///////////////////////////////////////////// // 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 #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; } /////////////////////////////////////////////////////////////////////////////////////////// */