Water Resources Analysis and Design
Frequency and risk
Flood and rainfall estimates are probabilistic. Return period T = 1/p, where p is annual exceedance probability. The risk of at least one event in n years is 1 − (1 − p)^n. A 100-year flood has p = 0.01 each year, so it is not a once-per-century schedule; over a 30-year mortgage it has about a 26% chance of occurring.
Design
Design storms are selected to match the facility: rational method for small urban drainage, unit hydrograph or curve number for larger catchments, and routing for storage. Spillways pass a design flood with freeboard to the dam crest; probable maximum flood (PMF) and probable maximum precipitation (PMP) are extreme, not routine design events. Detention storage cuts peak discharge but requires routing, not simple subtraction. Economic analysis compares present worth of benefits and costs over the project life.
Traps
Do not confuse annual exceedance probability with risk over the project life. Do not call the 100-year flood the flood expected once every 100 years. Peak inflow is not peak outflow when storage exists. Check whether freeboard is measured from normal pool, design flood, or crest. Frequency estimates from short records carry wide confidence bands.
Worked example
What is the chance of at least one 25-year event during a 10-year project? p = 1/25 = 0.04; risk = 1 − (1 − 0.04)^10 = 1 − 0.665 = 0.335, or about 33.5%.