Evaluating Alternate Methods of 4D-Var Data Assimilation in a Coupled Hydrodynamic-Four-Component Biogeochemical Model of the California Current System

Assimilating biogeochemical (BGC) data into ocean models using traditional four-dimensional variational data assimilation (4D-Var) includes the technical challenge of constructing tangent-linear (TLM) and adjoint (ADJ) models corresponding to the non-linear BGC model. This hurdle can be time-consuming, particularly for nonlinear BGC models experiencing active development, with regular updates to functional types or representation of key BGC processes. We evaluate two alternate approaches that greatly simplify TLM and ADJ construction and eliminate the need for code updates when the underlying, non-linear BGC model changes. One form of model-reduced data assimilation represents BGC interactions as a linear combination of orthogonal modes; we use empirical orthogonal functions and refer to this as the BioEOFs method. The second approach treats BGC variables as passive tracers that experience advection and diffusion by TLM and ADJ physics over an assimilation cycle, but are biochemically inactive. We evaluate the efficacy of these methods in a realistically configured, data-assimilative implementation of the Regional Ocean Modeling System with a simple nutrient- phytoplankton-zooplankton-detritus (NPZD) BGC model for the U.S. west coast. In a series of sequential data-assimilative model cycles, observations of temperature, salinity, sea-level anomaly, and phytoplankton biomass constrain the modeled state over the period spanning January-June 2019. We perform the assimilation in both physical and logarithmic-transformed space and compare results of the two approximate methods to traditional 4D-Var using TLM and ADJ models with BGC processes corresponding explicitly to the BGC model. While the full-adjoint 4D-Var results in the best correction to phytoplankton fields for analyses and forecasts, the BioEOFs and passive-tracer approaches also significantly reduce the model-observation misfit compared to a non-assimilative run and do so at reduced computational expense. The passive tracer performs generally better than BioEOFs, whose corrections exhibit large-scale structure across the domain. While the most accurate state estimate will result from development and application of the full TLM and ADJ, the log-transformed passive-tracer approach may be a viable alternative for performing BGC 4D-Var for state estimation when a full-adjoint option is not yet available.