# Daily Maximum Half-Hour Rain Value

&#x20;             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.&#x20;

&#x20;                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.&#x20;

&#x20;                 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

&#x20;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.&#x20;

&#x20;                     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.

| 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      |

