Table 1. Statistical parameters of the size, shape, and settling velocity distributions (plotted in Figs 1 and 3) of the natural Etna basalt (ETB) and Laacher See phonolite (LSP) ash particles used in the experiments and of the ideal, spherical particles used in the two-way (S2W) and four-way (S4W) coupling numerical simulations.

Experiments	n° tracked particles	Parameter	Mean	Median	Mode	Percentile (25th)	Percentile (75th)	Skewness	Kurtosis
ETB	8551
		de	252.13	223.91	154.36	183.73	297.63	1.26	4.31
		vp	2.86	2.75	1.09	2.10	3.49	0.48	2.68
		F	0.67	0.69	0.40	0.61	0.73	−0.55	3.18
		Ψ	0.74	0.75	0.76	0.71	0.76	−0.69	3.95
LSP	2453
		de	745.40	745.31	654.90	648.72	833.99	0.43	5.88
		vp	2.97	2.86	2.10	2.36	3.50	1.29	7.52
		F	0.63	0.66	0.28	0.51	0.71	−0.34	2.59
		Ψ	0.71	0.72	0.64	0.64	0.78	−0.36	3.78
Simulations	n° analysed samples
S2W
	48	f1 (10s)
		de	279.63	277.11	225.80	266.48	290.73	0.54	3.48
		vp	5.96	5.96	5.52	5.85	6.03	0.98	5.35
	182	f3 (40s)
		de	303.14	303.13	191.64	274.23	328.96	0.07	2.74
		vp	4.86	4.89	3.42	4.68	5.05	−0.74	5.22
	880	f5 (176s)
		de	277.47	277.83	252.15	260.44	295.99	−0.27	3.76
		vp	2.84	2.84	2.75	2.65	3.02	−0.27	3.03
		F	1.00	1.00	1.00	1.00	1.00
		Ψ	1.00	1.00	1.00	1.00	1.00
S4W
	95	f1 (10s)
		de	282.63	282.86	202.54	267.33	296.64	−0.01	3.66
		vp	4.53	4.54	3.62	4.28	4.81	−0.28	2.71
	397	f3 (40s)
		de	291.37	292.51	178.01	273.42	310.76	−0.36	4.03
		vp	4.07	4.12	3.69	3.80	4.38	−0.48	2.91
	705	f5 (176s)
		de	284.01	284.62	260.63	270.81	297.81	−0.06	4.42
		vp	2.60	2.61	2.55	2.48	2.72	−0.22	4.18
		F	1.00	1.00	1.00	1.00	1.00
		Ψ	1.00	1.00	1.00	1.00	1.00