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/*
* Copyright (C) 2015-2018 S[&]T, The Netherlands.
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are met:
*
* 1. Redistributions of source code must retain the above copyright notice,
* this list of conditions and the following disclaimer.
*
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* 3. Neither the name of the copyright holder nor the names of its
* contributors may be used to endorse or promote products derived from
* this software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
* LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
* CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
* SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
* INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
*/
#include "harp-internal.h"
#include "harp-constants.h"
#include "harp-geometry.h"
#include <math.h>
#include <stdlib.h>
/** Calculate the fraction of the day
* \param datetime Datetime [s since 2000-01-01]
* \return the fraction of the day [1]
*/
double harp_fraction_of_day_from_datetime(double datetime)
{
double datetime_in_days = datetime / 86400.0;
return datetime_in_days - floor(datetime_in_days);
}
/** Calculate the fraction of the year
* \param datetime Datetime [s since 2000-01-01]
* \return the fraction of the year [1]
*/
double harp_fraction_of_year_from_datetime(double datetime)
{
double datetime_in_years = datetime / (365.2422 * 86400.0);
return datetime_in_years - floor(datetime_in_years);
}
/** Calculate the equation of time (EOT) angle
* \param datetime Datetime [s since 2000-01-01]
* \return the equation of time [minutes]
*/
static double get_equation_of_time_from_datetime(double datetime)
{
double mean_angle, corrected_angle, angle_difference;
/* calculate Earths orbit angle at date (relative to solstice) */
/* add 10 days due to difference between December solstice and Jan 1st */
mean_angle = 2 * M_PI * harp_fraction_of_year_from_datetime(datetime + 10 * 86400);
/* correct for Earth's orbital eccentricity (0.0167) */
/* subtract 2 days due to difference between Jan 1st and Earth's perihelion */
corrected_angle =
mean_angle + 2 * 0.0167 * sin(2 * M_PI * harp_fraction_of_year_from_datetime(datetime - 2 * 86400));
/* calculate difference between mean spead and corrected speed angles (projected onto equatorial plane) */
/* divide by pi to get the difference as a fraction of a 'half turn' */
/* 23.44 [deg] is the obliquity (tilt) of the Earth's axis */
angle_difference = (mean_angle - atan2(tan(corrected_angle), cos(CONST_DEG2RAD * 23.44))) / M_PI;
/* wrap the fraction to [-0.5,0.5] and multiply by 720 (12 hours * 60 minutes) to get the amount of minutes */
return 720 * (angle_difference - floor(angle_difference + 0.5));
}
/** Convert (electromagnetic wave) wavelength to (electromagnetic wave) frequency
* \param wavelength Wavelength [m]
* \return the frequency [Hz]
*/
double harp_frequency_from_wavelength(double wavelength)
{
/* frequency = c / wavelength */
return (double)CONST_SPEED_OF_LIGHT / wavelength;
}
/** Convert (electromagnetic wave) wavenumber to (electromagnetic wave) frequency
* \param wavenumber Wavenumber [1/m]
* \return the frequency [Hz]
*/
double harp_frequency_from_wavenumber(double wavenumber)
{
/* frequency = c * wavenumber */
return (double)CONST_SPEED_OF_LIGHT *wavenumber;
}
/* Calculate the gravitational acceleration gsurf at the Earth's surface for a given latitude
* Using WGS84 Gravity formula
* \param latitude Latitude [degree_north]
* \return the gravitational acceleration at the Earth's surface gsurf [m/s2] */
double harp_gravity_at_surface_from_latitude(double latitude)
{
double g_e = 9.7803253359;
double k = 0.00193185265241;
double e2 = 0.00669437999013;
double sinphi = sin(latitude * CONST_DEG2RAD);
return g_e * (1 + k * sinphi * sinphi) / sqrt(1 - e2 * sinphi * sinphi);
}
/* Calculate the gravitational acceleration g for a given latitude and height.
