Considerations on Parameter and State Estimation with Ensemble Data Assimilation Methods – A Case Study with a Nonlinear Oscillator

This study investigates the effect of erroneous parameter values for state and parameter estimation using data assimilation. The numerical model chosen for this study solves the van der Pol equation, a second-order differential equation that can be used to simulate oscillatory processes, such as earthquakes. In the model, discrepancies in the parameter values can have a significant influence on the forecasted states of the model, which is even more significant if its behaviour is highly nonlinear. When observations of the state variables are assimilated to update the parameters along with the state variables, this improves the quality of the state forecasts. The results suggest that corrections in the model parameter not only recover the actual parameter values but also reduce state-variable errors after a certain time period. However, data assimilation that updates the state variables but not the parameter can lead to erroneous estimates as well as forecasts of the oscillation. Since the study is performed on a simplified nonlinear model framework, the consequences of these results for data assimilation in more realistic models remains to be investigated.