An optimal transformation method for inferring ocean tracer sources and sinks

Abstract. The geography of changes in the fluxes of heat, carbon, fresh water and other tracers at the sea surface are highly uncertain and are critical to our understanding of climate change and its impacts. We present a state estimation framework wherein the relative roles of ocean circulation, boundary fluxes and mixing, which describe the evolving state of water masses, can be balanced. In this framework, we define a discrete set of ocean water masses distinguished by their geographical and thermodynamic/chemical properties for specific time periods. Ocean circulation then moves these water masses in geographic space. In phase space, geographically adjacent water masses are able to mix together, representing a convergence, and air-sea property fluxes move the water masses over time. We define an optimisation problem whose solution is constrained by the physically permissible bounds of changes in ocean circulation, air-sea fluxes and mixing. As a proof of concept implementation, we use data from a historical numerical climate model simulation with a closed heat and salinity budget. An inverse model solution is found for the evolution of temperature and salinity consistent with `true' air-sea heat and fresh water fluxes which are introduced as model priors. When a constant bias is introduced to the prior fluxes, the inverse model finds a solution closer to the true fluxes. This framework, which we call the Optimal Transformation Method, represents a modular, relatively computationally cost effective, open source and transparent state estimation tool that complements existing approaches.