Numerical weather prediction (NWP) supports our daily lives. Weather models require higher spatiotemporal resolutions to prepare for extreme weather disasters and reduce the uncertainty of predictions. The accuracy of the initial state of the weather simulation is also critical; thus, we need more advanced data assimilation (DA) technology. By combining resolution and ensemble size, we have achieved the world’s largest weather DA experiment using a global cloud-resolving model and an ensemble Kalman filter method. The number of grid points was $\sim$4.4 trillion, and 1.3 PiB of data was passed from the model simulation part to the DA part. We adopted a data-centric application design and approximate computing to speed up the overall system of DA. Our DA system, named NICAM-LETKF, scales to 131,072 nodes (6,291,456 cores) of the supercomputer Fugaku with a sustained performance of 29 PFLOPS and 79 PFLOPS for the simulation and DA parts, respectively.