* Using WGS84 Gravity formula
* \param latitude Latitude [degree_north]
* \param height Height [m]
* \return the gravitational acceleration at the Earth's surface gsurf [m/s2] */
double harp_gravity_from_latitude_and_height(double latitude, double height)
{
double a = 6378137.0;
double f = 1 / 298.257223563;
double m = 0.00344978650684;
double sinphi = sin(latitude * CONST_DEG2RAD);
return harp_gravity_at_surface_from_latitude(latitude) *
(1 - (2 * (1 + f + m - 2 * f * sinphi * sinphi) + 3 * height / a) * height / a);
}
/* Calculate the local curvature radius Rsurf at the Earth's surface for a given latitude
* \param latitude Latitude [degree_north]
* \return the local curvature radius Rsurf [m] */
double harp_local_curvature_radius_at_surface_from_latitude(double latitude)
{
double Rsurf;
double deg2rad = (double)(CONST_DEG2RAD);
double phi = latitude * deg2rad;
double Rmin = 6356752.0; /* [m] */
double Rmax = 6378137.0; /* [m] */
Rsurf = 1.0 / sqrt(cos(phi) * cos(phi) / (Rmin * Rmin) + sin(phi) * sin(phi) / (Rmax * Rmax));
return Rsurf;
}
/** Convert radiance to normalized radiance
* \param radiance Radiance [mW m-2 sr-1]
* \param solar_irradiance Solar irradiance [mW m-2]
* \return the normalized radiance [1]
*/
double harp_normalized_radiance_from_radiance_and_solar_irradiance(double radiance, double solar_irradiance)
{
return M_PI * radiance / solar_irradiance;
}
/** Convert reflectance to normalized radiance
* \param reflectance Reflectance [1]
* \param solar_zenith_angle Solar zenith angle [degree]
* \return the normalized radiance [1]
*/
double harp_normalized_radiance_from_reflectance_and_solar_zenith_angle(double reflectance, double solar_zenith_angle)
{
return cos(solar_zenith_angle * CONST_DEG2RAD) * reflectance;
}
/** Convert normalized radiance to radiance
* \param normalized_radiance Normalized radiance [1]
* \param solar_irradiance Solar irradiance [mW m-2]
* \return the radiance [mW m-2 sr-1]
*/
double harp_radiance_from_normalized_radiance_and_solar_irradiance(double normalized_radiance, double solar_irradiance)
{
double radiance; /* Radiance [mW m-2 sr-1] */
double pi = (double)M_PI;
radiance = normalized_radiance * solar_irradiance / pi;
return radiance;
}
/** Convert reflectance to radiance
* \param reflectance Reflectance [1]
* \param solar_irradiance Solar irradiance [mW m-2]
* \param solar_zenith_angle Solar zenith angle [degree]
* \return the radiance [mW m-2 sr-1]
*/
double harp_radiance_from_reflectance_solar_irradiance_and_solar_zenith_angle(double reflectance,
double solar_irradiance,
double solar_zenith_angle)
{
double radiance; /* Radiance [mW m-2 sr-1] */
double pi = (double)M_PI;
double deg2rad = (double)CONST_DEG2RAD;
double mu0 = cos(solar_zenith_angle * deg2rad);
radiance = reflectance * mu0 * solar_irradiance / pi;
return radiance;
}
/** Convert radiance to reflectance
* \param radiance Radiance [mW m-2 sr-1]
* \param solar_irradiance Solar irradiance [mW m-2]
* \param solar_zenith_angle Solar zenith angle [degree]
* \return the reflectance [1]
*/
double harp_reflectance_from_radiance_solar_irradiance_and_solar_zenith_angle(double radiance,
double solar_irradiance,
double solar_zenith_angle)
{
double reflectance; /* Reflectance [1] */
double pi = (double)M_PI;
double deg2rad = (double)CONST_DEG2RAD;
double mu0 = cos(solar_zenith_angle * deg2rad);
