Global tropical cyclone climate has been investigated with indicators of frequency, intensity and activity. However, a full understanding of global warming’s influence on tropical cyclone climate remains elusive because of the incomplete nature of these indicators. Here we form a complete three-dimensional variability space of tropical cyclone climate where the variabilities are continuously linked and find that global ocean warmth best explains the out-of-phase relationship between intensity and frequency of global tropical cyclones. In a year with greater ocean warmth, the tropical troposphere is capped by higher pressure anomaly in the middle and upper troposphere even with higher moist static energy anomaly in the lower troposphere, which is thought to inhibit overall tropical cyclone occurrences but lead to greater intensities. A statistical consequence is the trade-off between intensity and frequency. We calculate an average increase in global tropical cyclone intensity of 1.3 m s−1 over the past 30 years of ocean warming occurring at the expense of 6.1 tropical cyclones worldwide.