a Examples of typical CPs on day 4 of A2b (15:35) and A5b (14:00) showing virtual potential temperature anomaly at z = 50 m (compare: boxes in Fig. 3b, e for context). Thin yellow lines show accumulated surface rainfall (1-, 5- and 10-mm contours) within the subsequent hour. A scale bar and an area Acrit are marked (compare: panel c). CP areas (bold black contours of −1 K anomalies) exceeding Acrit are rare in A2b, but frequent in A5b. The combined CPs in A5b can excite subsequent rainfall and feed the emergent MCS. b Respective x–z cross-sections along the white horizontal lines in a including the lifting condensation level (LCL) and level of free convection (LFC), and corresponding domain means (dashed). Marked regions correspond to lowered triggering probability (compare: panel c). c Schematic for the simplified model dynamics. (i) Low-density subdomain with vacant (white) and active sites (blue). (ii) Similar to (i) but for high density, showing also boundary sites (orange) with higher probability. d C(l) for ta = 0.5 K, analogous to Fig. 2a–c but now for the simplified model (days as marked). Note the double-logarithmic axis scaling. e, Analogous to d, but for smaller ta. Inset: diurnal cycle for rain area for the simplified model for two values of ta (compare: Fig. 1b–d). f Simple checkerboard model, explaining the increase in variance over time for large ta (red symbols) and small ta (blue symbols). The grids below show the patterns at days 1–4, 10 for large and small ta, respectively. Box colours white → faint red → red → dark red indicate increasing density.