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#!/usr/bin/env python |
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# -*- coding: utf-8 -*- |
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# Copyright (c) 2013, 2014, 2015, 2016, 2017 Adam.Dybbroe |
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# Author(s): |
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# Adam.Dybbroe <[email protected]> |
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# Panu Lahtinen <[email protected]> |
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# This program is free software: you can redistribute it and/or modify |
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# it under the terms of the GNU General Public License as published by |
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# the Free Software Foundation, either version 3 of the License, or |
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# (at your option) any later version. |
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# This program is distributed in the hope that it will be useful, |
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# but WITHOUT ANY WARRANTY; without even the implied warranty of |
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# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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# GNU General Public License for more details. |
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# You should have received a copy of the GNU General Public License |
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# along with this program. If not, see <http://www.gnu.org/licenses/>. |
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"""Planck radiation equation""" |
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import numpy as np |
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import logging |
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LOG = logging.getLogger(__name__) |
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H_PLANCK = 6.62606957 * 1e-34 # SI-unit = [J*s] |
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K_BOLTZMANN = 1.3806488 * 1e-23 # SI-unit = [J/K] |
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C_SPEED = 2.99792458 * 1e8 # SI-unit = [m/s] |
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EPSILON = 0.000001 |
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def blackbody_rad2temp(wavelength, radiance): |
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"""Derive brightness temperatures from radiance using the Planck |
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function. Wavelength space. Assumes SI units as input and returns |
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temperature in Kelvin |
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""" |
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mask = False |
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if np.isscalar(radiance): |
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rad = np.array([radiance, ], dtype='float64') |
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else: |
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rad = np.array(radiance, dtype='float64') |
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if np.ma.is_masked(radiance): |
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mask = radiance.mask |
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rad = np.ma.masked_array(rad, mask=mask) |
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rad = np.ma.masked_less_equal(rad, 0) |
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if np.isscalar(wavelength): |
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wvl = np.array([wavelength, ], dtype='float64') |
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else: |
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wvl = np.array(wavelength, dtype='float64') |
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const1 = H_PLANCK * C_SPEED / K_BOLTZMANN |
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const2 = 2 * H_PLANCK * C_SPEED**2 |
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res = const1 / (wvl * np.log(np.divide(const2, rad * wvl**5) + 1.0)) |
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shape = rad.shape |
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resshape = res.shape |
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if wvl.shape[0] == 1: |
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if rad.shape[0] == 1: |
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return res[0] |
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else: |
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return res[::].reshape(shape) |
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else: |
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if rad.shape[0] == 1: |
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return res[0, :] |
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else: |
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if len(shape) == 1: |
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return np.reshape(res, (shape[0], resshape[1])) |
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else: |
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return np.reshape(res, (shape[0], shape[1], resshape[1])) |
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def blackbody_wn_rad2temp(wavenumber, radiance): |
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"""Derive brightness temperatures from radiance using the Planck |
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function. Wavenumber space""" |
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if np.isscalar(radiance): |
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rad = np.array([radiance, ], dtype='float64') |
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else: |
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rad = np.array(radiance, dtype='float64') |
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if np.isscalar(wavenumber): |
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wavnum = np.array([wavenumber, ], dtype='float64') |
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else: |
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wavnum = np.array(wavenumber, dtype='float64') |
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const1 = H_PLANCK * C_SPEED / K_BOLTZMANN |
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const2 = 2 * H_PLANCK * C_SPEED**2 |
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res = const1 * wavnum / np.log(np.divide(const2 * wavnum**3, rad) + 1.0) |
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shape = rad.shape |
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resshape = res.shape |
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View Code Duplication |
if wavnum.shape[0] == 1: |
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if rad.shape[0] == 1: |
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return res[0] |
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else: |
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return res[::].reshape(shape) |
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else: |
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if rad.shape[0] == 1: |
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return res[0, :] |
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else: |
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if len(shape) == 1: |
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return np.reshape(res, (shape[0], resshape[1])) |
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else: |
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return np.reshape(res, (shape[0], shape[1], resshape[1])) |
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def planck(wave, temp, wavelength=True): |
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"""The Planck radiation or Blackbody radiation as a function of wavelength |
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or wavenumber. SI units. |
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_planck(wave, temperature, wavelength=True) |
