Maximum half-hour rainfall is required by SWAT+ to calculate the peak flow rate for runoff. When daily precipitation data are used by the model, the maximum half-hour rainfall may be calculated from a triangular distribution using monthly maximum half-hour rainfall data or the user may choose to use the monthly maximum half-hour rainfall for all days in the month. The maximum half-hour rainfall is calculated only on days where surface runoff has been generated.

For each month, users provide the maximum half-hour rain observed over the entire period of record. These extreme values are used to calculate representative monthly maximum half-hour rainfall fractions.

Prior to calculating the representative maximum half-hour rainfall fraction for each month, the extreme half-hour rainfall values are smoothed by calculating three month average values:

$R_{0.5sm(mon)}=\frac{R_{0.5x(mon-1)}+R_{0.5x(mon)}+R_{0.5x(mon+1)}}{3}$ 1:3.2.1

where $R_{0.5sm(mon)}$ is the smoothed maximum half-hour rainfall for a given month (mm H$_2$O) and $R_{0.5x}$ is the extreme maximum half-hour rainfall for the specified month (mm H$_2$O). Once the smoothed maximum half-hour rainfall is known, the representative half-hour rainfall fraction is calculated using the equation:

$\alpha_{0.5mon}=adj_{0.5\alpha}*[1-exp(\frac{R_{0.5sm(mon)}}{{\mu_{mon}}*ln*(\frac{0.5}{yrs*days_{wet}})})]$ 1:3.2.2

where $\alpha_{0.5mon}$ is the average half-hour rainfall fraction for the month, $adj_{0.5\alpha}$ is an adjustment factor, $R_{0.5sm}$ is the smoothed half-hour rainfall amount for the month (mm H$_2$O), $\mu_{mon}$ is the mean daily rainfall (mm H$_2$O) for the month, $yrs$ is the number of years of rainfall data used to obtain values for monthly extreme half-hour rainfalls, and $days_{wet}$ are the number of wet days in the month. The adjustment factor is included to allow users to modify estimations of half-hour rainfall fractions and peak flow rates for runoff.

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 sed_det in the basin input file (codes.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 $rnd_1\le(\frac{\alpha_{0.5mon}-\alpha_{0.5L}}{\alpha_{0.5U}-\alpha_{0.5L}})$ then

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