A Tracer-Contour Inverse Method for Estimating Ocean Circulation and Mixing

Abstract

A method is developed for estimating the along-isopycnal and vertical mixing coefficients (K and D) and the absolute velocity from time-averaged hydrographic data. The method focuses directly on transports down tracer gradients on isopycnals. When the tracer considered is salinity or an appropriate variable for heat, this downgradient transport constitutes the along-isopycnal component of the thermohaline overturning circulation. In the method, a geostrophic streamfunction is defined that is related on isopycnals by tracer contours and by the thermal wind relationship in the vertical. Volume and tracer conservation constraints are also included. The method is overdetermined and avoids much of the signal-to-noise error associated with differentiating hydrographic data in conventional inverse methods. The method is validated against output of a layered model. It is shown to resolve both K and D, the downgradient isopycnal transport, and the mean flow on isopycnals in the North Pacific and South Atlantic. Importantly, an understanding is established of both the physics underlying the method and the circumstances necessary for an inverse method to determine the mixing rates and the absolute velocity. If mixing is neglected, the method is the Bernoulli inverse method. At the limit of zero weight on the tracer-contour equations the method is a conventional box inverse method. Comparisons are drawn between each method and their relative merits are discussed. A new closed expression for the absolute velocity is also presented.