Evaluation of Bayesian Network Model for Estimation of Pan Evaporation

Evaporation is one of the main elements of hydrologic cycle. Accurate estimation of pan evaporation is very important in many water-related activities such as irrigation and drainage projects, water balance studies, reservoir operation, and the like. The class A pan is one of the main pan evaporation instruments, which is used in standard synoptic weather stations in Iran. Direct measurement of evaporation is expensive and time-consuming. Therefore, different empirical models, which use different meteorological variables, can be used to estimate pan evaporation. This is so crucial in arid and semi-arid countries such as Iran, where the climate is mostly hyper-arid and it is not easy to measure evaporation directly. In the recent decades, by the development of computers many data driven models have been created for estimating evaporation. One of the intelligent models widely used to hydrologic processes is Bayesian Network Model, which was introduced by Bentin in 1990, and then applied for neural networks by MacKey (1992). Bayesian networks (BNs), also known as belief networks (or Bayes nets for short), belong to the family of probabilistic graphical models (GMs). These graphical structures are used to represent knowledge about an uncertain domain. In particular, each node in the graph represents a random variable, while the edges between the nodes represent probabilistic dependencies among the corresponding random variables. These conditional dependencies in the graph are often estimated by using known statistical and computational methods. Hence, BNs combine principles from graph theory, probability theory, computer science, and statistics. GMs with undirected edges are generally called Markov random fields or Markov networks. These networks provide a simple definition of independence between any two distinct nodes based on the concept of a Markov blanket. Markov networks are popular in fields such as statistical physics and computer vision. BNs correspond to another GM structure known as a directed acyclic graph (DAG) that is popular in statistics, machine learning, and artificial intelligence societies. They enable an effective representation and computation of the joint probability distribution (JPD) over a set of random variables (Reggiani and Weerts, 2008). In addition, BNs model the quantitative strength of the connections between variables, allowing probabilistic beliefs about them to be updated automatically as new information becomes available. In this model, the unknown relationships between parameters in processes can be shown by a diagram. This diagram is non-circular, and has directions composed of nodes and curves for showing the possible relationships in parameters (Money et al, 2012). Therefore, the main objective of this study is modeling of daily class A pan evaporation using the Bayesian Network model in six stations of East Azerbaijan Province.