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solar-spa/src/spa.c
Ali Camarata f10c64c5f1 first commit
2023-03-31 23:26:40 -04:00

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/////////////////////////////////////////////
// Solar Position Algorithm (SPA) //
// for //
// Solar Radiation Application //
// //
// May 12, 2003 //
// //
// Filename: SPA.C //
// //
// Afshin Michael Andreas //
// Afshin.Andreas@NREL.gov (303)384-6383 //
// //
// Metrology Laboratory //
// Solar Radiation Research Laboratory //
// National Renewable Energy Laboratory //
// 15013 Denver W Pkwy, Golden, CO 80401 //
/////////////////////////////////////////////
/////////////////////////////////////////////
// See the SPA.H header file for usage //
// //
// This code is based on the NREL //
// technical report "Solar Position //
// Algorithm for Solar Radiation //
// Application" by I. Reda & A. Andreas //
/////////////////////////////////////////////
///////////////////////////////////////////////////////////////////////////////////////////////
//
// NOTICE
// Copyright (C) 2008-2011 Alliance for Sustainable Energy, LLC, All Rights Reserved
//
//The Solar Position Algorithm ("Software") is code in development prepared by employees of the
//Alliance for Sustainable Energy, LLC, (hereinafter the "Contractor"), under Contract No.
//DE-AC36-08GO28308 ("Contract") with the U.S. Department of Energy (the "DOE"). The United
//States Government has been granted for itself and others acting on its behalf a paid-up, non-
//exclusive, irrevocable, worldwide license in the Software to reproduce, prepare derivative
//works, and perform publicly and display publicly. Beginning five (5) years after the date
//permission to assert copyright is obtained from the DOE, and subject to any subsequent five
//(5) year renewals, the United States Government is granted for itself and others acting on
//its behalf a paid-up, non-exclusive, irrevocable, worldwide license in the Software to
//reproduce, prepare derivative works, distribute copies to the public, perform publicly and
//display publicly, and to permit others to do so. If the Contractor ceases to make this
//computer software available, it may be obtained from DOE's Office of Scientific and Technical
//Information's Energy Science and Technology Software Center (ESTSC) at P.O. Box 1020, Oak
//Ridge, TN 37831-1020. THIS SOFTWARE IS PROVIDED BY THE CONTRACTOR "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 CONTRACTOR OR THE
//U.S. GOVERNMENT BE LIABLE FOR ANY SPECIAL, INDIRECT OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
//WHATSOEVER, INCLUDING BUT NOT LIMITED TO CLAIMS ASSOCIATED WITH THE LOSS OF DATA OR PROFITS,
//WHICH MAY RESULT FROM AN ACTION IN CONTRACT, NEGLIGENCE OR OTHER TORTIOUS CLAIM THAT ARISES
//OUT OF OR IN CONNECTION WITH THE ACCESS, USE OR PERFORMANCE OF THIS SOFTWARE.
//
//The Software is being provided for internal, noncommercial purposes only and shall not be
//re-distributed. Please contact the NREL Commercialization and Technology Transfer Office
//for information concerning a commercial license to use the Software, visit:
//http://midcdmz.nrel.gov/spa/ for the contact information.
//
//As a condition of using the Software in an application, the developer of the application
//agrees to reference the use of the Software and make this Notice readily accessible to any
//end-user in a Help|About screen or equivalent manner.
//
///////////////////////////////////////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////////////////////////////////
// Revised 27-FEB-2004 Andreas
// Added bounds check on inputs and return value for spa_calculate().
// Revised 10-MAY-2004 Andreas
// Changed temperature bound check minimum from -273.15 to -273 degrees C.
// Revised 17-JUN-2004 Andreas
// Corrected a problem that caused a bogus sunrise/set/transit on the equinox.
// Revised 18-JUN-2004 Andreas
// Added a "function" input variable that allows the selecting of desired outputs.
// Revised 21-JUN-2004 Andreas
// Added 3 new intermediate output values to SPA structure (srha, ssha, & sta).
// Revised 23-JUN-2004 Andreas
// Enumerations for "function" were renamed and 2 were added.
// Prevented bound checks on inputs that are not used (based on function).
// Revised 01-SEP-2004 Andreas
// Changed a local variable from integer to double.
// Revised 12-JUL-2005 Andreas
// Put a limit on the EOT calculation, so that the result is between -20 and 20.
// Revised 26-OCT-2005 Andreas
// Set the atmos. refraction correction to zero, when sun is below horizon.
// Made atmos_refract input a requirement for all "functions".
// Changed atmos_refract bound check from +/- 10 to +/- 5 degrees.
// Revised 07-NOV-2006 Andreas
// Corrected 3 earth periodic terms in the L_TERMS array.
// Corrected 2 earth periodic terms in the R_TERMS array.
// Revised 10-NOV-2006 Andreas
// Corrected a constant used to calculate topocentric sun declination.
// Put a limit on observer hour angle, so result is between 0 and 360.
// Revised 13-NOV-2006 Andreas
// Corrected calculation of topocentric sun declination.
// Converted all floating point inputs in spa structure to doubles.
// Revised 27-FEB-2007 Andreas
// Minor correction made as to when atmos. refraction correction is set to zero.
// Revised 21-JAN-2008 Andreas
// Minor change to two variable declarations.
