# One of the most difficult problems in hydrology, and one of the most important, is to be able to predict as a function of input climate variable...

One of the most difficult problems in hydrology, and one of the most important, is to be able to predict as a function of input climate variables, precipitation P and solar energy (potential evapotranspiration, PET), what fraction of the precipitation runs off and which fraction is returned to the atmosphere through evapotranspiration ET. This problem has been recognized since the early 20th Century and researchers such as Schreiber, Oldekop, Turc, Pike, and Budyko have their names associated with phenomenological models of this partitioning, known as the water balance. It is noteworthy, that none of these is a theoretical model. We have recently developed a theory to predict ET/P as a function of PET/P. This theory has a single parameter, which is the plant root fractal dimensionality - the larger this value is, the more water is returned to the atmosphere. The analytical result was obtained as an optimization of the net primary productivity with respect to the hydrologic fluxes. Observed values of the root fractal dimensionality sweep out the observed values of ET/P, with the higher dimensionalities giving the higher values of ET. See our attached publication in GSA Today