Fig. 4: Scaling between temporal temperature gradients and extreme-rainfall intensities over northern tropical oceans.

a Observed scaling between temporal temperature gradients (\({T}_{g}^{r}\)) and 90th percentiles of rainfall rates (P⁹⁰) for episodes in July–August–September–October (JASO) sampled from all northern tropical ocean locations (between 0°N and 23°N). Rainfall episodes are split into 25 bins with respect to their preceding temporal temperature gradients (\({T}_{g}^{r}\)). The 90th percentile for each bin (P⁹⁰) is plotted as a black solid line with markers, the 95% confidence intervals are depicted as vertical black lines, but practically invisible because of their small size. The linear regression through all bins with a negative temporal temperature gradient is depicted as a dashed magenta line. The blue color indicates the 95% confidence interval, but is again too small to be visible. b Same as a, but restricted to rainfall episodes associated with TCs listed by the IBTrACS archive⁵⁷.