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The inference of a general Bayesian network has been shown to be an NP-hard problem, even for approximate solutions. Although k-dependence Bayesian (KDB) classifier can construct at arbitrary points (values of k) along the attribute dependence spectrum, it cannot identify the changes of interdependencies when attributes take different values. Local KDB, which learns in the framework of KDB, is proposed in this study to describe the local dependencies implicated in each test instance. Based on the analysis of functional dependencies, substitution-elimination resolution, a new type of semi-naive Bayesian operation, is proposed to substitute or eliminate generalization to achieve accurate estimation of conditional probability distribution while reducing computational complexity. The final classifier, averaged k-dependence Bayesian (AKDB) classifiers, will average the output of KDB and local KDB. Experimental results on the repository of machine learning databases from the University of California Irvine (UCI) showed that AKDB has significant advantages in zero-one loss and bias relative to naive Bayes (NB), tree augmented naive Bayes (TAN), Averaged one-dependence estimators (AODE), and KDB. Moreover, KDB and local KDB show mutually complementary characteristics with respect to variance.

Abstract. Evapotranspiration (ET) is a major component of the land surface process involved in energy fluxes and energy balance, especially in the hydrological cycle of agricultural ecosystems. While many models have been developed as powerful tools to simulate ET, there is no agreement on which model best describes the loss of water to the atmosphere. This study focuses on two aspects, evaluating the performance of four widely used ET models and identifying parameters, and the physical mechanisms that have significant impacts on the model performance. The four tested models are the Shuttleworth–Wallace (SW) model, Penman–Monteith (PM) model, Priestley–Taylor and Flint–Childs (PT–FC) model, and advection–aridity (AA) model. By incorporating the mathematically rigorous thermodynamic integration algorithm, the Bayesian model evidence (BME) approach is adopted to select the optimal model with half-hourly ET observations obtained at a spring maize field in an arid region. Our results reveal that the SW model has the best performance, and the extinction coefficient is not merely partitioning the total available energy into the canopy and surface but also including the energy imbalance correction. The extinction coefficient is well constrained in the SW model and poorly constrained in the PM model but not considered in PT–FC and AA models. This is one of the main reasons that the SW model outperforms the other models. Meanwhile, the good fitting of SW model to observations can counterbalance its higher complexity. In addition, the detailed analysis of the discrepancies between observations and model simulations during the crop growth season indicate that explicit treatment of energy imbalance and energy interaction will be the primary way of further improving ET model performance.

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