Two-Stage Trapezoid: A New Interpretation of the Land Surface Temperature and Fractional Vegetation Coverage Space

The land surface temperature and fractional vegetation coverage (LST/FVC) space has been widely used in modeling evapotranspiration and monitoring soil moisture. The triangle and trapezoid are two classical interpretations of the LST/FVC space. Within the triangle, the fully vegetated surface temperature (T_v) is assumed to be invariant, whereas the bare soil surface temperature (T_s) is variable. Within the trapezoid, both T_v and T_s are assumed to be variable. However, they are assumed to vary simultaneously in the conventional trapezoid. A two-stage trapezoid is suggested in this paper by considering that T_v should vary after T_s because vegetation can absorb deep soil moisture to maintain transpiration. To validate the rationality of the two-stage trapezoid, the SimSphere model is utilized to simulate the LST/FVC space. Simulations indicate that the two-stage trapezoid is more consistent with the simulated LST/FVC space. Additionally, both the two-stage trapezoid and the conventional trapezoid are compared in how well they estimate the evaporative fraction (EF) over a crop area in Yingke along the middle reaches of Heihe River Basin in China. More than 110 scenes of MODIS LST and vegetation index products were processed. Comparisons at six eddy covariance systems all indicate that the two-stage trapezoid is more effective at estimating EF. The two-stage trapezoid clearly demonstrates the evolution of the LST/FVC space from the triangular to the trapezoidal form. An uncertainty analysis indicates that it is more suitable for the areas and periods where water is the limiting factor for vegetation growth.