AIH Fundamentals of Hydrology Examination cheat sheet

Water balance for a catchment over a time interval: P = ET + Q + ΔS + ΔG, where P is precipitation, ET evapotranspiration, Q streamflow, ΔS storage change, and ΔG net groundwater loss.

Global freshwater is about 2.5% of total water; most of it is locked in glaciers and ice caps, and only a small fraction is readily accessible surface and shallow groundwater.

Hydrologic cycle fluxes are driven by solar energy (evaporation) and gravity (precipitation and runoff); residence times increase from atmosphere (days) to oceans (thousands of years).

Potential evapotranspiration (PET) is the atmospheric demand; actual ET is limited by water availability and cannot exceed PET.

The rational method peak flow: Q = C·i·A, with C a runoff coefficient (0–1), i rainfall intensity, and A drainage area; consistent units are required.

Time of concentration is the travel time from the hydraulically most distant point to the outlet; it sets the critical rainfall duration for design storms.

Unit hydrograph assumption: a rainfall excess of 1 unit over the catchment in a given duration produces a direct runoff hydrograph of fixed shape; linear superposition applies.

A hydrograph's rising limb reflects catchment response, the peak reflects the maximum combined runoff, and the recession limb is dominated by drainage of stored water.

Return period T and annual exceedance probability p are reciprocals: T = 1/p; a 100-year event has a 1% chance of being exceeded in any given year.

Manning's equation: V = (1/n)·R^(2/3)·S^(1/2), where n is roughness, R hydraulic radius (A/P), and S energy slope.

Discharge continuity: Q = V·A; for a rectangular channel, hydraulic radius R = (b·y)/(b + 2y) with b width and y depth.

Froude number Fr = V/√(g·D), with D hydraulic depth; Fr < 1 is subcritical, Fr = 1 critical, and Fr > 1 supercritical flow.

Specific energy E = y + V²/(2g); at critical flow, E is minimum for a given discharge and Fr = 1.

Critical depth in a rectangular channel: y_c = (q²/g)^(1/3), where q is discharge per unit width.

A hydraulic jump converts supercritical to subcritical flow with an energy loss; a weir or flume uses this to measure discharge.

Rating curves relate stage to discharge (often Q = a(h − h0)^b); extrapolation beyond gauged stages is unreliable.

Streamflow is commonly separated into baseflow (groundwater-fed) and direct runoff using graphical or digital filter methods.

Flood routing through a reach is described by continuity plus storage; the Muskingum method uses storage S = K[xI + (1 − x)O].

Darcy's law: Q = −K·A·(dh/dL), where K is hydraulic conductivity, A cross-sectional area, and dh/dL the hydraulic gradient.

Specific discharge (Darcy velocity) q = Q/A = −K·(dh/dL); average linear velocity v = q/n_e, where n_e is effective porosity.

Transmissivity T = K·b, where b is saturated thickness; storativity S relates water released per unit area per unit head change.

Theis solution describes drawdown in a confined aquifer under pumping: s = (Q/(4πT))·W(u), with u = r²S/(4Tt).

Cooper–Jacob approximation applies at large time: s ≈ (Q/(4πT))·ln(2.25Tt/(r²S)); semilog plots of s versus log t yield slope Δs per log cycle = 2.303Q/(4πT).

Pumping test analysis: confined aquifers use the Theis or Cooper–Jacob method; unconfined aquifers require correction for changes in saturated thickness.

Groundwater flows from high to low hydraulic head; flow nets show equipotential lines perpendicular to flow lines.

Porosity is total void fraction; specific yield is the drainable fraction, always less than or equal to porosity.

Saltwater intrusion occurs where freshwater head falls below the Ghyben–Herzberg relation, roughly 40 units of freshwater depth per 1 unit of freshwater above sea level.