Approximate sunrise and sunset times

October 17, 2007
By

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This function is not perfect, but it does a reasonable job estimating sunrise and sunset times for my field site. If more accurate data are required, try here. Note, the command to calculate day of year is: strptime(x, “%m/%d/%Y”)$yday+1

suncalc<-function(d,Lat=48.1442,Long=-122.7551){
## d is the day of year
## Lat is latitude in decimal degrees
## Long is longitude in decimal degrees (negative == West)

##This method is copied from:
##Teets, D.A. 2003. Predicting sunrise and sunset times.
## The College Mathematics Journal 34(4):317-321.

## At the default location the estimates of sunrise and sunset are within
## seven minutes of the correct times (http://aa.usno.navy.mil/data/docs/RS_OneYear.php)
## with a mean of 2.4 minutes error.

## Function to convert degrees to radians
rad<-function(x)pi*x/180

##Radius of the earth (km)
R=6378

##Radians between the xy-plane and the ecliptic plane
epsilon=rad(23.45)

##Convert observer's latitude to radians
L=rad(Lat)

## Calculate offset of sunrise based on longitude (min)
## If Long is negative, then the mod represents degrees West of
## a standard time meridian, so timing of sunrise and sunset should
## be made later.
timezone = -4*(abs(Long)%%15)*sign(Long)

## The earth's mean distance from the sun (km)
r = 149598000

theta = 2*pi/365.25*(d-80)

z.s = r*sin(theta)*sin(epsilon)
r.p = sqrt(r^2-z.s^2)

t0 = 1440/(2*pi)*acos((R-z.s*sin(L))/(r.p*cos(L)))

##a kludge adjustment for the radius of the sun
that = t0+5

## Adjust "noon" for the fact that the earth's orbit is not circular:
n = 720-10*sin(4*pi*(d-80)/365.25)+8*sin(2*pi*d/365.25)

## now sunrise and sunset are:
sunrise = (n-that+timezone)/60
sunset = (n+that+timezone)/60

return(list("sunrise" = sunrise,"sunset" = sunset))
}

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