A triangle method has been frequently used for a regional evapotranspiration (ET) or evaporative fraction (EF) estimation using the relationship between a vegetation index and surface temperature. A simple histogram based on an on-orbit EF estimation algorithm is developed to determine hot and cold edges in the triangle distribution using only remotely sensed data. A new histogram based on an EF estimation algorithm is developed and compared with different options of existing hot and cold edge algorithms. The selected algorithms are applied to 5-year Terra MODIS data products, and the on-orbit EF estimations are validated using ground truth data from southern Great Plains. Using numerous iterations among the tested EF algorithms with the triangle method, the "histogram"-based hot edge and newly proposed cold edge algorithm combinations provide an excellent performance between the ground truth and on-orbit EF estimations. It is shown that the histogram-based EF algorithm has enhanced correlation and mean bias values of 0.74 and 0.087, respectively, providing excellent accuracy for the regional on-orbit EF estimations. (C) 2017 Society of Photo-Optical Instrumentation Engineers (SPIE).