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  • Author or Editor: Timothy M. Hall x
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Darryn W. Waugh
and
Timothy M. Hall

Abstract

The propagation of a range of tracer signals in a simple model of the deep western boundary current is examined. Analytical expressions are derived in certain limits for the transit-time distributions and the propagation times (tracer ages) of tracers with exponentially growing or periodic concentration histories at the boundary current’s origin. If mixing between the boundary current and the surrounding ocean is either very slow or very rapid, then all tracer signals propagate at the same rate. In contrast, for intermediate mixing rates tracer ages generally depend on the history of the tracer variations at the origin and range from the advective time along the current to the much larger mean age. Close agreement of the model with chlorofluorocarbon (CFC) and tritium observations in the North Atlantic deep western boundary current (DWBC) is obtained when the model is in the intermediate mixing regime, with current speed around 5 cm s−1 and mixing time scale around 1 yr. In this regime anomalies in temperature and salinity of decadal or shorter period will propagate downstream at roughly the current speed, which is much faster than the spreading rate inferred from CFC or tritium–helium ages (approximately 5 cm s−1 as compared with 2 cm s−1). This rapid propagation of anomalies is consistent with observations in the subpolar DWBC, but is at odds with inferences from measurements in the tropical DWBC. This suggests that observed tropical temperature and salinity anomalies are not simply propagated signals from the north. The sensitivity of the tracer spreading rates to tracer and mixing time scales in the model suggests that tight constraints on the flow and transport in real DWBCs may be obtained from simultaneous measurements of several different tracers—in particular, hydrographic anomalies and steadily increasing transient tracers.

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Thomas W. N. Haine
and
Timothy M. Hall

Abstract

A general theory to describe and understand advective and diffusive ocean transport is reported. It allows any passive tracer field with an atmospheric source to be constructed by superposing sea surface contributions with a generalized Green's function called the boundary propagator of the passive tracer equation. The boundary propagator has the interpretation of the joint water-mass and transit-time distribution from the sea surface. The theory thus includes the classical oceanographic idea of water-mass analysis and extends it to allow for a distribution of transit times from the sea surface. The joint water-mass and transit-time distribution contains complete information about the transport processes in the flow. It captures this information in a more accessible way than using velocity and diffusivity fields, however, at least for the case of sequestration and transport of dissolved material by the ocean circulation. The boundary propagator is thus the natural quantity to consider when discussing both steady-state and transient ocean tracers, including the inverse problem of interpreting tracer data in terms of ocean circulation. Two constraints on the shape of the transit-time distributions are derived. First, the asymptotic behavior for a steady, or time-averaged, circulation is exponential decay. Second, integrated over the whole ocean, the transit-time distribution from the sea surface cannot increase. The theory is illustrated using a one-dimensional advection–diffusion model, a box model, and a North Atlantic general circulation model.

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Timothy M. Hall
and
Thomas W. N. Haine

Abstract

The idealized age tracer is commonly used to diagnose transport in ocean models and to help interpret ocean measurements. In most studies only the steady-state distribution, the result of many centuries of model integration, has been presented and analyzed. However, in principle the transient solution provides more information about the transport. Here it is shown that this information can be readily interpreted in terms of the ventilation histories of water masses. A simple relationship is derived, valid for stationary transport, between the transient evolution, τ id(r, t), of the idealized age tracer and the “age spectrum,” G (r, t), the distribution of times t since a water mass was last ventilated. Namely, G (r, t) = −∂ tt τ id(r, t). Implications of the relationship are discussed, and the relationship is illustrated with an idealized model.

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Timothy M. Hall
,
Thomas W. N. Haine
,
Darryn W. Waugh
,
Mark Holzer
,
Francesca Terenzi
, and
Deborah A. LeBel

Abstract

The intimate relationship among ventilation, transit-time distributions, and transient tracer budgets is analyzed. To characterize the advective–diffusive transport from the mixed layer to the interior ocean in terms of flux we employ a cumulative ventilation-rate distribution, Φ(τ), defined as the one-way mass flux of water that resides at least time τ in the interior before returning. A one-way (or gross) flux contrasts with the net advective flux, often called the subduction rate, which does not accommodate the effects of mixing, and it contrasts with the formation rate, which depends only on the net effects of advection and diffusive mixing. As τ decreases Φ(τ) increases, encompassing progressively more one-way flux. In general, Φ is a rapidly varying function of τ (it diverges at small τ), and there is no single residence time at which Φ can be evaluated to fully summarize the advective–diffusive flux. To reconcile discrepancies between estimates of formation rates in a recent GCM study, Φ(τ) is used. Then chlorofluorocarbon data are used to bound Φ(τ) for Subtropical Mode Water and Labrador Sea Water in the North Atlantic Ocean. The authors show that the neglect of diffusive mixing leads to spurious behavior, such as apparent time dependence in the formation, even when transport is steady.

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