卫星天顶⾓太阳天顶⾓⽅位⾓计算
卫星天顶⾓:The satellite zenith angle is the angle between the zenith line (pointing straight up) and the direction to the satellite. The satellite zenith angle is clo to zero degrees for pixels near the center of the raw image. It increas to over 68 degrees for pixels near the left/right ends of the image. Therefore, the angle values range from 0 to approximately 68 degrees.太阳⾼度⾓：The solar zenith angle is the angle between the zenith line and the direction to the sun. Values can range from 0 to 180 degrees. However, for the purpos of solar zenith angle correction, values greater than 85 degrees are considered invalid.⽅位⾓：The relative azimuth angle is defined as the absolute difference between the satellite azimuth angle and the solar azimuth angle. It ranges between 0 and 180 degrees. The relative azimuth angle is discontinuous at the center of the input image. This is due to the fact that the satellite azimuth angle is undefined exactly at the image center (since the satellite zenith angle is zero degrees there).CALCULATIONSBelow is a description of the equations and calculations ud to compute the three angle quantities.----------------------Satellite Zenith Angle----------------------Given: x = image pixel coordinate (ranges from 0.0 to 2048.0) SatAltitude = Satellite altitude (fixed at 833.3 km) EarthRadius = Earth equatorial radius (fixed at 6378.135 km)Step 1. Compute the satellite scan/view angle for the given
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pixel coordinate. (1024.0 - x) SatScanAngle = ------------ * 55.3846 degrees 1024.0Step 2. Compute the satellite zenith angle using the sine law. sin(SatZenAngle) sin(SatScanAngle) ------------------------- = ----------------
- SatAltitude + EarthRadius EarthRadius Values of SatZenAngle range from 0 to +68 degrees, regardless of which side of nadir the pixel is on.----------------------------Greenwich Mean Sidereal Time----------------------------Preliminaries: We work with Modified Julian Dates here instead of Julian Dates becau MJDs turnover at midnight instead of at noon - hence they are a little easier to work with. Refer to the Astronomical Almanac for details.Given: MJD = Modified Julian Date MJD2000 = 51544.5 = Modified Julian Date of Epoch J2000.0, which is defined as January 1, 2000, 12h UT. SecPerDay = 1440.0 SolarSiderealDayRatio = 1.00273790934Step 1. Compute the integral and fractional MJD. IntMJD = floor(MJD) FracMJD = MJD -IntMJDStep 2. Compute Tu, which is the interval of time, measured in Julian centuries of 36525 days of universal time (mean solar days), elapd since January 1, 2000, 12h UT. The Ast. Almanac gives the following equation for Tu: Tu = (JD - 2451545.0) / 36525 We will modify this equation to u a Modified Julian Date instead. The value of Tu is not affected becau there is a constant offt between JD and MJD
values - and MJD is also referenced against the January 1, 2000, 12h UT epoch. Tu = (IntMJD -MJD2000) / 36525.0;Step 3. Compute the GMST value at 0h UT. This value is in conds. GMST = 24110.54841 + 8640184.812866 * Tu + 0.093104 * Tu * Tu + (-6.2e-6) * Tu * Tu * Tu;Step 4. Now add the appropriate mean sidereal time interval to
GMST using the fractional day value. GMST = GMST + FracMJD * SecPerDay * SolarSiderealDayRatioStep 5. Reduce the GMST value to between 0 and 86400 conds. Then convert it to an angular measure (degrees). GMST = GMST / SecPerDay * 360.0 degrees--------------------------------Solar Hour Angle and Declination--------------------------------Given: MJD = Modified Julian Date GMST = Greenwich Mean Sidereal Time corresponding to MJD Lon = Longitude of some point on Earth's
