Hydrology: Rainfall-Runoff, Frequency, and Routing
Core ideas
Hydrologic analysis starts with the water balance, P = ET + Q + ΔS + G. The highest-yield exam topics are rainfall-runoff, frequency analysis, and routing.
Frequency. An IDF curve gives rainfall intensity for a duration and return period; intensity falls as duration rises. Return period T corresponds to annual exceedance probability 1/T, and the risk of at least one exceedance in n years is 1 − (1 − 1/T)^n. Areal rainfall can be estimated by arithmetic mean, Thiessen polygons, or isohyets.
Infiltration and runoff. Horton and Green-Ampt describe infiltration capacity. The NRCS curve number method uses S = 1000/CN − 10 and Q = (P − 0.2S)²/(P + 0.8S), with depths in inches; CN rises with imperviousness and poorer soil groups.
Unit hydrograph. The basin response is treated as linear and time-invariant: a unit hydrograph represents 1 inch of direct runoff for a stated duration. Larger storms are handled by scaling and lagging (convolution). Time of concentration is the travel time from the hydraulically most remote point and sets the storm duration for the rational method.
Rational method. Q = CiA, with Q in cfs, C dimensionless (0–1), i in in/hr, and A in acres. The intensity must correspond to a duration equal to tc.
Traps
Using rainfall depth where intensity is required; selecting intensity at the wrong duration; mixing SI and US units; and treating CN runoff as total flow rather than direct runoff above baseflow.
Worked example
A = 20 acres, C = 0.55, tc = 20 min. The 25-year IDF gives 3.6 in/hr at 20 min and 1.8 in/hr at 60 min. Q = 0.55 × 3.6 × 20 = 39.6 cfs, about 40 cfs. Using the 60-minute intensity halves the result - a classic distractor.