The normalized time to peak intensity is calculated by SWAT+ using a triangular distribution. The triangular distribution used to generate the normalized time to peak intensity requires four inputs: average time to peak intensity expressed as a fraction of total storm duration (t^peakM), maximum time to peak intensity expressed as a fraction of total storm duration (t^peakU), minimum time to peak intensity expressed as a fraction of total storm duration (t^peakL)and a random number between 0.0 and 1.0.
The maximum time to peak intensity, or upper limit of the triangular distribution, is set at 0.95. The minimum time to peak intensity, or lower limit of the triangular distribution is set at 0.05. The mean time to peak intensity is set at 0.25.
The triangular distribution uses one of two sets of equations to generate a normalized peak intensity for the day. If rnd1≤[t^peakU−t^peakLt^peakM−t^peakL] then
t^peak=t^peakM∗t^peak,meant^peakL+[rnd1∗(t^peakU−t^peakL)∗(t^peakM−t^peakL)]0.5 1:3.3.9
If rnd1>[t^peakU−t^peakLt^peakM−t^peakL] then
t^peak=t^peakM∗t^peak,meant^peakU−(t^peakU−t^peakM)∗[t^peakU−t^peakMt^peakU(1−rnd1)−t^peakL(1−rnd1)]0.5 1:3.3.10
where t^peak is the time from the beginning of the storm till the peak intensity expressed as a fraction of the total storm duration (0.0-1.0),t^peakMis the average time to peak intensity expressed as a fraction of storm duration, rnd1 is a random number generated by the model each day, t^peakL is the minimum time to peak intensity that can be generated,t^peakUis the maximum time to peak intensity that can be generated, and t^peak,mean is the mean of t^peakL,t^peakM and t^peakU .
