Surface Water Hydrology: Hydrographs, Frequency, and Routing
Core concepts
Surface water questions center on the streamflow hydrograph: rising limb, crest, recession, and baseflow separation. Candidates should understand the unit hydrograph, its convolution, and the assumptions of linearity and time invariance. Flow-duration curves describe the percentage of time a given discharge is equaled or exceeded, useful for water-supply yield. Flood frequency analysis uses probability distributions (Log-Pearson Type III in the U.S.) with return period T and exceedance probability 1/T.
Routing and statistics
Reservoir and channel routing (level-pool, Muskingum) modify the hydrograph by attenuating peak and delaying timing. Muskingum uses K (travel time) and X (weighting). Statistical concepts include return period, risk over a design life (risk = 1 − (1 − 1/T)^n), and the difference between a design storm and a design flood.
Traps to watch
A frequent trap is confusing the probability of a 100-year flood in any single year (1%) with the chance over a period. Another is treating a return period as a fixed interval rather than a long-run average. Watch for baseflow separation errors and for using a unit hydrograph on a catchment whose area differs from the derivation basin without scaling.
Worked example
Probability of at least one 50-year flood in 30 years: risk = 1 − (1 − 1/50)^30 = 1 − (0.98)^30 ≈ 1 − 0.545 = 0.455, or about 45%. Rule of thumb: the risk over n years approaches 63% when n equals the return period.