Flood Risk & Recurrence Intervals
Between June and August 2022, torrential rains and a combination of riverine, urban, and flash flooding led to an unprecedented disaster in Pakistan. According to the National Disaster Management Authority (NDMA), around 33 million people have been affected by the floods, including nearly 8 million displaced.
Historically, the monsoon currents start from the Bay of Bengal and enter the Indus Valley from Kashmir which serves as an entrance to Northern Punjab and Khyber Pakhtunkhwa. However, this year, instead of following its traditional route, it entered Sukkur, Khairpur, and the neighbouring districts of central Sindh short of Karachi, directly from Rajasthan and Gujarat in India, causing unprecedented rainfall and flash floods in regions not accustomed to monsoon rains.
This event is blend of five meteorological disasters happening simultaneously?and coinciding in various regions of the country:
Flood Return Periods
?In general, return period, which is also referred as recurrence interval, provides an estimate of the likelihood of any event in one year. These events include natural disasters such as floods or earthquakes. Return periods are used to convey the risks of rate events more effectively that simply stating the probabilities.
The recurrence interval is based on the probability that the given event will be equaled or exceeded in any given year
?The most common misconception about return periods, for example, the 100-year return period is that the flood of this magnitude will only occur once in 100 years. It is essential to understand that if a flood with a 100-year return period occurs now, it does not mean that another flood of this magnitude will not occur in the next 100 years. Return period simply provides an estimate of the probability of exceedance of a given flow.
For example, if the 100-year return period flow value for the Indus River is 5000 m3/s, it means that there is a 1 in a 100 or 1% chance that this flow will be exceeded in the river in a given year. The floodplain is the relatively flat lowland that borders a river, usually dry but subject to flooding. Property underwriters should consider NATCAT tools available in order to have historical trend of rainfall, topography, floods and climatological pre-conditions for a specific risk or a region.
Now let's determine the probability of a 100-year flood occurring over a 30-year period of a home insurance where the home is within the 100-year floodplain of a river. To do this, we use the formula
Exceedance probability = 1 – (1 – p)n
In this formula we consider all possible flows over the period of interest "n" and we can represent the whole set of flows with "1." Then (1–p) is the chance of the flow not occurring, or the non–exceedance probability, for any given year. Let's say the value "p" is the exceedance probability, in any given year. The exceedance probability may be formulated simply as the inverse of the return period.
Calculation for Probability of 100-Year Flood Over 30-Year Period
????????Exceedance Probability=???1 - (1 - p)n??????where?????????n = 30????????&???p = 0.01
n=30 and we see from the table, p=0.01 .
1 - (1 - 0.01)?30
= 1 - (0.99)?30
= 1 - 0.74
(Probability of non-occurrence = 0.74)
= 0.26 or 26% probability of occurrence
There is a 0.74 or 74 percent chance of the 100-year flood not occurring in the next 30 years.
But 1-0.74 is 0.26, which shows there is a 26 percent chance of the 100-year flood in that time.
This table shows the relationship between the return period, the annual exceedance probability and the annual non–exceedance probability for any single given year.
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