// Revised 12-JAN-2009 Andreas
// Changed timezone bound check from +/-12 to +/-18 hours.
// Revised 14-JAN-2009 Andreas
// Corrected a constant used to calculate ecliptic mean obliquity.
// Revised 01-APR-2013 Andreas
// Replace floor with new integer function for tech. report consistency, no affect on results.
// Add "utility" function prototypes to header file for use with NREL's SAMPA.
// Rename 4 "utility" function names (remove "sun") for clarity with NREL's SAMPA.
// Added delta_ut1 as required input, which the fractional second difference between UT and UTC.
// Time must be input w/o delta_ut1 adjustment, instead of assuming adjustment was pre-applied.
// Revised 10-JUL-2014 Andreas
// Change second in spa_data structure from an integer to double to allow fractional second
// Revised 08-SEP-2014 Andreas
// Corrected description of azm_rotation in header file
// Limited azimuth180 to range of 0 to 360 deg (instead of -180 to 180) for tech report consistency
// Changed all variables names from azimuth180 to azimuth_astro
// Renamed 2 "utility" function names for consistency
///////////////////////////////////////////////////////////////////////////////////////////////
#include <math.h>
#include "spa.h"
#define PI 3.1415926535897932384626433832795028841971
#define SUN_RADIUS 0.26667
#define L_COUNT 6
#define B_COUNT 2
#define R_COUNT 5
#define Y_COUNT 63
#define L_MAX_SUBCOUNT 64
#define B_MAX_SUBCOUNT 5
#define R_MAX_SUBCOUNT 40
enum {TERM_A, TERM_B, TERM_C, TERM_COUNT};
enum {TERM_X0, TERM_X1, TERM_X2, TERM_X3, TERM_X4, TERM_X_COUNT};
enum {TERM_PSI_A, TERM_PSI_B, TERM_EPS_C, TERM_EPS_D, TERM_PE_COUNT};
enum {JD_MINUS, JD_ZERO, JD_PLUS, JD_COUNT};
enum {SUN_TRANSIT, SUN_RISE, SUN_SET, SUN_COUNT};
#define TERM_Y_COUNT TERM_X_COUNT
const int l_subcount[L_COUNT] = {64,34,20,7,3,1};
const int b_subcount[B_COUNT] = {5,2};
const int r_subcount[R_COUNT] = {40,10,6,2,1};
///////////////////////////////////////////////////
/// Earth Periodic Terms
///////////////////////////////////////////////////
const double L_TERMS[L_COUNT][L_MAX_SUBCOUNT][TERM_COUNT]=
{
{
{175347046.0,0,0},
{3341656.0,4.6692568,6283.07585},
{34894.0,4.6261,12566.1517},
{3497.0,2.7441,5753.3849},
{3418.0,2.8289,3.5231},
{3136.0,3.6277,77713.7715},
{2676.0,4.4181,7860.4194},
{2343.0,6.1352,3930.2097},
{1324.0,0.7425,11506.7698},
{1273.0,2.0371,529.691},
{1199.0,1.1096,1577.3435},
{990,5.233,5884.927},
{902,2.045,26.298},
{857,3.508,398.149},
{780,1.179,5223.694},
{753,2.533,5507.553},
{505,4.583,18849.228},
{492,4.205,775.523},
{357,2.92,0.067},
{317,5.849,11790.629},
{284,1.899,796.298},
{271,0.315,10977.079},
{243,0.345,5486.778},
{206,4.806,2544.314},
{205,1.869,5573.143},
{202,2.458,6069.777},
{156,0.833,213.299},
{132,3.411,2942.463},
{126,1.083,20.775},
{115,0.645,0.98},
{103,0.636,4694.003},
{102,0.976,15720.839},
{102,4.267,7.114},
{99,6.21,2146.17},
{98,0.68,155.42},
{86,5.98,161000.69},
{85,1.3,6275.96},
{85,3.67,71430.7},
{80,1.81,17260.15},
{79,3.04,12036.46},
{75,1.76,5088.63},
{74,3.5,3154.69},
{74,4.68,801.82},
{70,0.83,9437.76},
{62,3.98,8827.39},
{61,1.82,7084.9},
{57,2.78,6286.6},
{56,4.39,14143.5},
{56,3.47,6279.55},
{52,0.19,12139.55},
{52,1.33,1748.02},
{51,0.28,5856.48},
{49,0.49,1194.45},
{41,5.37,8429.24},
{41,2.4,19651.05},
{39,6.17,10447.39},
{37,6.04,10213.29},
{37,2.57,1059.38},
{36,1.71,2352.87},
{36,1.78,6812.77},
{33,0.59,17789.85},
{30,0.44,83996.85},
{30,2.74,1349.87},
{25,3.16,4690.48}
},
{
{628331966747.0,0,0},
{206059.0,2.678235,6283.07585},
{4303.0,2.6351,12566.1517},
{425.0,1.59,3.523},
{119.0,5.796,26.298},
{109.0,2.966,1577.344},
{93,2.59,18849.23},
{72,1.14,529.69},
{68,1.87,398.15},
{67,4.41,5507.55},
{59,2.89,5223.69},
{56,2.17,155.42},
{45,0.4,796.3},
{36,0.47,775.52},
