Fig. 6: Visualization of examples when only assimilating upper-air temperature observations.

a Results of the 7-day medium forecast using ERA5 and state estimations only assimilating upper-air temperature observations as initial fields, separately. The RMSEs and ACCs of the selected variables (R500 for the first column, R850 for the second column, T500 for the third column, and T850 for the fourth column) are illustrated. b A typical example of background error (xb − xt) is represented. Two levels of relative humidity variables (R500 for the first column and R850 for the third column) and two levels of geopotential (T500 for the second column and T850 for the fourth column) are illustrated. c The visualization of analysis increment (xa − xb) of the compared models. For each case, 4DVarNet (first row), ViT (second row), and 4DVarFormer (third row) are shown. For all illustrated cases, the time is 00:00 UTC on 19 July 2021, for there is a tropical cyclone at this time in the East China region.