Fuzzy-Probabilistic Calculations of Evapotranspiration

Evaluation of evapotranspiration uncertainty is needed for proper decision-making in the fields of water resources and climatic predictions (Buttafuoco et al., 2010; Or and Hanks, 1992; Zhu et al., 2007). However, in spite of the recent progress in soil-water and climatic uncertainty quantification, using stochastic simulations, the estimates of potential (reference) evapotranspiration (Eo) and actual evapotranspiration (ET) using different methods/models, with input parameters presented as PDFs or fuzzy numbers, is a somewhat overlooked aspect of water-balance uncertainty evaluation (Kingston et al., 2009). One of the reasons for using a combination of different methods/models and presenting the final results as fuzzy numbers is that the selection of the model is often based on vague, inconsistent, incomplete, or subjective information. Such information would be insufficient for constructing a single reliable model with probability distributions, which, in turn, would limit the application of conventional stochastic methods. Several alternative approaches for modeling complex systems with uncertain models and parameters have been developed over the past ~50 years, based on fuzzy set theory and possibility theory (Zadeh, 1978; 1986; Dubois & Prade, 1994; Yager & Kelman, 1996). Some of these approaches include the blending of fuzzy-interval analysis with probabilistic methods (Ferson & Ginzburg, 1995; Ferson, 2002; Ferson et al., 2003). This type of analysis has recently been applied to hydrological research, risk assessment, and sustainable waterresource management under uncertainty (Chang, 2005), as well as to calculations of Eo, ET, and infiltration (Faybishenko, 2010). The objectives of this chapter are to illustrate the application of a combination of probability and possibility conceptual-mathematical approaches—using fuzzy-probabilistic models— for predictions of potential evapotranspiration (Eo) and actual evapotranspiration (ET) and their uncertainties, and to compare the results of calculations with field evapotranspiration measurements. As a case study, statistics based on monthly and annual climatic data from the Hanford site, Washington, USA, are used as input parameters into calculations of potential evapotranspiration, using the Bair-Robertson, Blaney-Criddle, Caprio, Hargreaves, Hamon, Jensen-Haise, Linacre, Makkink, Penman, Penman-Monteith, Priestly-Taylor, Thornthwaite, and Turc equations. These results are then used for calculations of evapotranspiration based on the modified Budyko (1974) model. Probabilistic calculations are performed using Monte