Author Contributions: Conceptualization, Z [...]

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Satellite remote sensing provides a promising way to estimate regional evapotranspiration (ET) in a spatially distributed manner. In this study, an enhanced two-source evapotranspiration model for land (ETEML) is proposed based on a trapezoid framework of the vegetation fractional cover and land surface temperature (VFC/LST) space. In ETEML, a VFC/LST trapezoid space is theoretically defined for each pixel, and a pixel-wise mixed surface temperature decomposition method is proposed. ETEML is based on a two-source scheme, and the crop water stress index (CWSI) concept is applied to parameterize the soil evaporation and the vegetation transpiration separately. The proposed model was applied to the Soil Moisture-Atmosphere Coupling Experiment (SMACEX) site in central Iowa, USA. Evaluation with a remotely sensed dataset from Landsat was carried out to assess the performance of ETEML. Compared with the tower observations, the mean absolute deviation (MAD) and the root mean square deviation (RMSD) for the ETEML estimated latent heat flux (LE) are, respectively, 49 W/m 2 and 59 W/m 2 , comparable to retrieval accuracies published in other studies. Comparison between ETEML and variations on a simpler trapezoid interpolation model (TIM1 and TIM2) indicates that ETEML reduces the subjectivity and uncertainties involved in TIM1 and TIM2. Overall, the results suggest that ETEML is promising and can expand the application of the trapezoid framework-based ET modeling approaches to heterogeneous surfaces.

SUMMARYThe generalized model of di erential hysteresis contains 13 control parameters with which it can curveÿt practically any hysteretic trace. Three identiÿcation algorithms are developed to estimate the control parameters of hysteresis for di erent classes of inelastic structures. These algorithms are based upon the simplex, extended Kalman ÿlter, and generalized reduced gradient methods. Novel techniques such as global search and internal constraints are incorporated to facilitate convergence and stability. E ectiveness of the devised algorithms is demonstrated through simulations of two inelastic systems with both pinching and degradation characteristics in their hysteretic traces. Owing to very modest computing requirements, these identiÿcation algorithms may become acceptable as a design tool for mapping the hysteretic traces of inelastic structures.