Abstract
When doing hydrologic analyses in very small drainage areas such as small urban stormwater catchments, airport runways, or professional sports fields where the time of concentration is short (e.g. <10 minutes), it is important to have rainfall data with a short enough time-interval to adequately observe the temporal distribution and accurately model the resulting infiltration and runoff. When the time-interval gets very small, such as 1-minute intervals, the traditional hyetograph technique of using a histogram to graph rainfall intensity as a function of time does not accurately represent the storm event. A new method to calculate and graph rainfall intensities was developed to address these problems by allowing the time-interval over which the intensity is calculated to vary while holding the depth-interval constant. This new variable-time method was then evaluated with three numerical differentiation techniques (forward-difference, central-difference, and three-point forward-difference) that were used to differentiate the rainfall mass curve to estimate intensities. The variable-time method proved to be a viable alternative, especially for graphically based analyses. The central-difference method is a good alternative to generate a continuous intensity function although it has the potential to underestimate the intensity of sudden short burst of rainfall. This does not occur with the forward-difference method but it does result in an overall shift of the data by one time-interval. Even though the three-point forward-difference method uses a higher order approximation of the mass curve, it proved to be the least preferred alternative because it was unable to realistically deal with sudden changes in the mass curve.