Evapotranspiration Uncertainty Modeling Using Fuzzy-Probabilistic and Maximum Likelihood Bayesian Averaging.

Multiple semi-empirical formulae have been developed for calculations of potential evapotranspiration (PET) and actual evapotranspiration (ET), using meteorological data and soil hydraulic parameters.  Selection of the most suitable model and corroboration with field observations of evapotranspiration is a challenging problem from both technical and modeling perspectives.  This presentation will focus on the evaluation of several types of uncertainties involved in the estimation of evapotranspiration, mainly, epistemic uncertainty, which is due to the lack or limited knowledge about the conceptual models, processes or parameters, and aleatory uncertainty, which is due to the spatial and temporal variability of meteorological parameters, and can be accounted for using geostatistical approaches.  Using daily and monthly meteorological data from the Savannah River Site, South Carolina, USA, PET calculations are first conducted from the Bair-Robertson, Blaney-Criddle, Caprio, Hargreaves-Samani, Hamon, Jensen-Haise, Linacre, Makkink, Penman, Penman-Monteith, Priestly-Taylor, Thornthwaite, and Turc equations.  The ET is then determined based on the modified Budyko and Zhan models. The combined epistemic and aleatory uncertainty of PET and ET calculations is evaluated by assigning probability density (Monte-Carlo simulations) and possibility distribution (fuzzy-probabilistic) functions of input meteorological parameters for multiple PET and ET equations.  A subset of five PET models was selected based on the highest fuzzy degree similarity index (FDSI), and these models were used for simulations of ET.  The corroboration of calculated and measured PET and ET time series is also provided using Maximum Likelihood Bayesian Model Averaging (MLBA) technique.  The fuzzy-probabilistic calculations provide conservative estimates of the uncertainty of PET and ET.  The developed approach can be used for advancing the development of field PET and ET measurements, selection of a subset of formulae for PET and ET calculations, and decision support systems.