{29,2.65,7.11},
{21,5.34,0.98},
{19,1.85,5486.78},
{19,4.97,213.3},
{17,2.99,6275.96},
{16,0.03,2544.31},
{16,1.43,2146.17},
{15,1.21,10977.08},
{12,2.83,1748.02},
{12,3.26,5088.63},
{12,5.27,1194.45},
{12,2.08,4694},
{11,0.77,553.57},
{10,1.3,6286.6},
{10,4.24,1349.87},
{9,2.7,242.73},
{9,5.64,951.72},
{8,5.3,2352.87},
{6,2.65,9437.76},
{6,4.67,4690.48}
},
{
{52919.0,0,0},
{8720.0,1.0721,6283.0758},
{309.0,0.867,12566.152},
{27,0.05,3.52},
{16,5.19,26.3},
{16,3.68,155.42},
{10,0.76,18849.23},
{9,2.06,77713.77},
{7,0.83,775.52},
{5,4.66,1577.34},
{4,1.03,7.11},
{4,3.44,5573.14},
{3,5.14,796.3},
{3,6.05,5507.55},
{3,1.19,242.73},
{3,6.12,529.69},
{3,0.31,398.15},
{3,2.28,553.57},
{2,4.38,5223.69},
{2,3.75,0.98}
},
{
{289.0,5.844,6283.076},
{35,0,0},
{17,5.49,12566.15},
{3,5.2,155.42},
{1,4.72,3.52},
{1,5.3,18849.23},
{1,5.97,242.73}
},
{
{114.0,3.142,0},
{8,4.13,6283.08},
{1,3.84,12566.15}
},
{
{1,3.14,0}
}
};
const double B_TERMS[B_COUNT][B_MAX_SUBCOUNT][TERM_COUNT]=
{
{
{280.0,3.199,84334.662},
{102.0,5.422,5507.553},
{80,3.88,5223.69},
{44,3.7,2352.87},
{32,4,1577.34}
},
{
{9,3.9,5507.55},
{6,1.73,5223.69}
}
};
const double R_TERMS[R_COUNT][R_MAX_SUBCOUNT][TERM_COUNT]=
{
{
{100013989.0,0,0},
{1670700.0,3.0984635,6283.07585},
{13956.0,3.05525,12566.1517},
{3084.0,5.1985,77713.7715},
{1628.0,1.1739,5753.3849},
{1576.0,2.8469,7860.4194},
{925.0,5.453,11506.77},
{542.0,4.564,3930.21},
{472.0,3.661,5884.927},
{346.0,0.964,5507.553},
{329.0,5.9,5223.694},
{307.0,0.299,5573.143},
{243.0,4.273,11790.629},
{212.0,5.847,1577.344},
{186.0,5.022,10977.079},
{175.0,3.012,18849.228},
{110.0,5.055,5486.778},
{98,0.89,6069.78},
{86,5.69,15720.84},
{86,1.27,161000.69},
{65,0.27,17260.15},
{63,0.92,529.69},
{57,2.01,83996.85},
{56,5.24,71430.7},
{49,3.25,2544.31},
{47,2.58,775.52},
{45,5.54,9437.76},
{43,6.01,6275.96},
{39,5.36,4694},
{38,2.39,8827.39},
{37,0.83,19651.05},
{37,4.9,12139.55},
{36,1.67,12036.46},
{35,1.84,2942.46},
{33,0.24,7084.9},
{32,0.18,5088.63},
{32,1.78,398.15},
{28,1.21,6286.6},
{28,1.9,6279.55},
{26,4.59,10447.39}
},
{
{103019.0,1.10749,6283.07585},
{1721.0,1.0644,12566.1517},
{702.0,3.142,0},
{32,1.02,18849.23},
{31,2.84,5507.55},
{25,1.32,5223.69},
{18,1.42,1577.34},
{10,5.91,10977.08},
{9,1.42,6275.96},
{9,0.27,5486.78}
},
{
{4359.0,5.7846,6283.0758},
{124.0,5.579,12566.152},
{12,3.14,0},
{9,3.63,77713.77},
{6,1.87,5573.14},
{3,5.47,18849.23}
},
{
{145.0,4.273,6283.076},
{7,3.92,12566.15}
},
{
{4,2.56,6283.08}
}
};
////////////////////////////////////////////////////////////////
/// Periodic Terms for the nutation in longitude and obliquity
////////////////////////////////////////////////////////////////
const int Y_TERMS[Y_COUNT][TERM_Y_COUNT]=
{
{0,0,0,0,1},
{-2,0,0,2,2},
{0,0,0,2,2},
{0,0,0,0,2},
{0,1,0,0,0},
{0,0,1,0,0},
{-2,1,0,2,2},
{0,0,0,2,1},
{0,0,1,2,2},
{-2,-1,0,2,2},
{-2,0,1,0,0},
{-2,0,0,2,1},
{0,0,-1,2,2},
{2,0,0,0,0},
{0,0,1,0,1},
{2,0,-1,2,2},
{0,0,-1,0,1},
{0,0,1,2,1},
{-2,0,2,0,0},
{0,0,-2,2,1},
{2,0,0,2,2},
{0,0,2,2,2},
{0,0,2,0,0},
{-2,0,1,2,2},
{0,0,0,2,0},
{-2,0,0,2,0},
{0,0,-1,2,1},
{0,2,0,0,0},
{2,0,-1,0,1},
{-2,2,0,2,2},
{0,1,0,0,1},
{-2,0,1,0,1},
{0,-1,0,0,1},
{0,0,2,-2,0},
{2,0,-1,2,1},
{2,0,1,2,2},
{0,1,0,2,2},
{-2,1,1,0,0},
{0,-1,0,2,2},
{2,0,0,2,1},
{2,0,1,0,0},
{-2,0,2,2,2},
{-2,0,1,2,1},
{2,0,-2,0,1},
{2,0,0,0,1},
{0,-1,1,0,0},
{-2,-1,0,2,1},
{-2,0,0,0,1},
{0,0,2,2,1},
{-2,0,2,0,1},
{-2,1,0,2,1},
{0,0,1,-2,0},
{-1,0,1,0,0},
{-2,1,0,0,0},
{1,0,0,0,0},
{0,0,1,2,0},
{0,0,-2,2,2},
{-1,-1,1,0,0},
{0,1,1,0,0},
{0,-1,1,2,2},
{2,-1,-1,2,2},
{0,0,3,2,2},
{2,-1,0,2,2},
};
const double PE_TERMS[Y_COUNT][TERM_PE_COUNT]={
{-171996,-174.2,92025,8.9},
{-13187,-1.6,5736,-3.1},
{-2274,-0.2,977,-0.5},
{2062,0.2,-895,0.5},
{1426,-3.4,54,-0.1},
