Deriving theoretical boundaries to address scale dependencies of triangle models for evapotranspiration estimation

[1] Satellite-based triangle models for evapotranspiration estimation are unique in interpreting the relationship between the normalized difference vegetation index (NDVI)/factional vegetation cover (fc) and surface radiative temperature (Trad) across large heterogeneous areas. However, output and performance of triangle models may depend on the size of the domain being studied and resolution of the satellite images being used. The objective of this study was to assess domain and resolution dependencies of triangle models using progressively larger domains and Landsat Thematic Mapper/Enhanced Thematic Mapper Plus and Moderate Resolution Imaging Spectroradiometer sensors at the Soil Moisture-Atmosphere Coupling Experiment site in central Iowa on days of year 174 and 182 in 2002. Results show domain and resolution dependencies of the triangle models with large uncertainties in evaporative fraction (EF) estimates in terms of a mean absolute percentage difference (MAPD) up to ∼50%. A trapezoid model which requires derivation of theoretical limiting edges of the NDVI-Trad space is proposed to constrain domain and resolution dependencies of triangle models. The theoretical warm edge can be derived by solving for temperatures of the driest bare surface and the fully vegetated surface with the largest water stress implicit in both radiation budget and energy balance equations. Areal average air temperature can be taken as the theoretical cold edge. The triangle model appears to perform well across large areas (∼104 km2) but fails to predict EF over small areas (∼102 km2). The trapezoid model can effectively reduce domain and resolution dependencies and constrain errors of the EF estimates with an MAPD of ∼10%.

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