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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:

α0.5U=1−exp(−125Rday+5)\alpha_{0.5U}=1-exp(\frac{-125}{R_{day}+5})α0.5U​=1−exp(Rday​+5−125​) 1:3.2.3

where is the largest half-hour fraction that can be generated on a given day, and is the precipitation on a given day (mm HO). The minimum half-hour fraction, or lower limit of the triangular distribution, , 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.

Variable Name
Definition
File Name

average amount of precipitation falling in month (mm HO)

.wgn

PCPD(mon)

: average number of days of precipitation in month (= PCPMM / PCPD)

.wgn

RAIN_YRS

: number of years of data used to obtain values for RAINHHMX

.wgn

PRECIPITATION

: amount of rain falling on a given day (mm HO)

.pcp

α0.5U\alpha_{0.5U}α0.5U​
RdayR_{day}Rday​
2_22​
α0.5L\alpha_{0.5L}α0.5L​
rnd1≤(α0.5mon−α0.5Lα0.5U−α0.5L)rnd_1\le(\frac{\alpha_{0.5mon}-\alpha_{0.5L}}{\alpha_{0.5U}-\alpha_{0.5L}})rnd1​≤(α0.5U​−α0.5L​α0.5mon​−α0.5L​​)
α0.5=α0.5mon∗α0.5L+[rnd1∗(α0.5U−α0.5L)∗(α0.5mon−α0.5L)]0.5α0.5mean\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}}α0.5​=α0.5mon​∗α0.5mean​α0.5L​+[rnd1​∗(α0.5U​−α0.5L​)∗(α0.5mon​−α0.5L​)]0.5​
rnd1>(α0.5mon−α0.5Lα0.5U−α0.5L)rnd_1>(\frac{\alpha_{0.5mon}-\alpha_{0.5L}}{\alpha_{0.5U}-\alpha_{0.5L}})rnd1​>(α0.5U​−α0.5L​α0.5mon​−α0.5L​​)
α0.5=α0.5mon∗(α0.5U−(α0.5U−α0.5mon)∗[α0.5U(1−rnd1)−α0.5L(1−rnd1)α0.5U−α0.5mon]0.5α0.5mean)\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}}) α0.5​=α0.5mon​∗(α0.5mean​α0.5U​−(α0.5U​−α0.5mon​)∗[α0.5U​−α0.5mon​α0.5U​(1−rnd1​)−α0.5L​(1−rnd1​)​]0.5​)
α0.5\alpha_{0.5}α0.5​
α0.5mon\alpha_{0.5mon}α0.5mon​
rnd1rnd_1rnd1​
α0.5L\alpha_{0.5L}α0.5L​
α0.5U\alpha_{0.5U}α0.5U​
α0.5mean\alpha_{0.5mean}α0.5mean​
α0.5L\alpha_{0.5L}α0.5L​
α0.5mon\alpha_{0.5mon}α0.5mon​
α0.5U\alpha_{0.5U}α0.5U​

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)

R0.5xR_{0.5x}R0.5x​: extreme half-hour rainfall for month (mm H2_22​O)

.wgn

ADJ_PKR

adj0.5αadj_{0.5\alpha}adj0.5α​: peak rate adjustment factor

.bsn

PCPMM(mon)

2_22​
dayswetdays_{wet}dayswet​
μmon\mu_{mon}μmon​
yrsyrsyrs
RdayR_{day}Rday​
2_22​