Theory and idealized simulations suggest that mesoscale motions of the atmosphere and ocean are well approximated by quasi-two-dimensional (2D) turbulence. An important characteristic that distinguishes 2D turbulence from fully 3D turbulence is the inverse energy cascade in which net energy transfers, due to the advection terms, provide a flux of energy that drives the larger scales at the expense of smaller scales. The theoretical foundations go back over 35 years, and numerical simulations of idealized flow soon confirmed these foundations. In the past decade laboratory experiments have also witnessed an upscale transfer of energy, but again in very idealized situations. Recently the atmospheric upscale energy flux has been measured using airplane data. For the oceanic mesoscale, only indirect evidence of the inverse cascade has been observed with real data. The author presents the first estimate of the upscale energy flux, which provides direct evidence to assess the applicability of the inverse energy cascade for the oceanic, surface mesoscale. The merged ERS and TOPEX/POSEIDON altimeter data product was used to estimate the surface, weekly, geostrophic flow anomalies. From this velocity field, the 3rd order longitudinal structure function was estimated. With the assumption of local homogeneity, this can be related to the energy transfer between length scales. The isotropy of the structure function will be broken by the beta-effect at length scales of order the Rhines scale and larger, if indeed Rossby waves arrest the inverse cascade. Because of the small Rhines scale in the ocean, between a few tens of kilometers to a few hundred kilometers, we cannot assume isotropy. The structure function was estimated in five directions to account for anisotropy. Results are presented and interpreted for various regions.