A novel approach to calculating water stress index

Abstract

Remote sensing technology provides an effective way to estimate evapotranspiration (ET). Numerous remotely sensed models aiming at estimating ET accurately have been developed. A key parameter for these models is water stress index (Λ), which is calculated from land surface temperature (LST). However, the satellite-derived LST was criticized for its uncertainties and limitations, which may result in false calculation of Λ. This study proposed a practical algorithm for determining Λ using top of the atmosphere (TOA) radiance, instead of satellite-derived LST. The proposed algorithm was derived theoretically on the basis of the radiance transfer equation and the Planck's law. If the atmospheric conditions over the area can be considered constant, the Λ value can be calculated accurately with TOA radiance. The methodology was validated using Moderate Resolution Imaging Spectroradiometer (MODIS) data over a heterogeneous area of the Poyang Lake basin. The TOA radiance-calculated Λ value and LST-determined Λ value were quite close with a correlation coefficient (R2) of 0.9483 and 0.9194. Besides, difference between the two Λ values of same pixel was also quantified. The results showed that the proposed algorithm using TOA radiance was accurate enough for calculating Λ. Overall, the proposed algorithm makes fewer assumptions and avoids the uncertainties associated with the LST product. It should be highly valuable for satellite processing and for determining Λ.