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# Copyright (c) 2008-2017 MetPy Developers. |
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# Distributed under the terms of the BSD 3-Clause License. |
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# SPDX-License-Identifier: BSD-3-Clause |
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"""Contains calculation of various derived indices.""" |
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import numpy as np |
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from .thermo import mixing_ratio, saturation_vapor_pressure |
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from .tools import get_layer |
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from ..constants import g, rho_l |
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from ..package_tools import Exporter |
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from ..units import check_units, concatenate, units |
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exporter = Exporter(globals()) |
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@exporter.export |
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@check_units('[temperature]', '[pressure]', '[pressure]') |
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def precipitable_water(dewpt, pressure, top=400 * units('hPa')): |
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r"""Calculate precipitable water through the depth of a sounding. |
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Default layer depth is sfc-400 hPa. Formula used is: |
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.. math:: \frac{1}{pg} \int\limits_0^d x \,dp |
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from [Tsonis2008]_, p. 170. |
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Parameters |
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---------- |
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dewpt : `pint.Quantity` |
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Atmospheric dewpoint profile |
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pressure : `pint.Quantity` |
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Atmospheric pressure profile |
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top: `pint.Quantity`, optional |
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The top of the layer, specified in pressure. Defaults to 400 hPa. |
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Returns |
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------- |
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`pint.Quantity` |
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The precipitable water in the layer |
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""" |
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sort_inds = np.argsort(pressure[::-1]) |
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pressure = pressure[sort_inds] |
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dewpt = dewpt[sort_inds] |
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pres_layer, dewpt_layer = get_layer(pressure, dewpt, depth=pressure[0] - top) |
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w = mixing_ratio(saturation_vapor_pressure(dewpt_layer), pres_layer) |
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# Since pressure is in decreasing order, pw will be the negative of what we want. |
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# Thus the *-1 |
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pw = -1. * (np.trapz(w.magnitude, pres_layer.magnitude) * (w.units * pres_layer.units) / |
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(g * rho_l)) |
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return pw.to('millimeters') |
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@exporter.export |
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@check_units('[pressure]') |
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def mean_pressure_weighted(pressure, *args, **kwargs): |
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r"""Calculate pressure-weighted mean of an arbitrary variable through a layer. |
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Layer top and bottom specified in height or pressure. |
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Parameters |
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---------- |
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pressure : `pint.Quantity` |
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Atmospheric pressure profile |
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*args : `pint.Quantity` |
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Parameters for which the pressure-weighted mean is to be calculated. |
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heights : `pint.Quantity`, optional |
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Heights from sounding. Standard atmosphere heights assumed (if needed) |
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if no heights are given. |
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bottom: `pint.Quantity`, optional |
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The bottom of the layer in either the provided height coordinate |
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or in pressure. Don't provide in meters AGL unless the provided |
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height coordinate is meters AGL. Default is the first observation, |
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assumed to be the surface. |
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depth: `pint.Quantity`, optional |
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The depth of the layer in meters or hPa. |
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Returns |
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------- |
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`pint.Quantity` |
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u_mean: u-component of layer mean wind. |
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`pint.Quantity` |
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v_mean: v-component of layer mean wind. |
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""" |
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heights = kwargs.pop('heights', None) |
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bottom = kwargs.pop('bottom', None) |
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depth = kwargs.pop('depth', None) |
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ret = [] # Returned variable means in layer |
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layer_arg = get_layer(pressure, *args, heights=heights, |
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bottom=bottom, depth=depth) |
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layer_p = layer_arg[0] |
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layer_arg = layer_arg[1:] |
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# Taking the integral of the weights (pressure) to feed into the weighting |
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# function. Said integral works out to this function: |
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pres_int = 0.5 * (layer_p[-1].magnitude**2 - layer_p[0].magnitude**2) |
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for i, datavar in enumerate(args): |
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arg_mean = np.trapz(layer_arg[i] * layer_p, x=layer_p) / pres_int |
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ret.append(arg_mean * datavar.units) |
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return ret |
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@exporter.export |
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@check_units('[pressure]', '[speed]', '[speed]', '[length]') |
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def bunkers_storm_motion(pressure, u, v, heights): |
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r"""Calculate the Bunkers right-mover and left-mover storm motions and sfc-6km mean flow. |
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Uses the storm motion calculation from [Bunkers2000]_. |
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Parameters |
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---------- |
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pressure : array-like |
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Pressure from sounding |
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u : array-like |
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U component of the wind |
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v : array-like |
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V component of the wind |
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heights : array-like |
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Heights from sounding |
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Returns |
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------- |
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right_mover: `pint.Quantity` |
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U and v component of Bunkers RM storm motion |
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left_mover: `pint.Quantity` |
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U and v component of Bunkers LM storm motion |
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wind_mean: `pint.Quantity` |
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U and v component of sfc-6km mean flow |
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""" |
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# mean wind from sfc-6km |
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wind_mean = concatenate(mean_pressure_weighted(pressure, u, v, heights=heights, |
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depth=6000 * units('meter'))) |
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# mean wind from sfc-500m |
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wind_500m = concatenate(mean_pressure_weighted(pressure, u, v, heights=heights, |
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depth=500 * units('meter'))) |
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# mean wind from 5.5-6km |
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wind_5500m = concatenate(mean_pressure_weighted(pressure, u, v, heights=heights, |
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depth=500 * units('meter'), |
