Why does the ground stay warm?

Sunlight warms the ground, and warm ground sends energy upward as thermal infrared. Imagine that energy crossing one simple atmospheric layer. If the layer absorbs more of it, why does the ground become warmer even when sunlight stays the same? First predict whether more absorption changes the energy that ultimately leaves the top of this model.

▶ Try it yourself in Greenhouse Balance: change effective infrared absorption and follow the energy through the surface, layer, and top-of-model ledgers.

See the exchange

The model fixes solar irradiance at 1,361 watts per square meter and albedo at 0.30. Spreading the absorbed sunlight over a sphere gives 238.175 watts per square meter on average. NASA reports solar-irradiance measurements near this reference value and describes the larger energy budget of Earth. The model keeps those inputs fixed so one relationship stays visible. NASA Goddard: Solar Irradiance Science; NASA Earth Observatory: Climate and Earth’s Energy Budget.

The ground emits infrared upward. The ideal gray layer absorbs a chosen fraction, then emits equal fluxes upward and downward; the rest of the surface infrared passes through. Raise the control, ε, from 0 to 1 while keeping sunlight and reflectivity fixed. The control describes effective infrared absorption in this model. It is not a carbon-dioxide concentration dial.

Predict, then test

At ε = 0, the layer is transparent: the model surface is about 254.6 K, no layer temperature is defined, and 238.2 watts per square meter leaves the top. At ε = 0.5, the model surface is about 273.6 K. It emits 317.6 watts per square meter upward; 158.8 is absorbed by the layer and 158.8 passes through. The layer emits 79.4 upward and 79.4 downward. The top ledger still totals 238.2 watts per square meter. At ε = 1, the model surface is about 302.7 K; the layer emits 238.2 upward and 238.2 downward, and the upward share balances the fixed solar input. These are calculated reference values for the idealized equations, not observations of Earth.

Follow three balances. At the surface, absorbed sunlight plus downward infrared equals surface emission. In the layer, absorbed surface infrared equals its upward and downward emission combined. At the top, transmitted surface infrared plus upward layer emission equals outgoing energy. The surface warms in this model because it must emit more to balance the fixed sunlight and the layer’s downward emission. At equilibrium, energy still leaves the top at the same rate it enters.

Connect the model to the real atmosphere

NASA describes greenhouse gases absorbing infrared and radiating energy in multiple directions. This experiment compresses that complex atmosphere into one isothermal gray layer with the same absorption share across infrared wavelengths. PhET’s The Greenhouse Effect is a related educational reference; this tool uses its own flux-ledger experiment, original artwork and implementation.

Real air has wavelength- and altitude-dependent absorption. The surface also exchanges energy through evaporation and moving air; clouds, aerosols, sunlight absorbed in the atmosphere, oceans, land, circulation and changing heat storage matter. This one-layer model omits those processes and assumes immediate radiative equilibrium. Its temperatures are outputs of the teaching equations, not Earth’s observed mean temperature, a climate sensitivity estimate, or a forecast.

Sources: NASA Goddard, Solar Irradiance Science; NASA Earth Observatory, Climate and Earth’s Energy Budget; UCAR Center for Science Education, The Greenhouse Effect; OpenStax, Blackbody Radiation; PhET, The Greenhouse Effect.