Parametric estimation of the stochastic dynamics of sea surface winds

In this study, the parameters of a stochastic–dynamical model of sea surface winds are estimated from long time series of sea surface wind observational data. The model was introduced by A. H. Monahan, who developed an idealized model from a highly simplified representation of the momentum budget of a surface atmospheric layer of fixed depth. Such estimation of model parameters is challenging, in particular for a multivariate model with nonlinear terms as is considered here. The authors use a method developed recently by Crommelin and Vanden-Eijnden, which approaches the estimation problem variationally, finding the spectrally “best fit” stochastic differential equation to a time series of observations. While the estimation procedure assumes forcing that is white in time, observed time series are generally better approximated as forced by red noise. Using a red-noise-forced linear system, the authors first show that the estimation procedure can still be used to estimate model parameters. Because the assumption of white noise is violated, these estimates lead to model autocorrelation functions that differ from the observed time series. Application of the estimation procedure to the wind data is further complicated by the fact that the boundary layer model is inconsistent with certain observed features of the wind. When these mismatches between the model and observations are accounted for, the estimation procedure generally results in parameter estimates consistent with the climatological features of the associated meteorological fields. Important exceptions to this result are the layer thickness and layer-top eddy diffusivity, which are poorly estimated where the vector winds are close to Gaussian.