reflectance = pi * radiance / (mu0 * solar_irradiance);
return reflectance;
}
/** Convert normalized radiance to reflectance
* \param normalized_radiance Normalized radiance [mW m-2 sr-1]
* \param solar_zenith_angle Solar zenith angle [degree]
* \return the reflectance [1]
*/
double harp_reflectance_from_normalized_radiance_and_solar_zenith_angle(double normalized_radiance,
double solar_zenith_angle)
{
double reflectance; /* Reflectance [1] */
double deg2rad = (double)CONST_DEG2RAD;
double mu0 = cos(solar_zenith_angle * deg2rad);
reflectance = normalized_radiance / mu0;
return reflectance;
}
/** Convert sensor and solar angles into scattering angle
* \param sensor_zenith_angle Sensor Zenith Angle [degree]
* \param solar_zenith_angle Solar Zenith Angle [degree]
* \param relative_azimuth_angle Relative Azimuth Angle [degree]
* \return the scattering angle [degree]
*/
double harp_scattering_angle_from_sensor_and_solar_angles(double sensor_zenith_angle, double solar_zenith_angle,
double relative_azimuth_angle)
{
double cosangle = -cos(sensor_zenith_angle * CONST_DEG2RAD) * cos(solar_zenith_angle * CONST_DEG2RAD) -
sin(sensor_zenith_angle * CONST_DEG2RAD) * sin(solar_zenith_angle * CONST_DEG2RAD) *
cos(relative_azimuth_angle * CONST_DEG2RAD);
HARP_CLAMP(cosangle, -1.0, 1.0);
return CONST_RAD2DEG * acos(cosangle);
}
/** Calculate the solar azimuth angle for the given time and location
* \param latitude Latitude [degree_north]
* \param solar_declination_angle Solar declination angle [deg]
* \param solar_hour_angle Solar hour angle [deg]
* \param solar_zenith_angle Solar zenith angle [deg]
* \return the solar elevation angle [degree]
*/
double harp_solar_azimuth_angle_from_latitude_and_solar_angles(double latitude, double solar_declination_angle,
double solar_hour_angle, double solar_zenith_angle)
{
double cosangle;
double angle;
double sin_sza;
/* Convert angles to [rad] */
latitude *= CONST_DEG2RAD;
solar_declination_angle *= CONST_DEG2RAD;
solar_hour_angle *= CONST_DEG2RAD;
solar_zenith_angle *= CONST_DEG2RAD;
sin_sza = sin(solar_zenith_angle);
if (sin_sza == 0)
{
return 0;
}
cosangle = (sin(solar_declination_angle) * cos(latitude) -
cos(solar_hour_angle) * cos(solar_declination_angle) * sin(latitude)) / sin_sza;
HARP_CLAMP(cosangle, -1.0, 1.0);
angle = CONST_RAD2DEG * acos(cosangle);
if (solar_hour_angle > 0)
{
/* afternoon */
return -angle;
}
/* morning */
return angle;
}
/** Calculate the solar declination angle
* \param datetime Datetime [s since 2000-01-01]
* \return the solar declination angle [degree]
*/
double harp_solar_declination_angle_from_datetime(double datetime)
{
double mean_angle, corrected_angle;
double sinangle;
/* calculate Earths orbit angle at date (relative to solstice) */
/* add 10 days due to difference between December solstice and Jan 1st */
mean_angle = 2 * M_PI * harp_fraction_of_year_from_datetime(datetime + 10 * 86400);
/* correct for Earth's orbital eccentricity (0.0167) */
/* subtract 2 days due to difference between Jan 1st and Earth's perihelion */
corrected_angle =
mean_angle + 2 * 0.0167 * sin(2 * M_PI * harp_fraction_of_year_from_datetime(datetime - 2 * 86400));
/* 23.44 [deg] is the obliquity (tilt) of the Earth's axis */
sinangle = sin(CONST_DEG2RAD * 23.44) * cos(corrected_angle);
HARP_CLAMP(sinangle, -1.0, 1.0);
return CONST_RAD2DEG * -asin(sinangle);
}
/** Calculate the solar hour angle for the given time and location
