Question 2 of 6: Hydrology Terminology

Question 2: Hydrology Terminology (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

a. Curve Number (CN). An empirical, dimensionless SCS/NRCS index (roughly 30–100) that characterizes a drainage area's runoff potential from its soil hydrologic group, land use/treatment and antecedent moisture condition. It sets the potential maximum retention $S=\dfrac{25400}{CN}-254$ (mm), which then converts total rainfall $P$ to direct runoff via $Q=\dfrac{(P-0.2S)^2}{P+0.8S}$ for $P\gt 0.2S$. A high CN (impervious surfaces, compacted or saturated soils) means low retention and a large runoff fraction.

b. Muskingum Method. A hydrologic (storage-based) channel flood-routing technique that represents in-reach storage as a weighted combination of inflow $I$ and outflow $O$: $S=K[xI+(1-x)O]$, where $K$ is the reach travel time and $x$ (typically 0–0.3) is a weighting factor for the "wedge" storage created as a flood wave advances. Combined with the continuity equation $dS/dt=I-O$ and finite-differenced over a time step, it yields the familiar routing formula $O_2=C_0I_2+C_1I_1+C_2O_1$ with $C_0+C_1+C_2=1$, used to propagate a hydrograph downstream through a river reach.

c. Saturated hydraulic conductivity ($K_{sat}$). The proportionality constant in Darcy's law, $q=-K\,dh/dl$, describing how readily water moves through a fully water-saturated porous medium under a unit hydraulic-head gradient. It governs the maximum (steady, deep-soil) infiltration rate, drain and tile spacing design, and groundwater flow rate (as used directly for the well-hydraulics analysis in Question 6), and is a required input — alongside the wetting-front suction $S$ — to physically based infiltration models such as Green–Ampt.

d. Depression storage. The volume of rainfall intercepted and held in small surface irregularities — furrows, potholes, cracks, wheel ruts — before any overland flow can begin. It must be satisfied first on every storm, so it delays the onset of runoff and disproportionately consumes small, low-intensity storms; unlike interception storage it drains mainly by infiltration and evaporation rather than immediate re-evaporation, so it also constitutes a genuine (if minor) volume loss from the runoff hydrograph.

e. Storm water management. The set of engineering practices — detention and retention ponds, infiltration basins, bioswales and other green infrastructure, and conveyance/outlet design — used to control the quantity, timing and quality of runoff generated by land development. The usual design objective is to attenuate the post-development peak discharge back toward (or below) the pre-development peak, protecting downstream channel capacity and water quality; the peak-shaving pond of Question 5 is a direct application.

f. Abstractions. The collective term for every process that removes water from gross precipitation before it can become direct surface runoff: infiltration, interception by vegetation, depression storage, and evaporation. The SCS-CN method lumps the earliest-acting of these into a single initial abstraction $I_a=0.2S$, with the remainder continuing as infiltration loss throughout the storm; the Horton model of Question 4 explicitly represents the infiltration component of abstractions as a time-varying rate.

g. Thiessen Polygons. A geometric method for area-weighting point rain-gauge measurements across a watershed, constructed by joining neighbouring gauges and drawing the perpendicular bisector of each connecting line; the resulting polygons partition the watershed so that every point inside a gauge's polygon is closer to that gauge than to any other. Watershed-average precipitation is then the area-weighted mean $\bar P=\dfrac{\sum A_iP_i}{\sum A_i}$, which (unlike a simple arithmetic average) accounts for uneven gauge spacing.

h. Hyetograph. A plot of rainfall intensity (or incremental depth) against time over the course of a storm — the input time series to a rainfall-runoff model, as distinct from a hydrograph, which is the resulting discharge response plotted against time (the object computed in Question 1).

i. Evapotranspiration (ET). The combined loss of water to the atmosphere from direct evaporation (bare soil, open water, and rain intercepted on foliage) and transpiration (water taken up by plant roots and released as vapour through leaf stomata). It is normally estimated with a combination method such as Penman–Monteith and forms a major term in the watershed water budget $P=ET+Q+\Delta S$; it is the quantity that determines how much of a golf course's pumped irrigation water is actually consumed rather than returned to the aquifer, as discussed in Question 6c.

j. Distributed vs Lumped hydrologic models. A lumped model represents an entire watershed (or sub-basin) with a single set of spatially averaged parameters and produces one aggregate output response — the unit-hydrograph approach of Question 1 is a lumped model. A distributed model instead divides the watershed into many grid cells or sub-units, each carrying its own soils, land-use, rainfall and state variables, and routes flow explicitly between them. Distributed models better represent real spatial variability and are preferred where inputs (soil, rainfall, land use) vary sharply across the basin, but they demand far more data, calibration effort and computation than a lumped model of comparable watershed size.