AIH Professional Hydrologist - Surface Water Examination cheat sheet

Hydrologic cycle: precipitation = evapotranspiration + runoff + change in storage (P = ET + Q + ΔS).

Water balance for a catchment over period Δt: P - ET - Q = ΔS; units must be consistent (e.g., mm).

Potential evapotranspiration (PET) can be estimated by Penman-Monteith (energy balance + aerodynamic) or Thornthwaite (temperature-based).

Actual evapotranspiration (AET) ≤ PET; AET limited by soil moisture. Budyko curve relates ET/P to PET/P.

Infiltration: Horton equation f(t) = fc + (f0 - fc)e^(-kt); Green-Ampt uses wetting front and soil suction.

Return period T = 1/(1 - P) for annual exceedance probability P; e.g., 100-year flood has 1% annual exceedance probability.

Unit hydrograph: 1 mm of direct runoff from a unit storm; linearity and superposition apply.

Time of concentration (Tc) estimated by Kirpich: Tc = 0.0195 L^0.77 S^(-0.385) (L in m, S in m/m, Tc in minutes).

Manning's equation for open channel flow: Q = (1/n) A R^(2/3) S^(1/2) (SI units).

Rational method: Q = C i A (Q in m³/s, i in m/s, A in m²); C is runoff coefficient (0-1).

Time of concentration for rational method: use Kirpich or similar; storm duration ≥ Tc.

SCS curve number (CN) method: S = (25400/CN) - 254 (mm); Q = (P - 0.2S)² / (P + 0.8S) for P > 0.2S.

CN ranges: 30-100; higher CN = more runoff (e.g., paved = 95-100, forest = 30-60).

Muskingum flood routing: S = K[XI + (1-X)Q]; K is travel time, X is weighting factor (0-0.5).

Flow duration curve: plots discharge vs percent exceedance; Q90 is flow exceeded 90% of time.

Hydrograph components: baseflow, direct runoff, rising limb, peak, recession limb; recession follows exponential decay.

Frequency analysis: fit log-Pearson Type III to annual peak flows; use skew coefficient.

Manning's n typical values: concrete 0.013, natural channel 0.025-0.04, floodplain 0.05-0.15.

Darcy's law: Q = -K A (dh/dL); specific discharge q = Q/A = -K i; i = hydraulic gradient.

Hydraulic conductivity K (m/s) depends on porous medium and fluid; intrinsic permeability k = K μ/(ρ g).

Transmissivity T = K b (b = saturated thickness); storativity S = Ss b (confined) or Sy (unconfined).

Theis equation: s = (Q/(4πT)) W(u), u = r²S/(4Tt); well function W(u) from tables.

Cooper-Jacob approximation valid for u < 0.01: s = (Q/(4πT)) ln(2.25Tt/(r²S)).

Pumping test: plot drawdown vs log time; slope Δs per log cycle gives T = 2.303Q/(4πΔs).

Specific yield (Sy) typical: sand 0.20-0.30, clay 0.01-0.05; specific retention = field capacity - wilting point.

Groundwater flow direction perpendicular to equipotential lines; flow from high head to low head.

Well efficiency = theoretical drawdown / actual drawdown; well loss increases with pumping rate squared.