Daily Maximum Half-Hour Rain Value

The user has the option of using the monthly maximum half-hour rainfall for all days in the month or generating a daily value. The variable ISED_DET in the basin input file (.bsn) defines which option the user prefers. The randomness of the triangular distribution used to generated daily values can cause the maximum half-hour rainfall value to jump around. For small plots or microwatersheds in particular, the variability of the triangular distribution is unrealistic.

The triangular distribution used to generate the maximum half-hour rainfall fraction requires four inputs: average monthly half-hour rainfall fraction, maximum value for half-hour rainfall fraction allowed in month, minimum value for half-hour rainfall fraction allowed in month, and a random number between 0.0 and 1.0.

The maximum half-hour rainfall fraction, or upper limit of the triangular distribution, is calculated from the daily amount of rainfall with the equation:

$\alpha_{0.5U}=1-exp(\frac{-125}{R_{day}+5})$ 1:3.2.3

where $\alpha_{0.5U}$ is the largest half-hour fraction that can be generated on a given day, and $R_{day}$ is the precipitation on a given day (mm H$_2$O). The minimum half-hour fraction, or lower limit of the triangular distribution, $\alpha_{0.5L}$, is set at 0.02083.

The triangular distribution uses one of two sets of equations to generate a maximum half-hour rainfall fraction for the day. If $rnd_1\le(\frac{\alpha_{0.5mon}-\alpha_{0.5L}}{\alpha_{0.5U}-\alpha_{0.5L}})$

$\alpha_{0.5}=\alpha_{0.5mon}*\frac{\alpha_{0.5L}+[rnd_1*(\alpha_{0.5U}-\alpha_{0.5L})*(\alpha_{0.5mon}-\alpha_{0.5L})]^{0.5}}{\alpha_{0.5mean}}$ 1:3.2.4

If $rnd_1>(\frac{\alpha_{0.5mon}-\alpha_{0.5L}}{\alpha_{0.5U}-\alpha_{0.5L}})$ then

$\alpha_{0.5}=\alpha_{0.5mon}*(\frac{\alpha_{0.5U}-(\alpha_{0.5U}-\alpha_{0.5mon})*[\frac{\alpha_{0.5U}(1-rnd_1)-\alpha_{0.5L}(1-rnd_1)}{\alpha_{0.5U}-\alpha_{0.5mon}}]^{0.5}}{\alpha_{0.5mean}})$ 1:3.2.5

where $\alpha_{0.5}$ is the maximum half-hour rainfall fraction for the day, $\alpha_{0.5mon}$is the average maximum half-hour rainfall fraction for the month, $rnd_1$ is a random number generated by the model each day, $\alpha_{0.5L}$ is the smallest half-hour rainfall fraction that can be generated, $\alpha_{0.5U}$ is the largest half-hour fraction that can be generated, and $\alpha_{0.5mean}$is the average of $\alpha_{0.5L}$, $\alpha_{0.5mon}$, and $\alpha_{0.5U}$.

Table 1:3-2: SWAT+ input variables that pertain to generation of maximum half-hour rainfall.

Variable Name	Definition	File Name
ISED_DET	Code governing calculation of daily maximum half-hour rainfall: 0-generate daily value 1-use monthly maximum half-hour rainfall value	.bsn
RAINHHMX(mon)	$R_{0.5x}$: extreme half-hour rainfall for month (mm H$_2$O)	.wgn
ADJ_PKR	$adj_{0.5\alpha}$: peak rate adjustment factor	.bsn
PCPMM(mon)	average amount of precipitation falling in month (mm H$_2$O)	.wgn
PCPD(mon)	$days_{wet}$: average number of days of precipitation in month ($\mu_{mon}$= PCPMM / PCPD)	.wgn
RAIN_YRS	$yrs$: number of years of data used to obtain values for RAINHHMX	.wgn
PRECIPITATION	$R_{day}$: amount of rain falling on a given day (mm H$_2$O)	.pcp