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bottom=heights[0] + |
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5500 * units('meter'))) |
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# Calculate the shear vector from sfc-500m to 5.5-6km |
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shear = wind_5500m - wind_500m |
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# Take the cross product of the wind shear and k, and divide by the vector magnitude and |
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# multiply by the deviaton empirically calculated in Bunkers (2000) (7.5 m/s) |
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shear_cross = concatenate([shear[1], -shear[0]]) |
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rdev = shear_cross * (7.5 * units('m/s').to(u.units) / np.hypot(*shear)) |
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# Add the deviations to the layer average wind to get the RM motion |
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right_mover = wind_mean + rdev |
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# Subtract the deviations to get the LM motion |
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left_mover = wind_mean - rdev |
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return right_mover, left_mover, wind_mean |
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@exporter.export |
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@check_units('[pressure]', '[speed]', '[speed]') |
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def bulk_shear(pressure, u, v, heights=None, bottom=None, depth=None): |
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r"""Calculate bulk shear through a layer. |
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Layer top and bottom specified in meters or pressure. |
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Parameters |
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---------- |
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pressure : `pint.Quantity` |
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Atmospheric pressure profile |
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u : `pint.Quantity` |
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U-component of wind. |
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v : `pint.Quantity` |
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V-component of wind. |
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height : `pint.Quantity`, optional |
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Heights from sounding |
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depth: `pint.Quantity`, optional |
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The depth of the layer in meters or hPa |
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bottom: `pint.Quantity`, optional |
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The bottom of the layer in meters or hPa. |
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If in meters, must be in the same coordinates as the given |
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heights (i.e., don't use meters AGL unless given heights |
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are in meters AGL.) Default is the surface (1st observation.) |
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Returns |
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------- |
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u_shr: `pint.Quantity` |
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u-component of layer bulk shear |
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v_shr: `pint.Quantity` |
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v-component of layer bulk shear |
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""" |
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_, u_layer, v_layer = get_layer(pressure, u, v, heights=heights, |
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bottom=bottom, depth=depth) |
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u_shr = u_layer[-1] - u_layer[0] |
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v_shr = v_layer[-1] - v_layer[0] |
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return u_shr, v_shr |
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@exporter.export |
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def supercell_composite(mucape, effective_storm_helicity, effective_shear): |
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r"""Calculate the supercell composite parameter. |
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The supercell composite parameter is designed to identify |
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environments favorable for the development of supercells, |
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and is calculated using the formula developed by |
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[Thompson2004]_: |
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SCP = (mucape / 1000 J/kg) * (effective_storm_helicity / 50 m^2/s^2) * |
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(effective_shear / 20 m/s) |
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The effective_shear term is set to zero below 10 m/s and |
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capped at 1 when effective_shear exceeds 20 m/s. |
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Parameters |
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---------- |
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mucape : `pint.Quantity` |
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Most-unstable CAPE |
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effective_storm_helicity : `pint.Quantity` |
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Effective-layer storm-relative helicity |
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effective_shear : `pint.Quantity` |
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Effective bulk shear |
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Returns |
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------- |
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array-like |
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supercell composite |
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""" |
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effective_shear = np.clip(effective_shear, None, 20 * units('m/s')) |
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effective_shear[effective_shear < 10 * units('m/s')] = 0 * units('m/s') |
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effective_shear = effective_shear / (20 * units('m/s')) |
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return ((mucape / (1000 * units('J/kg'))) * |
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(effective_storm_helicity / (50 * units('m^2/s^2'))) * |
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effective_shear).to('dimensionless') |
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@exporter.export |
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def significant_tornado(sbcape, sblcl, storm_helicity_1km, shear_6km): |
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r"""Calculate the significant tornado parameter (fixed layer). |
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The significant tornado parameter is designed to identify |
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environments favorable for the production of significant |
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tornadoes contingent upon the development of supercells. |
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It's calculated according to the formula used on the SPC |
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mesoanalysis page, updated in [Thompson2004]_: |
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sigtor = (sbcape / 1500 J/kg) * ((2000 m - sblcl) / 1000 m) * |
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(storm_helicity_1km / 150 m^s/s^2) * (shear_6km6 / 20 m/s) |
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The sblcl term is set to zero when the lcl is above 2000m and |
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capped at 1 when below 1000m, and the shr6 term is set to 0 |
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when shr6 is below 12.5 m/s and maxed out at 1.5 when shr6 |
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exceeds 30 m/s. |
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Parameters |
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---------- |
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sbcape : `pint.Quantity` |
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Surface-based CAPE |
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sblcl : `pint.Quantity` |
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Surface-based lifted condensation level |
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storm_helicity_1km : `pint.Quantity` |
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Surface-1km storm-relative helicity |
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shear_6km : `pint.Quantity` |
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Surface-6km bulk shear |
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Returns |
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------- |
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array-like |
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significant tornado parameter |
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""" |
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sblcl = np.clip(sblcl, 1000 * units('meter'), 2000 * units('meter')) |
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sblcl[sblcl > 2000 * units('meter')] = 0 * units('meter') |
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sblcl = (2000. * units('meter') - sblcl) / (1000. * units('meter')) |
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shear_6km = np.clip(shear_6km, None, 30 * units('m/s')) |
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shear_6km[shear_6km < 12.5 * units('m/s')] = 0 * units('m/s') |
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shear_6km = shear_6km / (20 * units('m/s')) |
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return ((sbcape / (1500. * units('J/kg'))) * |
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sblcl * (storm_helicity_1km / (150. * units('m^2/s^2'))) * shear_6km) |
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Unidata /
MetPy
