Solar position
Usage
solar_position(
x,
UTC = "UTC",
yday = "yday",
hour = "hour",
lon = "lon",
lat = "lat",
integral_steps = 1,
keep.all = TRUE,
verbose = getOption("merra2.verbose"),
...
)Arguments
- x
data.frame with MERRA-2 subset
- UTC
name (string) of the column in x with date and time in UTC format
- yday
optional name of column in x with the day of the year (consistent with UTC time), will be used if "UTC" is not provided
- hour
optional, the name of column with hour of the day (0 to 23, UTC time assumed)
- lon
longitude of the location
- lat
latitude of the location
- integral_steps
integer number of steps for calculation of solar_time, hour_angle, and zenith within an hour, and the logical variable; default is 2 (start and the end of every hour)
- keep.all
if TRUE, the interim variables declination, eq_time, solar_time, and hour_angle will be added to x and returned
- verbose
Details
List or data.frame with estimated following solar geometry variables:
Solar declination (\(\theta_d\)) \[\theta_d = \frac{23.45\pi}{180}\sin{\big(2\pi\frac{284+n}{365}\big)}\]
Equation of time (\(E_{qt}\)) \[ E_{qt} = \begin{cases} -14.2\sin{\big(\frac{\pi(n+7)}{111}\big)}& & {1 \leq n \leq 106}\newline 4.0\sin{\big(\frac{\pi(n-106)}{59}\big)}& & {107 \leq n \leq 166}\newline -6.5\sin{\big(\frac{\pi(n-166)}{80}\big)}& & {167 \leq n \leq 246}\newline 16.4\sin{\big(\frac{\pi(n-247)}{113}\big)}& & {247 \leq n \leq 365} \end{cases} \]
Apparent solar time (\(T_{solar}\)) \[T_{solar} = T_{UTC}+\frac{E_{qt}}{60}+longitude/15\]
Hour angle (\(\theta_{hr}\)) \[\theta_{hr} = \frac{T_{solar}-12}{12}\pi\]
Zenith angle \[zenith = \arccos\big({\sin{(latitude)}\sin{(\theta_d)}+\cos{(latitude)}\cos{(\theta_d)}\cos{(\theta_{hr})}\big)}\]
Azimuth angle \[ azimuth = \begin{cases} \arcsin{(A)}& & {A \geq 0, B \geq 0}\newline 180-\arcsin{(A)}& & {B < 0}\newline 360+\arcsin{(A)}& & {A < 0, B \geq 0} \end{cases} \] where
\(n - \text{day of the year}\)
\(A = \sin{(azimuth)} = -\frac{\sin{(\theta_{hr})}\cos{(\theta_d)}}{\sin{(zenith)}}\)
\(B = \cos{(azimuth)} = \frac{\sin{(\theta_d)}- \sin{(latitude)}\cos{(zenith)}}{\cos{(latitude)}\sin{(zenith)}}\)