4.4 Hydrologic Systems

The Hydrologic Cycle & Water Balance

The hydrologic cycle circulates water through precipitation, infiltration, evapotranspiration, surface runoff, and groundwater flow. , P = Q + ET + ΔS, where P is precipitation, Q is runoff, ET is evapotranspiration, and ΔS is storage change. Runoff is the portion of rainfall that reaches a channel after infiltration and other losses (abstractions) are subtracted. Abstractions include interception (vegetation), depression storage (ponding), evaporation, and especially infiltration — the movement of water into the soil, often modeled with Horton's or the NRCS curve-number method.

The difference between gross rainfall and abstractions is the excess (effective) rainfall that becomes direct runoff. Infiltration capacity is high at the start of a storm and decays as the soil saturates. The exam emphasizes estimating peak runoff for sizing storm sewers, culverts, channels, and detention basins, and distinguishing peak discharge (a flow rate, cfs) from runoff volume (a volume, acre-feet). Groundwater hydrology (Darcy's law, q = −K·dh/dL, with K the hydraulic conductivity) appears lightly and connects surface water to aquifer recharge.

The Rational Method

For small urban watersheds (typically < 200 acres), peak runoff is estimated with the Rational Method:

Q = C·i·A

where Q is peak flow, C is the dimensionless runoff coefficient (0 to 1), i is rainfall intensity, and A is drainage area. In US Customary units, when i is in inches/hour and A is in acres, Q comes out in cubic feet per second (cfs) because the conversion factor 1.008 ≈ 1.0. In SI, Q (m³/s) = C·i·A/360 with i in mm/hr and A in hectares.

Key assumptions and traps: rainfall is uniform in space and time over the area; the storm duration equals the time of concentration t_c (this gives the maximum peak because the whole basin is contributing at once); C is constant for the design storm; and the watershed is small enough that these hold. The method gives only the peak discharge, not a full hydrograph or a volume. For mixed land use, area-weight the coefficient: C_avg = Σ(C_j·A_j)/ΣA_j. For larger or more complex watersheds (typically > 200 acres) the Rational Method breaks down and engineers switch to unit-hydrograph or NRCS curve-number methods.

The runoff coefficient embodies all losses lumped into one number, so it implicitly depends on soil type, slope, land cover, and even storm return period (C is often increased for rarer, higher-intensity storms).

Intensity, Time of Concentration & Return Period

Rainfall intensity i is read from Intensity-Duration-Frequency (IDF) curves: choose a design return period T (e.g., 10-yr, 25-yr, 100-yr) and a duration; shorter, rarer storms are more intense. To apply the Rational Method, set the duration equal to the time of concentration t_c — the time for runoff to travel from the hydraulically most distant point of the watershed to the outlet (often via the Kirpich or NRCS equations). Longer t_c → lower intensity → lower peak, all else equal.

The return period T (years) and the annual exceedance probability are reciprocals: P = 1/T. A '100-year storm' has a 1% (0.01) chance of being equaled or exceeded in any single year — it is NOT 'once per 100 years.' The probability of at least one exceedance in n years is 1 − (1 − 1/T)^n; e.g., a 100-yr event has 1 − 0.99^30 ≈ 26% chance over a 30-year project life.

Hydrographs, Unit Hydrographs & Routing

A hydrograph plots discharge versus time at a point; its area under the curve is the total runoff volume. A unit hydrograph (UH) is the direct-runoff hydrograph from one unit (1 inch or 1 cm) of excess rainfall over a specified duration, uniformly over the basin. UH theory is linear: scale a UH by the rainfall depth and superpose (lag-and-add) successive storm increments to build the storm hydrograph.

Flood/reservoir routing translates an inflow hydrograph to an outflow hydrograph through storage, using the storage (continuity) equation I − O = dS/dt. Storage attenuates and delays the peak; outflow peaks where it crosses the falling limb of inflow. Detention basins apply this to limit the post-development peak flow to pre-development levels — required by most stormwater regulations because development raises C and shortens t_c, both of which increase peak runoff.

Key hydrograph features the exam expects you to identify: the rising limb, the peak (crest), the recession (falling) limb, the time to peak, and the base flow separating direct runoff from groundwater contribution. Doubling the rainfall depth doubles the ordinates of a unit hydrograph but does NOT change its time base — a defining property of the linear UH method. The NRCS (SCS) dimensionless unit hydrograph and the triangular UH are common standardized shapes used when no gauged data exist.

Worked Rational-Method Example

A 10-acre commercial site is 60% pavement (C = 0.90) and 40% lawn (C = 0.20). The 10-yr, t_c-duration intensity is i = 3.0 in/hr. Find the peak runoff.

• Weighted C = (0.6×0.90 + 0.4×0.20) = 0.54 + 0.08 = 0.62.
• Q = C·i·A = 0.62 × 3.0 in/hr × 10 ac = 18.6 cfs (since 1 ac·in/hr ≈ 1 cfs).