Fig. 2

a Ash fall forecast without 4D-Var. b Ash fall forecast with 4D-Var. c Ash fall observation [Regional Volcanic Observation and Warning Center, Fukuoka Regional Headquarters, JMA (2018) (minor postscripts were added by the author)]. The white triangle is plotted at the location of Aso volcano for all figures. In the left and centre figures, black cross-marks are “No Ash Fall and No Lapilli Fall”, black circles are “Ash Fall (g/m2), No Lapilli Fall”, and white circles are “ash fall and lapilli fall (g/m2)”. White solid lines in the left and centre figures are the main axis of ash fall forecast. The white dotted line is the main axis estimated from observation