An improved Forel–Ule index method for trophic state assessments of inland waters using Landsat 8 and sentinel archives

Abstract

The Forel–Ule index (FUI) is one of the indicators used to assess the trophic state of inland waters, which can be objectively determined based on satellite-retrieved corrected hue angles (α). However, the functions for α correction have been proposed based on a dataset from Dutch and the North Sea, which might be inadequate for the precise FUI-derived trophic state. This study proposed a method for FUI retrieval through improved α correction. First, the daily surface spectral reflectance product (MOD09GA) was corrected through simple band subtraction. The results showed that the FUI retrieved from the corrected MOD09GA was more reliable than those without corrections. Second, we obtained new offset functions through the fit between the sensor (α) and the error with α derived from the corrected MOD09GA. The results showed that: (1) for three atmospheric correction methods, the C2RCC (case 2 regional coast color) processor and the iCOR (image correction for atmospheric effects) performed better than 6S (Second Simulation of the Satellite Signal in the Solar Spectrum) in FUI calculations; and (2) with Pearson’s r square (r2) of 0.72, and percentage error (PE) values of 5.80% for FUI derived from Landsat 8, r2 of 0.52 and PE of 7.81% for results derived from Sentinel-2, r2 of 0.60 and PE of 19.40% for results retrieved from Sentinel-3, the FUI determined by the new offset-corrected greatly improved the assessment of trophic states for five waterbodies in and around Wuhan, China. Hue angles retrieved by the corrected-MOD09GA are available as references and the results also imply that hue angle correction the functions can be achieved in any place, even if without an in-situ hyperspectral dataset. The waters of the Xiajiasi Reservoir and the Daoguanhe Reservoir were mostly in mesotrophic status; while East Lake, Tangxun Lake and Liangzi Lake were eutrophic.