Foundations

Metamorphism changes mineral assemblage and texture under changed pressure, temperature, fluid and deformation conditions without requiring bulk melting.

Mechanical weathering changes fragment size; chemical weathering transforms or dissolves minerals through reactions such as hydrolysis and oxidation.

A distribution coefficient relates one species' concentrations in two specified coexisting phases.

In homogeneous constant-D batch melting, mass balance and equilibrium give melt enrichment Cℓ/C₀=1/[D+F(1−D)].

Streams carry bed load, suspended material and dissolved solutes through different processes.

Porosity measures pore-space fraction, while hydraulic permeability/conductivity concerns connected flow under stated fluid conditions.

Groundwater exchanges dissolved species with aquifer minerals and surfaces.

Glacier accumulation and ablation determine a mass budget; an equilibrium line separates zones in the specified surface-balance picture.

Moving ice can abrade and pluck bedrock, while transported debris can be deposited directly as till or sorted by meltwater.

Relative sea level is water level measured against local land.

When vertical acceleration is negligible, the vertical pressure gradient balances gravity: ∂p/∂z=−ρg for upward z.

For sufficiently slowly varying large-scale flow away from strong friction, horizontal pressure-gradient and Coriolis accelerations can approximately balance.

For an ideal dry gas with constant heat capacities, potential temperature θ=T(p₀/p)^(Rd/cp) is conserved in reversible adiabatic parcel motion.

Water-vapour amount and relative humidity are distinct; relative humidity compares vapour pressure with a specified saturation value at the current temperature.

Seawater density depends on temperature, salinity and pressure.

In the steady idealized surface Ekman layer, vertically integrated mass transport is ME=τ×ẑ/f.

Spatially varying wind stress can cause Ekman convergence/divergence and force interior ocean circulation.

Dissolved inorganic carbon includes aqueous CO₂/carbonic-acid convention, bicarbonate and carbonate.

Natural archives such as ice, sediments, corals and tree rings record properties related to past environments.

For a classical gas in local thermodynamic equilibrium, level ratios within one ionization stage obey N_b/N_a=(g_b/g_a)exp[−(E_b−E_a)/(k_BT)].

An absorption line's wavelength equivalent width is W_λ=∫[1−F_λ/F_{λ,c}]dλ, using the local continuum.

In an expanding FLRW model with present scale factor one, the line-of-sight comoving distance is D_C=c∫₀ᶻ dz′/H(z′), and the lookback time is t_L=∫₀ᶻ dz′/[(1+z′)H(z′)].

For transparent geometrical photon propagation in FLRW cosmology, angular diameter distance is D_A=D_M/(1+z), and luminosity distance is D_L=(1+z)D_M=(1+z)²D_A.

Radial stellar pulsation has a characteristic gravitational/acoustic period scale proportional to √[R³/(GM)].

A spherical planet intercepts stellar power over its projected disk and emits thermal power over its surface.

At an exobase radius r_ex and temperature T_ex, λ=GMm/(r_ex k_BT_ex) compares a species' binding energy with thermal energy.

Tides arise from gravitational acceleration differences across an extended body.

In a smooth stationary axisymmetric potential, expanding about a stable circular guiding radius R_g gives small radial oscillations at epicyclic frequency κ and vertical oscillations at ν.

For a razor-thin rotating ideal fluid disk, local axisymmetric tightly wound perturbations have dispersion ω²=κ²−2πGΣ|k|+c_s²k².

In a well-mixed closed gas-plus-star system with initially zero metallicity, instantaneous recycling and constant yield p per mass locked in long-lived stars, gas metallicity follows Z=p ln(1/μ), where μ=M_gas/M_total.