Inversion of Upper Ocean Temperature Time Series for Entrainment, Advection, and Diffusivity

Abstract

An inversion technique for estimating the terms of the oceanic near-surface heat transport is extended to include the vertical heat flux at the bottom of the surface mixed layer. The mixed-layer heat balance equation uses a conventional parameterization of the vertical heat flux via entrainment into the mixed layer of interior fluid during the mixed layer deepening. A heat conservation equation defined here for the sea temperature anomalies, deviations from the annual cycle, is driven by stochastic atmospheric forcing, thereby becoming essentially a stochastic partial differential equation. This equation is reduced to the regression estimator aimed on inversion of the sea temperature time series for the unknowns: vertical entrainment velocity, horizontal velocity and diffusivity, feedback factor, and atmospheric forcing parameter. The inversion scheme also involves the velocity divergence norm. The regression estimator is applied to the time series of vertical profiles of temperature anomalies compiled from the Comprehensive Ocean?Atmosphere Data Sets and the World Ocean Atlas 1994 on a 10-day mean basis over the spatial grid of 1° latitude ? 2° longitude in two regions of the North Pacific: 1) near the ocean western boundary east of Japan and 2) between the Hawaiian islands and California. The inversion is implemented for winter data (December?March) from 1965 to 1990. The entrainment velocities are found to be of the order of 10?5 m s?1. The entrainment effect is particularly significant in the Kuroshio?Oyashio frontal zone. The model skill is also substantially enhanced in this region: the inversion yields more realistic features of the Kuroshio transport as compared with the authors? previous study, which neglected the vertical heat flux.