Source code for metpy.calc.indices

# Copyright (c) 2017,2019 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 warnings

import numpy as np

from .tools import get_layer
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 Examples -------- >>> pressure = np.array([1000, 950, 900]) * units.hPa >>> dewpoint = np.array([20, 15, 10]) * units.degC >>> pw = precipitable_water(dewpoint, pressure) """ warnings.warn('Input variables will be reordered in 1.0 to be (pressure, dewpt, bottom,' 'top). To update to new input format before 1.0 is released, use' '`from metpy.future import precipitable_water`.', FutureWarning) from ..future import precipitable_water as _precipitable_water return _precipitable_water(pressure, dewpt, bottom=bottom, top=top)
[docs]@exporter.export @preprocess_xarray @check_units('[pressure]') def mean_pressure_weighted(pressure, *args, heights=None, bottom=None, depth=None): 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. """ 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).magnitude, x=layer_p.magnitude) / 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 : `pint.Quantity` Pressure from sounding u : `pint.Quantity` U component of the wind v : `pint.Quantity` V component of the wind heights : `pint.Quantity` 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]]) shear_mag = np.hypot(*(arg.magnitude for arg in shear)) * shear.units rdev = shear_cross * (7.5 * units('m/s').to(u.units) / shear_mag) # 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 ------- `pint.Quantity` 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 ------- `pint.Quantity` 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 ='m/s') v ='m/s') stormu ='m/s') stormv ='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 =, vsm) / (np.linalg.norm(vshr) * np.linalg.norm(vsm)) critical_angle = np.arccos(angle_c) * units('radian') return'degrees')