A Framework for Variational Inference and Data Assimilation of Soil Biogeochemical Models Using Normalizing Flows

Soil biogeochemical models (SBMs) represent soil variables and their responses to global change. Data assimilation approaches help determine whether SBMs accurately represent soil processes consistent with soil pool and flux measurements. Bayesian inference is commonly used in data assimilation procedures that estimate posterior parameter distributions with Markov chain Monte Carlo (MCMC) methods. The ability to account for data and parameter uncertainty is a strength of MCMC inference, but the computational inefficiency of MCMC methods remains a barrier to their wider application, especially with large data sets. Given the limitations of MCMC approaches, we developed an alternative variational inference framework that uses a method called normalizing flows from the field of machine learning. Normalizing flows rely on deep learning to map probability distributions and approximate SBMs that have been discretized into state space models. As a test of our method, we fit approximated SBMs to synthetic data sourced from known data-generating processes to identify discrepancies between the inference results and true parameter values. Our approach compares favorably with established MCMC methods and could be a viable alternative for SBM data assimilation that reduces computational time and resource needs. However, our method has some limitations, including challenges assimilating data with irregular measurement intervals, underestimation of posterior parameter uncertainty, and limited goodness-of-fit metrics for comparison to MCMC inference methods. Many of these limitations could be overcome with additional algorithm development based on the approaches we report here.