Surface temperature of the earth plays a uniquely important role in solar radiation energy entering the Earth system through the surface energy balance, that is, the partition of solar radiation into long-wave radiation and turbulent and conductive heat fluxes into the atmosphere and the earth. A fundamental physical principle governing the dynamics of surface temperature is the conservation of energy represented by the energy balance equation linking radiation and conductive/turbulent heat fluxes at the earth-atmosphere interface (Huang et al., 2017). Surface temperature and heat fluxes are commonly related through the temperature gradient-flux relationships that couple the surface temperature and fluxes to the temperature and heat fluxes of the interior atmosphere and earth. Prediction and simulation of surface temperature by solving partial differential equations describing the earth-atmosphere interaction processes are mathematically challenging and computationally costly in addition to the long-standing difficulty in physical parameterization of the turbulence of the atmospheric and oceanic boundary layer.Previous studies have revealed other fundamental physical principles underlying the dynamics of surface temperature than the conservation law. For example, surface temperature (and soil wetness) evolves in such a way that evapotranspiration (ET) over the land surface is maximized under the constraint of radiation energy supply (J. Wang et al., , 2007. The maximum principles of ET lay a theoretical foundation for a new dynamics of surface temperature (and the associated surface heat fluxes) without explicitly referring to the atmospheric and below-ground temperature distribution. The non-parametric expression of the maximum principles of ET opens the possibility of a general dynamic equation of surface temperature without specifying the parameterization of conductive and turbulent heat fluxes. The non-gradient formula of heat fluxes (

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