{712,0.1,-7,0},
{-517,1.2,224,-0.6},
{-386,-0.4,200,0},
{-301,0,129,-0.1},
{217,-0.5,-95,0.3},
{-158,0,0,0},
{129,0.1,-70,0},
{123,0,-53,0},
{63,0,0,0},
{63,0.1,-33,0},
{-59,0,26,0},
{-58,-0.1,32,0},
{-51,0,27,0},
{48,0,0,0},
{46,0,-24,0},
{-38,0,16,0},
{-31,0,13,0},
{29,0,0,0},
{29,0,-12,0},
{26,0,0,0},
{-22,0,0,0},
{21,0,-10,0},
{17,-0.1,0,0},
{16,0,-8,0},
{-16,0.1,7,0},
{-15,0,9,0},
{-13,0,7,0},
{-12,0,6,0},
{11,0,0,0},
{-10,0,5,0},
{-8,0,3,0},
{7,0,-3,0},
{-7,0,0,0},
{-7,0,3,0},
{-7,0,3,0},
{6,0,0,0},
{6,0,-3,0},
{6,0,-3,0},
{-6,0,3,0},
{-6,0,3,0},
{5,0,0,0},
{-5,0,3,0},
{-5,0,3,0},
{-5,0,3,0},
{4,0,0,0},
{4,0,0,0},
{4,0,0,0},
{-4,0,0,0},
{-4,0,0,0},
{-4,0,0,0},
{3,0,0,0},
{-3,0,0,0},
{-3,0,0,0},
{-3,0,0,0},
{-3,0,0,0},
{-3,0,0,0},
{-3,0,0,0},
{-3,0,0,0},
};
///////////////////////////////////////////////
double rad2deg(double radians)
{
return (180.0/PI)*radians;
}
double deg2rad(double degrees)
{
return (PI/180.0)*degrees;
}
int integer(double value)
{
return value;
}
double limit_degrees(double degrees)
{
double limited;
degrees /= 360.0;
limited = 360.0*(degrees-floor(degrees));
if (limited < 0) limited += 360.0;
return limited;
}
double limit_degrees180pm(double degrees)
{
double limited;
degrees /= 360.0;
limited = 360.0*(degrees-floor(degrees));
if (limited < -180.0) limited += 360.0;
else if (limited > 180.0) limited -= 360.0;
return limited;
}
double limit_degrees180(double degrees)
{
double limited;
degrees /= 180.0;
limited = 180.0*(degrees-floor(degrees));
if (limited < 0) limited += 180.0;
return limited;
}
double limit_zero2one(double value)
{
double limited;
limited = value - floor(value);
if (limited < 0) limited += 1.0;
return limited;
}
double limit_minutes(double minutes)
{
double limited=minutes;
if (limited < -20.0) limited += 1440.0;
else if (limited > 20.0) limited -= 1440.0;
return limited;
}
double dayfrac_to_local_hr(double dayfrac, double timezone)
{
return 24.0*limit_zero2one(dayfrac + timezone/24.0);
}
double third_order_polynomial(double a, double b, double c, double d, double x)
{
return ((a*x + b)*x + c)*x + d;
}
///////////////////////////////////////////////////////////////////////////////////////////////
int validate_inputs(spa_data *spa)
{
if ((spa->year < -2000) || (spa->year > 6000)) return 1;
if ((spa->month < 1 ) || (spa->month > 12 )) return 2;
if ((spa->day < 1 ) || (spa->day > 31 )) return 3;
if ((spa->hour < 0 ) || (spa->hour > 24 )) return 4;
if ((spa->minute < 0 ) || (spa->minute > 59 )) return 5;
if ((spa->second < 0 ) || (spa->second >=60 )) return 6;
if ((spa->pressure < 0 ) || (spa->pressure > 5000)) return 12;
if ((spa->temperature <= -273) || (spa->temperature > 6000)) return 13;
if ((spa->delta_ut1 <= -1 ) || (spa->delta_ut1 >= 1 )) return 17;
if ((spa->hour == 24 ) && (spa->minute > 0 )) return 5;
if ((spa->hour == 24 ) && (spa->second > 0 )) return 6;
if (fabs(spa->delta_t) > 8000 ) return 7;
if (fabs(spa->timezone) > 18 ) return 8;
if (fabs(spa->longitude) > 180 ) return 9;
if (fabs(spa->latitude) > 90 ) return 10;
if (fabs(spa->atmos_refract) > 5 ) return 16;
if ( spa->elevation < -6500000) return 11;
if ((spa->function == SPA_ZA_INC) || (spa->function == SPA_ALL))
{
if (fabs(spa->slope) > 360) return 14;
if (fabs(spa->azm_rotation) > 360) return 15;
}
return 0;
}
///////////////////////////////////////////////////////////////////////////////////////////////
double julian_day (int year, int month, int day, int hour, int minute, double second, double dut1, double tz)
{
double day_decimal, julian_day, a;
day_decimal = day + (hour - tz + (minute + (second + dut1)/60.0)/60.0)/24.0;
if (month < 3) {
month += 12;
year--;
}
julian_day = integer(365.25*(year+4716.0)) + integer(30.6001*(month+1)) + day_decimal - 1524.5;
