(pressure, u, v, heights):
r"""Calculate the Bunkers right-mover and left-mover storm motions and sfc-6km mean flow.
Uses the storm motion calculation from [Bunkers2000]_.
Parameters
----------
pressure : array-like
Pressure from sounding
u : array-like
U component of the wind
v : array-like
V component of the wind
heights : array-like
Heights from sounding
Returns
-------
right_mover: `pint.Quantity`
U and v component of Bunkers RM storm motion
left_mover: `pint.Quantity`
U and v component of Bunkers LM storm motion
wind_mean: `pint.Quantity`
U and v component of sfc-6km mean flow
"""
# mean wind from sfc-6km
wind_mean = concatenate(mean_pressure_weighted(pressure, u, v, heights=heights,
depth=6000 * units('meter')))
# mean wind from sfc-500m
wind_500m = concatenate(mean_pressure_weighted(pressure, u, v, heights=heights,
depth=500 * units('meter')))
# mean wind from 5.5-6km
wind_5500m = concatenate(mean_pressure_weighted(pressure, u, v, heights=heights,
depth=500 * units('meter'),
bottom=heights[0] + 5500 * units('meter')))
# Calculate the shear vector from sfc-500m to 5.5-6km
shear = wind_5500m - wind_500m
# Take the cross product of the wind shear and k, and divide by the vector magnitude and
# multiply by the deviaton empirically calculated in Bunkers (2000) (7.5 m/s)
shear_cross = concatenate([shear[1], -shear[0]])
rdev = shear_cross * (7.5 * units('m/s').to(u.units) / np.hypot(*shear))
# Add the deviations to the layer average wind to get the RM motion
right_mover = wind_mean + rdev
# Subtract the deviations to get the LM motion
left_mover = wind_mean - rdev
return right_mover, left_mover, wind_mean
[docs]@exporter.export
@preprocess_xarray
@check_units('[pressure]', '[speed]', '[speed]')
def bulk_shear(pressure, u, v, heights=None, bottom=None, depth=None):
r"""Calculate bulk shear through a layer.
Layer top and bottom specified in meters or pressure.
Parameters
----------
pressure : `pint.Quantity`
Atmospheric pressure profile
u : `pint.Quantity`
U-component of wind.
v : `pint.Quantity`
V-component of wind.
height : `pint.Quantity`, optional
Heights from sounding
depth: `pint.Quantity`, optional
The depth of the layer in meters or hPa. Defaults to 100 hPa.
bottom: `pint.Quantity`, optional
The bottom of the layer in height or pressure coordinates.
If using a height, it must be in the same coordinates as the given
heights (i.e., don't use meters AGL unless given heights
are in meters AGL.) Defaults to the highest pressure or lowest height given.
Returns
-------
u_shr: `pint.Quantity`
u-component of layer bulk shear
v_shr: `pint.Quantity`
v-component of layer bulk shear
"""
_, u_layer, v_layer = get_layer(pressure, u, v, heights=heights,
bottom=bottom, depth=depth)
u_shr = u_layer[-1] - u_layer[0]
v_shr = v_layer[-1] - v_layer[0]
return u_shr, v_shr
[docs]@exporter.export
@preprocess_xarray
@check_units('[energy] / [mass]', '[speed] * [speed]', '[speed]')
def supercell_composite(mucape, effective_storm_helicity, effective_shear):
r"""Calculate the supercell composite parameter.
The supercell composite parameter is designed to identify
environments favorable for the development of supercells,
and is calculated using the formula developed by
[Thompson2004]_:
.. math:: \text{SCP} = \frac{\text{MUCAPE}}{1000 \text{J/kg}} *
\frac{\text{Effective SRH}}{50 \text{m}^2/\text{s}^2} *
\frac{\text{Effective Shear}}{20 \text{m/s}}
The effective_shear term is set to zero below 10 m/s and
capped at 1 when effective_shear exceeds 20 m/s.
Parameters
----------
mucape : `pint.Quantity`
Most-unstable CAPE
effective_storm_helicity : `pint.Quantity`
Effective-layer storm-relative helicity
effective_shear : `pint.Quantity`
Effective bulk shear
Returns
-------
array-like
supercell composite
"""
effective_shear = np.clip(atleast_1d(effective_shear), None, 20 * units('m/s'))
effective_shear[effective_shear < 10 * units('m/s')] = 0 * units('m/s')
effective_shear = effective_shear / (20 * units('m/s'))
return ((mucape / (1000 * units('J/kg')))
* (effective_storm_helicity / (50 * units('m^2/s^2')))
* effective_shear).to('dimensionless')
[docs]@exporter.export
@preprocess_xarray
@check_units('[energy] / [mass]', '[length]', '[speed] * [speed]', '[speed]')
def significant_tornado(sbcape, surface_based_lcl_height, storm_helicity_1km, shear_6km):
r"""Calculate the significant tornado parameter (fixed layer).
