Foundations

Earth's energy storage changes when incoming and outgoing energy differ.

Infrared absorption and emission affect how Earth loses heat to space.

Weather describes short-term conditions; climate describes their longer-term patterns.

A defined area's water storage changes with total inflow and outflow.

Groundwater flow is often approximately linear in hydraulic-head gradient.

Wind, buoyancy changes and mixing contribute to ocean transport.

Unequal heating and rotation organize broad circulation patterns.

External changes can disturb climate's radiation budget.

Climate responses can amplify or damp a change.

Attribution compares observed changes with plausible drivers and variability.

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.

Specific storage S_s is water volume released per aquifer bulk volume per unit decline in hydraulic head.

For a vertically uniform confined aquifer of fixed thickness b, transmissivity is T=Kb and storativity S=S_sb.

Combining classical elastic storage with Darcy flux yields ∇·(K∇h)=S_s∂h/∂t in a saturated aquifer without internal sources.

Unsaturated water content θ and conductivity K depend on pressure head ψ and the medium's pore structure.

In a rigid porous medium with effectively incompressible water and fixed air pressure, local water conservation with unsaturated Darcy flux gives θ_t=∇·[K(ψ)(∇ψ+e_z)].