Albedo planet would drop to about 0 °C. In contrast, if the entire Earth was covered by water — a so-called aquaplanet — the average temperature on the planet would rise to almost 27 °C. For land surfaces, it has been shown that the albedo at a particular solar zenith angle "θ" can be approximated by the proportionate sum of two terms: the directional-hemispherical reflectance at that solar zenith angle, formula_1, and the bi-hemispherical reflectance, formula_2, with formula_3 being the proportion of direct radiation from a given solar angle, and formula_4 being the proportion of diffuse illumination. Hence, the actual albedo
Riemannian connection on a surface charting the historical development from before Gauss to modern times, is by . Graduate-level treatments of the Riemannian connection can be found in , and . Accessible introductions to Cartan's approach to connections using moving frames can be found in and . The classic treatment of connections can be found in . Riemannian connection on a surface In mathematics, the Riemannian connection on a surface or Riemannian 2-manifold refers to several intrinsic geometric structures discovered by Tullio Levi-Civita, Élie Cartan and Hermann Weyl in the early part of the twentieth century: parallel transport, covariant derivative and connection form . These