Parameter variability across different timescales in the energy balance-based model and its effect on evapotranspiration estimation

Evapotranspiration is a key consideration for addressing a number of scientific and engineering issues. There are considerable errors in current evapotranspiration models due to the high uncertainty in model parameters. Considering that evapotranspiration models maintain the same mathematical form when run on different timescales, we argue that the uncertainty in model parameters can be reduced by considering the parameter variability across different timescales. Here, the four key parameters in the energy balance-based evapotranspiration model, including aerodynamic roughness length, thermodynamic roughness length, surface conductance, and energy balance ratio, are retrieved and evaluated on instantaneous and daily timescales based on the observations from 113 sites in the FLUXNET2015 dataset. Then data-driven instantaneous and daily parameter models are built to estimate evapotranspiration. The results show that strong multi-timescale variability occurs in all four parameters. The coefficients of variation of the four instantaneous parameters range from 0.32 to 1.70. The links of parameters on different timescales are weak. The correlation coefficients of the daily mean value of instantaneous parameter values and daily parameter values vary from 0.44 to 0.83. By considering the multi-timescale variability of the parameters, the accuracy of evapotranspiration estimation can be largely improved, with RMSE of the instantaneous and daily evapotranspiration estimation decreasing from 35.76 to 9.52 W m-2 and from 12.01 to 3.01 W m-2, respectively. We also find that the parameter models perform well on their inherent timescales but degrade significantly when transferring to other timescales. This study proves the necessity of defining parameter variability across different timescales in evapotranspiration models and provides new insight into the model parameters.