Latitude Radiation Budget Calculator

The latitudinal radiation budget is the net top-of-atmosphere flux for a band of latitude: absorbed shortwave, Q times (1 minus albedo), minus outgoing longwave, eps sigma T to the fourth. Absorbed sunlight falls off toward the poles for two compounding reasons, because irradiance on a horizontal surface scales with the cosine of the solar zenith angle and because polar winter removes the Sun entirely for months at a time. Annual mean insolation at the top of the atmosphere runs near 416 W per square meter at the equator and about 172 W per square meter at the poles, a ratio of roughly 2.4, and albedo pushes the same direction, rising from near 0.20 over tropical ocean to 0.60 or more over sea ice and Antarctic snow. Outgoing longwave radiation is far flatter, spanning only about 280 W per square meter in the subtropics down to roughly 170 W per square meter over the poles, because atmospheric and oceanic transport hold the temperature contrast well below the insolation contrast. The result is a persistent surplus between about 38 degrees N and 38 degrees S, peaking near plus 60 to 70 W per square meter, and a deficit poleward of those latitudes reaching minus 100 W per square meter or worse in polar winter. That gap is closed by meridional energy transport of roughly 5 to 6 petawatts, peaking near 35 to 40 degrees in each hemisphere, carried mostly by the atmosphere at mid latitudes and mostly by the ocean within the deep tropics. A single-column calculation cannot represent transport, so a nonzero imbalance at any latitude should be read as the transport requirement rather than as local warming.

Latitudinal energy accounting predates satellites by decades. George Simpson published quantitative estimates of the radiation balance by latitude for the Royal Meteorological Society in 1928, working from surface observations and assumptions about atmospheric absorption, and concluded that the tropics gain while the poles lose. Mikhail Budyko in Leningrad compiled the first comprehensive atlases of the global heat balance in 1955 and 1963 using a similar approach. In 1969 Budyko and, independently, William Sellers published one-dimensional energy balance models that combined the latitudinal budget with diffusive heat transport and a mobile ice line, and both found the ice-albedo feedback capable of driving the planet into a fully glaciated state. Direct measurement began with the flat-plate radiometer designed by Verner Suomi and flown aboard Explorer 7 in 1959, which returned the first satellite estimates of reflected and emitted flux by latitude. Thomas Vonder Haar and Suomi published the first credible satellite-derived meridional profile in 1971, finding a smaller pole-to-equator gradient in outgoing longwave radiation than earlier surface-based estimates had suggested. The Earth Radiation Budget Experiment, launched in 1984, and the CERES instruments flying since the late 1990s raised accuracy to a few W per square meter. Kevin Trenberth and Julie Caron, in 2001, combined atmospheric reanalysis with satellite fluxes to separate atmospheric from oceanic transport, showing that the atmosphere dominates poleward of about 30 degrees latitude.