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The Maximum Entropy Production (MEP) method for modeling surface energy budget has been developed and validated at local, regional and global scale including the Arctic regions. The MEP model has solid theoretical foundation built on the Bayesian probability theory, information theory, non-equilibrium thermodynamics and boundary layer turbulence theory. Its formulation has advantageous features including closing energy budget at any space-time scales, independence of moisture and temperature gradient, wind speed and surface roughness, and free of tunable empirical parameters. Application of the MEP model has been covering all types of land covers including Arctic permafrost tundra, sea ice and snow surfaces. Recent tests using field experimental observations suggest that the MEP model using fewer input data and model parameters is able to simulate surface energy budget accurately. It is a more efficient alternative to the classical Penman-Monteith model of potential evapotranspiration. The MEP method has potential to influence the study of Arctic water-energy cycles and climate change.