Expert-level hydrology covering the water cycle, surface water hydrology, groundwater, watershed analysis, flood hydrology, water quality, and water resource management.
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Precipitation: rain, snow, hail — measured by rain gauges and radar. Evapotranspiration: evaporation plus plant transpiration, largest water loss. Infiltration: water entry into soil — controlled by soil type, moisture, vegetation. Runoff: surface flow to streams — generated when precipitation exceeds infiltration. Groundwater recharge: infiltrated water reaching saturated zone.
Streamflow: discharge Q = A x V, measured at gauging stations. Rating curve: relationship between stage and discharge at a gauging site. Hydrograph: streamflow vs time response to precipitation event. Unit hydrograph: 1 cm of effective rainfall over watershed in unit time. Base flow: groundwater contribution to streamflow during dry periods.
Aquifer types: unconfined (water table), confined (artesian), perched. Darcy law: Q = -KA dh/dl, K is hydraulic conductivity. Hydraulic head: elevation head plus pressure head. Theis equation: drawdown around pumping well in confined aquifer. Groundwater flow equation: combines Darcy law and continuity.
Return period: 100-year flood has 1% chance of exceedance in any year. Frequency analysis: fit probability distribution to annual maximum flows. Flood routing: tracking flood wave through channel or reservoir. Rational method: Q = CiA for small watersheds, C is runoff coefficient.
| Pitfall | Fix |
|---|---|
| Confusing return period with probability | 100-year flood does not mean once per century |
| Ignoring baseflow separation | Stormflow and baseflow behave differently |
| Applying Darcy law to turbulent flow | Check Reynolds number for flow regime |
| Assuming stationarity in frequency analysis | Climate change may shift flood frequency |
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Expert-level abstract algebra knowledge. Use when working with groups, rings, fields, modules, Galois theory, representation theory, or algebraic structures. Also use when the user mentions 'group', 'ring', 'field', 'homomorphism', 'isomorphism', 'normal subgroup', 'quotient group', 'Sylow theorem', 'Galois theory', 'polynomial ring', 'ideal', 'module', 'vector space', or 'representation theory'.
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Expert-level acoustics knowledge. Use when working with sound waves, acoustic propagation, resonance, standing waves, Doppler effect, room acoustics, ultrasound, noise control, musical acoustics, or architectural acoustics. Also use when the user mentions 'sound wave', 'decibel', 'frequency', 'resonance', 'standing wave', 'Doppler effect', 'acoustic impedance', 'reverberation', 'ultrasound', 'noise control', 'harmonics', or 'sound intensity'.
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Expert-level aerodynamics covering subsonic and supersonic flow, lift and drag, airfoil theory, boundary layers, compressible flow, and CFD methods.
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Expert-level air quality engineering covering pollutant sources, atmospheric dispersion, air quality standards, emission controls, and air quality modeling.
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Expert-level aircraft structures covering structural design philosophy, wing and fuselage analysis, fatigue and damage tolerance, composite structures, and certification.
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Expert-level algorithms and complexity theory covering sorting, searching, graph algorithms, dynamic programming, greedy algorithms, NP-completeness, and algorithm design paradigms.
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