Theoretical Model for Estimating the Scaling Error of the Two-Band Ratio of Red to Near-Infrared in Inhomogeneous Pixels: Simulation Using a Moving Window

This study develops a theoretical model to estimate the scaling error of the two-band ratio of red to near-infrared (TBRRN) in an inhomogeneous pixel. Three different imageries and a 3 × 3 moving window are used to verify and approximately estimate the scaling error of the TBRRN for remote-sensing imageries. The datasets are Landsat Thematic Mapper (Landsat/TM) imagery taken on 15 October 2005, satellite probatoire d´Observation de la terre (SPOT) imagery taken on 7 September 2005, and moderate-resolution imaging spectroradiometer (MODIS) imagery taken on 5 October 2005 of the Yellow River Estuary. It is found that 1) about 15.70%, 17.24% and 26.52% of SPOT, Landsat/TM and MODIS pixels have relative scaling error higher than 2% respectively, 2) the average relative scaling error increases with increasing scale of the image pixel, and 3) it is difficult to achieve the goal of the National Aeronautics and Space Administration of obtaining valid ocean-color data of the world´s oceans for estimating the chlorophyll-a concentration with uncertainty of less than 35% if the scaling error cannot be effectively reduced. Our results suggest the need for an in-depth study of scaling errors in water-color remote sensing.