* \param datetime Datetime [s since 2000-01-01]
* \param longitude Longitude [degree_east]
* \return the solar hour angle [degree]
*/
double harp_solar_hour_angle_from_datetime_and_longitude(double datetime, double longitude)
{
double local_fraction_of_day;
local_fraction_of_day = harp_fraction_of_day_from_datetime(datetime) +
get_equation_of_time_from_datetime(datetime) / (24 * 60);
return harp_wrap(longitude + 360 * local_fraction_of_day - 180, -180, 180);
}
/** Calculate the solar zenith angle for the given time and location
* \param latitude Latitude [degree_north]
* \param solar_declination_angle Solar declination angle [deg]
* \param solar_hour_angle Solar hour angle [deg]
* \return the solar zenith angle [degree]
*/
double harp_solar_zenith_angle_from_latitude_and_solar_angles(double latitude, double solar_declination_angle,
double solar_hour_angle)
{
double cosangle;
/* Convert angles to [rad] */
latitude *= CONST_DEG2RAD;
solar_declination_angle *= CONST_DEG2RAD;
solar_hour_angle *= CONST_DEG2RAD;
cosangle = sin(solar_declination_angle) * sin(latitude) +
cos(solar_hour_angle) * cos(solar_declination_angle) * cos(latitude);
HARP_CLAMP(cosangle, -1.0, 1.0);
return CONST_RAD2DEG * acos(cosangle);
}
/** Convert sensor and solar azimuth angles to relative azimuth angle
* \param sensor_azimuth_angle Sensor azimuth angle[degree]
* \param solar_azimuth_angle Solar azimuth angle[degree]
* \return the relative azimuth angle [degree]
*/
double harp_relative_azimuth_angle_from_sensor_and_solar_azimuth_angles(double sensor_azimuth_angle,
double solar_azimuth_angle)
{
double angle = sensor_azimuth_angle - solar_azimuth_angle;
while (angle < 0)
{
angle += 360;
}
while (angle >= 360)
{
angle -= 360;
}
if (angle > 180)
{
return 360 - angle;
}
return angle;
}
/** Convert zenith angle to elevation angle
* \param zenith_angle Zenith angle[degree]
* \return the elevation angle [degree]
*/
double harp_elevation_angle_from_zenith_angle(double zenith_angle)
{
return 90.0 - zenith_angle;
}
/** Convert zenith angle to elevation angle
* \param elevation_angle elevation angle [degree]
* \return the zenith angle [degree]
*/
double harp_zenith_angle_from_elevation_angle(double elevation_angle)
{
return 90.0 - elevation_angle;
}
/** Convert viewing angle (zenith, elevation, or azimuth) to sensor angle
* \param viewing_angle Viewing angle[degree]
* \return the sensor angle [degree]
*/
double harp_sensor_angle_from_viewing_angle(double viewing_angle)
{
return 180.0 - viewing_angle;
}
/** Convert sensor angle (zenith, elevation, or azimuth) to viewing angle
* \param sensor_angle sensor angle [degree]
* \return the viewing angle [degree]
*/
double harp_viewing_angle_from_sensor_angle(double sensor_angle)
{
return 180.0 - sensor_angle;
}
/** Convert the solar zenith angle, the sensor zenith angle and relative azimuth angle at one height to another height
* \param source_altitude Source altitude [m]
* \param source_solar_zenith_angle Solar zenith angle at source altitude [degree]
* \param source_sensor_zenith_angle Sensor zenith angle at source altitude [degree]
* \param source_relative_azimuth_angle Relative azimuth angle at source altitude [degree]
* \param target_altitude Target altitude [m]
* \param new_target_solar_zenith_angle Solar zenith angle at target altitude [degree]
