Flood prediction

• Flood prediction – is the study of rainfall patterns, catchment characteristics, and river

hydrographs to predict the future average frequency of occurrence of flood events. Flood predictions seek to estimate the probable discharge that, on average, will be exceeded only once in any particular period, hence the use of such terms as ‘50-year flood’ and ‘100-year flood’.

Frequency of Flooding

– we will see how flood frequencies can be determined for any given stream if data is available for discharge of the stream over an

extended period of time. Such data allows statistical analysis to determine how often a given discharge or stage of a river is expected. From this analysis a recurrence interval can be determined and a probability calculated for the likelihood of a given discharge in the stream for any year. The data needed to perform this analysis are the yearly maximum discharge of a stream from one gaging station over a long enough period of time.

• In order to determine the recurrence interval (RI), the yearly discharge values are first ranked. Each discharge is associated with a rank, m, with m = 1 given to the maximum discharge over the years of record, m = 2 given to the second highest discharge, m = 3 given to the third highest discharge, etc

• The smallest discharge will receive a rank equal to the number of years over which there is a record, n. Thus, the discharge with the smallest value will have m = n.

• The number of years of record, n, and the rank for each peak discharge are then used to calculate recurrence interval, R by the following equation, called the Weibull equation:

The Recurrence Interval (RI) is calculated as follows:

RI = (n +1) ÷ Rank, where n is the # of years of data

Year Qmax (cfs) Rank # RI (yrs

1975 195 20 1.1

1976 288 18 a.

1977 1251 b. 2.4

1978 496 16 c.

1979 109 21 1.05

1980 881 d. e.

1981 266 19 1.2

1982 950 f. g.

1983 2096 h. i.

1984 1685 5 j.

1985 1205 k. 2.2

Calculate the RI for the 21 years of data. (Some RI values have been determined for you.)

1986 1350 l. 2.8

1987 301 17 1.3

1988 661 15 1.5

1989 980 11 2.0

1990 3620 1 22

1991 1680 6 3.7

1992 1650 7 3.1

1993 2554 m. 7.3

1994 2831 n. 11.0

1995 906 13 1.7

Year Qmax (cfs) Rank # RI (yrs

Determining Flooding ProbabilitiesKeep in mind that every year the probability (P) of a Maximum Annual Peak Discharge (we'll call this a flood) with a given recurrence interval (RI) is 1 divided by the Recurrence IntervalP = 1 / RI

From that it follows that the probability of there NOT being a flood within one year isP(NOT) = (1 - 1 / RI)

Over a period of X years, the probability of there NOT being a flood with a certain recurrence interval is,P(NOT in X years) = P(NOT) X = (1 - 1 / RI) X

And finally, the probability of there bing a certain size flood in X years is P(Within X years) = 1 - P(NOT in X years) = 1 - (1 - 1 / RI) X

Answer these questions.

1. What's the probability of a 25 year flooding event occurring each year?

2. Given that a 25-year flooding event has a probability of 4 % of occurring each year (1/25), what is the probability that a 25-year flood will NOT occurr in a given year?

3. A 25 -year type flood had the probability of 4% (1/25) of occurring in a given year and a 96% probability of NOT occurring (100- 4). What's the probability that there will NOT be a 25 year type flood in a 10 year period?

4. A 25 -year type flood had the probability of 4% of occurring in a given year and a 96% probability of NOT occurring. There is a 66.5% probability that there will NOT be a 25 year flood in a 10 year period. What's the probability that there WILL be a 25 year flood with a 10 year period?

5. Using what you learned above, what's the probability of there being a 50 year type flood in a 20 year period?

Recurrence Interval(years

Probability each year P ( in 10 years) P (in 50 years) P (in 100 years)

2 50%

10 10% 65.1%

25 4% 33.5% 87% 5. ____%

50 1._____ % 18.3% 63.6% 86.7%

100 1.0% 3. ____% 39.5% 6. ____%

1000 0.1% 1% 4. % 9.5%

10000 2._____% 0.1% 0.5% 1.0%

We can use this equation to calculate how the probabilities change over time. The result is depicted in the graph below for P= 0.01 (100 year flood)

Two important points emerge:

• The probability of a 100 year flood occurring in 100 years is NOT 100%! (See below)

• The probability of a 100 year flood occurring in 30 years (the lifetime of the average home mortgage) is 26.0%