Atmospheric moisture cycling is an important aspect of the Earth's climate system, yet the processes determining atmospheric humidity are poorly understood. For example, direct evaporation of rain contributes significantly to the heat and moisture budgets of clouds, but few observations of these processes are available. Similarly, the relative contributions to atmospheric moisture over land from local evaporation and humidity from oceanic sources are uncertain. Lighter isotopes of water vapour preferentially evaporate whereas heavier isotopes preferentially condense and the isotopic composition of ocean water is known. Here we use this information combined with global measurements of the isotopic composition of tropospheric water vapour from the Tropospheric Emission Spectrometer (TES) aboard the Aura spacecraft, to investigate aspects of the atmospheric hydrological cycle that are not well constrained by observations of precipitation or atmospheric vapour content. Our measurements of the isotopic composition of water vapour near tropical clouds suggest that rainfall evaporation contributes significantly to lower troposphere humidity, with typically 20% and up to 50% of rainfall evaporating near convective clouds. Over the tropical continents the isotopic signature of tropospheric water vapour differs significantly from that of precipitation, suggesting that convection of vapour from both oceanic sources and evapotranspiration are the dominant moisture sources. Our measurements allow an assessment of the intensity of the present hydrological cycle and will help identify any future changes as they occur.