Why is a harbour town mild and a town 800 km inland extreme at the same latitude? Water stores far more heat per square metre than soil, so the sea warms and cools slowly and late, and its air is carried inland by the wind. Change the latitude, the ocean mixed-layer depth, the soil, the wind and a coastal mountain range, and watch five thermometers along the transect. A teaching model, not a weather forecast.
Curves: open sea (blue), coast (cyan), 300 km, 600 km and 1000 km inland. Inland curves swing wider and peak earlier.
The science
Surface slab. A surface of heat capacity C (J/m²/K) that loses heat to space and air at rate λ per kelvin obeys C dT′/dt = F′(t) − λ T′, where F′ is the seasonal swing in absorbed sunlight. For a sinusoidal swing of amplitude F₁ and frequency ω = 2π/year the periodic solution has amplitude F₁ / √(λ² + ω²C²) and lags the Sun by atan(ωC/λ)/ω. Sea water of mixed-layer depth h has C = ρc h ≈ 4.1×10⁶ h, so 50 m gives ω C ≈ 41 W/m²/K, far above λ; soil, with an effective annual-cycle depth of a metre or so (C ≈ 10⁷), gives ω C ≈ 2. Hence a small, late ocean cycle and a large, early land cycle.
Sunlight. Daily-mean insolation Q = (S₀/π)(h₀ sinφ sinδ + cosφ cosδ sin h₀) with solar declination δ from a circular orbit (obliquity 23.44°), and absorbed fraction 1 − 0.30. Annual mean temperature 28 − 42 sin²φ °C is an illustrative fit, not data.
Air over the transect. Wind of speed U carries marine air inland while it relaxes toward the land surface with time τ = 1 day: dT/dx = (T_land − T)/L, L = U τ, giving T(x) = T_land + (T_sea − T_land) e^(−x/L). A coastal range is modelled crudely by cutting L to 35 %. With offshore wind the roles reverse over the sea.
Continentality index. Gorczynski: K = 1.7 A / sin(φ + 10°) − 20.4, with A the annual range; larger means more continental. The climate label is a simplified rule on warmest/coldest month and range, not the full Köppen scheme (no precipitation).
Simplifications. Same albedo and feedback for land and sea, no ocean currents or heat transport (a real north-east Atlantic coast is warmer thanks to the Gulf Stream), no clouds, snow-albedo feedback, soil moisture or topography beyond the single range, one mixed-layer depth for the whole sea, no daily cycle, vertical exaggeration of terrain and trees. Typical values (λ = 9 W/m²/K, C_land = 10⁷ J/m²/K, τ = 1 day) are round illustrative numbers. Terrain, lighthouse, trees and thermometers modelled and baked in Blender, scene by Three.js.