Assessing the discrepancies and uncertainties of regional shared and pixel-specific trapezoidal feature spaces using a Priestley-Taylor-based evapotranspiration model

The vegetation index–land surface temperature (VI–LST) feature space method is widely used for regional evapotranspiration (ET) estimation, linking vegetation cover with the temperature–ET response while balancing model complexity and efficiency. The key challenge of the feature space method lies in accurately identifying the four extreme endmember temperatures. In regional shared feature space, all pixels use the same feature points, whereas pixel-by-pixel approaches assign unique points to each pixel. However, the discrepancies between these methods and their effects on ET uncertainty remain unclear, especially regarding the spatiotemporal variability of pixel-level feature points. Moreover, theoretical feature spaces may exhibit distortions, but their types, frequency, and impacts on ET have not been fully investigated. This study explored these issues by systematically comparing four Priestley-Taylor-based ET models using different methods to determine endmember temperatures: an empirical fitting method (EFM) as a reference, a shared theoretical method (STM) and a pixel-level theoretical method (PTM) at the regional scale, and PTM driven by flux-site meteorological data (PTMs). Results showed that PTM slightly outperformed STM, followed by PTMs, while EFM showed the lowest accuracy. Temperature differences between PTM and STM feature points displayed strong spatial variability, mostly within ± 10 K, though larger fluctuations occurred on some days. Positional deviations among different methods occur mainly at the dry edge, with all theoretical methods systematically higher than EFM. Envelope analysis indicated that STM, PTM, and PTMs failed to enclose all Fc–LST points in some days, with PTM most prone to anomalies; dry-edge failures in rare cases caused negative ET, while frequent wet-edge or LST < Ta cases led to overestimation of ET. Overall, PTM provides finer spatial detail and moderate accuracy improvement, but it generates systematically distorted feature spaces similar as STM that contributes to ET uncertainties. This study offers a comprehensive comparison of the representative trapezoidal framework and provides insights for improving ET model.