Budyko style equations are commonly used to represent a long-term average of a relationship between the principal hydrologic fluxes, evapotranspiration, run-off and precipitation, on the Earth's terrestrial surface (Budyko, 1958;Oldekop, 1911;Pike, 1964;Schreiber, 1904). Precipitating water, P, when it reaches the ground, may partition into several parts -some evaporates directly to the atmosphere, some may run-off along the surface, and some penetrates the surface. What enters the soil may be used by plants (transpiration), or reach deeper into the subsurface, where it may replenish oversubscribed aquifers or re-emerge in rivers or springs. Understanding this apportionment is a long-recognized need in the hydrologic scienc-