if (julian_day > 2299160.0) {
a = integer(year/100);
julian_day += (2 - a + integer(a/4));
}
return julian_day;
}
double julian_century(double jd)
{
return (jd-2451545.0)/36525.0;
}
double julian_ephemeris_day(double jd, double delta_t)
{
return jd+delta_t/86400.0;
}
double julian_ephemeris_century(double jde)
{
return (jde - 2451545.0)/36525.0;
}
double julian_ephemeris_millennium(double jce)
{
return (jce/10.0);
}
double earth_periodic_term_summation(const double terms[][TERM_COUNT], int count, double jme)
{
int i;
double sum=0;
for (i = 0; i < count; i++)
sum += terms[i][TERM_A]*cos(terms[i][TERM_B]+terms[i][TERM_C]*jme);
return sum;
}
double earth_values(double term_sum[], int count, double jme)
{
int i;
double sum=0;
for (i = 0; i < count; i++)
sum += term_sum[i]*pow(jme, i);
sum /= 1.0e8;
return sum;
}
double earth_heliocentric_longitude(double jme)
{
double sum[L_COUNT];
int i;
for (i = 0; i < L_COUNT; i++)
sum[i] = earth_periodic_term_summation(L_TERMS[i], l_subcount[i], jme);
return limit_degrees(rad2deg(earth_values(sum, L_COUNT, jme)));
}
double earth_heliocentric_latitude(double jme)
{
double sum[B_COUNT];
int i;
for (i = 0; i < B_COUNT; i++)
sum[i] = earth_periodic_term_summation(B_TERMS[i], b_subcount[i], jme);
return rad2deg(earth_values(sum, B_COUNT, jme));
}
double earth_radius_vector(double jme)
{
double sum[R_COUNT];
int i;
for (i = 0; i < R_COUNT; i++)
sum[i] = earth_periodic_term_summation(R_TERMS[i], r_subcount[i], jme);
return earth_values(sum, R_COUNT, jme);
}
double geocentric_longitude(double l)
{
double theta = l + 180.0;
if (theta >= 360.0) theta -= 360.0;
return theta;
}
double geocentric_latitude(double b)
{
return -b;
}
double mean_elongation_moon_sun(double jce)
{
return third_order_polynomial(1.0/189474.0, -0.0019142, 445267.11148, 297.85036, jce);
}
double mean_anomaly_sun(double jce)
{
return third_order_polynomial(-1.0/300000.0, -0.0001603, 35999.05034, 357.52772, jce);
}
double mean_anomaly_moon(double jce)
{
return third_order_polynomial(1.0/56250.0, 0.0086972, 477198.867398, 134.96298, jce);
}
double argument_latitude_moon(double jce)
{
return third_order_polynomial(1.0/327270.0, -0.0036825, 483202.017538, 93.27191, jce);
}
double ascending_longitude_moon(double jce)
{
return third_order_polynomial(1.0/450000.0, 0.0020708, -1934.136261, 125.04452, jce);
}
double xy_term_summation(int i, double x[TERM_X_COUNT])
{
int j;
double sum=0;
for (j = 0; j < TERM_Y_COUNT; j++)
sum += x[j]*Y_TERMS[i][j];
return sum;
}
void nutation_longitude_and_obliquity(double jce, double x[TERM_X_COUNT], double *del_psi,
double *del_epsilon)
{
int i;
double xy_term_sum, sum_psi=0, sum_epsilon=0;
for (i = 0; i < Y_COUNT; i++) {
xy_term_sum = deg2rad(xy_term_summation(i, x));
sum_psi += (PE_TERMS[i][TERM_PSI_A] + jce*PE_TERMS[i][TERM_PSI_B])*sin(xy_term_sum);
sum_epsilon += (PE_TERMS[i][TERM_EPS_C] + jce*PE_TERMS[i][TERM_EPS_D])*cos(xy_term_sum);
}
*del_psi = sum_psi / 36000000.0;
*del_epsilon = sum_epsilon / 36000000.0;
}
double ecliptic_mean_obliquity(double jme)
{
double u = jme/10.0;
return 84381.448 + u*(-4680.93 + u*(-1.55 + u*(1999.25 + u*(-51.38 + u*(-249.67 +
u*( -39.05 + u*( 7.12 + u*( 27.87 + u*( 5.79 + u*2.45)))))))));
}
double ecliptic_true_obliquity(double delta_epsilon, double epsilon0)
{
return delta_epsilon + epsilon0/3600.0;
}
double aberration_correction(double r)
{
return -20.4898 / (3600.0*r);
}
double apparent_sun_longitude(double theta, double delta_psi, double delta_tau)
{
return theta + delta_psi + delta_tau;
}
double greenwich_mean_sidereal_time (double jd, double jc)
{
return limit_degrees(280.46061837 + 360.98564736629 * (jd - 2451545.0) +
jc*jc*(0.000387933 - jc/38710000.0));
}
double greenwich_sidereal_time (double nu0, double delta_psi, double epsilon)
