Difference between solar time and local time

The city of Jena is located west of the timezone’s meridian. Hence, the sun culminates around 13 minutes later.

latDeg <- 50.93; longDeg <- 11.57
(localDiff <- computeSolarToLocalTimeDifference(longDeg, 1L)*60)

## [1] -13.72

The time difference shifts during the year because of earth orbit’s eccentricity.

doy <- 1:366
locaDiffDoi <- computeSolarToLocalTimeDifference(longDeg, 1L, doy)*60
plot(locaDiffDoi  ~ doy, ylab = "time difference solar - local time (min)")
abline(h = localDiff); abline(h = 0, lty = "dotted")

During most days, the sun culminates after noon, but during a few days in autumn the sun culminates earlier than noon of the local time zone.

Computing sun position

Using function computeSunPosition.

times <- seq( 
  ISOdate(2018, 11, 21, 0, tz = "Etc/GMT-1"), by = "2 hour", length.out = 13)
ans <- computeSunPosition(times, latDeg = latDeg, longDeg = longDeg)
cbind(data.frame(timestamp = times), as.data.frame(ans))

##              timestamp         hour declination   elevation     azimuth
## 1  2018-11-21 00:00:00  0.007677319  -0.3428584 -1.02475619 0.003645122
## 2  2018-11-21 02:00:00  2.007677319  -0.3428584 -0.88587017 0.843474263
## 3  2018-11-21 04:00:00  4.007677319  -0.3428584 -0.59048251 1.386239933
## 4  2018-11-21 06:00:00  6.007677319  -0.3428584 -0.26282498 1.793575561
## 5  2018-11-21 08:00:00  8.007677319  -0.3428584  0.03683142 2.188474356
## 6  2018-11-21 10:00:00 10.007677319  -0.3428584  0.25645552 2.635087174
## 7  2018-11-21 12:00:00 12.007677319  -0.3428584  0.33904050 3.143599850
## 8  2018-11-21 14:00:00 14.007677319  -0.3428584  0.25522232 3.651797949
## 9  2018-11-21 16:00:00 16.007677319  -0.3428584  0.03476366 4.097884290
## 10 2018-11-21 18:00:00 18.007677319  -0.3428584 -0.26529678 4.492580298
## 11 2018-11-21 20:00:00 20.007677319  -0.3428584 -0.59297225 4.900381623
## 12 2018-11-21 22:00:00 22.007677319  -0.3428584 -0.88775827 5.444904168
## 13 2018-11-22 00:00:00  0.003498418  -0.3467846 -1.02868424 0.001669479

The return value is a data.frame with polar coordinates of the sun in radian on the horizontal coordinatesystem:

• elevation: angle above the horizon,
• azimuth: angle around the horizon, measured from true north increasing eastward, and
• declination: angle between celestial equator and the observers, fundamental plane, i.e. the plane that contains the horizon
• fractional hour after midnight

In the example the azimuth increases from slightly more than zero at midnight to 2\(\pi\) at the following midnight. Elevation increases from negative values to 0 at sunset, maximum at noon declining to zero at sunset. Declination in early winter decreases to more negative values until it reaches the negative of the earth axial tilt on December solstice.

Sunrise and sunset

Sunrise and sunset are computed in fractional hours after midnight. Neglecting the difference between solar time and local time introduces a bias. Daylength is not biased by neglecting solar time correction.

today <- as.POSIXlt(ISOdate(2018,3,1,0, tz = "Etc/GMT-1"))
(sunrise <- computeSunriseHour(today, latDeg = latDeg
                               , isCorrectSolartime = FALSE))

## [1] 6.685696

(sunrise <- computeSunriseHour(today, latDeg = latDeg, longDeg = 11.586))

## [1] 7.129989

(sunset <- computeSunsetHour(today, latDeg = latDeg, longDeg = 11.586))

## [1] 17.7586

(daylength <- computeDayLength(today, latDeg = latDeg))

## [1] 10.62861

Sunrise is set to 12 for polar nights and 0 for polar days. Similarly, sunset is set to 12 for polar nights and to 0 for polar days.

doy <- 1:366
sunrise <- computeSunriseHourDoy( doy, latDeg = +80, isCorrectSolartime = FALSE)
sunset <- computeSunsetHourDoy( doy, latDeg = +80, isCorrectSolartime = FALSE)
par(mfrow = c(1,2)); plot(sunrise ~ doy ); plot(sunset ~ doy )

Further Utilities

Functions computeIsDayByHour and computeIsDayByLocation quickly classify daytime and nighttime records of a dataset.

dateSeq <- seq( 
  as.POSIXct("2017-03-20", tz = "Etc/GMT-1")
  , as.POSIXct("2017-03-21", tz = "Etc/GMT-1")
  , by = "30 min")
isDay <- computeIsDayByLocation(dateSeq, latDeg = 50.93, longDeg = 11.59)

Function getHoursAheadOfUTC provides the integer timeZone argument of a timestamp, required by other functions of the package. Similarly, getFractionalHours provides fractional hours after midnight of a timestamp.

#around daylight saving time step in Central European time
t1 <- as.POSIXct("2018-10-28 01:30", tz = "Europe/Berlin")
datesCET <- seq(t1, by = "30 min", length.out = 6)
datesUTC <- as.POSIXct(datesCET, tz = "UTC")
#
hoursAheadOfUTC <- getHoursAheadOfUTC(datesCET)
fracHours <- getFractionalHours(datesCET)
#
data.frame(datesUTC, datesCET, hoursAheadOfUTC, fracHours)

##              datesUTC            datesCET hoursAheadOfUTC fracHours
## 1 2018-10-27 23:30:00 2018-10-28 01:30:00               2       1.5
## 2 2018-10-28 00:00:00 2018-10-28 02:00:00               2       2.0
## 3 2018-10-28 00:30:00 2018-10-28 02:30:00               2       2.5
## 4 2018-10-28 01:00:00 2018-10-28 02:00:00               1       3.0
## 5 2018-10-28 01:30:00 2018-10-28 02:30:00               1       3.5
## 6 2018-10-28 02:00:00 2018-10-28 03:00:00               1       4.0