File content as of revision 0:fba19b344b6d:

/*============================================================================
*    Contains:
*        S_solpos     (computes solar position and intensity
*                      from time and place)
*
*            INPUTS:     (via posdata struct) year, daynum, hour,
*                        minute, second, latitude, longitude, timezone,
*                        intervl
*            OPTIONAL:   (via posdata struct) month, day, press, temp, tilt,
*                        aspect, function
*            OUTPUTS:    EVERY variable in the struct posdata
*                            (defined in solpos.h)
*
*                       NOTE: Certain conditions exist during which some of
*                       the output variables are undefined or cannot be
*                       calculated.  In these cases, the variables are
*                       returned with flag values indicating such.  In other
*                       cases, the variables may return a realistic, though
*                       invalid, value. These variables and the flag values
*                       or invalid conditions are listed below:
*
*                       amass     -1.0 at zenetr angles greater than 93.0
*                                 degrees
*                       ampress   -1.0 at zenetr angles greater than 93.0
*                                 degrees
*                       azim      invalid at zenetr angle 0.0 or latitude
*                                 +/-90.0 or at night
*                       elevetr   limited to -9 degrees at night
*                       etr       0.0 at night
*                       etrn      0.0 at night
*                       etrtilt   0.0 when cosinc is less than 0
*                       prime     invalid at zenetr angles greater than 93.0
*                                 degrees
*                       sretr     +/- 2999.0 during periods of 24 hour sunup or
*                                 sundown
*                       ssetr     +/- 2999.0 during periods of 24 hour sunup or
*                                 sundown
*                       ssha      invalid at the North and South Poles
*                       unprime   invalid at zenetr angles greater than 93.0
*                                 degrees
*                       zenetr    limited to 99.0 degrees at night
*
*        S_init       (optional initialization for all input parameters in
*                      the posdata struct)
*           INPUTS:     struct posdata*
*           OUTPUTS:    struct posdata*
*
*                     (Note: initializes the required S_solpos INPUTS above
*                      to out-of-bounds conditions, forcing the user to
*                      supply the parameters; initializes the OPTIONAL
*                      S_solpos inputs above to nominal values.)
*
*       S_decode      (optional utility for decoding the S_solpos return code)
*           INPUTS:     long integer S_solpos return value, struct posdata*
*           OUTPUTS:    text to stderr
*
*    Usage:
*         In calling program, just after other 'includes', insert:
*
*              #include "solpos00.h"
*
*         Function calls:
*              S_init(struct posdata*)  [optional]
*              .
*              .
*              [set time and location parameters before S_solpos call]
*              .
*              .
*              int retval = S_solpos(struct posdata*)
*              S_decode(int retval, struct posdata*) [optional]
*                  (Note: you should always look at the S_solpos return
*                   value, which contains error codes. S_decode is one option
*                   for examining these codes.  It can also serve as a
*                   template for building your own application-specific
*                   decoder.)
*
*    Martin Rymes
*    National Renewable Energy Laboratory
*    25 March 1998
*
*    27 April 1999 REVISION:  Corrected leap year in S_date.
*    13 January 2000 REVISION:  SMW converted to structure posdata parameter
*                               and subdivided into functions.
*    01 February 2001 REVISION: SMW corrected ecobli calculation 
*                               (changed sign). Error is small (max 0.015 deg
*                               in calculation of declination angle)
*----------------------------------------------------------------------------*/
#include <math.h>
#include <string.h>
#include <stdio.h>
#include "solpos00.h"

/*++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
*
* Structures defined for this module
*
*++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++*/
struct trigdata /* used to pass calculated values locally */
{
    float cd;       /* cosine of the declination */
    float ch;       /* cosine of the hour angle */
    float cl;       /* cosine of the latitude */
    float sd;       /* sine of the declination */
    float sl;       /* sine of the latitude */
};


/*++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
*
* Temporary global variables used only in this file:
*
*++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++*/
  static int  month_days[2][13] = { { 0,   0,  31,  59,  90, 120, 151,
                                       181, 212, 243, 273, 304, 334 },
                                    { 0,   0,  31,  60,  91, 121, 152,
                                       182, 213, 244, 274, 305, 335 } };
                   /* cumulative number of days prior to beginning of month */

  static float degrad = 57.295779513; /* converts from radians to degrees */
  static float raddeg = 0.0174532925; /* converts from degrees to radians */

/*============================================================================
*    Local function prototypes
============================================================================*/
static long int validate ( struct posdata *pdat);
static void dom2doy( struct posdata *pdat );
static void doy2dom( struct posdata *pdat );
static void geometry ( struct posdata *pdat );
static void zen_no_ref ( struct posdata *pdat, struct trigdata *tdat );
static void ssha( struct posdata *pdat, struct trigdata *tdat );
static void sbcf( struct posdata *pdat, struct trigdata *tdat );
static void tst( struct posdata *pdat );
static void srss( struct posdata *pdat );
static void sazm( struct posdata *pdat, struct trigdata *tdat );
static void refrac( struct posdata *pdat );
static void amass( struct posdata *pdat );
static void prime( struct posdata *pdat );
static void etr( struct posdata *pdat );
static void tilt( struct posdata *pdat );
static void localtrig( struct posdata *pdat, struct trigdata *tdat );

