Objectives: A major challenge for the development of marine biogeochemical parameterizations, and for the initialization of coupled Earth system model's using such parameterizations, is the computational cost of long spin-up runs. Because of the long timescales of ocean circulation, biogeochemical tracers do not equilibrate for thousands of years. Such integrations take months of wall- clock time on a super computer, making it infeasible to do a sufficient number of model runs to objectively optimize uncertain biogeochemical parameters using tracer observations.

This project will deliver: (1) An implementation of a scalable Newton-Krylov solver for the Biogeochemical Elemental Cycling (BEC) model that is anticipated to be between one and two orders of magnitude faster than the current time-stepping spin-up method. (2) The integration of the new solver with numerical optimization software so that BEC parameters can be objectively constrained using tracer observations. (3) Improvements in the BEC to include variable C:N:P stoichiometry in the plankton and in the sinking organic matter. (4) The development of a novel method for diagnosing possible imbalances in the marine nitrogen cycle based on long-lived biogeochemical modes. (5) A data- constrained simulation of the present day marine nitrogen cycle with global estimates of the rates of nitrogen fixation and denitrification together with uncertainty estimates for the possible imbalances between the sources and sinks.

Methods: We have assembled a team with combined expertise in marine biogeochemistry, global-scale ocean tracer transport and computer science, to implement recently developed New- ton Krylov (NK) solvers in the BEC model, a key component of the Community Earth System Model (CESM). Preliminary results using offline biogeochemical ocean models and a coarse- resolution ocean-alone version of CCSM3 show that the method can be 30 to 100 times faster than spinning up the model using the traditional time-stepping method. To ensure scalability and robustness on high performance computers, we will implement our Newton Krylov solver using the Trilinos library developed at the Sandia National Laboratory. We will use gridded macronutrient distributions from the 2009 World Ocean Atlas and available iron concentrations and ¹⁵ N/ ¹⁴ N isotopic ratios measurements to objectively optimize uncertain biogeochemical parameters associated with the marine nitrogen cycle. The optimization will make use of numerical minimization techniques to find parameter values that minimize the difference between observed and simulated tracer data.

Potential Impacts: The efficiency of the new NK solver will accelerate the development of new, calibrated biogeochemical parameterizations. Our proposed improvements to the BEC will make it possible for the Earth system modeling community to use CESM to investigate the nitrogen-carbon-climate interactions that will affect the trajectory of climate in the corning century.