To understand the influence of biomass flows on ecosystems, we need to characterize and quantify migrations at various spatial and temporal scales. Representing the movements of migrating birds as a fluid, we applied a flow model to bird density and velocity maps retrieved from the European weather radar network, covering almost a year. We quantified how many birds take-off, fly, and land across Western Europe to (1) track bird migration waves between nights, (2) cumulate the number of birds on the ground and (3) quantify the seasonal flow into and out of the study area through several regional transects. Our results identified several migration waves that crossed the study area in 4 days only and included up to 188 million (M) birds that took-off in a single night. In spring, we estimated that 494 M birds entered the study area, 251 M left it, and 243 M birds remained within the study area. In autumn, 314 M birds entered the study area while 858 M left it. In addition to identifying fundamental quantities, our study highlights the potential of combining interdisciplinary data and methods to elucidate the dynamics of avian migration from nightly to yearly time scales and from regional to continental spatial scales.