Friday, 22 March 2013

Calculate Sunrise and Sunset

More than a year ago when I was building Weather Dog which is a 3D weather app for mobile I realized that the weather API provided to me didn't include the times for sunrise and sunset.
After a quick search I found this simple but really useful algorithm which I simply translated to UnityScript (Javascript):
static function CalculateSunRiseSunSet(date: System.DateTime, lat: float, lng: float, offset: float)
{
 // calc the day of the year
 var N1: float = Mathf.Floor(275.0 * date.Month /9.0);
 var N2: float = Mathf.Floor((date.Month +9.0)/12.0);
 var N3: float = 1 + Mathf.Floor((date.Year - 4 * Mathf.Floor(date.Year / 4) + 2) / 3);
 var N = N1 - (N2 * N3) + date.Day - 30;
 
 // convert the longitude to hour value and calculate an approximate time

 var lngHour: float = lng / 15.0;

 var tRise = N + ((6 - lngHour) / 24.0);
 var tSet = N + ((18 - lngHour) / 24.0);
  
 // calculate the Sun's mean anomaly

 var MRise = (0.9856 * tRise) - 3.289;
 var MSet = (0.9856 * tSet) - 3.289;

 // calculate the Sun's true longitude

 var LRise = MRise + (1.916 * Mathf.Sin(Mathf.PI/180.0 *MRise)) + (0.020 * Mathf.Sin(Mathf.PI/180.0 *2 * MRise)) + 282.634;
 var LSet = MSet + (1.916 * Mathf.Sin(Mathf.PI/180.0 *MSet)) + (0.020 * Mathf.Sin(Mathf.PI/180.0 *2 * MSet)) + 282.634;
 
 if(LRise < 0)
 {
  LRise += 360;
 }
 if(LSet < 0)
 {
  LSet += 360;
 }
 if(LRise >= 360)
 {
  LRise -= 360;
 }
 if(LSet >= 360)
 {
  LSet -= 360;
 }
 // calculate the Sun's right ascension

 var RARise = (180.0/Mathf.PI) * Mathf.Atan(0.91764 * Mathf.Tan(Mathf.PI/180.0 *LRise));
 var RASet = (180.0/Mathf.PI) * Mathf.Atan(0.91764 * Mathf.Tan(Mathf.PI/180.0 *LSet));

 if(RARise < 0)
 {
  RARise += 360;
 }
 if(RASet < 0)
 {
  RASet += 360;
 }
 if(RARise >= 360)
 {
  RARise -= 360;
 }
 if(RASet >= 360)
 {
  RASet -= 360;
 }
 
 // right ascension value needs to be in the same quadrant as L

 var LquadrantRise  = (Mathf.Floor( LRise/90.0)) * 90;
 var RAquadrantRise = (Mathf.Floor(RARise/90.0)) * 90;
 RARise = RARise + (LquadrantRise - RAquadrantRise);
 var LquadrantSet  = (Mathf.Floor( LSet/90.0)) * 90;
 var RAquadrantSet = (Mathf.Floor(RASet/90.0)) * 90;
 RASet = RASet + (LquadrantSet - RAquadrantSet);
 
 //right ascension value needs to be converted into hours

 RARise = RARise / 15.0;
 RASet = RASet / 15.0;
 
 //calculate the Sun's declination

 var sinDecRise = 0.39782 * Mathf.Sin(Mathf.PI/180.0 *LRise);
 var cosDecRise = Mathf.Cos(Mathf.PI/180.0 *(180.0/Mathf.PI) *Mathf.Asin(sinDecRise));
 var sinDecSet = 0.39782 * Mathf.Sin(Mathf.PI/180.0 *LSet);
 var cosDecSet = Mathf.Cos(Mathf.PI/180.0 *(180.0/Mathf.PI) *Mathf.Asin(sinDecSet));
 
 //calculate the Sun's local hour angle
 var cosHRise = (Mathf.Cos(Mathf.PI/180.0 *90.5) - (sinDecRise * Mathf.Sin(Mathf.PI/180.0 *lat))) / (cosDecRise * Mathf.Cos(Mathf.PI/180.0 *lat));
 var cosHSet = (Mathf.Cos(Mathf.PI/180.0 *90.5) - (sinDecSet * Mathf.Sin(Mathf.PI/180.0 *lat))) / (cosDecSet * Mathf.Cos(Mathf.PI/180.0 *lat));
 if (cosHRise >  1)
  return;
 if (cosHSet < -1)
  return;
  
 // finish calculating H and convert into hours

 var HRise =(360 - ( (180.0/Mathf.PI) *Mathf.Acos(cosHRise)));
 var HSet = (180.0/Mathf.PI) *Mathf.Acos(cosHSet);
 HRise = HRise / 15.0;
 HSet = HSet / 15.0;
  
 //calculate local mean time of rising/setting

 var TRise = HRise + RARise - (0.06571 * tRise) - 6.622;
 var TSet = HSet + RASet - (0.06571 * tSet) - 6.622;
 
 // adjust back to UTC

 var UTRise = TRise - lngHour;
 var UTSet = TSet - lngHour;
 if(UTRise < 0)
 {
  UTRise += 24;
 }
 else if(UTRise >= 24)
 {
  UTRise -= 24;
 }
 if(UTSet < 0)
 {
  UTSet += 24;
 }
 else if(UTSet >= 24)
 {
  UTSet -= 24;
 }
 
 // convert UT value to local time zone of latitude/longitude

 var RiseTime: float = UTRise + offset;
 var SetTime: float = UTSet + offset;
 
 if(RiseTime < 0)
 {
  RiseTime += 24;
 }
 else if(RiseTime >= 24)
 {
  RiseTime -= 24;
 }
 
 if(SetTime < 0)
 {
  SetTime += 24;
 }
 else if(SetTime >= 24)
 {
  SetTime -= 24;
 }

        // now you can use the RiseTime & SetTime as you wish
} 

3 comments:

  1. if(LRise > 360)
    {
    LRise -= 360;
    Not accurate code. The more correct is as follows:
    if(LRise >= 360.)
    {
    LRise -= 360.;

    The same thing is with 24.

    ReplyDelete
    Replies
    1. Thanks! In my haste I didn't notice

      Delete