Variational Assimilation Problem Research Articles

Problems of variational assimilation of observational data for ocean general circulation models and methods for their solution

Problems of the variational assimilation of satellite observational data on the temperature and level of the ocean surface, as well as data on the temperature and salinity of the ocean from the ARGO system of buoys, are formulated with the use of the global three-dimensional model of ocean thermodynamics developed at the Institute of Numerical Mathematics, Russian Academy of Sciences (INM RAS). Algorithms for numerical solutions of the problems are developed and substantiated, and data assimilation blocks are developed and incorporated into the global three-dimensional model. Numerical experiments are performed with the use of the Indian Ocean or the entire World Ocean as examples. These numerical experiments support the theoretical conclusions and demonstrate that the use of a model with an assimilation block of operational observational data is expedient.

Numerical solution to the problem of variational assimilation of operational observational data on the ocean surface temperature

The problem of variational assimilation of satellite observational data on the ocean surface temperature is formulated and numerically investigated in order to reconstruct surface heat fluxes with the use of the global three-dimensional model of ocean hydrothermodynamics developed at the Institute of Numerical Mathematics, Russian Academy of Sciences (INM RAS), and observational data close to the data actually observed in specified time intervals. The algorithms of the numerical solution to the problem are elaborated and substantiated, and the data assimilation block is developed and incorporated into the global three-dimensional model. Numerical experiments are carried out with the use of the Indian Ocean water area as an example. The data on the ocean surface temperature over the year 2000 are used as observational data. Numerical experiments confirm the theoretical conclusions obtained and demonstrate the expediency of combining the model with a block of assimilating operational observational data on the surface temperature.

Some algorithms for studying solution sensitivity in the problem of variational assimilation of observation data for a model of ocean thermodynamics

Some new algorithms for studying the sensitivity of errors of the optimal solution of the problem of the ocean surface temperature data assimilation problem to observation data inaccuracies are proposed in order to reconstruct the heat flux for a nonstationary system of thermodynamics equations. Numerical experiments are performed in application to the Indian Ocean.

Numerical algorithm for variational assimilation of sea surface temperature data

The problem of variational assimilation of sea surface temperature data is formulated and studied. An algorithm for solving the problem is developed. Numerical results are presented.

An algorithm for the solution of the ocean hydrothermodynamics problem with variational assimilation of the sea level function data

A new ocean hydrothermodynamics model is developed. The problem of variational assimilation of sea level function data is formulated and investigated. The results of numerical experiments are given.

Variational data assimilation for a nonstationary heat conduction problem with nonlinear diffusion

We consider the problem of variational assimilation of observational data with the aim to reconstruct the initial condition in a locally one-dimensional model of vertical heat exchange in the ocean, which is described by the nonstationary heat equation with a nonlinear diffusion coefficient. We investigate the solvability of the data assimilation problem, develop and justify algorithms for its numerical solution. The results of numerical experiments are given.

Variational data assimilation for a nonstationary heat conduction problem with nonlinear diffusion

We consider the problem of variational assimilation of observational data with the aim to reconstruct the initial condition in a locally one-dimensional model of vertical heat exchange in the ocean, which is described by the nonstationary heat equation with a nonlinear diffusion coefficient. We investigate the solvability of the data assimilation problem, develop and justify algorithms for its numerical solution. The results of numerical experiments are given.

Application of the Quasi-Inverse Method to Data Assimilation

Four-dimensional variational data assimilation (4D-Var) seeks to find an optimal initial field that minimizes a cost function defined as the squared distance between model solutions and observations within an assimilation window. For a perfect linear model, Lorenc showed that the 4D-Var forecast at the end of the window coincides with a Kalman filter analysis if two conditions are fulfilled: (a) addition to the cost function of a term that measures the distance to the background at the beginning of the assimilation window, and (b) use of the Kalman filter background error covariance in this term. The standard 4D-Var requires minimization algorithms along with adjoint models to compute gradient information needed for the minimization. In this study, an alternative method is suggested based on the use of the quasi-inverse model that, for certain applications, may help accelerate the solution of problems close to 4D-Var. The quasi-inverse approach for the forecast sensitivity problem is introduced, and then a closely related variational assimilation problem using the quasi-inverse model is formulated (i.e., the model is integrated backward but changing the sign of the dissipation terms). It is shown that if the cost function has no background term, and has a complete set of observations (as assumed in many classical 4D-Var papers), the new method solves the 4D-Var-minimization problem efficiently, and is in fact equivalent to the Newton algorithm but without having to compute a Hessian. If the background term is included but computed at the end of the interval, allowing the use of observations that are not complete, the minimization can still be carried out very efficiently. In this case, however, the method is much closer to a 3D-Var formulation in which the analysis is attained through a model integration. For this reason, the method is called ‘‘inverse 3D-Var’’ (I3D-Var). The I3D-Var method was applied to simple models (viscous Burgers’ equation and Lorenz model), and it was found that when the background term is ignored and complete fields of noisy observations are available at multiple times, the inverse 3D-Var method minimizes the same cost function as 4D-Var but converges much faster. Tests with the Advanced Regional Prediction System (ARPS) indicate that I3D-Var is about twice as fast as the adjoint Newton method and many times faster than the quasi-Newton LBFGS algorithm, which uses the adjoint model. Potential problems (including the growth of random errors during the integration back in time) and possible applications to preconditioning, and to problems such as storm-scale data assimilation and reanalysis are also discussed.