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.
Andreassian, V., & Sari, T. (2019). Technical Note: On the puzzling similarity of two water balance formulas - Turc-Mezentsev vs. Tixeront-Fu. Hydrology and Earth System Sciences, 23(5), 2339–2350. https://doi.org/10.5194/hess-23-2339-2019