* \param new_target_sensor_zenith_angle Sensor zenith angle at target altitude [degree]
* \param new_target_relative_azimuth_angle Relative azimuth angle at target altitude [degree]
*/
int harp_sensor_geometry_angles_at_altitude_from_other_altitude(double source_altitude,
double source_solar_zenith_angle,
double source_sensor_zenith_angle,
double source_relative_azimuth_angle,
double target_altitude,
double *new_target_solar_zenith_angle,
double *new_target_sensor_zenith_angle,
double *new_target_relative_azimuth_angle)
{
double target_solar_zenith_angle;
double target_sensor_zenith_angle;
double target_relative_azimuth_angle;
double Earth_radius = (double)(CONST_EARTH_RADIUS_WGS84_SPHERE);
double deg2rad = (double)(CONST_DEG2RAD);
double rad2deg = (double)(CONST_RAD2DEG);
double theta0 = source_solar_zenith_angle * deg2rad; /* Solar zenith angle [rad] */
double thetaV = source_sensor_zenith_angle * deg2rad; /* Sensor zenith angle [rad] */
double deltaphi = source_relative_azimuth_angle * deg2rad; /* Relative azimuth angle [rad] */
double sintheta0 = sin(theta0);
double costheta0 = cos(theta0);
double sinthetaV = sin(thetaV);
double cosdeltaphi = cos(deltaphi);
double sintheta0k;
double costheta0k;
double sinthetaVk;
double theta0k;
double thetaVk;
double sinbeta;
double cosbeta;
double cosdeltaphik;
double deltaphik;
double fk;
int nadir;
nadir = (source_sensor_zenith_angle == 0.0);
if (nadir || (target_altitude == source_altitude))
{
/* The output angles are identical to the input angles */
target_solar_zenith_angle = source_solar_zenith_angle;
target_sensor_zenith_angle = source_sensor_zenith_angle;
if (source_relative_azimuth_angle > 180.0)
{
target_relative_azimuth_angle = 360.0 - source_relative_azimuth_angle;
}
else
{
target_relative_azimuth_angle = source_relative_azimuth_angle;
}
}
else
{
/* Calculate the sensor zenith angles */
fk = (Earth_radius + source_altitude) / (Earth_radius + target_altitude);
sinthetaVk = fk * sinthetaV;
HARP_CLAMP(sinthetaVk, -1.0, 1.0);
thetaVk = asin(sinthetaVk);
/* Calculate the polar angle beta between the lines
* (Earth centre -- target_altitude) and (Earth centre -- source_altitude) */
sinbeta = thetaVk - thetaV;
cosbeta = sqrt(1.0 - sinbeta * sinbeta);
/* Calculate the solar zenith angles */
costheta0k = costheta0 * cosbeta + sintheta0 * sinbeta * cosdeltaphi;
HARP_CLAMP(costheta0k, -1.0, 1.0);
theta0k = acos(costheta0k);
sintheta0k = sqrt(1.0 - costheta0k * costheta0k);
/* Calculate the sensor azimuth angles */
if (sintheta0k == 0.0)
{
/* The sun is in zenith, so the azimuth angle is arbitrary. Set to zero. */
deltaphik = 0.0;
}
else
{
cosdeltaphik = (costheta0 - costheta0k * cosbeta) / (sintheta0k * sinbeta);
HARP_CLAMP(cosdeltaphik, -1.0, 1.0);
deltaphik = M_PI - acos(cosdeltaphik);
if (deltaphik > M_PI)
{
deltaphik = 2.0 * M_PI - deltaphik;
}
}
target_solar_zenith_angle = theta0k * rad2deg;
target_sensor_zenith_angle = thetaVk * rad2deg;
target_relative_azimuth_angle = deltaphik * rad2deg;
}
*new_target_solar_zenith_angle = target_solar_zenith_angle;
*new_target_sensor_zenith_angle = target_sensor_zenith_angle;
*new_target_relative_azimuth_angle = target_relative_azimuth_angle;
return 0;
}
/** Calculate the solar zenith angle, the sensor zenith angle, and the relative azimuth angle for the requested altitudes
* \param altitude Height corresponding to the input angles (reference altitude) [m]
