Abstract
Abstract The theory of first-passage time distribution functions and its extension to last-passage time distribution functions are applied to the problem of tracking the movement of water masses to and from the surface mixed layer in a global ocean general circulation model. The first-passage time distribution function is used to determine in a probabilistic sense when and where a fluid element will make its first contact with the surface as a function of its position in the ocean interior. The last-passage time distribution is used to determine when and where a fluid element made its last contact with the surface. A computationally efficient method is presented for recursively computing the first few moments of the first- and last-passage time distributions by directly inverting the forward and adjoint transport operator. This approach allows integrated transport information to be obtained directly from the differential form of the transport operator without the need to perform lengthy multitracer time integration of the transport equations. The method, which relies on the stationarity of the transport operator, is applied to the time-averaged transport operator obtained from a three-dimensional global ocean simulation performed with an OGCM. With this approach, the author (i) computes surface maps showing the fraction of the total ocean volume per unit area that ventilates at each point on the surface of the ocean, (ii) partitions interior water masses based on their formation region at the surface, and (iii) computes the three-dimensional spatial distribution of the mean and standard deviation of the age distribution of water.
Highlights
The interaction of the ocean with the rest of the climate system happens primarily at the sea surface through air–sea fluxes
In this paper we explore when, where, and how much fluid is exchanged between the surface mixed layer and the interior ocean in a global ocean general circulation model (OGCM) by computing first- and last-passage time distributions
We begin by considering a fluid element located below the sea surface in the ocean interior, and denote by r, the total amount of time the fluid element will spend in the ocean interior—that is, the amount of time between its last contact with the sea surface and its contact with the sea surface
Summary
The interaction of the ocean with the rest of the climate system happens primarily at the sea surface through air–sea fluxes These air–sea fluxes imprint the current physical and chemical state of the atmosphere on water parcels. In an oceanographic context, Haine and Hall (2002) combined the familiar concepts of water mass and age into a generalized theory formulated in terms of the surface boundary condition propagator (boundary Green function) of the ocean’s advection– diffusion transport equation. The connection between the surface-to-interior transit time distribution and the different concepts of tracer age used by oceanographers is discussed in Hall and Haine (2002) and in Waugh et al (2003). In this paper we explore when, where, and how much fluid is exchanged between the surface mixed layer and the interior ocean in a global ocean general circulation model (OGCM) by computing first- and last-passage time distributions..
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