Announcement of the Frontiers Research Topic -------------------------------------------------------------------------------------- Data Assimilation of Nonlocal Observations in Complex Systems -------------------------------------------------------------------------------------- Natural complex systems exhibit spatio-temporal dynamics on multiple scales that are difficult to predict and understand. To gain deeper insights into the system's dynamics and to be able to predict its evolution, observations of that system are analyzed which allows to derive or motivate models that fit that system. In general, one may distinguish two types of data. The so-called in-situ or local observations capture direct measurements of the system itself, such as temperature at a specific height in the atmosphere or electric potentials in biological cells. Other observations are not measured at a certain location but represent the integral of some relevant quantities manifesting the system's activity. Examples in meteorology for such nonlocal observations are satellite radiances, slant delays and radio occultation based on GPS data, or radar reflectivities. In biological systems, the non-invasive measurement techniques provide nonlocal observations, such as electro- and magnetoencephalogram or Magnetic Resonance Imaging. In addition to observations, realistic models are essential to improve the understanding of natural complex systems and to predict their dynamical evolution. To merge both models and observations, it is essential to develop techniques that optimally estimate the system activity well-adapted to a model and observed data. Data assimilation comprises a number of methods to merge diverse experimental data with an underlying model. Data assimilation optimally combines observations and a model to achieve a certain goal, such as optimal fitting of model parameters or providing optimal forecasts of the system's dynamics. Since the recent years have shown an increasing number of observation techniques capturing integrals of system activity, data assimilation of nonlocal observations becomes more and more important. The present Research Topic aims to bring together recent theoretical work in data assimilation of nonlocal observations with a strong link to specific applications. This article collection reflects the state-of-the-art in this research field. Examples of theoretical topics (as an unconstrained open list) are Kalman filters, variational assimilation techniques, regression techniques and stochastic optimization techniques. Applications may range from the parameter estimation in genetic regulatory networks over prediction of brain dynamics to weather forecast. We invite you to submit an abstract until November 30, 2018 and the manuscript until June 30, 2019. Contributions will be published as soon as they are accepted and synchronously gathered in the Research Topic volume. For more information, do not hesitate to contact us (email of Axel Hutt: digitalesbad@gmail.com). The organisers Lili Lei (Nanjing University) Marc Bocquet (Ecole des Ponts ParisTech) Alberto Carrassi (Nansen Environmental Remote Sensing Center) Axel Hutt (Deutscher Wetterdienst) Roland Potthast (Deutscher Wetterdienst) -- Axel Hutt Directeur de Recherche Deutscher Wetterdienst - German Meteorological Service Research and Development, Department FE 12 (Data Assimilation) Frankfurter Strasse 135, 63067 Offenbach, Germany Tel.: +49 69 8062 2750 http://www.geocities.ws/digitalbath/