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Technical Note: On the puzzling similarity of two water balance formulas – Turc–Mezentsev vs. Tixeront–Fu

Abstract. This Technical Note documents and analyzes the puzzling similarity of two widely used water balance formulas:
Turc–Mezentsev and Tixeront–Fu. It details their history and their
hydrological and mathematical properties, and discusses the mathematical
reasoning behind their slight differences. Apart from the difference in their
partial differential expressions, both formulas share the same hydrological
properties, and it seems impossible to recommend one over the other as more
“hydrologically founded”: hydrologists should feel free to choose the one
they feel more comfortable with.
