The lateral size of sea ice floes is receiving increasing attention as an important variable for the polar climate system. We have developed a model for prognostic evolution of the floe size distribution, which emerges due to five key physical processes: new ice formation, welding of floes in freezing conditions, lateral growth and melt, and fracture of floes by ocean surface waves. As a result of the model’s foundation in the governing physics, free parameters occurring in the equations can be directly constrained by observations. Initial model experiments provided insight into the relative importance of various processes, showing floe freezing processes were particularly important for simulation of the floe size distribution. Previously, physical descriptions of lateral growth and welding together of floes had not been constrained by observations. This motivated an analysis of images obtained by drifting wave buoys (SWIFTs) deployed in the autumn Arctic Ocean to quantify these processes in-situ for the first time. We separated floe area growth due to welding from that due to lateral expansion, and compared observations to our physical descriptions of the individual processes. We also found a strong limitation on floe sizes imposed by the wave field. These results have been used to inform new physical descriptions of processes important for the sea ice floe size distribution.