Question

How does water from the earth surface escape into the atmosphere

Answer 1

Water from the earth surface absorbs heat and gets converted into water vapour and gets stick to the dust in the atmosphere or to the molecules of the components of air and makes the atmosphere humid and this way it comes into the atmosphere.
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Answer 2

The water from the earth escape to the atmosphere by the process of evaporation.The water present in seas, rivers , oceans get heated by the sunlight and the sunlight converts it into water vapour
This water vapour goes into atmosphere and form little droplets which later appears as big droplets of water during rain.