/*============================================================================
*    Long integer function S_solpos, adapted from the VAX solar libraries
*
*    This function calculates the apparent solar position and the
*    intensity of the sun (theoretical maximum solar energy) from
*    time and place on Earth.
*
*    Requires (from the struct posdata parameter):
*        Date and time:
*            year
*            daynum   (requirement depends on the S_DOY switch)
*            month    (requirement depends on the S_DOY switch)
*            day      (requirement depends on the S_DOY switch)
*            hour
*            minute
*            second
*            interval  DEFAULT 0
*        Location:
*            latitude
*            longitude
*        Location/time adjuster:
*            timezone
*        Atmospheric pressure and temperature:
*            press     DEFAULT 1013.0 mb
*            temp      DEFAULT 10.0 degrees C
*        Tilt of flat surface that receives solar energy:
*            aspect    DEFAULT 180 (South)
*            tilt      DEFAULT 0 (Horizontal)
*        Function Switch (codes defined in solpos.h)
*            function  DEFAULT S_ALL
*
*    Returns (via the struct posdata parameter):
*        everything defined in the struct posdata in solpos.h.
*----------------------------------------------------------------------------*/
long S_solpos (struct posdata *pdat)
{
  long int retval;

  struct trigdata trigdat, *tdat;

  tdat = &trigdat;   /* point to the structure */

  /* initialize the trig structure */
  tdat->sd = -999.0; /* flag to force calculation of trig data */
  tdat->cd =    1.0;
  tdat->ch =    1.0; /* set the rest of these to something safe */
  tdat->cl =    1.0;
  tdat->sl =    1.0;

  if ((retval = validate ( pdat )) != 0) /* validate the inputs */
    return retval;


  if ( pdat->function & L_DOY )
    doy2dom( pdat );                /* convert input doy to month-day */
  else
    dom2doy( pdat );                /* convert input month-day to doy */

  if ( pdat->function & L_GEOM )
    geometry( pdat );               /* do basic geometry calculations */

  if ( pdat->function & L_ZENETR )  /* etr at non-refracted zenith angle */
    zen_no_ref( pdat, tdat );

  if ( pdat->function & L_SSHA )    /* Sunset hour calculation */
    ssha( pdat, tdat );

  if ( pdat->function & L_SBCF )    /* Shadowband correction factor */
    sbcf( pdat, tdat );

  if ( pdat->function & L_TST )     /* true solar time */
    tst( pdat );

  if ( pdat->function & L_SRSS )    /* sunrise/sunset calculations */
    srss( pdat );

  if ( pdat->function & L_SOLAZM )  /* solar azimuth calculations */
    sazm( pdat, tdat );

  if ( pdat->function & L_REFRAC )  /* atmospheric refraction calculations */
    refrac( pdat );

  if ( pdat->function & L_AMASS )   /* airmass calculations */
    amass( pdat );

  if ( pdat->function & L_PRIME )   /* kt-prime/unprime calculations */
    prime( pdat );

  if ( pdat->function & L_ETR )     /* ETR and ETRN (refracted) */
    etr( pdat );

  if ( pdat->function & L_TILT )    /* tilt calculations */
    tilt( pdat );

    return 0;
}


/*============================================================================
*    Void function S_init
*
*    This function initiates all of the input parameters in the struct
*    posdata passed to S_solpos().  Initialization is either to nominal
*    values or to out of range values, which forces the calling program to
*    specify parameters.
*
*    NOTE: This function is optional if you initialize ALL input parameters
*          in your calling code.  Note that the required parameters of date
*          and location are deliberately initialized out of bounds to force
*          the user to enter real-world values.
*
*    Requires: Pointer to a posdata structure, members of which are
*           initialized.
*
*    Returns: Void
*----------------------------------------------------------------------------*/
void S_init(struct posdata *pdat)
{
  pdat->day       =    -99;   /* Day of month (May 27 = 27, etc.) */
  pdat->daynum    =   -999;   /* Day number (day of year; Feb 1 = 32 ) */
  pdat->hour      =    -99;   /* Hour of day, 0 - 23 */
  pdat->minute    =    -99;   /* Minute of hour, 0 - 59 */
  pdat->month     =    -99;   /* Month number (Jan = 1, Feb = 2, etc.) */
  pdat->second    =    -99;   /* Second of minute, 0 - 59 */
  pdat->year      =    -99;   /* 4-digit year */
  pdat->interval  =      0;   /* instantaneous measurement interval */
  pdat->aspect    =  180.0;   /* Azimuth of panel surface (direction it
                                    faces) N=0, E=90, S=180, W=270 */
  pdat->latitude  =  -99.0;   /* Latitude, degrees north (south negative) */
  pdat->longitude = -999.0;   /* Longitude, degrees east (west negative) */
  pdat->press     = 1013.0;   /* Surface pressure, millibars */
  pdat->solcon    = 1367.0;   /* Solar constant, 1367 W/sq m */
  pdat->temp      =   15.0;   /* Ambient dry-bulb temperature, degrees C */
  pdat->tilt      =    0.0;   /* Degrees tilt from horizontal of panel */
  pdat->timezone  =  -99.0;   /* Time zone, east (west negative). */
  pdat->sbwid     =    7.6;   /* Eppley shadow band width */
  pdat->sbrad     =   31.7;   /* Eppley shadow band radius */
  pdat->sbsky     =   0.04;   /* Drummond factor for partly cloudy skies */
  pdat->function  =  S_ALL;   /* compute all parameters */
}


