Nonlinear Processes in Geophysics www.nonlin-processes-geophys.net 1023-5809 1607-7946 12 4 2005 10.5194/npg-12-481-2005 http://www.nonlin-processes-geophys.net/12/481/2005/ http://www.nonlin-processes-geophys.net/12/481/2005/npg-12-481-2005.html http://www.nonlin-processes-geophys.net/12/481/2005/npg-12-481-2005.pdf 481 490 2005-05-13 On deterministic error analysis in variational data assimilation F. -X. Le Dimet V. Shutyaev LMC-IMAG, Université Joseph Fourier, Grenoble, France Institute of Numerical Mathematics, Russian Academy of Sciences, Moscow, Russia The problem of variational data assimilation for a nonlinear evolution model is considered to identify the initial condition. The equation for the error of the optimal initial-value function through the errors of the input data is derived, based on the Hessian of the misfit functional and the second order adjoint techniques. The fundamental control functions are introduced to be used for error analysis. The sensitivity of the optimal solution to the input data (observation and model errors, background errors) is studied using the singular vectors of the specific response operators in the error equation. The relation between "quality of the model" and "quality of the prediction" via data assimilation is discussed.