8.5.2 Parameter Estimation

The procedure for determining the constants for the empirical IDF curve was discussed previously in the Intensity Duration Frequency Curves section. The only constant that is required for the Chicago design storm is the ratio of the time before the peak to the storm duration, r. Two procedures may be used to determine the value of r:

1. The ratio of time to peak intensity to the storm duration is computed for a series of events for various duration. For a given duration, the average time to peak is determined from a number of rainfall events of that duration. This is done for a set of duration. The mean value of the time to peak to the storm duration ratio is computed as a weighted average. The following equation (is an example of how r is computed.
   (44)
   where, , , are the durations of the different rainfall occurrences, , , are the average time to peak for the different rainfall occurrences and r is the ratio of time to peak to total storm duration.
   

2. The ratio can be computed by analyzing local storm distributions to determine the rainfall depth before the peak intensity. The design storm duration is then chosen. The rainfall depth prior to the peak is determined for durations less than the design storm. A weighted average for r is determined based on the ratio of the antecedent rainfall depth to the total rainfall depth. This is done by using:
   (45)
   where:
   = depth of antecedent rainfall,
   = design storm duration,
   t = rainfall duration,
   = maximum average intensity for the total duration,
   = maximum average intensity for duration t.

Specific applications of each procedure have been documented. For example, McPherson (1958) has criticized the second procedure while both have been demonstrated by Bandyopadhyay (1972). The later obtained a value 0.416 for the first procedure and an r value of 0.37 for the second. Table 6 presents a list of r values obtained by different researchers.
 
Table 6 Values of r for the Chicago design storm