/*============================================================================
*    Local long int function validate
*
*    Validates the input parameters
*----------------------------------------------------------------------------*/
static long int validate ( struct posdata *pdat)
{

  long int retval = 0;  /* start with no errors */

  /* No absurd dates, please. */
  if ( pdat->function & L_GEOM )
  {
    if ( (pdat->year < 1950) || (pdat->year > 2050) ) /* limits of algoritm */
      retval |= (1L << S_YEAR_ERROR);
    if ( !(pdat->function & S_DOY) && ((pdat->month < 1) || (pdat->month > 12)))
      retval |= (1L << S_MONTH_ERROR);
    if ( !(pdat->function & S_DOY) && ((pdat->day < 1) || (pdat->day > 31)) )
      retval |= (1L << S_DAY_ERROR);
    if ( (pdat->function & S_DOY) && ((pdat->daynum < 1) || (pdat->daynum > 366)) )
      retval |= (1L << S_DOY_ERROR);

    /* No absurd times, please. */
    if ( (pdat->hour < 0) || (pdat->hour > 24) )
      retval |= (1L << S_HOUR_ERROR);
    if ( (pdat->minute < 0) || (pdat->minute > 59) )
      retval |= (1L << S_MINUTE_ERROR);
    if ( (pdat->second < 0) || (pdat->second > 59) )
      retval |= (1L << S_SECOND_ERROR);
    if ( (pdat->hour == 24) && (pdat->minute > 0) ) /* no more than 24 hrs */
      retval |= ( (1L << S_HOUR_ERROR) | (1L << S_MINUTE_ERROR) );
    if ( (pdat->hour == 24) && (pdat->second > 0) ) /* no more than 24 hrs */
      retval |= ( (1L << S_HOUR_ERROR) | (1L << S_SECOND_ERROR) );
    if ( fabs (pdat->timezone) > 12.0 )
      retval |= (1L << S_TZONE_ERROR);
    if ( (pdat->interval < 0) || (pdat->interval > 28800) )
      retval |= (1L << S_INTRVL_ERROR);

    /* No absurd locations, please. */
    if ( fabs (pdat->longitude) > 180.0 )
      retval |= (1L << S_LON_ERROR);
    if ( fabs (pdat->latitude) > 90.0 )
      retval |= (1L << S_LAT_ERROR);
  }

  /* No silly temperatures or pressures, please. */
  if ( (pdat->function & L_REFRAC) && (fabs (pdat->temp) > 100.0) )
    retval |= (1L << S_TEMP_ERROR);
  if ( (pdat->function & L_REFRAC) &&
    (pdat->press < 0.0) || (pdat->press > 2000.0) )
    retval |= (1L << S_PRESS_ERROR);

  /* No out of bounds tilts, please */
  if ( (pdat->function & L_TILT) && (fabs (pdat->tilt) > 180.0) )
    retval |= (1L << S_TILT_ERROR);
  if ( (pdat->function & L_TILT) && (fabs (pdat->aspect) > 360.0) )
    retval |= (1L << S_ASPECT_ERROR);

  /* No oddball shadowbands, please */
  if ( (pdat->function & L_SBCF) &&
       (pdat->sbwid < 1.0) || (pdat->sbwid > 100.0) )
    retval |= (1L << S_SBWID_ERROR);
  if ( (pdat->function & L_SBCF) &&
       (pdat->sbrad < 1.0) || (pdat->sbrad > 100.0) )
    retval |= (1L << S_SBRAD_ERROR);
  if ( (pdat->function & L_SBCF) && ( fabs (pdat->sbsky) > 1.0) )
    retval |= (1L << S_SBSKY_ERROR);

  return retval;
}


/*============================================================================
*    Local Void function dom2doy
*
*    Converts day-of-month to day-of-year
*
*    Requires (from struct posdata parameter):
*            year
*            month
*            day
*
*    Returns (via the struct posdata parameter):
*            year
*            daynum
*----------------------------------------------------------------------------*/
static void dom2doy( struct posdata *pdat )
{
  pdat->daynum = pdat->day + month_days[0][pdat->month];

