Day length for a latitude and date

Computes the number of hours between sunrise and sunset at a given latitude on a given date, using the CBM model of Forsythe et al. (1995). The calculation is a closed form – no lookup tables, network access, or location database is involved.

Only latitude is needed. Longitude and time zone shift when sunrise and sunset occur but not the interval between them, so they are not arguments.

Usage

day_length(lat, date, horizon = "sunset")

Arguments

lat: Numeric latitude in decimal degrees, positive north, in [-90, 90]. Recycled against date.
date: A Date vector (or anything as.Date() accepts). Recycled against lat.
horizon: How far the sun must be below the horizon for the day to count as over. Either one of "sunset" (the default; 0.833 degrees, accounting for the solar disc and atmospheric refraction), "civil" (6), "nautical" (12), "astronomical" (18), or a number giving the depression angle in degrees directly.

Value

A numeric vector of day lengths in hours, the length of the longer of lat and date.

Details

Day length is astronomical, and the effort estimators want something else. In Hoenig et al. (1993) and Pope et al. (Ch. 17), the daily expansion factor \(T_d\) is the length of the period the counts were randomised within – a property of the survey design, set by regulation, access hours, or the field protocol. It is often close to daylight and it is not the same quantity. Use day_length() to build simulated or planned surveys, and pass the period your protocol actually used to add_counts().

Above the Arctic and Antarctic circles the sun may not rise or set at all. In those cases the result saturates at 0 or 24 rather than erroring.

References

Forsythe, W.C., Rykiel, E.J., Stahl, R.S., Wu, H., Schoolfield, R.M. (1995). A model comparison for daylength as a function of latitude and day of year. Ecological Modelling 80:87-95. doi:10.1016/0304-3800(94)00034-F

Hoenig, J.M., Robson, D.S., Jones, C.M., Pollock, K.H. (1993). Scheduling counts in the instantaneous and progressive count methods for estimating sportfishing effort. North American Journal of Fisheries Management 13:723-736.

Examples

# A single day at Kearney, Nebraska
day_length(40.699, as.Date("2024-06-21"))
#> [1] 15.09385

# A whole season, for use as a simulated expansion factor
season <- seq(as.Date("2024-05-01"), as.Date("2024-08-31"), by = "day")
summary(day_length(40.699, season))
#>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
#>   13.14   14.14   14.63   14.50   14.97   15.09 

# Anglers fish into twilight; civil twilight adds roughly an hour in June
day_length(40.699, as.Date("2024-06-21"), horizon = "civil")
#> [1] 16.2079

# Latitude drives the seasonal swing
day_length(c(25, 45, 65), as.Date("2024-12-21"))
#> [1] 10.580278  8.761470  3.571631