Re-discovering Robert E. Horton's Lake Evaporation Formulae: New Directions for Evaporation Physics
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Abstract. Evaporation from open water is among the most rigorously studied problems in hydrology. Robert E. Horton, unbeknownst to most investigators on the subject, studied it in great detail by conducting experiments and heuristically relating his observations to physical laws. His work furthered known theories of lake evaporation, but it appears that it got dismissed as simply empirical. This is unfortunate, because Hortons century-old insights on the topic, which we summarize here, seem relevant for contemporary climate change-era problems. In re-discovering his overlooked lake evaporation works, in this paper we: 1) examine his several publications in the period 19151944 and identify his theory sources for evaporation physics among scientists of the late 1800s; 2) illustrate his lake evaporation formulae which require several equations, tables, thresholds, and conditions based on physical factors and assumptions; and 3) assess his evaporation results over continental U.S., and analyse the performance of his formula in a subarctic Canadian catchment by comparing it with five other calibrated (aerodynamic and mass transfer) evaporation formulae of varying complexity. We find that Hortons method, due to its unique variable vapor pressure deficit (VVPD) term, outperforms all other methods by ~315% of R2 consistently across timescales (days to months), and an order of magnitude higher at sub-daily scales (we assessed up to 30mins). Surprisingly, when his method uses input vapor pressure disaggregated from reanalysis data, it still outperforms other methods which use local measurements. This indicates that the vapor pressure deficit (VPD) term currently used in all other evaporation methods is not as good an independent control for lake evaporation as Horton's VVPD. Therefore, Horton's evaporation formula is held to be a major improvement in lake evaporation theory which, in part, may: A) supplant or improve existing evaporation formulae including the aerodynamic part of the combination (Penman) method; B) point to new directions in lake evaporation physics as it leads to a "constant" and a non-dimensional ratio the former is due to him, John Dalton (1802), and Gustav Schbler (1831), and the latter to him and Josef Stefan (1881); C) offer better insights behind the physics of the evaporation paradox (i.e. globally, decreasing trends in pan evaporation are unanimously observed, while the opposite is expected due to global warming). Curiously, his rare observations of convective vapor plumes from lakes may also help explain the mythical origins of Greek deity Venus and the dancing Nereids.