  /* (adjust for leap year) */
  if ( ((pdat->year % 4) == 0) &&
         ( ((pdat->year % 100) != 0) || ((pdat->year % 400) == 0) ) &&
         (pdat->month > 2) )
      pdat->daynum += 1;
}


/*============================================================================
*    Local void function doy2dom
*
*    This function computes the month/day from the day number.
*
*    Requires (from struct posdata parameter):
*        Year and day number:
*            year
*            daynum
*
*    Returns (via the struct posdata parameter):
*            year
*            month
*            day
*----------------------------------------------------------------------------*/
static void doy2dom(struct posdata *pdat)
{
  int  imon;  /* Month (month_days) array counter */
  int  leap;  /* leap year switch */

    /* Set the leap year switch */
    if ( ((pdat->year % 4) == 0) &&
         ( ((pdat->year % 100) != 0) || ((pdat->year % 400) == 0) ) )
        leap = 1;
    else
        leap = 0;

    /* Find the month */
    imon = 12;
    while ( pdat->daynum <= month_days [leap][imon] )
        --imon;

    /* Set the month and day of month */
    pdat->month = imon;
    pdat->day   = pdat->daynum - month_days[leap][imon];
}


/*============================================================================
*    Local Void function geometry
*
*    Does the underlying geometry for a given time and location
*----------------------------------------------------------------------------*/
static void geometry ( struct posdata *pdat )
{
  float bottom;      /* denominator (bottom) of the fraction */
  float c2;          /* cosine of d2 */
  float cd;          /* cosine of the day angle or delination */
  float d2;          /* pdat->dayang times two */
  float delta;       /* difference between current year and 1949 */
  float s2;          /* sine of d2 */
  float sd;          /* sine of the day angle */
  float top;         /* numerator (top) of the fraction */
  int   leap;        /* leap year counter */

  /* Day angle */
      /*  Iqbal, M.  1983.  An Introduction to Solar Radiation.
            Academic Press, NY., page 3 */
     pdat->dayang = 360.0 * ( pdat->daynum - 1 ) / 365.0;

    /* Earth radius vector * solar constant = solar energy */
        /*  Spencer, J. W.  1971.  Fourier series representation of the
            position of the sun.  Search 2 (5), page 172 */
    sd     = sin (raddeg * pdat->dayang);
    cd     = cos (raddeg * pdat->dayang);
    d2     = 2.0 * pdat->dayang;
    c2     = cos (raddeg * d2);
    s2     = sin (raddeg * d2);

    pdat->erv  = 1.000110 + 0.034221 * cd + 0.001280 * sd;
    pdat->erv  += 0.000719 * c2 + 0.000077 * s2;

    /* Universal Coordinated (Greenwich standard) time */
        /*  Michalsky, J.  1988.  The Astronomical Almanac's algorithm for
            approximate solar position (1950-2050).  Solar Energy 40 (3),
            pp. 227-235. */
    pdat->utime =
        pdat->hour * 3600.0 +
        pdat->minute * 60.0 +
        pdat->second -
        (float)pdat->interval / 2.0;
    pdat->utime = pdat->utime / 3600.0 - pdat->timezone;

    /* Julian Day minus 2,400,000 days (to eliminate roundoff errors) */
        /*  Michalsky, J.  1988.  The Astronomical Almanac's algorithm for
            approximate solar position (1950-2050).  Solar Energy 40 (3),
            pp. 227-235. */

    /* No adjustment for century non-leap years since this function is
       bounded by 1950 - 2050 */
    delta    = pdat->year - 1949;
    leap     = (int) ( delta / 4.0 );
    pdat->julday =
        32916.5 + delta * 365.0 + leap + pdat->daynum + pdat->utime / 24.0;

    /* Time used in the calculation of ecliptic coordinates */
    /* Noon 1 JAN 2000 = 2,400,000 + 51,545 days Julian Date */
        /*  Michalsky, J.  1988.  The Astronomical Almanac's algorithm for
            approximate solar position (1950-2050).  Solar Energy 40 (3),
            pp. 227-235. */
    pdat->ectime = pdat->julday - 51545.0;

    /* Mean longitude */
        /*  Michalsky, J.  1988.  The Astronomical Almanac's algorithm for
            approximate solar position (1950-2050).  Solar Energy 40 (3),
            pp. 227-235. */
    pdat->mnlong  = 280.460 + 0.9856474 * pdat->ectime;

    /* (dump the multiples of 360, so the answer is between 0 and 360) */
    pdat->mnlong -= 360.0 * (int) ( pdat->mnlong / 360.0 );
    if ( pdat->mnlong < 0.0 )
        pdat->mnlong += 360.0;

    /* Mean anomaly */
        /*  Michalsky, J.  1988.  The Astronomical Almanac's algorithm for
            approximate solar position (1950-2050).  Solar Energy 40 (3),
            pp. 227-235. */
    pdat->mnanom  = 357.528 + 0.9856003 * pdat->ectime;