The significant tornado parameter is designed to identify
environments favorable for the production of significant
tornadoes contingent upon the development of supercells.
It's calculated according to the formula used on the SPC
mesoanalysis page, updated in [Thompson2004]_:
.. math:: \text{SIGTOR} = \frac{\text{SBCAPE}}{1500 \text{J/kg}} * \frac{(2000 \text{m} -
\text{LCL}_\text{SB})}{1000 \text{m}} *
\frac{SRH_{\text{1km}}}{150 \text{m}^\text{s}/\text{s}^2} *
\frac{\text{Shear}_\text{6km}}{20 \text{m/s}}
The lcl height is set to zero when the lcl is above 2000m and
capped at 1 when below 1000m, and the shr6 term is set to 0
when shr6 is below 12.5 m/s and maxed out at 1.5 when shr6
exceeds 30 m/s.
Parameters
----------
sbcape : `pint.Quantity`
Surface-based CAPE
surface_based_lcl_height : `pint.Quantity`
Surface-based lifted condensation level
storm_helicity_1km : `pint.Quantity`
Surface-1km storm-relative helicity
shear_6km : `pint.Quantity`
Surface-6km bulk shear
Returns
-------
array-like
significant tornado parameter
"""
surface_based_lcl_height = np.clip(atleast_1d(surface_based_lcl_height),
1000 * units.m, 2000 * units.m)
surface_based_lcl_height[surface_based_lcl_height > 2000 * units.m] = 0 * units.m
surface_based_lcl_height = ((2000. * units.m - surface_based_lcl_height)
/ (1000. * units.m))
shear_6km = np.clip(atleast_1d(shear_6km), None, 30 * units('m/s'))
shear_6km[shear_6km < 12.5 * units('m/s')] = 0 * units('m/s')
shear_6km /= 20 * units('m/s')
return ((sbcape / (1500. * units('J/kg')))
* surface_based_lcl_height
* (storm_helicity_1km / (150. * units('m^2/s^2')))
* shear_6km)
[docs]@exporter.export
@preprocess_xarray
@check_units('[pressure]', '[speed]', '[speed]', '[length]', '[speed]', '[speed]')
def critical_angle(pressure, u, v, heights, stormu, stormv):
r"""Calculate the critical angle.
The critical angle is the angle between the 10m storm-relative inflow vector
and the 10m-500m shear vector. A critical angle near 90 degrees indicates
that a storm in this environment on the indicated storm motion vector
is likely ingesting purely streamwise vorticity into its updraft, and [Esterheld2008]_
showed that significantly tornadic supercells tend to occur in environments
with critical angles near 90 degrees.
Parameters
----------
pressure : `pint.Quantity`
Pressures from sounding.
u : `pint.Quantity`
U-component of sounding winds.
v : `pint.Quantity`
V-component of sounding winds.
heights : `pint.Quantity`
Heights from sounding.
stormu : `pint.Quantity`
U-component of storm motion.
stormv : `pint.Quantity`
V-component of storm motion.
Returns
-------
`pint.Quantity`
critical angle in degrees
"""
# Convert everything to m/s
u = u.to('m/s')
v = v.to('m/s')
stormu = stormu.to('m/s')
stormv = stormv.to('m/s')
sort_inds = np.argsort(pressure[::-1])
pressure = pressure[sort_inds]
heights = heights[sort_inds]
u = u[sort_inds]
v = v[sort_inds]
# Calculate sfc-500m shear vector
shr5 = bulk_shear(pressure, u, v, heights=heights, depth=500 * units('meter'))
# Make everything relative to the sfc wind orientation
umn = stormu - u[0]
vmn = stormv - v[0]
vshr = np.asarray([shr5[0].magnitude, shr5[1].magnitude])
vsm = np.asarray([umn.magnitude, vmn.magnitude])
angle_c = np.dot(vshr, vsm) / (np.linalg.norm(vshr) * np.linalg.norm(vsm))
critical_angle = np.arccos(angle_c) * units('radian')
return critical_angle.to('degrees')