太阳路径的计算

我正在编写几种计算太阳穿过特定点的路径所需的方法。我使用两个不同的源编写代码进行计算，但都没有产生所需的结果。来源是：http://www.pveducation.org/pvcdrom/properties-of-sunlight/suns-position and http://www.esrl.noaa.gov/gmd/grad/solcalc/solareqns.PDF

注意：度数转弧分为 Deg * 60 分钟。

1. localSolartime：我已将经度转换为“分钟”，从 localStandardTimeMeridian 方法派生的当地标准时间子午线（lstm）返回一个以“分钟”为单位的值，而equationOfTime也以“分钟”为单位返回。使用 pveducation 中的方程，我计算了时间校正，该校正考虑了给定时区内的微小时间变化。当我将此结果和 localTime（均以分钟为单位）应用于当地太阳时 (lst) 方程时，结果为 676.515（此时），这对我来说没有任何意义。据我了解，当地太阳时代表相对于太阳的时间，当太阳在当地天空中处于最高点时，被认为是太阳正午。 676.515 没有意义。有谁明白可能是什么原因造成的。

2. HourAngle：我希望一旦修复了 localSolarTime 方法，就不需要纠正这个问题。

我选择华盛顿特区作为纬度和经度。天顶角和方位角读数都应该是正值，对于我所在的区域，此时分别为 66 和 201。

public class PathOfSun {
    static LocalTime localTime = LocalTime.now();
    static double dcLat = 38.83;
    static double dcLong =  -77.02;
    static DecimalFormat df = new DecimalFormat("#.0");

    public static void main(String [] args) {
        int day = dayOfYear();
        double equationOfTime = equationOfTime(day);
        double lstm = localTimeMeridian();
        double lst = localSolarTime(equationOfTime, dcLong, lstm);
        double declination = declination(day);
        double hourAngle = hourAngle(lst);

        double zenith = zenith(dcLat, declination, hourAngle);
        double azimuth = azimuth(dcLong, declination, zenith, hourAngle); 

    }

    //Longitude of timezone meridian
    public static double localTimeMeridian() {
        TimeZone gmt = TimeZone.getTimeZone("GMT");
        TimeZone est = TimeZone.getTimeZone("EST");
        int td = gmt.getRawOffset() - est.getRawOffset();
        double localStandardTimeMeridian = 15 * (td/(1000*60*60)); //convert td to hours
        //System.out.println("Local Time Meridian: " + localStandardTimeMeridian);
        return localStandardTimeMeridian;
    }

    //Get the number of days since Jan. 1
    public static int dayOfYear() {
        Calendar localCalendar = Calendar.getInstance(TimeZone.getDefault());
        int dayOfYear = localCalendar.get(Calendar.DAY_OF_YEAR); 
        //System.out.println("Day: " + dayOfYear);
        return dayOfYear;
    }

    //Emperical equation to correct the eccentricity of Earth's orbit and axial tilt
    public static double equationOfTime (double day) {
        double d =(360.0/365.0)*(day - 81);
        d = Math.toRadians(d);
        double equationTime = 9.87*sin(2*d)-7.53*cos(d)-1.54*sin(d); 
        //System.out.println("Equation Of Time: " + equationTime);
        return equationTime;
    }
    //The angle between the equator and a line drawn from the center of the Sun(degrees)
    public static double declination(int dayOfYear) {
        double declination = 23.5*sin((Math.toRadians(360.0/365.0))*(dayOfYear - 81));
        //System.out.println("Declination: " + df.format(declination));
        return declination;
    }

    //Add the number of minutes past midnight localtime//
    public static double hourAngle(double localSolarTime) {
        double hourAngle = 15 * (localSolarTime - 13); 
        System.out.println("Hour Angle: " + df.format(hourAngle)); //(degrees)
        return hourAngle;
    }

    //Account for the variation within timezone - increases accuracy
    public static double localSolarTime(double equationOfTime, double longitude, double lstm) { 
        //LocalSolarTime = 4min * (longitude + localStandardTimeMeridian) + equationOfTime
        //Time Correction is time variation within given time zone (minutes)
        //longitude = longitude/60; //convert degrees to arcminutes
        double localStandardTimeMeridian = lstm;
        double timeCorrection = (4 * (longitude + localStandardTimeMeridian) + equationOfTime);
        System.out.println("Time Correction: " + timeCorrection); //(in minutes)
        //localSolarTime represents solar time where noon represents sun's is highest position 
        // in sky and the hour angle is 0 -- hour angle is negative in morning, and positive after solar noon.
        double localSolarTime = (localTime.toSecondOfDay() + (timeCorrection*60)); //(seconds)
        localSolarTime = localSolarTime/(60*60);  //convert from seconds to hours
        //Convert double to Time (HH:mm:ss) for console output
        int hours = (int) Math.floor(localSolarTime);
        int minutes = (int) ((localSolarTime - hours) * 60);
        //-1 for the daylight savings
        Time solarTime = new Time((hours-1), minutes, 0);
        System.out.println("Local Solar Time: " + solarTime); //hours