    /* (dump the multiples of 360, so the answer is between 0 and 360) */
    pdat->mnanom -= 360.0 * (int) ( pdat->mnanom / 360.0 );
    if ( pdat->mnanom < 0.0 )
        pdat->mnanom += 360.0;

    /* Ecliptic longitude */
        /*  Michalsky, J.  1988.  The Astronomical Almanac's algorithm for
            approximate solar position (1950-2050).  Solar Energy 40 (3),
            pp. 227-235. */
    pdat->eclong  = pdat->mnlong + 1.915 * sin ( pdat->mnanom * raddeg ) +
                    0.020 * sin ( 2.0 * pdat->mnanom * raddeg );

    /* (dump the multiples of 360, so the answer is between 0 and 360) */
    pdat->eclong -= 360.0 * (int) ( pdat->eclong / 360.0 );
    if ( pdat->eclong < 0.0 )
        pdat->eclong += 360.0;

    /* Obliquity of the ecliptic */
        /*  Michalsky, J.  1988.  The Astronomical Almanac's algorithm for
            approximate solar position (1950-2050).  Solar Energy 40 (3),
            pp. 227-235. */

    /* 02 Feb 2001 SMW corrected sign in the following line */
/*  pdat->ecobli = 23.439 + 4.0e-07 * pdat->ectime;     */
    pdat->ecobli = 23.439 - 4.0e-07 * pdat->ectime;

    /* Declination */
        /*  Michalsky, J.  1988.  The Astronomical Almanac's algorithm for
            approximate solar position (1950-2050).  Solar Energy 40 (3),
            pp. 227-235. */
    pdat->declin = degrad * asin ( sin (pdat->ecobli * raddeg) *
                               sin (pdat->eclong * raddeg) );

    /* Right ascension */
        /*  Michalsky, J.  1988.  The Astronomical Almanac's algorithm for
            approximate solar position (1950-2050).  Solar Energy 40 (3),
            pp. 227-235. */
    top      =  cos ( raddeg * pdat->ecobli ) * sin ( raddeg * pdat->eclong );
    bottom   =  cos ( raddeg * pdat->eclong );

    pdat->rascen =  degrad * atan2 ( top, bottom );

    /* (make it a positive angle) */
    if ( pdat->rascen < 0.0 )
        pdat->rascen += 360.0;

    /* Greenwich mean sidereal time */
        /*  Michalsky, J.  1988.  The Astronomical Almanac's algorithm for
            approximate solar position (1950-2050).  Solar Energy 40 (3),
            pp. 227-235. */
    pdat->gmst  = 6.697375 + 0.0657098242 * pdat->ectime + pdat->utime;

    /* (dump the multiples of 24, so the answer is between 0 and 24) */
    pdat->gmst -= 24.0 * (int) ( pdat->gmst / 24.0 );
    if ( pdat->gmst < 0.0 )
        pdat->gmst += 24.0;

    /* Local mean sidereal time */
        /*  Michalsky, J.  1988.  The Astronomical Almanac's algorithm for
            approximate solar position (1950-2050).  Solar Energy 40 (3),
            pp. 227-235. */
    pdat->lmst  = pdat->gmst * 15.0 + pdat->longitude;

    /* (dump the multiples of 360, so the answer is between 0 and 360) */
    pdat->lmst -= 360.0 * (int) ( pdat->lmst / 360.0 );
    if ( pdat->lmst < 0.)
        pdat->lmst += 360.0;

    /* Hour angle */
        /*  Michalsky, J.  1988.  The Astronomical Almanac's algorithm for
            approximate solar position (1950-2050).  Solar Energy 40 (3),
            pp. 227-235. */
    pdat->hrang = pdat->lmst - pdat->rascen;

    /* (force it between -180 and 180 degrees) */
    if ( pdat->hrang < -180.0 )
        pdat->hrang += 360.0;
    else if ( pdat->hrang > 180.0 )
        pdat->hrang -= 360.0;
}


/*============================================================================
*    Local Void function zen_no_ref
*
*    ETR solar zenith angle
*       Iqbal, M.  1983.  An Introduction to Solar Radiation.
*            Academic Press, NY., page 15
*----------------------------------------------------------------------------*/
static void zen_no_ref ( struct posdata *pdat, struct trigdata *tdat )
{
  float cz;          /* cosine of the solar zenith angle */

    localtrig( pdat, tdat );
    cz = tdat->sd * tdat->sl + tdat->cd * tdat->cl * tdat->ch;

    /* (watch out for the roundoff errors) */
    if ( fabs (cz) > 1.0 ) {
        if ( cz >= 0.0 )
            cz =  1.0;
        else
            cz = -1.0;
    }

    pdat->zenetr   = acos ( cz ) * degrad;

