Spectral Probability Distribution of Closed Connected Water and Remote Sensing Statistical Inference for Yellow Substance

Unlike traditional remote sensing inversion, this study proposes a new distribution–distribution scheme, which uses statistical inferences to estimate the probability distribution of in-water components based on the probability distribution of the observed spectra. The distribution–distribution scheme has the advantages that it rapidly gives the statistical information of the water of interest, assists the traditional scheme in improving models, and provides more valuable information for water classification and aquatic environment analysis. In this study, based on Landsat-8 images, we analyzed the spectral probability distributions of 688 global waters and found that many of them were normal, log normal, and exponential distributions with diverse patterns in distribution parameters such as the mean, standard deviation, skewness, and kurtosis. Using simulated and field-measured data, we propose a bootstrap-based distribution–distribution scheme and develop some simple remote sensing statistical inference models to estimate the distribution parameters of yellow substance in water.