On the assimilation of absolute geodetic dynamic topography in a global ocean model: impact on the deep ocean state

General ocean circulation models are not perfect. Forced with observed atmospheric fluxes they gradually drift away from measured distributions of temperature and salinity. We suggest data assimilation of absolute dynamical ocean topography (DOT) observed from space geodetic missions as an option to reduce these differences. Sea surface information of DOT is transferred into the deep ocean by defining the analysed ocean state as a weighted average of an ensemble of fully consistent model solutions using an error-subspace ensemble Kalman filter technique. Success of the technique is demonstrated by assimilation into a global configuration of the ocean circulation model FESOM over 1 year. The dynamic ocean topography data are obtained from a combination of multi-satellite altimetry and geoid measurements. The assimilation result is assessed using independent temperature and salinity analysis derived from profiling buoys of the AGRO float data set. The largest impact of the assimilation occurs at the first few analysis steps where both the model ocean topography and the steric height (i.e. temperature and salinity) are improved. The continued data assimilation over 1 year further improves the model state gradually. Deep ocean fields quickly adjust in a sustained manner: A model forecast initialized from the model state estimated by the data assimilation after only 1 month shows that improvements induced by the data assimilation remain in the model state for a long time. Even after 11 months, the modelled ocean topography and temperature fields show smaller errors than the model forecast without any data assimilation

On domain localization in ensemble based Kalman filter algorithms

Ensemble Kalman filter methods are typically used in combination with one of two localization techniques. One technique is covariance localization, or direct forecast error localization, in which the ensemble-derived forecast error covariance matrix is Schur multiplied with a chosen correlation matrix. The second way of localization is by domain decomposition. Here, the assimilation is split into local domains in which the assimilation update is performed independently. Domain localization is frequently used in combination with filter algorithms that use the analysis error covariance matrix for the calculation of the gain like the ensemble transform Kalman filter (ETKF) and the singular evolutive interpolated Kalman filter (SEIK). However, since the local assimilations are performed independently, smoothness of the analysis fields across the subdomain boundaries becomes an issue of concern. To address the problem of smoothness, an algorithm is introduced that uses domain localization in combination with a Schur product localization of the forecast error covariance matrix for each local subdomain. On a simple example, using the Lorenz-40 system, it is demonstrated that this modification can produce results comparable to those obtained with direct forecast error localization. In addition, these results are compared to the method that uses domain localization in combination with weighting of observations. In the simple example, the method using weighting of observations is less accurate than the new method, particularly if the observation errors are small. Domain localization with weighting of observations is further examined in the case of assimilation of satellite data into the global finite-element ocean circulation model (FEOM) using the local SEIK filter. In this example, the use of observational weighting improves the accuracy of the analysis. In addition, depending on the correlation function used for weighting, the spectral properties of the solution can be improved

Numerical discretization causing error variance loss and the need for inflation

The effects of model discretization errors on the propagation of error covariance have a more complex nature than the effect on the state variable. The analysis is carried out for the advection transport equation, where the continuous (in space and time) propagation of the related error covariance function can be written, solved and compared with the discrete model applied to the covariance matrix. The numerical analysis of the problem is carried out with a 1D-problem, but is also illustrated with a 3D chemical transport model (CTM) used for chemical data assimilation. It is shown that variance loss (compared to the continuous propagation solution) depends on the covariance function itself as well as the numerical discretization scheme. The variance loss is particularly sensitive to the correlation length. In a simple first-order discretization, an analytical expression is obtained and is used to derive an analytical expression for inflation. Experiments show, for example, that following an analysis over a dense network of observations (with spatially uncorrelated errors) a significant variance loss occurs in the propagation step. With the (variance) inflation scheme, we are able to restore the variance lost at each grid point, and at each timestep, during the entire integration. The variance inflation scheme applied to an EnKF can be formulated to change the variance spread of the ensemble or to act directly on the state

Improved turbulent air-sea flux bulk parameters for controlling the response of the ocean mixed layer: a sequential data assimilation approach

International audienc

Sequential assimilation of multi-mission dynamical topography into a global finite-element ocean model

This study focuses on an estimation of ocean circulation via assimilationof satellite measurements of dynamical ocean topography(DOT) into the global finite-element ocean model (FEOM).The DOT data are derived from a complex analysis of multimissionaltimetry data combined with a referenced earth geoid.The goal of this work is exploring the feasibility of assimilationof the global altimetric signal based on sequential assimilationtechnique. Two different sequential assimilation techniques wereimplemented