    /* (limit the degrees below the horizon to 9 [+90 -> 99]) */
    if ( pdat->zenetr > 99.0 )
        pdat->zenetr = 99.0;

    pdat->elevetr = 90.0 - pdat->zenetr;
}


/*============================================================================
*    Local Void function ssha
*
*    Sunset hour angle, degrees
*       Iqbal, M.  1983.  An Introduction to Solar Radiation.
*            Academic Press, NY., page 16
*----------------------------------------------------------------------------*/
static void ssha( struct posdata *pdat, struct trigdata *tdat )
{
  float cssha;       /* cosine of the sunset hour angle */
  float cdcl;        /* ( cd * cl ) */

    localtrig( pdat, tdat );
    cdcl    = tdat->cd * tdat->cl;

    if ( fabs ( cdcl ) >= 0.001 ) {
        cssha = -tdat->sl * tdat->sd / cdcl;

        /* This keeps the cosine from blowing on roundoff */
        if ( cssha < -1.0  )
            pdat->ssha = 180.0;
        else if ( cssha > 1.0 )
            pdat->ssha = 0.0;
        else
            pdat->ssha = degrad * acos ( cssha );
    }
    else if ( ((pdat->declin >= 0.0) && (pdat->latitude > 0.0 )) ||
              ((pdat->declin <  0.0) && (pdat->latitude < 0.0 )) )
        pdat->ssha = 180.0;
    else
        pdat->ssha = 0.0;
}


/*============================================================================
*    Local Void function sbcf
*
*    Shadowband correction factor
*       Drummond, A. J.  1956.  A contribution to absolute pyrheliometry.
*            Q. J. R. Meteorol. Soc. 82, pp. 481-493
*----------------------------------------------------------------------------*/
static void sbcf( struct posdata *pdat, struct trigdata *tdat )
{
  float p, t1, t2;   /* used to compute sbcf */

    localtrig( pdat, tdat );
    p       = 0.6366198 * pdat->sbwid / pdat->sbrad * pow (tdat->cd,3);
    t1      = tdat->sl * tdat->sd * pdat->ssha * raddeg;
    t2      = tdat->cl * tdat->cd * sin ( pdat->ssha * raddeg );
    pdat->sbcf = pdat->sbsky + 1.0 / ( 1.0 - p * ( t1 + t2 ) );

}


/*============================================================================
*    Local Void function tst
*
*    TST -> True Solar Time = local standard time + TSTfix, time
*      in minutes from midnight.
*        Iqbal, M.  1983.  An Introduction to Solar Radiation.
*            Academic Press, NY., page 13
*----------------------------------------------------------------------------*/
static void tst( struct posdata *pdat )
{
    pdat->tst    = ( 180.0 + pdat->hrang ) * 4.0;
    pdat->tstfix =
        pdat->tst -
        (float)pdat->hour * 60.0 -
        pdat->minute -
        (float)pdat->second / 60.0 +
        (float)pdat->interval / 120.0; /* add back half of the interval */

    /* bound tstfix to this day */
    while ( pdat->tstfix >  720.0 )
        pdat->tstfix -= 1440.0;
    while ( pdat->tstfix < -720.0 )
        pdat->tstfix += 1440.0;

    pdat->eqntim =
        pdat->tstfix + 60.0 * pdat->timezone - 4.0 * pdat->longitude;

}


/*============================================================================
*    Local Void function srss
*
*    Sunrise and sunset times (minutes from midnight)
*----------------------------------------------------------------------------*/
static void srss( struct posdata *pdat )
{
    if ( pdat->ssha <= 1.0 ) {
        pdat->sretr   =  2999.0;
        pdat->ssetr   = -2999.0;
    }
    else if ( pdat->ssha >= 179.0 ) {
        pdat->sretr   = -2999.0;
        pdat->ssetr   =  2999.0;
    }
    else {
        pdat->sretr   = 720.0 - 4.0 * pdat->ssha - pdat->tstfix;
        pdat->ssetr   = 720.0 + 4.0 * pdat->ssha - pdat->tstfix;
    }
}


/*============================================================================
*    Local Void function sazm
*
*    Solar azimuth angle
*       Iqbal, M.  1983.  An Introduction to Solar Radiation.
*            Academic Press, NY., page 15
*----------------------------------------------------------------------------*/
static void sazm( struct posdata *pdat, struct trigdata *tdat )
{
  float ca;          /* cosine of the solar azimuth angle */
  float ce;          /* cosine of the solar elevation */
  float cecl;        /* ( ce * cl ) */
  float se;          /* sine of the solar elevation */

    localtrig( pdat, tdat );
    ce         = cos ( raddeg * pdat->elevetr );
    se         = sin ( raddeg * pdat->elevetr );

    pdat->azim     = 180.0;
    cecl       = ce * tdat->cl;
    if ( fabs ( cecl ) >= 0.001 ) {
        ca     = ( se * tdat->sl - tdat->sd ) / cecl;
        if ( ca > 1.0 )
            ca = 1.0;
        else if ( ca < -1.0 )
            ca = -1.0;

        pdat->azim = 180.0 - acos ( ca ) * degrad;
        if ( pdat->hrang > 0 )
            pdat->azim  = 360.0 - pdat->azim;
    }
}


