Forecast of Spectral Features by Ensemble Data Assimilation - Hutt, Axel; Potthast, Roland (Frontiers in Applied Mathematics and Statistics, 2018)
Data assimilation permits to compute optimal forecasts in high-dimensional systems as, e.g., in weather forecasting. Typically such forecasts are spatially distributed time series of system variables. We hypothesise that such forecasts are not optimal if the major interest does not lie in the temporal evolution of system variables but in time series composites or features. For instance, in neuroscience spectral features of neural activity are the primar functional elements. The present work proposes a data assimilation framework for forecasts of time-frequency distributions. The framework comprises the ensemble Kalman filter and a detailed statistical ensemble verification. The performance of the framework is evaluated for a simulated FitzHugh-Nagumo model, various measurement noise levels and for {\em in situ-}, nonlocal and speed observations. We discover a resonance effect in forecast errors between forecast time and frequencies in observations.