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Title: An introduction to the hyperspace of Penman-Monteith reference evapotranspiration

Authors: Naim Haie; Rui M.S. Pereira; Gaspar J. Machado; Shakib Shahidian

Addresses: Civil Engineering Department, School of Engineering, University of Minho, Guimaraes, Portugal; International Water Resources Association (IWRA), Paris, France ' Department of Mathematics, School of Sciences, University of Minho, Guimaraes, Portugal ' Department of Mathematics, School of Sciences, University of Minho, Guimaraes, Portugal ' Rural Engineering Department, University of Evora, Evora, Portugal

Abstract: Evapotranspiration is crucial and very relevant to hydrology, particularly under global warming and the growing water scarcity. The FAO Penman-Monteith is the highly used method to calculate the daily standardised reference evapotranspiration (ETo). It utilises seven variables, mostly climatic and produces a complex n-dimensional domain (or hyperspace). No study has presented the internal structure of this 8D space which forms the objective of the present work. To this end, a computer program called HyperET is developed to facilitate the advancement of two intertwined processes: creating windows into the hyperspace and understanding the resulting regions of the domain. The former gives 2D figures for partial analysis and the latter presents significant infeasible regions which are subspaces composed of ETo values outside its chosen minimum and maximum (or thresholds). HyperET is expensive computationally and presents an ETo domain that resembles Swiss holey cheese with three types of infeasible regions and emerging nonlinearity.

Keywords: Penman-Monteith evapotranspiration (ETo); hydrology; irrigation; water management and design; infeasible regions of ETo; climate change; water scarcity; hyperspace; HyperET; domain discretisation; n-dimensional analysis; sefficiency.

DOI: 10.1504/IJHST.2019.096797

International Journal of Hydrology Science and Technology, 2019 Vol.9 No.1, pp.48 - 64

Available online: 13 Nov 2018 *

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