The relationship between cloud height and lightning activity is examined using data from the Tropical Rainfall Measuring Mission (TRMM) satellite. Coincident data from the precipitation radar (PR) and Lightning Imaging Sensor abroad the TRMM satellite are used to examine whether lightning flash rate is proportional to the fifth power of cloud top height. This study is unique in that (1) the relationship between instantaneous rather than maximum storm height and flash rate is obtained and (2) relatively unbiased full data sets for different locations and seasons over the globe are used. The relationship between thunderstorm height and flash rate is nonlinear with large variance. The overall trend shows that flash rate increases exponentially with storm height. Some tall thunderstorms do not have large flash rates, but the reverse situation never occurs. The fifth power dependency that is derived from scaling laws is not inconsistent with, but not necessarily required by, the observed data. ¿ 2001 American Geophysical Union