A Linear Stochastic Field Model of Midlatitude Mesoscale Variability

Abstract

AbstractA semiempirical model of midlatitude sea surface height (SSH) variability is formulated and tested against two decades of weekly global fields of merged altimeter data. The model is constrained to match approximately the observed SSH wavenumber power spectrum, but it predicts the spatiotemporal SSH field structure as a propagating, damped, linear response to a stochastic forcing field. An objective, coherent-eddy identification and tracking procedure is applied to the model and altimeter SSH fields, with a focus on eddies with lifetimes L ≥ 16 weeks. The model eddy dataset reproduces the basic global-mean characteristics of the altimeter eddy dataset, including the structure of mean amplitude and scale life cycles, the number distributions versus lifetime, and the distributions of all eddy length scale realizations. The model underpredicts the numbers of eddy realizations with large amplitudes and large scales, overpredicts the growth of mean amplitude and scale with lifetime, and modestly overpredicts the curvature of the mean amplitude life cycle and the number of eddies with intermediate lifetimes. The stochastic forcing evidently represents nonlinear dynamical interactions, implying that eddy splitting and merging events are equally likely, and that mesoscale nonlinearity is weaker than longwave linearity but as strong as shortwave dispersion. The time-reversal symmetry of the life cycles is explained by the time reversibility of the underlying stochastic model. The random SSH increment processes are effectively continuous on the derived 25-week damping time scale, with SSH-increment standard deviation σW ≈ 2.5 × 10−3 cm s−1/2.