Observing the general circulation with floats

Abstract

The prospect for describing advection and eddy transport of tracers in the general circulation using floats is examined. This is done within the context of a recently proposed generalization of the advection-diffusion equation for passive scalars in which eddy transport is governed by a time-dependent eddy diffusivity tensor κ(t) which at large t approaches the constant κ(∞) appropriate to pure advection-diffusion models. A minimal description of the general circulation would include the Eulerian mean velocity U(x) and the diffusivity κ(t). Given sufficient numbers of current-followers which adequately follow ideal fluid particles, both the horizontal components of U and the purely horizontal components of K could be measured.The connection between these transport parameters and statistics of ideal particles shows that if the mean density of the float array is nonuniform then the mean velocity deduced from it will be in error by an array bias produced by downgradient diffusion of floats; this same phenomenon is responsible for the bias of Lagrangian mean velocity away from U toward high eddy diffusivity. A bias also affects diffusivity estimates when the sampling array is not uniform in the mean. The effects of nonuniform sampling make it difficult to piece together an accurate description of the general circulation from floats deployed in localized regional arrays.Both horizontal and vertical separations develop between initially paired floats and fluid particles because floats do not follow vertical water motion. The effect of this on the U and κ measured with floats is examined and is found to be negligible outside of strong currents.With floats, Eulerian statistics must be estimated from a combination of space and time averaging. The uncertainty, σU, of a measured U then depends on the spatial averaging scale A. The trade-off between accuracy and resolution is at the analyst's control by adjusting the averaging scale, but the product σU·λ is fixed by the sampling density and eddy field properties. The measurement uncertainty of the diffusivity κ(t) increases with t, even after κ has reached its asymptote κ∞.Numerical simulation of particle motion is used to test the generalized advection-diffusion equation upon which the development is based, to study how the diffusivity depends on properties of the eddy field, and to explore problems in mapping the general circulation in the presence of statistically inhomogeneous eddies, boundaries and strong currents. When the mean float density is reasonably uniform, then measurements of mean flow and the fully horizontal components of the eddy diffusivity are accurate and are equally useful in strong boundary currents and in broad interior flows.