Question

Using the data available about rainfall extreme depths at different durations, develop IDF curves for 5, 25, 50- and 100-year return periods.

Answer 1

Empirical Plotting Position Approach To illustrate the first approach, select for example the 30-min duration data from Table 1 and proceed as follows: 1) Rank the observations in descending order (Table 2 Column 1) 2) Compute the exceedance probability associated with each rainfall volume using he following expression (Table 2 Column 4): rank PTm+ where m is the number of observations, p is the exceedance probability and T is the corresponding return period (Table 2 Column 5). 3) Transform the volume data into rainfall intensity by dividing volume by the corresponding duration (Table 2, Column 6). 4) Plot empirical distribution of rainfall intensity (Columns 5 and 6 in Figure 1). As indicated above, this procedure is repeated for each of the desired durations. Table 1. Maximum Annual Rainfall Intensity for the shown Duration Smin | 10 min 0.17 hr 12 hr 12 har 0.08 hr 2hr 6 hr 1983 Mean Annual Rainfall Volume for the Shown Duration mm 15 min 30 min Ihr 2 hr 6 hr 0.25 hr 0.50 hr Thr 10.9 242 168 17.7 27.7 13.7 56.1 41.2 1987 99 38 24 hr 24 hr 304 84.7 65.3 51.8 509 786 1009 544 69 41.4 105 10.7 17.4 45.6 52.1 66.4 41.9 38.2 26.1 EEEEEEEEEEEEEEEEEEE 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 10.8 10.1 309 06 5.9 14.4 317 826 Eନ ଆସ ଆସ ଆସ ଆସ ଆସ ଆs ଆ 2222322283 22:22 a 25 DESDEBERE 2823-82285 15.9 21.2 50,7 50.3 548 46.7 38 609 4.3 105 15.9 14.4 315 159 301 2012 45 594 476 45.2 36.2 2.9 5.5 13.2 2001 2002 2003 4.4 48 14.5 64.9 72.6 455 2008 3.9 7.6 102 15.2 139 27.7 2005 145 41.7 4.86 Mean St. Dev. 265 02 3.84 1 29 56 706 250 10:22 257 15:42 261 31.76 604 44.73 79 6 069 16 69

Table 2. 30-min rainfall - Frequency Analysis I Rank ! । । ୪ 30 min Year 0.50 hr P T Intensity mm/hr M5Isq Osh । ପ୍ରs I୦୨ohn 2s Y qtOI -। is is is so O । 0 ao IN OT 16 IUs | 690 11 I INT 61046115 i it -8 Es:ଆa: ଆe -3 2 i ୨62050 ଏ 20k । in IS Iଭus୨ ୦ Is7 | ଏs7 02 1 03 as q75 0. NO 1 ( 2 qn10, 116 n 51 0.୨] IO noss 1 (0.95 0.05 ::: i 2 10. 10 » | 10 6 Frequency Analysis 30-min Rain Intensity Ratu Period

Figure 1. Theoretical Extreme Value (EV) Distribution Approach To illustrate the second approach, let us select the Gumbel (Type 1) distribution as our EV distribution. The Gumbel Type I distribution is, GE.M.B) where is the location parameter and B is the scale parameter. It can be shown that the value of the random variable Xs associated with a given return period, T. may be obtained from the following expression, X = X+K S (3) where is the mean of the observations (e.g., arithmetic average of the observations), and Sis the standard deviation of the observations. The frequency factor associated with return period 7 Ky, is given by x = ,05712+ Inancy? » Equations (1), (2) and (3) are applied to each set of annual maxima corresponding to each duration, as follows: 1. Compute the frequency factors associated with the desired return periods (e.g., 2, 5, 10, 25, 50, 100, 1000) using equation (4). Table 3. Frequency Factors K 194574 2.0438459 25922880 3.1 366806 2. For each duration (e.g., 5-min, 10-min, ...etc.), compute the sample mean and sample standard deviations of the series of annual maxima, (x.........In) (see Table 1). 3- and s----

3. Use equation (3) to compute the precipitation intensity associated with each return Tc (min) 5 YEARS 25 YEARS 50 YEARS 100 YEARS 5 38 9041 51.9281 5 73221 62676 101 285 38.759 429731 47.155 15 24.6 34.12il 063 41.976 17.719 24336 27.076 29.797 16.085 17.657 19.218 1038 11.096 1107 6,025 4.254 3.0291 5.2255 3.951 .626 331 1440 4 4. Plot the results (Figure 2). Rainfall Intensity - Duration - Frequency Curves Kent County, Delaware . R Rainfal Intensity (in/hr) 0 20 140 160 180 40 60 80 100 120 Time of Concentration (min) 5-year ---25-year ------ 50-year Figure 2