# Definition

The daylight hours are maximum possible duration of sunshine for a given day of the year (Allen et al. 1998).

# Formula

## Formulation according to FAO:

The daylight hours $$N$$ are obtained as follows (Allen et al. 1998):

$N=\dfrac{24}{\pi}\cdot\omega_s$

where $$\omega_s$$ is the sunset hour angle [rad], which is calculated as follows:

$\omega_s=\arccos [-\tan\varphi\cdot\tan\delta]$

where $$\delta$$ is the solar declination [rad], and $$\varphi$$ the latitude [rad].

The solar declination $$\delta$$ is calculated as follows:

$\delta=0.409\cdot\sin\bigg(\dfrac{2\pi}{365}\cdot J-1.39\bigg)$

where $$J$$ is the number of the day in the year between 1 (1 January) and 365 or 366 (31 December).

The conversion from decimal degrees to radians is obtained as follows:

$\mbox{[Radians]}=\dfrac{\pi}{180} \mbox{ [decimal degrees]}$

NB: for calculating potential evapotranspiration according to Thornthwaite, a daylight coefficient $$C$$ is required, which corresponds to the duration of sunlight in units of 12 hours. This daylight coefficient $$C$$ is thus given by:

$C=\dfrac{N}{12}$

## Formulation according to NFDRS

The procedure for determining daylight hours $$N_{nfdrs}$$ proposed by (Cohen & Deeming (1985) in order to calculate some components of the NFDRS is slightly different from that proposed by (Allen et al. (1998):

$N_{nfdrs}=24\cdot\bigg(1-\dfrac{\arccos(\tan\varphi\cdot\tan\delta)}{\pi}\bigg)$

where $$\varphi$$ is latitude [rad] and $$\delta$$ the solar declination [rad].

The latitude $$\varphi$$ [rad] is given by:

$\varphi=\varphi_{deg}\cdot{0.01745}$

where $$\varphi_{deg}$$ is the latitude in decimal degrees.

The solar declination $$\delta$$ is calculated as follows:

$\delta=0.41008\cdot\sin\Big((J-82)\cdot{0.01745}\Big)$

where $$J$$ is the Julian date.

# Reference

Cohen & Deeming (1985)
Allen et al. (1998)