Can We Accurately Quantify a Lateral Diffusivity from a Single Tracer Release?

Abstract

Abstract Mixing along sloping isopycnals plays a key role in the transport and uptake of heat and carbon by the ocean. This mixing is quantified by a lateral diffusivity, which can be measured by tracking the lateral spreading of point release tracer patches. We present a definition for the area of a tracer patch, the time derivative of which provides the lateral diffusivity. To accurately estimate the diffusivity, an ensemble mean concentration field of many tracer release experiments is required. We use numerical experiments to quantify how accurately the “true” lateral diffusivity (obtained from the ensemble mean concentration field) can be estimated from a single tracer release experiment (one ensemble member). To simulate observational campaigns, we also estimate the diffusivity from a single tracer release that is spatially and/or temporally subsampled, quantifying how the error between the estimated diffusivity and the true diffusivity grows as this sampling resolution worsens. We perform these numerical experiments in a two-layer quasigeostrophic model of turbulent flow on a β plane, using an ensemble of 50 passive tracer release experiments, each initialized as a 2D Gaussian but with differing realizations of the turbulent flow. We find that the diffusivity estimates from the single tracer releases have a relative root-mean-square error (RMSE) of 1.43% from the true diffusivity. Subsampling a single tracer release experiment every 956 km increases the relative RMSE from the true diffusivity to 3.1%; also subsampling every 277 days raises this figure to 6.5%.