= Solution
The low-latitude regions of <Earth> absorb more incoming solar <radiation> than they emit as outgoing <thermal radiation>, whereas high latitudes have a net annual <radiation> deficit. The obliquity of solar incidence and the distribution of daylight create a strong latitude dependence of absorbed solar <energy>; emitted <thermal radiation> varies less strongly because terrestrial <temperature> contrasts are smaller. The <terrestrial atmosphere> and <ocean> therefore carry <energy> from the tropical surplus toward the polar deficits. Otherwise the low latitudes would keep warming and the high latitudes cooling until a different local <radiative equilibrium> was reached.
For a steady, zonally averaged <energy balance>, let $R(\phi)$ be net downward radiation at the top of the <terrestrial atmosphere> and $H(\phi)$ the total northward <energy> transport across latitude $\phi$. A narrow spherical band and <conservation of energy> give
$$
\frac{dH}{d\phi}=2\pi a^2\cos\phi\,R(\phi),\qquad
H(\phi)=2\pi a^2\int_{-\pi/2}^{\phi}R(\varphi)\cos\varphi\,d\varphi.
$$
The poleward direction is northward in the Northern Hemisphere and southward in the Southern Hemisphere. Seasonal <internal energy> storage modifies the instantaneous balance, but not the annual need for poleward redistribution.
Several circulation structures contribute in addition to the transient <eddies> produced by <baroclinic instability> of the middle latitudes:
* The <Hadley cells>, mainly between the equator and about $30^\circ$ latitude, export <energy> in their upper poleward branches and return air equatorward near the surface. The transported quantity includes <enthalpy>, <gravitational potential energy> and <latent heat>; the upper and lower branches have different thermal properties. The cross-equatorial <Hadley cell> is especially important in the seasonal cycle.
* Quasi-stationary <Rossby waves>, associated with mountains and continental heating contrasts, carry <heat> in the extratropical <terrestrial atmosphere>. Their meridional <velocity> and <temperature> anomalies can have a poleward correlation. These are an additional time-mean contribution alongside travelling weather disturbances.
* The <ocean gyres> in tropical and subtropical basins redistribute warm water poleward in strong <western boundary currents> and return cooler water equatorward over broader regions. The thermal difference between the branches produces net <heat transport> despite little net meridional volume transport.
* The <oceanic overturning circulation>, including the <Atlantic meridional overturning circulation>, combines warm upper water moving poleward with colder deep return water. It transports substantial <heat> through the tropical and subtropical Atlantic toward the northern high latitudes. Wind forcing, <buoyancy> exchange and mixing all help maintain this global circulation.
The <Brewer-Dobson circulation> additionally redistributes <energy> in the <stratosphere>, with tropical ascent and extratropical descent, although most total atmospheric <heat transport> occurs lower down. An <Eulerian mean> middle-latitude <Ferrel cell> is thermally indirect and can oppose the poleward transport by <eddies>; listing every meridional circulation as a direct poleward heat carrier would be incorrect.
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