Fitting Nonlinear Equations with the Levenberg–Marquardt Method on Google Earth Engine

Abstract

Google Earth Engine (GEE) has been widely used to process geospatial data in recent years. Although the current GEE platform includes functions for fitting linear regression models, it does not have the function to fit nonlinear models, limiting the GEE platform’s capacity and application. To circumvent this limitation, this work proposes a general adaptation of the Levenberg–Marquardt (LM) method for fitting nonlinear models to a parallel processing framework and its integration into GEE. We compared two commonly used nonlinear fitting methods, the LM and nonlinear least square (NLS) methods. We found that the LM method was superior to the NLS method when we compared the convergence speed, initial value stability, and the accuracy of fitted parameters; therefore, we then applied the LM method to develop a nonlinear fitting function for the GEE platform. We further tested this function by fitting a double-logistic equation with the global leaf area index (LAI), normalized difference vegetation index (NDVI), and enhanced vegetation index (EVI) data to the GEE platform. We concluded that the nonlinear fitting function we developed for the GEE platform was fast, stable, and accurate in fitting double-logistic models with remote sensing data. Given the generality of the LM algorithm, we believe that the nonlinear function can also be used to fit other types of nonlinear equations with other sorts of datasets on the GEE platform.