{
return nu0 + delta_psi*cos(deg2rad(epsilon));
}
double geocentric_right_ascension(double lamda, double epsilon, double beta)
{
double lamda_rad = deg2rad(lamda);
double epsilon_rad = deg2rad(epsilon);
return limit_degrees(rad2deg(atan2(sin(lamda_rad)*cos(epsilon_rad) -
tan(deg2rad(beta))*sin(epsilon_rad), cos(lamda_rad))));
}
double geocentric_declination(double beta, double epsilon, double lamda)
{
double beta_rad = deg2rad(beta);
double epsilon_rad = deg2rad(epsilon);
return rad2deg(asin(sin(beta_rad)*cos(epsilon_rad) +
cos(beta_rad)*sin(epsilon_rad)*sin(deg2rad(lamda))));
}
double observer_hour_angle(double nu, double longitude, double alpha_deg)
{
return limit_degrees(nu + longitude - alpha_deg);
}
double sun_equatorial_horizontal_parallax(double r)
{
return 8.794 / (3600.0 * r);
}
void right_ascension_parallax_and_topocentric_dec(double latitude, double elevation,
double xi, double h, double delta, double *delta_alpha, double *delta_prime)
{
double delta_alpha_rad;
double lat_rad = deg2rad(latitude);
double xi_rad = deg2rad(xi);
double h_rad = deg2rad(h);
double delta_rad = deg2rad(delta);
double u = atan(0.99664719 * tan(lat_rad));
double y = 0.99664719 * sin(u) + elevation*sin(lat_rad)/6378140.0;
double x = cos(u) + elevation*cos(lat_rad)/6378140.0;
delta_alpha_rad = atan2( - x*sin(xi_rad) *sin(h_rad),
cos(delta_rad) - x*sin(xi_rad) *cos(h_rad));
*delta_prime = rad2deg(atan2((sin(delta_rad) - y*sin(xi_rad))*cos(delta_alpha_rad),
cos(delta_rad) - x*sin(xi_rad) *cos(h_rad)));
*delta_alpha = rad2deg(delta_alpha_rad);
}
double topocentric_right_ascension(double alpha_deg, double delta_alpha)
{
return alpha_deg + delta_alpha;
}
double topocentric_local_hour_angle(double h, double delta_alpha)
{
return h - delta_alpha;
}
double topocentric_elevation_angle(double latitude, double delta_prime, double h_prime)
{
double lat_rad = deg2rad(latitude);
double delta_prime_rad = deg2rad(delta_prime);
return rad2deg(asin(sin(lat_rad)*sin(delta_prime_rad) +
cos(lat_rad)*cos(delta_prime_rad) * cos(deg2rad(h_prime))));
}
double atmospheric_refraction_correction(double pressure, double temperature,
double atmos_refract, double e0)
{
double del_e = 0;
if (e0 >= -1*(SUN_RADIUS + atmos_refract))
del_e = (pressure / 1010.0) * (283.0 / (273.0 + temperature)) *
1.02 / (60.0 * tan(deg2rad(e0 + 10.3/(e0 + 5.11))));
return del_e;
}
double topocentric_elevation_angle_corrected(double e0, double delta_e)
{
return e0 + delta_e;
}
double topocentric_zenith_angle(double e)
{
return 90.0 - e;
}
double topocentric_azimuth_angle_astro(double h_prime, double latitude, double delta_prime)
{
double h_prime_rad = deg2rad(h_prime);
double lat_rad = deg2rad(latitude);
return limit_degrees(rad2deg(atan2(sin(h_prime_rad),
cos(h_prime_rad)*sin(lat_rad) - tan(deg2rad(delta_prime))*cos(lat_rad))));
}
double topocentric_azimuth_angle(double azimuth_astro)
{
return limit_degrees(azimuth_astro + 180.0);
}
double surface_incidence_angle(double zenith, double azimuth_astro, double azm_rotation,
double slope)
{
double zenith_rad = deg2rad(zenith);
double slope_rad = deg2rad(slope);
return rad2deg(acos(cos(zenith_rad)*cos(slope_rad) +
sin(slope_rad )*sin(zenith_rad) * cos(deg2rad(azimuth_astro - azm_rotation))));
}
double sun_mean_longitude(double jme)
{
return limit_degrees(280.4664567 + jme*(360007.6982779 + jme*(0.03032028 +
jme*(1/49931.0 + jme*(-1/15300.0 + jme*(-1/2000000.0))))));
}
double eot(double m, double alpha, double del_psi, double epsilon)
{
return limit_minutes(4.0*(m - 0.0057183 - alpha + del_psi*cos(deg2rad(epsilon))));
}
double approx_sun_transit_time(double alpha_zero, double longitude, double nu)
{
return (alpha_zero - longitude - nu) / 360.0;
}
double sun_hour_angle_at_rise_set(double latitude, double delta_zero, double h0_prime)
