Modeling Turbidity Retrieval of Glacial Lakes Based on Logistic Regression—A Nonlinear Transformation Method and Its Mathematical Principles

Abstract

Against the backdrop of accelerated glacier melting caused by global warming, dynamic monitoring of glacial lake water quality has become an important topic in environmental science. There is a significant correlation between lake water color and turbidity, but this relationship is often nonlinear. This paper introduces the logistic regression equation, applies a Logit transformation to turbidity data to convert the nonlinear relationship into a linear one, and then establishes a regression model using the least squares method. Taking a set of simulated RGB image data from a glacial lake as an example, this paper demonstrates the scientific research paradigm of “problem definition to data transformation to linear modeling to inverse transformation prediction to statistical testing”. The results show that the logistic regression-based modeling method can effectively fit the S-shaped relationship between water color and turbidity, with a coefficient of determination R 2 reaching 0.996 and a mean absolute error of 0.292 NTU. This paper reveals the extended application of basic mathematics in real scientific research and provides a case study for helping secondary school students understand nonlinear modeling ideas.