1:3.5.2 Generated Daily Value

The triangular distribution used to generate daily relative humidity values requires four inputs: mean monthly relative humidity, maximum relative humidity value allowed in month, minimum relative humidity value allowed in month, and a random number between 0.0 and 1.0.

The maximum relative humidity value, or upper limit of the triangular distribution, is calculated from the mean monthly relative humidity with the equation:

$R_{hUmon}=R_{hmon}+(1-R_{hmon})*exp(R_{hmon}-1)$ 1:3.5.4

where $R_{hUmon}$ is the largest relative humidity value that can be generated on a given day in the month, and $R_{hmon}$ is the average relative humidity for the month.

The minimum relative humidity value, or lower limit of the triangular distribution, is calculated from the mean monthly relative humidity with the equation:

$R_{hLmon}=R_{hmon}*(1-exp(-R_{hmon}))$ 1:3.5.5

where $R_{hLmon}$ is the smallest relative humidity value that can be generated on a given day in the month, and $R_{hmon}$ is the average relative humidity for the month.

The triangular distribution uses one of two sets of equations to generate a relative humidity value for the day. If $rnd_1 \le (\frac{R_{hmon}-R_{hLmon}}{R_{hUmon}-R_{hLmon}})$ then

$R_h=R_{hmon}*\frac{R_{hLmon}+[rnd_1*(R_{hUmon}-R_{hLmon})*(R_{hmon}-R_{hLmon})]^{0.5}}{R_{hmon,mean}}$ 1:3.5.6

If $rnd_1>(\frac{R_{hmon}-R_{hLmon}}{R_{hUmon}-R_{hLmon}})$ then

$R_h=R_{hmon}*\frac{R_{hUmon}-(R_{hUmon}-R_{hmon})*[\frac{R_{hUmon}(1-rnd_1)-R_{hLmon}(1-rnd_1)}{R_{hUmon}-R_{hmon}}]^{0.5}}{R_{hmon,mean}}$ 1:3.5.7

where $R_h$ is the average relative humidity calculated for the day, $rnd_1$ is a random number generated by the model each day, $R_{hmon}$ is the average relative humidity for the month, $R_{hLmon}$ is the smallest relative humidity value that can be generated on a given day in the month, $R_{hUmon}$ is the largest relative humidity value that can be generated on a given day in the month, and $R_{hmon,mean}$ is the mean of $R_{hLmon},R_{hmon},$ and $R_{hUmon}$.