/*============================================================================
*    Local Int function refrac
*
*    Refraction correction, degrees
*        Zimmerman, John C.  1981.  Sun-pointing programs and their
*            accuracy.
*            SAND81-0761, Experimental Systems Operation Division 4721,
*            Sandia National Laboratories, Albuquerque, NM.
*----------------------------------------------------------------------------*/
static void refrac( struct posdata *pdat )
{
  float prestemp;    /* temporary pressure/temperature correction */
  float refcor;      /* temporary refraction correction */
  float tanelev;     /* tangent of the solar elevation angle */

    /* If the sun is near zenith, the algorithm bombs; refraction near 0 */
    if ( pdat->elevetr > 85.0 )
        refcor = 0.0;

    /* Otherwise, we have refraction */
    else {
        tanelev = tan ( raddeg * pdat->elevetr );
        if ( pdat->elevetr >= 5.0 )
            refcor  = 58.1 / tanelev -
                      0.07 / ( pow (tanelev,3) ) +
                      0.000086 / ( pow (tanelev,5) );
        else if ( pdat->elevetr >= -0.575 )
            refcor  = 1735.0 +
                      pdat->elevetr * ( -518.2 + pdat->elevetr * ( 103.4 +
                      pdat->elevetr * ( -12.79 + pdat->elevetr * 0.711 ) ) );
        else
            refcor  = -20.774 / tanelev;

        prestemp    =
            ( pdat->press * 283.0 ) / ( 1013.0 * ( 273.0 + pdat->temp ) );
        refcor     *= prestemp / 3600.0;
    }

    /* Refracted solar elevation angle */
    pdat->elevref = pdat->elevetr + refcor;

    /* (limit the degrees below the horizon to 9) */
    if ( pdat->elevref < -9.0 )
        pdat->elevref = -9.0;

    /* Refracted solar zenith angle */
    pdat->zenref  = 90.0 - pdat->elevref;
    pdat->coszen  = cos( raddeg * pdat->zenref );
}


/*============================================================================
*    Local Void function  amass
*
*    Airmass
*       Kasten, F. and Young, A.  1989.  Revised optical air mass
*            tables and approximation formula.  Applied Optics 28 (22),
*            pp. 4735-4738
*----------------------------------------------------------------------------*/
static void amass( struct posdata *pdat )
{
    if ( pdat->zenref > 93.0 )
    {
        pdat->amass   = -1.0;
        pdat->ampress = -1.0;
    }
    else
    {
        pdat->amass =
            1.0 / ( cos (raddeg * pdat->zenref) + 0.50572 *
            pow ((96.07995 - pdat->zenref),-1.6364) );

        pdat->ampress   = pdat->amass * pdat->press / 1013.0;
    }
}


/*============================================================================
*    Local Void function prime
*
*    Prime and Unprime
*    Prime  converts Kt to normalized Kt', etc.
*       Unprime deconverts Kt' to Kt, etc.
*            Perez, R., P. Ineichen, Seals, R., & Zelenka, A.  1990.  Making
*            full use of the clearness index for parameterizing hourly
*            insolation conditions. Solar Energy 45 (2), pp. 111-114
*----------------------------------------------------------------------------*/
static void prime( struct posdata *pdat )
{
    pdat->unprime = 1.031 * exp ( -1.4 / ( 0.9 + 9.4 / pdat->amass ) ) + 0.1;
    pdat->prime   = 1.0 / pdat->unprime;
}


/*============================================================================
*    Local Void function etr
*
*    Extraterrestrial (top-of-atmosphere) solar irradiance
*----------------------------------------------------------------------------*/
static void etr( struct posdata *pdat )
{
    if ( pdat->coszen > 0.0 ) {
        pdat->etrn = pdat->solcon * pdat->erv;
        pdat->etr  = pdat->etrn * pdat->coszen;
    }
    else {
        pdat->etrn = 0.0;
        pdat->etr  = 0.0;
    }
}


/*============================================================================
*    Local Void function localtrig
*
*    Does trig on internal variable used by several functions
*----------------------------------------------------------------------------*/
static void localtrig( struct posdata *pdat, struct trigdata *tdat )
{
/* define masks to prevent calculation of uninitialized variables */
#define SD_MASK ( L_ZENETR | L_SSHA | S_SBCF | S_SOLAZM )
#define SL_MASK ( L_ZENETR | L_SSHA | S_SBCF | S_SOLAZM )
#define CL_MASK ( L_ZENETR | L_SSHA | S_SBCF | S_SOLAZM )
#define CD_MASK ( L_ZENETR | L_SSHA | S_SBCF )
#define CH_MASK ( L_ZENETR )

    if ( tdat->sd < -900.0 )  /* sd was initialized -999 as flag */
    {
      tdat->sd = 1.0;  /* reflag as having completed calculations */
      if ( pdat->function | CD_MASK )
        tdat->cd = cos ( raddeg * pdat->declin );
      if ( pdat->function | CH_MASK )
        tdat->ch = cos ( raddeg * pdat->hrang );
      if ( pdat->function | CL_MASK )
        tdat->cl = cos ( raddeg * pdat->latitude );
      if ( pdat->function | SD_MASK )
        tdat->sd = sin ( raddeg * pdat->declin );
      if ( pdat->function | SL_MASK )
        tdat->sl = sin ( raddeg * pdat->latitude );
    }
}