        return localSolarTime;
    }

    public static double azimuth(double lat, double declination, double zenith, double hourAngle) {
        double azimuthDegree = 0;
        double elevation = 90 - zenith;
        elevation = Math.toRadians(elevation);
        zenith = Math.toRadians(zenith);
        lat = Math.toRadians(lat);
        declination = Math.toRadians(declination);
        hourAngle = Math.round(hourAngle);
        hourAngle = Math.toRadians(hourAngle);

        //double azimuthRadian = -sin(hourAngle)*cos(declination) / cos(elevation);
        double azimuthRadian = ((sin(declination)*cos(lat)) - (cos(hourAngle)*cos(declination)*
                sin(lat)))/cos(elevation);

        //Account for time quadrants
        Calendar cal = Calendar.getInstance();
        int hour = cal.get(Calendar.HOUR_OF_DAY);
        if(hour > 0 && hour < 6) {
        azimuthDegree =  Math.toDegrees(acos(azimuthRadian));
        }
        else if(hour >= 6 && hour < 12) {
            azimuthDegree = Math.toDegrees(acos(azimuthRadian));
            azimuthDegree = 180 - azimuthDegree;
        } else if (hour >= 12 && hour < 18) {
            azimuthDegree = Math.toDegrees(acos(azimuthRadian));
            azimuthDegree = azimuthDegree - 180;
        } else if (hour >= 18 && hour < 24) {
            azimuthDegree = Math.toDegrees(acos(azimuthRadian));
            azimuthDegree = 360 - azimuthDegree;
        }

        System.out.println("Azimuth: " + df.format(azimuthDegree));
        return azimuthDegree;
    }

    public static double zenith(double lat, double declination, double hourAngle) {
        lat = Math.toRadians(lat);
        declination = Math.toRadians(declination);
        hourAngle = Math.round(hourAngle);
        hourAngle = Math.toRadians(hourAngle);
        //Solar Zenith Angle 
        double zenith = Math.toDegrees(acos(sin(lat)*sin(declination) + (cos(lat)*cos(declination)*cos(hourAngle))));
        //Solar Elevation Angle
        double elevation = Math.toDegrees(asin(sin(lat)*sin(declination) + (cos(lat)*cos(declination)*cos(hourAngle))));
        System.out.println("Elevation: " + df.format(elevation));
        System.out.println("Zenith: " + df.format(zenith));
        return zenith;
    }
}

Just to reiterate, the day, local time meridian are exactly correct, and the equation of time and declination are accurate but not exact. ----UPDATE OUTPUT----

- - -更新 - - - 使用散点图显示全天太阳的高度/方位角。我仍然无法确定方位角输出。它在很长一段时间内都是正确的，但随后它会从增加变为减少（~270-->0）。一旦我最终得到正确的输出，我一定会更新代码。

您将经度传递给localSolarTime()作为度数，然后将其除以 60，并带有注释，声称这是为了转换为弧分。这是错误的；你后面的计算需要度数，即使你需要弧分，你也会乘以 60，而不是除法。

这种错误的划分导致经度为 -1.3°，当您找到当地时间子午线与您的位置之间的角度时，您会得到一个很大的角度（大约 75°）。应该是一个小角度，一般为±7.5°。大角度会导致大量的时间校正，并且使一切都变得混乱。

Update:在更新版本中azimuth()方法中，象限选择应基于太阳的时角，或者等效地，基于当地太阳时，而不是标准挂钟时间。并且，所有计算中使用的小时角不应四舍五入。该方法可以如下所示，而不是测试四个不同的象限：

public static double azimuth(double lat, double declination, double zenith, double hourAngle)
{
  double elevation = Math.toRadians(90 - zenith);
  lat = Math.toRadians(lat);
  declination = Math.toRadians(declination);
  hourAngle = Math.toRadians(hourAngle);
  double azimuthRadian = acos(((sin(declination) * cos(lat)) - (cos(hourAngle) * cos(declination) * sin(lat))) / cos(elevation));
  double azimuthDegree = Math.toDegrees(azimuthRadian);
  if (hourAngle > 0)
    azimuthDegree = 360 - azimuthDegree;
  System.out.println("Azimuth: " + df.format(azimuthDegree));
  return azimuthDegree;
}

终于，你通过了dcLong在作为lat的参数azimuth()方法;这应该是dcLat.

我建议在内部始终使用弧度，并且仅在输入和输出上进行度数转换。这将有助于防止错误，并减少舍入错误和不必要的混乱。