Discrepancies and Uncertainties in the Application of the Fc-LST Theoretical Trapezoid Framework at Pixel and Areal Scales Using a Priestley-Taylor based Evapotranspiration Model

Evapotranspiration (ET) is the primary pathway for dissipating terrestrial water resources, and a key process in regulating surface temperature. The Ts-VI feature space method is an important evapotranspiration simulation approach, reflecting the relationship between vegetation cover and the temperature-evapotranspiration response, while effectively balancing model complexity and efficiency. The key issue for Ts-VI feature space methods lies in the accurate identification of the four extreme endmember temperatures. However, the differences in feature points caused by applying the theoretical trapezoid framework at the pixel or areal scale have received little attention. The discrepancies and uncertainties between these two approaches, along with the resulting contradictions in trapezoid framework and differences in evapotranspiration simulation, are often neglected. This study firstly develops a fully explicit theoretical method for determining extreme endmember temperatures, simplifying the process and improving computational efficiency. Secondly, using the above explicit equation, a systematic comparison is conducted across four single-source Priestley-Taylor-based evapotranspiration models using four methods for determining extreme endmember temperatures: the empirical fitting method (EFM) as a reference, envelope theoretical method (ETM) and pixel theoretical method (PTM) at the areal scale, and the same pixel theoretical method with flux site observational meteorological data (PTMs). Thirdly, we analyzed the spatiotemporal variations of extreme endmember temperatures and their positional relationships within the trapezoidal framework across these different methods, and discussed their uncertainties through envelope analysis and sensitivity analysis. Using all site-year data from 9 AmeriFlux sites in the Southern Great Plains, along with MODIS and NCEP products from 2017. The results show that the proposed explicit theoretical calculation method is effective, with the four methods demonstrating the best validation results when compared to observed flux data, closed using the residual method, yielding RMSE values of 1.70 mm/d, 1.55 mm/d, 1.53 mm/d, and 1.51 mm/d, respectively. During the growing season of 2017, ETM exhibited an exceptionally high peak at the dry edge, while PTM and PTMs displayed frequent and dense high-value spikes, with particularly pronounced intensity. The positional discrepancies among the different trapezoidal frameworks were primarily observed at the dry edge, with PTM and PTMs showing a higher probability of the highest dry edge. Envelope analysis revealed that ETM, PTM, and PTMs occasionally failed to envelope all Fc-LST scatter points, leading to overestimations of evapotranspiration, particularly at the wet edge. In summary, this study provides a comprehensive understanding of the theoretical trapezoidal framework, highlighting the discrepancies and uncertainties across different scales, and offers valuable insights for model implementation and improvement.