{
double h0 = -99999;
double latitude_rad = deg2rad(latitude);
double delta_zero_rad = deg2rad(delta_zero);
double argument = (sin(deg2rad(h0_prime)) - sin(latitude_rad)*sin(delta_zero_rad)) /
(cos(latitude_rad)*cos(delta_zero_rad));
if (fabs(argument) <= 1) h0 = limit_degrees180(rad2deg(acos(argument)));
return h0;
}
void approx_sun_rise_and_set(double *m_rts, double h0)
{
double h0_dfrac = h0/360.0;
m_rts[SUN_RISE] = limit_zero2one(m_rts[SUN_TRANSIT] - h0_dfrac);
m_rts[SUN_SET] = limit_zero2one(m_rts[SUN_TRANSIT] + h0_dfrac);
m_rts[SUN_TRANSIT] = limit_zero2one(m_rts[SUN_TRANSIT]);
}
double rts_alpha_delta_prime(double *ad, double n)
{
double a = ad[JD_ZERO] - ad[JD_MINUS];
double b = ad[JD_PLUS] - ad[JD_ZERO];
if (fabs(a) >= 2.0) a = limit_zero2one(a);
if (fabs(b) >= 2.0) b = limit_zero2one(b);
return ad[JD_ZERO] + n * (a + b + (b-a)*n)/2.0;
}
double rts_sun_altitude(double latitude, double delta_prime, double h_prime)
{
double latitude_rad = deg2rad(latitude);
double delta_prime_rad = deg2rad(delta_prime);
return rad2deg(asin(sin(latitude_rad)*sin(delta_prime_rad) +
cos(latitude_rad)*cos(delta_prime_rad)*cos(deg2rad(h_prime))));
}
double sun_rise_and_set(double *m_rts, double *h_rts, double *delta_prime, double latitude,
double *h_prime, double h0_prime, int sun)
{
return m_rts[sun] + (h_rts[sun] - h0_prime) /
(360.0*cos(deg2rad(delta_prime[sun]))*cos(deg2rad(latitude))*sin(deg2rad(h_prime[sun])));
}
////////////////////////////////////////////////////////////////////////////////////////////////
// Calculate required SPA parameters to get the right ascension (alpha) and declination (delta)
// Note: JD must be already calculated and in structure
////////////////////////////////////////////////////////////////////////////////////////////////
void calculate_geocentric_sun_right_ascension_and_declination(spa_data *spa)
{
double x[TERM_X_COUNT];
spa->jc = julian_century(spa->jd);
spa->jde = julian_ephemeris_day(spa->jd, spa->delta_t);
spa->jce = julian_ephemeris_century(spa->jde);
spa->jme = julian_ephemeris_millennium(spa->jce);
spa->l = earth_heliocentric_longitude(spa->jme);
spa->b = earth_heliocentric_latitude(spa->jme);
spa->r = earth_radius_vector(spa->jme);
spa->theta = geocentric_longitude(spa->l);
spa->beta = geocentric_latitude(spa->b);
x[TERM_X0] = spa->x0 = mean_elongation_moon_sun(spa->jce);
x[TERM_X1] = spa->x1 = mean_anomaly_sun(spa->jce);
x[TERM_X2] = spa->x2 = mean_anomaly_moon(spa->jce);
x[TERM_X3] = spa->x3 = argument_latitude_moon(spa->jce);
x[TERM_X4] = spa->x4 = ascending_longitude_moon(spa->jce);
nutation_longitude_and_obliquity(spa->jce, x, &(spa->del_psi), &(spa->del_epsilon));
spa->epsilon0 = ecliptic_mean_obliquity(spa->jme);
spa->epsilon = ecliptic_true_obliquity(spa->del_epsilon, spa->epsilon0);
spa->del_tau = aberration_correction(spa->r);
spa->lamda = apparent_sun_longitude(spa->theta, spa->del_psi, spa->del_tau);
spa->nu0 = greenwich_mean_sidereal_time (spa->jd, spa->jc);
spa->nu = greenwich_sidereal_time (spa->nu0, spa->del_psi, spa->epsilon);
spa->alpha = geocentric_right_ascension(spa->lamda, spa->epsilon, spa->beta);
spa->delta = geocentric_declination(spa->beta, spa->epsilon, spa->lamda);
}
////////////////////////////////////////////////////////////////////////
// Calculate Equation of Time (EOT) and Sun Rise, Transit, & Set (RTS)
////////////////////////////////////////////////////////////////////////
void calculate_eot_and_sun_rise_transit_set(spa_data *spa)
{
spa_data sun_rts;
double nu, m, h0, n;
double alpha[JD_COUNT], delta[JD_COUNT];
double m_rts[SUN_COUNT], nu_rts[SUN_COUNT], h_rts[SUN_COUNT];
double alpha_prime[SUN_COUNT], delta_prime[SUN_COUNT], h_prime[SUN_COUNT];
double h0_prime = -1*(SUN_RADIUS + spa->atmos_refract);
