New Methods for Estimating Ocean Eddy Heat Transport Using Satellite Altimetry

Abstract

Attempts to monitor ocean eddy heat transport are strongly limited by the sparseness of available observations and the fact that heat transport is a quadratic, sign-indefinite quantity that is particularly sensitive to unresolved scales. In this article, a suite of stochastic filtering strategies for estimating eddy heat transport are tested in idealized two-layer simulations of mesoscale oceanic turbulence at high and low latitudes under a range of observation scenarios. A novel feature of these filtering strategies is the use of computationally inexpensive stochastic models to forecast the underlying nonlinear dynamics. The stochastic model parameters can be estimated by regression fitting to climatological energy spectra and correlation times or by adaptively learning these parameters “on-the-fly” from the observations themselves. The authors show that, by extracting high-wavenumber information that has been aliased into the low wavenumber band, “stochastically super-resolved” velocity fields with a nominal resolution increase of a factor of 2 or more can be derived. Observations of the upper-layer streamfunction are projected onto an empirical orthogonal function basis for the vertical structure to produce filtered estimates for both upper- and lower-layer streamfunctions and hence net heat transport. The resulting time-mean poleward eddy heat transport is significantly closer to the true value when compared with standard estimates based upon optimal interpolation. By contrast, the temporal variability of the heat transport is underestimated because of poor temporal resolution. Implications for estimating poleward eddy heat transport using current and next-generation altimeters are discussed.

Statistically accurate low-order models for uncertainty quantification in turbulent dynamical systems

“…We consider the Phillips model in a barotropicbaroclinic mode formulation (23)(24)(25) with periodic boundary conditions given by ∂q ∂t = LðqÞ + Bðq; qÞ…”

“…Here we set δ = 0:2, r = 9, β = 10, and λ = 10; this set of parameters corresponds to the high-latitude ocean case (25). The critical parameters here are the large baroclinic deformation wavenumber, λ, typical of the high-latitude ocean, the strength of the shear U, and the bottom drag coefficient, r. The natural inner product that guarantees the energy conservation property, Bðq; qÞ:q = 0, is defined through the sum of the barotropic and baroclinic energies and is given by…”

“…Here the ROMQG algorithm has remarkably robust skill for UQ in the transient response to general random external forcing for truncations as low as one, two, or three leading Fourier modes. The second application involves a prototype example of twolayer ocean baroclinic turbulence (23)(24)(25). Here the turbulent system has over 125,000 degrees of freedom, so validation through transient Monte-Carlo simulations is impossible and only the nonlinear statistical steady-state response to the change in shear can be tested for various perturbation levels.…”

Quantifying Bayesian filter performance for turbulent dynamical systems through information theory

“…It was shown earlier in [15,37,61,31,30,11] that in this idealized setting, cheaper reduced filters with judicious model errors often have much higher skill than standard ensemble Kalman methods for filtering signals with rough turbulent spectra in physical space. Moreover, numerous later studies showed agreement of these guidelines in much more complex scenarios ranging from filtering sparsely observed atmospheric and oceanic flows in [38,61,60,12], to estimating the poleward eddy heat flux in the oceans from sparse satellite altimetry data in [45]. Below, we first briefly summarize the canonical test model of [59,15,37,60] and introduce a suite of imperfect models which are obtained via the finite-difference approximations of the true dynamics in (3.1).…”

“…(ii) Filters that maximize the mutual information M (u u u m ,ū u u m|m ) in (2.19) provide the best estimates of the truth signal in terms of pattern correlation (see Section 2.2.2); this property is useful, for example, when stochastic filtering is used for deriving flux estimates from partial noisy observations [45,12]. (iii) The relative entropy P(u u u m ,ū u u m|m ) in (2.23) is useful for assessing the error in the statistics of the estimated signal (see also Section 2.3); filters with the smallest P(u u u m ,ū u u m|m ) yield estimates with the smallest lack of information relative to the statistics of the truth dynamics.…”