Adjoint-Free Variational Data Assimilation into a Regional Wave Model

Abstract

A variational data assimilation algorithm is developed for the ocean wave prediction model [Wave Model (WAM)]. The algorithm employs the adjoint-free technique and was tested in a series of data assimilation experiments with synthetic observations in the Chukchi Sea region from various platforms. The types of considered observations are directional spectra estimated from point measurements by stationary buoys, significant wave height (SWH) observations by coastal high-frequency radars (HFRs) within a geographic sector, and SWH from satellite altimeter along a geographic track. Numerical experiments demonstrate computational feasibility and robustness of the adjoint-free variational algorithm with the regional configuration of WAM. The largest improvement of the model forecast skill is provided by assimilating HFR data (the most numerous among the considered types). Assimilating observations of the wave spectrum from a moored platform provides only moderate improvement of the skill, which disappears after 3 h of running WAM in the forecast mode, whereas skill improvement provided by HFRs is shown to persist up to 9 h. Spaceborne observations, being the least numerous, do not have a significant impact on the forecast skill but appear to have a noticeable effect when assimilated in combination with other types of data. In particular, when spectral data from a single mooring are used, the satellite data are found to be the most beneficial as a supplemental data type, suggesting the importance of spatial coverage of the domain by observations.

Wave modelling in coastal and inner seas

“…During the last decades several attempts have been made to implement wave DA routines in enclosed seas and nearshore scenarios. Good examples are provided by Voorrips et al (1997), Siddons et al (2009), Portilla (2009), Veeramony et al (2010), Waters et al, (2013), Rusu and Soares (2015), Wahle et al (2015), Panteleev et al (2015. In most of the cases the data have routinely been assimilated using a simple Optimal Interpolation scheme with static error covariance specification (e.g., Abdalla et al, 2010). In general there are a couple of bottlenecks in these developments.…”

Ensemble-Based Variational Method for Nonlinear Inversion of Surface Gravity Waves

“…There are ensemble-based method variants that use different ensemble generation approaches and optimization schemes. The adjoint-free 4DVar uses empirical orthogonal function (EOF) modes of the model trajectory and/or misfits between the model and observations to generate ensemble members (Panteleev et al 2015;Yaremchuk et al 2016;Y17;Yaremchuk et al 2017b). En4DVar (Liu et al 2008(Liu et al , 2009 utilizes meteorological forecasting ensemble members.…”

“…The Jacobian matrix H of the model-data projection operator H(x 0 ) varies with initial condition x 0 because of nonlinearity of the physical and observational systems; dY pre is a linear approximation of H(x 0 ) around x 0 of the previous iterations, and deviates from the approximation around x 0 of the current iteration because x 0 is updated during the optimization process. Previous studies (Yaremchuk et al 2009;Panteleev et al 2015;Yaremchuk et al 2017b) proposed reinitializing perturbations P and dY at certain conditions defined for the cost function's decay rate (Yaremchuk et al 2016) or the eigenvalues of dY T R 21 dY (Y17). Consequently, the concatenated perturbation matrix has a limited dimension because of this reinitialization.…”

“…We chose appropriate perturbation modes to increase a4DVar's convergence speed. Previous studies utilized EOF modes of spatiotemporal model data to project misfit y t 2 H t (x t ) onto a physical model space (Panteleev et al 2015;Yaremchuk et al 2016Yaremchuk et al , 2017b. For efficiency, only those EOF modes with large eigenvalues at each iteration were chosen as new ensemble members P new .…”

“…The original a4DVar (Yaremchuk et al 2009;Panteleev et al 2015) orthogonalizes P with respect to the Hessian matrixH 5 H T R 21 H 1 B 21 to avoid search directions that have been already explored and efficiently reuse perturbed data. In contrast, our proposed method does not require orthogonalization as the Fourier modes are approximately orthogonal with respect to the Hessian matrixH, if correlations among dY m can be ignored.…”