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wave = Wavelength/wavenumber or a sequence of wavelengths/wavenumbers (m or m^-1) |
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temp = Temperature (scalar) or a sequence of temperatures (K) |
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Output: Wavelength space: The spectral radiance per meter (not micron!) |
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Unit = W/m^2 sr^-1 m^-1 |
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Wavenumber space: The spectral radiance in Watts per square meter |
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per steradian per m-1: |
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Unit = W/m^2 sr^-1 (m^-1)^-1 = W/m sr^-1 |
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Converting from SI units to mW/m^2 sr^-1 (cm^-1)^-1: |
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1.0 W/m^2 sr^-1 (m^-1)^-1 = 0.1 mW/m^2 sr^-1 (cm^-1)^-1 |
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""" |
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units = ['wavelengths', 'wavenumbers'] |
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if wavelength: |
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LOG.debug("Using {0} when calculating the Blackbody radiance".format( |
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units[(wavelength == True) - 1])) |
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if np.isscalar(temp): |
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temperature = np.array([temp, ], dtype='float64') |
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else: |
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temperature = np.array(temp, dtype='float64') |
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shape = temperature.shape |
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if np.isscalar(wave): |
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wln = np.array([wave, ], dtype='float64') |
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else: |
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wln = np.array(wave, dtype='float64') |
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if wavelength: |
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const = 2 * H_PLANCK * C_SPEED ** 2 |
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nom = const / wln ** 5 |
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arg1 = H_PLANCK * C_SPEED / (K_BOLTZMANN * wln) |
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else: |
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nom = 2 * H_PLANCK * (C_SPEED ** 2) * (wln ** 3) |
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arg1 = H_PLANCK * C_SPEED * wln / K_BOLTZMANN |
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arg2 = np.where(np.greater(np.abs(temperature), EPSILON), |
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np.array(1. / temperature), -9).reshape(-1, 1) |
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arg2 = np.ma.masked_array(arg2, mask=arg2 == -9) |
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LOG.debug("Max and min - arg1: %s %s", str(arg1.max()), str(arg1.min())) |
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LOG.debug("Max and min - arg2: %s %s", str(arg2.max()), str(arg2.min())) |
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try: |
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exp_arg = np.multiply(arg1.astype('float32'), arg2.astype('float32')) |
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except MemoryError: |
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LOG.warning(("Dimensions used in numpy.multiply probably reached " |
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"limit!\n" |
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"Make sure the Radiance<->Tb table has been created " |
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"and try running again")) |
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raise |
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LOG.debug("Max and min before exp: %s %s", str(exp_arg.max()), |
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str(exp_arg.min())) |
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if exp_arg.min() < 0: |
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LOG.warning("Something is fishy: \n" + |
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"\tDenominator might be zero or negative in radiance derivation:") |
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dubious = np.where(exp_arg < 0)[0] |
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LOG.warning( |
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"Number of items having dubious values: " + str(dubious.shape[0])) |
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denom = np.exp(exp_arg) - 1 |
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rad = nom / denom |
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radshape = rad.shape |
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if wln.shape[0] == 1: |
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if temperature.shape[0] == 1: |
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return rad[0, 0] |
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else: |
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return rad[:, 0].reshape(shape) |
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else: |
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if temperature.shape[0] == 1: |
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return rad[0, :] |
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else: |
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if len(shape) == 1: |
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return np.reshape(rad, (shape[0], radshape[1])) |
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else: |
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return np.reshape(rad, (shape[0], shape[1], radshape[1])) |
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def blackbody_wn(wavenumber, temp): |
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"""The Planck radiation or Blackbody radiation as a function of wavenumber |
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SI units! |
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blackbody_wn(wavnum, temperature) |
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wavenumber = A wavenumber (scalar) or a sequence of wave numbers (m-1) |
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temp = A temperatfure (scalar) or a sequence of temperatures (K) |
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Output: The spectral radiance in Watts per square meter per steradian |
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per m-1: |
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Unit = W/m^2 sr^-1 (m^-1)^-1 = W/m sr^-1 |
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Converting from SI units to mW/m^2 sr^-1 (cm^-1)^-1: |
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1.0 W/m^2 sr^-1 (m^-1)^-1 = 0.1 mW/m^2 sr^-1 (cm^-1)^-1 |
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""" |
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return planck(wavenumber, temp, wavelength=False) |
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def blackbody(wavel, temp): |
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"""The Planck radiation or Blackbody radiation as a function of wavelength |
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SI units. |
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blackbody(wavelength, temperature) |
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wavel = Wavelength or a sequence of wavelengths (m) |
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temp = Temperature (scalar) or a sequence of temperatures (K) |
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Output: The spectral radiance per meter (not micron!) |
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View Code Duplication |
Unit = W/m^2 sr^-1 m^-1 |
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""" |
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return planck(wavel, temp, wavelength=True) |
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pytroll /
pyspectral
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