Development of a sensitivity analysis framework for aquatic biogeochemical models using machine learning

Abstract

Our evolving understanding of ecosystem functioning along with the advent of computational power have paved the way for the development of complex mathematical models that explicitly represent the functional diversity of biotic communities and multiple biogeochemical cycles. The ever-growing demand for more complex models underscores the importance of robust sensitivity analysis (SA) to elucidate the impact of the uncertainty on model inputs and to untangle the parameter covariance patterns that ultimately lead to the emergence of equifinality problems. In this study, we propose a novel multi-pronged SA framework that integrates advanced statistical and machine learning (ML) techniques. Principal component analysis (PCA) is first applied to dissect the wide array of predictive outputs and identify modes of variability in time and/or space. Classification and Regression Tree (CART) analysis is then used to identify a set of splitting decisions connecting threshold values of key state variables and model parameters with different ranges of predictive outputs with management interest. Self-Organizing Maps (SOM) are implemented as a final step to unravel any non-linear associations between model parameters and responses. As a proof-of-concept, we used a complex aquatic biogeochemical model developed for the Bay of Quinte, a eutrophic embayment in Lake Ontario, to examine competition patterns and structural shifts among multiple functional phytoplankton (diatoms, N-fixing cyanobacteria, and Microcystis) and zooplankton (herbivores and omnivores) groups. Our sensitivity analysis framework showed that the parameters representing the dependence of growth and metabolic processes on temperature are particularly influential to recreate plankton community dynamics during the cold period of the year, whereas the interplay among the interspecific resource competition, strength of the prey-predator interactions, and phosphorus availability mainly regulate their dynamics during the growing season. The growth strategies of diatoms, their nutritional quality that determines the assimilation efficiency by zooplankton, along with the ambient nutrient availability determine our capacity to reproduce patterns of cyanobacteria dominance and faithfully depict the severity of harmful algal blooms. Finally, our study discusses the benefits of a broader use of the ML-based SA framework to unravel influential parametric interactions in modulating the behaviors of complex mathematical models.