Surface Water Hydrology: Frequency Analysis, Routing, and Design Floods
Return period and frequency analysis
A design flow with return period T has exceedance probability p = 1/T in any given year. The 100-year flood is not "once per century" but a 1% annual exceedance probability; two 100-year events can occur in consecutive years. Traps: confusing return period with recurrence interval certainty, and misreading a frequency curve plotted on probability (or log) paper.
Hydrograph separation and unit hydrograph
A unit hydrograph is the direct runoff from 1 unit (e.g. 1 mm) of effective rainfall over a specified duration. Linearity and superposition let you scale it to other storm depths, but only for the same duration and catchment conditions. Traps: applying a 1-hour unit hydrograph to a 3-hour storm without adjusting duration, and forgetting that baseflow is added after, not scaled with, direct runoff.
Flood routing
Reservoir (level-pool) routing uses continuity and storage–discharge relations; channel routing (Muskingum) uses K (travel time) and X (weighting). Attenuation reduces peak and delays it downstream. Traps: expecting peak to increase downstream in a storage-dominated reach, and misapplying K and X outside their physical range (0 ≤ X ≤ 0.5).
Worked rule of thumb for return period
Probability of at least one T-year event in n years is P = 1 − (1 − 1/T)^n. For T = 50, n = 10: 1 − (0.98)^10 ≈ 1 − 0.817 = 0.183, about 18%. Always state whether the question asks for annual exceedance probability (1/T) or risk over n years.