# 1:3.2.1 Monthly Maximum Half-Hour Rain

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  ($$mm\space H\_2O$$), $$\mu\_{mon}$$ is the mean daily rainfall  ($$mm\space H\_2O$$) for the month, $$yrs$$ is the number of years of rainfall data used to obtain values for monthly extreme half-hour rainfalls, and $$days\_{wet}$$ 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.


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