/*============================================================================
*    Local Void function tilt
*
*    ETR on a tilted surface
*----------------------------------------------------------------------------*/
static void tilt( struct posdata *pdat )
{
  float ca;          /* cosine of the solar azimuth angle */
  float cp;          /* cosine of the panel aspect */
  float ct;          /* cosine of the panel tilt */
  float sa;          /* sine of the solar azimuth angle */
  float sp;          /* sine of the panel aspect */
  float st;          /* sine of the panel tilt */
  float sz;          /* sine of the refraction corrected solar zenith angle */


    /* Cosine of the angle between the sun and a tipped flat surface,
       useful for calculating solar energy on tilted surfaces */
    ca      = cos ( raddeg * pdat->azim );
    cp      = cos ( raddeg * pdat->aspect );
    ct      = cos ( raddeg * pdat->tilt );
    sa      = sin ( raddeg * pdat->azim );
    sp      = sin ( raddeg * pdat->aspect );
    st      = sin ( raddeg * pdat->tilt );
    sz      = sin ( raddeg * pdat->zenref );
    pdat->cosinc  = pdat->coszen * ct + sz * st * ( ca * cp + sa * sp );

    if ( pdat->cosinc > 0.0 )
        pdat->etrtilt = pdat->etrn * pdat->cosinc;
    else
        pdat->etrtilt = 0.0;

}


/*============================================================================
*    Void function S_decode
*
*    This function decodes the error codes from S_solpos return value
*
*    Requires the long integer return value from S_solpos
*
*    Returns descriptive text to stderr
*----------------------------------------------------------------------------*/
void S_decode(long code, struct posdata *pdat)
{
  if ( code & (1L << S_YEAR_ERROR) )
    fprintf(stderr, "S_decode ==> Please fix the year: %d [1950-2050]\n",
      pdat->year);
  if ( code & (1L << S_MONTH_ERROR) )
    fprintf(stderr, "S_decode ==> Please fix the month: %d\n",
      pdat->month);
  if ( code & (1L << S_DAY_ERROR) )
    fprintf(stderr, "S_decode ==> Please fix the day-of-month: %d\n",
      pdat->day);
  if ( code & (1L << S_DOY_ERROR) )
    fprintf(stderr, "S_decode ==> Please fix the day-of-year: %d\n",
      pdat->daynum);
  if ( code & (1L << S_HOUR_ERROR) )
    fprintf(stderr, "S_decode ==> Please fix the hour: %d\n",
      pdat->hour);
  if ( code & (1L << S_MINUTE_ERROR) )
    fprintf(stderr, "S_decode ==> Please fix the minute: %d\n",
      pdat->minute);
  if ( code & (1L << S_SECOND_ERROR) )
    fprintf(stderr, "S_decode ==> Please fix the second: %d\n",
      pdat->second);
  if ( code & (1L << S_TZONE_ERROR) )
    fprintf(stderr, "S_decode ==> Please fix the time zone: %f\n",
      pdat->timezone);
  if ( code & (1L << S_INTRVL_ERROR) )
    fprintf(stderr, "S_decode ==> Please fix the interval: %d\n",
      pdat->interval);
  if ( code & (1L << S_LAT_ERROR) )
    fprintf(stderr, "S_decode ==> Please fix the latitude: %f\n",
      pdat->latitude);
  if ( code & (1L << S_LON_ERROR) )
    fprintf(stderr, "S_decode ==> Please fix the longitude: %f\n",
      pdat->longitude);
  if ( code & (1L << S_TEMP_ERROR) )
    fprintf(stderr, "S_decode ==> Please fix the temperature: %f\n",
      pdat->temp);
  if ( code & (1L << S_PRESS_ERROR) )
    fprintf(stderr, "S_decode ==> Please fix the pressure: %f\n",
      pdat->press);
  if ( code & (1L << S_TILT_ERROR) )
    fprintf(stderr, "S_decode ==> Please fix the tilt: %f\n",
      pdat->tilt);
  if ( code & (1L << S_ASPECT_ERROR) )
    fprintf(stderr, "S_decode ==> Please fix the aspect: %f\n",
      pdat->aspect);
  if ( code & (1L << S_SBWID_ERROR) )
    fprintf(stderr, "S_decode ==> Please fix the shadowband width: %f\n",
      pdat->sbwid);
  if ( code & (1L << S_SBRAD_ERROR) )
    fprintf(stderr, "S_decode ==> Please fix the shadowband radius: %f\n",
      pdat->sbrad);
  if ( code & (1L << S_SBSKY_ERROR) )
    fprintf(stderr, "S_decode ==> Please fix the shadowband sky factor: %f\n",
      pdat->sbsky);
}