surface (degrees East) Lat = Latitude of some point on Earth's
surface (degrees North) MJD2000 = 51544.5 = Modified Julian Date of Epoch
J2000.0, which is defined as January 1, 2000, 12h UT.Step 1. Compute the number of days from J2000.0. Days = MJD - MJD2000Step 2. Compute the mean longitude and the mean anomaly of the Sun. The formulae can be found on page C24 of the 1988 Ast Almanac. Me
anLongitude = 280.460 + 0.9856474 * Days MeanAnomaly = 357.528 + 0.9856003 * DaysStep 3. Compute the ecliptic longitude of the Sun. See page C24 of the Ast. Almanac. EclipticLongitude = MeanLongitude + 1.915 * sin(MeanAnomaly)
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复前行+ 0.020 * sin(2.0 * MeanAnomaly);Step 4. Compute the obliquity of the ecliptic in radians. See C24. ObliquityOfEcliptic = 23.439 - 0.0000004 * DaysStep 5. Compute the right ascension of the Sun. See page C24. Ensure that the right ascension and ecliptic longitude values are in the same hemisphere. tan(SolarRightAscension)
组织生活会内容= cos(ObliquityOfEcliptic) * tan(EclipticLongitude)Step 6. Compute the declination of the Sun. sin(SolarDeclination) = sin(ObliquityOfEcliptic) * sin(EclipticLongitude)Step 7. Compute the local (apparent) sidereal time (as an angle). U GMST as a clo approximation to GST (Greenwich Apparent Sidereal Time). LST = GST + LonStep 8.欲言又止的意思
Compute the hour angle of the Sun. A negative hour angle means the Sun is east of the obrver's location. SolarHourAngle = LST - SolarRightAscension------------------Solar Zenith Angle------------------Given: Lat = North latitude of a point on Earth's
鱿鱼的功效surface SolarHourAngle already computed SolarDeclination already computedStep 1. Com
pute the solar zenith angle using this formula from [R1]. cos(SolarZenithAngle) =
sin(SolarDeclination) * sin(Lat) + cos(SolarDeclination) * cos(Lat) *
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cos(SolarHourAngle)----------------------Relative Azimuth Angle----------------------Given: Lon = East longitude of a point on Earth's surface Lat = North latitude of a point on Earth's surface SatLon = East longitude of satellite nadir. SatLat = North latitude of satellite nadir. SatScanAngle already computed SolarHourAngle already computed SolarDeclination already computed SolarZenithAngle already computed SatelliteZenithAngle already computedStep 1. Compute the solar azimuth angle using equation 2.7 from [R1]. sin(SolarDeclination) = cos(SolarZenithAngle) *
sin(Lat) + sin(SolarZenithAngle) * cos(Lat) * cos(SolarAzimuthAngle) If SolarHourAngle < 0.0 Then SolarAzimuthAngle = -1 *
SolarAzimuthAngle EndIfStep 2. Compute the Earth angle, which is the angle from
the point on the Earth's surface - to the center of the Earth - to the
satellite. EarthAngle = SatelliteZenithAngle - SatScanAngleStep 3. Compute the satellite hour a
ngle and declination. SatelliteHourAngle = Lon - SatLon SatelliteDeclination = SatLatStep 4. Compute the satellite azimuth angle using equation 2.7 of
[R1]. sin(SatelliteDeclination) = cos(EarthAngle) * sin(Lat) + sin(EarthAngle) *
cos(Lat) * cos(SatelliteAzimuthAngle) If SatelliteHourAngle < 0.0
Then SatelliteAzimuthAngle = -1 * SatelliteAzimuthAngle EndIfStep 5. Compute the relative azimuth angle. RelativeAzimuthAngle = fabs(SolarAzimuthAngle -SatelliteAzimuthAngle) If ( RelativeAzimuthAngle > 180 degrees )
Then RelativeAzimuthAngle = 360 degrees - RelativeAzimuthAngle EndIf---------------------------------References for Angle Computations---------------------------------[R1] Green, Robin M., "Spherical Astronomy", Cambridge University Press, 1985.[R2] 1988 Astronomical Almanac./cgi-
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