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• Both one-phase and two-phase trapezoids are examined in separating ET soil and ET veg. • Two typical methods determining four endmembers are integrated into two trapezoids. • Analytical deductions of differences of ET soil and ET veg fraction are made. • ET veg /ET are intercompared with those by five typical partitioning methods. Partition of land surface evapotranspiration (ET) into soil evaporation (ET soil) and vegetation transpiration (ET veg) is of great significance for scheduling agricultural irrigation, improving water-use efficiency of crop, and managing water resources. This study made a comprehensive evaluation of one-phase and two-phase surface temperature versus fractional vegetation cover trapezoids in the separation of soil evaporation from vegetation transpiration through analytical deductions and model applications, with surface temperatures at four end-members determined from the layered approach and the patch approach. The two trapezoids were tested on the MODIS data during June to September in 2012 at Daman superstation in Northwest China. The trapezoid-estimated ratios of transpiration to total ET (ET veg /ET) were intercompared with the ET veg /ET from five typical partitioning methods, namely, the stable isotope-method, the underlying water-use efficiency (uWUE) method, the transpiration estimation algorithm (TEA), the Pérez-Priego method, and the Wei method. Results showed that: 1) The two-phase trapezoid integrated with the layered approach and the one-phase trapezoid integrated with the layered approach performed the best and worst with root-mean-square errors of 52.6 W/m2 and 78.6 W/m2, respectively, when the estimated total ET was validated against the Bowen Ratio corrected eddy covariance measurements. 2) The five partitioning methods produced largely different ET veg /ET, with the highest values from the TEA method and the lowest values from the Pérez-Priego method. 3) The estimated vegetation transpiration and ET veg /ET by the two-phase trapezoid were generally higher than those by the one-phase trapezoid. 4) In the intercomparison of ET veg /ET, the layered approach agreed better with the five partitioning methods than the patch approach. 5) The two-phase trapezoid integrated with the layered approach overall produced the most consistent estimates of ET veg /ET with those from the five partitioning methods, with the lowest bias varying between -30.9% and 8.7% and root-mean-square differences varying between 16.8% and 36.8%. In summary, the two-phase trapezoid is theoretically more rational and appears to outperform the one-phase trapezoid. This study is beneficial for a better understanding of the differences, similarities, advantages and weaknesses of the one-phase and two-phase trapezoids in the partition of total ET to its soil and vegetation components. [ABSTRACT FROM AUTHOR]