* \param solar_zenith_angle Solar zenith angle at reference altitude [degree]
* \param sensor_zenith_angle Sensor zenith angle at reference altitude [degree]
* \param relative_azimuth_angle Relative azimuth angle at reference altitude [degree]
* \param num_levels Number of levels
* \param altitude_profile Altitude profile [m]
* \param solar_zenith_angle_profile Solar zenith angles at profile altitudes [degree]
* \param sensor_zenith_angle_profile Sensor zenith angles at profile altitudes [degree]
* \param relative_azimuth_angle_profile Relative azimuth angles at profile altitudes [degree]
*/
int harp_sensor_geometry_angle_profiles_from_sensor_geometry_angles(double altitude,
double solar_zenith_angle,
double sensor_zenith_angle,
double relative_azimuth_angle,
long num_levels,
const double *altitude_profile,
double *solar_zenith_angle_profile,
double *sensor_zenith_angle_profile,
double *relative_azimuth_angle_profile)
{
long k;
if (altitude_profile == NULL)
{
harp_set_error(HARP_ERROR_INVALID_ARGUMENT, "altitude profile is empty (%s:%u)", __FILE__, __LINE__);
return -1;
}
if (solar_zenith_angle_profile == NULL)
{
harp_set_error(HARP_ERROR_INVALID_ARGUMENT, "solar zenith angle profile is empty (%s:%u)", __FILE__, __LINE__);
return -1;
}
if (sensor_zenith_angle_profile == NULL)
{
harp_set_error(HARP_ERROR_INVALID_ARGUMENT, "sensor zenith angle profile is empty (%s:%u)", __FILE__, __LINE__);
return -1;
}
if (relative_azimuth_angle_profile == NULL)
{
harp_set_error(HARP_ERROR_INVALID_ARGUMENT, "relative azimuth angle profile is empty (%s:%u)", __FILE__,
__LINE__);
return -1;
}
for (k = 0; k < num_levels; k++)
{
if (harp_sensor_geometry_angles_at_altitude_from_other_altitude(altitude,
solar_zenith_angle,
sensor_zenith_angle,
relative_azimuth_angle,
altitude_profile[k],
&(solar_zenith_angle_profile[k]),
&(sensor_zenith_angle_profile[k]),
&(relative_azimuth_angle_profile[k])) != 0)
{
return -1;
}
}
return 0;
}
/** Convert (electromagnetic wave) frequency to (electromagnetic wave) wavelength
* \param frequency Frequency [Hz]
* \return Wavelength [m]
*/
double harp_wavelength_from_frequency(double frequency)
{
return (double)CONST_SPEED_OF_LIGHT / frequency;
}
/** Convert (electromagnetic wave) wavenumber to (electromagnetic wave) wavelength
* \param wavenumber Wavenumber [1/m]
* \return Wavelength [m]
*/
double harp_wavelength_from_wavenumber(double wavenumber)
{
return 1.0 / wavenumber;
}
/** Convert (electromagnetic wave) frequency to (electromagnetic wave) wavenumber
* \param frequency Frequency [Hz]
* \return Wavenumber [1/m]
*/
double harp_wavenumber_from_frequency(double frequency)
{
return frequency / (double)CONST_SPEED_OF_LIGHT;
}
/** Convert (electromagnetic wave) wavelength to (electromagnetic wave) wavenumber
* \param wavelength Wavelength [m]
* \return Wavenumber [1/m]
*/
double harp_wavenumber_from_wavelength(double wavelength)
{
return 1.0 / wavelength;
}
/** Wrap a value to the given min/max range
* The result is: min + (value - min) % (max - min)
* \param value Value to wrap to the given range
* \param min Minimum value of the range
* \param max Maximum value of the range
* \return Wrapped value
*/
double harp_wrap(double value, double min, double max)
{
if (value < min)
{
return max + fmod(value - min, max - min);
}
return min + fmod(value - min, max - min);
}
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