AbstractThe movements of migratory birds constitute huge biomass flows that influence ecosystems and human economy, agriculture and health through the transport of energy, nutrients, seeds, and parasites. To better understand the influence on ecosystems and the corresponding services and disservices, we need to characterize and quantify the migratory movements at various spatial and temporal scales.Representing the flow of birds in the air as a fluid, we applied a flow model to interpolated maps of bird density and velocity retrieved from the European weather radar network, covering almost a full year. Using this model, we quantified how many birds take-off, fly, and land across Western Europe, (1) to track waves of bird migration between nights, (2) cumulate the number of bird on the ground and (3) quantify the seasonal flow into and out of the study area through several regional transects.Our results show that up to 188 million (M) birds take-off over a single night. Exemplarily, we tracked a migration wave in spring, in which birds crossed the study area in 4 days with nocturnal flights of approximately 300 km. Over the course of a season, we estimated that 494 million (M) birds entered through the southern transects and, at the same time, 251 M left in the northern transects, creating a surplus of 243 M birds within the study area. Similarly, in autumn, 544 M more birds departed than arrived: 314 M birds entered through the northern transects while 858 M left through the southern transects.Our study show-cases the potential of combining interdisciplinary data and methods to elucidate the dynamics of avian migration from nightly to seasonal and yearly time-scales and from regional to continental spatial scales.