# 2:1.3.3 Rainfall Intensity

The rainfall intensity is the average rainfall rate during the time of concentration. Based on this definition, it can be calculated with the equation:

$$i=\frac{R\_{tc}}{t\_{conc}}$$                                                                                                                                                                   2:1.3.16

where $$i$$ is the rainfall intensity (mm/hr), $$R\_{tc}$$ is the amount of rain falling during the time of concentration (mm H$$*2$$O), and $$t*{conc}$$ is the time of concentration for the subbasin (hr).

An analysis of rainfall data collected by Hershfield (1961) for different durations and frequencies showed that the amount of rain falling during the time of concentration was proportional to the amount of rain falling during the 24-hr period.

$$R\_{tc}=\alpha\_{tc}\*R\_{day}$$                                                                                                                                                 2:1.3.17

where $$R\_{tc}$$ is the amount of rain falling during the time of concentration (mm H$$*2$$O), $$\alpha*{tc}$$ is the fraction of daily rainfall that occurs during the time of concentration, and $$R\_{day}$$ is the amount of rain falling during the day (mm H$$\_2$$O).     

For short duration storms, all or most of the rain will fall during the time of concentration, causing $$\alpha\_{tc}$$ to approach its upper limit of 1.0. The minimum value of $$\alpha\_{tc}$$ would be seen in storms of uniform intensity             ($$i\_{24}=i$$). This minimum value can be defined by substituting the products of time and rainfall intensity into equation 2:1.3.17

$$\alpha\_{tc,min}=\frac{R\_{tc}}{R\_{day}}=\frac{i\*t\_{conc}}{i\_{24}\*24}=\frac{t\_{conc}}{24}$$                                                                                                                        2:1.3.18

Thus, $$\alpha\_{tc}$$ falls in the range $$t\_{conc}/24 \le \alpha\_{tc} \le1.0$$

SWAT+ estimates the fraction of rain falling in the time of concentration as a function of the fraction of daily rain falling in the half-hour of highest intensity rainfall.

$$\alpha\_{tc}=1-exp\[2\*t\_{conc}\*ln(1-\alpha\_{0.5})]$$                                                                                                       2:1.3.19

where $$\alpha\_{0.5}$$ is the fraction of daily rain falling in the half-hour highest intensity rainfall, and $$t\_{conc}$$ is the time of concentration for the subbasin (hr). The determination of a value for $$\alpha\_{0.5}$$ is discussed in Chapters 1:2 and 1:3.