int i;
sun_rts = *spa;
m = sun_mean_longitude(spa->jme);
spa->eot = eot(m, spa->alpha, spa->del_psi, spa->epsilon);
sun_rts.hour = sun_rts.minute = sun_rts.second = 0;
sun_rts.delta_ut1 = sun_rts.timezone = 0.0;
sun_rts.jd = julian_day (sun_rts.year, sun_rts.month, sun_rts.day, sun_rts.hour,
sun_rts.minute, sun_rts.second, sun_rts.delta_ut1, sun_rts.timezone);
calculate_geocentric_sun_right_ascension_and_declination(&sun_rts);
nu = sun_rts.nu;
sun_rts.delta_t = 0;
sun_rts.jd--;
for (i = 0; i < JD_COUNT; i++) {
calculate_geocentric_sun_right_ascension_and_declination(&sun_rts);
alpha[i] = sun_rts.alpha;
delta[i] = sun_rts.delta;
sun_rts.jd++;
}
m_rts[SUN_TRANSIT] = approx_sun_transit_time(alpha[JD_ZERO], spa->longitude, nu);
h0 = sun_hour_angle_at_rise_set(spa->latitude, delta[JD_ZERO], h0_prime);
if (h0 >= 0) {
approx_sun_rise_and_set(m_rts, h0);
for (i = 0; i < SUN_COUNT; i++) {
nu_rts[i] = nu + 360.985647*m_rts[i];
n = m_rts[i] + spa->delta_t/86400.0;
alpha_prime[i] = rts_alpha_delta_prime(alpha, n);
delta_prime[i] = rts_alpha_delta_prime(delta, n);
h_prime[i] = limit_degrees180pm(nu_rts[i] + spa->longitude - alpha_prime[i]);
h_rts[i] = rts_sun_altitude(spa->latitude, delta_prime[i], h_prime[i]);
}
spa->srha = h_prime[SUN_RISE];
spa->ssha = h_prime[SUN_SET];
spa->sta = h_rts[SUN_TRANSIT];
spa->suntransit = dayfrac_to_local_hr(m_rts[SUN_TRANSIT] - h_prime[SUN_TRANSIT] / 360.0,
spa->timezone);
spa->sunrise = dayfrac_to_local_hr(sun_rise_and_set(m_rts, h_rts, delta_prime,
spa->latitude, h_prime, h0_prime, SUN_RISE), spa->timezone);
spa->sunset = dayfrac_to_local_hr(sun_rise_and_set(m_rts, h_rts, delta_prime,
spa->latitude, h_prime, h0_prime, SUN_SET), spa->timezone);
} else spa->srha= spa->ssha= spa->sta= spa->suntransit= spa->sunrise= spa->sunset= -99999;
}
///////////////////////////////////////////////////////////////////////////////////////////
// Calculate all SPA parameters and put into structure
// Note: All inputs values (listed in header file) must already be in structure
///////////////////////////////////////////////////////////////////////////////////////////
int spa_calculate(spa_data *spa)
{
int result;
result = validate_inputs(spa);
if (result == 0)
{
spa->jd = julian_day (spa->year, spa->month, spa->day, spa->hour,
spa->minute, spa->second, spa->delta_ut1, spa->timezone);
calculate_geocentric_sun_right_ascension_and_declination(spa);
spa->h = observer_hour_angle(spa->nu, spa->longitude, spa->alpha);
spa->xi = sun_equatorial_horizontal_parallax(spa->r);
right_ascension_parallax_and_topocentric_dec(spa->latitude, spa->elevation, spa->xi,
spa->h, spa->delta, &(spa->del_alpha), &(spa->delta_prime));
spa->alpha_prime = topocentric_right_ascension(spa->alpha, spa->del_alpha);
spa->h_prime = topocentric_local_hour_angle(spa->h, spa->del_alpha);
spa->e0 = topocentric_elevation_angle(spa->latitude, spa->delta_prime, spa->h_prime);
spa->del_e = atmospheric_refraction_correction(spa->pressure, spa->temperature,
spa->atmos_refract, spa->e0);
spa->e = topocentric_elevation_angle_corrected(spa->e0, spa->del_e);
spa->zenith = topocentric_zenith_angle(spa->e);
spa->azimuth_astro = topocentric_azimuth_angle_astro(spa->h_prime, spa->latitude,
spa->delta_prime);
spa->azimuth = topocentric_azimuth_angle(spa->azimuth_astro);
if ((spa->function == SPA_ZA_INC) || (spa->function == SPA_ALL))
spa->incidence = surface_incidence_angle(spa->zenith, spa->azimuth_astro,
spa->azm_rotation, spa->slope);
if ((spa->function == SPA_ZA_RTS) || (spa->function == SPA_ALL))
calculate_eot_and_sun_rise_transit_set(spa);
}
return result;
}
///////////////////////////////////////////////////////////////////////////////////////////
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