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 ($mm\space H_2O$) and $R_{0.5x}$ is the extreme maximum half-hour rainfall for the specified month ($mm\space H_2O$). 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 (), is the mean daily rainfall () for the month, is the number of years of rainfall data used to obtain values for monthly extreme half-hour rainfalls, and 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 ($mm\space H_2O$). 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 then

1:3.2.4

If then

1:3.2.5

where is the maximum half-hour rainfall fraction for the day, is the average maximum half-hour rainfall fraction for the month, is a random number generated by the model each day, is the smallest half-hour rainfall fraction that can be generated, is the largest half-hour fraction that can be generated, and is the average of , , and .

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

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.