Initial condition and parameter estimation in physical ‘on–off’ processes by variational data assimilation

In this paper we investigate the feasibility of using the variational data assimilation method to estimate both the initial condition and parameter in an idealized simple model with parametrized discontinuity.Amethod based on the non-linear perturbation equation (NPE) is applied to calculate the gradient of the cost function with respect to the control variables used in the minimization procedure. The results obtained by this method and by the conventional treatment (ignoring the variation of the switch point due to the perturbation in initial condition, i.e. keeping the switching point in the tangent linear model the same as in the basic state) are compared through numerical experiment. Because the cost function could have artificial minima after time discretization, the optimization algorithm combined with the NPE method is less sensitive to the first guess in retrieving the optimal initial condition and parameter value. It is shown that the gradient computation deserves consideration when there are discontinuities in the model used in variational data assimilation.