Abstract
Abstract. High-Frequency (HF) radars measure the ocean surface currents at various spatial and temporal scales. These include tidal currents, wind-driven circulation, density-driven circulation and Stokes drift. Sequential assimilation methods updating the model state have been proven successful to correct the density-driven currents by assimilation of observations such as sea surface height, sea surface temperature and in-situ profiles. However, the situation is different for tides in coastal models since these are not generated within the domain, but are rather propagated inside the domain through the boundary conditions. For improving the modeled tidal variability it is therefore not sufficient to update the model state via data assimilation without updating the boundary conditions. The optimization of boundary conditions to match observations inside the domain is traditionally achieved through variational assimilation methods. In this work we present an ensemble smoother to improve the tidal boundary values so that the model represents more closely the observed currents. To create an ensemble of dynamically realistic boundary conditions, a cost function is formulated which is directly related to the probability of each boundary condition perturbation. This cost function ensures that the boundary condition perturbations are spatially smooth and that the structure of the perturbations satisfies approximately the harmonic linearized shallow water equations. Based on those perturbations an ensemble simulation is carried out using the full three-dimensional General Estuarine Ocean Model (GETM). Optimized boundary values are obtained by assimilating all observations using the covariances of the ensemble simulation.
Highlights
Most ensemble-based assimilation schemes such as the EnKF (Ensemble Kalman Filter, Evensen, 2003, 2004), ESSE (Error Subspace Statistical Estimation, Lermusiaux and Robinson, 1999), SEIK filter (Singular Evolutive Interpolated Kalman filter, Pham, 2001) are sequential: the ensemble is updated using observations at the time they are measured
Since tidal boundary conditions are determined by an ensemble assimilation scheme, the ensemble perturbations are required to satisfy approximately the harmonic shallow water equations
An ensemble based on this method was successfully used to improve M2 boundary conditions by assimilation of HF radar and tidal data derived from altimetry
Summary
Most ensemble-based assimilation schemes such as the EnKF (Ensemble Kalman Filter, Evensen, 2003, 2004), ESSE (Error Subspace Statistical Estimation, Lermusiaux and Robinson, 1999), SEIK filter (Singular Evolutive Interpolated Kalman filter, Pham, 2001) are sequential: the ensemble is updated using observations at the time they are measured In this sequential approach the model undergoes a sometimes vigorous adjustment process when the model is restarted Instead of applying the analysis correction at the assimilation time, in the Incremental Analysis Update (Bloom et al, 1996) the correction is added incrementally over several time steps, reducing the generation of spurious gravity waves This scheme has been used with largescale ocean models This scheme has been used with largescale ocean models (e.g. Keppenne et al, 2005; Ourmieres et al, 2006) but it is questionable if it can be used in regional models representing fast ocean processes such as tides
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