LASSO (L1) Regularization for Development of Sparse Remote-Sensing Models with Applications in Optically Complex Waters Using GEE Tools

Abstract

Remote-sensing data are used extensively to monitor water quality parameters such as clarity, temperature, and chlorophyll-a (chl-a) content. This is generally achieved by collecting in situ data coincident with satellite data collections and then creating empirical water quality models using approaches such as multi-linear regression or step-wise linear regression. These approaches, which require modelers to select model parameters, may not be well suited for optically complex waters, where interference from suspended solids, dissolved organic matter, or other constituents may act as “confusers”. For these waters, it may be useful to include non-standard terms, which might not be considered when using traditional methods. Recent machine-learning work has demonstrated an ability to explore large feature spaces and generate accurate empirical models that do not require parameter selection. However, these methods, because of the large number of included terms involved, result in models that are not explainable and cannot be analyzed. We explore the use of Least Absolute Shrinkage and Select Operator (LASSO), or L1, regularization to fit linear regression models and produce parsimonious models with limited terms to enable interpretation and explainability. We demonstrate this approach with a case study in which chl-a models are developed for Utah Lake, Utah, USA., an optically complex freshwater body, and compare the resulting model terms to model terms from the literature. We discuss trade-offs between interpretability and model performance while using L1 regularization as a tool. The resulting model terms are both similar to and distinct from those in the literature, thereby suggesting that this approach is useful for the development of models for optically complex water bodies where standard model terms may not be optimal. We investigate the effect of non-coincident data, that is, the length of time between satellite image collection and in situ sampling, on model performance. We find that, for Utah Lake (for which there are extensive data available), three days is the limit, but 12 h provides the best trade-off. This value is site-dependent, and researchers should use site-specific numbers. To document and explain our approach, we provide Colab notebooks for compiling near-coincident data pairs of remote-sensing and in situ data using Google Earth Engine (GEE) and a second notebook implementing L1 model creation using scikitlearn. The second notebook includes data-engineering routines with which to generate band ratios, logs, and other combinations. The notebooks can be easily modified to adapt them to other locations, sensors, or parameters.

Keywords

• remote sensing
• water quality
• model development
• linear regression
• LASSO regularization
• L1