AIH Professional Hydrologist - Groundwater Examination cheat sheet

Hydrologic cycle water balance: P = ET + Q + ΔS + G, where P is precipitation, ET evapotranspiration, Q surface runoff, ΔS storage change, and G net groundwater outflow.

Potential evapotranspiration (Thornthwaite) is driven by temperature; actual ET is limited by available soil moisture and is less than potential when soil water is depleted.

Field capacity is the water content retained after free drainage; wilting point is the moisture below which plants cannot extract water; available water capacity is the difference between them.

Infiltration follows Horton behavior: an initially high rate decays exponentially toward a constant rate as the soil surface seals and wets.

Manning's equation for open-channel flow: v = (1/n) R^(2/3) S^(1/2), with v velocity, n roughness, R hydraulic radius, S slope.

Rational method peak discharge: Q = C i A, where C is a runoff coefficient, i rainfall intensity, and A drainage area (consistent units).

The unit hydrograph is the direct runoff from one unit of effective rainfall over a fixed duration; larger storms scale linearly in volume but not in timing.

Time of concentration is the travel time from the hydraulically most distant point to the outlet; it controls the critical rainfall duration for peak flow.

A flow-duration curve plots discharge versus percent of time exceeded; the median flow (Q50) is a common low-flow reference index.

Baseflow separation divides a hydrograph into direct runoff and delayed groundwater contribution; baseflow recession follows an exponential decay curve.

A rating curve relates stage to discharge (typically Q = a(h - h0)^b); extrapolation beyond measured stage is a major source of uncertainty.

The SCS curve number method estimates runoff depth: Q = (P - 0.2S)^2 / (P + 0.8S) for P > 0.2S, with S = (25400/CN) - 254 in millimeters.

Flood frequency analysis uses a fitted distribution (e.g., log-Pearson III) to estimate the discharge exceeded at a given return period; return period T = 1/(1 - p) for annual exceedance probability p.

Muskingum routing uses storage S = K[xI + (1-x)O], with K a travel-time constant and x a weighting factor (0 to 0.5) controlling attenuation.

Rational method assumptions: uniform rainfall intensity over the drainage area for a duration equal to the time of concentration, and constant runoff coefficient.

Double-mass analysis plots cumulative station catch against cumulative reference catch to detect inhomogeneity or a change in gauge record.

The water year in most U.S. practice runs October 1 through September 30, chosen to bracket a complete snow-accumulation and melt cycle.

Darcy's law: Q = -K A (dh/dL), where K is hydraulic conductivity, A cross-sectional area, and dh/dL the hydraulic gradient; valid for laminar flow.

Specific yield (Sy) is the drainable porosity; specific retention holds water against gravity; storativity S = Sy + b·Ss for an unconfined aquifer.

Transmissivity T = K·b (conductivity times saturated thickness), with units of length squared per time.

The Theis equation for drawdown in a confined aquifer: s = (Q / 4πT) W(u), with u = r²S / (4Tt) and W(u) the well function.

Cooper-Jacob approximation applies when u < 0.01, giving s = (2.303 Q / 4πT) log10(2.25 T t / r² S).

Thiem equation for steady radial flow to a well: Q = 2πT (h2 - h1) / ln(r2 / r1).

Pumping test analysis plots drawdown versus log time; the straight-line slope gives T and the intercept (or recovery) gives storativity.

Groundwater flow direction is perpendicular to potentiometric contours, from high to low head; flow nets use orthogonal equipotential and flow lines.

Saltwater intrusion boundary follows the Ghyben-Herzberg relation: freshwater lens thickness below sea level is about 40 times the water-table elevation above sea level.