# Monthly Maximum Half-Hour Rain

&#x20;                     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.       &#x20;

&#x20;                     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 H$$_2$$O) and $$R_{0.5x}$$ is the extreme maximum half-hour rainfall for the specified month (mm H$$_2$$O). 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 H$$_2$$O), $$\mu_{mon}$$ is the mean daily rainfall (mm H$$_2$$O) 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.

