MULTIVARIATE ERROR COVARIANCE ESTIMATES BY MONTE-CARLO SIMULATION FOR OCEANOGRAPHIC ASSIMILATION STUDIES

Abstract

One of the most difficult aspects of ocean state estimation is the prescription of the model forecast error covariances. Simple covariances are usually prescribed, rarely are cross-covariances between different model variables used. A multivariate model of the forecast error covariance is developed for an Optimal Interpolation (OI) assimilation scheme (MvOI) and compared to simpler Gaussian univariate model (UOI).

For the MvOI an estimate of the forecast error statistics is made by Monte Carlo techniques from an ensemble of model forecasts. An important advantage of using an ensemble of ocean states is that it provides a natural way to estimate cross-covariances between the fields of different physical variables constituting the model state vector, at the same time incorporating the model's dynamical and thermodynamical constraints. The robustness of the error covariance estimates as well as the analyses has been established by comparing multiple populations of the ensemble.

Temperature observations from the Tropical Atmosphere-Ocean (TAO) array have been assimilated in this study. Data assimilation experiments are validated with a large independent set of subsurface observations of salinity, zonal velocity and temperature. The performance of the UOI and MvOI is similar in temperature. The salinity and velocity fields are greatly improved in the MvOI, as evident from the analyses of the rms differences between these fields and independent observations. The MvOI assimilation is found to improve upon the control (no assimilation) run in generating water masses with properties close to those observed, while the UOI fails to maintain the temperature-salinity relationship.

The feasibility of representing a reduced error subspace through empirical orthogonal functions (EOFs) is discussed and a method proposed to substitute the local noise-like variability by a simple model. While computationally efficient, this method produces results only slightly inferior to the MvOI with the full set of EOFs.

An assimilation scheme with a multivariate forecast error model has the capability to simultaneously process observations of different types. This was tested using temperature data and synthetic salinity observations. The resulting subsurface structures both in temperature and salinity are the closest to the observed, while the currents structure is maintained in dynamically consistent manner.