As per the early Ancient observations the four days commencing from the eigth day in the light half of the month of jyestha (i.e 4 days after the mid of the month of the may and june – from 15th may to 15th june) fall in may and june month are Known as Vayu Dharan- The days when the winds movements seen and observed in the jyestha month freely from North-west to East direction with full of rich amount of moisture in it. Those 4 days when wind is heavy moving near around moon movement in Swati to visakha nakashtra are vital clue for judging the nature of health of the Pregnancy of the rain-clouds for up-coming monsoon seasons. Here observation of wind direction and its richness with Apah, movement in these particular 4 days is most important.If there is no wind in those 4 days we can expect coming months will be much dry in nature as well as humidity will be more.
If there is enough winds in those 4 days, should be like gentle , agreeable and if the Sky Should be covered by fine, bright clouds than there will be possibility of good rainfall in Monsoon else monsoon will be bit delayed and level of humidity will be more.
From 15th June onward if you observe any possibility of rain drops or moisture contents in air than there should be enough rainfall in continues 4 days when Moon will Passes through Swati to Jyestha Nakashtra (Libra Sign to first Half of Vishkha).
This is an easiest way to time entry of monsoon via own sense of judgement and to get clear understanding on clue for rainfall during Sharavana and Karttika month. Only thing required is you need to keep observing the movement in sky, the direction and pregnancy of winds and clouds.
If there is an Indication of rain in this nakashtras than you can expect monsoon is very soon to come.
Source, Reference and links
Brihat Samhita of Varahmihira by Ramkrishna Bhat
Astrology in Predicting Weather and Earthquakes by Dr B.V Raman